0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.13 % Command : run_E %s %d THM 0.14/0.35 % Computer : n017.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1440 0.14/0.35 % WCLimit : 180 0.14/0.35 % DateTime : Thu Jul 4 08:00:39 EDT 2024 0.14/0.35 % CPUTime : 0.23/0.51 Running higher-order theorem proving 0.23/0.54 Running: /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.Et5BI9ZfO1/E---3.1_15766.p 392.69/52.86 # Version: 3.2.0-ho 392.69/52.86 # Preprocessing class: HSLMSLSSLLLCHFA. 392.69/52.86 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 392.69/52.86 # Starting ehoh_best5 with 180s (1) cores 392.69/52.86 # Starting almost_fo_3_lam with 180s (1) cores 392.69/52.86 # Starting new_bool_5 with 180s (1) cores 392.69/52.86 # Starting pre_casc_3 with 180s (1) cores 392.69/52.86 # Starting ho_unfolding_8 with 180s (1) cores 392.69/52.86 # Starting new_ho_10_cnf2 with 180s (1) cores 392.69/52.86 # Starting new_bool_3 with 180s (1) cores 392.69/52.86 # Starting new_ho_5 with 180s (1) cores 392.69/52.86 # new_bool_5 with pid 15942 completed with status 0 392.69/52.86 # Result found by new_bool_5 392.69/52.86 # Preprocessing class: HSLMSLSSLLLCHFA. 392.69/52.86 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 392.69/52.86 # Starting ehoh_best5 with 180s (1) cores 392.69/52.86 # Starting almost_fo_3_lam with 180s (1) cores 392.69/52.86 # Starting new_bool_5 with 180s (1) cores 392.69/52.86 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 392.69/52.86 # Search class: HGHSM-FSLM31-MHFMMSBN 392.69/52.86 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 392.69/52.86 # Starting new_ho_10_cnf2 with 98s (1) cores 392.69/52.86 # new_ho_10_cnf2 with pid 15968 completed with status 0 392.69/52.86 # Result found by new_ho_10_cnf2 392.69/52.86 # Preprocessing class: HSLMSLSSLLLCHFA. 392.69/52.86 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 392.69/52.86 # Starting ehoh_best5 with 180s (1) cores 392.69/52.86 # Starting almost_fo_3_lam with 180s (1) cores 392.69/52.86 # Starting new_bool_5 with 180s (1) cores 392.69/52.86 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 392.69/52.86 # Search class: HGHSM-FSLM31-MHFMMSBN 392.69/52.86 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 392.69/52.86 # Starting new_ho_10_cnf2 with 98s (1) cores 392.69/52.86 # Preprocessing time : 0.003 s 392.69/52.86 # Presaturation interreduction done 392.69/52.86 392.69/52.86 # Proof found! 392.69/52.86 # SZS status Theorem 392.69/52.86 # SZS output start CNFRefutation 392.69/52.86 thf(decl_22, type, in: $i > $i > $o). 392.69/52.86 thf(decl_23, type, exu: ($i > $o) > $o). 392.69/52.86 thf(decl_24, type, setextAx: $o). 392.69/52.86 thf(decl_25, type, emptyset: $i). 392.69/52.86 thf(decl_26, type, emptysetAx: $o). 392.69/52.86 thf(decl_27, type, setadjoin: $i > $i > $i). 392.69/52.86 thf(decl_28, type, setadjoinAx: $o). 392.69/52.86 thf(decl_29, type, powerset: $i > $i). 392.69/52.86 thf(decl_30, type, powersetAx: $o). 392.69/52.86 thf(decl_31, type, setunion: $i > $i). 392.69/52.86 thf(decl_32, type, setunionAx: $o). 392.69/52.86 thf(decl_33, type, omega: $i). 392.69/52.86 thf(decl_34, type, omega0Ax: $o). 392.69/52.86 thf(decl_35, type, omegaSAx: $o). 392.69/52.86 thf(decl_36, type, omegaIndAx: $o). 392.69/52.86 thf(decl_37, type, replAx: $o). 392.69/52.86 thf(decl_38, type, foundationAx: $o). 392.69/52.86 thf(decl_39, type, wellorderingAx: $o). 392.69/52.86 thf(decl_40, type, descr: ($i > $o) > $i). 392.69/52.86 thf(decl_41, type, descrp: $o). 392.69/52.86 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 392.69/52.86 thf(decl_43, type, dsetconstrI: $o). 392.69/52.86 thf(decl_44, type, dsetconstrEL: $o). 392.69/52.86 thf(decl_45, type, dsetconstrER: $o). 392.69/52.86 thf(decl_46, type, exuE1: $o). 392.69/52.86 thf(decl_47, type, prop2set: $o > $i). 392.69/52.86 thf(decl_48, type, prop2setE: $o). 392.69/52.86 thf(decl_49, type, emptysetE: $o). 392.69/52.86 thf(decl_50, type, emptysetimpfalse: $o). 392.69/52.86 thf(decl_51, type, notinemptyset: $o). 392.69/52.86 thf(decl_52, type, exuE3e: $o). 392.69/52.86 thf(decl_53, type, setext: $o). 392.69/52.86 thf(decl_54, type, emptyI: $o). 392.69/52.86 thf(decl_55, type, noeltsimpempty: $o). 392.69/52.86 thf(decl_56, type, setbeta: $o). 392.69/52.86 thf(decl_57, type, nonempty: $i > $o). 392.69/52.86 thf(decl_58, type, nonemptyE1: $o). 392.69/52.86 thf(decl_59, type, nonemptyI: $o). 392.69/52.86 thf(decl_60, type, nonemptyI1: $o). 392.69/52.86 thf(decl_61, type, setadjoinIL: $o). 392.69/52.86 thf(decl_62, type, emptyinunitempty: $o). 392.69/52.86 thf(decl_63, type, setadjoinIR: $o). 392.69/52.86 thf(decl_64, type, setadjoinE: $o). 392.69/52.86 thf(decl_65, type, setadjoinOr: $o). 392.69/52.86 thf(decl_66, type, setoftrueEq: $o). 392.69/52.86 thf(decl_67, type, powersetI: $o). 392.69/52.86 thf(decl_68, type, emptyinPowerset: $o). 392.69/52.86 thf(decl_69, type, emptyInPowerset: $o). 392.69/52.86 thf(decl_70, type, powersetE: $o). 392.69/52.86 thf(decl_71, type, setunionI: $o). 392.69/52.86 thf(decl_72, type, setunionE: $o). 392.69/52.86 thf(decl_73, type, subPowSU: $o). 392.69/52.86 thf(decl_74, type, exuE2: $o). 392.69/52.86 thf(decl_75, type, nonemptyImpWitness: $o). 392.69/52.86 thf(decl_76, type, uniqinunit: $o). 392.69/52.86 thf(decl_77, type, notinsingleton: $o). 392.69/52.86 thf(decl_78, type, eqinunit: $o). 392.69/52.86 thf(decl_79, type, singletonsswitch: $o). 392.69/52.86 thf(decl_80, type, upairsetE: $o). 392.69/52.86 thf(decl_81, type, upairsetIL: $o). 392.69/52.86 thf(decl_82, type, upairsetIR: $o). 392.69/52.86 thf(decl_83, type, emptyE1: $o). 392.69/52.86 thf(decl_84, type, vacuousDall: $o). 392.69/52.86 thf(decl_85, type, quantDeMorgan1: $o). 392.69/52.86 thf(decl_86, type, quantDeMorgan2: $o). 392.69/52.86 thf(decl_87, type, quantDeMorgan3: $o). 392.69/52.86 thf(decl_88, type, quantDeMorgan4: $o). 392.69/52.86 thf(decl_89, type, prop2setI: $o). 392.69/52.86 thf(decl_91, type, prop2set2propI: $o). 392.69/52.86 thf(decl_92, type, notdexE: $o). 392.69/52.86 thf(decl_93, type, notdallE: $o). 392.69/52.86 thf(decl_94, type, exuI1: $o). 392.69/52.86 thf(decl_95, type, exuI3: $o). 392.69/52.86 thf(decl_96, type, exuI2: $o). 392.69/52.86 thf(decl_97, type, inCongP: $o). 392.69/52.86 thf(decl_98, type, in__Cong: $o). 392.69/52.86 thf(decl_99, type, exuE3u: $o). 392.69/52.86 thf(decl_100, type, exu__Cong: $o). 392.69/52.86 thf(decl_101, type, emptyset__Cong: $o). 392.69/52.86 thf(decl_102, type, setadjoin__Cong: $o). 392.69/52.86 thf(decl_103, type, powerset__Cong: $o). 392.69/52.86 thf(decl_104, type, setunion__Cong: $o). 392.69/52.86 thf(decl_105, type, omega__Cong: $o). 392.69/52.86 thf(decl_106, type, exuEu: $o). 392.69/52.86 thf(decl_107, type, descr__Cong: $o). 392.69/52.86 thf(decl_108, type, dsetconstr__Cong: $o). 392.69/52.86 thf(decl_109, type, subset: $i > $i > $o). 392.69/52.86 thf(decl_112, type, subsetI1: $o). 392.69/52.86 thf(decl_113, type, eqimpsubset2: $o). 392.69/52.86 thf(decl_114, type, eqimpsubset1: $o). 392.69/52.86 thf(decl_115, type, subsetI2: $o). 392.69/52.86 thf(decl_116, type, emptysetsubset: $o). 392.69/52.86 thf(decl_117, type, subsetE: $o). 392.69/52.86 thf(decl_118, type, subsetE2: $o). 392.69/52.86 thf(decl_119, type, notsubsetI: $o). 392.69/52.86 thf(decl_120, type, notequalI1: $o). 392.69/52.86 thf(decl_121, type, notequalI2: $o). 392.69/52.86 thf(decl_122, type, subsetRefl: $o). 392.69/52.86 thf(decl_123, type, subsetTrans: $o). 392.69/52.86 thf(decl_124, type, setadjoinSub: $o). 392.69/52.86 thf(decl_125, type, setadjoinSub2: $o). 392.69/52.86 thf(decl_126, type, subset2powerset: $o). 392.69/52.86 thf(decl_127, type, setextsub: $o). 392.69/52.86 thf(decl_128, type, subsetemptysetimpeq: $o). 392.69/52.86 thf(decl_129, type, powersetI1: $o). 392.69/52.86 thf(decl_130, type, powersetE1: $o). 392.69/52.86 thf(decl_131, type, inPowerset: $o). 392.69/52.86 thf(decl_132, type, powersetsubset: $o). 392.69/52.86 thf(decl_133, type, sepInPowerset: $o). 392.69/52.86 thf(decl_134, type, sepSubset: $o). 392.69/52.86 thf(decl_135, type, binunion: $i > $i > $i). 392.69/52.86 thf(decl_136, type, binunionIL: $o). 392.69/52.86 thf(decl_137, type, upairset2IR: $o). 392.69/52.86 thf(decl_138, type, binunionIR: $o). 392.69/52.86 thf(decl_139, type, binunionEcases: $o). 392.69/52.86 thf(decl_140, type, binunionE: $o). 392.69/52.86 thf(decl_141, type, binunionLsub: $o). 392.69/52.86 thf(decl_142, type, binunionRsub: $o). 392.69/52.86 thf(decl_143, type, binintersect: $i > $i > $i). 392.69/52.86 thf(decl_144, type, binintersectI: $o). 392.69/52.86 thf(decl_145, type, binintersectSubset5: $o). 392.69/52.86 thf(decl_146, type, binintersectEL: $o). 392.69/52.86 thf(decl_147, type, binintersectLsub: $o). 392.69/52.86 thf(decl_148, type, binintersectSubset2: $o). 392.69/52.86 thf(decl_149, type, binintersectSubset3: $o). 392.69/52.86 thf(decl_150, type, binintersectER: $o). 392.69/52.86 thf(decl_151, type, disjointsetsI1: $o). 392.69/52.86 thf(decl_152, type, binintersectRsub: $o). 392.69/52.86 thf(decl_153, type, binintersectSubset4: $o). 392.69/52.86 thf(decl_154, type, binintersectSubset1: $o). 392.69/52.86 thf(decl_155, type, bs114d: $o). 392.69/52.86 thf(decl_157, type, setminus: $i > $i > $i). 392.69/52.86 thf(decl_158, type, setminusI: $o). 392.69/52.86 thf(decl_159, type, setminusEL: $o). 392.69/52.86 thf(decl_160, type, setminusER: $o). 392.69/52.86 thf(decl_161, type, setminusSubset2: $o). 392.69/52.86 thf(decl_162, type, setminusERneg: $o). 392.69/52.86 thf(decl_163, type, setminusELneg: $o). 392.69/52.86 thf(decl_164, type, setminusILneg: $o). 392.69/52.86 thf(decl_165, type, setminusIRneg: $o). 392.69/52.86 thf(decl_166, type, setminusLsub: $o). 392.69/52.86 thf(decl_167, type, setminusSubset1: $o). 392.69/52.86 thf(decl_168, type, symdiff: $i > $i > $i). 392.69/52.86 thf(decl_169, type, symdiffE: $o). 392.69/52.86 thf(decl_170, type, symdiffI1: $o). 392.69/52.86 thf(decl_171, type, symdiffI2: $o). 392.69/52.86 thf(decl_172, type, symdiffIneg1: $o). 392.69/52.86 thf(decl_173, type, symdiffIneg2: $o). 392.69/52.86 thf(decl_174, type, iskpair: $i > $o). 392.69/52.86 thf(decl_175, type, secondinupair: $o). 392.69/52.86 thf(decl_176, type, setukpairIL: $o). 392.69/52.86 thf(decl_177, type, setukpairIR: $o). 392.69/52.86 thf(decl_178, type, kpairiskpair: $o). 392.69/52.86 thf(decl_179, type, kpair: $i > $i > $i). 392.69/52.86 thf(decl_180, type, kpairp: $o). 392.69/52.86 thf(decl_181, type, cartprod: $i > $i > $i). 392.69/52.86 thf(decl_182, type, singletonsubset: $o). 392.69/52.86 thf(decl_183, type, singletoninpowerset: $o). 392.69/52.86 thf(decl_184, type, singletoninpowunion: $o). 392.69/52.86 thf(decl_185, type, upairset2E: $o). 392.69/52.86 thf(decl_186, type, upairsubunion: $o). 392.69/52.86 thf(decl_187, type, upairinpowunion: $o). 392.69/52.86 thf(decl_188, type, ubforcartprodlem1: $o). 392.69/52.86 thf(decl_189, type, ubforcartprodlem2: $o). 392.69/52.86 thf(decl_190, type, ubforcartprodlem3: $o). 392.69/52.86 thf(decl_191, type, cartprodpairin: $o). 392.69/52.86 thf(decl_192, type, cartprodmempair1: $o). 392.69/52.86 thf(decl_193, type, cartprodmempair: $o). 392.69/52.86 thf(decl_194, type, setunionE2: $o). 392.69/52.86 thf(decl_195, type, setunionsingleton1: $o). 392.69/52.86 thf(decl_196, type, setunionsingleton2: $o). 392.69/52.86 thf(decl_197, type, setunionsingleton: $o). 392.69/52.86 thf(decl_198, type, singleton: $i > $o). 392.69/52.86 thf(decl_199, type, singletonprop: $o). 392.69/52.86 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 392.69/52.86 thf(decl_201, type, ex1E1: $o). 392.69/52.86 thf(decl_202, type, ex1I: $o). 392.69/52.86 thf(decl_203, type, ex1I2: $o). 392.69/52.86 thf(decl_204, type, singletonsuniq: $o). 392.69/52.86 thf(decl_209, type, setukpairinjL1: $o). 392.69/52.86 thf(decl_210, type, kfstsingleton: $o). 392.69/52.86 thf(decl_211, type, theprop: $o). 392.69/52.86 thf(decl_212, type, kfst: $i > $i). 392.69/52.86 thf(decl_213, type, kfstpairEq: $o). 392.69/52.86 thf(decl_214, type, epred1_0: $o). 392.69/52.86 thf(decl_215, type, esk1_2: $i > $i > $i). 392.69/52.86 thf(decl_216, type, esk2_2: $i > $i > $i). 392.69/52.86 thf(decl_217, type, esk3_2: $i > $i > $i). 392.69/52.86 thf(decl_218, type, esk4_1: $i > $i). 392.69/52.86 thf(decl_219, type, esk5_2: ($i > $i > $o) > $i > $i). 392.69/52.86 thf(decl_220, type, esk6_2: ($i > $i > $o) > $i > $i). 392.69/52.86 thf(decl_221, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 392.69/52.86 thf(decl_222, type, esk8_1: $i > $i). 392.69/52.86 thf(decl_223, type, esk9_1: ($i > $o) > $i). 392.69/52.86 thf(decl_224, type, esk10_1: ($i > $o) > $i). 392.69/52.86 thf(decl_225, type, esk11_2: $i > $i > $i). 392.69/52.86 thf(decl_226, type, esk12_2: $i > $i > $i). 392.69/52.86 thf(decl_227, type, esk13_1: $i > $i). 392.69/52.86 thf(decl_228, type, esk14_1: $i > $i). 392.69/52.86 thf(decl_229, type, esk15_1: $i > $i). 392.69/52.86 thf(decl_230, type, esk16_2: $i > $i > $i). 392.69/52.86 thf(decl_231, type, esk17_3: $i > $i > $o > $i). 392.69/52.86 thf(decl_232, type, esk18_1: ($i > $o) > $i). 392.69/52.86 thf(decl_233, type, esk19_1: $i > $i). 392.69/52.86 thf(decl_234, type, esk20_2: $i > ($i > $o) > $i). 392.69/52.86 thf(decl_235, type, esk21_2: $i > ($i > $o) > $i). 392.69/52.86 thf(decl_236, type, esk22_2: $i > ($i > $o) > $i). 392.69/52.86 thf(decl_237, type, esk23_2: $i > ($i > $o) > $i). 392.69/52.86 thf(decl_238, type, esk24_2: $i > ($i > $o) > $i). 392.69/52.86 thf(decl_239, type, esk25_2: $i > ($i > $o) > $i). 392.69/52.86 thf(decl_240, type, esk26_2: ($i > $o) > $i > $i). 392.69/52.86 thf(decl_241, type, esk27_1: ($i > $o) > $i). 392.69/52.86 thf(decl_242, type, esk28_1: ($i > $o) > $i). 392.69/52.86 thf(decl_243, type, esk29_2: ($i > $o) > $i > $i). 392.69/52.86 thf(decl_244, type, esk30_2: ($i > $o) > ($i > $o) > $i). 392.69/52.86 thf(decl_245, type, esk31_2: ($i > $o) > ($i > $o) > $i). 392.69/52.86 thf(decl_246, type, esk32_2: ($i > $o) > ($i > $o) > $i). 392.69/52.86 thf(decl_247, type, esk33_2: ($i > $o) > ($i > $o) > $i). 392.69/52.86 thf(decl_248, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 392.69/52.86 thf(decl_249, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 392.69/52.86 thf(decl_250, type, esk36_2: $i > $i > $i). 392.69/52.86 thf(decl_251, type, esk37_2: $i > $i > $i). 392.69/52.86 thf(decl_252, type, esk38_2: $i > $i > $i). 392.69/52.86 thf(decl_253, type, esk39_3: $i > $i > $i > $i). 392.69/52.86 thf(decl_254, type, esk40_3: $i > $i > $i > $i). 392.69/52.86 thf(decl_255, type, esk41_2: $i > $i > $i). 392.69/52.86 thf(decl_256, type, esk42_2: $i > ($i > $o) > $i). 392.69/52.86 thf(decl_257, type, esk43_2: $i > ($i > $o) > $i). 392.69/52.86 thf(decl_258, type, esk44_2: $i > ($i > $o) > $i). 392.69/52.86 thf(decl_259, type, esk45_3: $i > ($i > $o) > $i > $i). 392.69/52.86 thf(decl_260, type, esk46_2: $i > ($i > $o) > $i). 392.69/52.86 thf(decl_261, type, esk47_2: $i > ($i > $o) > $i). 392.69/52.86 thf(decl_262, type, esk48_0: $i). 392.69/52.86 thf(decl_263, type, esk49_0: $i). 392.69/52.86 thf(decl_264, type, esk50_0: $i). 392.69/52.86 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', dsetconstr__Cong)). 392.69/52.86 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', exuI3)). 392.69/52.86 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', exuI1)). 392.69/52.86 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.Et5BI9ZfO1/E---3.1_15766.p', exuI2)). 392.69/52.86 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.Et5BI9ZfO1/E---3.1_15766.p', emptyE1)). 392.69/52.86 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', sepInPowerset)). 392.69/52.86 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setoftrueEq)). 392.69/52.86 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', exuE3u)). 392.69/52.86 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', exu__Cong)). 392.69/52.86 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', nonemptyI)). 392.69/52.86 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', dsetconstrER)). 392.69/52.86 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', dsetconstrEL)). 392.69/52.86 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', descrp)). 392.69/52.86 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', exuEu)). 392.69/52.86 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', descr__Cong)). 392.69/52.86 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', replAx)). 392.69/52.86 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', ex1I)). 392.69/52.86 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', singletonprop)). 392.69/52.86 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', kfstsingleton)). 392.69/52.86 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', ex1I2)). 392.69/52.86 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', ex1E1)). 392.69/52.86 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', sepSubset)). 392.69/52.86 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.Et5BI9ZfO1/E---3.1_15766.p', exuE2)). 392.69/52.86 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setbeta)). 392.69/52.86 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', exuE3e)). 392.69/52.86 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', exuE1)). 392.69/52.86 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', dsetconstrI)). 392.69/52.86 thf(cartprodfstin, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((((((((dsetconstrI)=>((((exuE1)=>((prop2setE)=>(((emptysetimpfalse)=>(((exuE3e)=>((setext)=>((emptyI)=>(((setbeta)=>((nonemptyE1)=>((((((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>(((powersetI)=>((((powersetE)=>(((setunionE)=>(((exuE2)=>((nonemptyImpWitness)=>(((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>(((upairsetIL)=>((upairsetIR)=>((((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>((((((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>(((setadjoin__Cong)=>((((omega__Cong)=>((exuEu)=>((descr__Cong)=>(((((eqimpsubset1)=>((((subsetE)=>(((notsubsetI)=>((((subsetRefl)=>((subsetTrans)=>((((subset2powerset)=>(((subsetemptysetimpeq)=>((powersetI1)=>(((inPowerset)=>(((sepInPowerset)=>((((upairset2IR)=>((((binunionE)=>((binunionLsub)=>((((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((((disjointsetsI1)=>((binintersectRsub)=>(((binintersectSubset1)=>(((setminusI)=>((setminusEL)=>((setminusER)=>((((setminusELneg)=>(((((setminusSubset1)=>(((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>(((setukpairIR)=>((((singletonsubset)=>((((upairset2E)=>(((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>(((((cartprodmempair)=>(((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>(((ex1I)=>((((((theprop)=>(![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))<=(kfstpairEq)))<=(kfstsingleton))<=(setukpairinjL1))<=(singletonsuniq))<=(ex1I2)))<=(ex1E1))))))<=(setunionE2)))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3)))))<=(upairsubunion)))<=(singletoninpowunion))<=(singletoninpowerset)))<=(kpairp))<=(kpairiskpair)))<=(setukpairIL)))))))<=(symdiffE)))<=(setminusLsub))<=(setminusIRneg))<=(setminusILneg)))<=(setminusERneg))<=(setminusSubset2)))))<=(bs114d)))<=(binintersectSubset4))))<=(binintersectER))<=(binintersectSubset3))))))<=(binintersectI))<=(binunionRsub))))<=(binunionEcases))<=(binunionIR)))<=(binunionIL))<=(sepSubset)))<=(powersetsubset)))<=(powersetE1))))<=(setextsub)))<=(setadjoinSub2))<=(setadjoinSub))))<=(notequalI2))<=(notequalI1)))<=(subsetE2)))<=(emptysetsubset))<=(subsetI2)))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong)))))<=(setunion__Cong))<=(powerset__Cong)))<=(emptyset__Cong)))))))<=(exuI3))<=(exuI1))<=(notdallE))<=(notdexE))))<=(quantDeMorgan4)))))<=(vacuousDall))<=(emptyE1))))<=(upairsetE)))))<=(uniqinunit))))<=(subPowSU)))<=(setunionI)))<=(emptyInPowerset))<=(emptyinPowerset)))<=(setoftrueEq)))))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI))))<=(noeltsimpempty)))))<=(notinemptyset)))<=(emptysetE))))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp))<=(wellorderingAx))<=(foundationAx))<=(replAx))<=(omegaIndAx))<=(omegaSAx)))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', cartprodfstin)). 392.69/52.86 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', eqinunit)). 392.69/52.86 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', emptyInPowerset)). 392.69/52.86 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', omegaSAx)). 392.69/52.86 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', notequalI1)). 392.69/52.86 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', notinsingleton)). 392.69/52.86 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', subsetE2)). 392.69/52.86 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', upairsetIR)). 392.69/52.86 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', emptysetsubset)). 392.69/52.86 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', subsetI2)). 392.69/52.86 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', quantDeMorgan1)). 392.69/52.86 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', eqimpsubset2)). 392.69/52.86 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', subsetI1)). 392.69/52.86 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', quantDeMorgan2)). 392.69/52.86 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setunion__Cong)). 392.69/52.86 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', powerset__Cong)). 392.69/52.86 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', quantDeMorgan3)). 392.69/52.86 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', emptyset__Cong)). 392.69/52.86 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', prop2setI)). 392.69/52.86 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', notdallE)). 392.69/52.86 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', notdexE)). 392.69/52.86 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', quantDeMorgan4)). 392.69/52.86 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', vacuousDall)). 392.69/52.86 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', upairsetE)). 392.69/52.86 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', inCongP)). 392.69/52.86 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', uniqinunit)). 392.69/52.86 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', subPowSU)). 392.69/52.86 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', in__Cong)). 392.69/52.86 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setunionI)). 392.69/52.86 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', emptyinPowerset)). 392.69/52.86 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', emptyinunitempty)). 392.69/52.86 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setadjoinIL)). 392.69/52.86 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', nonemptyI1)). 392.69/52.86 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', noeltsimpempty)). 392.69/52.86 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setadjoin__Cong)). 392.69/52.86 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', notinemptyset)). 392.69/52.86 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', emptysetE)). 392.69/52.86 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', omega__Cong)). 392.69/52.86 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', wellorderingAx)). 392.69/52.86 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', foundationAx)). 392.69/52.86 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.Et5BI9ZfO1/E---3.1_15766.p', omegaIndAx)). 392.69/52.86 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', eqimpsubset1)). 392.69/52.86 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', subsetE)). 392.69/52.86 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', singletonsswitch)). 392.69/52.86 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', notsubsetI)). 392.69/52.86 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', subsetRefl)). 392.69/52.86 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', subsetTrans)). 392.69/52.86 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', subset2powerset)). 392.69/52.86 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', subsetemptysetimpeq)). 392.69/52.86 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', powersetI1)). 392.69/52.86 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', inPowerset)). 392.69/52.86 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', theprop)). 392.69/52.86 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', upairset2IR)). 392.69/52.86 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binunionE)). 392.69/52.86 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binunionLsub)). 392.69/52.86 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binintersectSubset5)). 392.69/52.86 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binintersectEL)). 392.69/52.86 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binintersectLsub)). 392.69/52.86 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binintersectSubset2)). 392.69/52.86 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', disjointsetsI1)). 392.69/52.86 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binintersectRsub)). 392.69/52.86 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', upairsetIL)). 392.69/52.86 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binintersectSubset1)). 392.69/52.86 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setminusI)). 392.69/52.86 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setminusEL)). 392.69/52.86 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setminusER)). 392.69/52.86 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setminusELneg)). 392.69/52.86 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setminusSubset1)). 392.69/52.86 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', symdiffI1)). 392.69/52.86 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', symdiffI2)). 392.69/52.86 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', symdiffIneg1)). 392.69/52.86 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', symdiffIneg2)). 392.69/52.86 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', secondinupair)). 392.69/52.86 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setukpairIR)). 392.69/52.86 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', singletonsubset)). 392.69/52.86 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', upairset2E)). 392.69/52.86 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.Et5BI9ZfO1/E---3.1_15766.p', upairinpowunion)). 392.69/52.86 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.Et5BI9ZfO1/E---3.1_15766.p', ubforcartprodlem1)). 392.69/52.86 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.Et5BI9ZfO1/E---3.1_15766.p', ubforcartprodlem2)). 392.69/52.86 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', cartprodmempair)). 392.69/52.86 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setunionsingleton1)). 392.69/52.86 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setunionsingleton2)). 392.69/52.86 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setunionsingleton)). 392.69/52.86 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', kfstpairEq)). 392.69/52.86 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setukpairinjL1)). 392.69/52.86 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', singletonsuniq)). 392.69/52.86 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setunionE2)). 392.69/52.86 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', cartprodmempair1)). 392.69/52.86 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', cartprodpairin)). 392.69/52.86 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', ubforcartprodlem3)). 392.69/52.86 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', upairsubunion)). 392.69/52.86 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', singletoninpowunion)). 392.69/52.86 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', singletoninpowerset)). 392.69/52.86 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', kpairp)). 392.69/52.86 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.Et5BI9ZfO1/E---3.1_15766.p', kpairiskpair)). 392.69/52.86 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.Et5BI9ZfO1/E---3.1_15766.p', setukpairIL)). 392.69/52.86 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.Et5BI9ZfO1/E---3.1_15766.p', symdiffE)). 392.69/52.86 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setminusLsub)). 392.69/52.86 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setminusIRneg)). 392.69/52.86 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setminusILneg)). 392.69/52.86 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setminusERneg)). 392.69/52.86 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setminusSubset2)). 392.69/52.86 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', bs114d)). 392.69/52.86 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binintersectSubset4)). 392.69/52.86 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binintersectER)). 392.69/52.86 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binintersectSubset3)). 392.69/52.86 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binintersectI)). 392.69/52.86 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binunionRsub)). 392.69/52.86 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.Et5BI9ZfO1/E---3.1_15766.p', binunionEcases)). 392.69/52.86 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binunionIR)). 392.69/52.86 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', binunionIL)). 392.69/52.86 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', powersetsubset)). 392.69/52.86 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', powersetE1)). 392.69/52.86 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setextsub)). 392.69/52.86 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setadjoinSub2)). 392.69/52.86 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setadjoinSub)). 392.69/52.86 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', notequalI2)). 392.69/52.86 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', nonemptyImpWitness)). 392.69/52.86 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setunionE)). 392.69/52.86 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', powersetE)). 392.69/52.86 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', powersetI)). 392.69/52.86 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setadjoinOr)). 392.69/52.86 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.Et5BI9ZfO1/E---3.1_15766.p', setadjoinE)). 392.69/52.86 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setadjoinIR)). 392.69/52.86 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', nonemptyE1)). 392.69/52.86 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', emptyI)). 392.69/52.86 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setext)). 392.69/52.86 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', emptysetimpfalse)). 392.69/52.86 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', prop2setE)). 392.69/52.86 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', omega0Ax)). 392.69/52.86 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setunionAx)). 392.69/52.86 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', powersetAx)). 392.69/52.86 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setadjoinAx)). 392.69/52.86 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', emptysetAx)). 392.69/52.86 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Et5BI9ZfO1/E---3.1_15766.p', setextAx)). 392.69/52.86 thf(c_0_162, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 392.69/52.86 thf(c_0_163, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 392.69/52.86 thf(c_0_164, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 392.69/52.86 thf(c_0_165, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 392.69/52.86 thf(c_0_166, 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])). 392.69/52.86 thf(c_0_167, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 392.69/52.86 thf(c_0_168, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 392.69/52.86 thf(c_0_169, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 392.69/52.86 thf(c_0_170, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 392.69/52.86 thf(c_0_171, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 392.69/52.86 thf(c_0_172, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 392.69/52.86 thf(c_0_173, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 392.69/52.86 thf(c_0_174, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 392.69/52.86 thf(c_0_175, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 392.69/52.86 thf(c_0_176, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 392.69/52.86 thf(c_0_177, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 392.69/52.86 thf(c_0_178, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 392.69/52.86 thf(c_0_179, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 392.69/52.86 thf(c_0_180, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 392.69/52.86 thf(c_0_181, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 392.69/52.86 thf(c_0_182, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 392.69/52.86 thf(c_0_183, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 392.69/52.86 thf(c_0_184, 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])). 392.69/52.86 thf(c_0_185, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 392.69/52.86 thf(c_0_186, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 392.69/52.86 thf(c_0_187, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 392.69/52.86 thf(c_0_188, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 392.69/52.86 thf(c_0_189, plain, ((epred1_0)<=>![X866:$i]:(?[X867:$i]:((((![X868:$i]:(((in @ X868 @ X867)=>![X869:$i]:(((in @ X869 @ X868)=>(in @ X869 @ X866)))))&![X870:$i, X871:$i]:((((in @ X870 @ X866)&(in @ X871 @ X866))=>(![X872:$i]:(((in @ X872 @ X867)=>((in @ X870 @ X872)<=>(in @ X871 @ X872))))=>((X870)=(X871))))))&![X873:$i, X874:$i]:((((in @ X873 @ X867)&(in @ X874 @ X867))=>(![X875:$i]:(((in @ X875 @ X873)=>(in @ X875 @ X874)))|![X876:$i]:(((in @ X876 @ X874)=>(in @ X876 @ X873)))))))&![X877:$i]:(((![X878:$i]:(((in @ X878 @ X877)=>(in @ X878 @ X866)))&?[X879:$i]:((in @ X879 @ X877)))=>?[X880:$i, X881:$i]:(((((in @ X880 @ X867)&(in @ X881 @ X877))&~(?[X882:$i]:(((in @ X882 @ X880)&(in @ X882 @ X877)))))&![X883:$i]:(((in @ X883 @ X867)=>(![X884:$i]:(((in @ X884 @ X883)=>(in @ X884 @ X880)))|(in @ X881 @ X883)))))))))))), introduced(definition)). 392.69/52.86 thf(c_0_190, negated_conjecture, ~((![X462:$i, X463:$i]:((![X464:$i]:(((in @ X464 @ X462)<=>(in @ X464 @ X463)))=>((X462)=(X463))))=>(![X465:$i]:(~(in @ X465 @ emptyset))=>(![X466:$i, X467:$i, X468:$i]:(((in @ X468 @ (setadjoin @ X466 @ X467))<=>(((X468)=(X466))|(in @ X468 @ X467))))=>(![X469:$i, X470:$i]:(((in @ X470 @ (powerset @ X469))<=>![X471:$i]:(((in @ X471 @ X470)=>(in @ X471 @ X469)))))=>(![X472:$i, X473:$i]:(((in @ X473 @ (setunion @ X472))<=>?[X474:$i]:(((in @ X473 @ X474)&(in @ X474 @ X472)))))=>((in @ emptyset @ omega)=>(![X898:$i]:(((in @ X898 @ omega)=>(in @ (setadjoin @ X898 @ X898) @ omega)))=>(![X895:$i]:((((in @ emptyset @ X895)&![X896:$i]:((((in @ X896 @ omega)&(in @ X896 @ X895))=>(in @ (setadjoin @ X896 @ X896) @ X895))))=>![X897:$i]:(((in @ X897 @ omega)=>(in @ X897 @ X895)))))=>(![X889:$i > $i > $o, X890:$i]:((![X891:$i]:(((in @ X891 @ X890)=>(exu @ (X889 @ X891))))=>?[X892:$i]:(![X893:$i]:(((in @ X893 @ X892)<=>?[X894:$i]:(((in @ X894 @ X890)&(X889 @ X894 @ X893))))))))=>(![X885:$i]:((?[X886:$i]:((in @ X886 @ X885))=>?[X887:$i]:(((in @ X887 @ X885)&~(?[X888:$i]:(((in @ X888 @ X887)&(in @ X888 @ X885))))))))=>((epred1_0)=>(![X865:$i > $o]:(((exu @ X865)=>(X865 @ (descr @ (^[Z0/* 17 */:$i]:(X865 @ Z0))))))=>(![X475:$i, X476:$i > $o, X477:$i]:(((in @ X477 @ X475)=>((X476 @ X477)=>(in @ X477 @ (dsetconstr @ X475 @ X476)))))=>(![X862:$i, X863:$i > $o, X864:$i]:(((in @ X864 @ (dsetconstr @ X862 @ X863))=>(in @ X864 @ X862)))=>(![X859:$i, X860:$i > $o, X861:$i]:(((in @ X861 @ (dsetconstr @ X859 @ X860))=>(X860 @ X861)))=>(![X478:$i > $o]:(((exu @ X478)=>?[X479:$i]:(((X478 @ X479)&![X480:$i]:(((X478 @ X480)=>((X479)=(X480))))))))=>(![X481:$o, X482:$i]:(((in @ X482 @ (prop2set @ ((X481))))=>(X481)))=>(![X857:$i]:(((in @ X857 @ emptyset)=>![X858:$o]:((X858))))=>(![X483:$i]:(((in @ X483 @ emptyset)=>~($true)))=>(![X856:$i]:(~(in @ X856 @ emptyset))=>(![X484:$i > $o]:(((exu @ X484)=>?[X485:$i]:((X484 @ X485))))=>(![X486:$i, X487:$i]:((![X488:$i]:(((in @ X488 @ X486)=>(in @ X488 @ X487)))=>(![X489:$i]:(((in @ X489 @ X487)=>(in @ X489 @ X486)))=>((X486)=(X487)))))=>(![X490:$i]:((![X491:$i]:(~(in @ X491 @ X490))=>((X490)=(emptyset))))=>(![X854:$i]:((![X855:$i]:(~(in @ X855 @ X854))=>((X854)=(emptyset))))=>(![X492:$i, X493:$i > $o, X494:$i]:(((in @ X494 @ X492)=>((in @ X494 @ (dsetconstr @ X492 @ X493))<=>(X493 @ X494))))=>(![X495:$i]:(((nonempty @ X495)=>?[X496:$i]:((in @ X496 @ X495))))=>(![X851:$i, X852:$i > $o, X853:$i]:(((in @ X853 @ X851)=>((X852 @ X853)=>(nonempty @ (dsetconstr @ X851 @ X852)))))=>(![X849:$i]:((?[X850:$i]:((in @ X850 @ X849))=>(nonempty @ X849)))=>(![X847:$i, X848:$i]:((in @ X847 @ (setadjoin @ X847 @ X848)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X497:$i, X498:$i, X499:$i]:(((in @ X499 @ X498)=>(in @ X499 @ (setadjoin @ X497 @ X498))))=>(![X500:$i, X501:$i, X502:$i]:(((in @ X502 @ (setadjoin @ X500 @ X501))=>![X503:$o]:(((((X502)=(X500))=>(X503))=>(((in @ X502 @ X501)=>(X503))=>(X503))))))=>(![X504:$i, X505:$i, X506:$i]:(((in @ X506 @ (setadjoin @ X504 @ X505))=>(((X506)=(X504))|(in @ X506 @ X505))))=>(![X846:$i]:(((dsetconstr @ X846 @ (^[Z0/* 1 */:$i]:($true)))=(X846)))=>(![X507:$i, X508:$i]:((![X509:$i]:(((in @ X509 @ X508)=>(in @ X509 @ X507)))=>(in @ X508 @ (powerset @ X507))))=>(![X845:$i]:((in @ emptyset @ (powerset @ X845)))=>(![X844:$i]:((in @ emptyset @ (powerset @ X844)))=>(![X510:$i, X511:$i, X512:$i]:(((in @ X511 @ (powerset @ X510))=>((in @ X512 @ X511)=>(in @ X512 @ X510))))=>(![X841:$i, X842:$i, X843:$i]:(((in @ X842 @ X843)=>((in @ X843 @ X841)=>(in @ X842 @ (setunion @ X841)))))=>(![X513:$i, X514:$i]:(((in @ X514 @ (setunion @ X513))=>![X515:$o]:((![X516:$i]:(((in @ X514 @ X516)=>((in @ X516 @ X513)=>(X515))))=>(X515)))))=>(![X839:$i, X840:$i]:(((in @ X840 @ X839)=>(in @ X840 @ (powerset @ (setunion @ X839)))))=>(![X517:$i > $o]:(((exu @ X517)=>?[X518:$i]:(![X519:$i]:(((X517 @ X519)<=>((X519)=(X518)))))))=>(![X520:$i]:(((nonempty @ X520)=>?[X521:$i]:(((in @ X521 @ X520)&$true))))=>(![X837:$i, X838:$i]:(((in @ X837 @ (setadjoin @ X838 @ emptyset))=>((X837)=(X838))))=>(![X522:$i, X523:$i]:((((X522)!=(X523))=>~(in @ X523 @ (setadjoin @ X522 @ emptyset))))=>(![X524:$i, X525:$i]:((((X524)=(X525))=>(in @ X524 @ (setadjoin @ X525 @ emptyset))))=>(![X526:$i, X527:$i]:(((in @ X526 @ (setadjoin @ X527 @ emptyset))=>(in @ X527 @ (setadjoin @ X526 @ emptyset))))=>(![X834:$i, X835:$i, X836:$i]:(((in @ X836 @ (setadjoin @ X834 @ (setadjoin @ X835 @ emptyset)))=>(((X836)=(X834))|((X836)=(X835)))))=>(![X528:$i, X529:$i]:((in @ X528 @ (setadjoin @ X528 @ (setadjoin @ X529 @ emptyset))))=>(![X530:$i, X531:$i]:((in @ X531 @ (setadjoin @ X530 @ (setadjoin @ X531 @ emptyset))))=>(![X831:$i, X832:$i > $o]:((?[X833:$i]:(((in @ X833 @ X831)&(X832 @ X833)))=>(((dsetconstr @ X831 @ X832)=(emptyset))=>~($true))))=>(![X829:$i > $o, X830:$i]:(((in @ X830 @ emptyset)=>(X829 @ X830)))=>(![X532:$i, X533:$i > $o]:((~(![X534:$i]:(((in @ X534 @ X532)=>(X533 @ X534))))=>?[X535:$i]:(((in @ X535 @ X532)&~((X533 @ X535))))))=>(![X536:$i, X537:$i > $o]:((![X538:$i]:(((in @ X538 @ X536)=>~((X537 @ X538))))=>~(?[X539:$i]:(((in @ X539 @ X536)&(X537 @ X539))))))=>(![X540:$i, X541:$i > $o]:((~(?[X542:$i]:(((in @ X542 @ X540)&(X541 @ X542))))=>![X543:$i]:(((in @ X543 @ X540)=>~((X541 @ X543))))))=>(![X825:$i, X826:$i > $o]:((?[X827:$i]:(((in @ X827 @ X825)&~((X826 @ X827))))=>~(![X828:$i]:(((in @ X828 @ X825)=>(X826 @ X828))))))=>(![X544:$o]:(((X544)=>(in @ emptyset @ (prop2set @ ((X544))))))=>((prop2set2propI)=>(![X821:$i, X822:$i > $o]:((~(?[X823:$i]:(((in @ X823 @ X821)&(X822 @ X823))))=>![X824:$i]:(((in @ X824 @ X821)=>~((X822 @ X824))))))=>(![X817:$i, X818:$i > $o]:((~(![X819:$i]:(((in @ X819 @ X817)=>(X818 @ X819))))=>?[X820:$i]:(((in @ X820 @ X817)&~((X818 @ X820))))))=>(![X814:$i > $o]:((?[X815:$i]:(((X814 @ X815)&![X816:$i]:(((X814 @ X816)=>((X815)=(X816))))))=>(exu @ X814)))=>(![X810:$i > $o]:((?[X811:$i]:((X810 @ X811))=>(![X812:$i, X813:$i]:(((X810 @ X812)=>((X810 @ X813)=>((X812)=(X813)))))=>(exu @ X810))))=>(![X545:$i > $o]:((?[X546:$i]:(![X547:$i]:(((X545 @ X547)<=>((X547)=(X546)))))=>(exu @ X545)))=>(![X548:$i, X549:$i]:((((X548)=(X549))=>![X550:$i, X551:$i]:((((X550)=(X551))=>((in @ X550 @ X548)=>(in @ X551 @ X549))))))=>(![X552:$i, X553:$i]:((((X552)=(X553))=>![X554:$i, X555:$i]:((((X554)=(X555))=>((in @ X554 @ X552)<=>(in @ X555 @ X553))))))=>(![X556:$i > $o]:(((exu @ X556)=>![X557:$i, X558:$i]:(((X556 @ X557)=>((X556 @ X558)=>((X557)=(X558)))))))=>(![X559:$i > $o, X560:$i > $o]:((![X561:$i, X562:$i]:((((X561)=(X562))=>((X559 @ X561)<=>(X560 @ X562))))=>((exu @ X559)<=>(exu @ X560))))=>(((emptyset)=(emptyset))=>(![X563:$i, X564:$i]:((((X563)=(X564))=>![X565:$i, X566:$i]:((((X565)=(X566))=>((setadjoin @ X563 @ X565)=(setadjoin @ X564 @ X566))))))=>(![X808:$i, X809:$i]:((((X808)=(X809))=>((powerset @ X808)=(powerset @ X809))))=>(![X806:$i, X807:$i]:((((X806)=(X807))=>((setunion @ X806)=(setunion @ X807))))=>(((omega)=(omega))=>(![X567:$i > $o]:(((exu @ X567)=>![X568:$i, X569:$i]:(((X567 @ X568)=>((X567 @ X569)=>((X568)=(X569)))))))=>(![X570:$i > $o, X571:$i > $o]:((![X572:$i, X573:$i]:((((X572)=(X573))=>((X570 @ X572)<=>(X571 @ X573))))=>((exu @ X570)=>((exu @ X571)=>((descr @ X570)=(descr @ X571))))))=>(![X800:$i, X801:$i]:((((X800)=(X801))=>![X802:$i > $o, X803:$i > $o]:((![X804:$i]:(((in @ X804 @ X800)=>![X805:$i]:(((in @ X805 @ X801)=>(((X804)=(X805))=>((X802 @ X804)<=>(X803 @ X805)))))))=>((dsetconstr @ X800 @ X802)=(dsetconstr @ X801 @ X803))))))=>(![X797:$i, X798:$i]:((![X799:$i]:(((in @ X799 @ X797)=>(in @ X799 @ X798)))=>(subset @ X797 @ X798)))=>(![X795:$i, X796:$i]:((((X795)=(X796))=>(subset @ X796 @ X795)))=>(![X574:$i, X575:$i]:((((X574)=(X575))=>(subset @ X574 @ X575)))=>(![X792:$i, X793:$i]:((![X794:$i]:(((in @ X794 @ X792)=>(in @ X794 @ X793)))=>(subset @ X792 @ X793)))=>(![X791:$i]:((subset @ emptyset @ X791))=>(![X576:$i, X577:$i, X578:$i]:(((subset @ X576 @ X577)=>((in @ X578 @ X576)=>(in @ X578 @ X577))))=>(![X788:$i, X789:$i, X790:$i]:(((subset @ X788 @ X789)=>(~(in @ X790 @ X789)=>~(in @ X790 @ X788))))=>(![X579:$i, X580:$i, X581:$i]:(((in @ X581 @ X579)=>(~(in @ X581 @ X580)=>~(subset @ X579 @ X580))))=>(![X786:$i, X787:$i]:((~(subset @ X786 @ X787)=>((X786)!=(X787))))=>(![X783:$i, X784:$i, X785:$i]:(((in @ X785 @ X783)=>(~(in @ X785 @ X784)=>((X783)!=(X784)))))=>(![X582:$i]:((subset @ X582 @ X582))=>(![X583:$i, X584:$i, X585:$i]:(((subset @ X583 @ X584)=>((subset @ X584 @ X585)=>(subset @ X583 @ X585))))=>(![X781:$i, X782:$i]:((subset @ X782 @ (setadjoin @ X781 @ X782)))=>(![X778:$i, X779:$i, X780:$i]:(((subset @ X778 @ X780)=>(subset @ X778 @ (setadjoin @ X779 @ X780))))=>(![X586:$i, X587:$i]:(((subset @ X586 @ X587)=>(in @ X586 @ (powerset @ X587))))=>(![X776:$i, X777:$i]:(((subset @ X776 @ X777)=>((subset @ X777 @ X776)=>((X776)=(X777)))))=>(![X588:$i]:(((subset @ X588 @ emptyset)=>((X588)=(emptyset))))=>(![X589:$i, X590:$i]:(((subset @ X590 @ X589)=>(in @ X590 @ (powerset @ X589))))=>(![X774:$i, X775:$i]:(((in @ X775 @ (powerset @ X774))=>(subset @ X775 @ X774)))=>(![X591:$i]:((in @ X591 @ (powerset @ X591)))=>(![X772:$i, X773:$i]:(((subset @ X772 @ X773)=>(subset @ (powerset @ X772) @ (powerset @ X773))))=>(![X592:$i, X593:$i > $o]:((in @ (dsetconstr @ X592 @ X593) @ (powerset @ X592)))=>(![X770:$i, X771:$i > $o]:((subset @ (dsetconstr @ X770 @ X771) @ X770))=>(![X767:$i, X768:$i, X769:$i]:(((in @ X769 @ X767)=>(in @ X769 @ (binunion @ X767 @ X768))))=>(![X594:$i, X595:$i]:((in @ X595 @ (setadjoin @ X594 @ (setadjoin @ X595 @ emptyset))))=>(![X764:$i, X765:$i, X766:$i]:(((in @ X766 @ X765)=>(in @ X766 @ (binunion @ X764 @ X765))))=>(![X760:$i, X761:$i, X762:$i, X763:$o]:(((in @ X762 @ (binunion @ X760 @ X761))=>(((in @ X762 @ X760)=>(X763))=>(((in @ X762 @ X761)=>(X763))=>(X763)))))=>(![X596:$i, X597:$i, X598:$i]:(((in @ X598 @ (binunion @ X596 @ X597))=>((in @ X598 @ X596)|(in @ X598 @ X597))))=>(![X599:$i, X600:$i]:((subset @ X599 @ (binunion @ X599 @ X600)))=>(![X758:$i, X759:$i]:((subset @ X759 @ (binunion @ X758 @ X759)))=>(![X755:$i, X756:$i, X757:$i]:(((in @ X757 @ X755)=>((in @ X757 @ X756)=>(in @ X757 @ (binintersect @ X755 @ X756)))))=>(![X601:$i, X602:$i, X603:$i]:(((subset @ X603 @ X601)=>((subset @ X603 @ X602)=>(subset @ X603 @ (binintersect @ X601 @ X602)))))=>(![X604:$i, X605:$i, X606:$i]:(((in @ X606 @ (binintersect @ X604 @ X605))=>(in @ X606 @ X604)))=>(![X607:$i, X608:$i]:((subset @ (binintersect @ X607 @ X608) @ X607))=>(![X609:$i, X610:$i]:(((subset @ X609 @ X610)=>((binintersect @ X609 @ X610)=(X609))))=>(![X753:$i, X754:$i]:((((binintersect @ X753 @ X754)=(X754))=>(subset @ X754 @ X753)))=>(![X750:$i, X751:$i, X752:$i]:(((in @ X752 @ (binintersect @ X750 @ X751))=>(in @ X752 @ X751)))=>(![X611:$i, X612:$i]:((~(?[X613:$i]:(((in @ X613 @ X611)&(in @ X613 @ X612))))=>((binintersect @ X611 @ X612)=(emptyset))))=>(![X614:$i, X615:$i]:((subset @ (binintersect @ X614 @ X615) @ X615))=>(![X748:$i, X749:$i]:(((subset @ X749 @ X748)=>((binintersect @ X748 @ X749)=(X749))))=>(![X616:$i, X617:$i]:((((binintersect @ X616 @ X617)=(X616))=>(subset @ X616 @ X617)))=>(![X745:$i, X746:$i, X747:$i]:(((binintersect @ X745 @ (binunion @ X746 @ X747))=(binunion @ (binintersect @ X745 @ X746) @ (binintersect @ X745 @ X747))))=>(![X618:$i, X619:$i, X620:$i]:(((in @ 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X676)=>((X677 @ X679)=>((X679)=(X678)))))=>(ex1 @ X676 @ X677)))))=>(![X689:$i, X690:$i > $o]:((![X691:$i]:(((in @ X691 @ X689)=>![X692:$i]:(((in @ X692 @ X689)=>((X690 @ X691)=>((X690 @ X692)=>((X691)=(X692))))))))=>(?[X693:$i]:(((in @ X693 @ X689)&(X690 @ X693)))=>(ex1 @ X689 @ X690))))=>(![X687:$i, X688:$i]:((((setadjoin @ X687 @ emptyset)=(setadjoin @ X688 @ emptyset))=>((X687)=(X688))))=>(![X684:$i, X685:$i, X686:$i]:(((in @ (setadjoin @ X686 @ emptyset) @ (setadjoin @ (setadjoin @ X684 @ emptyset) @ (setadjoin @ (setadjoin @ X684 @ (setadjoin @ X685 @ emptyset)) @ emptyset)))=>((X684)=(X686))))=>(![X683:$i]:(((iskpair @ X683)=>(singleton @ (dsetconstr @ (setunion @ X683) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X683)))))))=>(![X680:$i]:(((singleton @ X680)=>(in @ (setunion @ X680) @ X680)))=>(![X681:$i, X682:$i]:(((kfst @ (kpair @ X681 @ X682))=(X681)))=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[cartprodfstin]), eqinunit]), emptyInPowerset]), omegaSAx]), notequalI1]), notinsingleton]), subsetE2]), upairsetIR]), emptysetsubset]), subsetI2]), quantDeMorgan1]), eqimpsubset2]), subsetI1]), c_0_162]), quantDeMorgan2]), setunion__Cong]), powerset__Cong]), quantDeMorgan3]), emptyset__Cong]), c_0_163]), c_0_164]), prop2setI]), notdallE]), notdexE]), c_0_165]), quantDeMorgan4]), vacuousDall]), c_0_166]), upairsetE]), inCongP]), uniqinunit]), subPowSU]), in__Cong]), setunionI]), c_0_167]), emptyinPowerset]), c_0_168]), c_0_169]), emptyinunitempty]), setadjoinIL]), c_0_170]), nonemptyI1]), c_0_171]), noeltsimpempty]), setadjoin__Cong]), notinemptyset]), emptysetE]), omega__Cong]), c_0_172]), c_0_173]), c_0_174]), c_0_175]), wellorderingAx]), foundationAx]), c_0_176]), c_0_177]), omegaIndAx]), eqimpsubset1]), subsetE]), singletonsswitch]), notsubsetI]), subsetRefl]), subsetTrans]), subset2powerset]), subsetemptysetimpeq]), powersetI1]), inPowerset]), c_0_178]), theprop]), upairset2IR]), binunionE]), binunionLsub]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), disjointsetsI1]), binintersectRsub]), upairsetIL]), binintersectSubset1]), setminusI]), setminusEL]), setminusER]), setminusELneg]), setminusSubset1]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIR]), singletonsubset]), upairset2E]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), cartprodmempair]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_179]), kfstpairEq]), c_0_180]), setukpairinjL1]), singletonsuniq]), c_0_181]), c_0_182]), setunionE2]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), upairsubunion]), singletoninpowunion]), singletoninpowerset]), kpairp]), kpairiskpair]), setukpairIL]), symdiffE]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusERneg]), setminusSubset2]), bs114d]), binintersectSubset4]), binintersectER]), binintersectSubset3]), binintersectI]), binunionRsub]), binunionEcases]), binunionIR]), binunionIL]), c_0_183]), powersetsubset]), powersetE1]), setextsub]), setadjoinSub2]), setadjoinSub]), notequalI2]), nonemptyImpWitness]), c_0_184]), setunionE]), powersetE]), powersetI]), setadjoinOr]), setadjoinE]), setadjoinIR]), nonemptyE1]), c_0_185]), emptyI]), setext]), c_0_186]), emptysetimpfalse]), prop2setE]), c_0_187]), c_0_188]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_189])). 392.69/52.86 thf(c_0_191, negated_conjecture, ![X899:$i, X900:$i, X902:$i, X903:$i, X904:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X912:$i, X913:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$i, X921:$i, X922:$i > $i > $o, X923:$i, X926:$i, X928:$i, X929:$i, X930:$i, X931:$i, X933:$i, X934:$i > $o, X935:$i, X936:$i > $o, X937:$i, X938:$i, X939:$i > $o, X940:$i, X941:$i, X942:$i > $o, X943:$i, X944:$i > $o, X946:$i, X947:$o, X948:$i, X949:$i, X950:$o, X951:$i, X952:$i, X953:$i > $o, X955:$i, X956:$i, X959:$i, X961:$i, X963:$i, X964:$i > $o, X965:$i, X966:$i, X968:$i, X969:$i > $o, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i, X977:$i, X978:$i, X979:$i, X980:$i, X981:$o, X982:$i, X983:$i, X984:$i, X985:$i, X986:$i, X987:$i, X989:$i, X990:$i, X991:$i, X992:$i, X993:$i, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i, X999:$o, X1001:$i, X1002:$i, X1003:$i > $o, X1005:$i, X1006:$i, X1007:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i > $o, X1026:$i, X1027:$i > $o, X1028:$i, X1029:$i, X1030:$i > $o, X1031:$i, X1033:$i, X1034:$i > $o, X1036:$i, X1037:$i, X1038:$i > $o, X1040:$i, X1041:$i, X1042:$i > $o, X1043:$i, X1045:$o, X1046:$i, X1047:$i > $o, X1049:$i, X1050:$i, X1051:$i > $o, X1052:$i, X1054:$i > $o, X1055:$i, X1057:$i > $o, X1058:$i, X1061:$i > $o, X1062:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i > $o, X1073:$i, X1074:$i, X1075:$i > $o, X1076:$i > $o, X1079:$i, X1080:$i, X1081:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i > $o, X1088:$i, X1089:$i, X1090:$i > $o, X1091:$i > $o, X1094:$i, X1095:$i, X1096:$i > $o, X1097:$i > $o, X1100:$i, X1101:$i, X1103:$i, X1104:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i > $o, X1148:$i, X1149:$i > $o, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$o, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1228:$i, X1229:$o, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$i, X1264:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i > $o, X1304:$i, X1305:$i, X1306:$i > $o, X1308:$i, X1309:$i > $o, X1310:$i, X1312:$i, X1313:$i > $o, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i]:((((~(in @ (esk1_2 @ X899 @ X900) @ X899)|~(in @ (esk1_2 @ X899 @ X900) @ X900)|((X899)=(X900)))&((in @ (esk1_2 @ X899 @ X900) @ X899)|(in @ (esk1_2 @ X899 @ X900) @ X900)|((X899)=(X900))))&(~(in @ X902 @ emptyset)&(((~(in @ X905 @ (setadjoin @ X903 @ X904))|(((X905)=(X903))|(in @ X905 @ X904)))&((((X905)!=(X903))|(in @ X905 @ (setadjoin @ X903 @ X904)))&(~(in @ X905 @ X904)|(in @ X905 @ (setadjoin @ X903 @ X904)))))&(((~(in @ X907 @ (powerset @ X906))|(~(in @ X908 @ X907)|(in @ X908 @ X906)))&(((in @ (esk2_2 @ X909 @ X910) @ X910)|(in @ X910 @ (powerset @ X909)))&(~(in @ (esk2_2 @ X909 @ X910) @ X909)|(in @ X910 @ (powerset @ X909)))))&(((((in @ X913 @ (esk3_2 @ X912 @ X913))|~(in @ X913 @ (setunion @ X912)))&((in @ (esk3_2 @ X912 @ X913) @ X912)|~(in @ X913 @ (setunion @ X912))))&(~(in @ X916 @ X917)|~(in @ X917 @ X915)|(in @ X916 @ (setunion @ X915))))&((in @ emptyset @ omega)&((~(in @ X918 @ omega)|(in @ (setadjoin @ X918 @ X918) @ omega))&(((((in @ (esk4_1 @ X919) @ omega)|~(in @ emptyset @ X919)|(~(in @ X921 @ omega)|(in @ X921 @ X919)))&((in @ (esk4_1 @ X919) @ X919)|~(in @ emptyset @ X919)|(~(in @ X921 @ omega)|(in @ X921 @ X919))))&(~(in @ (setadjoin @ (esk4_1 @ X919) @ (esk4_1 @ X919)) @ X919)|~(in @ emptyset @ X919)|(~(in @ X921 @ omega)|(in @ X921 @ X919))))&((((((in @ (esk7_3 @ X922 @ X923 @ X926) @ X923)|~(in @ X926 @ (esk6_2 @ X922 @ X923))|(in @ (esk5_2 @ X922 @ X923) @ X923))&((X922 @ (esk7_3 @ X922 @ X923 @ X926) @ X926)|~(in @ X926 @ (esk6_2 @ X922 @ X923))|(in @ (esk5_2 @ X922 @ X923) @ X923)))&(~(in @ X929 @ X923)|~(X922 @ X929 @ X928)|(in @ X928 @ (esk6_2 @ X922 @ X923))|(in @ (esk5_2 @ X922 @ X923) @ X923)))&((((in @ (esk7_3 @ X922 @ X923 @ X926) @ X923)|~(in @ X926 @ (esk6_2 @ X922 @ X923))|~(exu @ (X922 @ (esk5_2 @ X922 @ X923))))&((X922 @ (esk7_3 @ X922 @ X923 @ X926) @ X926)|~(in @ X926 @ (esk6_2 @ X922 @ X923))|~(exu @ (X922 @ (esk5_2 @ X922 @ X923)))))&(~(in @ X929 @ X923)|~(X922 @ X929 @ X928)|(in @ X928 @ (esk6_2 @ X922 @ X923))|~(exu @ (X922 @ (esk5_2 @ X922 @ X923))))))&((((in @ (esk8_1 @ X930) @ X930)|~(in @ X931 @ X930))&(~(in @ X933 @ (esk8_1 @ X930))|~(in @ X933 @ X930)|~(in @ X931 @ X930)))&((epred1_0)&((~(exu @ X934)|(X934 @ (descr @ X934)))&((~(in @ X937 @ X935)|(~(X936 @ X937)|(in @ X937 @ (dsetconstr @ X935 @ X936))))&((~(in @ X940 @ (dsetconstr @ X938 @ X939))|(in @ X940 @ X938))&((~(in @ X943 @ (dsetconstr @ X941 @ X942))|(X942 @ X943))&((((X944 @ (esk9_1 @ X944))|~(exu @ X944))&(~(X944 @ X946)|((esk9_1 @ X944)=(X946))|~(exu @ X944)))&((~(in @ X948 @ (prop2set @ ((X947))))|(X947))&((~(in @ X949 @ emptyset)|(X950))&((~(in @ X951 @ emptyset)|~($true))&(~(in @ X952 @ emptyset)&((~(exu @ X953)|(X953 @ (esk10_1 @ X953)))&(((((in @ (esk12_2 @ X955 @ X956) @ X956)|((X955)=(X956))|(in @ (esk11_2 @ X955 @ X956) @ X955))&(~(in @ (esk12_2 @ X955 @ X956) @ X955)|((X955)=(X956))|(in @ (esk11_2 @ X955 @ X956) @ X955)))&(((in @ (esk12_2 @ X955 @ X956) @ X956)|((X955)=(X956))|~(in @ (esk11_2 @ X955 @ X956) @ X956))&(~(in @ (esk12_2 @ X955 @ X956) @ X955)|((X955)=(X956))|~(in @ (esk11_2 @ X955 @ X956) @ X956))))&(((in @ (esk13_1 @ X959) @ X959)|((X959)=(emptyset)))&(((in @ (esk14_1 @ X961) @ X961)|((X961)=(emptyset)))&(((~(in @ X965 @ (dsetconstr @ X963 @ X964))|(X964 @ X965)|~(in @ X965 @ X963))&(~(X964 @ X965)|(in @ X965 @ (dsetconstr @ X963 @ X964))|~(in @ X965 @ X963)))&((~(nonempty @ X966)|(in @ (esk15_1 @ X966) @ X966))&((~(in @ X970 @ X968)|(~(X969 @ X970)|(nonempty @ (dsetconstr @ X968 @ X969))))&((~(in @ X972 @ X971)|(nonempty @ X971))&((in @ X973 @ (setadjoin @ X973 @ X974))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X977 @ X976)|(in @ X977 @ (setadjoin @ X975 @ X976)))&(((((in @ X980 @ X979)|(X981)|((X980)=(X978))|~(in @ X980 @ (setadjoin @ X978 @ X979)))&(~(X981)|(X981)|((X980)=(X978))|~(in @ X980 @ (setadjoin @ X978 @ X979))))&(((in @ X980 @ X979)|(X981)|~(X981)|~(in @ X980 @ (setadjoin @ X978 @ X979)))&(~(X981)|(X981)|~(X981)|~(in @ X980 @ (setadjoin @ X978 @ X979)))))&((~(in @ X984 @ (setadjoin @ X982 @ X983))|(((X984)=(X982))|(in @ X984 @ X983)))&(((dsetconstr @ X985 @ (^[Z0/* 1 */:$i]:($true)))=(X985))&((((in @ (esk16_2 @ X986 @ X987) @ X987)|(in @ X987 @ (powerset @ X986)))&(~(in @ (esk16_2 @ X986 @ X987) @ X986)|(in @ X987 @ (powerset @ X986))))&((in @ emptyset @ (powerset @ X989))&((in @ emptyset @ (powerset @ X990))&((~(in @ X992 @ (powerset @ X991))|(~(in @ X993 @ X992)|(in @ X993 @ X991)))&((~(in @ X995 @ X996)|(~(in @ X996 @ X994)|(in @ X995 @ (setunion @ X994))))&((((in @ X998 @ (esk17_3 @ X997 @ 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X1086)))&(((omega)=(omega))&((~(exu @ X1087)|(~(X1087 @ X1088)|(~(X1087 @ X1089)|((X1088)=(X1089)))))&(((((esk32_2 @ X1090 @ X1091)=(esk33_2 @ X1090 @ X1091))|(~(exu @ X1090)|(~(exu @ X1091)|((descr @ X1090)=(descr @ X1091)))))&((~(X1090 @ (esk32_2 @ X1090 @ X1091))|~(X1091 @ (esk33_2 @ X1090 @ X1091))|(~(exu @ X1090)|(~(exu @ X1091)|((descr @ X1090)=(descr @ X1091)))))&((X1090 @ (esk32_2 @ X1090 @ X1091))|(X1091 @ (esk33_2 @ X1090 @ X1091))|(~(exu @ X1090)|(~(exu @ X1091)|((descr @ X1090)=(descr @ X1091)))))))&((((in @ (esk34_4 @ X1094 @ X1095 @ X1096 @ X1097) @ X1094)|((dsetconstr @ X1094 @ X1096)=(dsetconstr @ X1095 @ X1097))|((X1094)!=(X1095)))&(((in @ (esk35_4 @ X1094 @ X1095 @ X1096 @ X1097) @ X1095)|((dsetconstr @ X1094 @ X1096)=(dsetconstr @ X1095 @ X1097))|((X1094)!=(X1095)))&((((esk34_4 @ X1094 @ X1095 @ X1096 @ X1097)=(esk35_4 @ X1094 @ X1095 @ X1096 @ X1097))|((dsetconstr @ X1094 @ X1096)=(dsetconstr @ X1095 @ X1097))|((X1094)!=(X1095)))&((~(X1096 @ (esk34_4 @ X1094 @ X1095 @ X1096 @ X1097))|~(X1097 @ (esk35_4 @ X1094 @ X1095 @ X1096 @ X1097))|((dsetconstr @ X1094 @ X1096)=(dsetconstr @ X1095 @ X1097))|((X1094)!=(X1095)))&((X1096 @ (esk34_4 @ X1094 @ X1095 @ X1096 @ X1097))|(X1097 @ (esk35_4 @ X1094 @ X1095 @ X1096 @ X1097))|((dsetconstr @ X1094 @ X1096)=(dsetconstr @ X1095 @ X1097))|((X1094)!=(X1095)))))))&((((in @ (esk36_2 @ X1100 @ X1101) @ X1100)|(subset @ X1100 @ X1101))&(~(in @ (esk36_2 @ X1100 @ X1101) @ X1101)|(subset @ X1100 @ X1101)))&((((X1103)!=(X1104))|(subset @ X1104 @ X1103))&((((X1105)!=(X1106))|(subset @ X1105 @ X1106))&((((in @ (esk37_2 @ X1107 @ X1108) @ X1107)|(subset @ X1107 @ X1108))&(~(in @ (esk37_2 @ X1107 @ X1108) @ X1108)|(subset @ X1107 @ X1108)))&((subset @ emptyset @ X1110)&((~(subset @ X1111 @ X1112)|(~(in @ X1113 @ X1111)|(in @ X1113 @ X1112)))&((~(subset @ X1114 @ X1115)|((in @ X1116 @ X1115)|~(in @ X1116 @ X1114)))&((~(in @ X1119 @ X1117)|((in @ X1119 @ X1118)|~(subset @ X1117 @ X1118)))&(((subset @ X1120 @ X1121)|((X1120)!=(X1121)))&((~(in @ X1124 @ X1122)|((in @ X1124 @ X1123)|((X1122)!=(X1123))))&((subset @ X1125 @ X1125)&((~(subset @ X1126 @ X1127)|(~(subset @ X1127 @ X1128)|(subset @ X1126 @ X1128)))&((subset @ X1130 @ (setadjoin @ X1129 @ X1130))&((~(subset @ X1131 @ X1133)|(subset @ X1131 @ (setadjoin @ X1132 @ X1133)))&((~(subset @ X1134 @ X1135)|(in @ X1134 @ (powerset @ X1135)))&((~(subset @ X1136 @ X1137)|(~(subset @ X1137 @ X1136)|((X1136)=(X1137))))&((~(subset @ X1138 @ emptyset)|((X1138)=(emptyset)))&((~(subset @ X1140 @ X1139)|(in @ X1140 @ (powerset @ X1139)))&((~(in @ X1142 @ (powerset @ X1141))|(subset @ X1142 @ X1141))&((in @ X1143 @ (powerset @ X1143))&((~(subset @ X1144 @ X1145)|(subset @ (powerset @ X1144) @ (powerset @ X1145)))&((in @ (dsetconstr @ X1146 @ X1147) @ (powerset @ X1146))&((subset @ (dsetconstr @ X1148 @ X1149) @ X1148)&((~(in @ X1152 @ X1150)|(in @ X1152 @ (binunion @ X1150 @ X1151)))&((in @ X1154 @ (setadjoin @ X1153 @ (setadjoin @ X1154 @ emptyset)))&((~(in @ X1157 @ X1156)|(in @ X1157 @ (binunion @ X1155 @ X1156)))&(((((in @ X1160 @ X1159)|(X1161)|(in @ X1160 @ X1158)|~(in @ X1160 @ (binunion @ X1158 @ X1159)))&(~(X1161)|(X1161)|(in @ X1160 @ X1158)|~(in @ X1160 @ (binunion @ X1158 @ X1159))))&(((in @ X1160 @ X1159)|(X1161)|~(X1161)|~(in @ X1160 @ (binunion @ X1158 @ X1159)))&(~(X1161)|(X1161)|~(X1161)|~(in @ X1160 @ (binunion @ X1158 @ X1159)))))&((~(in @ X1164 @ (binunion @ X1162 @ X1163))|((in @ X1164 @ X1162)|(in @ X1164 @ X1163)))&((subset @ X1165 @ (binunion @ X1165 @ X1166))&((subset @ X1168 @ (binunion @ X1167 @ X1168))&((~(in @ X1171 @ X1169)|(~(in @ X1171 @ X1170)|(in @ X1171 @ (binintersect @ X1169 @ X1170))))&((~(subset @ X1174 @ X1172)|(~(subset @ X1174 @ X1173)|(subset @ X1174 @ (binintersect @ X1172 @ X1173))))&((~(in @ X1177 @ (binintersect @ X1175 @ X1176))|(in @ X1177 @ X1175))&((subset @ (binintersect @ X1178 @ X1179) @ X1178)&((~(subset @ X1180 @ X1181)|((binintersect @ X1180 @ X1181)=(X1180)))&((((binintersect @ X1182 @ X1183)!=(X1183))|(subset @ X1183 @ X1182))&((~(in @ X1186 @ (binintersect @ X1184 @ X1185))|(in @ X1186 @ X1185))&((((in @ (esk38_2 @ X1187 @ X1188) @ X1187)|((binintersect @ X1187 @ X1188)=(emptyset)))&((in @ (esk38_2 @ X1187 @ X1188) @ X1188)|((binintersect @ X1187 @ X1188)=(emptyset))))&((subset @ (binintersect @ X1190 @ X1191) @ X1191)&((~(subset @ X1193 @ X1192)|((binintersect @ X1192 @ X1193)=(X1193)))&((((binintersect @ X1194 @ X1195)!=(X1194))|(subset @ X1194 @ X1195))&(((binintersect @ X1196 @ (binunion @ X1197 @ X1198))=(binunion @ (binintersect @ X1196 @ X1197) @ (binintersect @ X1196 @ X1198)))&((~(in @ X1201 @ X1199)|((in @ X1201 @ X1200)|(in @ X1201 @ (setminus @ X1199 @ X1200))))&((~(in @ X1204 @ (setminus @ X1202 @ X1203))|(in @ X1204 @ X1202))&((~(in @ X1207 @ (setminus @ X1205 @ X1206))|~(in @ X1207 @ X1206))&((~(subset @ X1208 @ X1209)|((setminus @ X1208 @ X1209)=(emptyset)))&(((in @ X1212 @ (setminus @ X1210 @ X1211))|(~(in @ X1212 @ X1210)|(in @ X1212 @ X1211)))&(((in @ X1215 @ (setminus @ X1213 @ X1214))|((in @ X1215 @ X1214)|~(in @ X1215 @ X1213)))&(((in @ X1218 @ X1216)|~(in @ X1218 @ (setminus @ X1216 @ X1217)))&((~(in @ X1221 @ X1220)|~(in @ X1221 @ (setminus @ X1219 @ X1220)))&((subset @ (setminus @ X1222 @ X1223) @ X1222)&((((setminus @ X1224 @ X1225)!=(emptyset))|(subset @ X1224 @ X1225))&((((~(in @ X1228 @ X1226)|(X1229)|(in @ X1228 @ X1226)|~(in @ X1228 @ (symdiff @ X1226 @ X1227)))&(((in @ X1228 @ X1227)|(X1229)|(in @ X1228 @ X1226)|~(in @ X1228 @ (symdiff @ X1226 @ X1227)))&(~(X1229)|(X1229)|(in @ X1228 @ X1226)|~(in @ X1228 @ (symdiff @ X1226 @ X1227)))))&(((~(in @ X1228 @ X1226)|(X1229)|~(in @ X1228 @ X1227)|~(in @ X1228 @ (symdiff @ X1226 @ X1227)))&(((in @ X1228 @ X1227)|(X1229)|~(in @ X1228 @ X1227)|~(in @ X1228 @ (symdiff @ X1226 @ X1227)))&(~(X1229)|(X1229)|~(in @ X1228 @ X1227)|~(in @ X1228 @ (symdiff @ X1226 @ X1227)))))&((~(in @ X1228 @ X1226)|(X1229)|~(X1229)|~(in @ X1228 @ (symdiff @ X1226 @ X1227)))&(((in @ X1228 @ X1227)|(X1229)|~(X1229)|~(in @ X1228 @ (symdiff @ X1226 @ X1227)))&(~(X1229)|(X1229)|~(X1229)|~(in @ X1228 @ (symdiff @ X1226 @ X1227)))))))&((~(in @ X1232 @ X1230)|((in @ X1232 @ X1231)|(in @ X1232 @ (symdiff @ X1230 @ X1231))))&(((in @ X1235 @ X1233)|(~(in @ X1235 @ X1234)|(in @ X1235 @ (symdiff @ X1233 @ X1234))))&((~(in @ X1238 @ X1236)|(~(in @ X1238 @ X1237)|~(in @ X1238 @ (symdiff @ X1236 @ X1237))))&(((in @ X1241 @ X1239)|((in @ X1241 @ X1240)|~(in @ X1241 @ (symdiff @ X1239 @ X1240))))&((in @ X1243 @ (setadjoin @ X1242 @ (setadjoin @ X1243 @ emptyset)))&((in @ X1244 @ (setunion @ (setadjoin @ (setadjoin @ X1244 @ emptyset) @ (setadjoin @ (setadjoin @ X1244 @ (setadjoin @ X1245 @ emptyset)) @ emptyset))))&((in @ X1247 @ (setunion @ (setadjoin @ (setadjoin @ X1246 @ emptyset) @ (setadjoin @ (setadjoin @ X1246 @ (setadjoin @ X1247 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1248 @ emptyset) @ (setadjoin @ (setadjoin @ X1248 @ (setadjoin @ X1249 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1250 @ X1251))&((~(in @ X1253 @ X1252)|(subset @ (setadjoin @ X1253 @ emptyset) @ X1252))&((~(in @ X1255 @ X1254)|(in @ (setadjoin @ X1255 @ emptyset) @ (powerset @ X1254)))&((~(in @ X1258 @ X1256)|(in @ (setadjoin @ X1258 @ emptyset) @ (powerset @ (binunion @ X1256 @ X1257))))&((~(in @ X1261 @ (setadjoin @ X1259 @ (setadjoin @ X1260 @ emptyset)))|(((X1261)=(X1259))|((X1261)=(X1260))))&((~(in @ X1264 @ X1262)|(~(in @ X1265 @ X1263)|(subset @ (setadjoin @ X1264 @ (setadjoin @ X1265 @ emptyset)) @ (binunion @ X1262 @ X1263))))&((~(in @ X1268 @ X1266)|(~(in @ X1269 @ X1267)|(in @ (setadjoin @ X1268 @ (setadjoin @ X1269 @ emptyset)) @ (powerset @ (binunion @ X1266 @ X1267)))))&((~(in @ X1272 @ X1270)|(~(in @ X1273 @ X1271)|(subset @ (setadjoin @ (setadjoin @ X1272 @ emptyset) @ (setadjoin @ (setadjoin @ X1272 @ (setadjoin @ X1273 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1270 @ X1271)))))&((~(in @ X1276 @ X1274)|(~(in @ X1277 @ X1275)|(in @ (setadjoin @ (setadjoin @ X1276 @ emptyset) @ (setadjoin @ (setadjoin @ X1276 @ (setadjoin @ X1277 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1274 @ X1275))))))&((~(in @ X1280 @ X1278)|(~(in @ X1281 @ X1279)|(in @ (kpair @ X1280 @ X1281) @ (powerset @ (powerset @ (binunion @ X1278 @ X1279))))))&((~(in @ X1284 @ X1282)|(~(in @ X1285 @ X1283)|(in @ (kpair @ X1284 @ X1285) @ (cartprod @ X1282 @ X1283))))&((((in @ (esk39_3 @ X1286 @ X1287 @ X1288) @ X1286)|~(in @ X1288 @ (cartprod @ X1286 @ X1287)))&(((in @ (esk40_3 @ X1286 @ X1287 @ X1288) @ X1287)|~(in @ X1288 @ (cartprod @ X1286 @ X1287)))&(((X1288)=(kpair @ (esk39_3 @ X1286 @ X1287 @ X1288) @ (esk40_3 @ X1286 @ X1287 @ X1288)))|~(in @ X1288 @ (cartprod @ X1286 @ X1287)))))&((~(in @ X1293 @ (cartprod @ X1291 @ X1292))|(iskpair @ X1293))&((((in @ (esk41_2 @ X1294 @ X1295) @ X1294)|~(in @ X1295 @ (setunion @ X1294)))&((in @ X1295 @ (esk41_2 @ X1294 @ X1295))|~(in @ X1295 @ (setunion @ X1294))))&((subset @ (setunion @ (setadjoin @ X1297 @ emptyset)) @ X1297)&((subset @ X1298 @ (setunion @ (setadjoin @ X1298 @ emptyset)))&(((setunion @ (setadjoin @ X1299 @ emptyset))=(X1299))&((((in @ (esk42_2 @ X1300 @ X1301) @ X1300)|(~(in @ X1304 @ X1300)|~(X1301 @ X1304)|(singleton @ (dsetconstr @ X1300 @ X1301))))&(((in @ (esk43_2 @ X1300 @ X1301) @ X1300)|(~(in @ X1304 @ X1300)|~(X1301 @ X1304)|(singleton @ (dsetconstr @ X1300 @ X1301))))&(((X1301 @ (esk42_2 @ X1300 @ X1301))|(~(in @ X1304 @ X1300)|~(X1301 @ X1304)|(singleton @ (dsetconstr @ X1300 @ X1301))))&(((X1301 @ (esk43_2 @ X1300 @ X1301))|(~(in @ X1304 @ X1300)|~(X1301 @ X1304)|(singleton @ (dsetconstr @ X1300 @ X1301))))&(((esk42_2 @ X1300 @ X1301)!=(esk43_2 @ X1300 @ X1301))|(~(in @ X1304 @ X1300)|~(X1301 @ X1304)|(singleton @ (dsetconstr @ X1300 @ X1301))))))))&((((in @ (esk44_2 @ X1305 @ X1306) @ X1305)|~(ex1 @ X1305 @ X1306))&((X1306 @ (esk44_2 @ X1305 @ X1306))|~(ex1 @ X1305 @ X1306)))&((((in @ (esk45_3 @ X1308 @ X1309 @ X1310) @ X1308)|(ex1 @ X1308 @ X1309)|~(X1309 @ X1310)|~(in @ X1310 @ X1308))&(((X1309 @ (esk45_3 @ X1308 @ X1309 @ X1310))|(ex1 @ X1308 @ X1309)|~(X1309 @ X1310)|~(in @ X1310 @ X1308))&(((esk45_3 @ X1308 @ X1309 @ X1310)!=(X1310))|(ex1 @ X1308 @ X1309)|~(X1309 @ X1310)|~(in @ X1310 @ X1308))))&((((in @ (esk46_2 @ X1312 @ X1313) @ X1312)|(~(in @ X1316 @ X1312)|~(X1313 @ X1316)|(ex1 @ X1312 @ X1313)))&(((in @ (esk47_2 @ X1312 @ X1313) @ X1312)|(~(in @ X1316 @ X1312)|~(X1313 @ X1316)|(ex1 @ X1312 @ X1313)))&(((X1313 @ (esk46_2 @ X1312 @ X1313))|(~(in @ X1316 @ X1312)|~(X1313 @ X1316)|(ex1 @ X1312 @ X1313)))&(((X1313 @ (esk47_2 @ X1312 @ X1313))|(~(in @ X1316 @ X1312)|~(X1313 @ X1316)|(ex1 @ X1312 @ X1313)))&(((esk46_2 @ X1312 @ X1313)!=(esk47_2 @ X1312 @ X1313))|(~(in @ X1316 @ X1312)|~(X1313 @ X1316)|(ex1 @ X1312 @ X1313)))))))&((((setadjoin @ X1317 @ emptyset)!=(setadjoin @ X1318 @ emptyset))|((X1317)=(X1318)))&((~(in @ (setadjoin @ X1321 @ emptyset) @ (setadjoin @ (setadjoin @ X1319 @ emptyset) @ (setadjoin @ (setadjoin @ X1319 @ (setadjoin @ X1320 @ emptyset)) @ emptyset)))|((X1319)=(X1321)))&((~(iskpair @ X1322)|(singleton @ (dsetconstr @ (setunion @ X1322) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1322))))))&((~(singleton @ X1323)|(in @ (setunion @ X1323) @ X1323))&(((kfst @ (kpair @ X1324 @ X1325))=(X1324))&((in @ esk50_0 @ (cartprod @ esk48_0 @ esk49_0))&~(in @ (kfst @ esk50_0) @ esk48_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_190])])])])])])])). 392.69/52.86 thf(c_0_192, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_191])). 392.69/52.86 thf(c_0_193, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((X2)=(kpair @ (esk39_3 @ X3 @ X4 @ X2) @ (esk40_3 @ X3 @ X4 @ X2)))|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_191])). 392.69/52.86 thf(c_0_194, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ (esk39_3 @ X2 @ X3 @ X4) @ X2)|~((in @ X4 @ (cartprod @ X2 @ X3))))), inference(split_conjunct,[status(thm)],[c_0_191])). 392.69/52.86 thf(c_0_195, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((((esk39_3 @ X2 @ X3 @ X4)=(kfst @ X4))|~((in @ X4 @ (cartprod @ X2 @ X3))))), inference(spm,[status(thm)],[c_0_192, c_0_193])). 392.69/52.86 thf(c_0_196, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (kfst @ X2) @ X3)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(spm,[status(thm)],[c_0_194, c_0_195])). 392.69/52.86 thf(c_0_197, negated_conjecture, (in @ esk50_0 @ (cartprod @ esk48_0 @ esk49_0)), inference(split_conjunct,[status(thm)],[c_0_191])). 392.69/52.86 thf(c_0_198, negated_conjecture, ~((in @ (kfst @ esk50_0) @ esk48_0)), inference(split_conjunct,[status(thm)],[c_0_191])). 392.69/52.86 thf(c_0_199, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_196, c_0_197]), c_0_198]), ['proof']). 392.69/52.86 # SZS output end CNFRefutation 392.69/52.86 # Parsed axioms : 361 392.69/52.86 # Removed by relevancy pruning/SinE : 199 392.69/52.86 # Initial clauses : 259 392.69/52.86 # Removed in clause preprocessing : 25 392.69/52.86 # Initial clauses in saturation : 234 392.69/52.86 # Processed clauses : 15436 392.69/52.86 # ...of these trivial : 829 392.69/52.86 # ...subsumed : 6868 392.69/52.86 # ...remaining for further processing : 7739 392.69/52.86 # Other redundant clauses eliminated : 151 392.69/52.86 # Clauses deleted for lack of memory : 100354 392.69/52.86 # Backward-subsumed : 512 392.69/52.86 # Backward-rewritten : 180 392.69/52.86 # Generated clauses : 2378869 392.69/52.86 # ...of the previous two non-redundant : 2341883 392.69/52.86 # ...aggressively subsumed : 0 392.69/52.86 # Contextual simplify-reflections : 17 392.69/52.86 # Paramodulations : 2378580 392.69/52.86 # Factorizations : 124 392.69/52.86 # NegExts : 0 392.69/52.86 # Equation resolutions : 152 392.69/52.86 # Disequality decompositions : 0 392.69/52.86 # Total rewrite steps : 93171 392.69/52.86 # ...of those cached : 88732 392.69/52.86 # Propositional unsat checks : 0 392.69/52.86 # Propositional check models : 0 392.69/52.86 # Propositional check unsatisfiable : 0 392.69/52.86 # Propositional clauses : 0 392.69/52.86 # Propositional clauses after purity: 0 392.69/52.86 # Propositional unsat core size : 0 392.69/52.86 # Propositional preprocessing time : 0.000 392.69/52.86 # Propositional encoding time : 0.000 392.69/52.86 # Propositional solver time : 0.000 392.69/52.86 # Success case prop preproc time : 0.000 392.69/52.86 # Success case prop encoding time : 0.000 392.69/52.86 # Success case prop solver time : 0.000 392.69/52.86 # Current number of processed clauses : 6825 392.69/52.86 # Positive orientable unit clauses : 375 392.69/52.86 # Positive unorientable unit clauses: 0 392.69/52.86 # Negative unit clauses : 354 392.69/52.86 # Non-unit-clauses : 6096 392.69/52.86 # Current number of unprocessed clauses: 1335597 392.69/52.86 # ...number of literals in the above : 5199022 392.69/52.86 # Current number of archived formulas : 0 392.69/52.86 # Current number of archived clauses : 903 392.69/52.86 # Clause-clause subsumption calls (NU) : 2949768 392.69/52.86 # Rec. Clause-clause subsumption calls : 1434928 392.69/52.86 # Non-unit clause-clause subsumptions : 2730 392.69/52.86 # Unit Clause-clause subsumption calls : 150733 392.69/52.86 # Rewrite failures with RHS unbound : 0 392.69/52.86 # BW rewrite match attempts : 413 392.69/52.86 # BW rewrite match successes : 95 392.69/52.86 # Condensation attempts : 15436 392.69/52.86 # Condensation successes : 100 392.69/52.86 # Termbank termtop insertions : 58528845 392.69/52.86 # Search garbage collected termcells : 1201764 392.69/52.86 392.69/52.86 # ------------------------------------------------- 392.69/52.86 # User time : 47.417 s 392.69/52.86 # System time : 1.188 s 392.69/52.86 # Total time : 48.604 s 392.69/52.86 # Maximum resident set size: 5460 pages 392.69/52.86 392.69/52.86 # ------------------------------------------------- 392.69/52.86 # User time : 47.428 s 392.69/52.86 # System time : 1.190 s 392.69/52.86 # Total time : 48.618 s 392.69/52.86 # Maximum resident set size: 2196 pages 392.69/52.86 % E---3.1 exiting 392.69/52.86 % E exiting 392.69/52.86 EOF