0.03/0.14 % Problem : Vampire---4.8_19254 : TPTP v0.0.0. Released v0.0.0. 0.03/0.15 % Command : run_E %s %d THM 0.15/0.36 % Computer : n011.cluster.edu 0.15/0.36 % Model : x86_64 x86_64 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.36 % Memory : 8042.1875MB 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.36 % CPULimit : 1440 0.15/0.36 % WCLimit : 180 0.15/0.36 % DateTime : Mon Jul 3 13:03:39 EDT 2023 0.15/0.37 % CPUTime : 0.21/0.52 Running higher-order theorem provingRunning: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254 0.21/0.53 # Version: 3.1pre001-ho 0.36/0.57 # Preprocessing class: HSLMSLSSLLLCHFA. 0.36/0.57 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.36/0.57 # Starting ehoh_best5 with 180s (1) cores 0.36/0.57 # Starting almost_fo_3_lam with 180s (1) cores 0.36/0.57 # Starting new_bool_5 with 180s (1) cores 0.36/0.57 # Starting pre_casc_3 with 180s (1) cores 0.36/0.57 # Starting ho_unfolding_8 with 180s (1) cores 0.36/0.57 # Starting new_ho_10_cnf2 with 180s (1) cores 0.36/0.57 # Starting new_bool_3 with 180s (1) cores 0.36/0.57 # Starting new_ho_5 with 180s (1) cores 0.36/0.57 # new_bool_3 with pid 19438 completed with status 0 0.36/0.57 # Result found by new_bool_3 0.36/0.57 # Preprocessing class: HSLMSLSSLLLCHFA. 0.36/0.57 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.36/0.57 # Starting ehoh_best5 with 180s (1) cores 0.36/0.57 # Starting almost_fo_3_lam with 180s (1) cores 0.36/0.57 # Starting new_bool_5 with 180s (1) cores 0.36/0.57 # Starting pre_casc_3 with 180s (1) cores 0.36/0.57 # Starting ho_unfolding_8 with 180s (1) cores 0.36/0.57 # Starting new_ho_10_cnf2 with 180s (1) cores 0.36/0.57 # Starting new_bool_3 with 180s (1) cores 0.36/0.57 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.36/0.57 # Search class: HGHSM-FSLS31-MHFMMSBN 0.36/0.57 # Scheduled 5 strats onto 1 cores with 180 seconds (180 total) 0.36/0.57 # Starting pre_casc_7 with 109s (1) cores 0.36/0.57 # pre_casc_7 with pid 19441 completed with status 0 0.36/0.57 # Result found by pre_casc_7 0.36/0.57 # Preprocessing class: HSLMSLSSLLLCHFA. 0.36/0.57 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.36/0.57 # Starting ehoh_best5 with 180s (1) cores 0.36/0.57 # Starting almost_fo_3_lam with 180s (1) cores 0.36/0.57 # Starting new_bool_5 with 180s (1) cores 0.36/0.57 # Starting pre_casc_3 with 180s (1) cores 0.36/0.57 # Starting ho_unfolding_8 with 180s (1) cores 0.36/0.57 # Starting new_ho_10_cnf2 with 180s (1) cores 0.36/0.57 # Starting new_bool_3 with 180s (1) cores 0.36/0.57 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.36/0.57 # Search class: HGHSM-FSLS31-MHFMMSBN 0.36/0.57 # Scheduled 5 strats onto 1 cores with 180 seconds (180 total) 0.36/0.57 # Starting pre_casc_7 with 109s (1) cores 0.36/0.57 # Preprocessing time : 0.005 s 0.36/0.57 0.36/0.57 # Proof found! 0.36/0.57 # SZS status Theorem 0.36/0.57 # SZS output start CNFRefutation 0.36/0.57 thf(decl_22, type, in: $i > $i > $o). 0.36/0.57 thf(decl_23, type, exu: ($i > $o) > $o). 0.36/0.57 thf(decl_24, type, setextAx: $o). 0.36/0.57 thf(decl_25, type, emptyset: $i). 0.36/0.57 thf(decl_26, type, emptysetAx: $o). 0.36/0.57 thf(decl_27, type, setadjoin: $i > $i > $i). 0.36/0.57 thf(decl_28, type, setadjoinAx: $o). 0.36/0.57 thf(decl_29, type, powerset: $i > $i). 0.36/0.57 thf(decl_30, type, powersetAx: $o). 0.36/0.57 thf(decl_31, type, setunion: $i > $i). 0.36/0.57 thf(decl_32, type, setunionAx: $o). 0.36/0.57 thf(decl_33, type, omega: $i). 0.36/0.57 thf(decl_34, type, omega0Ax: $o). 0.36/0.57 thf(decl_35, type, omegaSAx: $o). 0.36/0.57 thf(decl_36, type, omegaIndAx: $o). 0.36/0.57 thf(decl_37, type, replAx: $o). 0.36/0.57 thf(decl_38, type, foundationAx: $o). 0.36/0.57 thf(decl_39, type, wellorderingAx: $o). 0.36/0.57 thf(decl_40, type, descr: ($i > $o) > $i). 0.36/0.57 thf(decl_41, type, descrp: $o). 0.36/0.57 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.36/0.57 thf(decl_43, type, dsetconstrI: $o). 0.36/0.57 thf(decl_44, type, dsetconstrEL: $o). 0.36/0.57 thf(decl_45, type, dsetconstrER: $o). 0.36/0.57 thf(decl_46, type, exuE1: $o). 0.36/0.57 thf(decl_47, type, prop2set: $o > $i). 0.36/0.57 thf(decl_48, type, prop2setE: $o). 0.36/0.57 thf(decl_49, type, emptysetE: $o). 0.36/0.57 thf(decl_50, type, emptysetimpfalse: $o). 0.36/0.57 thf(decl_51, type, notinemptyset: $o). 0.36/0.57 thf(decl_52, type, exuE3e: $o). 0.36/0.57 thf(decl_53, type, setext: $o). 0.36/0.57 thf(decl_54, type, emptyI: $o). 0.36/0.57 thf(decl_55, type, noeltsimpempty: $o). 0.36/0.57 thf(decl_56, type, setbeta: $o). 0.36/0.57 thf(decl_57, type, nonempty: $i > $o). 0.36/0.57 thf(decl_58, type, nonemptyE1: $o). 0.36/0.57 thf(decl_59, type, nonemptyI: $o). 0.36/0.57 thf(decl_60, type, nonemptyI1: $o). 0.36/0.57 thf(decl_61, type, setadjoinIL: $o). 0.36/0.57 thf(decl_62, type, emptyinunitempty: $o). 0.36/0.57 thf(decl_63, type, setadjoinIR: $o). 0.36/0.57 thf(decl_64, type, setadjoinE: $o). 0.36/0.57 thf(decl_65, type, setadjoinOr: $o). 0.36/0.57 thf(decl_66, type, setoftrueEq: $o). 0.36/0.57 thf(decl_67, type, powersetI: $o). 0.36/0.57 thf(decl_68, type, emptyinPowerset: $o). 0.36/0.57 thf(decl_69, type, emptyInPowerset: $o). 0.36/0.57 thf(decl_70, type, powersetE: $o). 0.36/0.57 thf(decl_71, type, setunionI: $o). 0.36/0.57 thf(decl_72, type, setunionE: $o). 0.36/0.57 thf(decl_73, type, subPowSU: $o). 0.36/0.57 thf(decl_74, type, exuE2: $o). 0.36/0.57 thf(decl_75, type, nonemptyImpWitness: $o). 0.36/0.57 thf(decl_76, type, uniqinunit: $o). 0.36/0.57 thf(decl_77, type, notinsingleton: $o). 0.36/0.57 thf(decl_78, type, eqinunit: $o). 0.36/0.57 thf(decl_79, type, singletonsswitch: $o). 0.36/0.57 thf(decl_80, type, upairsetE: $o). 0.36/0.57 thf(decl_81, type, upairsetIL: $o). 0.36/0.57 thf(decl_82, type, upairsetIR: $o). 0.36/0.57 thf(decl_83, type, emptyE1: $o). 0.36/0.57 thf(decl_84, type, vacuousDall: $o). 0.36/0.57 thf(decl_85, type, quantDeMorgan1: $o). 0.36/0.57 thf(decl_86, type, quantDeMorgan2: $o). 0.36/0.57 thf(decl_87, type, quantDeMorgan3: $o). 0.36/0.57 thf(decl_88, type, quantDeMorgan4: $o). 0.36/0.57 thf(decl_89, type, prop2setI: $o). 0.36/0.57 thf(decl_91, type, prop2set2propI: $o). 0.36/0.57 thf(decl_92, type, notdexE: $o). 0.36/0.57 thf(decl_93, type, notdallE: $o). 0.36/0.57 thf(decl_94, type, exuI1: $o). 0.36/0.57 thf(decl_95, type, exuI3: $o). 0.36/0.57 thf(decl_96, type, exuI2: $o). 0.36/0.57 thf(decl_97, type, inCongP: $o). 0.36/0.57 thf(decl_98, type, in__Cong: $o). 0.36/0.57 thf(decl_99, type, exuE3u: $o). 0.36/0.57 thf(decl_100, type, exu__Cong: $o). 0.36/0.57 thf(decl_101, type, emptyset__Cong: $o). 0.36/0.57 thf(decl_102, type, setadjoin__Cong: $o). 0.36/0.57 thf(decl_103, type, powerset__Cong: $o). 0.36/0.57 thf(decl_104, type, setunion__Cong: $o). 0.36/0.57 thf(decl_105, type, omega__Cong: $o). 0.36/0.57 thf(decl_106, type, exuEu: $o). 0.36/0.57 thf(decl_107, type, descr__Cong: $o). 0.36/0.57 thf(decl_108, type, dsetconstr__Cong: $o). 0.36/0.57 thf(decl_109, type, subset: $i > $i > $o). 0.36/0.57 thf(decl_112, type, subsetI1: $o). 0.36/0.57 thf(decl_113, type, eqimpsubset2: $o). 0.36/0.57 thf(decl_114, type, eqimpsubset1: $o). 0.36/0.57 thf(decl_115, type, subsetI2: $o). 0.36/0.57 thf(decl_116, type, emptysetsubset: $o). 0.36/0.57 thf(decl_117, type, subsetE: $o). 0.36/0.57 thf(decl_118, type, subsetE2: $o). 0.36/0.57 thf(decl_119, type, notsubsetI: $o). 0.36/0.57 thf(decl_120, type, notequalI1: $o). 0.36/0.57 thf(decl_121, type, notequalI2: $o). 0.36/0.57 thf(decl_122, type, subsetRefl: $o). 0.36/0.57 thf(decl_123, type, subsetTrans: $o). 0.36/0.57 thf(decl_124, type, setadjoinSub: $o). 0.36/0.57 thf(decl_125, type, setadjoinSub2: $o). 0.36/0.57 thf(decl_126, type, subset2powerset: $o). 0.36/0.57 thf(decl_127, type, setextsub: $o). 0.36/0.57 thf(decl_128, type, subsetemptysetimpeq: $o). 0.36/0.57 thf(decl_129, type, powersetI1: $o). 0.36/0.57 thf(decl_130, type, powersetE1: $o). 0.36/0.57 thf(decl_131, type, inPowerset: $o). 0.36/0.57 thf(decl_132, type, powersetsubset: $o). 0.36/0.57 thf(decl_133, type, sepInPowerset: $o). 0.36/0.57 thf(decl_134, type, sepSubset: $o). 0.36/0.57 thf(decl_135, type, binunion: $i > $i > $i). 0.36/0.57 thf(decl_136, type, binunionIL: $o). 0.36/0.57 thf(decl_137, type, upairset2IR: $o). 0.36/0.57 thf(decl_138, type, binunionIR: $o). 0.36/0.57 thf(decl_139, type, binunionEcases: $o). 0.36/0.57 thf(decl_140, type, binunionE: $o). 0.36/0.57 thf(decl_141, type, binunionLsub: $o). 0.36/0.57 thf(decl_142, type, binunionRsub: $o). 0.36/0.57 thf(decl_143, type, binintersect: $i > $i > $i). 0.36/0.57 thf(decl_144, type, binintersectI: $o). 0.36/0.57 thf(decl_145, type, binintersectSubset5: $o). 0.36/0.57 thf(decl_146, type, binintersectEL: $o). 0.36/0.57 thf(decl_147, type, epred1_0: $o). 0.36/0.57 thf(decl_148, type, esk1_2: $i > $i > $i). 0.36/0.57 thf(decl_149, type, esk2_2: $i > $i > $i). 0.36/0.57 thf(decl_150, type, esk3_2: $i > $i > $i). 0.36/0.57 thf(decl_151, type, esk4_1: $i > $i). 0.36/0.57 thf(decl_152, type, esk5_2: ($i > $i > $o) > $i > $i). 0.36/0.57 thf(decl_153, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 0.36/0.57 thf(decl_154, type, esk7_2: ($i > $i > $o) > $i > $i). 0.36/0.57 thf(decl_155, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 0.36/0.57 thf(decl_156, type, esk9_1: $i > $i). 0.36/0.57 thf(decl_157, type, esk10_2: ($i > $o) > $i > $i). 0.36/0.57 thf(decl_158, type, esk11_2: ($i > $o) > $i > $i). 0.36/0.57 thf(decl_159, type, esk12_1: ($i > $o) > $i). 0.36/0.57 thf(decl_160, type, esk13_2: ($i > $o) > $i > $i). 0.36/0.57 thf(decl_161, type, esk14_1: ($i > $o) > $i). 0.36/0.57 thf(decl_162, type, esk15_2: $i > $i > $i). 0.36/0.57 thf(decl_163, type, esk16_2: $i > $i > $i). 0.36/0.57 thf(decl_164, type, esk17_1: $i > $i). 0.36/0.57 thf(decl_165, type, esk18_1: $i > $i). 0.36/0.57 thf(decl_166, type, esk19_1: $i > $i). 0.36/0.57 thf(decl_167, type, esk20_2: $i > $i > $i). 0.36/0.57 thf(decl_168, type, esk21_3: $i > $i > $o > $i). 0.36/0.57 thf(decl_169, type, esk22_2: ($i > $o) > $i > $i). 0.36/0.57 thf(decl_170, type, esk23_1: ($i > $o) > $i). 0.36/0.57 thf(decl_171, type, esk24_1: $i > $i). 0.36/0.57 thf(decl_172, type, esk25_2: $i > ($i > $o) > $i). 0.36/0.57 thf(decl_173, type, esk26_2: $i > ($i > $o) > $i). 0.36/0.57 thf(decl_174, type, esk27_2: $i > ($i > $o) > $i). 0.36/0.57 thf(decl_175, type, esk28_2: $i > ($i > $o) > $i). 0.36/0.57 thf(decl_176, type, esk29_2: $i > ($i > $o) > $i). 0.36/0.57 thf(decl_177, type, esk30_2: $i > ($i > $o) > $i). 0.36/0.57 thf(decl_178, type, esk31_2: ($i > $o) > $i > $i). 0.36/0.57 thf(decl_179, type, esk32_1: ($i > $o) > $i). 0.36/0.57 thf(decl_180, type, esk33_1: ($i > $o) > $i). 0.36/0.57 thf(decl_181, type, esk34_1: ($i > $o) > $i). 0.36/0.57 thf(decl_182, type, esk35_1: ($i > $o) > $i). 0.36/0.57 thf(decl_183, type, esk36_2: ($i > $o) > $i > $i). 0.36/0.57 thf(decl_184, type, esk37_1: ($i > $o) > $i). 0.36/0.57 thf(decl_185, type, esk38_2: ($i > $o) > $i > $i). 0.36/0.57 thf(decl_186, type, esk39_2: ($i > $o) > ($i > $o) > $i). 0.36/0.57 thf(decl_187, type, esk40_2: ($i > $o) > ($i > $o) > $i). 0.36/0.57 thf(decl_188, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 0.36/0.57 thf(decl_189, type, esk42_2: ($i > $o) > ($i > $o) > $i). 0.36/0.57 thf(decl_190, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 0.36/0.57 thf(decl_191, type, esk44_2: ($i > $o) > ($i > $o) > $i). 0.36/0.57 thf(decl_192, type, esk45_2: ($i > $o) > $i > $i). 0.36/0.57 thf(decl_193, type, esk46_2: ($i > $o) > ($i > $o) > $i). 0.36/0.57 thf(decl_194, type, esk47_2: ($i > $o) > ($i > $o) > $i). 0.36/0.57 thf(decl_195, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 0.36/0.57 thf(decl_196, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 0.36/0.57 thf(decl_197, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.36/0.57 thf(decl_198, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.36/0.57 thf(decl_199, type, esk52_2: $i > $i > $i). 0.36/0.57 thf(decl_200, type, esk53_2: $i > $i > $i). 0.36/0.57 thf(decl_201, type, esk54_0: $i). 0.36/0.57 thf(decl_202, type, esk55_0: $i). 0.36/0.57 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', nonempty)). 0.36/0.57 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', nonemptyI)). 0.36/0.57 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', exuE3e)). 0.36/0.57 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', exu)). 0.36/0.57 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', descrp)). 0.36/0.57 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', replAx)). 0.36/0.57 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', descr__Cong)). 0.36/0.57 thf(binintersect, axiom, ((binintersect)=(^[X4:$i, X5:$i]:(dsetconstr @ X4 @ (^[X2:$i]:((in @ X2 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', binintersect)). 0.36/0.57 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.ZVTBIenZAH/Vampire---4.8_19254', exuEu)). 0.36/0.57 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', exu__Cong)). 0.36/0.57 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', exuE3u)). 0.36/0.57 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.ZVTBIenZAH/Vampire---4.8_19254', exuI2)). 0.36/0.57 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', exuI3)). 0.36/0.57 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', exuI1)). 0.36/0.57 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.ZVTBIenZAH/Vampire---4.8_19254', exuE2)). 0.36/0.57 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.ZVTBIenZAH/Vampire---4.8_19254', exuE1)). 0.36/0.57 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setoftrueEq)). 0.36/0.57 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', nonemptyI1)). 0.36/0.57 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', dsetconstrEL)). 0.36/0.57 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', sepSubset)). 0.36/0.57 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', binintersectI)). 0.36/0.57 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', binintersectSubset5)). 0.36/0.57 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', binintersectEL)). 0.36/0.57 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', sepInPowerset)). 0.36/0.57 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', dsetconstr__Cong)). 0.36/0.57 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.ZVTBIenZAH/Vampire---4.8_19254', emptyE1)). 0.36/0.57 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', nonemptyImpWitness)). 0.36/0.57 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', nonemptyE1)). 0.36/0.57 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setbeta)). 0.36/0.57 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', dsetconstrER)). 0.36/0.57 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', dsetconstrI)). 0.36/0.57 thf(binintersectLsub, conjecture, ((((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>(((omegaIndAx)=>(((foundationAx)=>((((dsetconstrI)=>(((dsetconstrER)=>((exuE1)=>(((emptysetE)=>(((((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>(((((powersetI)=>((emptyinPowerset)=>(((((setunionE)=>((subPowSU)=>(((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>(((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((((quantDeMorgan1)=>((quantDeMorgan2)=>(((quantDeMorgan4)=>((prop2setI)=>((((notdallE)=>(((((inCongP)=>((in__Cong)=>(((((setadjoin__Cong)=>((((omega__Cong)=>(((descr__Cong)=>((((eqimpsubset2)=>((eqimpsubset1)=>((((subsetE)=>(((notsubsetI)=>((notequalI1)=>((notequalI2)=>(((((setadjoinSub2)=>((subset2powerset)=>(((subsetemptysetimpeq)=>(((((powersetsubset)=>(((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4)))))))<=(binunionE))<=(binunionEcases))))))<=(sepInPowerset)))<=(inPowerset))<=(powersetE1))<=(powersetI1)))<=(setextsub))))<=(setadjoinSub))<=(subsetTrans))<=(subsetRefl)))))<=(subsetE2)))<=(emptysetsubset))<=(subsetI2))))<=(subsetI1))<=(dsetconstr__Cong)))<=(exuEu)))<=(setunion__Cong))<=(powerset__Cong)))<=(emptyset__Cong))<=(exu__Cong))<=(exuE3u))))<=(exuI2))<=(exuI3))<=(exuI1)))<=(notdexE))<=(prop2set2propI))))<=(quantDeMorgan3))))<=(vacuousDall))<=(emptyE1)))))<=(singletonsswitch))))))<=(exuE2))))<=(setunionI))<=(powersetE))<=(emptyInPowerset))))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE)))))<=(nonemptyI1))<=(nonemptyI)))))))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE))))<=(dsetconstrEL)))<=(descrp))<=(wellorderingAx)))<=(replAx)))<=(omegaSAx))))))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', binintersectLsub)). 0.36/0.57 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', upairsetIL)). 0.36/0.57 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setextAx)). 0.36/0.57 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', emptyInPowerset)). 0.36/0.57 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setadjoinOr)). 0.36/0.57 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.ZVTBIenZAH/Vampire---4.8_19254', setadjoinE)). 0.36/0.57 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', quantDeMorgan4)). 0.36/0.57 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', prop2setI)). 0.36/0.57 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', notinemptyset)). 0.36/0.57 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', emptysetimpfalse)). 0.36/0.57 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', notdallE)). 0.36/0.57 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', prop2setE)). 0.36/0.57 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', inCongP)). 0.36/0.57 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.ZVTBIenZAH/Vampire---4.8_19254', wellorderingAx)). 0.36/0.57 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', upairsetE)). 0.36/0.57 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', omegaSAx)). 0.36/0.57 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.ZVTBIenZAH/Vampire---4.8_19254', in__Cong)). 0.36/0.57 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', emptysetAx)). 0.36/0.57 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setadjoin__Cong)). 0.36/0.57 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', binunionIR)). 0.36/0.57 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', omega__Cong)). 0.36/0.57 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', eqimpsubset2)). 0.36/0.57 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', eqimpsubset1)). 0.36/0.57 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', subsetE)). 0.36/0.57 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', notsubsetI)). 0.36/0.57 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', notequalI1)). 0.36/0.57 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', notequalI2)). 0.36/0.57 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', upairsetIR)). 0.36/0.57 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setadjoinSub2)). 0.36/0.57 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', subset2powerset)). 0.36/0.57 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', subsetemptysetimpeq)). 0.36/0.57 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', powersetsubset)). 0.36/0.57 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', binunionIL)). 0.36/0.57 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', upairset2IR)). 0.36/0.57 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', binunionLsub)). 0.36/0.57 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', binunionRsub)). 0.36/0.57 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', binunionE)). 0.36/0.57 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', binunionEcases)). 0.36/0.57 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', quantDeMorgan1)). 0.36/0.57 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', inPowerset)). 0.36/0.57 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', powersetE1)). 0.36/0.57 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', powersetI1)). 0.36/0.57 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setextsub)). 0.36/0.57 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setadjoinSub)). 0.36/0.57 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', subsetTrans)). 0.36/0.57 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', subsetRefl)). 0.36/0.57 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', subsetE2)). 0.36/0.57 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', emptysetsubset)). 0.36/0.57 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', subsetI2)). 0.36/0.57 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', subsetI1)). 0.36/0.57 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setunion__Cong)). 0.36/0.57 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', powerset__Cong)). 0.36/0.57 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', quantDeMorgan2)). 0.36/0.57 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', emptyset__Cong)). 0.36/0.57 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', notdexE)). 0.36/0.57 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', quantDeMorgan3)). 0.36/0.57 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', vacuousDall)). 0.36/0.57 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', singletonsswitch)). 0.36/0.57 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setunionI)). 0.36/0.57 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', powersetE)). 0.36/0.57 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', eqinunit)). 0.36/0.57 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', notinsingleton)). 0.36/0.57 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', uniqinunit)). 0.36/0.57 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', subPowSU)). 0.36/0.57 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.ZVTBIenZAH/Vampire---4.8_19254', setunionE)). 0.36/0.57 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', emptyinPowerset)). 0.36/0.57 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', powersetI)). 0.36/0.57 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setadjoinIR)). 0.36/0.57 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', emptyinunitempty)). 0.36/0.57 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setadjoinIL)). 0.36/0.57 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', noeltsimpempty)). 0.36/0.57 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', emptyI)). 0.36/0.57 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setext)). 0.36/0.57 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', emptysetE)). 0.36/0.57 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', foundationAx)). 0.36/0.57 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.ZVTBIenZAH/Vampire---4.8_19254', omegaIndAx)). 0.36/0.57 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', omega0Ax)). 0.36/0.57 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setunionAx)). 0.36/0.57 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', powersetAx)). 0.36/0.57 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZVTBIenZAH/Vampire---4.8_19254', setadjoinAx)). 0.36/0.57 thf(c_0_111, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.36/0.57 thf(c_0_112, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.36/0.57 thf(c_0_113, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.36/0.57 thf(c_0_114, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.36/0.57 thf(c_0_115, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.36/0.57 thf(c_0_116, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.36/0.57 thf(c_0_117, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.36/0.57 thf(c_0_118, plain, ((binintersect)=(^[Z0/* 19 */:$i, Z1:$i]:(dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((in @ Z2 @ Z1)))))), inference(fof_simplification,[status(thm)],[binintersect])). 0.36/0.57 thf(c_0_119, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.36/0.57 thf(c_0_120, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.36/0.57 thf(c_0_121, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 0.36/0.57 thf(c_0_122, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.36/0.57 thf(c_0_123, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.36/0.57 thf(c_0_124, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 0.36/0.57 thf(c_0_125, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.36/0.57 thf(c_0_126, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.36/0.57 thf(c_0_127, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.36/0.57 thf(c_0_128, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_111])). 0.36/0.57 thf(c_0_129, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_112, c_0_111])). 0.36/0.57 thf(c_0_130, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X317:$i]:((((X1 @ X317))&![X318:$i]:((((X1 @ X318))=>((X317)=(X318)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_113, c_0_114])). 0.36/0.57 thf(c_0_131, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.36/0.57 thf(c_0_132, plain, ((descrp)=(![X1:$i > $o]:(((?[X313:$i]:((((X1 @ X313))&![X314:$i]:((((X1 @ X314))=>((X313)=(X314)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_115, c_0_114])). 0.36/0.57 thf(c_0_133, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X311:$i]:((((X6 @ X2 @ X311))&![X312:$i]:((((X6 @ X2 @ X312))=>((X311)=(X312)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_116, c_0_114])). 0.36/0.57 thf(c_0_134, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X335:$i]:((((X1 @ X335))&![X336:$i]:((((X1 @ X336))=>((X335)=(X336)))))))=>((?[X337:$i]:((((X17 @ X337))&![X338:$i]:((((X17 @ X338))=>((X337)=(X338)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_117, c_0_114])). 0.36/0.57 thf(c_0_135, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.36/0.57 thf(c_0_136, axiom, ((binintersectI)=(![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((in @ Z0 @ X5)))))))))), inference(apply_def,[status(thm)],[binintersectI, c_0_118])). 0.36/0.57 thf(c_0_137, axiom, ((binintersectSubset5)=(![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((in @ Z0 @ X5)))))))))), inference(apply_def,[status(thm)],[binintersectSubset5, c_0_118])). 0.36/0.57 thf(c_0_138, axiom, ((binintersectEL)=(![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((in @ Z0 @ X5)))))=>(in @ X2 @ X4))))), inference(apply_def,[status(thm)],[binintersectEL, c_0_118])). 0.36/0.57 thf(c_0_139, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.36/0.57 thf(c_0_140, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.36/0.57 thf(c_0_141, plain, ((exuEu)=(![X1:$i > $o]:(((?[X333:$i]:((((X1 @ X333))&![X334:$i]:((((X1 @ X334))=>((X333)=(X334)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_119, c_0_114])). 0.36/0.57 thf(c_0_142, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X329:$i]:((((X1 @ X329))&![X330:$i]:((((X1 @ X330))=>((X329)=(X330)))))))<=>(?[X331:$i]:((((X17 @ X331))&![X332:$i]:((((X17 @ X332))=>((X331)=(X332)))))))))))), inference(apply_def,[status(thm)],[c_0_120, c_0_114])). 0.36/0.57 thf(c_0_143, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X327:$i]:((((X1 @ X327))&![X328:$i]:((((X1 @ X328))=>((X327)=(X328)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_121, c_0_114])). 0.36/0.57 thf(c_0_144, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X325:$i]:((((X1 @ X325))&![X326:$i]:((((X1 @ X326))=>((X325)=(X326))))))))))), inference(apply_def,[status(thm)],[c_0_122, c_0_114])). 0.36/0.57 thf(c_0_145, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X323:$i]:((((X1 @ X323))&![X324:$i]:((((X1 @ X324))=>((X323)=(X324)))))))))))), inference(apply_def,[status(thm)],[c_0_123, c_0_114])). 0.36/0.57 thf(c_0_146, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X321:$i]:((((X1 @ X321))&![X322:$i]:((((X1 @ X322))=>((X321)=(X322))))))))))), inference(apply_def,[status(thm)],[c_0_124, c_0_114])). 0.36/0.57 thf(c_0_147, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 0.36/0.57 thf(c_0_148, plain, ((exuE2)=(![X1:$i > $o]:(((?[X319:$i]:((((X1 @ X319))&![X320:$i]:((((X1 @ X320))=>((X319)=(X320)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_125, c_0_114])). 0.36/0.57 thf(c_0_149, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_111])). 0.36/0.57 thf(c_0_150, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_111])). 0.36/0.57 thf(c_0_151, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.36/0.57 thf(c_0_152, plain, ((exuE1)=(![X1:$i > $o]:(((?[X315:$i]:((((X1 @ X315))&![X316:$i]:((((X1 @ X316))=>((X315)=(X316)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_126, c_0_114])). 0.36/0.57 thf(c_0_153, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.36/0.57 thf(c_0_154, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.36/0.57 thf(c_0_155, plain, ((epred1_0)<=>![X624:$i]:(?[X625:$i]:((((![X626:$i]:(((in @ X626 @ X625)=>![X627:$i]:(((in @ X627 @ X626)=>(in @ X627 @ X624)))))&![X628:$i, X629:$i]:((((in @ X628 @ X624)&(in @ X629 @ X624))=>(![X630:$i]:(((in @ X630 @ X625)=>((in @ X628 @ X630)<=>(in @ X629 @ X630))))=>((X628)=(X629))))))&![X631:$i, X632:$i]:((((in @ X631 @ X625)&(in @ X632 @ X625))=>(![X633:$i]:(((in @ X633 @ X631)=>(in @ X633 @ X632)))|![X634:$i]:(((in @ X634 @ X632)=>(in @ X634 @ X631)))))))&![X635:$i]:(((![X636:$i]:(((in @ X636 @ X635)=>(in @ X636 @ X624)))&?[X637:$i]:((in @ X637 @ X635)))=>?[X638:$i, X639:$i]:(((((in @ X638 @ X625)&(in @ X639 @ X635))&~(?[X640:$i]:(((in @ X640 @ X638)&(in @ X640 @ X635)))))&![X641:$i]:(((in @ X641 @ X625)=>(![X642:$i]:(((in @ X642 @ X641)=>(in @ X642 @ X638)))|(in @ X639 @ X641)))))))))))), introduced(definition)). 0.36/0.57 thf(c_0_156, negated_conjecture, ~((![X653:$i, X654:$i]:((![X655:$i]:(((in @ X655 @ X653)<=>(in @ X655 @ X654)))=>((X653)=(X654))))=>(![X652:$i]:(~(in @ X652 @ emptyset))=>(![X339:$i, X340:$i, X341:$i]:(((in @ X341 @ (setadjoin @ X339 @ X340))<=>(((X341)=(X339))|(in @ X341 @ X340))))=>(![X342:$i, X343:$i]:(((in @ X343 @ (powerset @ X342))<=>![X344:$i]:(((in @ X344 @ X343)=>(in @ X344 @ X342)))))=>(![X345:$i, X346:$i]:(((in @ X346 @ (setunion @ X345))<=>?[X347:$i]:(((in @ X346 @ X347)&(in @ X347 @ X345)))))=>((in @ emptyset @ omega)=>(![X651:$i]:(((in @ X651 @ omega)=>(in @ (setadjoin @ X651 @ X651) @ omega)))=>(![X348:$i]:((((in @ emptyset @ X348)&![X349:$i]:((((in @ X349 @ omega)&(in @ X349 @ X348))=>(in @ (setadjoin @ X349 @ X349) @ X348))))=>![X350:$i]:(((in @ X350 @ omega)=>(in @ X350 @ X348)))))=>(![X643:$i > $i > $o, X644:$i]:((![X645:$i]:(((in @ X645 @ X644)=>?[X646:$i]:(((X643 @ X645 @ X646)&![X647:$i]:(((X643 @ X645 @ X647)=>((X646)=(X647))))))))=>?[X648:$i]:(![X649:$i]:(((in @ X649 @ X648)<=>?[X650:$i]:(((in @ X650 @ X644)&(X643 @ X650 @ X649))))))))=>(![X351:$i]:((?[X352:$i]:((in @ X352 @ X351))=>?[X353:$i]:(((in @ X353 @ X351)&~(?[X354:$i]:(((in @ X354 @ X353)&(in @ X354 @ X351))))))))=>((epred1_0)=>(![X621:$i > $o]:((?[X622:$i]:(((X621 @ X622)&![X623:$i]:(((X621 @ X623)=>((X622)=(X623))))))=>(X621 @ (descr @ (^[Z0/* 3 */:$i]:((X621 @ Z0)))))))=>(![X355:$i, X356:$i > $o, X357:$i]:(((in @ X357 @ X355)=>((X356 @ X357)=>(in @ X357 @ (dsetconstr @ X355 @ (^[Z0/* 3 */:$i]:((X356 @ Z0))))))))=>(![X618:$i, X619:$i > $o, X620:$i]:(((in @ X620 @ (dsetconstr @ X618 @ (^[Z0/* 3 */:$i]:((X619 @ Z0)))))=>(in @ X620 @ X618)))=>(![X358:$i, X359:$i > $o, X360:$i]:(((in @ X360 @ (dsetconstr @ X358 @ (^[Z0/* 3 */:$i]:((X359 @ Z0)))))=>(X359 @ X360)))=>(![X361:$i > $o]:((?[X362:$i]:(((X361 @ X362)&![X363:$i]:(((X361 @ X363)=>((X362)=(X363))))))=>?[X364:$i]:(((X361 @ X364)&![X365:$i]:(((X361 @ X365)=>((X364)=(X365))))))))=>(![X616:$o, X617:$i]:(((in @ X617 @ (prop2set @ ((X616))))=>(X616)))=>(![X366:$i]:(((in @ X366 @ emptyset)=>![X367:$o]:((X367))))=>(![X615:$i]:(~(in @ X615 @ emptyset))=>(![X614:$i]:(~(in @ X614 @ emptyset))=>(![X610:$i > $o]:((?[X611:$i]:(((X610 @ X611)&![X612:$i]:(((X610 @ X612)=>((X611)=(X612))))))=>?[X613:$i]:((X610 @ X613))))=>(![X368:$i, X369:$i]:((![X370:$i]:(((in @ X370 @ X368)=>(in @ X370 @ X369)))=>(![X371:$i]:(((in @ X371 @ X369)=>(in @ X371 @ X368)))=>((X368)=(X369)))))=>(![X372:$i]:((![X373:$i]:(~(in @ X373 @ X372))=>((X372)=(emptyset))))=>(![X374:$i]:((![X375:$i]:(~(in @ X375 @ X374))=>((X374)=(emptyset))))=>(![X376:$i, X377:$i > $o, X378:$i]:(((in @ X378 @ X376)=>((in @ X378 @ (dsetconstr @ X376 @ (^[Z0/* 3 */:$i]:((X377 @ Z0)))))<=>(X377 @ X378))))=>(![X379:$i]:((((X379)!=(emptyset))=>?[X380:$i]:((in @ X380 @ X379))))=>(![X607:$i, X608:$i > $o, X609:$i]:(((in @ X609 @ X607)=>((X608 @ X609)=>((dsetconstr @ X607 @ (^[Z0/* 3 */:$i]:((X608 @ Z0))))!=(emptyset)))))=>(![X605:$i]:((?[X606:$i]:((in @ X606 @ X605))=>((X605)!=(emptyset))))=>(![X381:$i, X382:$i]:((in @ X381 @ (setadjoin @ X381 @ X382)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X383:$i, X384:$i, X385:$i]:(((in @ X385 @ X384)=>(in @ X385 @ (setadjoin @ X383 @ X384))))=>(![X601:$i, X602:$i, X603:$i]:(((in @ X603 @ (setadjoin @ X601 @ X602))=>![X604:$o]:(((((X603)=(X601))=>(X604))=>(((in @ X603 @ X602)=>(X604))=>(X604))))))=>(![X598:$i, X599:$i, X600:$i]:(((in @ X600 @ (setadjoin @ X598 @ X599))=>(((X600)=(X598))|(in @ X600 @ X599))))=>(![X597:$i]:(((dsetconstr @ X597 @ (^[Z0/* 3 */:$i]:(($true))))=(X597)))=>(![X386:$i, X387:$i]:((![X388:$i]:(((in @ X388 @ X387)=>(in @ X388 @ X386)))=>(in @ X387 @ (powerset @ X386))))=>(![X389:$i]:((in @ emptyset @ (powerset @ X389)))=>(![X596:$i]:((in @ emptyset @ (powerset @ X596)))=>(![X593:$i, X594:$i, X595:$i]:(((in @ X594 @ (powerset @ X593))=>((in @ X595 @ X594)=>(in @ X595 @ X593))))=>(![X590:$i, X591:$i, X592:$i]:(((in @ X591 @ X592)=>((in @ X592 @ X590)=>(in @ X591 @ (setunion @ X590)))))=>(![X390:$i, X391:$i]:(((in @ X391 @ (setunion @ X390))=>![X392:$o]:((![X393:$i]:(((in @ X391 @ X393)=>((in @ X393 @ X390)=>(X392))))=>(X392)))))=>(![X394:$i, X395:$i]:(((in @ X395 @ X394)=>(in @ X395 @ (powerset @ (setunion @ X394)))))=>(![X585:$i > $o]:((?[X586:$i]:(((X585 @ X586)&![X587:$i]:(((X585 @ X587)=>((X586)=(X587))))))=>?[X588:$i]:(![X589:$i]:(((X585 @ X589)<=>((X589)=(X588)))))))=>(![X396:$i]:((((X396)!=(emptyset))=>?[X397:$i]:((in @ X397 @ X396))))=>(![X398:$i, X399:$i]:(((in @ X398 @ (setadjoin @ X399 @ emptyset))=>((X398)=(X399))))=>(![X400:$i, X401:$i]:((((X400)!=(X401))=>~(in @ X401 @ (setadjoin @ X400 @ emptyset))))=>(![X402:$i, X403:$i]:((((X402)=(X403))=>(in @ X402 @ (setadjoin @ X403 @ emptyset))))=>(![X583:$i, X584:$i]:(((in @ X583 @ (setadjoin @ X584 @ emptyset))=>(in @ X584 @ (setadjoin @ X583 @ emptyset))))=>(![X404:$i, X405:$i, X406:$i]:(((in @ X406 @ (setadjoin @ X404 @ (setadjoin @ X405 @ emptyset)))=>(((X406)=(X404))|((X406)=(X405)))))=>(![X407:$i, X408:$i]:((in @ X407 @ (setadjoin @ X407 @ (setadjoin @ X408 @ emptyset))))=>(![X409:$i, X410:$i]:((in @ X410 @ (setadjoin @ X409 @ (setadjoin @ X410 @ emptyset))))=>(![X580:$i, X581:$i > $o]:((?[X582:$i]:(((in @ X582 @ X580)&(X581 @ X582)))=>((dsetconstr @ X580 @ (^[Z0/* 3 */:$i]:((X581 @ Z0))))!=(emptyset))))=>(![X578:$i > $o, X579:$i]:(((in @ X579 @ emptyset)=>(X578 @ X579)))=>(![X411:$i, X412:$i > $o]:((~(![X413:$i]:(((in @ X413 @ X411)=>(X412 @ X413))))=>?[X414:$i]:(((in @ X414 @ X411)&~(X412 @ X414)))))=>(![X415:$i, X416:$i > $o]:((![X417:$i]:(((in @ X417 @ X415)=>~(X416 @ X417)))=>~(?[X418:$i]:(((in @ X418 @ X415)&(X416 @ X418))))))=>(![X574:$i, X575:$i > $o]:((~(?[X576:$i]:(((in @ X576 @ X574)&(X575 @ X576))))=>![X577:$i]:(((in @ X577 @ X574)=>~(X575 @ X577)))))=>(![X419:$i, X420:$i > $o]:((?[X421:$i]:(((in @ X421 @ X419)&~(X420 @ X421)))=>~(![X422:$i]:(((in @ X422 @ X419)=>(X420 @ X422))))))=>(![X423:$o]:(((X423)=>(in @ emptyset @ (prop2set @ ((X423))))))=>((prop2set2propI)=>(![X570:$i, X571:$i > $o]:((~(?[X572:$i]:(((in @ X572 @ X570)&(X571 @ X572))))=>![X573:$i]:(((in @ X573 @ X570)=>~(X571 @ X573)))))=>(![X424:$i, X425:$i > $o]:((~(![X426:$i]:(((in @ X426 @ X424)=>(X425 @ X426))))=>?[X427:$i]:(((in @ X427 @ X424)&~(X425 @ X427)))))=>(![X565:$i > $o]:((?[X566:$i]:(((X565 @ X566)&![X567:$i]:(((X565 @ X567)=>((X566)=(X567))))))=>?[X568:$i]:(((X565 @ X568)&![X569:$i]:(((X565 @ X569)=>((X568)=(X569))))))))=>(![X559:$i > $o]:((?[X560:$i]:((X559 @ X560))=>(![X561:$i, X562:$i]:(((X559 @ X561)=>((X559 @ 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X437:$i]:((((X436)=(X437))=>![X438:$i, X439:$i]:((((X438)=(X439))=>((setadjoin @ X436 @ X438)=(setadjoin @ X437 @ X439))))))=>(![X539:$i, X540:$i]:((((X539)=(X540))=>((powerset @ X539)=(powerset @ X540))))=>(![X537:$i, X538:$i]:((((X537)=(X538))=>((setunion @ X537)=(setunion @ X538))))=>(((omega)=(omega))=>(![X532:$i > $o]:((?[X533:$i]:(((X532 @ X533)&![X534:$i]:(((X532 @ X534)=>((X533)=(X534))))))=>![X535:$i, X536:$i]:(((X532 @ X535)=>((X532 @ X536)=>((X535)=(X536)))))))=>(![X440:$i > $o, X441:$i > $o]:((![X442:$i, X443:$i]:((((X442)=(X443))=>((X440 @ X442)<=>(X441 @ X443))))=>(?[X444:$i]:(((X440 @ X444)&![X445:$i]:(((X440 @ X445)=>((X444)=(X445))))))=>(?[X446:$i]:(((X441 @ X446)&![X447:$i]:(((X441 @ X447)=>((X446)=(X447))))))=>((descr @ (^[Z0/* 3 */:$i]:((X440 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X441 @ Z0)))))))))=>(![X526:$i, X527:$i]:((((X526)=(X527))=>![X528:$i > $o, X529:$i > $o]:((![X530:$i]:(((in @ X530 @ X526)=>![X531:$i]:(((in @ X531 @ X527)=>(((X530)=(X531))=>((X528 @ 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X461)=>((X460)!=(X461)))))=>(![X515:$i]:((subset @ X515 @ X515))=>(![X512:$i, X513:$i, X514:$i]:(((subset @ X512 @ X513)=>((subset @ X513 @ X514)=>(subset @ X512 @ X514))))=>(![X510:$i, X511:$i]:((subset @ X511 @ (setadjoin @ X510 @ X511)))=>(![X463:$i, X464:$i, X465:$i]:(((subset @ X463 @ X465)=>(subset @ X463 @ (setadjoin @ X464 @ X465))))=>(![X466:$i, X467:$i]:(((subset @ X466 @ X467)=>(in @ X466 @ (powerset @ X467))))=>(![X508:$i, X509:$i]:(((subset @ X508 @ X509)=>((subset @ X509 @ X508)=>((X508)=(X509)))))=>(![X468:$i]:(((subset @ X468 @ emptyset)=>((X468)=(emptyset))))=>(![X506:$i, X507:$i]:(((subset @ X507 @ X506)=>(in @ X507 @ (powerset @ X506))))=>(![X504:$i, X505:$i]:(((in @ X505 @ (powerset @ X504))=>(subset @ X505 @ X504)))=>(![X503:$i]:((in @ X503 @ (powerset @ X503)))=>(![X469:$i, X470:$i]:(((subset @ X469 @ X470)=>(subset @ (powerset @ X469) @ (powerset @ X470))))=>(![X501:$i, X502:$i > $o]:((in @ (dsetconstr @ X501 @ (^[Z0/* 3 */:$i]:((X502 @ Z0)))) @ (powerset @ X501)))=>(![X471:$i, X472:$i > $o]:((subset @ (dsetconstr @ X471 @ (^[Z0/* 3 */:$i]:((X472 @ Z0)))) @ X471))=>(![X473:$i, X474:$i, X475:$i]:(((in @ X475 @ X473)=>(in @ X475 @ (binunion @ X473 @ X474))))=>(![X476:$i, X477:$i]:((in @ X477 @ (setadjoin @ X476 @ (setadjoin @ X477 @ emptyset))))=>(![X478:$i, X479:$i, X480:$i]:(((in @ X480 @ X479)=>(in @ X480 @ (binunion @ X478 @ X479))))=>(![X497:$i, X498:$i, X499:$i, X500:$o]:(((in @ X499 @ (binunion @ X497 @ X498))=>(((in @ X499 @ X497)=>(X500))=>(((in @ X499 @ X498)=>(X500))=>(X500)))))=>(![X494:$i, X495:$i, X496:$i]:(((in @ X496 @ (binunion @ X494 @ X495))=>((in @ X496 @ X494)|(in @ X496 @ X495))))=>(![X481:$i, X482:$i]:((subset @ X481 @ (binunion @ X481 @ X482)))=>(![X483:$i, X484:$i]:((subset @ X484 @ (binunion @ X483 @ X484)))=>(![X485:$i, X486:$i, X487:$i]:(((in @ X487 @ X485)=>((in @ X487 @ X486)=>(in @ X487 @ (dsetconstr @ X485 @ (^[Z0/* 3 */:$i]:((in @ Z0 @ X486))))))))=>(![X488:$i, X489:$i, X490:$i]:(((subset @ X490 @ X488)=>((subset @ X490 @ X489)=>(subset @ X490 @ (dsetconstr @ X488 @ (^[Z0/* 3 */:$i]:((in @ Z0 @ X489))))))))=>(![X491:$i, X492:$i, X493:$i]:(((in @ X493 @ (dsetconstr @ X491 @ (^[Z0/* 3 */:$i]:((in @ Z0 @ X492)))))=>(in @ X493 @ X491)))=>![X4:$i, X5:$i]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((in @ Z0 @ X5)))) @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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(assume_negation,[status(cth)],[binintersectLsub]), upairsetIL]), setextAx]), emptyInPowerset]), c_0_127]), setadjoinOr]), setadjoinE]), quantDeMorgan4]), c_0_128]), c_0_129]), prop2setI]), c_0_130]), notinemptyset]), emptysetimpfalse]), notdallE]), prop2setE]), c_0_131]), inCongP]), c_0_132]), wellorderingAx]), c_0_133]), upairsetE]), omegaSAx]), in__Cong]), emptysetAx]), setadjoin__Cong]), binunionIR]), omega__Cong]), c_0_134]), eqimpsubset2]), eqimpsubset1]), subsetE]), notsubsetI]), notequalI1]), notequalI2]), upairsetIR]), setadjoinSub2]), subset2powerset]), subsetemptysetimpeq]), powersetsubset]), c_0_135]), binunionIL]), upairset2IR]), binunionLsub]), binunionRsub]), c_0_136]), c_0_137]), c_0_138]), c_0_118]), binunionE]), binunionEcases]), c_0_139]), quantDeMorgan1]), inPowerset]), powersetE1]), powersetI1]), setextsub]), setadjoinSub]), subsetTrans]), subsetRefl]), subsetE2]), emptysetsubset]), subsetI2]), subsetI1]), c_0_140]), c_0_141]), setunion__Cong]), powerset__Cong]), quantDeMorgan2]), emptyset__Cong]), c_0_142]), c_0_143]), c_0_144]), c_0_145]), c_0_146]), notdexE]), quantDeMorgan3]), vacuousDall]), c_0_147]), singletonsswitch]), c_0_148]), setunionI]), powersetE]), eqinunit]), notinsingleton]), uniqinunit]), c_0_149]), subPowSU]), setunionE]), emptyinPowerset]), powersetI]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_150]), c_0_151]), noeltsimpempty]), emptyI]), setext]), emptysetE]), c_0_152]), c_0_153]), c_0_154]), foundationAx]), omegaIndAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx])]), c_0_155])). 0.36/0.57 thf(c_0_157, negated_conjecture, ![X656:$i, X657:$i, X659:$i, X660:$i, X661:$i, X662:$i, X663:$i, X664:$i, X665:$i, X666:$i, X667:$i, X669:$i, X670:$i, X672:$i, X673:$i, X674:$i, X675:$i, X676:$i, X678:$i, X679:$i > $i > $o, X680:$i, X682:$i, X685:$i, X687:$i, X688:$i, X689:$i, X690:$i, X692:$i, X693:$i > $o, X694:$i, X696:$i, X697:$i > $o, X698:$i, X699:$i, X700:$i > $o, X701:$i, X702:$i, X703:$i > $o, X704:$i, X705:$i > $o, X706:$i, X709:$i, X710:$o, X711:$i, X712:$i, X713:$o, X714:$i, X715:$i, X716:$i > $o, X717:$i, X720:$i, X721:$i, X724:$i, X726:$i, X728:$i, X729:$i > $o, X730:$i, X731:$i, X733:$i, X734:$i > $o, X735:$i, X736:$i, X737:$i, X738:$i, X739:$i, X740:$i, X741:$i, X742:$i, X743:$i, X744:$i, X745:$i, X746:$o, X747:$i, X748:$i, X749:$i, X750:$i, X751:$i, X752:$i, X754:$i, X755:$i, X756:$i, X757:$i, X758:$i, X759:$i, X760:$i, X761:$i, X762:$i, X763:$i, X764:$o, X766:$i, X767:$i, X768:$i > $o, X769:$i, X772:$i, X773:$i, X774:$i, X776:$i, X777:$i, X778:$i, X779:$i, X780:$i, X781:$i, X782:$i, X783:$i, X784:$i, X785:$i, X786:$i, X787:$i, X788:$i, X789:$i, X790:$i, X791:$i, X792:$i > $o, X793:$i, X794:$i > $o, X795:$i, X796:$i, X797:$i > $o, X798:$i, X800:$i, X801:$i > $o, X803:$i, X804:$i, X805:$i > $o, X807:$i, X808:$i, X809:$i > $o, X810:$i, X812:$o, X813:$i, X814:$i > $o, X816:$i, X817:$i, X818:$i > $o, X819:$i, X821:$i > $o, X822:$i, X825:$i, X826:$i > $o, X827:$i, X831:$i, X832:$i > $o, X833:$i, X836:$i, X837:$i, X838:$i, X839:$i, X840:$i, X841:$i, X842:$i, X843:$i, X844:$i, X845:$i > $o, X846:$i, X848:$i, X849:$i, X850:$i > $o, X851:$i > $o, X854:$i, X857:$i, X858:$i, X861:$i, X862:$i, X863:$i, X864:$i, X865:$i, X866:$i, X867:$i, X868:$i, X869:$i, X870:$i > $o, X871:$i, X873:$i, X874:$i, X875:$i > $o, X876:$i > $o, X879:$i, X881:$i, X883:$i, X884:$i, X885:$i > $o, X886:$i > $o, X889:$i, X890:$i, X892:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X904:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X912:$i, X913:$i, X914:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$i, X920:$i, X921:$i, X922:$i, X923:$i, X924:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i, X932:$i, X933:$i, X934:$i, X935:$i, X936:$i > $o, X937:$i, X938:$i > $o, X939:$i, X940:$i, X941:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X949:$i, X950:$o, X951:$i, X952:$i, X953:$i, X954:$i, X955:$i, X956:$i, X957:$i, X958:$i, X959:$i, 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X875 @ X876 @ X879))|~(X875 @ X879))|(~(X875 @ (esk46_2 @ X875 @ X876))|~(X876 @ (esk47_2 @ X875 @ X876)))))&(((X876 @ (esk49_3 @ X875 @ X876 @ X881))|~(X876 @ X881)|((descr @ (^[Z0/* 3 */:$i]:((X875 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X876 @ Z0)))))|(((X879)!=(esk48_3 @ X875 @ X876 @ X879))|~(X875 @ X879))|(~(X875 @ (esk46_2 @ X875 @ X876))|~(X876 @ (esk47_2 @ X875 @ X876))))&(((X881)!=(esk49_3 @ X875 @ X876 @ X881))|~(X876 @ X881)|((descr @ (^[Z0/* 3 */:$i]:((X875 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X876 @ Z0)))))|(((X879)!=(esk48_3 @ X875 @ X876 @ X879))|~(X875 @ X879))|(~(X875 @ (esk46_2 @ X875 @ X876))|~(X876 @ (esk47_2 @ X875 @ X876))))))&((((X876 @ (esk49_3 @ X875 @ X876 @ X881))|~(X876 @ X881)|((descr @ (^[Z0/* 3 */:$i]:((X875 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X876 @ Z0)))))|((X875 @ (esk48_3 @ X875 @ X876 @ X879))|~(X875 @ X879))|((X875 @ (esk46_2 @ X875 @ X876))|(X876 @ (esk47_2 @ X875 @ X876))))&(((X881)!=(esk49_3 @ X875 @ X876 @ X881))|~(X876 @ X881)|((descr @ (^[Z0/* 3 */:$i]:((X875 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X876 @ Z0)))))|((X875 @ (esk48_3 @ X875 @ X876 @ X879))|~(X875 @ X879))|((X875 @ (esk46_2 @ X875 @ X876))|(X876 @ (esk47_2 @ X875 @ X876)))))&(((X876 @ (esk49_3 @ X875 @ X876 @ X881))|~(X876 @ X881)|((descr @ (^[Z0/* 3 */:$i]:((X875 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X876 @ Z0)))))|(((X879)!=(esk48_3 @ X875 @ X876 @ X879))|~(X875 @ X879))|((X875 @ (esk46_2 @ X875 @ X876))|(X876 @ (esk47_2 @ X875 @ X876))))&(((X881)!=(esk49_3 @ X875 @ X876 @ X881))|~(X876 @ X881)|((descr @ (^[Z0/* 3 */:$i]:((X875 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X876 @ Z0)))))|(((X879)!=(esk48_3 @ X875 @ X876 @ X879))|~(X875 @ X879))|((X875 @ (esk46_2 @ X875 @ X876))|(X876 @ (esk47_2 @ X875 @ X876))))))))&((((in @ (esk50_4 @ X883 @ X884 @ X885 @ X886) @ X883)|((dsetconstr @ X883 @ (^[Z0/* 3 */:$i]:((X885 @ Z0))))=(dsetconstr @ X884 @ (^[Z0/* 3 */:$i]:((X886 @ Z0)))))|((X883)!=(X884)))&(((in @ (esk51_4 @ X883 @ X884 @ X885 @ X886) @ X884)|((dsetconstr @ X883 @ (^[Z0/* 3 */:$i]:((X885 @ Z0))))=(dsetconstr @ X884 @ (^[Z0/* 3 */:$i]:((X886 @ Z0)))))|((X883)!=(X884)))&((((esk50_4 @ X883 @ X884 @ X885 @ X886)=(esk51_4 @ X883 @ X884 @ X885 @ X886))|((dsetconstr @ X883 @ (^[Z0/* 3 */:$i]:((X885 @ Z0))))=(dsetconstr @ X884 @ (^[Z0/* 3 */:$i]:((X886 @ Z0)))))|((X883)!=(X884)))&((~(X885 @ (esk50_4 @ X883 @ X884 @ X885 @ X886))|~(X886 @ (esk51_4 @ X883 @ X884 @ X885 @ X886))|((dsetconstr @ X883 @ (^[Z0/* 3 */:$i]:((X885 @ Z0))))=(dsetconstr @ X884 @ (^[Z0/* 3 */:$i]:((X886 @ Z0)))))|((X883)!=(X884)))&((X885 @ (esk50_4 @ X883 @ X884 @ X885 @ X886))|(X886 @ (esk51_4 @ X883 @ X884 @ X885 @ X886))|((dsetconstr @ X883 @ (^[Z0/* 3 */:$i]:((X885 @ Z0))))=(dsetconstr @ X884 @ (^[Z0/* 3 */:$i]:((X886 @ Z0)))))|((X883)!=(X884)))))))&((((in @ (esk52_2 @ X889 @ X890) @ X889)|(subset @ X889 @ X890))&(~(in @ (esk52_2 @ X889 @ X890) @ X890)|(subset @ X889 @ X890)))&((((X892)!=(X893))|(subset @ X893 @ X892))&((((X894)!=(X895))|(subset @ X894 @ X895))&((((in @ (esk53_2 @ X896 @ X897) @ X896)|(subset @ X896 @ X897))&(~(in @ (esk53_2 @ X896 @ X897) @ X897)|(subset @ X896 @ X897)))&((subset @ emptyset @ X899)&((~(subset @ X900 @ X901)|(~(in @ X902 @ X900)|(in @ X902 @ X901)))&((~(subset @ X903 @ X904)|((in @ X905 @ X904)|~(in @ X905 @ X903)))&((~(in @ X908 @ X906)|((in @ X908 @ X907)|~(subset @ X906 @ X907)))&(((subset @ X909 @ X910)|((X909)!=(X910)))&((~(in @ X913 @ X911)|((in @ X913 @ X912)|((X911)!=(X912))))&((subset @ X914 @ X914)&((~(subset @ X915 @ X916)|(~(subset @ X916 @ X917)|(subset @ X915 @ X917)))&((subset @ X919 @ (setadjoin @ X918 @ X919))&((~(subset @ X920 @ X922)|(subset @ X920 @ (setadjoin @ X921 @ X922)))&((~(subset @ X923 @ X924)|(in @ X923 @ (powerset @ X924)))&((~(subset @ X925 @ X926)|(~(subset @ X926 @ X925)|((X925)=(X926))))&((~(subset @ X927 @ emptyset)|((X927)=(emptyset)))&((~(subset @ X929 @ X928)|(in @ X929 @ (powerset @ X928)))&((~(in @ X931 @ (powerset @ X930))|(subset @ X931 @ X930))&((in @ X932 @ (powerset @ X932))&((~(subset @ X933 @ X934)|(subset @ (powerset @ X933) @ (powerset @ X934)))&((in @ (dsetconstr @ X935 @ (^[Z0/* 3 */:$i]:((X936 @ Z0)))) @ (powerset @ X935))&((subset @ (dsetconstr @ X937 @ (^[Z0/* 3 */:$i]:((X938 @ Z0)))) @ X937)&((~(in @ X941 @ X939)|(in @ X941 @ (binunion @ X939 @ X940)))&((in @ X943 @ (setadjoin @ X942 @ (setadjoin @ X943 @ emptyset)))&((~(in @ X946 @ X945)|(in @ X946 @ (binunion @ X944 @ X945)))&(((((in @ X949 @ X948)|(X950)|(in @ X949 @ X947)|~(in @ X949 @ (binunion @ X947 @ X948)))&(~(X950)|(X950)|(in @ X949 @ X947)|~(in @ X949 @ (binunion @ X947 @ X948))))&(((in @ X949 @ X948)|(X950)|~(X950)|~(in @ X949 @ (binunion @ X947 @ X948)))&(~(X950)|(X950)|~(X950)|~(in @ X949 @ (binunion @ X947 @ X948)))))&((~(in @ X953 @ (binunion @ X951 @ X952))|((in @ X953 @ X951)|(in @ X953 @ X952)))&((subset @ X954 @ (binunion @ X954 @ X955))&((subset @ X957 @ (binunion @ X956 @ X957))&((~(in @ X960 @ X958)|(~(in @ X960 @ X959)|(in @ X960 @ (dsetconstr @ X958 @ (^[Z0/* 3 */:$i]:((in @ Z0 @ X959)))))))&((~(subset @ X963 @ X961)|(~(subset @ X963 @ X962)|(subset @ X963 @ (dsetconstr @ X961 @ (^[Z0/* 3 */:$i]:((in @ Z0 @ X962)))))))&((~(in @ X966 @ (dsetconstr @ X964 @ (^[Z0/* 3 */:$i]:((in @ Z0 @ X965)))))|(in @ X966 @ X964))&~(subset @ (dsetconstr @ esk54_0 @ (^[Z0/* 3 */:$i]:((in @ Z0 @ esk55_0)))) @ esk54_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_156])])])])])])). 0.36/0.57 thf(c_0_158, negated_conjecture, ~((subset @ (dsetconstr @ esk54_0 @ (^[Z0/* 3 */:$i]:((in @ Z0 @ esk55_0)))) @ esk54_0)), inference(split_conjunct,[status(thm)],[c_0_157])). 0.36/0.57 thf(c_0_159, negated_conjecture, ![X1:$i > $o, X2:$i]:((subset @ (dsetconstr @ X2 @ X1) @ X2)), inference(split_conjunct,[status(thm)],[c_0_157])). 0.36/0.57 thf(c_0_160, negated_conjecture, ($false), inference(spm,[status(thm)],[c_0_158, c_0_159]), ['proof']). 0.36/0.57 # SZS output end CNFRefutation 0.36/0.57 # Parsed axioms : 237 0.36/0.57 # Removed by relevancy pruning/SinE : 126 0.36/0.57 # Initial clauses : 221 0.36/0.57 # Removed in clause preprocessing : 16 0.36/0.57 # Initial clauses in saturation : 205 0.36/0.57 # Processed clauses : 25 0.36/0.57 # ...of these trivial : 1 0.36/0.57 # ...subsumed : 3 0.36/0.57 # ...remaining for further processing : 21 0.36/0.57 # Other redundant clauses eliminated : 2 0.36/0.57 # Clauses deleted for lack of memory : 0 0.36/0.57 # Backward-subsumed : 0 0.36/0.57 # Backward-rewritten : 1 0.36/0.57 # Generated clauses : 7 0.36/0.57 # ...of the previous two non-redundant : 2 0.36/0.57 # ...aggressively subsumed : 0 0.36/0.57 # Contextual simplify-reflections : 0 0.36/0.57 # Paramodulations : 2 0.36/0.57 # Factorizations : 0 0.36/0.57 # NegExts : 1 0.36/0.57 # Equation resolutions : 2 0.36/0.57 # Total rewrite steps : 4 0.36/0.57 # Propositional unsat checks : 0 0.36/0.57 # Propositional check models : 0 0.36/0.57 # Propositional check unsatisfiable : 0 0.36/0.57 # Propositional clauses : 0 0.36/0.57 # Propositional clauses after purity: 0 0.36/0.57 # Propositional unsat core size : 0 0.36/0.57 # Propositional preprocessing time : 0.000 0.36/0.57 # Propositional encoding time : 0.000 0.36/0.57 # Propositional solver time : 0.000 0.36/0.57 # Success case prop preproc time : 0.000 0.36/0.57 # Success case prop encoding time : 0.000 0.36/0.57 # Success case prop solver time : 0.000 0.36/0.57 # Current number of processed clauses : 19 0.36/0.57 # Positive orientable unit clauses : 14 0.36/0.57 # Positive unorientable unit clauses: 0 0.36/0.57 # Negative unit clauses : 5 0.36/0.57 # Non-unit-clauses : 0 0.36/0.57 # Current number of unprocessed clauses: 182 0.36/0.57 # ...number of literals in the above : 657 0.36/0.57 # Current number of archived formulas : 0 0.36/0.57 # Current number of archived clauses : 1 0.36/0.57 # Clause-clause subsumption calls (NU) : 0 0.36/0.57 # Rec. Clause-clause subsumption calls : 0 0.36/0.57 # Non-unit clause-clause subsumptions : 0 0.36/0.57 # Unit Clause-clause subsumption calls : 10 0.36/0.57 # Rewrite failures with RHS unbound : 0 0.36/0.57 # BW rewrite match attempts : 6 0.36/0.57 # BW rewrite match successes : 1 0.36/0.57 # Condensation attempts : 25 0.36/0.57 # Condensation successes : 0 0.36/0.57 # Termbank termtop insertions : 24473 0.36/0.57 0.36/0.57 # ------------------------------------------------- 0.36/0.57 # User time : 0.028 s 0.36/0.57 # System time : 0.008 s 0.36/0.57 # Total time : 0.036 s 0.36/0.57 # Maximum resident set size: 4736 pages 0.79/180.03 0.79/180.03 # ------------------------------------------------- 0.79/180.03 # User time : 0.033 s 0.79/180.03 # System time : 0.012 s 0.79/180.03 # Total time : 0.045 s 0.79/180.03 # Maximum resident set size: 2064 pages 0.79/180.03 % E---3.1 exiting 0.79/180.03 EOF