0.11/0.15 % Problem : Vampire---4.8_26390 : TPTP v0.0.0. Released v0.0.0. 0.11/0.16 % Command : run_E %s %d THM 0.16/0.37 % Computer : n007.cluster.edu 0.16/0.37 % Model : x86_64 x86_64 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.37 % Memory : 8042.1875MB 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.37 % CPULimit : 1440 0.16/0.37 % WCLimit : 180 0.16/0.37 % DateTime : Mon Jul 3 12:51:58 EDT 2023 0.16/0.37 % CPUTime : 0.23/0.55 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.PmrisFvij7/Vampire---4.8_26390 0.23/0.55 # Version: 3.1pre001-ho 69.39/9.26 # Preprocessing class: HSLMSLSSLLLCHFA. 69.39/9.26 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 69.39/9.26 # Starting ehoh_best5 with 180s (1) cores 69.39/9.26 # Starting almost_fo_3_lam with 180s (1) cores 69.39/9.26 # Starting new_bool_5 with 180s (1) cores 69.39/9.26 # Starting pre_casc_3 with 180s (1) cores 69.39/9.26 # Starting ho_unfolding_8 with 180s (1) cores 69.39/9.26 # Starting new_ho_10_cnf2 with 180s (1) cores 69.39/9.26 # Starting new_bool_3 with 180s (1) cores 69.39/9.26 # Starting new_ho_5 with 180s (1) cores 69.39/9.26 # new_bool_5 with pid 26695 completed with status 0 69.39/9.26 # Result found by new_bool_5 69.39/9.26 # Preprocessing class: HSLMSLSSLLLCHFA. 69.39/9.26 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 69.39/9.26 # Starting ehoh_best5 with 180s (1) cores 69.39/9.26 # Starting almost_fo_3_lam with 180s (1) cores 69.39/9.26 # Starting new_bool_5 with 180s (1) cores 69.39/9.26 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 69.39/9.26 # Search class: HGHSM-FSLM31-MHFMMSBN 69.39/9.26 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 69.39/9.26 # Starting new_ho_10_cnf2 with 98s (1) cores 69.39/9.26 # new_ho_10_cnf2 with pid 26702 completed with status 0 69.39/9.26 # Result found by new_ho_10_cnf2 69.39/9.26 # Preprocessing class: HSLMSLSSLLLCHFA. 69.39/9.26 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 69.39/9.26 # Starting ehoh_best5 with 180s (1) cores 69.39/9.26 # Starting almost_fo_3_lam with 180s (1) cores 69.39/9.26 # Starting new_bool_5 with 180s (1) cores 69.39/9.26 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 69.39/9.26 # Search class: HGHSM-FSLM31-MHFMMSBN 69.39/9.26 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 69.39/9.26 # Starting new_ho_10_cnf2 with 98s (1) cores 69.39/9.26 # Preprocessing time : 0.004 s 69.39/9.26 # Presaturation interreduction done 69.39/9.26 69.39/9.26 # Proof found! 69.39/9.26 # SZS status Theorem 69.39/9.26 # SZS output start CNFRefutation 69.39/9.26 thf(decl_22, type, in: $i > $i > $o). 69.39/9.26 thf(decl_23, type, exu: ($i > $o) > $o). 69.39/9.26 thf(decl_24, type, setextAx: $o). 69.39/9.26 thf(decl_25, type, emptyset: $i). 69.39/9.26 thf(decl_26, type, emptysetAx: $o). 69.39/9.26 thf(decl_27, type, setadjoin: $i > $i > $i). 69.39/9.26 thf(decl_28, type, setadjoinAx: $o). 69.39/9.26 thf(decl_29, type, powerset: $i > $i). 69.39/9.26 thf(decl_30, type, powersetAx: $o). 69.39/9.26 thf(decl_31, type, setunion: $i > $i). 69.39/9.26 thf(decl_32, type, setunionAx: $o). 69.39/9.26 thf(decl_33, type, omega: $i). 69.39/9.26 thf(decl_34, type, omega0Ax: $o). 69.39/9.26 thf(decl_35, type, omegaSAx: $o). 69.39/9.26 thf(decl_36, type, omegaIndAx: $o). 69.39/9.26 thf(decl_37, type, replAx: $o). 69.39/9.26 thf(decl_38, type, foundationAx: $o). 69.39/9.26 thf(decl_39, type, wellorderingAx: $o). 69.39/9.26 thf(decl_40, type, descr: ($i > $o) > $i). 69.39/9.26 thf(decl_41, type, descrp: $o). 69.39/9.26 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 69.39/9.26 thf(decl_43, type, dsetconstrI: $o). 69.39/9.26 thf(decl_44, type, dsetconstrEL: $o). 69.39/9.26 thf(decl_45, type, dsetconstrER: $o). 69.39/9.26 thf(decl_46, type, exuE1: $o). 69.39/9.26 thf(decl_47, type, prop2set: $o > $i). 69.39/9.26 thf(decl_48, type, prop2setE: $o). 69.39/9.26 thf(decl_49, type, emptysetE: $o). 69.39/9.26 thf(decl_50, type, emptysetimpfalse: $o). 69.39/9.26 thf(decl_51, type, notinemptyset: $o). 69.39/9.26 thf(decl_52, type, exuE3e: $o). 69.39/9.26 thf(decl_53, type, setext: $o). 69.39/9.26 thf(decl_54, type, emptyI: $o). 69.39/9.26 thf(decl_55, type, noeltsimpempty: $o). 69.39/9.26 thf(decl_56, type, setbeta: $o). 69.39/9.26 thf(decl_57, type, nonempty: $i > $o). 69.39/9.26 thf(decl_58, type, nonemptyE1: $o). 69.39/9.26 thf(decl_59, type, nonemptyI: $o). 69.39/9.26 thf(decl_60, type, nonemptyI1: $o). 69.39/9.26 thf(decl_61, type, setadjoinIL: $o). 69.39/9.26 thf(decl_62, type, emptyinunitempty: $o). 69.39/9.26 thf(decl_63, type, setadjoinIR: $o). 69.39/9.26 thf(decl_64, type, setadjoinE: $o). 69.39/9.26 thf(decl_65, type, setadjoinOr: $o). 69.39/9.26 thf(decl_66, type, setoftrueEq: $o). 69.39/9.26 thf(decl_67, type, powersetI: $o). 69.39/9.26 thf(decl_68, type, emptyinPowerset: $o). 69.39/9.26 thf(decl_69, type, emptyInPowerset: $o). 69.39/9.26 thf(decl_70, type, powersetE: $o). 69.39/9.26 thf(decl_71, type, setunionI: $o). 69.39/9.26 thf(decl_72, type, setunionE: $o). 69.39/9.26 thf(decl_73, type, subPowSU: $o). 69.39/9.26 thf(decl_74, type, exuE2: $o). 69.39/9.26 thf(decl_75, type, nonemptyImpWitness: $o). 69.39/9.26 thf(decl_76, type, uniqinunit: $o). 69.39/9.26 thf(decl_77, type, notinsingleton: $o). 69.39/9.26 thf(decl_78, type, eqinunit: $o). 69.39/9.26 thf(decl_79, type, singletonsswitch: $o). 69.39/9.26 thf(decl_80, type, upairsetE: $o). 69.39/9.26 thf(decl_81, type, upairsetIL: $o). 69.39/9.26 thf(decl_82, type, upairsetIR: $o). 69.39/9.26 thf(decl_83, type, emptyE1: $o). 69.39/9.26 thf(decl_84, type, vacuousDall: $o). 69.39/9.26 thf(decl_85, type, quantDeMorgan1: $o). 69.39/9.26 thf(decl_86, type, quantDeMorgan2: $o). 69.39/9.26 thf(decl_87, type, quantDeMorgan3: $o). 69.39/9.26 thf(decl_88, type, quantDeMorgan4: $o). 69.39/9.26 thf(decl_89, type, prop2setI: $o). 69.39/9.26 thf(decl_91, type, prop2set2propI: $o). 69.39/9.26 thf(decl_92, type, notdexE: $o). 69.39/9.26 thf(decl_93, type, notdallE: $o). 69.39/9.26 thf(decl_94, type, exuI1: $o). 69.39/9.26 thf(decl_95, type, exuI3: $o). 69.39/9.26 thf(decl_96, type, exuI2: $o). 69.39/9.26 thf(decl_97, type, inCongP: $o). 69.39/9.26 thf(decl_98, type, in__Cong: $o). 69.39/9.26 thf(decl_99, type, exuE3u: $o). 69.39/9.26 thf(decl_100, type, exu__Cong: $o). 69.39/9.26 thf(decl_101, type, emptyset__Cong: $o). 69.39/9.26 thf(decl_102, type, setadjoin__Cong: $o). 69.39/9.26 thf(decl_103, type, powerset__Cong: $o). 69.39/9.26 thf(decl_104, type, setunion__Cong: $o). 69.39/9.26 thf(decl_105, type, omega__Cong: $o). 69.39/9.26 thf(decl_106, type, exuEu: $o). 69.39/9.26 thf(decl_107, type, descr__Cong: $o). 69.39/9.26 thf(decl_108, type, dsetconstr__Cong: $o). 69.39/9.26 thf(decl_109, type, subset: $i > $i > $o). 69.39/9.26 thf(decl_112, type, subsetI1: $o). 69.39/9.26 thf(decl_113, type, eqimpsubset2: $o). 69.39/9.26 thf(decl_114, type, eqimpsubset1: $o). 69.39/9.26 thf(decl_115, type, subsetI2: $o). 69.39/9.26 thf(decl_116, type, emptysetsubset: $o). 69.39/9.26 thf(decl_117, type, subsetE: $o). 69.39/9.26 thf(decl_118, type, subsetE2: $o). 69.39/9.26 thf(decl_119, type, notsubsetI: $o). 69.39/9.26 thf(decl_120, type, notequalI1: $o). 69.39/9.26 thf(decl_121, type, notequalI2: $o). 69.39/9.26 thf(decl_122, type, subsetRefl: $o). 69.39/9.26 thf(decl_123, type, subsetTrans: $o). 69.39/9.26 thf(decl_124, type, setadjoinSub: $o). 69.39/9.26 thf(decl_125, type, setadjoinSub2: $o). 69.39/9.26 thf(decl_126, type, subset2powerset: $o). 69.39/9.26 thf(decl_127, type, setextsub: $o). 69.39/9.26 thf(decl_128, type, subsetemptysetimpeq: $o). 69.39/9.26 thf(decl_129, type, powersetI1: $o). 69.39/9.26 thf(decl_130, type, powersetE1: $o). 69.39/9.26 thf(decl_131, type, inPowerset: $o). 69.39/9.26 thf(decl_132, type, powersetsubset: $o). 69.39/9.26 thf(decl_133, type, sepInPowerset: $o). 69.39/9.26 thf(decl_134, type, sepSubset: $o). 69.39/9.26 thf(decl_135, type, binunion: $i > $i > $i). 69.39/9.26 thf(decl_136, type, binunionIL: $o). 69.39/9.26 thf(decl_137, type, upairset2IR: $o). 69.39/9.26 thf(decl_138, type, binunionIR: $o). 69.39/9.26 thf(decl_139, type, binunionEcases: $o). 69.39/9.26 thf(decl_140, type, binunionE: $o). 69.39/9.26 thf(decl_141, type, binunionLsub: $o). 69.39/9.26 thf(decl_142, type, binunionRsub: $o). 69.39/9.26 thf(decl_143, type, binintersect: $i > $i > $i). 69.39/9.26 thf(decl_144, type, binintersectI: $o). 69.39/9.26 thf(decl_145, type, binintersectSubset5: $o). 69.39/9.26 thf(decl_146, type, binintersectEL: $o). 69.39/9.26 thf(decl_147, type, binintersectLsub: $o). 69.39/9.26 thf(decl_148, type, binintersectSubset2: $o). 69.39/9.26 thf(decl_149, type, binintersectSubset3: $o). 69.39/9.26 thf(decl_150, type, binintersectER: $o). 69.39/9.26 thf(decl_151, type, disjointsetsI1: $o). 69.39/9.26 thf(decl_152, type, binintersectRsub: $o). 69.39/9.26 thf(decl_153, type, binintersectSubset4: $o). 69.39/9.26 thf(decl_154, type, binintersectSubset1: $o). 69.39/9.26 thf(decl_155, type, bs114d: $o). 69.39/9.26 thf(decl_157, type, setminus: $i > $i > $i). 69.39/9.26 thf(decl_158, type, setminusI: $o). 69.39/9.26 thf(decl_159, type, setminusEL: $o). 69.39/9.26 thf(decl_160, type, setminusER: $o). 69.39/9.26 thf(decl_161, type, setminusSubset2: $o). 69.39/9.26 thf(decl_162, type, setminusERneg: $o). 69.39/9.26 thf(decl_163, type, setminusELneg: $o). 69.39/9.26 thf(decl_164, type, setminusILneg: $o). 69.39/9.26 thf(decl_165, type, setminusIRneg: $o). 69.39/9.26 thf(decl_166, type, setminusLsub: $o). 69.39/9.26 thf(decl_167, type, setminusSubset1: $o). 69.39/9.26 thf(decl_168, type, symdiff: $i > $i > $i). 69.39/9.26 thf(decl_169, type, symdiffE: $o). 69.39/9.26 thf(decl_170, type, symdiffI1: $o). 69.39/9.26 thf(decl_171, type, symdiffI2: $o). 69.39/9.26 thf(decl_172, type, symdiffIneg1: $o). 69.39/9.26 thf(decl_173, type, symdiffIneg2: $o). 69.39/9.26 thf(decl_174, type, iskpair: $i > $o). 69.39/9.26 thf(decl_175, type, secondinupair: $o). 69.39/9.26 thf(decl_176, type, setukpairIL: $o). 69.39/9.26 thf(decl_177, type, setukpairIR: $o). 69.39/9.26 thf(decl_178, type, kpairiskpair: $o). 69.39/9.26 thf(decl_179, type, kpair: $i > $i > $i). 69.39/9.26 thf(decl_180, type, kpairp: $o). 69.39/9.26 thf(decl_181, type, cartprod: $i > $i > $i). 69.39/9.26 thf(decl_182, type, singletonsubset: $o). 69.39/9.26 thf(decl_183, type, singletoninpowerset: $o). 69.39/9.26 thf(decl_184, type, singletoninpowunion: $o). 69.39/9.26 thf(decl_185, type, upairset2E: $o). 69.39/9.26 thf(decl_186, type, upairsubunion: $o). 69.39/9.26 thf(decl_187, type, upairinpowunion: $o). 69.39/9.26 thf(decl_188, type, ubforcartprodlem1: $o). 69.39/9.26 thf(decl_189, type, ubforcartprodlem2: $o). 69.39/9.26 thf(decl_190, type, ubforcartprodlem3: $o). 69.39/9.26 thf(decl_191, type, epred1_0: $o). 69.39/9.26 thf(decl_192, type, esk1_2: $i > $i > $i). 69.39/9.26 thf(decl_193, type, esk2_2: $i > $i > $i). 69.39/9.26 thf(decl_194, type, esk3_2: $i > $i > $i). 69.39/9.26 thf(decl_195, type, esk4_1: $i > $i). 69.39/9.26 thf(decl_196, type, esk5_2: ($i > $i > $o) > $i > $i). 69.39/9.26 thf(decl_197, type, esk6_2: ($i > $i > $o) > $i > $i). 69.39/9.26 thf(decl_198, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 69.39/9.26 thf(decl_199, type, esk8_1: $i > $i). 69.39/9.26 thf(decl_200, type, esk9_1: ($i > $o) > $i). 69.39/9.26 thf(decl_201, type, esk10_1: ($i > $o) > $i). 69.39/9.26 thf(decl_202, type, esk11_2: $i > $i > $i). 69.39/9.26 thf(decl_203, type, esk12_2: $i > $i > $i). 69.39/9.26 thf(decl_204, type, esk13_1: $i > $i). 69.39/9.26 thf(decl_205, type, esk14_1: $i > $i). 69.39/9.26 thf(decl_206, type, esk15_1: $i > $i). 69.39/9.26 thf(decl_207, type, esk16_2: $i > $i > $i). 69.39/9.26 thf(decl_208, type, esk17_3: $i > $i > $o > $i). 69.39/9.26 thf(decl_209, type, esk18_1: ($i > $o) > $i). 69.39/9.26 thf(decl_210, type, esk19_1: $i > $i). 69.39/9.26 thf(decl_211, type, esk20_2: $i > ($i > $o) > $i). 69.39/9.26 thf(decl_212, type, esk21_2: $i > ($i > $o) > $i). 69.39/9.26 thf(decl_213, type, esk22_2: $i > ($i > $o) > $i). 69.39/9.26 thf(decl_214, type, esk23_2: $i > ($i > $o) > $i). 69.39/9.26 thf(decl_215, type, esk24_2: $i > ($i > $o) > $i). 69.39/9.26 thf(decl_216, type, esk25_2: $i > ($i > $o) > $i). 69.39/9.26 thf(decl_217, type, esk26_2: ($i > $o) > $i > $i). 69.39/9.26 thf(decl_218, type, esk27_1: ($i > $o) > $i). 69.39/9.26 thf(decl_219, type, esk28_1: ($i > $o) > $i). 69.39/9.26 thf(decl_220, type, esk29_2: ($i > $o) > $i > $i). 69.39/9.26 thf(decl_221, type, esk30_2: ($i > $o) > ($i > $o) > $i). 69.39/9.26 thf(decl_222, type, esk31_2: ($i > $o) > ($i > $o) > $i). 69.39/9.26 thf(decl_223, type, esk32_2: ($i > $o) > ($i > $o) > $i). 69.39/9.26 thf(decl_224, type, esk33_2: ($i > $o) > ($i > $o) > $i). 69.39/9.26 thf(decl_225, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 69.39/9.26 thf(decl_226, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 69.39/9.26 thf(decl_227, type, esk36_2: $i > $i > $i). 69.39/9.26 thf(decl_228, type, esk37_2: $i > $i > $i). 69.39/9.26 thf(decl_229, type, esk38_2: $i > $i > $i). 69.39/9.26 thf(decl_230, type, esk39_0: $i). 69.39/9.26 thf(decl_231, type, esk40_0: $i). 69.39/9.26 thf(decl_232, type, esk41_0: $i). 69.39/9.26 thf(decl_233, type, esk42_0: $i). 69.39/9.26 thf(decl_240, type, epred3_2: $i > $i > $i > $o). 69.39/9.26 thf(decl_241, type, esk48_3: $i > $i > $i > $i). 69.39/9.26 thf(decl_242, type, esk49_3: $i > $i > $i > $i). 69.39/9.26 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', dsetconstrI)). 69.39/9.26 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.PmrisFvij7/Vampire---4.8_26390', emptyE1)). 69.39/9.26 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.PmrisFvij7/Vampire---4.8_26390', exuE2)). 69.39/9.26 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setoftrueEq)). 69.39/9.26 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', nonemptyI)). 69.39/9.26 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', exuE1)). 69.39/9.26 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', dsetconstrER)). 69.39/9.26 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', replAx)). 69.39/9.26 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', sepInPowerset)). 69.39/9.26 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', sepSubset)). 69.39/9.26 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', descr__Cong)). 69.39/9.26 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', exuEu)). 69.39/9.26 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', exu__Cong)). 69.39/9.26 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', exuE3u)). 69.39/9.26 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', exuI3)). 69.39/9.26 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', exuI1)). 69.39/9.26 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', dsetconstr__Cong)). 69.39/9.26 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', exuI2)). 69.39/9.26 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setbeta)). 69.39/9.26 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', exuE3e)). 69.39/9.26 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', dsetconstrEL)). 69.39/9.26 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', descrp)). 69.39/9.26 thf(cartprodpairin, conjecture, ((setextAx)=>(((setadjoinAx)=>(((setunionAx)=>(((omegaSAx)=>((omegaIndAx)=>(((foundationAx)=>(((descrp)=>(((dsetconstrEL)=>((((prop2setE)=>((((notinemptyset)=>((exuE3e)=>(((emptyI)=>((noeltsimpempty)=>((setbeta)=>((((nonemptyI1)=>((setadjoinIL)=>((((((((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>(((setunionE)=>(((((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>(((upairsetIR)=>(((((((quantDeMorgan4)=>(((prop2set2propI)=>((((((exuI2)=>((((((((powerset__Cong)=>((((((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>((notequalI1)=>(((((setadjoinSub)=>((setadjoinSub2)=>((((subsetemptysetimpeq)=>((powersetI1)=>(((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>(((binunionIL)=>((upairset2IR)=>(((binunionEcases)=>((((binunionRsub)=>((binintersectI)=>(((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>(((binintersectRsub)=>(((((setminusI)=>(((setminusER)=>(((setminusERneg)=>(((setminusILneg)=>((((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((((symdiffIneg2)=>((secondinupair)=>((((kpairiskpair)=>((((singletoninpowerset)=>((singletoninpowunion)=>(((((ubforcartprodlem1)=>((![X4:$i, X5:$i, X2:$i]:((![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))<=(in @ X2 @ X4)))<=(ubforcartprodlem3))<=(ubforcartprodlem2)))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E))))<=(singletonsubset))<=(kpairp)))<=(setukpairIR))<=(setukpairIL))))<=(symdiffIneg1))<=(symdiffI2)))))<=(setminusLsub))<=(setminusIRneg)))<=(setminusELneg)))<=(setminusSubset2)))<=(setminusEL)))<=(bs114d))<=(binintersectSubset1))<=(binintersectSubset4)))<=(disjointsetsI1)))))<=(binintersectLsub)))<=(binintersectSubset5))))<=(binunionLsub))<=(binunionE)))<=(binunionIR))))<=(sepSubset)))))<=(powersetE1))))<=(setextsub))<=(subset2powerset))))<=(subsetTrans))<=(subsetRefl))<=(notequalI2)))))<=(subsetE))))))))<=(descr__Cong))<=(exuEu))<=(omega__Cong))<=(setunion__Cong)))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong))<=(exuE3u))<=(in__Cong))<=(inCongP)))<=(exuI3))<=(exuI1))<=(notdallE))<=(notdexE)))<=(prop2setI)))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall))<=(emptyE1)))<=(upairsetIL)))))))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU)))<=(setunionI)))))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty))))<=(nonemptyI))<=(nonemptyE1)))))<=(setext))))<=(emptysetimpfalse))<=(emptysetE)))<=(exuE1))<=(dsetconstrER)))<=(dsetconstrI)))<=(wellorderingAx)))<=(replAx))))<=(omega0Ax)))<=(powersetAx)))<=(emptysetAx))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', cartprodpairin)). 69.39/9.26 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', eqimpsubset2)). 69.39/9.26 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', emptysetAx)). 69.39/9.26 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', quantDeMorgan1)). 69.39/9.26 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', vacuousDall)). 69.39/9.26 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', subsetE2)). 69.39/9.26 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', upairsetIL)). 69.39/9.26 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', nonemptyImpWitness)). 69.39/9.26 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', notsubsetI)). 69.39/9.26 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', subPowSU)). 69.39/9.26 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', notequalI1)). 69.39/9.26 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setunionI)). 69.39/9.26 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', powersetI)). 69.39/9.26 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setadjoinSub)). 69.39/9.26 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setadjoinOr)). 69.39/9.26 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.PmrisFvij7/Vampire---4.8_26390', setadjoinE)). 69.39/9.26 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setadjoinSub2)). 69.39/9.26 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setadjoinIR)). 69.39/9.26 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', emptyinunitempty)). 69.39/9.26 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', subsetI1)). 69.39/9.26 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', nonemptyE1)). 69.39/9.26 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', subsetemptysetimpeq)). 69.39/9.26 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.PmrisFvij7/Vampire---4.8_26390', setext)). 69.39/9.26 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', emptysetimpfalse)). 69.39/9.26 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', powersetI1)). 69.39/9.26 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', emptysetE)). 69.39/9.26 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', wellorderingAx)). 69.39/9.26 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', inPowerset)). 69.39/9.26 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', omega0Ax)). 69.39/9.26 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', powersetsubset)). 69.39/9.26 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', powersetAx)). 69.39/9.26 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binunionIL)). 69.39/9.26 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', upairset2IR)). 69.39/9.26 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.PmrisFvij7/Vampire---4.8_26390', binunionEcases)). 69.39/9.26 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binunionRsub)). 69.39/9.26 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binintersectI)). 69.39/9.26 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binintersectEL)). 69.39/9.26 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', eqimpsubset1)). 69.39/9.26 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binintersectSubset2)). 69.39/9.26 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binintersectSubset3)). 69.39/9.26 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binintersectER)). 69.39/9.26 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binintersectRsub)). 69.39/9.26 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setminusI)). 69.39/9.26 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setminusER)). 69.39/9.26 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setminusERneg)). 69.39/9.26 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binintersectSubset5)). 69.39/9.26 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binunionLsub)). 69.39/9.26 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binunionE)). 69.39/9.26 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binunionIR)). 69.39/9.26 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setminusILneg)). 69.39/9.26 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setminusSubset1)). 69.39/9.26 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.PmrisFvij7/Vampire---4.8_26390', symdiffE)). 69.39/9.26 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', symdiffI1)). 69.39/9.26 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', symdiffIneg2)). 69.39/9.26 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', secondinupair)). 69.39/9.26 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.PmrisFvij7/Vampire---4.8_26390', kpairiskpair)). 69.39/9.26 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', singletoninpowerset)). 69.39/9.26 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', singletoninpowunion)). 69.39/9.26 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', ubforcartprodlem1)). 69.39/9.26 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', subsetI2)). 69.39/9.26 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.PmrisFvij7/Vampire---4.8_26390', ubforcartprodlem3)). 69.39/9.26 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.PmrisFvij7/Vampire---4.8_26390', ubforcartprodlem2)). 69.39/9.26 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.PmrisFvij7/Vampire---4.8_26390', upairinpowunion)). 69.39/9.26 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.PmrisFvij7/Vampire---4.8_26390', upairsubunion)). 69.39/9.26 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', upairset2E)). 69.39/9.26 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', singletonsubset)). 69.39/9.26 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', kpairp)). 69.39/9.26 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setukpairIR)). 69.39/9.26 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', emptysetsubset)). 69.39/9.26 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.PmrisFvij7/Vampire---4.8_26390', setukpairIL)). 69.39/9.26 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', symdiffIneg1)). 69.39/9.26 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', symdiffI2)). 69.39/9.26 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setminusLsub)). 69.39/9.26 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setminusIRneg)). 69.39/9.26 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setminusELneg)). 69.39/9.26 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setminusSubset2)). 69.39/9.26 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setminusEL)). 69.39/9.26 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', bs114d)). 69.39/9.26 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binintersectSubset1)). 69.39/9.26 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binintersectSubset4)). 69.39/9.26 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', disjointsetsI1)). 69.39/9.26 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', binintersectLsub)). 69.39/9.26 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', powersetE1)). 69.39/9.26 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setextsub)). 69.39/9.26 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', subset2powerset)). 69.39/9.26 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', subsetTrans)). 69.39/9.26 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', subsetRefl)). 69.39/9.26 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', notequalI2)). 69.39/9.26 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', subsetE)). 69.39/9.26 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', omega__Cong)). 69.39/9.26 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setunion__Cong)). 69.39/9.26 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setadjoin__Cong)). 69.39/9.26 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', emptyset__Cong)). 69.39/9.26 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', in__Cong)). 69.39/9.26 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', inCongP)). 69.39/9.26 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', notdallE)). 69.39/9.26 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', notdexE)). 69.39/9.26 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', prop2setI)). 69.39/9.26 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', quantDeMorgan3)). 69.39/9.26 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', quantDeMorgan2)). 69.39/9.26 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', powerset__Cong)). 69.39/9.26 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', quantDeMorgan4)). 69.39/9.26 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', upairsetIR)). 69.39/9.26 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', upairsetE)). 69.39/9.26 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', singletonsswitch)). 69.39/9.26 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', eqinunit)). 69.39/9.26 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', notinsingleton)). 69.39/9.26 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', uniqinunit)). 69.39/9.26 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.PmrisFvij7/Vampire---4.8_26390', setunionE)). 69.39/9.26 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', powersetE)). 69.39/9.26 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', emptyInPowerset)). 69.39/9.26 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', emptyinPowerset)). 69.39/9.26 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setadjoinIL)). 69.39/9.26 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', nonemptyI1)). 69.39/9.26 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', noeltsimpempty)). 69.39/9.26 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', emptyI)). 69.39/9.26 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', notinemptyset)). 69.39/9.26 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', prop2setE)). 69.39/9.26 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.PmrisFvij7/Vampire---4.8_26390', foundationAx)). 69.39/9.26 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', omegaIndAx)). 69.39/9.26 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', omegaSAx)). 69.39/9.26 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setunionAx)). 69.39/9.26 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setadjoinAx)). 69.39/9.26 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.PmrisFvij7/Vampire---4.8_26390', setextAx)). 69.39/9.26 thf(cartprod, axiom, ((cartprod)=(^[X4:$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.PmrisFvij7/Vampire---4.8_26390', cartprod)). 69.39/9.26 thf(c_0_147, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 69.39/9.26 thf(c_0_148, plain, ((emptyE1)<=>![X4:$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])). 69.39/9.26 thf(c_0_149, 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])). 69.39/9.26 thf(c_0_150, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 69.39/9.26 thf(c_0_151, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 69.39/9.26 thf(c_0_152, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 69.39/9.26 thf(c_0_153, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 69.39/9.26 thf(c_0_154, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 69.39/9.26 thf(c_0_155, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 69.39/9.26 thf(c_0_156, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 69.39/9.26 thf(c_0_157, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 69.39/9.26 thf(c_0_158, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 69.39/9.26 thf(c_0_159, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 69.39/9.26 thf(c_0_160, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 69.39/9.26 thf(c_0_161, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 69.39/9.26 thf(c_0_162, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 69.39/9.26 thf(c_0_163, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 69.39/9.26 thf(c_0_164, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 69.39/9.26 thf(c_0_165, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 69.39/9.26 thf(c_0_166, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 69.39/9.26 thf(c_0_167, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 69.39/9.26 thf(c_0_168, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 69.39/9.26 thf(c_0_169, plain, ((epred1_0)<=>![X782:$i]:(?[X783:$i]:((((![X784:$i]:(((in @ X784 @ X783)=>![X785:$i]:(((in @ X785 @ X784)=>(in @ X785 @ X782)))))&![X786:$i, X787:$i]:((((in @ X786 @ X782)&(in @ X787 @ X782))=>(![X788:$i]:(((in @ X788 @ X783)=>((in @ X786 @ X788)<=>(in @ X787 @ X788))))=>((X786)=(X787))))))&![X789:$i, X790:$i]:((((in @ X789 @ X783)&(in @ X790 @ X783))=>(![X791:$i]:(((in @ X791 @ X789)=>(in @ X791 @ X790)))|![X792:$i]:(((in @ X792 @ X790)=>(in @ X792 @ X789)))))))&![X793:$i]:(((![X794:$i]:(((in @ X794 @ X793)=>(in @ X794 @ X782)))&?[X795:$i]:((in @ X795 @ X793)))=>?[X796:$i, X797:$i]:(((((in @ X796 @ X783)&(in @ X797 @ X793))&~(?[X798:$i]:(((in @ X798 @ X796)&(in @ X798 @ X793)))))&![X799:$i]:(((in @ X799 @ X783)=>(![X800:$i]:(((in @ X800 @ X799)=>(in @ X800 @ X796)))|(in @ X797 @ X799)))))))))))), introduced(definition)). 69.39/9.26 thf(c_0_170, negated_conjecture, ~((![X418:$i, X419:$i]:((![X420:$i]:(((in @ X420 @ X418)<=>(in @ X420 @ X419)))=>((X418)=(X419))))=>(![X810:$i]:(~(in @ X810 @ emptyset))=>(![X421:$i, X422:$i, X423:$i]:(((in @ X423 @ (setadjoin @ X421 @ X422))<=>(((X423)=(X421))|(in @ X423 @ X422))))=>(![X807:$i, X808:$i]:(((in @ X808 @ (powerset @ X807))<=>![X809:$i]:(((in @ X809 @ X808)=>(in @ X809 @ X807)))))=>(![X424:$i, X425:$i]:(((in @ X425 @ (setunion @ X424))<=>?[X426:$i]:(((in @ X425 @ X426)&(in @ X426 @ X424)))))=>((in @ emptyset @ omega)=>(![X427:$i]:(((in @ X427 @ omega)=>(in @ (setadjoin @ X427 @ X427) @ omega)))=>(![X428:$i]:((((in @ emptyset @ X428)&![X429:$i]:((((in @ X429 @ omega)&(in @ X429 @ X428))=>(in @ (setadjoin @ X429 @ X429) @ X428))))=>![X430:$i]:(((in @ X430 @ omega)=>(in @ X430 @ X428)))))=>(![X801:$i > $i > $o, X802:$i]:((![X803:$i]:(((in @ X803 @ X802)=>(exu @ (^[Z0/* 3 */:$i]:((X801 @ X803 @ Z0))))))=>?[X804:$i]:(![X805:$i]:(((in @ X805 @ X804)<=>?[X806:$i]:(((in @ X806 @ X802)&(X801 @ X806 @ X805))))))))=>(![X431:$i]:((?[X432:$i]:((in @ X432 @ X431))=>?[X433:$i]:(((in @ X433 @ X431)&~(?[X434:$i]:(((in @ X434 @ X433)&(in @ X434 @ X431))))))))=>((epred1_0)=>(![X435:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X435 @ Z0))))=>(X435 @ (descr @ (^[Z0/* 3 */:$i]:((X435 @ Z0)))))))=>(![X779:$i, X780:$i > $o, X781:$i]:(((in @ X781 @ X779)=>((X780 @ X781)=>(in @ X781 @ (dsetconstr @ X779 @ (^[Z0/* 3 */:$i]:((X780 @ Z0))))))))=>(![X436:$i, X437:$i > $o, X438:$i]:(((in @ X438 @ (dsetconstr @ X436 @ (^[Z0/* 3 */:$i]:((X437 @ Z0)))))=>(in @ X438 @ X436)))=>(![X776:$i, X777:$i > $o, X778:$i]:(((in @ X778 @ (dsetconstr @ X776 @ (^[Z0/* 3 */:$i]:((X777 @ Z0)))))=>(X777 @ X778)))=>(![X773:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X773 @ Z0))))=>?[X774:$i]:(((X773 @ X774)&![X775:$i]:(((X773 @ X775)=>((X774)=(X775))))))))=>(![X439:$o, X440:$i]:(((in @ X440 @ (prop2set @ ((X439))))=>(X439)))=>(![X771:$i]:(((in @ X771 @ emptyset)=>![X772:$o]:((X772))))=>(![X770:$i]:(~(in @ X770 @ emptyset))=>(![X441:$i]:(~(in @ X441 @ emptyset))=>(![X442:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X442 @ Z0))))=>?[X443:$i]:((X442 @ X443))))=>(![X766:$i, X767:$i]:((![X768:$i]:(((in @ X768 @ X766)=>(in @ X768 @ X767)))=>(![X769:$i]:(((in @ X769 @ X767)=>(in @ X769 @ X766)))=>((X766)=(X767)))))=>(![X444:$i]:((![X445:$i]:(~(in @ X445 @ X444))=>((X444)=(emptyset))))=>(![X446:$i]:((![X447:$i]:(~(in @ X447 @ X446))=>((X446)=(emptyset))))=>(![X448:$i, X449:$i > $o, X450:$i]:(((in @ X450 @ X448)=>((in @ X450 @ (dsetconstr @ X448 @ (^[Z0/* 3 */:$i]:((X449 @ Z0)))))<=>(X449 @ X450))))=>(![X764:$i]:(((nonempty @ X764)=>?[X765:$i]:((in @ X765 @ X764))))=>(![X761:$i, X762:$i > $o, X763:$i]:(((in @ X763 @ X761)=>((X762 @ X763)=>(nonempty @ (dsetconstr @ X761 @ (^[Z0/* 3 */:$i]:((X762 @ Z0))))))))=>(![X451:$i]:((?[X452:$i]:((in @ X452 @ X451))=>(nonempty @ X451)))=>(![X453:$i, X454:$i]:((in @ X453 @ (setadjoin @ X453 @ X454)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X758:$i, X759:$i, X760:$i]:(((in @ X760 @ X759)=>(in @ X760 @ (setadjoin @ X758 @ X759))))=>(![X754:$i, X755:$i, X756:$i]:(((in @ X756 @ (setadjoin @ X754 @ X755))=>![X757:$o]:(((((X756)=(X754))=>(X757))=>(((in @ X756 @ X755)=>(X757))=>(X757))))))=>(![X751:$i, X752:$i, X753:$i]:(((in @ X753 @ (setadjoin @ X751 @ X752))=>(((X753)=(X751))|(in @ X753 @ X752))))=>(![X750:$i]:(((dsetconstr @ X750 @ (^[Z0/* 3 */:$i]:(($true))))=(X750)))=>(![X747:$i, X748:$i]:((![X749:$i]:(((in @ X749 @ X748)=>(in @ X749 @ X747)))=>(in @ X748 @ (powerset @ X747))))=>(![X455:$i]:((in @ emptyset @ (powerset @ X455)))=>(![X456:$i]:((in @ emptyset @ (powerset @ X456)))=>(![X457:$i, X458:$i, X459:$i]:(((in @ X458 @ (powerset @ X457))=>((in @ X459 @ X458)=>(in @ X459 @ X457))))=>(![X744:$i, X745:$i, X746:$i]:(((in @ X745 @ X746)=>((in @ X746 @ X744)=>(in @ X745 @ (setunion @ X744)))))=>(![X460:$i, X461:$i]:(((in @ X461 @ (setunion @ X460))=>![X462:$o]:((![X463:$i]:(((in @ X461 @ X463)=>((in @ X463 @ X460)=>(X462))))=>(X462)))))=>(![X742:$i, X743:$i]:(((in @ X743 @ X742)=>(in @ X743 @ (powerset @ (setunion @ X742)))))=>(![X739:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X739 @ Z0))))=>?[X740:$i]:(![X741:$i]:(((X739 @ X741)<=>((X741)=(X740)))))))=>(![X737:$i]:(((nonempty @ X737)=>?[X738:$i]:((in @ X738 @ X737))))=>(![X464:$i, X465:$i]:(((in @ X464 @ (setadjoin @ X465 @ emptyset))=>((X464)=(X465))))=>(![X466:$i, X467:$i]:((((X466)!=(X467))=>~(in @ X467 @ (setadjoin @ X466 @ emptyset))))=>(![X468:$i, X469:$i]:((((X468)=(X469))=>(in @ X468 @ (setadjoin @ X469 @ emptyset))))=>(![X470:$i, X471:$i]:(((in @ X470 @ (setadjoin @ X471 @ emptyset))=>(in @ X471 @ (setadjoin @ X470 @ emptyset))))=>(![X472:$i, X473:$i, X474:$i]:(((in @ X474 @ (setadjoin @ X472 @ (setadjoin @ X473 @ emptyset)))=>(((X474)=(X472))|((X474)=(X473)))))=>(![X735:$i, X736:$i]:((in @ X735 @ (setadjoin @ X735 @ (setadjoin @ X736 @ emptyset))))=>(![X475:$i, X476:$i]:((in @ X476 @ (setadjoin @ X475 @ (setadjoin @ X476 @ emptyset))))=>(![X732:$i, X733:$i > $o]:((?[X734:$i]:(((in @ X734 @ X732)&(X733 @ X734)))=>((dsetconstr @ X732 @ (^[Z0/* 3 */:$i]:((X733 @ Z0))))!=(emptyset))))=>(![X730:$i > $o, X731:$i]:(((in @ X731 @ emptyset)=>(X730 @ X731)))=>(![X726:$i, X727:$i > $o]:((~(![X728:$i]:(((in @ X728 @ X726)=>(X727 @ X728))))=>?[X729:$i]:(((in @ X729 @ X726)&~(X727 @ X729)))))=>(![X722:$i, X723:$i > $o]:((![X724:$i]:(((in @ X724 @ X722)=>~(X723 @ X724)))=>~(?[X725:$i]:(((in @ X725 @ X722)&(X723 @ X725))))))=>(![X718:$i, X719:$i > $o]:((~(?[X720:$i]:(((in @ X720 @ X718)&(X719 @ X720))))=>![X721:$i]:(((in @ X721 @ X718)=>~(X719 @ X721)))))=>(![X477:$i, X478:$i > $o]:((?[X479:$i]:(((in @ X479 @ X477)&~(X478 @ X479)))=>~(![X480:$i]:(((in @ X480 @ X477)=>(X478 @ X480))))))=>(![X717:$o]:(((X717)=>(in @ emptyset @ (prop2set @ ((X717))))))=>((prop2set2propI)=>(![X713:$i, X714:$i > $o]:((~(?[X715:$i]:(((in @ X715 @ X713)&(X714 @ X715))))=>![X716:$i]:(((in @ X716 @ X713)=>~(X714 @ X716)))))=>(![X709:$i, X710:$i > $o]:((~(![X711:$i]:(((in @ X711 @ X709)=>(X710 @ X711))))=>?[X712:$i]:(((in @ X712 @ X709)&~(X710 @ X712)))))=>(![X706:$i > $o]:((?[X707:$i]:(((X706 @ X707)&![X708:$i]:(((X706 @ X708)=>((X707)=(X708))))))=>(exu @ (^[Z0/* 3 */:$i]:((X706 @ Z0))))))=>(![X702:$i > $o]:((?[X703:$i]:((X702 @ X703))=>(![X704:$i, X705:$i]:(((X702 @ X704)=>((X702 @ X705)=>((X704)=(X705)))))=>(exu @ (^[Z0/* 3 */:$i]:((X702 @ Z0)))))))=>(![X481:$i > $o]:((?[X482:$i]:(![X483:$i]:(((X481 @ X483)<=>((X483)=(X482)))))=>(exu @ (^[Z0/* 3 */:$i]:((X481 @ Z0))))))=>(![X698:$i, X699:$i]:((((X698)=(X699))=>![X700:$i, X701:$i]:((((X700)=(X701))=>((in @ X700 @ X698)=>(in @ X701 @ X699))))))=>(![X694:$i, X695:$i]:((((X694)=(X695))=>![X696:$i, X697:$i]:((((X696)=(X697))=>((in @ X696 @ X694)<=>(in @ X697 @ X695))))))=>(![X691:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X691 @ Z0))))=>![X692:$i, X693:$i]:(((X691 @ X692)=>((X691 @ X693)=>((X692)=(X693)))))))=>(![X687:$i > $o, X688:$i > $o]:((![X689:$i, X690:$i]:((((X689)=(X690))=>((X687 @ X689)<=>(X688 @ X690))))=>((exu @ (^[Z0/* 3 */:$i]:((X687 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X688 @ Z0)))))))=>(((emptyset)=(emptyset))=>(![X683:$i, X684:$i]:((((X683)=(X684))=>![X685:$i, X686:$i]:((((X685)=(X686))=>((setadjoin @ X683 @ X685)=(setadjoin @ X684 @ X686))))))=>(![X484:$i, X485:$i]:((((X484)=(X485))=>((powerset @ X484)=(powerset @ X485))))=>(![X681:$i, X682:$i]:((((X681)=(X682))=>((setunion @ X681)=(setunion @ X682))))=>(((omega)=(omega))=>(![X678:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X678 @ Z0))))=>![X679:$i, X680:$i]:(((X678 @ X679)=>((X678 @ X680)=>((X679)=(X680)))))))=>(![X674:$i > $o, X675:$i > $o]:((![X676:$i, X677:$i]:((((X676)=(X677))=>((X674 @ X676)<=>(X675 @ X677))))=>((exu @ (^[Z0/* 3 */:$i]:((X674 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X675 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X674 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X675 @ Z0)))))))))=>(![X486:$i, X487:$i]:((((X486)=(X487))=>![X488:$i > $o, X489:$i > $o]:((![X490:$i]:(((in @ X490 @ X486)=>![X491:$i]:(((in @ X491 @ X487)=>(((X490)=(X491))=>((X488 @ X490)<=>(X489 @ X491)))))))=>((dsetconstr @ X486 @ (^[Z0/* 3 */:$i]:((X488 @ Z0))))=(dsetconstr @ X487 @ (^[Z0/* 3 */:$i]:((X489 @ Z0)))))))))=>(![X492:$i, X493:$i]:((![X494:$i]:(((in @ X494 @ X492)=>(in @ X494 @ X493)))=>(subset @ X492 @ X493)))=>(![X495:$i, X496:$i]:((((X495)=(X496))=>(subset @ X496 @ X495)))=>(![X497:$i, X498:$i]:((((X497)=(X498))=>(subset @ X497 @ X498)))=>(![X499:$i, X500:$i]:((![X501:$i]:(((in @ X501 @ X499)=>(in @ X501 @ X500)))=>(subset @ X499 @ X500)))=>(![X502:$i]:((subset @ emptyset @ X502))=>(![X671:$i, X672:$i, X673:$i]:(((subset @ X671 @ X672)=>((in @ X673 @ X671)=>(in @ X673 @ X672))))=>(![X503:$i, X504:$i, X505:$i]:(((subset @ X503 @ X504)=>(~(in @ X505 @ X504)=>~(in @ X505 @ X503))))=>(![X506:$i, X507:$i, X508:$i]:(((in @ X508 @ X506)=>(~(in @ X508 @ X507)=>~(subset @ X506 @ X507))))=>(![X509:$i, X510:$i]:((~(subset @ X509 @ X510)=>((X509)!=(X510))))=>(![X668:$i, X669:$i, X670:$i]:(((in @ X670 @ X668)=>(~(in @ X670 @ X669)=>((X668)!=(X669)))))=>(![X667:$i]:((subset @ X667 @ X667))=>(![X664:$i, X665:$i, X666:$i]:(((subset @ X664 @ X665)=>((subset @ X665 @ X666)=>(subset @ X664 @ X666))))=>(![X511:$i, X512:$i]:((subset @ X512 @ (setadjoin @ X511 @ X512)))=>(![X513:$i, X514:$i, X515:$i]:(((subset @ X513 @ X515)=>(subset @ X513 @ (setadjoin @ X514 @ X515))))=>(![X662:$i, X663:$i]:(((subset @ X662 @ X663)=>(in @ X662 @ (powerset @ X663))))=>(![X660:$i, X661:$i]:(((subset @ X660 @ X661)=>((subset @ X661 @ X660)=>((X660)=(X661)))))=>(![X516:$i]:(((subset @ X516 @ emptyset)=>((X516)=(emptyset))))=>(![X517:$i, X518:$i]:(((subset @ X518 @ X517)=>(in @ X518 @ (powerset @ X517))))=>(![X658:$i, X659:$i]:(((in @ X659 @ (powerset @ X658))=>(subset @ X659 @ X658)))=>(![X519:$i]:((in @ X519 @ (powerset @ X519)))=>(![X520:$i, X521:$i]:(((subset @ X520 @ X521)=>(subset @ (powerset @ X520) @ (powerset @ X521))))=>(![X522:$i, X523:$i > $o]:((in @ (dsetconstr @ X522 @ (^[Z0/* 3 */:$i]:((X523 @ Z0)))) @ (powerset @ X522)))=>(![X656:$i, X657:$i > $o]:((subset @ (dsetconstr @ X656 @ (^[Z0/* 3 */:$i]:((X657 @ Z0)))) @ X656))=>(![X524:$i, X525:$i, X526:$i]:(((in @ X526 @ X524)=>(in @ X526 @ (binunion @ X524 @ X525))))=>(![X527:$i, X528:$i]:((in @ X528 @ (setadjoin @ X527 @ (setadjoin @ X528 @ emptyset))))=>(![X653:$i, X654:$i, X655:$i]:(((in @ X655 @ X654)=>(in @ X655 @ (binunion @ X653 @ X654))))=>(![X529:$i, X530:$i, X531:$i, X532:$o]:(((in @ X531 @ (binunion @ X529 @ X530))=>(((in @ X531 @ X529)=>(X532))=>(((in @ X531 @ X530)=>(X532))=>(X532)))))=>(![X650:$i, X651:$i, X652:$i]:(((in @ X652 @ (binunion @ X650 @ X651))=>((in @ X652 @ X650)|(in @ X652 @ X651))))=>(![X648:$i, X649:$i]:((subset @ X648 @ (binunion @ X648 @ X649)))=>(![X533:$i, X534:$i]:((subset @ X534 @ (binunion @ X533 @ X534)))=>(![X535:$i, X536:$i, X537:$i]:(((in @ X537 @ X535)=>((in @ X537 @ X536)=>(in @ X537 @ (binintersect @ X535 @ X536)))))=>(![X645:$i, X646:$i, X647:$i]:(((subset @ X647 @ X645)=>((subset @ X647 @ X646)=>(subset @ X647 @ (binintersect @ X645 @ X646)))))=>(![X538:$i, X539:$i, X540:$i]:(((in @ X540 @ (binintersect @ X538 @ X539))=>(in @ X540 @ X538)))=>(![X643:$i, X644:$i]:((subset @ (binintersect @ X643 @ X644) @ X643))=>(![X541:$i, X542:$i]:(((subset @ X541 @ X542)=>((binintersect @ X541 @ X542)=(X541))))=>(![X543:$i, X544:$i]:((((binintersect @ X543 @ X544)=(X544))=>(subset @ X544 @ X543)))=>(![X545:$i, X546:$i, X547:$i]:(((in @ X547 @ (binintersect @ X545 @ X546))=>(in @ X547 @ X546)))=>(![X640:$i, X641:$i]:((~(?[X642:$i]:(((in @ X642 @ X640)&(in @ X642 @ X641))))=>((binintersect @ X640 @ X641)=(emptyset))))=>(![X548:$i, X549:$i]:((subset @ (binintersect @ X548 @ X549) @ X549))=>(![X638:$i, X639:$i]:(((subset @ X639 @ X638)=>((binintersect @ X638 @ X639)=(X639))))=>(![X636:$i, X637:$i]:((((binintersect @ X636 @ X637)=(X636))=>(subset @ X636 @ X637)))=>(![X633:$i, X634:$i, X635:$i]:(((binintersect @ X633 @ (binunion @ X634 @ X635))=(binunion @ (binintersect @ X633 @ X634) @ (binintersect @ X633 @ X635))))=>(![X550:$i, X551:$i, X552:$i]:(((in @ X552 @ X550)=>(~(in @ X552 @ X551)=>(in @ X552 @ (setminus @ X550 @ X551)))))=>(![X630:$i, X631:$i, X632:$i]:(((in @ X632 @ (setminus @ X630 @ X631))=>(in @ X632 @ X630)))=>(![X553:$i, X554:$i, X555:$i]:(((in @ X555 @ (setminus @ X553 @ X554))=>~(in @ X555 @ X554)))=>(![X628:$i, X629:$i]:(((subset @ X628 @ X629)=>((setminus @ X628 @ X629)=(emptyset))))=>(![X556:$i, X557:$i, X558:$i]:((~(in @ X558 @ (setminus @ X556 @ X557))=>((in @ X558 @ X556)=>(in @ X558 @ X557))))=>(![X625:$i, X626:$i, X627:$i]:((~(in @ X627 @ (setminus @ X625 @ X626))=>(~(in @ X627 @ X626)=>~(in @ X627 @ X625))))=>(![X559:$i, X560:$i, X561:$i]:((~(in @ X561 @ X559)=>~(in @ X561 @ (setminus @ X559 @ X560))))=>(![X622:$i, X623:$i, X624:$i]:(((in @ X624 @ X623)=>~(in @ X624 @ (setminus @ X622 @ X623))))=>(![X620:$i, X621:$i]:((subset @ (setminus @ X620 @ X621) @ X620))=>(![X562:$i, X563:$i]:((((setminus @ X562 @ X563)=(emptyset))=>(subset @ X562 @ X563)))=>(![X564:$i, X565:$i, X566:$i]:(((in @ X566 @ (symdiff @ X564 @ X565))=>![X567:$o]:((((in @ X566 @ X564)=>(~(in @ X566 @ X565)=>(X567)))=>((~(in @ X566 @ X564)=>((in @ X566 @ X565)=>(X567)))=>(X567))))))=>(![X568:$i, X569:$i, X570:$i]:(((in @ X570 @ X568)=>(~(in @ X570 @ X569)=>(in @ X570 @ (symdiff @ X568 @ X569)))))=>(![X617:$i, X618:$i, X619:$i]:((~(in @ X619 @ X617)=>((in @ X619 @ X618)=>(in @ X619 @ (symdiff @ X617 @ X618)))))=>(![X614:$i, X615:$i, X616:$i]:(((in @ X616 @ X614)=>((in @ X616 @ X615)=>~(in @ X616 @ (symdiff @ X614 @ X615)))))=>(![X571:$i, X572:$i, X573:$i]:((~(in @ X573 @ X571)=>(~(in @ X573 @ X572)=>~(in @ X573 @ (symdiff @ X571 @ X572)))))=>(![X574:$i, X575:$i]:((in @ X575 @ (setadjoin @ X574 @ (setadjoin @ X575 @ emptyset))))=>(![X612:$i, X613:$i]:((in @ X612 @ (setunion @ (setadjoin @ (setadjoin @ X612 @ emptyset) @ (setadjoin @ (setadjoin @ X612 @ 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(setadjoin @ X601 @ (setadjoin @ X602 @ emptyset)) @ (binunion @ X599 @ X600))))))=>(![X595:$i, X596:$i, X597:$i]:(((in @ X597 @ X595)=>![X598:$i]:(((in @ X598 @ X596)=>(in @ (setadjoin @ X597 @ (setadjoin @ X598 @ emptyset)) @ (powerset @ (binunion @ X595 @ X596)))))))=>(![X583:$i, X584:$i, X585:$i]:(((in @ X585 @ X583)=>![X586:$i]:(((in @ X586 @ X584)=>(subset @ (setadjoin @ (setadjoin @ X585 @ emptyset) @ (setadjoin @ (setadjoin @ X585 @ (setadjoin @ X586 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X583 @ X584)))))))=>(![X591:$i, X592:$i, X593:$i]:(((in @ X593 @ X591)=>![X594:$i]:(((in @ X594 @ X592)=>(in @ (setadjoin @ (setadjoin @ X593 @ emptyset) @ (setadjoin @ (setadjoin @ X593 @ (setadjoin @ X594 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X591 @ X592))))))))=>(![X587:$i, X588:$i, X589:$i]:(((in @ X589 @ X587)=>![X590:$i]:(((in @ X590 @ X588)=>(in @ (kpair @ X589 @ X590) @ (powerset @ (powerset @ (binunion @ X587 @ X588))))))))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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(assume_negation,[status(cth)],[cartprodpairin]), eqimpsubset2]), c_0_147]), emptysetAx]), quantDeMorgan1]), vacuousDall]), subsetE2]), c_0_148]), upairsetIL]), nonemptyImpWitness]), notsubsetI]), c_0_149]), subPowSU]), notequalI1]), setunionI]), powersetI]), c_0_150]), setadjoinSub]), setadjoinOr]), setadjoinE]), setadjoinSub2]), setadjoinIR]), emptyinunitempty]), c_0_151]), subsetI1]), nonemptyE1]), subsetemptysetimpeq]), setext]), emptysetimpfalse]), powersetI1]), emptysetE]), c_0_152]), c_0_153]), wellorderingAx]), inPowerset]), c_0_154]), omega0Ax]), powersetsubset]), powersetAx]), c_0_155]), binunionIL]), upairset2IR]), binunionEcases]), binunionRsub]), binintersectI]), binintersectEL]), eqimpsubset1]), binintersectSubset2]), binintersectSubset3]), binintersectER]), binintersectRsub]), setminusI]), setminusER]), setminusERneg]), binintersectSubset5]), binunionLsub]), binunionE]), binunionIR]), setminusILneg]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffIneg2]), secondinupair]), kpairiskpair]), singletoninpowerset]), singletoninpowunion]), ubforcartprodlem1]), subsetI2]), ubforcartprodlem3]), ubforcartprodlem2]), upairinpowunion]), upairsubunion]), upairset2E]), singletonsubset]), kpairp]), setukpairIR]), emptysetsubset]), setukpairIL]), symdiffIneg1]), symdiffI2]), setminusLsub]), setminusIRneg]), setminusELneg]), setminusSubset2]), setminusEL]), bs114d]), binintersectSubset1]), binintersectSubset4]), disjointsetsI1]), binintersectLsub]), c_0_156]), powersetE1]), setextsub]), subset2powerset]), subsetTrans]), subsetRefl]), notequalI2]), subsetE]), c_0_157]), c_0_158]), omega__Cong]), setunion__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_159]), c_0_160]), in__Cong]), inCongP]), c_0_161]), c_0_162]), notdallE]), notdexE]), prop2setI]), quantDeMorgan3]), quantDeMorgan2]), c_0_163]), powerset__Cong]), c_0_164]), quantDeMorgan4]), upairsetIR]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), setunionE]), powersetE]), emptyInPowerset]), emptyinPowerset]), setadjoinIL]), nonemptyI1]), c_0_165]), noeltsimpempty]), emptyI]), c_0_166]), notinemptyset]), prop2setE]), c_0_167]), c_0_168]), foundationAx]), omegaIndAx]), omegaSAx]), setunionAx]), setadjoinAx]), setextAx])]), c_0_169])). 69.39/9.26 thf(c_0_171, plain, ![X811:$i, X812:$i]:(((cartprod @ X811 @ X812)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X811 @ X812))) @ (^[Z0/* 5 */:$i]:(?[X3:$i]:(((in @ X3 @ X811)&?[X14:$i]:(((in @ X14 @ X812)&((Z0)=(kpair @ X3 @ X14))))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[cartprod])])). 69.39/9.26 thf(c_0_172, negated_conjecture, ![X815:$i, X816:$i, X818:$i, X819:$i, X820:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$i, X826:$i, X828:$i, X829:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i, X837:$i, X838:$i > $i > $o, X839:$i, X842:$i, X844:$i, X845:$i, X846:$i, X847:$i, X849:$i, X850:$i > $o, X851:$i, X852:$i > $o, X853:$i, X854:$i, X855:$i > $o, X856:$i, X857:$i, X858:$i > $o, X859:$i, X860:$i > $o, X862:$i, X863:$o, X864:$i, X865:$i, X866:$o, X867:$i, X868:$i, X869:$i > $o, X871:$i, X872:$i, X875:$i, X877:$i, X879:$i, X880:$i > $o, X881:$i, X882:$i, X884:$i, X885:$i > $o, X886:$i, X887:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$o, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X912:$i, X913:$i, X914:$i, X915:$o, X917:$i, X918:$i, X919:$i > $o, X921:$i, X922:$i, X923:$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, X937:$i, X938:$i, X939:$i, X940:$i, X941:$i > $o, X942:$i, X943:$i > $o, X944:$i, X945:$i, X946:$i > $o, X947:$i, X949:$i, X950:$i > $o, X952:$i, X953:$i, X954:$i > $o, X956:$i, X957:$i, X958:$i > $o, X959:$i, X961:$o, X962:$i, X963:$i > $o, X965:$i, X966:$i, X967:$i > $o, X968:$i, X970:$i > $o, X971:$i, X973:$i > $o, X974:$i, X977:$i > $o, X978:$i, X980:$i, X981:$i, X982:$i, X983:$i, X984:$i, X985:$i, X986:$i, X987:$i, X988:$i > $o, X989:$i, X990:$i, X991:$i > $o, X992:$i > $o, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i > $o, X1004:$i, X1005:$i, X1006:$i > $o, X1007:$i > $o, X1010:$i, X1011:$i, X1012:$i > $o, X1013:$i > $o, X1016:$i, X1017:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1055:$i, X1056:$i, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i > $o, X1064:$i, X1065:$i > $o, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1075:$i, X1076:$i, X1077:$o, X1078:$i, X1079:$i, X1080:$i, X1081:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$o, 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:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i]:((((~(in @ (esk1_2 @ X815 @ X816) @ X815)|~(in @ (esk1_2 @ X815 @ X816) @ X816)|((X815)=(X816)))&((in @ (esk1_2 @ X815 @ X816) @ X815)|(in @ (esk1_2 @ X815 @ X816) @ X816)|((X815)=(X816))))&(~(in @ X818 @ emptyset)&(((~(in @ X821 @ (setadjoin @ X819 @ X820))|(((X821)=(X819))|(in @ X821 @ X820)))&((((X821)!=(X819))|(in @ X821 @ (setadjoin @ X819 @ X820)))&(~(in @ X821 @ X820)|(in @ X821 @ (setadjoin @ X819 @ X820)))))&(((~(in @ X823 @ (powerset @ X822))|(~(in @ X824 @ X823)|(in @ X824 @ X822)))&(((in @ (esk2_2 @ X825 @ X826) @ X826)|(in @ X826 @ (powerset @ X825)))&(~(in @ (esk2_2 @ X825 @ X826) @ X825)|(in @ X826 @ (powerset @ X825)))))&(((((in @ X829 @ (esk3_2 @ X828 @ X829))|~(in @ X829 @ (setunion @ X828)))&((in @ (esk3_2 @ X828 @ X829) @ X828)|~(in @ X829 @ (setunion @ X828))))&(~(in @ X832 @ X833)|~(in @ X833 @ X831)|(in @ X832 @ (setunion @ X831))))&((in @ emptyset @ omega)&((~(in @ X834 @ omega)|(in @ (setadjoin @ X834 @ X834) @ omega))&(((((in @ (esk4_1 @ X835) @ omega)|~(in @ emptyset @ X835)|(~(in @ X837 @ omega)|(in @ X837 @ X835)))&((in @ (esk4_1 @ X835) @ X835)|~(in @ emptyset @ X835)|(~(in @ X837 @ omega)|(in @ X837 @ X835))))&(~(in @ (setadjoin @ (esk4_1 @ X835) @ (esk4_1 @ X835)) @ X835)|~(in @ emptyset @ X835)|(~(in @ X837 @ omega)|(in @ X837 @ X835))))&((((((in @ (esk7_3 @ X838 @ X839 @ X842) @ X839)|~(in @ X842 @ (esk6_2 @ X838 @ X839))|(in @ (esk5_2 @ X838 @ X839) @ X839))&((X838 @ (esk7_3 @ X838 @ X839 @ X842) @ X842)|~(in @ X842 @ (esk6_2 @ X838 @ X839))|(in @ (esk5_2 @ X838 @ X839) @ X839)))&(~(in @ X845 @ X839)|~(X838 @ X845 @ X844)|(in @ X844 @ (esk6_2 @ X838 @ X839))|(in @ (esk5_2 @ X838 @ X839) @ X839)))&((((in @ (esk7_3 @ X838 @ X839 @ X842) @ X839)|~(in @ X842 @ (esk6_2 @ X838 @ X839))|~(exu @ (^[Z0/* 3 */:$i]:((X838 @ (esk5_2 @ X838 @ X839) @ Z0)))))&((X838 @ (esk7_3 @ X838 @ X839 @ X842) @ X842)|~(in @ X842 @ (esk6_2 @ X838 @ X839))|~(exu @ (^[Z0/* 3 */:$i]:((X838 @ (esk5_2 @ X838 @ X839) @ Z0))))))&(~(in @ X845 @ X839)|~(X838 @ X845 @ X844)|(in @ X844 @ (esk6_2 @ X838 @ X839))|~(exu @ (^[Z0/* 3 */:$i]:((X838 @ (esk5_2 @ X838 @ X839) @ Z0)))))))&((((in @ (esk8_1 @ X846) @ X846)|~(in @ X847 @ X846))&(~(in @ X849 @ (esk8_1 @ X846))|~(in @ X849 @ X846)|~(in @ X847 @ X846)))&((epred1_0)&((~(exu @ (^[Z0/* 3 */:$i]:((X850 @ Z0))))|(X850 @ (descr @ (^[Z0/* 3 */:$i]:((X850 @ Z0))))))&((~(in @ X853 @ X851)|(~(X852 @ X853)|(in @ X853 @ (dsetconstr @ X851 @ (^[Z0/* 3 */:$i]:((X852 @ Z0)))))))&((~(in @ X856 @ (dsetconstr @ X854 @ (^[Z0/* 3 */:$i]:((X855 @ Z0)))))|(in @ X856 @ X854))&((~(in @ X859 @ (dsetconstr @ X857 @ (^[Z0/* 3 */:$i]:((X858 @ Z0)))))|(X858 @ X859))&((((X860 @ (esk9_1 @ X860))|~(exu @ (^[Z0/* 3 */:$i]:((X860 @ Z0)))))&(~(X860 @ X862)|((esk9_1 @ X860)=(X862))|~(exu @ (^[Z0/* 3 */:$i]:((X860 @ Z0))))))&((~(in @ X864 @ (prop2set @ ((X863))))|(X863))&((~(in @ X865 @ emptyset)|(X866))&(~(in @ X867 @ emptyset)&(~(in @ 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@ X889 @ (setadjoin @ X889 @ X890))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X893 @ X892)|(in @ X893 @ (setadjoin @ X891 @ X892)))&(((((in @ X896 @ X895)|(X897)|((X896)=(X894))|~(in @ X896 @ (setadjoin @ X894 @ X895)))&(~(X897)|(X897)|((X896)=(X894))|~(in @ X896 @ (setadjoin @ X894 @ X895))))&(((in @ X896 @ X895)|(X897)|~(X897)|~(in @ X896 @ (setadjoin @ X894 @ X895)))&(~(X897)|(X897)|~(X897)|~(in @ X896 @ (setadjoin @ X894 @ X895)))))&((~(in @ X900 @ (setadjoin @ X898 @ X899))|(((X900)=(X898))|(in @ X900 @ X899)))&(((dsetconstr @ X901 @ (^[Z0/* 3 */:$i]:(($true))))=(X901))&((((in @ (esk16_2 @ X902 @ X903) @ X903)|(in @ X903 @ (powerset @ X902)))&(~(in @ (esk16_2 @ X902 @ X903) @ X902)|(in @ X903 @ (powerset @ X902))))&((in @ emptyset @ (powerset @ X905))&((in @ emptyset @ (powerset @ X906))&((~(in @ X908 @ (powerset @ X907))|(~(in @ X909 @ X908)|(in @ X909 @ X907)))&((~(in @ X911 @ X912)|(~(in @ X912 @ X910)|(in @ X911 @ (setunion @ X910))))&((((in @ X914 @ (esk17_3 @ X913 @ X914 @ X915))|(X915)|~(in @ X914 @ (setunion @ X913)))&(((in @ (esk17_3 @ X913 @ X914 @ X915) @ X913)|(X915)|~(in @ X914 @ (setunion @ X913)))&(~(X915)|(X915)|~(in @ X914 @ (setunion @ X913)))))&((~(in @ X918 @ X917)|(in @ X918 @ (powerset @ (setunion @ X917))))&(((~(X919 @ X921)|((X921)=(esk18_1 @ X919))|~(exu @ (^[Z0/* 3 */:$i]:((X919 @ Z0)))))&(((X922)!=(esk18_1 @ X919))|(X919 @ X922)|~(exu @ (^[Z0/* 3 */:$i]:((X919 @ Z0))))))&((~(nonempty @ X923)|(in @ (esk19_1 @ X923) @ X923))&((~(in @ X925 @ (setadjoin @ X926 @ emptyset))|((X925)=(X926)))&((((X927)=(X928))|~(in @ X928 @ (setadjoin @ X927 @ emptyset)))&((((X929)!=(X930))|(in @ X929 @ (setadjoin @ X930 @ emptyset)))&((~(in @ X931 @ (setadjoin @ X932 @ emptyset))|(in @ X932 @ (setadjoin @ X931 @ emptyset)))&((~(in @ X935 @ (setadjoin @ X933 @ (setadjoin @ X934 @ emptyset)))|(((X935)=(X933))|((X935)=(X934))))&((in @ X936 @ (setadjoin @ X936 @ (setadjoin @ X937 @ emptyset)))&((in @ X939 @ (setadjoin @ X938 @ (setadjoin @ X939 @ emptyset)))&((~(in @ X942 @ X940)|~(X941 @ X942)|((dsetconstr @ X940 @ (^[Z0/* 3 */:$i]:((X941 @ Z0))))!=(emptyset)))&((~(in @ X944 @ emptyset)|(X943 @ X944))&((((in @ (esk20_2 @ X945 @ X946) @ X945)|(~(in @ X947 @ X945)|(X946 @ X947)))&(~(X946 @ (esk20_2 @ X945 @ X946))|(~(in @ X947 @ X945)|(X946 @ X947))))&((((in @ (esk21_2 @ X949 @ X950) @ X949)|(~(in @ X952 @ X949)|~(X950 @ X952)))&((X950 @ (esk21_2 @ X949 @ X950))|(~(in @ X952 @ X949)|~(X950 @ X952))))&((((in @ (esk22_2 @ X953 @ X954) @ X953)|(~(in @ X956 @ X953)|~(X954 @ X956)))&((X954 @ (esk22_2 @ X953 @ X954))|(~(in @ X956 @ X953)|~(X954 @ X956))))&((((in @ (esk23_2 @ X957 @ X958) @ X957)|(~(in @ X959 @ X957)|(X958 @ X959)))&(~(X958 @ (esk23_2 @ X957 @ X958))|(~(in @ X959 @ X957)|(X958 @ X959))))&((~(X961)|(in @ emptyset @ (prop2set @ ((X961)))))&((prop2set2propI)&((((in @ (esk24_2 @ X962 @ X963) @ X962)|(~(in @ X965 @ X962)|~(X963 @ X965)))&((X963 @ (esk24_2 @ X962 @ X963))|(~(in @ X965 @ X962)|~(X963 @ X965))))&((((in @ (esk25_2 @ X966 @ X967) @ X966)|(~(in @ X968 @ X966)|(X967 @ X968)))&(~(X967 @ (esk25_2 @ X966 @ X967))|(~(in @ X968 @ X966)|(X967 @ X968))))&((((X970 @ (esk26_2 @ X970 @ X971))|~(X970 @ X971)|(exu @ (^[Z0/* 3 */:$i]:((X970 @ Z0)))))&(((X971)!=(esk26_2 @ X970 @ X971))|~(X970 @ X971)|(exu @ (^[Z0/* 3 */:$i]:((X970 @ Z0))))))&((((X973 @ (esk27_1 @ X973))|(exu @ (^[Z0/* 3 */:$i]:((X973 @ Z0))))|~(X973 @ X974))&(((X973 @ (esk28_1 @ X973))|(exu @ (^[Z0/* 3 */:$i]:((X973 @ Z0))))|~(X973 @ X974))&(((esk27_1 @ X973)!=(esk28_1 @ X973))|(exu @ (^[Z0/* 3 */:$i]:((X973 @ Z0))))|~(X973 @ X974))))&(((~(X977 @ (esk29_2 @ X977 @ X978))|((esk29_2 @ X977 @ X978)!=(X978))|(exu @ (^[Z0/* 3 */:$i]:((X977 @ Z0)))))&((X977 @ (esk29_2 @ X977 @ X978))|((esk29_2 @ X977 @ X978)=(X978))|(exu @ (^[Z0/* 3 */:$i]:((X977 @ Z0))))))&((((X980)!=(X981))|(((X982)!=(X983))|(~(in @ X982 @ X980)|(in @ X983 @ X981))))&(((~(in @ X986 @ X984)|(in @ X987 @ X985)|((X986)!=(X987))|((X984)!=(X985)))&(~(in @ X987 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X992))|(X992 @ (esk31_2 @ X991 @ X992)))))))&(((emptyset)=(emptyset))&((((X995)!=(X996))|(((X997)!=(X998))|((setadjoin @ X995 @ X997)=(setadjoin @ X996 @ X998))))&((((X999)!=(X1000))|((powerset @ X999)=(powerset @ X1000)))&((((X1001)!=(X1002))|((setunion @ X1001)=(setunion @ X1002)))&(((omega)=(omega))&((~(exu @ (^[Z0/* 3 */:$i]:((X1003 @ Z0))))|(~(X1003 @ X1004)|(~(X1003 @ X1005)|((X1004)=(X1005)))))&(((((esk32_2 @ X1006 @ X1007)=(esk33_2 @ X1006 @ X1007))|(~(exu @ (^[Z0/* 3 */:$i]:((X1006 @ Z0))))|(~(exu @ (^[Z0/* 3 */:$i]:((X1007 @ Z0))))|((descr @ (^[Z0/* 3 */:$i]:((X1006 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1007 @ Z0))))))))&((~(X1006 @ (esk32_2 @ X1006 @ X1007))|~(X1007 @ (esk33_2 @ X1006 @ X1007))|(~(exu @ (^[Z0/* 3 */:$i]:((X1006 @ Z0))))|(~(exu @ (^[Z0/* 3 */:$i]:((X1007 @ Z0))))|((descr @ (^[Z0/* 3 */:$i]:((X1006 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1007 @ Z0))))))))&((X1006 @ (esk32_2 @ X1006 @ X1007))|(X1007 @ (esk33_2 @ X1006 @ X1007))|(~(exu @ (^[Z0/* 3 */:$i]:((X1006 @ Z0))))|(~(exu @ (^[Z0/* 3 */:$i]:((X1007 @ Z0))))|((descr @ (^[Z0/* 3 */:$i]:((X1006 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1007 @ Z0))))))))))&((((in @ (esk34_4 @ X1010 @ X1011 @ X1012 @ X1013) @ X1010)|((dsetconstr @ X1010 @ (^[Z0/* 3 */:$i]:((X1012 @ Z0))))=(dsetconstr @ X1011 @ (^[Z0/* 3 */:$i]:((X1013 @ Z0)))))|((X1010)!=(X1011)))&(((in @ (esk35_4 @ X1010 @ X1011 @ X1012 @ X1013) @ X1011)|((dsetconstr @ X1010 @ (^[Z0/* 3 */:$i]:((X1012 @ Z0))))=(dsetconstr @ X1011 @ (^[Z0/* 3 */:$i]:((X1013 @ Z0)))))|((X1010)!=(X1011)))&((((esk34_4 @ X1010 @ X1011 @ X1012 @ X1013)=(esk35_4 @ X1010 @ X1011 @ X1012 @ X1013))|((dsetconstr @ X1010 @ (^[Z0/* 3 */:$i]:((X1012 @ Z0))))=(dsetconstr @ X1011 @ (^[Z0/* 3 */:$i]:((X1013 @ Z0)))))|((X1010)!=(X1011)))&((~(X1012 @ (esk34_4 @ X1010 @ X1011 @ X1012 @ X1013))|~(X1013 @ (esk35_4 @ X1010 @ X1011 @ X1012 @ X1013))|((dsetconstr @ X1010 @ (^[Z0/* 3 */:$i]:((X1012 @ Z0))))=(dsetconstr @ X1011 @ (^[Z0/* 3 */:$i]:((X1013 @ Z0)))))|((X1010)!=(X1011)))&((X1012 @ (esk34_4 @ X1010 @ X1011 @ X1012 @ X1013))|(X1013 @ (esk35_4 @ X1010 @ X1011 @ X1012 @ X1013))|((dsetconstr @ X1010 @ (^[Z0/* 3 */:$i]:((X1012 @ Z0))))=(dsetconstr @ X1011 @ (^[Z0/* 3 */:$i]:((X1013 @ Z0)))))|((X1010)!=(X1011)))))))&((((in @ (esk36_2 @ X1016 @ X1017) @ X1016)|(subset @ X1016 @ X1017))&(~(in @ (esk36_2 @ X1016 @ X1017) @ X1017)|(subset @ X1016 @ X1017)))&((((X1019)!=(X1020))|(subset @ X1020 @ X1019))&((((X1021)!=(X1022))|(subset @ X1021 @ X1022))&((((in @ (esk37_2 @ X1023 @ X1024) @ X1023)|(subset @ X1023 @ X1024))&(~(in @ (esk37_2 @ X1023 @ X1024) @ X1024)|(subset @ X1023 @ X1024)))&((subset @ emptyset @ X1026)&((~(subset @ X1027 @ X1028)|(~(in @ X1029 @ X1027)|(in @ X1029 @ X1028)))&((~(subset @ X1030 @ X1031)|((in @ X1032 @ X1031)|~(in @ X1032 @ X1030)))&((~(in @ X1035 @ X1033)|((in @ X1035 @ X1034)|~(subset @ X1033 @ X1034)))&(((subset @ X1036 @ X1037)|((X1036)!=(X1037)))&((~(in @ X1040 @ X1038)|((in @ X1040 @ X1039)|((X1038)!=(X1039))))&((subset @ X1041 @ X1041)&((~(subset @ X1042 @ X1043)|(~(subset @ X1043 @ X1044)|(subset @ X1042 @ X1044)))&((subset @ X1046 @ (setadjoin @ X1045 @ X1046))&((~(subset @ X1047 @ X1049)|(subset @ X1047 @ (setadjoin @ X1048 @ X1049)))&((~(subset @ X1050 @ X1051)|(in @ X1050 @ (powerset @ X1051)))&((~(subset @ X1052 @ X1053)|(~(subset @ X1053 @ X1052)|((X1052)=(X1053))))&((~(subset @ X1054 @ emptyset)|((X1054)=(emptyset)))&((~(subset @ X1056 @ X1055)|(in @ X1056 @ (powerset @ X1055)))&((~(in @ X1058 @ (powerset @ X1057))|(subset @ X1058 @ X1057))&((in @ X1059 @ (powerset @ X1059))&((~(subset @ X1060 @ X1061)|(subset @ (powerset @ X1060) @ (powerset @ X1061)))&((in @ (dsetconstr @ X1062 @ (^[Z0/* 3 */:$i]:((X1063 @ Z0)))) @ (powerset @ X1062))&((subset @ (dsetconstr @ X1064 @ (^[Z0/* 3 */:$i]:((X1065 @ Z0)))) @ X1064)&((~(in @ X1068 @ X1066)|(in @ X1068 @ (binunion @ X1066 @ X1067)))&((in @ X1070 @ (setadjoin @ X1069 @ (setadjoin @ X1070 @ emptyset)))&((~(in @ X1073 @ X1072)|(in @ X1073 @ (binunion @ X1071 @ X1072)))&(((((in @ X1076 @ X1075)|(X1077)|(in @ X1076 @ X1074)|~(in @ X1076 @ (binunion @ X1074 @ X1075)))&(~(X1077)|(X1077)|(in @ X1076 @ X1074)|~(in @ X1076 @ (binunion @ X1074 @ X1075))))&(((in @ X1076 @ X1075)|(X1077)|~(X1077)|~(in @ X1076 @ (binunion @ X1074 @ X1075)))&(~(X1077)|(X1077)|~(X1077)|~(in @ X1076 @ (binunion @ X1074 @ X1075)))))&((~(in @ X1080 @ (binunion @ X1078 @ X1079))|((in @ X1080 @ X1078)|(in @ X1080 @ X1079)))&((subset @ X1081 @ (binunion @ X1081 @ X1082))&((subset @ X1084 @ (binunion @ X1083 @ X1084))&((~(in @ X1087 @ X1085)|(~(in @ X1087 @ X1086)|(in @ X1087 @ (binintersect @ X1085 @ X1086))))&((~(subset @ X1090 @ X1088)|(~(subset @ X1090 @ X1089)|(subset @ X1090 @ (binintersect @ X1088 @ X1089))))&((~(in @ X1093 @ (binintersect @ X1091 @ X1092))|(in @ X1093 @ X1091))&((subset @ (binintersect @ X1094 @ X1095) @ X1094)&((~(subset @ X1096 @ X1097)|((binintersect @ X1096 @ X1097)=(X1096)))&((((binintersect @ X1098 @ X1099)!=(X1099))|(subset @ X1099 @ X1098))&((~(in @ X1102 @ (binintersect @ X1100 @ X1101))|(in @ X1102 @ X1101))&((((in @ (esk38_2 @ X1103 @ X1104) @ X1103)|((binintersect @ X1103 @ X1104)=(emptyset)))&((in @ (esk38_2 @ X1103 @ X1104) @ X1104)|((binintersect @ X1103 @ X1104)=(emptyset))))&((subset @ (binintersect @ X1106 @ X1107) @ X1107)&((~(subset @ X1109 @ X1108)|((binintersect @ X1108 @ X1109)=(X1109)))&((((binintersect @ X1110 @ X1111)!=(X1110))|(subset @ X1110 @ X1111))&(((binintersect @ X1112 @ (binunion @ X1113 @ X1114))=(binunion @ (binintersect @ X1112 @ X1113) @ (binintersect @ X1112 @ X1114)))&((~(in @ X1117 @ X1115)|((in @ X1117 @ X1116)|(in @ X1117 @ (setminus @ X1115 @ X1116))))&((~(in @ X1120 @ (setminus @ X1118 @ X1119))|(in @ X1120 @ X1118))&((~(in @ X1123 @ (setminus @ X1121 @ X1122))|~(in @ X1123 @ X1122))&((~(subset @ X1124 @ X1125)|((setminus @ X1124 @ X1125)=(emptyset)))&(((in @ X1128 @ (setminus @ X1126 @ X1127))|(~(in @ X1128 @ X1126)|(in @ X1128 @ X1127)))&(((in @ X1131 @ (setminus @ X1129 @ X1130))|((in @ X1131 @ X1130)|~(in @ X1131 @ X1129)))&(((in @ X1134 @ X1132)|~(in @ X1134 @ (setminus @ X1132 @ X1133)))&((~(in @ X1137 @ X1136)|~(in @ X1137 @ (setminus @ X1135 @ X1136)))&((subset @ (setminus @ X1138 @ X1139) @ X1138)&((((setminus @ X1140 @ X1141)!=(emptyset))|(subset @ X1140 @ X1141))&((((~(in @ X1144 @ X1142)|(X1145)|(in @ X1144 @ X1142)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(((in @ X1144 @ X1143)|(X1145)|(in @ X1144 @ X1142)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(~(X1145)|(X1145)|(in @ X1144 @ X1142)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))))&(((~(in @ X1144 @ X1142)|(X1145)|~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(((in @ X1144 @ X1143)|(X1145)|~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(~(X1145)|(X1145)|~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))))&((~(in @ X1144 @ X1142)|(X1145)|~(X1145)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(((in @ X1144 @ X1143)|(X1145)|~(X1145)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(~(X1145)|(X1145)|~(X1145)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))))))&((~(in @ X1148 @ X1146)|((in @ X1148 @ X1147)|(in @ X1148 @ (symdiff @ X1146 @ X1147))))&(((in @ X1151 @ X1149)|(~(in @ X1151 @ X1150)|(in @ X1151 @ (symdiff @ X1149 @ X1150))))&((~(in @ X1154 @ X1152)|(~(in @ X1154 @ X1153)|~(in @ X1154 @ (symdiff @ X1152 @ X1153))))&(((in @ X1157 @ X1155)|((in @ X1157 @ X1156)|~(in @ X1157 @ (symdiff @ X1155 @ X1156))))&((in @ X1159 @ (setadjoin @ X1158 @ (setadjoin @ X1159 @ emptyset)))&((in @ X1160 @ (setunion @ (setadjoin @ (setadjoin @ X1160 @ emptyset) @ (setadjoin @ (setadjoin @ X1160 @ (setadjoin @ X1161 @ emptyset)) @ emptyset))))&((in @ X1163 @ (setunion @ (setadjoin @ (setadjoin @ X1162 @ emptyset) @ (setadjoin @ (setadjoin @ X1162 @ (setadjoin @ X1163 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1164 @ emptyset) @ (setadjoin @ (setadjoin @ X1164 @ (setadjoin @ X1165 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1166 @ X1167))&((~(in @ X1169 @ X1168)|(subset @ (setadjoin @ X1169 @ emptyset) @ X1168))&((~(in @ X1171 @ X1170)|(in @ (setadjoin @ X1171 @ emptyset) @ (powerset @ X1170)))&((~(in @ X1174 @ X1172)|(in @ (setadjoin @ X1174 @ emptyset) @ (powerset @ (binunion @ X1172 @ X1173))))&((~(in @ X1177 @ (setadjoin @ X1175 @ (setadjoin @ X1176 @ emptyset)))|(((X1177)=(X1175))|((X1177)=(X1176))))&((~(in @ X1180 @ X1178)|(~(in @ X1181 @ X1179)|(subset @ (setadjoin @ X1180 @ (setadjoin @ X1181 @ emptyset)) @ (binunion @ X1178 @ X1179))))&((~(in @ X1184 @ X1182)|(~(in @ X1185 @ X1183)|(in @ (setadjoin @ X1184 @ (setadjoin @ X1185 @ emptyset)) @ (powerset @ (binunion @ X1182 @ X1183)))))&((~(in @ X1188 @ X1186)|(~(in @ X1189 @ X1187)|(subset @ (setadjoin @ (setadjoin @ X1188 @ emptyset) @ (setadjoin @ (setadjoin @ X1188 @ (setadjoin @ X1189 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1186 @ X1187)))))&((~(in @ X1192 @ X1190)|(~(in @ X1193 @ X1191)|(in @ (setadjoin @ (setadjoin @ X1192 @ emptyset) @ (setadjoin @ (setadjoin @ X1192 @ (setadjoin @ X1193 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1190 @ X1191))))))&((~(in @ X1196 @ X1194)|(~(in @ X1197 @ X1195)|(in @ (kpair @ X1196 @ X1197) @ (powerset @ (powerset @ (binunion @ X1194 @ X1195))))))&((in @ esk41_0 @ esk39_0)&((in @ esk42_0 @ esk40_0)&~(in @ (kpair @ esk41_0 @ esk42_0) @ (cartprod @ esk39_0 @ esk40_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_170])])])])])])). 69.39/9.26 thf(c_0_173, plain, ![X1202:$i, X1203:$i]:(((cartprod @ X1202 @ X1203)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X1202 @ X1203))) @ (^[Z0/* 5 */:$i]:(?[X3:$i]:(((in @ X3 @ X1202)&?[X14:$i]:(((in @ X14 @ X1203)&((Z0)=(kpair @ X3 @ X14))))))))))), inference(variable_rename,[status(thm)],[c_0_171])). 69.39/9.26 thf(c_0_174, plain, ![X1228:$i, X2:$i, X3:$i]:(((epred3_2 @ X3 @ X2 @ X1228)<=>?[X1226:$i]:(((in @ X1226 @ X2)&?[X1227:$i]:(((in @ X1227 @ X3)&((X1228)=(kpair @ X1226 @ X1227)))))))), introduced(definition)). 69.39/9.26 thf(c_0_175, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((X1 @ X2))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_172])). 69.39/9.26 thf(c_0_176, plain, ![X3:$i, X2:$i]:(((cartprod @ X2 @ X3)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X2 @ X3))) @ (epred3_2 @ X3 @ X2)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_173]), c_0_174])). 69.39/9.26 thf(c_0_177, negated_conjecture, ~((in @ (kpair @ esk41_0 @ esk42_0) @ (cartprod @ esk39_0 @ esk40_0))), inference(split_conjunct,[status(thm)],[c_0_172])). 69.39/9.26 thf(c_0_178, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X2 @ (cartprod @ X3 @ X4))|~((in @ X2 @ (powerset @ (powerset @ (binunion @ X3 @ X4)))))|~((epred3_2 @ X4 @ X3 @ X2)))), inference(spm,[status(thm)],[c_0_175, c_0_176])). 69.39/9.26 thf(c_0_179, plain, ![X1230:$i, X1231:$i, X1232:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i]:(((((in @ (esk48_3 @ X1230 @ X1231 @ X1232) @ X1231)|~(epred3_2 @ X1232 @ X1231 @ X1230))&(((in @ (esk49_3 @ X1230 @ X1231 @ X1232) @ X1232)|~(epred3_2 @ X1232 @ X1231 @ X1230))&(((X1230)=(kpair @ (esk48_3 @ X1230 @ X1231 @ X1232) @ (esk49_3 @ X1230 @ X1231 @ X1232)))|~(epred3_2 @ X1232 @ X1231 @ X1230))))&(~(in @ X1238 @ X1236)|(~(in @ X1239 @ X1237)|((X1235)!=(kpair @ X1238 @ X1239)))|(epred3_2 @ X1237 @ X1236 @ X1235)))), 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)],[])])])])])])). 69.39/9.26 thf(c_0_180, negated_conjecture, (~((in @ (kpair @ esk41_0 @ esk42_0) @ (powerset @ (powerset @ (binunion @ esk39_0 @ esk40_0)))))|~((epred3_2 @ esk40_0 @ esk39_0 @ (kpair @ esk41_0 @ esk42_0)))), inference(spm,[status(thm)],[c_0_177, c_0_178])). 69.39/9.26 thf(c_0_181, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i]:(((in @ (kpair @ X2 @ X4) @ (powerset @ (powerset @ (binunion @ X3 @ X5))))|~((in @ X2 @ X3))|~((in @ X4 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_172])). 69.39/9.26 thf(c_0_182, negated_conjecture, (in @ esk42_0 @ esk40_0), inference(split_conjunct,[status(thm)],[c_0_172])). 69.39/9.26 thf(c_0_183, negated_conjecture, (in @ esk41_0 @ esk39_0), inference(split_conjunct,[status(thm)],[c_0_172])). 69.39/9.26 thf(c_0_184, plain, ![X3:$i, X2:$i, X7:$i, X5:$i, X4:$i]:(((epred3_2 @ X5 @ X3 @ X7)|~((in @ X2 @ X3))|~((in @ X4 @ X5))|((X7)!=(kpair @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_179])). 69.39/9.26 thf(c_0_185, negated_conjecture, ~((epred3_2 @ esk40_0 @ esk39_0 @ (kpair @ esk41_0 @ esk42_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180, c_0_181]), c_0_182]), c_0_183])])). 69.39/9.26 thf(c_0_186, plain, ![X2:$i, X5:$i, X4:$i, X3:$i]:(((epred3_2 @ X2 @ X3 @ (kpair @ X4 @ X5))|~((in @ X5 @ X2))|~((in @ X4 @ X3)))), inference(er,[status(thm)],[c_0_184])). 69.39/9.26 thf(c_0_187, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185, c_0_186]), c_0_182]), c_0_183])]), ['proof']). 69.39/9.26 # SZS output end CNFRefutation 69.39/9.26 # Parsed axioms : 321 69.39/9.26 # Removed by relevancy pruning/SinE : 173 69.39/9.26 # Initial clauses : 232 69.39/9.26 # Removed in clause preprocessing : 23 69.39/9.26 # Initial clauses in saturation : 209 69.39/9.26 # Processed clauses : 4727 69.39/9.26 # ...of these trivial : 118 69.39/9.26 # ...subsumed : 1556 69.39/9.26 # ...remaining for further processing : 3053 69.39/9.26 # Other redundant clauses eliminated : 90 69.39/9.26 # Clauses deleted for lack of memory : 0 69.39/9.26 # Backward-subsumed : 437 69.39/9.26 # Backward-rewritten : 47 69.39/9.26 # Generated clauses : 496796 69.39/9.26 # ...of the previous two non-redundant : 492384 69.39/9.26 # ...aggressively subsumed : 0 69.39/9.26 # Contextual simplify-reflections : 10 69.39/9.26 # Paramodulations : 496585 69.39/9.26 # Factorizations : 110 69.39/9.26 # NegExts : 0 69.39/9.26 # Equation resolutions : 90 69.39/9.26 # Total rewrite steps : 8986 69.39/9.26 # Propositional unsat checks : 0 69.39/9.26 # Propositional check models : 0 69.39/9.26 # Propositional check unsatisfiable : 0 69.39/9.26 # Propositional clauses : 0 69.39/9.26 # Propositional clauses after purity: 0 69.39/9.26 # Propositional unsat core size : 0 69.39/9.26 # Propositional preprocessing time : 0.000 69.39/9.26 # Propositional encoding time : 0.000 69.39/9.26 # Propositional solver time : 0.000 69.39/9.26 # Success case prop preproc time : 0.000 69.39/9.26 # Success case prop encoding time : 0.000 69.39/9.26 # Success case prop solver time : 0.000 69.39/9.26 # Current number of processed clauses : 2373 69.39/9.26 # Positive orientable unit clauses : 171 69.39/9.26 # Positive unorientable unit clauses: 0 69.39/9.26 # Negative unit clauses : 125 69.39/9.26 # Non-unit-clauses : 2077 69.39/9.26 # Current number of unprocessed clauses: 486453 69.39/9.26 # ...number of literals in the above : 2112300 69.39/9.26 # Current number of archived formulas : 0 69.39/9.26 # Current number of archived clauses : 668 69.39/9.26 # Clause-clause subsumption calls (NU) : 600013 69.39/9.26 # Rec. Clause-clause subsumption calls : 304164 69.39/9.26 # Non-unit clause-clause subsumptions : 707 69.39/9.26 # Unit Clause-clause subsumption calls : 21146 69.39/9.26 # Rewrite failures with RHS unbound : 0 69.39/9.26 # BW rewrite match attempts : 270 69.39/9.26 # BW rewrite match successes : 44 69.39/9.26 # Condensation attempts : 4727 69.39/9.26 # Condensation successes : 26 69.39/9.26 # Termbank termtop insertions : 9969371 69.39/9.26 69.39/9.26 # ------------------------------------------------- 69.39/9.26 # User time : 8.415 s 69.39/9.26 # System time : 0.271 s 69.39/9.26 # Total time : 8.686 s 69.39/9.26 # Maximum resident set size: 4908 pages 70.27/9.44 70.27/9.44 # ------------------------------------------------- 70.27/9.44 # User time : 8.423 s 70.27/9.44 # System time : 0.273 s 70.27/9.44 # Total time : 8.696 s 70.27/9.44 # Maximum resident set size: 2096 pages 70.27/9.45 % E---3.1 exiting 70.27/9.45 EOF