0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.11 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM 0.11/0.32 % Computer : n003.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 1920 0.11/0.32 % WCLimit : 240 0.11/0.32 % DateTime : Wed Jul 30 03:40:04 EDT 2025 0.11/0.32 % CPUTime : 0.19/0.46 Running higher-order theorem proving 0.19/0.49 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=240 /export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p 0.77/0.64 # Version: 3.0.0-ho 0.77/0.64 # Preprocessing class: HSLMSLSSLLLCHFA. 0.77/0.64 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 0.77/0.64 # Starting ehoh_best5 with 240s (1) cores 0.77/0.64 # Starting almost_fo_3_lam with 240s (1) cores 0.77/0.64 # Starting new_bool_5 with 240s (1) cores 0.77/0.64 # Starting pre_casc_3 with 240s (1) cores 0.77/0.64 # Starting ho_unfolding_8 with 240s (1) cores 0.77/0.64 # Starting new_ho_10_cnf2 with 240s (1) cores 0.77/0.64 # Starting new_bool_3 with 240s (1) cores 0.77/0.64 # Starting new_ho_5 with 240s (1) cores 0.77/0.64 # new_bool_3 with pid 29536 completed with status 0 0.77/0.64 # Result found by new_bool_3 0.77/0.64 # Preprocessing class: HSLMSLSSLLLCHFA. 0.77/0.64 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 0.77/0.64 # Starting ehoh_best5 with 240s (1) cores 0.77/0.64 # Starting almost_fo_3_lam with 240s (1) cores 0.77/0.64 # Starting new_bool_5 with 240s (1) cores 0.77/0.64 # Starting pre_casc_3 with 240s (1) cores 0.77/0.64 # Starting ho_unfolding_8 with 240s (1) cores 0.77/0.64 # Starting new_ho_10_cnf2 with 240s (1) cores 0.77/0.64 # Starting new_bool_3 with 240s (1) cores 0.77/0.64 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.77/0.64 # Search class: HGHSM-FSLM31-MHFMMSBN 0.77/0.64 # Scheduled 6 strats onto 1 cores with 240 seconds (240 total) 0.77/0.64 # Starting new_ho_10_cnf2 with 130s (1) cores 0.77/0.64 # new_ho_10_cnf2 with pid 29544 completed with status 0 0.77/0.64 # Result found by new_ho_10_cnf2 0.77/0.64 # Preprocessing class: HSLMSLSSLLLCHFA. 0.77/0.64 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 0.77/0.64 # Starting ehoh_best5 with 240s (1) cores 0.77/0.64 # Starting almost_fo_3_lam with 240s (1) cores 0.77/0.64 # Starting new_bool_5 with 240s (1) cores 0.77/0.64 # Starting pre_casc_3 with 240s (1) cores 0.77/0.64 # Starting ho_unfolding_8 with 240s (1) cores 0.77/0.64 # Starting new_ho_10_cnf2 with 240s (1) cores 0.77/0.64 # Starting new_bool_3 with 240s (1) cores 0.77/0.64 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.77/0.64 # Search class: HGHSM-FSLM31-MHFMMSBN 0.77/0.64 # Scheduled 6 strats onto 1 cores with 240 seconds (240 total) 0.77/0.64 # Starting new_ho_10_cnf2 with 130s (1) cores 0.77/0.64 # Preprocessing time : 0.006 s 0.77/0.64 # Presaturation interreduction done 0.77/0.64 0.77/0.64 # Proof found! 0.77/0.64 # SZS status Theorem 0.77/0.64 # SZS output start CNFRefutation 0.77/0.64 thf(decl_23, type, in: $i > $i > $o). 0.77/0.64 thf(decl_24, type, exu: ($i > $o) > $o). 0.77/0.64 thf(decl_25, type, setextAx: $o). 0.77/0.64 thf(decl_26, type, emptyset: $i). 0.77/0.64 thf(decl_27, type, emptysetAx: $o). 0.77/0.64 thf(decl_28, type, setadjoin: $i > $i > $i). 0.77/0.64 thf(decl_29, type, setadjoinAx: $o). 0.77/0.64 thf(decl_30, type, powerset: $i > $i). 0.77/0.64 thf(decl_31, type, powersetAx: $o). 0.77/0.64 thf(decl_32, type, setunion: $i > $i). 0.77/0.64 thf(decl_33, type, setunionAx: $o). 0.77/0.64 thf(decl_34, type, omega: $i). 0.77/0.64 thf(decl_35, type, omega0Ax: $o). 0.77/0.64 thf(decl_36, type, omegaSAx: $o). 0.77/0.64 thf(decl_37, type, omegaIndAx: $o). 0.77/0.64 thf(decl_38, type, replAx: $o). 0.77/0.64 thf(decl_39, type, foundationAx: $o). 0.77/0.64 thf(decl_40, type, wellorderingAx: $o). 0.77/0.64 thf(decl_41, type, descr: ($i > $o) > $i). 0.77/0.64 thf(decl_42, type, descrp: $o). 0.77/0.64 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_44, type, dsetconstrI: $o). 0.77/0.64 thf(decl_45, type, dsetconstrEL: $o). 0.77/0.64 thf(decl_46, type, dsetconstrER: $o). 0.77/0.64 thf(decl_47, type, exuE1: $o). 0.77/0.64 thf(decl_48, type, prop2set: $o > $i). 0.77/0.64 thf(decl_49, type, prop2setE: $o). 0.77/0.64 thf(decl_50, type, emptysetE: $o). 0.77/0.64 thf(decl_51, type, emptysetimpfalse: $o). 0.77/0.64 thf(decl_52, type, notinemptyset: $o). 0.77/0.64 thf(decl_53, type, exuE3e: $o). 0.77/0.64 thf(decl_54, type, setext: $o). 0.77/0.64 thf(decl_55, type, emptyI: $o). 0.77/0.64 thf(decl_56, type, noeltsimpempty: $o). 0.77/0.64 thf(decl_57, type, setbeta: $o). 0.77/0.64 thf(decl_58, type, nonempty: $i > $o). 0.77/0.64 thf(decl_59, type, nonemptyE1: $o). 0.77/0.64 thf(decl_60, type, nonemptyI: $o). 0.77/0.64 thf(decl_61, type, nonemptyI1: $o). 0.77/0.64 thf(decl_62, type, setadjoinIL: $o). 0.77/0.64 thf(decl_63, type, emptyinunitempty: $o). 0.77/0.64 thf(decl_64, type, setadjoinIR: $o). 0.77/0.64 thf(decl_65, type, setadjoinE: $o). 0.77/0.64 thf(decl_66, type, setadjoinOr: $o). 0.77/0.64 thf(decl_67, type, setoftrueEq: $o). 0.77/0.64 thf(decl_68, type, powersetI: $o). 0.77/0.64 thf(decl_69, type, emptyinPowerset: $o). 0.77/0.64 thf(decl_70, type, emptyInPowerset: $o). 0.77/0.64 thf(decl_71, type, powersetE: $o). 0.77/0.64 thf(decl_72, type, setunionI: $o). 0.77/0.64 thf(decl_73, type, setunionE: $o). 0.77/0.64 thf(decl_74, type, subPowSU: $o). 0.77/0.64 thf(decl_75, type, exuE2: $o). 0.77/0.64 thf(decl_76, type, nonemptyImpWitness: $o). 0.77/0.64 thf(decl_77, type, uniqinunit: $o). 0.77/0.64 thf(decl_78, type, notinsingleton: $o). 0.77/0.64 thf(decl_79, type, eqinunit: $o). 0.77/0.64 thf(decl_80, type, singletonsswitch: $o). 0.77/0.64 thf(decl_81, type, upairsetE: $o). 0.77/0.64 thf(decl_82, type, upairsetIL: $o). 0.77/0.64 thf(decl_83, type, upairsetIR: $o). 0.77/0.64 thf(decl_84, type, emptyE1: $o). 0.77/0.64 thf(decl_85, type, vacuousDall: $o). 0.77/0.64 thf(decl_86, type, quantDeMorgan1: $o). 0.77/0.64 thf(decl_87, type, quantDeMorgan2: $o). 0.77/0.64 thf(decl_88, type, quantDeMorgan3: $o). 0.77/0.64 thf(decl_89, type, quantDeMorgan4: $o). 0.77/0.64 thf(decl_90, type, prop2setI: $o). 0.77/0.64 thf(decl_92, type, prop2set2propI: $o). 0.77/0.64 thf(decl_93, type, notdexE: $o). 0.77/0.64 thf(decl_94, type, notdallE: $o). 0.77/0.64 thf(decl_95, type, exuI1: $o). 0.77/0.64 thf(decl_96, type, exuI3: $o). 0.77/0.64 thf(decl_97, type, exuI2: $o). 0.77/0.64 thf(decl_98, type, inCongP: $o). 0.77/0.64 thf(decl_99, type, in__Cong: $o). 0.77/0.64 thf(decl_100, type, exuE3u: $o). 0.77/0.64 thf(decl_101, type, exu__Cong: $o). 0.77/0.64 thf(decl_102, type, emptyset__Cong: $o). 0.77/0.64 thf(decl_103, type, setadjoin__Cong: $o). 0.77/0.64 thf(decl_104, type, powerset__Cong: $o). 0.77/0.64 thf(decl_105, type, setunion__Cong: $o). 0.77/0.64 thf(decl_106, type, omega__Cong: $o). 0.77/0.64 thf(decl_107, type, exuEu: $o). 0.77/0.64 thf(decl_108, type, descr__Cong: $o). 0.77/0.64 thf(decl_109, type, dsetconstr__Cong: $o). 0.77/0.64 thf(decl_110, type, subset: $i > $i > $o). 0.77/0.64 thf(decl_113, type, subsetI1: $o). 0.77/0.64 thf(decl_114, type, eqimpsubset2: $o). 0.77/0.64 thf(decl_115, type, eqimpsubset1: $o). 0.77/0.64 thf(decl_116, type, subsetI2: $o). 0.77/0.64 thf(decl_117, type, emptysetsubset: $o). 0.77/0.64 thf(decl_118, type, subsetE: $o). 0.77/0.64 thf(decl_119, type, subsetE2: $o). 0.77/0.64 thf(decl_120, type, notsubsetI: $o). 0.77/0.64 thf(decl_121, type, notequalI1: $o). 0.77/0.64 thf(decl_122, type, notequalI2: $o). 0.77/0.64 thf(decl_123, type, subsetRefl: $o). 0.77/0.64 thf(decl_124, type, subsetTrans: $o). 0.77/0.64 thf(decl_125, type, setadjoinSub: $o). 0.77/0.64 thf(decl_126, type, setadjoinSub2: $o). 0.77/0.64 thf(decl_127, type, subset2powerset: $o). 0.77/0.64 thf(decl_128, type, setextsub: $o). 0.77/0.64 thf(decl_129, type, subsetemptysetimpeq: $o). 0.77/0.64 thf(decl_130, type, powersetI1: $o). 0.77/0.64 thf(decl_131, type, powersetE1: $o). 0.77/0.64 thf(decl_132, type, inPowerset: $o). 0.77/0.64 thf(decl_133, type, powersetsubset: $o). 0.77/0.64 thf(decl_134, type, sepInPowerset: $o). 0.77/0.64 thf(decl_135, type, sepSubset: $o). 0.77/0.64 thf(decl_136, type, binunion: $i > $i > $i). 0.77/0.64 thf(decl_137, type, binunionIL: $o). 0.77/0.64 thf(decl_138, type, upairset2IR: $o). 0.77/0.64 thf(decl_139, type, binunionIR: $o). 0.77/0.64 thf(decl_140, type, binunionEcases: $o). 0.77/0.64 thf(decl_141, type, binunionE: $o). 0.77/0.64 thf(decl_142, type, binunionLsub: $o). 0.77/0.64 thf(decl_143, type, binunionRsub: $o). 0.77/0.64 thf(decl_144, type, binintersect: $i > $i > $i). 0.77/0.64 thf(decl_145, type, binintersectI: $o). 0.77/0.64 thf(decl_146, type, binintersectSubset5: $o). 0.77/0.64 thf(decl_147, type, binintersectEL: $o). 0.77/0.64 thf(decl_148, type, binintersectLsub: $o). 0.77/0.64 thf(decl_149, type, binintersectSubset2: $o). 0.77/0.64 thf(decl_150, type, binintersectSubset3: $o). 0.77/0.64 thf(decl_151, type, binintersectER: $o). 0.77/0.64 thf(decl_152, type, disjointsetsI1: $o). 0.77/0.64 thf(decl_153, type, binintersectRsub: $o). 0.77/0.64 thf(decl_154, type, binintersectSubset4: $o). 0.77/0.64 thf(decl_155, type, binintersectSubset1: $o). 0.77/0.64 thf(decl_156, type, bs114d: $o). 0.77/0.64 thf(decl_158, type, setminus: $i > $i > $i). 0.77/0.64 thf(decl_159, type, setminusI: $o). 0.77/0.64 thf(decl_160, type, setminusEL: $o). 0.77/0.64 thf(decl_161, type, setminusER: $o). 0.77/0.64 thf(decl_162, type, setminusSubset2: $o). 0.77/0.64 thf(decl_163, type, setminusERneg: $o). 0.77/0.64 thf(decl_164, type, setminusELneg: $o). 0.77/0.64 thf(decl_165, type, setminusILneg: $o). 0.77/0.64 thf(decl_166, type, setminusIRneg: $o). 0.77/0.64 thf(decl_167, type, setminusLsub: $o). 0.77/0.64 thf(decl_168, type, setminusSubset1: $o). 0.77/0.64 thf(decl_169, type, symdiff: $i > $i > $i). 0.77/0.64 thf(decl_170, type, symdiffE: $o). 0.77/0.64 thf(decl_171, type, symdiffI1: $o). 0.77/0.64 thf(decl_172, type, symdiffI2: $o). 0.77/0.64 thf(decl_173, type, symdiffIneg1: $o). 0.77/0.64 thf(decl_174, type, symdiffIneg2: $o). 0.77/0.64 thf(decl_175, type, iskpair: $i > $o). 0.77/0.64 thf(decl_176, type, secondinupair: $o). 0.77/0.64 thf(decl_177, type, setukpairIL: $o). 0.77/0.64 thf(decl_178, type, setukpairIR: $o). 0.77/0.64 thf(decl_179, type, kpairiskpair: $o). 0.77/0.64 thf(decl_180, type, kpair: $i > $i > $i). 0.77/0.64 thf(decl_181, type, kpairp: $o). 0.77/0.64 thf(decl_182, type, cartprod: $i > $i > $i). 0.77/0.64 thf(decl_183, type, singletonsubset: $o). 0.77/0.64 thf(decl_184, type, singletoninpowerset: $o). 0.77/0.64 thf(decl_185, type, singletoninpowunion: $o). 0.77/0.64 thf(decl_186, type, upairset2E: $o). 0.77/0.64 thf(decl_187, type, upairsubunion: $o). 0.77/0.64 thf(decl_188, type, upairinpowunion: $o). 0.77/0.64 thf(decl_189, type, ubforcartprodlem1: $o). 0.77/0.64 thf(decl_190, type, ubforcartprodlem2: $o). 0.77/0.64 thf(decl_191, type, ubforcartprodlem3: $o). 0.77/0.64 thf(decl_192, type, cartprodpairin: $o). 0.77/0.64 thf(decl_193, type, cartprodmempair1: $o). 0.77/0.64 thf(decl_194, type, cartprodmempair: $o). 0.77/0.64 thf(decl_195, type, setunionE2: $o). 0.77/0.64 thf(decl_196, type, setunionsingleton1: $o). 0.77/0.64 thf(decl_197, type, setunionsingleton2: $o). 0.77/0.64 thf(decl_198, type, setunionsingleton: $o). 0.77/0.64 thf(decl_199, type, singleton: $i > $o). 0.77/0.64 thf(decl_200, type, singletonprop: $o). 0.77/0.64 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 0.77/0.64 thf(decl_202, type, ex1E1: $o). 0.77/0.64 thf(decl_203, type, ex1I: $o). 0.77/0.64 thf(decl_204, type, ex1I2: $o). 0.77/0.64 thf(decl_205, type, singletonsuniq: $o). 0.77/0.64 thf(decl_210, type, epred1_0: $o). 0.77/0.64 thf(decl_211, type, esk1_2: $i > $i > $i). 0.77/0.64 thf(decl_212, type, esk2_2: $i > $i > $i). 0.77/0.64 thf(decl_213, type, esk3_2: $i > $i > $i). 0.77/0.64 thf(decl_214, type, esk4_1: $i > $i). 0.77/0.64 thf(decl_215, type, esk5_2: ($i > $i > $o) > $i > $i). 0.77/0.64 thf(decl_216, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 0.77/0.64 thf(decl_217, type, esk7_2: ($i > $i > $o) > $i > $i). 0.77/0.64 thf(decl_218, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 0.77/0.64 thf(decl_219, type, esk9_1: $i > $i). 0.77/0.64 thf(decl_220, type, esk10_2: ($i > $o) > $i > $i). 0.77/0.64 thf(decl_221, type, esk11_2: ($i > $o) > $i > $i). 0.77/0.64 thf(decl_222, type, esk12_1: ($i > $o) > $i). 0.77/0.64 thf(decl_223, type, esk13_2: ($i > $o) > $i > $i). 0.77/0.64 thf(decl_224, type, esk14_1: ($i > $o) > $i). 0.77/0.64 thf(decl_225, type, esk15_2: $i > $i > $i). 0.77/0.64 thf(decl_226, type, esk16_2: $i > $i > $i). 0.77/0.64 thf(decl_227, type, esk17_1: $i > $i). 0.77/0.64 thf(decl_228, type, esk18_1: $i > $i). 0.77/0.64 thf(decl_229, type, esk19_1: $i > $i). 0.77/0.64 thf(decl_230, type, esk20_2: $i > $i > $i). 0.77/0.64 thf(decl_231, type, esk21_3: $i > $i > $o > $i). 0.77/0.64 thf(decl_232, type, esk22_2: ($i > $o) > $i > $i). 0.77/0.64 thf(decl_233, type, esk23_1: ($i > $o) > $i). 0.77/0.64 thf(decl_234, type, esk24_1: $i > $i). 0.77/0.64 thf(decl_235, type, esk25_2: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_236, type, esk26_2: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_237, type, esk27_2: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_238, type, esk28_2: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_239, type, esk29_2: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_240, type, esk30_2: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_241, type, esk31_2: ($i > $o) > $i > $i). 0.77/0.64 thf(decl_242, type, esk32_1: ($i > $o) > $i). 0.77/0.64 thf(decl_243, type, esk33_1: ($i > $o) > $i). 0.77/0.64 thf(decl_244, type, esk34_1: ($i > $o) > $i). 0.77/0.64 thf(decl_245, type, esk35_1: ($i > $o) > $i). 0.77/0.64 thf(decl_246, type, esk36_2: ($i > $o) > $i > $i). 0.77/0.64 thf(decl_247, type, esk37_1: ($i > $o) > $i). 0.77/0.64 thf(decl_248, type, esk38_2: ($i > $o) > $i > $i). 0.77/0.64 thf(decl_249, type, esk39_2: ($i > $o) > ($i > $o) > $i). 0.77/0.64 thf(decl_250, type, esk40_2: ($i > $o) > ($i > $o) > $i). 0.77/0.64 thf(decl_251, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 0.77/0.64 thf(decl_252, type, esk42_2: ($i > $o) > ($i > $o) > $i). 0.77/0.64 thf(decl_253, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 0.77/0.64 thf(decl_254, type, esk44_2: ($i > $o) > ($i > $o) > $i). 0.77/0.64 thf(decl_255, type, esk45_2: ($i > $o) > $i > $i). 0.77/0.64 thf(decl_256, type, esk46_2: ($i > $o) > ($i > $o) > $i). 0.77/0.64 thf(decl_257, type, esk47_2: ($i > $o) > ($i > $o) > $i). 0.77/0.64 thf(decl_258, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 0.77/0.64 thf(decl_259, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 0.77/0.64 thf(decl_260, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.77/0.64 thf(decl_261, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.77/0.64 thf(decl_262, type, esk52_2: $i > $i > $i). 0.77/0.64 thf(decl_263, type, esk53_2: $i > $i > $i). 0.77/0.64 thf(decl_264, type, esk54_2: $i > $i > $i). 0.77/0.64 thf(decl_265, type, esk55_2: $i > $i > $i). 0.77/0.64 thf(decl_266, type, esk56_2: $i > $i > $i). 0.77/0.64 thf(decl_267, type, esk57_2: $i > $i > $i). 0.77/0.64 thf(decl_268, type, esk58_2: $i > $i > $i). 0.77/0.64 thf(decl_269, type, esk59_3: $i > $i > $i > $i). 0.77/0.64 thf(decl_270, type, esk60_3: $i > $i > $i > $i). 0.77/0.64 thf(decl_271, type, esk61_3: $i > $i > $i > $i). 0.77/0.64 thf(decl_272, type, esk62_3: $i > $i > $i > $i). 0.77/0.64 thf(decl_273, type, esk63_2: $i > $i > $i). 0.77/0.64 thf(decl_274, type, esk64_2: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_275, type, esk65_2: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_276, type, esk66_2: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_277, type, esk67_2: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_278, type, esk68_3: $i > ($i > $o) > $i > $i). 0.77/0.64 thf(decl_279, type, esk69_3: $i > ($i > $o) > $i > $i). 0.77/0.64 thf(decl_280, type, esk70_2: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_281, type, esk71_2: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_282, type, esk72_2: $i > ($i > $o) > $i). 0.77/0.64 thf(decl_283, type, esk73_0: $i). 0.77/0.64 thf(decl_284, type, esk74_0: $i). 0.77/0.64 thf(decl_285, type, esk75_0: $i). 0.77/0.64 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', ex1)). 0.77/0.64 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', singleton)). 0.77/0.64 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.LPqKExJpH2/E---3.1_29452.p', exuEu)). 0.77/0.64 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', exu)). 0.77/0.64 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', nonempty)). 0.77/0.64 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', nonemptyI)). 0.77/0.64 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', exuE3e)). 0.77/0.64 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', descrp)). 0.77/0.64 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', replAx)). 0.77/0.64 thf(iskpair, axiom, ((iskpair)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ (setunion @ X4))&?[X3:$i]:(((in @ X3 @ (setunion @ X4))&((X4)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', iskpair)). 0.77/0.64 thf(kpair, axiom, ((kpair)=(^[X2:$i, X3:$i]:(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', kpair)). 0.77/0.64 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', ex1I2)). 0.77/0.64 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.LPqKExJpH2/E---3.1_29452.p', ex1I)). 0.77/0.64 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', ex1E1)). 0.77/0.64 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', singletonprop)). 0.77/0.64 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', descr__Cong)). 0.77/0.64 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', exuI2)). 0.77/0.64 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', exuI3)). 0.77/0.64 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', exuI1)). 0.77/0.64 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', exu__Cong)). 0.77/0.64 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', exuE3u)). 0.77/0.64 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.LPqKExJpH2/E---3.1_29452.p', exuE2)). 0.77/0.64 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.LPqKExJpH2/E---3.1_29452.p', exuE1)). 0.77/0.64 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', nonemptyImpWitness)). 0.77/0.64 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', nonemptyI1)). 0.77/0.64 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setbeta)). 0.77/0.64 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', sepSubset)). 0.77/0.64 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', dsetconstrI)). 0.77/0.64 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', kpairiskpair)). 0.77/0.64 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', kpairp)). 0.77/0.64 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.LPqKExJpH2/E---3.1_29452.p', cartprodmempair1)). 0.77/0.64 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', cartprodmempair)). 0.77/0.64 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', cartprodpairin)). 0.77/0.64 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', ubforcartprodlem3)). 0.77/0.64 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', sepInPowerset)). 0.77/0.64 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', dsetconstr__Cong)). 0.77/0.64 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.LPqKExJpH2/E---3.1_29452.p', emptyE1)). 0.77/0.64 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setoftrueEq)). 0.77/0.64 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', nonemptyE1)). 0.77/0.64 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', dsetconstrER)). 0.77/0.64 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', dsetconstrEL)). 0.77/0.64 thf(setukpairinjL1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>(((omega0Ax)=>(((((foundationAx)=>(((((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>(((emptysetimpfalse)=>((((((((nonemptyE1)=>((((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>(((setoftrueEq)=>(((emptyinPowerset)=>((((setunionI)=>(((subPowSU)=>((exuE2)=>((((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>(((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>(((quantDeMorgan3)=>((((((notdallE)=>(((((((exuE3u)=>((exu__Cong)=>(((setadjoin__Cong)=>(((setunion__Cong)=>(((exuEu)=>(((((eqimpsubset2)=>((((emptysetsubset)=>((subsetE)=>(((notsubsetI)=>(((((subsetTrans)=>(((setadjoinSub2)=>((subset2powerset)=>((((powersetI1)=>((((powersetsubset)=>(((sepSubset)=>(((((((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((((((binintersectSubset1)=>(((setminusI)=>(((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((((setminusSubset1)=>((symdiffE)=>(((symdiffI2)=>((symdiffIneg1)=>(((secondinupair)=>(((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>(((upairinpowunion)=>(((ubforcartprodlem2)=>((((cartprodmempair1)=>((cartprodmempair)=>(((setunionsingleton1)=>((setunionsingleton2)=>((((((ex1I2)=>((singletonsuniq)=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))))<=(ex1I))<=(ex1E1))<=(singletonprop))<=(setunionsingleton))))<=(setunionE2))))<=(cartprodpairin))<=(ubforcartprodlem3)))<=(ubforcartprodlem1)))<=(upairsubunion)))))))))<=(setukpairIL)))<=(symdiffIneg2))))<=(symdiffI1))))<=(setminusLsub))<=(setminusIRneg)))))))<=(setminusEL)))<=(bs114d)))<=(binintersectSubset4))<=(binintersectRsub))<=(disjointsetsI1))<=(binintersectER))))<=(binintersectLsub)))))))<=(binunionE))<=(binunionEcases))<=(binunionIR))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset)))<=(inPowerset))<=(powersetE1)))<=(subsetemptysetimpeq))<=(setextsub))))<=(setadjoinSub)))<=(subsetRefl))<=(notequalI2))<=(notequalI1)))<=(subsetE2))))<=(subsetI2))<=(eqimpsubset1)))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong)))<=(omega__Cong)))<=(powerset__Cong)))<=(emptyset__Cong))))<=(in__Cong))<=(inCongP))<=(exuI2))<=(exuI3))<=(exuI1)))<=(notdexE))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4)))<=(quantDeMorgan2)))))))<=(upairsetE)))))<=(uniqinunit))<=(nonemptyImpWitness))))<=(setunionE)))<=(powersetE))<=(emptyInPowerset)))<=(powersetI)))<=(setadjoinOr))))))<=(nonemptyI1))<=(nonemptyI)))<=(setbeta))<=(noeltsimpempty))<=(emptyI))<=(setext))<=(exuE3e))<=(notinemptyset)))<=(emptysetE))))))<=(dsetconstrI))<=(descrp))<=(wellorderingAx)))<=(replAx))<=(omegaIndAx))<=(omegaSAx)))<=(setunionAx)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setukpairinjL1)). 0.77/0.64 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setunionAx)). 0.77/0.64 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', quantDeMorgan4)). 0.77/0.64 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', quantDeMorgan2)). 0.77/0.64 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', upairsetE)). 0.77/0.64 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', uniqinunit)). 0.77/0.64 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', subsetTrans)). 0.77/0.64 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setunionE)). 0.77/0.64 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setadjoinSub2)). 0.77/0.64 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', powersetE)). 0.77/0.64 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', emptyInPowerset)). 0.77/0.64 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', powersetI)). 0.77/0.64 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', subset2powerset)). 0.77/0.64 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setadjoinOr)). 0.77/0.64 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', powersetI1)). 0.77/0.64 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', noeltsimpempty)). 0.77/0.64 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', eqimpsubset2)). 0.77/0.64 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', emptyI)). 0.77/0.64 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', powersetsubset)). 0.77/0.64 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.LPqKExJpH2/E---3.1_29452.p', setext)). 0.77/0.64 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', notinemptyset)). 0.77/0.64 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', emptysetE)). 0.77/0.64 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', symdiffE)). 0.77/0.64 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binunionLsub)). 0.77/0.64 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.LPqKExJpH2/E---3.1_29452.p', wellorderingAx)). 0.77/0.64 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binunionRsub)). 0.77/0.64 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', omegaIndAx)). 0.77/0.64 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', omegaSAx)). 0.77/0.64 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', emptysetsubset)). 0.77/0.64 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binintersectI)). 0.77/0.64 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binintersectSubset5)). 0.77/0.64 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binintersectEL)). 0.77/0.64 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binintersectSubset2)). 0.77/0.64 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binintersectSubset3)). 0.77/0.64 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binintersectSubset1)). 0.77/0.64 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setminusI)). 0.77/0.64 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setminusER)). 0.77/0.64 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setminusSubset2)). 0.77/0.64 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setminusERneg)). 0.77/0.64 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setminusELneg)). 0.77/0.64 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setminusILneg)). 0.77/0.64 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setminusSubset1)). 0.77/0.64 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setminusLsub)). 0.77/0.64 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setminusIRneg)). 0.77/0.64 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setminusEL)). 0.77/0.64 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', symdiffI2)). 0.77/0.64 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', symdiffIneg1)). 0.77/0.64 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', secondinupair)). 0.77/0.64 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setukpairIR)). 0.77/0.64 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', singletonsubset)). 0.77/0.64 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', singletoninpowerset)). 0.77/0.64 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', subsetE)). 0.77/0.64 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', singletoninpowunion)). 0.77/0.64 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', notsubsetI)). 0.77/0.64 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', upairset2E)). 0.77/0.64 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', upairinpowunion)). 0.77/0.64 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', ubforcartprodlem2)). 0.77/0.64 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setunionsingleton1)). 0.77/0.64 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setunionsingleton2)). 0.77/0.64 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', singletonsuniq)). 0.77/0.64 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setunionsingleton)). 0.77/0.64 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setunionE2)). 0.77/0.64 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', ubforcartprodlem1)). 0.77/0.64 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', upairsubunion)). 0.77/0.64 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setukpairIL)). 0.77/0.64 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', symdiffIneg2)). 0.77/0.64 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', symdiffI1)). 0.77/0.64 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', bs114d)). 0.77/0.64 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binintersectSubset4)). 0.77/0.64 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binintersectRsub)). 0.77/0.64 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', disjointsetsI1)). 0.77/0.64 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binintersectER)). 0.77/0.64 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binintersectLsub)). 0.77/0.64 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binunionE)). 0.77/0.64 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binunionEcases)). 0.77/0.64 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binunionIR)). 0.77/0.64 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', upairset2IR)). 0.77/0.64 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', binunionIL)). 0.77/0.64 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', inPowerset)). 0.77/0.64 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', powersetE1)). 0.77/0.64 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', subsetemptysetimpeq)). 0.77/0.64 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setextsub)). 0.77/0.64 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setadjoinSub)). 0.77/0.64 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', subsetRefl)). 0.77/0.64 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', notequalI2)). 0.77/0.64 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', notequalI1)). 0.77/0.64 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', subsetE2)). 0.77/0.64 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', subsetI2)). 0.77/0.64 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', eqimpsubset1)). 0.77/0.64 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', subsetI1)). 0.77/0.64 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', omega__Cong)). 0.77/0.64 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', powerset__Cong)). 0.77/0.64 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', emptyset__Cong)). 0.77/0.64 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.LPqKExJpH2/E---3.1_29452.p', in__Cong)). 0.77/0.64 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.LPqKExJpH2/E---3.1_29452.p', inCongP)). 0.77/0.64 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', notdexE)). 0.77/0.64 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', prop2setI)). 0.77/0.64 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setunion__Cong)). 0.77/0.64 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.LPqKExJpH2/E---3.1_29452.p', setadjoin__Cong)). 0.77/0.64 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', notdallE)). 0.77/0.64 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', quantDeMorgan3)). 0.77/0.64 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', quantDeMorgan1)). 0.77/0.64 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', vacuousDall)). 0.77/0.64 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', upairsetIR)). 0.77/0.64 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', upairsetIL)). 0.77/0.64 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', singletonsswitch)). 0.77/0.64 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', eqinunit)). 0.77/0.64 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', notinsingleton)). 0.77/0.64 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', subPowSU)). 0.77/0.64 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setunionI)). 0.77/0.64 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', emptyinPowerset)). 0.77/0.64 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.LPqKExJpH2/E---3.1_29452.p', setadjoinE)). 0.77/0.64 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setadjoinIR)). 0.77/0.64 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', emptyinunitempty)). 0.77/0.64 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setadjoinIL)). 0.77/0.64 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', emptysetimpfalse)). 0.77/0.64 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', prop2setE)). 0.77/0.64 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', foundationAx)). 0.77/0.64 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', omega0Ax)). 0.77/0.64 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', powersetAx)). 0.77/0.64 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setadjoinAx)). 0.77/0.64 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', emptysetAx)). 0.77/0.64 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.LPqKExJpH2/E---3.1_29452.p', setextAx)). 0.77/0.64 thf(c_0_164, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X490:$i]:(((in @ X490 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X490 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])). 0.77/0.64 thf(c_0_165, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])). 0.77/0.64 thf(c_0_166, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.77/0.64 thf(c_0_167, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.77/0.64 thf(c_0_168, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.77/0.64 thf(c_0_169, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.77/0.64 thf(c_0_170, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.77/0.64 thf(c_0_171, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.77/0.64 thf(c_0_172, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.77/0.64 thf(c_0_173, plain, ((iskpair)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ (setunion @ Z0))&?[X3:$i]:(((in @ X3 @ (setunion @ Z0))&((Z0)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))), inference(fof_simplification,[status(thm)],[iskpair])). 0.77/0.64 thf(c_0_174, plain, ((kpair)=(^[Z0/* 19 */:$i, Z1:$i]:(setadjoin @ (setadjoin @ Z0 @ emptyset) @ (setadjoin @ (setadjoin @ Z0 @ (setadjoin @ Z1 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[kpair])). 0.77/0.64 thf(c_0_175, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 0.77/0.64 thf(c_0_176, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X490:$i]:(((in @ X490 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X490 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_164, c_0_165])). 0.77/0.64 thf(c_0_177, 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])). 0.77/0.64 thf(c_0_178, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 0.77/0.64 thf(c_0_179, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 0.77/0.64 thf(c_0_180, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.77/0.64 thf(c_0_181, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.77/0.64 thf(c_0_182, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.77/0.64 thf(c_0_183, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 0.77/0.64 thf(c_0_184, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.77/0.64 thf(c_0_185, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 0.77/0.64 thf(c_0_186, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.77/0.64 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])). 0.77/0.64 thf(c_0_188, plain, ((exuEu)=(![X1:$i > $o]:(((?[X477:$i]:((((X1 @ X477))&![X478:$i]:((((X1 @ X478))=>((X477)=(X478)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_166, c_0_167])). 0.77/0.64 thf(c_0_189, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_168])). 0.77/0.64 thf(c_0_190, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_168])). 0.77/0.64 thf(c_0_191, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_169, c_0_168])). 0.77/0.64 thf(c_0_192, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.77/0.64 thf(c_0_193, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X461:$i]:((((X1 @ X461))&![X462:$i]:((((X1 @ X462))=>((X461)=(X462)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_170, c_0_167])). 0.77/0.64 thf(c_0_194, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.77/0.64 thf(c_0_195, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.77/0.64 thf(c_0_196, plain, ((descrp)=(![X1:$i > $o]:(((?[X457:$i]:((((X1 @ X457))&![X458:$i]:((((X1 @ X458))=>((X457)=(X458)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_171, c_0_167])). 0.77/0.64 thf(c_0_197, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X455:$i]:((((X6 @ X2 @ X455))&![X456:$i]:((((X6 @ X2 @ X456))=>((X455)=(X456)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_172, c_0_167])). 0.77/0.64 thf(c_0_198, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X483:$i]:(((in @ X483 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X484:$i]:(((in @ X484 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X483 @ emptyset) @ (setadjoin @ (setadjoin @ X483 @ (setadjoin @ X484 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_173])). 0.77/0.64 thf(c_0_199, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X485:$i]:(((in @ X485 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X486:$i]:(((in @ X486 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X485 @ emptyset) @ (setadjoin @ (setadjoin @ X485 @ (setadjoin @ X486 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[kpairp, c_0_174]), c_0_173])). 0.77/0.64 thf(c_0_200, axiom, ((cartprodmempair1)=(![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[cartprodmempair1, c_0_174])). 0.77/0.64 thf(c_0_201, axiom, ((cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(?[X487:$i]:(((in @ X487 @ (setunion @ X18))&?[X488:$i]:(((in @ X488 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X487 @ emptyset) @ (setadjoin @ (setadjoin @ X487 @ (setadjoin @ X488 @ emptyset)) @ emptyset)))))))))))), inference(apply_def,[status(thm)],[cartprodmempair, c_0_173])). 0.77/0.64 thf(c_0_202, 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)))=>(?[X493:$i]:(((in @ X493 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X493 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_175, c_0_176])). 0.77/0.64 thf(c_0_203, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X492:$i]:(((in @ X492 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X492 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_177, c_0_176])). 0.77/0.64 thf(c_0_204, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X491:$i]:(((in @ X491 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X491 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_178, c_0_176])). 0.77/0.64 thf(c_0_205, plain, ((singletonprop)=(![X4:$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)))=>(?[X489:$i]:(((in @ X489 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X489 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_179, c_0_165])). 0.77/0.64 thf(c_0_206, axiom, ((cartprodpairin)=(![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (cartprod @ X4 @ X5)))))))), inference(apply_def,[status(thm)],[cartprodpairin, c_0_174])). 0.77/0.64 thf(c_0_207, axiom, ((ubforcartprodlem3)=(![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))))))), inference(apply_def,[status(thm)],[ubforcartprodlem3, c_0_174])). 0.77/0.64 thf(c_0_208, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.77/0.64 thf(c_0_209, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.77/0.64 thf(c_0_210, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X479:$i]:((((X1 @ X479))&![X480:$i]:((((X1 @ X480))=>((X479)=(X480)))))))=>((?[X481:$i]:((((X17 @ X481))&![X482:$i]:((((X17 @ X482))=>((X481)=(X482)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_180, c_0_167])). 0.77/0.64 thf(c_0_211, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X469:$i]:((((X1 @ X469))&![X470:$i]:((((X1 @ X470))=>((X469)=(X470))))))))))), inference(apply_def,[status(thm)],[c_0_181, c_0_167])). 0.77/0.64 thf(c_0_212, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X467:$i]:((((X1 @ X467))&![X468:$i]:((((X1 @ X468))=>((X467)=(X468)))))))))))), inference(apply_def,[status(thm)],[c_0_182, c_0_167])). 0.77/0.64 thf(c_0_213, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X465:$i]:((((X1 @ X465))&![X466:$i]:((((X1 @ X466))=>((X465)=(X466))))))))))), inference(apply_def,[status(thm)],[c_0_183, c_0_167])). 0.77/0.64 thf(c_0_214, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X473:$i]:((((X1 @ X473))&![X474:$i]:((((X1 @ X474))=>((X473)=(X474)))))))<=>(?[X475:$i]:((((X17 @ X475))&![X476:$i]:((((X17 @ X476))=>((X475)=(X476)))))))))))), inference(apply_def,[status(thm)],[c_0_184, c_0_167])). 0.77/0.64 thf(c_0_215, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X471:$i]:((((X1 @ X471))&![X472:$i]:((((X1 @ X472))=>((X471)=(X472)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_185, c_0_167])). 0.77/0.64 thf(c_0_216, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 0.77/0.64 thf(c_0_217, plain, ((exuE2)=(![X1:$i > $o]:(((?[X463:$i]:((((X1 @ X463))&![X464:$i]:((((X1 @ X464))=>((X463)=(X464)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_186, c_0_167])). 0.77/0.64 thf(c_0_218, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.77/0.64 thf(c_0_219, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_168])). 0.77/0.64 thf(c_0_220, plain, ((exuE1)=(![X1:$i > $o]:(((?[X459:$i]:((((X1 @ X459))&![X460:$i]:((((X1 @ X460))=>((X459)=(X460)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_187, c_0_167])). 0.77/0.64 thf(c_0_221, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.77/0.64 thf(c_0_222, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.77/0.64 thf(c_0_223, plain, ((epred1_0)<=>![X928:$i]:(?[X929:$i]:((((![X930:$i]:(((in @ X930 @ X929)=>![X931:$i]:(((in @ X931 @ X930)=>(in @ X931 @ X928)))))&![X932:$i, X933:$i]:((((in @ X932 @ X928)&(in @ X933 @ X928))=>(![X934:$i]:(((in @ X934 @ X929)=>((in @ X932 @ X934)<=>(in @ X933 @ X934))))=>((X932)=(X933))))))&![X935:$i, X936:$i]:((((in @ X935 @ X929)&(in @ X936 @ X929))=>(![X937:$i]:(((in @ X937 @ X935)=>(in @ X937 @ X936)))|![X938:$i]:(((in @ X938 @ X936)=>(in @ X938 @ X935)))))))&![X939:$i]:(((![X940:$i]:(((in @ X940 @ X939)=>(in @ X940 @ X928)))&?[X941:$i]:((in @ X941 @ X939)))=>?[X942:$i, X943:$i]:(((((in @ X942 @ X929)&(in @ X943 @ X939))&~(?[X944:$i]:(((in @ X944 @ X942)&(in @ X944 @ X939)))))&![X945:$i]:(((in @ X945 @ X929)=>(![X946:$i]:(((in @ X946 @ X945)=>(in @ X946 @ X942)))|(in @ X943 @ X945)))))))))))), introduced(definition)). 0.77/0.64 thf(c_0_224, negated_conjecture, ~((![X494:$i, X495:$i]:((![X496:$i]:(((in @ X496 @ X494)<=>(in @ X496 @ X495)))=>((X494)=(X495))))=>(![X497:$i]:(~(in @ X497 @ emptyset))=>(![X498:$i, X499:$i, X500:$i]:(((in @ X500 @ (setadjoin @ X498 @ X499))<=>(((X500)=(X498))|(in @ X500 @ X499))))=>(![X501:$i, X502:$i]:(((in @ X502 @ (powerset @ X501))<=>![X503:$i]:(((in @ X503 @ X502)=>(in @ X503 @ X501)))))=>(![X959:$i, X960:$i]:(((in @ X960 @ (setunion @ X959))<=>?[X961:$i]:(((in @ X960 @ X961)&(in @ X961 @ X959)))))=>((in @ emptyset @ omega)=>(![X958:$i]:(((in @ X958 @ omega)=>(in @ (setadjoin @ X958 @ X958) @ omega)))=>(![X955:$i]:((((in @ emptyset @ X955)&![X956:$i]:((((in @ X956 @ omega)&(in @ X956 @ X955))=>(in @ (setadjoin @ X956 @ X956) @ X955))))=>![X957:$i]:(((in @ X957 @ omega)=>(in @ X957 @ X955)))))=>(![X947:$i > $i > $o, X948:$i]:((![X949:$i]:(((in @ X949 @ X948)=>?[X950:$i]:(((X947 @ X949 @ X950)&![X951:$i]:(((X947 @ X949 @ X951)=>((X950)=(X951))))))))=>?[X952:$i]:(![X953:$i]:(((in @ X953 @ X952)<=>?[X954:$i]:(((in @ X954 @ X948)&(X947 @ X954 @ X953))))))))=>(![X504:$i]:((?[X505:$i]:((in @ X505 @ X504))=>?[X506:$i]:(((in @ X506 @ X504)&~(?[X507:$i]:(((in @ X507 @ X506)&(in @ X507 @ X504))))))))=>((epred1_0)=>(![X925:$i > $o]:((?[X926:$i]:(((X925 @ X926)&![X927:$i]:(((X925 @ X927)=>((X926)=(X927))))))=>(X925 @ (descr @ (^[Z0/* 17 */:$i]:(X925 @ Z0))))))=>(![X922:$i, X923:$i > $o, X924:$i]:(((in @ X924 @ X922)=>((X923 @ X924)=>(in @ X924 @ (dsetconstr @ X922 @ X923)))))=>(![X508:$i, X509:$i > $o, X510:$i]:(((in @ X510 @ (dsetconstr @ X508 @ X509))=>(in @ X510 @ X508)))=>(![X511:$i, X512:$i > $o, X513:$i]:(((in @ X513 @ (dsetconstr @ X511 @ X512))=>(X512 @ X513)))=>(![X514:$i > $o]:((?[X515:$i]:(((X514 @ X515)&![X516:$i]:(((X514 @ X516)=>((X515)=(X516))))))=>?[X517:$i]:(((X514 @ X517)&![X518:$i]:(((X514 @ X518)=>((X517)=(X518))))))))=>(![X519:$o, X520:$i]:(((in @ X520 @ (prop2set @ ((X519))))=>(X519)))=>(![X920:$i]:(((in @ X920 @ emptyset)=>![X921:$o]:((X921))))=>(![X521:$i]:(((in @ X521 @ emptyset)=>~($true)))=>(![X919:$i]:(~(in @ X919 @ emptyset))=>(![X915:$i > $o]:((?[X916:$i]:(((X915 @ X916)&![X917:$i]:(((X915 @ X917)=>((X916)=(X917))))))=>?[X918:$i]:((X915 @ X918))))=>(![X911:$i, X912:$i]:((![X913:$i]:(((in @ X913 @ X911)=>(in @ X913 @ X912)))=>(![X914:$i]:(((in @ X914 @ X912)=>(in @ X914 @ X911)))=>((X911)=(X912)))))=>(![X909:$i]:((![X910:$i]:(~(in @ X910 @ X909))=>((X909)=(emptyset))))=>(![X907:$i]:((![X908:$i]:(~(in @ X908 @ X907))=>((X907)=(emptyset))))=>(![X904:$i, X905:$i > $o, X906:$i]:(((in @ X906 @ X904)=>((in @ X906 @ (dsetconstr @ X904 @ X905))<=>(X905 @ X906))))=>(![X522:$i]:((((X522)!=(emptyset))=>?[X523:$i]:((in @ X523 @ X522))))=>(![X901:$i, X902:$i > $o, X903:$i]:(((in @ X903 @ X901)=>((X902 @ X903)=>((dsetconstr @ X901 @ X902)!=(emptyset)))))=>(![X899:$i]:((?[X900:$i]:((in @ X900 @ X899))=>((X899)!=(emptyset))))=>(![X524:$i, X525:$i]:((in @ X524 @ (setadjoin @ X524 @ X525)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X526:$i, X527:$i, X528:$i]:(((in @ X528 @ X527)=>(in @ X528 @ (setadjoin @ X526 @ X527))))=>(![X529:$i, X530:$i, X531:$i]:(((in @ X531 @ (setadjoin @ X529 @ X530))=>![X532:$o]:(((((X531)=(X529))=>(X532))=>(((in @ X531 @ X530)=>(X532))=>(X532))))))=>(![X896:$i, X897:$i, X898:$i]:(((in @ X898 @ (setadjoin @ X896 @ X897))=>(((X898)=(X896))|(in @ X898 @ X897))))=>(![X533:$i]:(((dsetconstr @ X533 @ (^[Z0/* 1 */:$i]:($true)))=(X533)))=>(![X893:$i, X894:$i]:((![X895:$i]:(((in @ X895 @ X894)=>(in @ X895 @ X893)))=>(in @ X894 @ (powerset @ X893))))=>(![X534:$i]:((in @ emptyset @ (powerset @ X534)))=>(![X892:$i]:((in @ emptyset @ (powerset @ X892)))=>(![X889:$i, X890:$i, X891:$i]:(((in @ X890 @ (powerset @ X889))=>((in @ X891 @ X890)=>(in @ X891 @ X889))))=>(![X535:$i, X536:$i, X537:$i]:(((in @ X536 @ X537)=>((in @ X537 @ X535)=>(in @ X536 @ (setunion @ X535)))))=>(![X885:$i, X886:$i]:(((in @ X886 @ (setunion @ X885))=>![X887:$o]:((![X888:$i]:(((in @ X886 @ X888)=>((in @ X888 @ X885)=>(X887))))=>(X887)))))=>(![X538:$i, X539:$i]:(((in @ X539 @ X538)=>(in @ X539 @ (powerset @ (setunion @ X538)))))=>(![X540:$i > $o]:((?[X541:$i]:(((X540 @ X541)&![X542:$i]:(((X540 @ X542)=>((X541)=(X542))))))=>?[X543:$i]:(![X544:$i]:(((X540 @ X544)<=>((X544)=(X543)))))))=>(![X883:$i]:((((X883)!=(emptyset))=>?[X884:$i]:(((in @ X884 @ X883)&$true))))=>(![X881:$i, X882:$i]:(((in @ X881 @ (setadjoin @ X882 @ emptyset))=>((X881)=(X882))))=>(![X545:$i, X546:$i]:((((X545)!=(X546))=>~(in @ X546 @ (setadjoin @ X545 @ emptyset))))=>(![X547:$i, X548:$i]:((((X547)=(X548))=>(in @ X547 @ (setadjoin @ X548 @ emptyset))))=>(![X549:$i, X550:$i]:(((in @ X549 @ (setadjoin @ X550 @ emptyset))=>(in @ X550 @ (setadjoin @ X549 @ emptyset))))=>(![X878:$i, X879:$i, X880:$i]:(((in @ X880 @ (setadjoin @ X878 @ (setadjoin @ X879 @ emptyset)))=>(((X880)=(X878))|((X880)=(X879)))))=>(![X551:$i, X552:$i]:((in @ X551 @ (setadjoin @ X551 @ (setadjoin @ X552 @ emptyset))))=>(![X553:$i, X554:$i]:((in @ X554 @ (setadjoin @ X553 @ (setadjoin @ X554 @ emptyset))))=>(![X555:$i, X556:$i > $o]:((?[X557:$i]:(((in @ X557 @ X555)&(X556 @ X557)))=>(((dsetconstr @ X555 @ X556)=(emptyset))=>~($true))))=>(![X558:$i > $o, X559:$i]:(((in @ X559 @ emptyset)=>(X558 @ X559)))=>(![X560:$i, X561:$i > $o]:((~(![X562:$i]:(((in @ X562 @ X560)=>(X561 @ X562))))=>?[X563:$i]:(((in @ X563 @ X560)&~((X561 @ X563))))))=>(![X874:$i, X875:$i > $o]:((![X876:$i]:(((in @ X876 @ X874)=>~((X875 @ X876))))=>~(?[X877:$i]:(((in @ X877 @ X874)&(X875 @ X877))))))=>(![X564:$i, X565:$i > $o]:((~(?[X566:$i]:(((in @ X566 @ X564)&(X565 @ X566))))=>![X567:$i]:(((in @ X567 @ X564)=>~((X565 @ X567))))))=>(![X870:$i, X871:$i > $o]:((?[X872:$i]:(((in @ X872 @ X870)&~((X871 @ X872))))=>~(![X873:$i]:(((in @ X873 @ X870)=>(X871 @ X873))))))=>(![X869:$o]:(((X869)=>(in @ emptyset @ (prop2set @ ((X869))))))=>((prop2set2propI)=>(![X865:$i, X866:$i > $o]:((~(?[X867:$i]:(((in @ X867 @ X865)&(X866 @ X867))))=>![X868:$i]:(((in @ X868 @ X865)=>~((X866 @ X868))))))=>(![X568:$i, X569:$i > $o]:((~(![X570:$i]:(((in @ X570 @ X568)=>(X569 @ X570))))=>?[X571:$i]:(((in @ X571 @ X568)&~((X569 @ X571))))))=>(![X860:$i > $o]:((?[X861:$i]:(((X860 @ X861)&![X862:$i]:(((X860 @ X862)=>((X861)=(X862))))))=>?[X863:$i]:(((X860 @ X863)&![X864:$i]:(((X860 @ X864)=>((X863)=(X864))))))))=>(![X854:$i > $o]:((?[X855:$i]:((X854 @ X855))=>(![X856:$i, X857:$i]:(((X854 @ X856)=>((X854 @ X857)=>((X856)=(X857)))))=>?[X858:$i]:(((X854 @ X858)&![X859:$i]:(((X854 @ X859)=>((X858)=(X859)))))))))=>(![X849:$i > $o]:((?[X850:$i]:(![X851:$i]:(((X849 @ X851)<=>((X851)=(X850)))))=>?[X852:$i]:(((X849 @ X852)&![X853:$i]:(((X849 @ X853)=>((X852)=(X853))))))))=>(![X845:$i, X846:$i]:((((X845)=(X846))=>![X847:$i, X848:$i]:((((X847)=(X848))=>((in @ X847 @ X845)=>(in @ X848 @ X846))))))=>(![X841:$i, X842:$i]:((((X841)=(X842))=>![X843:$i, X844:$i]:((((X843)=(X844))=>((in @ X843 @ X841)<=>(in @ X844 @ X842))))))=>(![X572:$i > $o]:((?[X573:$i]:(((X572 @ X573)&![X574:$i]:(((X572 @ X574)=>((X573)=(X574))))))=>![X575:$i, X576:$i]:(((X572 @ X575)=>((X572 @ X576)=>((X575)=(X576)))))))=>(![X577:$i > $o, X578:$i > $o]:((![X579:$i, X580:$i]:((((X579)=(X580))=>((X577 @ X579)<=>(X578 @ X580))))=>(?[X581:$i]:(((X577 @ X581)&![X582:$i]:(((X577 @ X582)=>((X581)=(X582))))))<=>?[X583:$i]:(((X578 @ X583)&![X584:$i]:(((X578 @ X584)=>((X583)=(X584)))))))))=>(((emptyset)=(emptyset))=>(![X585:$i, X586:$i]:((((X585)=(X586))=>![X587:$i, X588:$i]:((((X587)=(X588))=>((setadjoin @ X585 @ X587)=(setadjoin @ X586 @ X588))))))=>(![X839:$i, X840:$i]:((((X839)=(X840))=>((powerset @ X839)=(powerset @ X840))))=>(![X589:$i, X590:$i]:((((X589)=(X590))=>((setunion @ X589)=(setunion @ X590))))=>(((omega)=(omega))=>(![X591:$i > $o]:((?[X592:$i]:(((X591 @ X592)&![X593:$i]:(((X591 @ X593)=>((X592)=(X593))))))=>![X594:$i, X595:$i]:(((X591 @ X594)=>((X591 @ X595)=>((X594)=(X595)))))))=>(![X831:$i > $o, X832:$i > $o]:((![X833:$i, X834:$i]:((((X833)=(X834))=>((X831 @ X833)<=>(X832 @ X834))))=>(?[X835:$i]:(((X831 @ X835)&![X836:$i]:(((X831 @ X836)=>((X835)=(X836))))))=>(?[X837:$i]:(((X832 @ X837)&![X838:$i]:(((X832 @ X838)=>((X837)=(X838))))))=>((descr @ X831)=(descr @ X832))))))=>(![X825:$i, X826:$i]:((((X825)=(X826))=>![X827:$i > $o, X828:$i > $o]:((![X829:$i]:(((in @ X829 @ X825)=>![X830:$i]:(((in @ X830 @ X826)=>(((X829)=(X830))=>((X827 @ X829)<=>(X828 @ X830)))))))=>((dsetconstr @ X825 @ X827)=(dsetconstr @ X826 @ X828))))))=>(![X822:$i, X823:$i]:((![X824:$i]:(((in @ X824 @ X822)=>(in @ X824 @ X823)))=>(subset @ X822 @ X823)))=>(![X596:$i, X597:$i]:((((X596)=(X597))=>(subset @ X597 @ X596)))=>(![X820:$i, X821:$i]:((((X820)=(X821))=>(subset @ X820 @ X821)))=>(![X817:$i, X818:$i]:((![X819:$i]:(((in @ X819 @ X817)=>(in @ X819 @ X818)))=>(subset @ X817 @ X818)))=>(![X598:$i]:((subset @ emptyset @ X598))=>(![X599:$i, X600:$i, X601:$i]:(((subset @ X599 @ X600)=>((in @ X601 @ X599)=>(in @ X601 @ X600))))=>(![X814:$i, X815:$i, X816:$i]:(((subset @ X814 @ X815)=>(~(in @ X816 @ X815)=>~(in @ X816 @ X814))))=>(![X602:$i, X603:$i, X604:$i]:(((in @ X604 @ X602)=>(~(in @ X604 @ X603)=>~(subset @ X602 @ X603))))=>(![X812:$i, X813:$i]:((~(subset @ X812 @ X813)=>((X812)!=(X813))))=>(![X809:$i, X810:$i, X811:$i]:(((in @ X811 @ X809)=>(~(in @ X811 @ X810)=>((X809)!=(X810)))))=>(![X808:$i]:((subset @ X808 @ X808))=>(![X605:$i, X606:$i, X607:$i]:(((subset @ X605 @ X606)=>((subset @ X606 @ X607)=>(subset @ X605 @ X607))))=>(![X806:$i, X807:$i]:((subset @ X807 @ (setadjoin @ X806 @ X807)))=>(![X608:$i, X609:$i, X610:$i]:(((subset @ X608 @ X610)=>(subset @ X608 @ (setadjoin @ X609 @ X610))))=>(![X611:$i, X612:$i]:(((subset @ X611 @ X612)=>(in @ X611 @ (powerset @ X612))))=>(![X804:$i, X805:$i]:(((subset @ X804 @ X805)=>((subset @ X805 @ X804)=>((X804)=(X805)))))=>(![X803:$i]:(((subset @ X803 @ emptyset)=>((X803)=(emptyset))))=>(![X613:$i, X614:$i]:(((subset @ X614 @ X613)=>(in @ X614 @ (powerset @ X613))))=>(![X801:$i, X802:$i]:(((in @ X802 @ (powerset @ X801))=>(subset @ X802 @ X801)))=>(![X800:$i]:((in @ X800 @ (powerset @ X800)))=>(![X615:$i, X616:$i]:(((subset @ X615 @ X616)=>(subset @ (powerset @ X615) @ (powerset @ X616))))=>(![X798:$i, X799:$i > $o]:((in @ (dsetconstr @ X798 @ X799) @ (powerset @ X798)))=>(![X617:$i, X618:$i > $o]:((subset @ (dsetconstr @ X617 @ X618) @ X617))=>(![X795:$i, X796:$i, X797:$i]:(((in @ X797 @ X795)=>(in @ X797 @ (binunion @ X795 @ X796))))=>(![X793:$i, X794:$i]:((in @ X794 @ (setadjoin @ X793 @ (setadjoin @ X794 @ emptyset))))=>(![X790:$i, X791:$i, X792:$i]:(((in @ X792 @ X791)=>(in @ X792 @ (binunion @ X790 @ X791))))=>(![X786:$i, X787:$i, X788:$i, X789:$o]:(((in @ X788 @ (binunion @ X786 @ X787))=>(((in @ X788 @ X786)=>(X789))=>(((in @ X788 @ X787)=>(X789))=>(X789)))))=>(![X783:$i, X784:$i, X785:$i]:(((in @ X785 @ (binunion @ X783 @ X784))=>((in @ X785 @ X783)|(in @ X785 @ X784))))=>(![X619:$i, X620:$i]:((subset @ X619 @ (binunion @ X619 @ X620)))=>(![X621:$i, X622:$i]:((subset @ X622 @ (binunion @ X621 @ X622)))=>(![X623:$i, X624:$i, X625:$i]:(((in @ X625 @ X623)=>((in @ X625 @ X624)=>(in @ X625 @ (binintersect @ X623 @ X624)))))=>(![X626:$i, X627:$i, X628:$i]:(((subset @ X628 @ X626)=>((subset @ X628 @ X627)=>(subset @ X628 @ (binintersect @ X626 @ X627)))))=>(![X629:$i, X630:$i, X631:$i]:(((in @ X631 @ (binintersect @ X629 @ X630))=>(in @ X631 @ X629)))=>(![X781:$i, X782:$i]:((subset @ (binintersect @ X781 @ X782) @ X781))=>(![X632:$i, X633:$i]:(((subset @ X632 @ X633)=>((binintersect @ X632 @ X633)=(X632))))=>(![X634:$i, X635:$i]:((((binintersect @ X634 @ X635)=(X635))=>(subset @ X635 @ X634)))=>(![X778:$i, X779:$i, X780:$i]:(((in @ X780 @ (binintersect @ X778 @ X779))=>(in @ X780 @ X779)))=>(![X775:$i, X776:$i]:((~(?[X777:$i]:(((in @ X777 @ X775)&(in @ X777 @ X776))))=>((binintersect @ X775 @ X776)=(emptyset))))=>(![X773:$i, X774:$i]:((subset @ (binintersect @ X773 @ X774) @ X774))=>(![X771:$i, X772:$i]:(((subset @ X772 @ X771)=>((binintersect @ X771 @ X772)=(X772))))=>(![X636:$i, X637:$i]:((((binintersect @ X636 @ X637)=(X636))=>(subset @ X636 @ X637)))=>(![X768:$i, X769:$i, X770:$i]:(((binintersect @ X768 @ (binunion @ X769 @ X770))=(binunion @ (binintersect @ X768 @ X769) @ (binintersect @ X768 @ X770))))=>(![X638:$i, X639:$i, X640:$i]:(((in @ X640 @ X638)=>(~(in @ X640 @ X639)=>(in @ X640 @ (setminus @ X638 @ X639)))))=>(![X765:$i, X766:$i, X767:$i]:(((in @ X767 @ (setminus @ X765 @ X766))=>(in @ X767 @ X765)))=>(![X641:$i, X642:$i, X643:$i]:(((in @ X643 @ (setminus @ X641 @ X642))=>~(in @ X643 @ X642)))=>(![X644:$i, X645:$i]:(((subset @ X644 @ X645)=>((setminus @ X644 @ X645)=(emptyset))))=>(![X646:$i, X647:$i, X648:$i]:((~(in @ X648 @ (setminus @ X646 @ X647))=>((in @ X648 @ X646)=>(in @ X648 @ X647))))=>(![X649:$i, X650:$i, X651:$i]:((~(in @ X651 @ (setminus @ X649 @ X650))=>(~(in @ X651 @ X650)=>~(in @ X651 @ X649))))=>(![X652:$i, X653:$i, X654:$i]:((~(in @ X654 @ X652)=>~(in @ X654 @ (setminus @ X652 @ X653))))=>(![X762:$i, X763:$i, X764:$i]:(((in @ X764 @ X763)=>~(in @ X764 @ (setminus @ X762 @ X763))))=>(![X760:$i, X761:$i]:((subset @ (setminus @ X760 @ X761) @ X760))=>(![X655:$i, X656:$i]:((((setminus @ X655 @ X656)=(emptyset))=>(subset @ X655 @ X656)))=>(![X657:$i, X658:$i, X659:$i]:(((in @ X659 @ (symdiff @ X657 @ X658))=>![X660:$o]:((((in @ X659 @ X657)=>(~(in @ X659 @ X658)=>(X660)))=>((~(in @ X659 @ X657)=>((in @ X659 @ X658)=>(X660)))=>(X660))))))=>(![X757:$i, X758:$i, X759:$i]:(((in @ X759 @ X757)=>(~(in @ X759 @ X758)=>(in @ X759 @ (symdiff @ X757 @ X758)))))=>(![X661:$i, X662:$i, X663:$i]:((~(in @ X663 @ X661)=>((in @ X663 @ X662)=>(in @ X663 @ (symdiff @ X661 @ X662)))))=>(![X664:$i, X665:$i, X666:$i]:(((in @ X666 @ X664)=>((in @ X666 @ X665)=>~(in @ X666 @ (symdiff @ X664 @ X665)))))=>(![X754:$i, X755:$i, X756:$i]:((~(in @ X756 @ X754)=>(~(in @ X756 @ X755)=>~(in @ X756 @ (symdiff @ X754 @ X755)))))=>(![X667:$i, X668:$i]:((in @ X668 @ (setadjoin @ X667 @ (setadjoin @ X668 @ 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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(assume_negation,[status(cth)],[setukpairinjL1]), setunionAx]), quantDeMorgan4]), c_0_188]), quantDeMorgan2]), upairsetE]), uniqinunit]), subsetTrans]), c_0_189]), setunionE]), setadjoinSub2]), powersetE]), emptyInPowerset]), powersetI]), subset2powerset]), setadjoinOr]), c_0_190]), powersetI1]), c_0_191]), c_0_192]), noeltsimpempty]), eqimpsubset2]), emptyI]), powersetsubset]), setext]), c_0_193]), c_0_194]), notinemptyset]), emptysetE]), symdiffE]), c_0_195]), binunionLsub]), c_0_196]), wellorderingAx]), c_0_197]), binunionRsub]), omegaIndAx]), omegaSAx]), emptysetsubset]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectSubset2]), binintersectSubset3]), binintersectSubset1]), setminusI]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusEL]), symdiffI2]), symdiffIneg1]), secondinupair]), setukpairIR]), c_0_198]), c_0_199]), singletonsubset]), singletoninpowerset]), subsetE]), singletoninpowunion]), notsubsetI]), upairset2E]), upairinpowunion]), ubforcartprodlem2]), c_0_200]), c_0_201]), setunionsingleton1]), setunionsingleton2]), c_0_202]), singletonsuniq]), c_0_203]), c_0_204]), c_0_205]), setunionsingleton]), setunionE2]), c_0_206]), c_0_207]), ubforcartprodlem1]), upairsubunion]), setukpairIL]), symdiffIneg2]), symdiffI1]), bs114d]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), binintersectER]), binintersectLsub]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), c_0_208]), inPowerset]), powersetE1]), subsetemptysetimpeq]), setextsub]), setadjoinSub]), subsetRefl]), notequalI2]), notequalI1]), subsetE2]), subsetI2]), eqimpsubset1]), subsetI1]), c_0_209]), c_0_210]), omega__Cong]), powerset__Cong]), emptyset__Cong]), in__Cong]), inCongP]), c_0_211]), c_0_212]), c_0_213]), notdexE]), prop2setI]), setunion__Cong]), setadjoin__Cong]), c_0_214]), c_0_215]), notdallE]), quantDeMorgan3]), quantDeMorgan1]), vacuousDall]), c_0_216]), upairsetIR]), upairsetIL]), singletonsswitch]), eqinunit]), notinsingleton]), c_0_217]), subPowSU]), setunionI]), emptyinPowerset]), c_0_218]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_219]), emptysetimpfalse]), prop2setE]), c_0_220]), c_0_221]), c_0_222]), foundationAx]), omega0Ax]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_223])). 0.77/0.64 thf(c_0_225, negated_conjecture, ![X962:$i, X963:$i, X965:$i, X966:$i, X967:$i, X968:$i, X969:$i, X970:$i, X971:$i, X972:$i, X973:$i, X975:$i, X976:$i, X978:$i, X979:$i, X980:$i, X981:$i, X982:$i, X984:$i, X985:$i > $i > $o, X986:$i, X988:$i, X991:$i, X993:$i, X994:$i, X995:$i, X996:$i, X998:$i, X999:$i > $o, X1000:$i, X1002:$i, X1003:$i > $o, X1004:$i, X1005:$i, X1006:$i > $o, X1007:$i, X1008:$i, X1009:$i > $o, X1010:$i, X1011:$i > $o, X1012:$i, X1015:$i, X1016:$o, X1017:$i, X1018:$i, X1019:$o, X1020:$i, X1021:$i, X1022:$i > $o, X1023:$i, X1026:$i, X1027:$i, X1030:$i, X1032:$i, X1034:$i, X1035:$i > $o, X1036:$i, X1037:$i, X1039:$i, X1040:$i > $o, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$o, X1053:$i, X1054:$i, X1055:$i, X1056:$i, X1057:$i, X1058:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$o, X1072:$i, X1073:$i, X1074:$i > $o, X1075:$i, X1078:$i, X1079:$i, X1080:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i > $o, X1099:$i, X1100:$i > $o, X1101:$i, X1102:$i, X1103:$i > $o, X1104:$i, X1106:$i, X1107:$i > $o, X1109:$i, X1110:$i, X1111:$i > $o, X1113:$i, X1114:$i, X1115:$i > $o, X1116:$i, X1118:$o, X1119:$i, X1120:$i > $o, X1122:$i, X1123:$i, X1124:$i > $o, X1125:$i, X1127:$i > $o, X1128:$i, X1131:$i, X1132:$i > $o, X1133:$i, X1137:$i, X1138:$i > $o, X1139:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$i > $o, X1152:$i, X1154:$i, X1155:$i, X1156:$i > $o, X1157:$i > $o, X1160:$i, X1163:$i, X1164:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i > $o, X1177:$i, X1179:$i, X1180:$i, X1181:$i > $o, X1182:$i > $o, X1185:$i, X1187:$i, X1189:$i, X1190:$i, X1191:$i > $o, X1192:$i > $o, X1195:$i, X1196:$i, X1198:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1205:$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:$i, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i > $o, X1243:$i, X1244:$i > $o, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$o, X1257:$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, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$o, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1347:$i, X1348:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1390:$i, X1391:$i, X1392:$i, X1395:$i, X1396:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i > $o, X1405:$i, X1407:$i, X1408:$i > $o, X1409:$i, X1411:$i, X1412:$i > $o, X1413:$i, X1416:$i, X1417:$i > $o, X1420:$i, X1422:$i, X1423:$i]:((((~(in @ (esk1_2 @ X962 @ X963) @ X962)|~(in @ (esk1_2 @ X962 @ X963) @ X963)|((X962)=(X963)))&((in @ (esk1_2 @ X962 @ X963) @ X962)|(in @ (esk1_2 @ X962 @ X963) @ X963)|((X962)=(X963))))&(~(in @ X965 @ emptyset)&(((~(in @ X968 @ (setadjoin @ X966 @ X967))|(((X968)=(X966))|(in @ X968 @ X967)))&((((X968)!=(X966))|(in @ X968 @ (setadjoin @ X966 @ X967)))&(~(in @ X968 @ X967)|(in @ X968 @ (setadjoin @ X966 @ X967)))))&(((~(in @ X970 @ (powerset @ X969))|(~(in @ X971 @ X970)|(in @ X971 @ X969)))&(((in @ (esk2_2 @ X972 @ X973) 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X1278 @ X1277))&((~(in @ X1281 @ (binintersect @ X1279 @ X1280))|(in @ X1281 @ X1280))&((((in @ (esk54_2 @ X1282 @ X1283) @ X1282)|((binintersect @ X1282 @ X1283)=(emptyset)))&((in @ (esk54_2 @ X1282 @ X1283) @ X1283)|((binintersect @ X1282 @ X1283)=(emptyset))))&((subset @ (binintersect @ X1285 @ X1286) @ X1286)&((~(subset @ X1288 @ X1287)|((binintersect @ X1287 @ X1288)=(X1288)))&((((binintersect @ X1289 @ X1290)!=(X1289))|(subset @ X1289 @ X1290))&(((binintersect @ X1291 @ (binunion @ X1292 @ X1293))=(binunion @ (binintersect @ X1291 @ X1292) @ (binintersect @ X1291 @ X1293)))&((~(in @ X1296 @ X1294)|((in @ X1296 @ X1295)|(in @ X1296 @ (setminus @ X1294 @ X1295))))&((~(in @ X1299 @ (setminus @ X1297 @ X1298))|(in @ X1299 @ X1297))&((~(in @ X1302 @ (setminus @ X1300 @ X1301))|~(in @ X1302 @ X1301))&((~(subset @ X1303 @ X1304)|((setminus @ X1303 @ X1304)=(emptyset)))&(((in @ X1307 @ (setminus @ X1305 @ X1306))|(~(in @ X1307 @ X1305)|(in @ X1307 @ X1306)))&(((in @ X1310 @ (setminus @ X1308 @ X1309))|((in @ X1310 @ X1309)|~(in @ X1310 @ X1308)))&(((in @ X1313 @ X1311)|~(in @ X1313 @ (setminus @ X1311 @ X1312)))&((~(in @ X1316 @ X1315)|~(in @ X1316 @ (setminus @ X1314 @ X1315)))&((subset @ (setminus @ X1317 @ X1318) @ X1317)&((((setminus @ X1319 @ X1320)!=(emptyset))|(subset @ X1319 @ X1320))&((((~(in @ X1323 @ X1321)|(X1324)|(in @ X1323 @ X1321)|~(in @ X1323 @ (symdiff @ X1321 @ X1322)))&(((in @ X1323 @ X1322)|(X1324)|(in @ X1323 @ X1321)|~(in @ X1323 @ (symdiff @ X1321 @ X1322)))&(~(X1324)|(X1324)|(in @ X1323 @ X1321)|~(in @ X1323 @ (symdiff @ X1321 @ X1322)))))&(((~(in @ X1323 @ X1321)|(X1324)|~(in @ X1323 @ X1322)|~(in @ X1323 @ (symdiff @ X1321 @ X1322)))&(((in @ X1323 @ X1322)|(X1324)|~(in @ X1323 @ X1322)|~(in @ X1323 @ (symdiff @ X1321 @ X1322)))&(~(X1324)|(X1324)|~(in @ X1323 @ X1322)|~(in @ X1323 @ (symdiff @ X1321 @ X1322)))))&((~(in @ X1323 @ X1321)|(X1324)|~(X1324)|~(in @ X1323 @ (symdiff @ X1321 @ X1322)))&(((in @ X1323 @ X1322)|(X1324)|~(X1324)|~(in @ X1323 @ (symdiff @ X1321 @ X1322)))&(~(X1324)|(X1324)|~(X1324)|~(in @ X1323 @ (symdiff @ X1321 @ X1322)))))))&((~(in @ X1327 @ X1325)|((in @ X1327 @ X1326)|(in @ X1327 @ (symdiff @ X1325 @ X1326))))&(((in @ X1330 @ X1328)|(~(in @ X1330 @ X1329)|(in @ X1330 @ (symdiff @ X1328 @ X1329))))&((~(in @ X1333 @ X1331)|(~(in @ X1333 @ X1332)|~(in @ X1333 @ (symdiff @ X1331 @ X1332))))&(((in @ X1336 @ X1334)|((in @ X1336 @ X1335)|~(in @ X1336 @ (symdiff @ X1334 @ X1335))))&((in @ X1338 @ (setadjoin @ X1337 @ (setadjoin @ X1338 @ emptyset)))&((in @ X1339 @ (setunion @ (setadjoin @ (setadjoin @ X1339 @ emptyset) @ (setadjoin @ (setadjoin @ X1339 @ (setadjoin @ X1340 @ emptyset)) @ emptyset))))&((in @ X1342 @ (setunion @ (setadjoin @ (setadjoin @ X1341 @ emptyset) @ (setadjoin @ (setadjoin @ X1341 @ (setadjoin @ X1342 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1343 @ X1344) @ (setunion @ (setadjoin @ (setadjoin @ X1343 @ emptyset) @ (setadjoin @ (setadjoin @ X1343 @ (setadjoin @ X1344 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1343 @ X1344) @ (setunion @ (setadjoin @ (setadjoin @ X1343 @ emptyset) @ (setadjoin @ (setadjoin @ X1343 @ (setadjoin @ X1344 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1343 @ emptyset) @ (setadjoin @ (setadjoin @ X1343 @ (setadjoin @ X1344 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1343 @ X1344) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1343 @ X1344) @ (setadjoin @ (esk56_2 @ X1343 @ X1344) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1347 @ X1348) @ (setunion @ (setadjoin @ (setadjoin @ X1347 @ emptyset) @ (setadjoin @ (setadjoin @ X1347 @ (setadjoin @ X1348 @ emptyset)) @ emptyset))))&((in @ (esk58_2 @ X1347 @ X1348) @ (setunion @ (setadjoin @ (setadjoin @ X1347 @ emptyset) @ (setadjoin @ (setadjoin @ X1347 @ (setadjoin @ X1348 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1347 @ emptyset) @ (setadjoin @ (setadjoin @ X1347 @ (setadjoin @ X1348 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk57_2 @ X1347 @ X1348) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1347 @ X1348) @ (setadjoin @ (esk58_2 @ X1347 @ X1348) @ emptyset)) @ emptyset)))))&((~(in @ X1352 @ X1351)|(subset @ (setadjoin @ X1352 @ emptyset) @ X1351))&((~(in @ X1354 @ X1353)|(in @ (setadjoin @ X1354 @ emptyset) @ (powerset @ X1353)))&((~(in @ X1357 @ X1355)|(in @ (setadjoin @ X1357 @ emptyset) @ (powerset @ (binunion @ X1355 @ X1356))))&((~(in @ X1360 @ (setadjoin @ X1358 @ (setadjoin @ X1359 @ emptyset)))|(((X1360)=(X1358))|((X1360)=(X1359))))&((~(in @ X1363 @ X1361)|(~(in @ X1364 @ X1362)|(subset @ (setadjoin @ X1363 @ (setadjoin @ X1364 @ emptyset)) @ (binunion @ X1361 @ X1362))))&((~(in @ X1367 @ X1365)|(~(in @ X1368 @ X1366)|(in @ (setadjoin @ X1367 @ (setadjoin @ X1368 @ emptyset)) @ (powerset @ (binunion @ X1365 @ X1366)))))&((~(in @ X1371 @ X1369)|(~(in @ X1372 @ X1370)|(subset @ (setadjoin @ (setadjoin @ X1371 @ emptyset) @ (setadjoin @ (setadjoin @ X1371 @ (setadjoin @ X1372 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1369 @ X1370)))))&((~(in @ X1375 @ X1373)|(~(in @ X1376 @ X1374)|(in @ (setadjoin @ (setadjoin @ X1375 @ emptyset) @ (setadjoin @ (setadjoin @ X1375 @ (setadjoin @ X1376 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1373 @ X1374))))))&((~(in @ X1379 @ X1377)|(~(in @ X1380 @ X1378)|(in @ (setadjoin @ (setadjoin @ X1379 @ emptyset) @ (setadjoin @ (setadjoin @ X1379 @ (setadjoin @ X1380 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1377 @ X1378))))))&((~(in @ X1383 @ X1381)|(~(in @ X1384 @ X1382)|(in @ (setadjoin @ (setadjoin @ X1383 @ emptyset) @ (setadjoin @ (setadjoin @ X1383 @ (setadjoin @ X1384 @ emptyset)) @ emptyset)) @ (cartprod @ X1381 @ X1382))))&((((in @ (esk59_3 @ X1385 @ X1386 @ X1387) @ X1385)|~(in @ X1387 @ (cartprod @ X1385 @ X1386)))&(((in @ (esk60_3 @ X1385 @ X1386 @ X1387) @ X1386)|~(in @ X1387 @ (cartprod @ X1385 @ X1386)))&(((X1387)=(setadjoin @ (setadjoin @ (esk59_3 @ X1385 @ X1386 @ X1387) @ emptyset) @ (setadjoin @ (setadjoin @ (esk59_3 @ X1385 @ X1386 @ X1387) @ (setadjoin @ (esk60_3 @ X1385 @ X1386 @ X1387) @ emptyset)) @ emptyset)))|~(in @ X1387 @ (cartprod @ X1385 @ X1386)))))&((((in @ (esk61_3 @ X1390 @ X1391 @ X1392) @ (setunion @ X1392))|~(in @ X1392 @ (cartprod @ X1390 @ X1391)))&(((in @ (esk62_3 @ X1390 @ X1391 @ X1392) @ (setunion @ X1392))|~(in @ X1392 @ (cartprod @ X1390 @ X1391)))&(((X1392)=(setadjoin @ (setadjoin @ (esk61_3 @ X1390 @ X1391 @ X1392) @ emptyset) @ (setadjoin @ (setadjoin @ (esk61_3 @ X1390 @ X1391 @ X1392) @ (setadjoin @ (esk62_3 @ X1390 @ X1391 @ X1392) @ emptyset)) @ emptyset)))|~(in @ X1392 @ (cartprod @ X1390 @ X1391)))))&((((in @ (esk63_2 @ X1395 @ X1396) @ X1395)|~(in @ X1396 @ (setunion @ X1395)))&((in @ X1396 @ (esk63_2 @ X1395 @ X1396))|~(in @ X1396 @ (setunion @ X1395))))&((subset @ (setunion @ (setadjoin @ X1398 @ emptyset)) @ X1398)&((subset @ X1399 @ (setunion @ (setadjoin @ X1399 @ emptyset)))&(((setunion @ (setadjoin @ X1400 @ emptyset))=(X1400))&(((((in @ (esk66_2 @ X1401 @ X1402) @ (dsetconstr @ X1401 @ X1402))|(~(in @ X1405 @ X1401)|~(X1402 @ X1405))|(in @ (esk64_2 @ X1401 @ X1402) @ X1401))&(((dsetconstr @ X1401 @ X1402)=(setadjoin @ (esk66_2 @ X1401 @ X1402) @ emptyset))|(~(in @ X1405 @ X1401)|~(X1402 @ X1405))|(in @ (esk64_2 @ X1401 @ X1402) @ X1401)))&((((in @ (esk66_2 @ X1401 @ X1402) @ (dsetconstr @ X1401 @ X1402))|(~(in @ X1405 @ X1401)|~(X1402 @ X1405))|(in @ (esk65_2 @ X1401 @ X1402) @ X1401))&(((dsetconstr @ X1401 @ X1402)=(setadjoin @ (esk66_2 @ X1401 @ X1402) @ emptyset))|(~(in @ X1405 @ X1401)|~(X1402 @ X1405))|(in @ (esk65_2 @ X1401 @ X1402) @ X1401)))&((((in @ (esk66_2 @ X1401 @ X1402) @ (dsetconstr @ X1401 @ X1402))|(~(in @ X1405 @ X1401)|~(X1402 @ X1405))|(X1402 @ (esk64_2 @ X1401 @ X1402)))&(((dsetconstr @ X1401 @ X1402)=(setadjoin @ (esk66_2 @ X1401 @ X1402) @ emptyset))|(~(in @ X1405 @ X1401)|~(X1402 @ X1405))|(X1402 @ (esk64_2 @ X1401 @ X1402))))&((((in @ (esk66_2 @ X1401 @ X1402) @ (dsetconstr @ X1401 @ X1402))|(~(in @ X1405 @ X1401)|~(X1402 @ X1405))|(X1402 @ (esk65_2 @ X1401 @ X1402)))&(((dsetconstr @ X1401 @ X1402)=(setadjoin @ (esk66_2 @ X1401 @ X1402) @ emptyset))|(~(in @ X1405 @ X1401)|~(X1402 @ X1405))|(X1402 @ (esk65_2 @ X1401 @ X1402))))&(((in @ (esk66_2 @ X1401 @ X1402) @ (dsetconstr @ X1401 @ X1402))|(~(in @ X1405 @ X1401)|~(X1402 @ X1405))|((esk64_2 @ X1401 @ X1402)!=(esk65_2 @ X1401 @ X1402)))&(((dsetconstr @ X1401 @ X1402)=(setadjoin @ (esk66_2 @ X1401 @ X1402) @ emptyset))|(~(in @ X1405 @ X1401)|~(X1402 @ X1405))|((esk64_2 @ X1401 @ X1402)!=(esk65_2 @ X1401 @ X1402))))))))&((((in @ (esk67_2 @ X1407 @ X1408) @ X1407)|(~(in @ X1409 @ (dsetconstr @ X1407 @ X1408))|((dsetconstr @ X1407 @ X1408)!=(setadjoin @ X1409 @ emptyset))))&((X1408 @ (esk67_2 @ X1407 @ X1408))|(~(in @ X1409 @ (dsetconstr @ X1407 @ X1408))|((dsetconstr @ X1407 @ X1408)!=(setadjoin @ X1409 @ emptyset)))))&(((((in @ (esk69_3 @ X1411 @ X1412 @ X1413) @ (dsetconstr @ X1411 @ X1412))|(in @ (esk68_3 @ X1411 @ X1412 @ X1413) @ X1411)|~(X1412 @ X1413)|~(in @ X1413 @ X1411))&(((dsetconstr @ X1411 @ X1412)=(setadjoin @ (esk69_3 @ X1411 @ X1412 @ X1413) @ emptyset))|(in @ (esk68_3 @ X1411 @ X1412 @ X1413) @ X1411)|~(X1412 @ X1413)|~(in @ X1413 @ X1411)))&((((in @ (esk69_3 @ X1411 @ X1412 @ X1413) @ (dsetconstr @ X1411 @ X1412))|(X1412 @ (esk68_3 @ X1411 @ X1412 @ X1413))|~(X1412 @ X1413)|~(in @ X1413 @ X1411))&(((dsetconstr @ X1411 @ X1412)=(setadjoin @ (esk69_3 @ X1411 @ X1412 @ X1413) @ emptyset))|(X1412 @ (esk68_3 @ X1411 @ X1412 @ X1413))|~(X1412 @ X1413)|~(in @ X1413 @ X1411)))&(((in @ (esk69_3 @ X1411 @ X1412 @ X1413) @ (dsetconstr @ X1411 @ X1412))|((esk68_3 @ X1411 @ X1412 @ X1413)!=(X1413))|~(X1412 @ X1413)|~(in @ X1413 @ X1411))&(((dsetconstr @ X1411 @ X1412)=(setadjoin @ (esk69_3 @ X1411 @ X1412 @ X1413) @ emptyset))|((esk68_3 @ X1411 @ X1412 @ X1413)!=(X1413))|~(X1412 @ X1413)|~(in @ X1413 @ X1411)))))&(((((in @ (esk72_2 @ X1416 @ X1417) @ (dsetconstr @ X1416 @ X1417))|(~(in @ X1420 @ X1416)|~(X1417 @ X1420))|(in @ (esk70_2 @ X1416 @ X1417) @ X1416))&(((dsetconstr @ X1416 @ X1417)=(setadjoin @ (esk72_2 @ X1416 @ X1417) @ emptyset))|(~(in @ X1420 @ X1416)|~(X1417 @ X1420))|(in @ (esk70_2 @ X1416 @ X1417) @ X1416)))&((((in @ (esk72_2 @ X1416 @ X1417) @ (dsetconstr @ X1416 @ X1417))|(~(in @ X1420 @ X1416)|~(X1417 @ X1420))|(in @ (esk71_2 @ X1416 @ X1417) @ X1416))&(((dsetconstr @ X1416 @ X1417)=(setadjoin @ (esk72_2 @ X1416 @ X1417) @ emptyset))|(~(in @ X1420 @ X1416)|~(X1417 @ X1420))|(in @ (esk71_2 @ X1416 @ X1417) @ X1416)))&((((in @ (esk72_2 @ X1416 @ X1417) @ (dsetconstr @ X1416 @ X1417))|(~(in @ X1420 @ X1416)|~(X1417 @ X1420))|(X1417 @ (esk70_2 @ X1416 @ X1417)))&(((dsetconstr @ X1416 @ X1417)=(setadjoin @ (esk72_2 @ X1416 @ X1417) @ emptyset))|(~(in @ X1420 @ X1416)|~(X1417 @ X1420))|(X1417 @ (esk70_2 @ X1416 @ X1417))))&((((in @ (esk72_2 @ X1416 @ X1417) @ (dsetconstr @ X1416 @ X1417))|(~(in @ X1420 @ X1416)|~(X1417 @ X1420))|(X1417 @ (esk71_2 @ X1416 @ X1417)))&(((dsetconstr @ X1416 @ X1417)=(setadjoin @ (esk72_2 @ X1416 @ X1417) @ emptyset))|(~(in @ X1420 @ X1416)|~(X1417 @ X1420))|(X1417 @ (esk71_2 @ X1416 @ X1417))))&(((in @ (esk72_2 @ X1416 @ X1417) @ (dsetconstr @ X1416 @ X1417))|(~(in @ X1420 @ X1416)|~(X1417 @ X1420))|((esk70_2 @ X1416 @ X1417)!=(esk71_2 @ X1416 @ X1417)))&(((dsetconstr @ X1416 @ X1417)=(setadjoin @ (esk72_2 @ X1416 @ X1417) @ emptyset))|(~(in @ X1420 @ X1416)|~(X1417 @ X1420))|((esk70_2 @ X1416 @ X1417)!=(esk71_2 @ X1416 @ X1417))))))))&((((setadjoin @ X1422 @ emptyset)!=(setadjoin @ X1423 @ emptyset))|((X1422)=(X1423)))&((in @ (setadjoin @ esk75_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk73_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk73_0 @ (setadjoin @ esk74_0 @ emptyset)) @ emptyset)))&((esk73_0)!=(esk75_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_224])])])])])])])). 0.77/0.64 thf(c_0_226, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((X2)=(X3))|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)))))), inference(split_conjunct,[status(thm)],[c_0_225])). 0.77/0.64 thf(c_0_227, negated_conjecture, (in @ (setadjoin @ esk75_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk73_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk73_0 @ (setadjoin @ esk74_0 @ emptyset)) @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_225])). 0.77/0.64 thf(c_0_228, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_225])). 0.77/0.64 thf(c_0_229, negated_conjecture, (((setadjoin @ esk73_0 @ (setadjoin @ esk74_0 @ emptyset))=(setadjoin @ esk75_0 @ emptyset))|((setadjoin @ esk75_0 @ emptyset)=(setadjoin @ esk73_0 @ emptyset))), inference(spm,[status(thm)],[c_0_226, c_0_227])). 0.77/0.64 thf(c_0_230, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_225])])])). 0.77/0.64 thf(c_0_231, negated_conjecture, (((setadjoin @ esk75_0 @ emptyset)=(setadjoin @ esk73_0 @ emptyset))|(in @ esk73_0 @ (setadjoin @ esk75_0 @ emptyset))), inference(spm,[status(thm)],[c_0_228, c_0_229])). 0.77/0.64 thf(c_0_232, negated_conjecture, ((esk73_0)!=(esk75_0)), inference(split_conjunct,[status(thm)],[c_0_225])). 0.77/0.64 thf(c_0_233, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_225])). 0.77/0.64 thf(c_0_234, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(split_conjunct,[status(thm)],[c_0_225])). 0.77/0.64 thf(c_0_235, negated_conjecture, ((setadjoin @ esk75_0 @ emptyset)=(setadjoin @ esk73_0 @ emptyset)), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_230, c_0_231]), c_0_232]), c_0_233])). 0.77/0.64 thf(c_0_236, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234, c_0_235]), c_0_234]), c_0_232]), ['proof']). 0.77/0.64 # SZS output end CNFRefutation 0.77/0.64 # Parsed axioms : 352 0.77/0.64 # Removed by relevancy pruning/SinE : 188 0.77/0.64 # Initial clauses : 315 0.77/0.64 # Removed in clause preprocessing : 24 0.77/0.64 # Initial clauses in saturation : 291 0.77/0.64 # Processed clauses : 526 0.77/0.64 # ...of these trivial : 12 0.77/0.64 # ...subsumed : 68 0.77/0.64 # ...remaining for further processing : 446 0.77/0.64 # Other redundant clauses eliminated : 18 0.77/0.64 # Clauses deleted for lack of memory : 0 0.77/0.64 # Backward-subsumed : 0 0.77/0.64 # Backward-rewritten : 8 0.77/0.64 # Generated clauses : 2020 0.77/0.64 # ...of the previous two non-redundant : 1896 0.77/0.64 # ...aggressively subsumed : 0 0.77/0.64 # Contextual simplify-reflections : 0 0.77/0.64 # Paramodulations : 2001 0.77/0.64 # Factorizations : 0 0.77/0.64 # NegExts : 0 0.77/0.64 # Equation resolutions : 19 0.77/0.64 # Disequality decompositions : 0 0.77/0.64 # Total rewrite steps : 180 0.77/0.64 # ...of those cached : 131 0.77/0.64 # Propositional unsat checks : 0 0.77/0.64 # Propositional check models : 0 0.77/0.64 # Propositional check unsatisfiable : 0 0.77/0.64 # Propositional clauses : 0 0.77/0.64 # Propositional clauses after purity: 0 0.77/0.64 # Propositional unsat core size : 0 0.77/0.64 # Propositional preprocessing time : 0.000 0.77/0.64 # Propositional encoding time : 0.000 0.77/0.64 # Propositional solver time : 0.000 0.77/0.64 # Success case prop preproc time : 0.000 0.77/0.64 # Success case prop encoding time : 0.000 0.77/0.64 # Success case prop solver time : 0.000 0.77/0.64 # Current number of processed clauses : 172 0.77/0.64 # Positive orientable unit clauses : 41 0.77/0.64 # Positive unorientable unit clauses: 0 0.77/0.64 # Negative unit clauses : 3 0.77/0.64 # Non-unit-clauses : 128 0.77/0.64 # Current number of unprocessed clauses: 1876 0.77/0.64 # ...number of literals in the above : 5425 0.77/0.64 # Current number of archived formulas : 0 0.77/0.64 # Current number of archived clauses : 261 0.77/0.64 # Clause-clause subsumption calls (NU) : 11426 0.77/0.64 # Rec. Clause-clause subsumption calls : 5080 0.77/0.64 # Non-unit clause-clause subsumptions : 41 0.77/0.64 # Unit Clause-clause subsumption calls : 74 0.77/0.64 # Rewrite failures with RHS unbound : 0 0.77/0.64 # BW rewrite match attempts : 22 0.77/0.64 # BW rewrite match successes : 6 0.77/0.64 # Condensation attempts : 526 0.77/0.64 # Condensation successes : 4 0.77/0.64 # Termbank termtop insertions : 73935 0.77/0.64 # Search garbage collected termcells : 15983 0.77/0.64 0.77/0.64 # ------------------------------------------------- 0.77/0.64 # User time : 0.102 s 0.77/0.64 # System time : 0.012 s 0.77/0.64 # Total time : 0.114 s 0.77/0.64 # Maximum resident set size: 5764 pages 0.77/0.64 0.77/0.64 # ------------------------------------------------- 0.77/0.64 # User time : 0.112 s 0.77/0.64 # System time : 0.013 s 0.77/0.64 # Total time : 0.126 s 0.77/0.64 # Maximum resident set size: 2204 pages 0.77/0.64 % E exiting 0.77/0.64 % E exiting 0.77/0.64 EOF