0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.11 % Command : run_E %s %d THM 0.11/0.32 % Computer : n024.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 : 1440 0.11/0.32 % WCLimit : 180 0.11/0.32 % DateTime : Thu Jul 4 08:27:53 EDT 2024 0.11/0.32 % CPUTime : 0.18/0.46 Running higher-order theorem proving 0.18/0.49 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p 0.56/0.60 # Version: 3.2.0-ho 0.56/0.60 # Preprocessing class: HSLMSLSSLLLCHFA. 0.56/0.60 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.56/0.60 # Starting ehoh_best5 with 180s (1) cores 0.56/0.60 # Starting almost_fo_3_lam with 180s (1) cores 0.56/0.60 # Starting new_bool_5 with 180s (1) cores 0.56/0.60 # Starting pre_casc_3 with 180s (1) cores 0.56/0.60 # Starting ho_unfolding_8 with 180s (1) cores 0.56/0.60 # Starting new_ho_10_cnf2 with 180s (1) cores 0.56/0.60 # Starting new_bool_3 with 180s (1) cores 0.56/0.60 # Starting new_ho_5 with 180s (1) cores 0.56/0.60 # new_ho_5 with pid 5267 completed with status 0 0.56/0.60 # Result found by new_ho_5 0.56/0.60 # Preprocessing class: HSLMSLSSLLLCHFA. 0.56/0.60 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.56/0.60 # Starting ehoh_best5 with 180s (1) cores 0.56/0.60 # Starting almost_fo_3_lam with 180s (1) cores 0.56/0.60 # Starting new_bool_5 with 180s (1) cores 0.56/0.60 # Starting pre_casc_3 with 180s (1) cores 0.56/0.60 # Starting ho_unfolding_8 with 180s (1) cores 0.56/0.60 # Starting new_ho_10_cnf2 with 180s (1) cores 0.56/0.60 # Starting new_bool_3 with 180s (1) cores 0.56/0.60 # Starting new_ho_5 with 180s (1) cores 0.56/0.60 # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true) 0.56/0.60 # Search class: HGHSM-FSLM31-MHFMMSBN 0.56/0.60 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 0.56/0.60 # Starting new_ho_10_cnf2 with 98s (1) cores 0.56/0.60 # new_ho_10_cnf2 with pid 5268 completed with status 0 0.56/0.60 # Result found by new_ho_10_cnf2 0.56/0.60 # Preprocessing class: HSLMSLSSLLLCHFA. 0.56/0.60 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.56/0.60 # Starting ehoh_best5 with 180s (1) cores 0.56/0.60 # Starting almost_fo_3_lam with 180s (1) cores 0.56/0.60 # Starting new_bool_5 with 180s (1) cores 0.56/0.60 # Starting pre_casc_3 with 180s (1) cores 0.56/0.60 # Starting ho_unfolding_8 with 180s (1) cores 0.56/0.60 # Starting new_ho_10_cnf2 with 180s (1) cores 0.56/0.60 # Starting new_bool_3 with 180s (1) cores 0.56/0.60 # Starting new_ho_5 with 180s (1) cores 0.56/0.60 # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true) 0.56/0.60 # Search class: HGHSM-FSLM31-MHFMMSBN 0.56/0.60 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 0.56/0.60 # Starting new_ho_10_cnf2 with 98s (1) cores 0.56/0.60 # Preprocessing time : 0.004 s 0.56/0.60 # Presaturation interreduction done 0.56/0.60 0.56/0.60 # Proof found! 0.56/0.60 # SZS status Theorem 0.56/0.60 # SZS output start CNFRefutation 0.56/0.60 thf(decl_22, type, in: $i > $i > $o). 0.56/0.60 thf(decl_23, type, exu: ($i > $o) > $o). 0.56/0.60 thf(decl_24, type, setextAx: $o). 0.56/0.60 thf(decl_25, type, emptyset: $i). 0.56/0.60 thf(decl_26, type, emptysetAx: $o). 0.56/0.60 thf(decl_27, type, setadjoin: $i > $i > $i). 0.56/0.60 thf(decl_28, type, setadjoinAx: $o). 0.56/0.60 thf(decl_29, type, powerset: $i > $i). 0.56/0.60 thf(decl_30, type, powersetAx: $o). 0.56/0.60 thf(decl_31, type, setunion: $i > $i). 0.56/0.60 thf(decl_32, type, setunionAx: $o). 0.56/0.60 thf(decl_33, type, omega: $i). 0.56/0.60 thf(decl_34, type, omega0Ax: $o). 0.56/0.60 thf(decl_35, type, omegaSAx: $o). 0.56/0.60 thf(decl_36, type, omegaIndAx: $o). 0.56/0.60 thf(decl_37, type, replAx: $o). 0.56/0.60 thf(decl_38, type, foundationAx: $o). 0.56/0.60 thf(decl_39, type, wellorderingAx: $o). 0.56/0.60 thf(decl_40, type, descr: ($i > $o) > $i). 0.56/0.60 thf(decl_41, type, descrp: $o). 0.56/0.60 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_43, type, dsetconstrI: $o). 0.56/0.60 thf(decl_44, type, dsetconstrEL: $o). 0.56/0.60 thf(decl_45, type, dsetconstrER: $o). 0.56/0.60 thf(decl_46, type, exuE1: $o). 0.56/0.60 thf(decl_47, type, prop2set: $o > $i). 0.56/0.60 thf(decl_48, type, prop2setE: $o). 0.56/0.60 thf(decl_49, type, emptysetE: $o). 0.56/0.60 thf(decl_50, type, emptysetimpfalse: $o). 0.56/0.60 thf(decl_51, type, notinemptyset: $o). 0.56/0.60 thf(decl_52, type, exuE3e: $o). 0.56/0.60 thf(decl_53, type, setext: $o). 0.56/0.60 thf(decl_54, type, emptyI: $o). 0.56/0.60 thf(decl_55, type, noeltsimpempty: $o). 0.56/0.60 thf(decl_56, type, setbeta: $o). 0.56/0.60 thf(decl_57, type, nonempty: $i > $o). 0.56/0.60 thf(decl_58, type, nonemptyE1: $o). 0.56/0.60 thf(decl_59, type, nonemptyI: $o). 0.56/0.60 thf(decl_60, type, nonemptyI1: $o). 0.56/0.60 thf(decl_61, type, setadjoinIL: $o). 0.56/0.60 thf(decl_62, type, emptyinunitempty: $o). 0.56/0.60 thf(decl_63, type, setadjoinIR: $o). 0.56/0.60 thf(decl_64, type, setadjoinE: $o). 0.56/0.60 thf(decl_65, type, setadjoinOr: $o). 0.56/0.60 thf(decl_66, type, setoftrueEq: $o). 0.56/0.60 thf(decl_67, type, powersetI: $o). 0.56/0.60 thf(decl_68, type, emptyinPowerset: $o). 0.56/0.60 thf(decl_69, type, emptyInPowerset: $o). 0.56/0.60 thf(decl_70, type, powersetE: $o). 0.56/0.60 thf(decl_71, type, setunionI: $o). 0.56/0.60 thf(decl_72, type, setunionE: $o). 0.56/0.60 thf(decl_73, type, subPowSU: $o). 0.56/0.60 thf(decl_74, type, exuE2: $o). 0.56/0.60 thf(decl_75, type, nonemptyImpWitness: $o). 0.56/0.60 thf(decl_76, type, uniqinunit: $o). 0.56/0.60 thf(decl_77, type, notinsingleton: $o). 0.56/0.60 thf(decl_78, type, eqinunit: $o). 0.56/0.60 thf(decl_79, type, singletonsswitch: $o). 0.56/0.60 thf(decl_80, type, upairsetE: $o). 0.56/0.60 thf(decl_81, type, upairsetIL: $o). 0.56/0.60 thf(decl_82, type, upairsetIR: $o). 0.56/0.60 thf(decl_83, type, emptyE1: $o). 0.56/0.60 thf(decl_84, type, vacuousDall: $o). 0.56/0.60 thf(decl_85, type, quantDeMorgan1: $o). 0.56/0.60 thf(decl_86, type, quantDeMorgan2: $o). 0.56/0.60 thf(decl_87, type, quantDeMorgan3: $o). 0.56/0.60 thf(decl_88, type, quantDeMorgan4: $o). 0.56/0.60 thf(decl_89, type, prop2setI: $o). 0.56/0.60 thf(decl_90, type, set2prop: $i > $o). 0.56/0.60 thf(decl_91, type, prop2set2propI: $o). 0.56/0.60 thf(decl_92, type, notdexE: $o). 0.56/0.60 thf(decl_93, type, notdallE: $o). 0.56/0.60 thf(decl_94, type, exuI1: $o). 0.56/0.60 thf(decl_95, type, exuI3: $o). 0.56/0.60 thf(decl_96, type, exuI2: $o). 0.56/0.60 thf(decl_97, type, inCongP: $o). 0.56/0.60 thf(decl_98, type, in__Cong: $o). 0.56/0.60 thf(decl_99, type, exuE3u: $o). 0.56/0.60 thf(decl_100, type, exu__Cong: $o). 0.56/0.60 thf(decl_101, type, emptyset__Cong: $o). 0.56/0.60 thf(decl_102, type, setadjoin__Cong: $o). 0.56/0.60 thf(decl_103, type, powerset__Cong: $o). 0.56/0.60 thf(decl_104, type, setunion__Cong: $o). 0.56/0.60 thf(decl_105, type, omega__Cong: $o). 0.56/0.60 thf(decl_106, type, exuEu: $o). 0.56/0.60 thf(decl_107, type, descr__Cong: $o). 0.56/0.60 thf(decl_108, type, dsetconstr__Cong: $o). 0.56/0.60 thf(decl_109, type, subset: $i > $i > $o). 0.56/0.60 thf(decl_112, type, subsetI1: $o). 0.56/0.60 thf(decl_113, type, eqimpsubset2: $o). 0.56/0.60 thf(decl_114, type, eqimpsubset1: $o). 0.56/0.60 thf(decl_115, type, subsetI2: $o). 0.56/0.60 thf(decl_116, type, emptysetsubset: $o). 0.56/0.60 thf(decl_117, type, subsetE: $o). 0.56/0.60 thf(decl_118, type, subsetE2: $o). 0.56/0.60 thf(decl_119, type, notsubsetI: $o). 0.56/0.60 thf(decl_120, type, notequalI1: $o). 0.56/0.60 thf(decl_121, type, notequalI2: $o). 0.56/0.60 thf(decl_122, type, subsetRefl: $o). 0.56/0.60 thf(decl_123, type, subsetTrans: $o). 0.56/0.60 thf(decl_124, type, setadjoinSub: $o). 0.56/0.60 thf(decl_125, type, setadjoinSub2: $o). 0.56/0.60 thf(decl_126, type, subset2powerset: $o). 0.56/0.60 thf(decl_127, type, setextsub: $o). 0.56/0.60 thf(decl_128, type, subsetemptysetimpeq: $o). 0.56/0.60 thf(decl_129, type, powersetI1: $o). 0.56/0.60 thf(decl_130, type, powersetE1: $o). 0.56/0.60 thf(decl_131, type, inPowerset: $o). 0.56/0.60 thf(decl_132, type, powersetsubset: $o). 0.56/0.60 thf(decl_133, type, sepInPowerset: $o). 0.56/0.60 thf(decl_134, type, sepSubset: $o). 0.56/0.60 thf(decl_135, type, binunion: $i > $i > $i). 0.56/0.60 thf(decl_136, type, binunionIL: $o). 0.56/0.60 thf(decl_137, type, upairset2IR: $o). 0.56/0.60 thf(decl_138, type, binunionIR: $o). 0.56/0.60 thf(decl_139, type, binunionEcases: $o). 0.56/0.60 thf(decl_140, type, binunionE: $o). 0.56/0.60 thf(decl_141, type, binunionLsub: $o). 0.56/0.60 thf(decl_142, type, binunionRsub: $o). 0.56/0.60 thf(decl_143, type, binintersect: $i > $i > $i). 0.56/0.60 thf(decl_144, type, binintersectI: $o). 0.56/0.60 thf(decl_145, type, binintersectSubset5: $o). 0.56/0.60 thf(decl_146, type, binintersectEL: $o). 0.56/0.60 thf(decl_147, type, binintersectLsub: $o). 0.56/0.60 thf(decl_148, type, binintersectSubset2: $o). 0.56/0.60 thf(decl_149, type, binintersectSubset3: $o). 0.56/0.60 thf(decl_150, type, binintersectER: $o). 0.56/0.60 thf(decl_151, type, disjointsetsI1: $o). 0.56/0.60 thf(decl_152, type, binintersectRsub: $o). 0.56/0.60 thf(decl_153, type, binintersectSubset4: $o). 0.56/0.60 thf(decl_154, type, binintersectSubset1: $o). 0.56/0.60 thf(decl_155, type, bs114d: $o). 0.56/0.60 thf(decl_157, type, setminus: $i > $i > $i). 0.56/0.60 thf(decl_158, type, setminusI: $o). 0.56/0.60 thf(decl_159, type, setminusEL: $o). 0.56/0.60 thf(decl_160, type, setminusER: $o). 0.56/0.60 thf(decl_161, type, setminusSubset2: $o). 0.56/0.60 thf(decl_162, type, setminusERneg: $o). 0.56/0.60 thf(decl_163, type, setminusELneg: $o). 0.56/0.60 thf(decl_164, type, setminusILneg: $o). 0.56/0.60 thf(decl_165, type, setminusIRneg: $o). 0.56/0.60 thf(decl_166, type, setminusLsub: $o). 0.56/0.60 thf(decl_167, type, setminusSubset1: $o). 0.56/0.60 thf(decl_168, type, symdiff: $i > $i > $i). 0.56/0.60 thf(decl_169, type, symdiffE: $o). 0.56/0.60 thf(decl_170, type, symdiffI1: $o). 0.56/0.60 thf(decl_171, type, symdiffI2: $o). 0.56/0.60 thf(decl_172, type, symdiffIneg1: $o). 0.56/0.60 thf(decl_173, type, symdiffIneg2: $o). 0.56/0.60 thf(decl_174, type, iskpair: $i > $o). 0.56/0.60 thf(decl_175, type, secondinupair: $o). 0.56/0.60 thf(decl_176, type, setukpairIL: $o). 0.56/0.60 thf(decl_177, type, setukpairIR: $o). 0.56/0.60 thf(decl_178, type, kpairiskpair: $o). 0.56/0.60 thf(decl_179, type, kpair: $i > $i > $i). 0.56/0.60 thf(decl_180, type, kpairp: $o). 0.56/0.60 thf(decl_181, type, cartprod: $i > $i > $i). 0.56/0.60 thf(decl_182, type, singletonsubset: $o). 0.56/0.60 thf(decl_183, type, singletoninpowerset: $o). 0.56/0.60 thf(decl_184, type, singletoninpowunion: $o). 0.56/0.60 thf(decl_185, type, upairset2E: $o). 0.56/0.60 thf(decl_186, type, upairsubunion: $o). 0.56/0.60 thf(decl_187, type, upairinpowunion: $o). 0.56/0.60 thf(decl_188, type, ubforcartprodlem1: $o). 0.56/0.60 thf(decl_189, type, ubforcartprodlem2: $o). 0.56/0.60 thf(decl_190, type, ubforcartprodlem3: $o). 0.56/0.60 thf(decl_191, type, cartprodpairin: $o). 0.56/0.60 thf(decl_192, type, cartprodmempair1: $o). 0.56/0.60 thf(decl_193, type, cartprodmempair: $o). 0.56/0.60 thf(decl_194, type, setunionE2: $o). 0.56/0.60 thf(decl_195, type, setunionsingleton1: $o). 0.56/0.60 thf(decl_196, type, setunionsingleton2: $o). 0.56/0.60 thf(decl_197, type, setunionsingleton: $o). 0.56/0.60 thf(decl_198, type, singleton: $i > $o). 0.56/0.60 thf(decl_199, type, singletonprop: $o). 0.56/0.60 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 0.56/0.60 thf(decl_201, type, ex1E1: $o). 0.56/0.60 thf(decl_202, type, ex1I: $o). 0.56/0.60 thf(decl_203, type, ex1I2: $o). 0.56/0.60 thf(decl_204, type, singletonsuniq: $o). 0.56/0.60 thf(decl_209, type, setukpairinjL1: $o). 0.56/0.60 thf(decl_210, type, kfstsingleton: $o). 0.56/0.60 thf(decl_211, type, theprop: $o). 0.56/0.60 thf(decl_212, type, kfst: $i > $i). 0.56/0.60 thf(decl_213, type, kfstpairEq: $o). 0.56/0.60 thf(decl_214, type, cartprodfstin: $o). 0.56/0.60 thf(decl_215, type, setukpairinjL2: $o). 0.56/0.60 thf(decl_216, type, setukpairinjL: $o). 0.56/0.60 thf(decl_217, type, setukpairinjR11: $o). 0.56/0.60 thf(decl_218, type, setukpairinjR12: $o). 0.56/0.60 thf(decl_219, type, setukpairinjR1: $o). 0.56/0.60 thf(decl_220, type, upairequniteq: $o). 0.56/0.60 thf(decl_221, type, setukpairinjR2: $o). 0.56/0.60 thf(decl_222, type, setukpairinjR: $o). 0.56/0.60 thf(decl_223, type, ksndsingleton: $o). 0.56/0.60 thf(decl_224, type, ksnd: $i > $i). 0.56/0.60 thf(decl_225, type, ksndpairEq: $o). 0.56/0.60 thf(decl_226, type, epred1_0: $o). 0.56/0.60 thf(decl_227, type, esk1_2: $i > $i > $i). 0.56/0.60 thf(decl_228, type, esk2_2: $i > $i > $i). 0.56/0.60 thf(decl_229, type, esk3_2: $i > $i > $i). 0.56/0.60 thf(decl_230, type, esk4_1: $i > $i). 0.56/0.60 thf(decl_231, type, esk5_2: ($i > $i > $o) > $i > $i). 0.56/0.60 thf(decl_232, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 0.56/0.60 thf(decl_233, type, esk7_2: ($i > $i > $o) > $i > $i). 0.56/0.60 thf(decl_234, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 0.56/0.60 thf(decl_235, type, esk9_1: $i > $i). 0.56/0.60 thf(decl_236, type, esk10_2: ($i > $o) > $i > $i). 0.56/0.60 thf(decl_237, type, esk11_2: ($i > $o) > $i > $i). 0.56/0.60 thf(decl_238, type, esk12_1: ($i > $o) > $i). 0.56/0.60 thf(decl_239, type, esk13_2: ($i > $o) > $i > $i). 0.56/0.60 thf(decl_240, type, esk14_1: ($i > $o) > $i). 0.56/0.60 thf(decl_241, type, esk15_2: $i > $i > $i). 0.56/0.60 thf(decl_242, type, esk16_2: $i > $i > $i). 0.56/0.60 thf(decl_243, type, esk17_1: $i > $i). 0.56/0.60 thf(decl_244, type, esk18_1: $i > $i). 0.56/0.60 thf(decl_245, type, esk19_1: $i > $i). 0.56/0.60 thf(decl_246, type, esk20_2: $i > $i > $i). 0.56/0.60 thf(decl_247, type, esk21_3: $i > $i > $o > $i). 0.56/0.60 thf(decl_248, type, esk22_2: ($i > $o) > $i > $i). 0.56/0.60 thf(decl_249, type, esk23_1: ($i > $o) > $i). 0.56/0.60 thf(decl_250, type, esk24_1: $i > $i). 0.56/0.60 thf(decl_251, type, esk25_2: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_252, type, esk26_2: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_253, type, esk27_2: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_254, type, esk28_2: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_255, type, esk29_2: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_256, type, esk30_2: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_257, type, esk31_2: ($i > $o) > $i > $i). 0.56/0.60 thf(decl_258, type, esk32_1: ($i > $o) > $i). 0.56/0.60 thf(decl_259, type, esk33_1: ($i > $o) > $i). 0.56/0.60 thf(decl_260, type, esk34_1: ($i > $o) > $i). 0.56/0.60 thf(decl_261, type, esk35_1: ($i > $o) > $i). 0.56/0.60 thf(decl_262, type, esk36_2: ($i > $o) > $i > $i). 0.56/0.60 thf(decl_263, type, esk37_1: ($i > $o) > $i). 0.56/0.60 thf(decl_264, type, esk38_2: ($i > $o) > $i > $i). 0.56/0.60 thf(decl_265, type, esk39_2: ($i > $o) > ($i > $o) > $i). 0.56/0.60 thf(decl_266, type, esk40_2: ($i > $o) > ($i > $o) > $i). 0.56/0.60 thf(decl_267, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 0.56/0.60 thf(decl_268, type, esk42_2: ($i > $o) > ($i > $o) > $i). 0.56/0.60 thf(decl_269, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 0.56/0.60 thf(decl_270, type, esk44_2: ($i > $o) > ($i > $o) > $i). 0.56/0.60 thf(decl_271, type, esk45_2: ($i > $o) > $i > $i). 0.56/0.60 thf(decl_272, type, esk46_2: ($i > $o) > ($i > $o) > $i). 0.56/0.60 thf(decl_273, type, esk47_2: ($i > $o) > ($i > $o) > $i). 0.56/0.60 thf(decl_274, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 0.56/0.60 thf(decl_275, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 0.56/0.60 thf(decl_276, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.56/0.60 thf(decl_277, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.56/0.60 thf(decl_278, type, esk52_2: $i > $i > $i). 0.56/0.60 thf(decl_279, type, esk53_2: $i > $i > $i). 0.56/0.60 thf(decl_280, type, esk54_2: $i > $i > $i). 0.56/0.60 thf(decl_281, type, esk55_2: $i > $i > $i). 0.56/0.60 thf(decl_282, type, esk56_2: $i > $i > $i). 0.56/0.60 thf(decl_283, type, esk57_2: $i > $i > $i). 0.56/0.60 thf(decl_284, type, esk58_2: $i > $i > $i). 0.56/0.60 thf(decl_285, type, esk59_3: $i > $i > $i > $i). 0.56/0.60 thf(decl_286, type, esk60_3: $i > $i > $i > $i). 0.56/0.60 thf(decl_287, type, esk61_3: $i > $i > $i > $i). 0.56/0.60 thf(decl_288, type, esk62_3: $i > $i > $i > $i). 0.56/0.60 thf(decl_289, type, esk63_2: $i > $i > $i). 0.56/0.60 thf(decl_290, type, esk64_2: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_291, type, esk65_2: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_292, type, esk66_2: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_293, type, esk67_2: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_294, type, esk68_3: $i > ($i > $o) > $i > $i). 0.56/0.60 thf(decl_295, type, esk69_3: $i > ($i > $o) > $i > $i). 0.56/0.60 thf(decl_296, type, esk70_2: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_297, type, esk71_2: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_298, type, esk72_2: $i > ($i > $o) > $i). 0.56/0.60 thf(decl_299, type, esk73_1: $i > $i). 0.56/0.60 thf(decl_300, type, esk74_1: $i > $i). 0.56/0.60 thf(decl_301, type, esk75_0: $i). 0.56/0.60 thf(decl_302, type, esk76_0: $i). 0.56/0.60 thf(decl_303, type, esk77_0: $i). 0.56/0.60 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', ex1)). 0.56/0.60 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', singleton)). 0.56/0.60 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', exuE2)). 0.56/0.60 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', exu)). 0.56/0.60 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', nonemptyI)). 0.56/0.60 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', nonempty)). 0.56/0.60 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', exuE3e)). 0.56/0.60 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', exuE1)). 0.56/0.60 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', descrp)). 0.56/0.60 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', replAx)). 0.56/0.60 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', kfstsingleton)). 0.56/0.60 thf(iskpair, axiom, ((iskpair)=(^[X4:$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/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', iskpair)). 0.56/0.60 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', ex1I2)). 0.56/0.60 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', singletonprop)). 0.56/0.60 thf(ex1I, axiom, ((ex1I)<=>![X4:$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/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', ex1I)). 0.56/0.60 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', ksndsingleton)). 0.56/0.60 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', ex1E1)). 0.56/0.60 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', descr__Cong)). 0.56/0.60 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', exu__Cong)). 0.56/0.60 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', exuI2)). 0.56/0.60 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', exuI3)). 0.56/0.60 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', exuEu)). 0.56/0.60 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/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', exuE3u)). 0.56/0.60 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/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', exuI1)). 0.56/0.60 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', dsetconstrI)). 0.56/0.60 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', sepInPowerset)). 0.56/0.60 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', sepSubset)). 0.56/0.60 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', dsetconstrER)). 0.56/0.60 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', theprop)). 0.56/0.60 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', kpairp)). 0.56/0.60 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', kpairiskpair)). 0.56/0.60 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', cartprodmempair)). 0.56/0.60 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', dsetconstr__Cong)). 0.56/0.60 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', emptyE1)). 0.56/0.60 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', nonemptyImpWitness)). 0.56/0.60 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setoftrueEq)). 0.56/0.60 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', nonemptyI1)). 0.56/0.60 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', nonemptyE1)). 0.56/0.60 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setbeta)). 0.56/0.60 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', dsetconstrEL)). 0.56/0.60 thf(kpairsurjEq, conjecture, ((((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((((wellorderingAx)=>((((dsetconstrEL)=>(((((emptysetE)=>(((notinemptyset)=>(((setext)=>((((setbeta)=>((nonemptyE1)=>(((nonemptyI1)=>((setadjoinIL)=>(((((setadjoinOr)=>((setoftrueEq)=>(((emptyinPowerset)=>((((setunionI)=>(((((nonemptyImpWitness)=>((uniqinunit)=>(((((upairsetE)=>((upairsetIL)=>((((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>((((exuI1)=>((((inCongP)=>(((exuE3u)=>((((setadjoin__Cong)=>(((((exuEu)=>(((((eqimpsubset2)=>((eqimpsubset1)=>(((emptysetsubset)=>((subsetE)=>(((notsubsetI)=>(((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>(((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>(((((sepInPowerset)=>((sepSubset)=>((binunionIL)=>(((((binunionE)=>((((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((((disjointsetsI1)=>((binintersectRsub)=>(((binintersectSubset1)=>((bs114d)=>(((setminusEL)=>(((setminusSubset2)=>((setminusERneg)=>(((setminusILneg)=>(((setminusLsub)=>(((((((symdiffIneg2)=>((secondinupair)=>((((kpairiskpair)=>((kpairp)=>((singletonsubset)=>(((singletoninpowunion)=>((((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((((((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>(((singletonprop)=>(((ex1I)=>(((singletonsuniq)=>((setukpairinjL1)=>(((theprop)=>((((setukpairinjL2)=>(((((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((![X18:$i]:((((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))<=(iskpair @ X18)))<=(ksndpairEq))<=(ksndsingleton))))))<=(setukpairinjR12))<=(setukpairinjR11))<=(setukpairinjL)))<=(cartprodfstin))<=(kfstpairEq)))<=(kfstsingleton))))<=(ex1I2)))<=(ex1E1)))<=(setunionsingleton)))))<=(cartprodmempair))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3)))))<=(upairsubunion))<=(upairset2E)))<=(singletoninpowerset)))))<=(setukpairIR))<=(setukpairIL))))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1))<=(symdiffE))<=(setminusSubset1)))<=(setminusIRneg)))<=(setminusELneg))))<=(setminusER)))<=(setminusI))))<=(binintersectSubset4))))<=(binintersectER))<=(binintersectSubset3)))))))<=(binunionRsub))<=(binunionLsub)))<=(binunionEcases))<=(binunionIR))<=(upairset2IR)))))<=(powersetsubset))<=(inPowerset))<=(powersetE1))))))<=(setadjoinSub2))))))<=(notequalI1)))<=(subsetE2))))<=(subsetI2))))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong)))<=(omega__Cong))<=(setunion__Cong))<=(powerset__Cong)))<=(emptyset__Cong))<=(exu__Cong)))<=(in__Cong)))<=(exuI2))<=(exuI3)))<=(notdallE))<=(notdexE))))<=(quantDeMorgan4))))))<=(emptyE1))<=(upairsetIR))))<=(singletonsswitch))<=(eqinunit))<=(notinsingleton))))<=(exuE2))<=(subPowSU))<=(setunionE)))<=(powersetE))<=(emptyInPowerset)))<=(powersetI))))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty))))<=(nonemptyI))))<=(noeltsimpempty))<=(emptyI)))<=(exuE3e)))<=(emptysetimpfalse)))<=(prop2setE))<=(exuE1))<=(dsetconstrER)))<=(dsetconstrI))<=(descrp)))<=(foundationAx))<=(replAx))))))))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', kpairsurjEq)). 0.56/0.60 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', notequalI2)). 0.56/0.60 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setextAx)). 0.56/0.60 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', singletonsswitch)). 0.56/0.60 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', eqinunit)). 0.56/0.60 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', notinsingleton)). 0.56/0.60 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setadjoinSub)). 0.56/0.60 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', subPowSU)). 0.56/0.60 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', subset2powerset)). 0.56/0.60 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/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setunionE)). 0.56/0.60 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', powersetE)). 0.56/0.60 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', emptyInPowerset)). 0.56/0.60 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setextsub)). 0.56/0.60 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', powersetI)). 0.56/0.60 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setadjoinE)). 0.56/0.60 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', subsetemptysetimpeq)). 0.56/0.60 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setadjoinIR)). 0.56/0.60 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', emptyinunitempty)). 0.56/0.60 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', powersetI1)). 0.56/0.60 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', noeltsimpempty)). 0.56/0.60 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', notsubsetI)). 0.56/0.60 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', emptyI)). 0.56/0.60 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', emptysetimpfalse)). 0.56/0.60 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', prop2setE)). 0.56/0.60 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setminusLsub)). 0.56/0.60 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binunionIL)). 0.56/0.60 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', foundationAx)). 0.56/0.60 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', emptysetAx)). 0.56/0.60 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binunionE)). 0.56/0.60 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binintersectI)). 0.56/0.60 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binintersectSubset5)). 0.56/0.60 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binintersectEL)). 0.56/0.60 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binintersectLsub)). 0.56/0.60 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binintersectSubset2)). 0.56/0.60 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', disjointsetsI1)). 0.56/0.60 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binintersectRsub)). 0.56/0.60 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binintersectSubset1)). 0.56/0.60 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', bs114d)). 0.56/0.60 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setminusEL)). 0.56/0.60 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setminusSubset2)). 0.56/0.60 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setminusERneg)). 0.56/0.60 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setminusILneg)). 0.56/0.60 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', symdiffIneg2)). 0.56/0.60 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', secondinupair)). 0.56/0.60 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', singletonsubset)). 0.56/0.60 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', singletoninpowunion)). 0.56/0.60 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', upairinpowunion)). 0.56/0.60 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', ubforcartprodlem1)). 0.56/0.60 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', ubforcartprodlem2)). 0.56/0.60 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', subsetRefl)). 0.56/0.60 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setunionE2)). 0.56/0.60 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setunionsingleton1)). 0.56/0.60 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', subsetTrans)). 0.56/0.60 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setunionsingleton2)). 0.56/0.60 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', singletonsuniq)). 0.56/0.60 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setukpairinjL1)). 0.56/0.60 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setukpairinjL2)). 0.56/0.60 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setukpairinjR1)). 0.56/0.60 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', upairequniteq)). 0.56/0.60 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setukpairinjR2)). 0.56/0.60 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setukpairinjR)). 0.56/0.60 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', ksndpairEq)). 0.56/0.60 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setukpairinjR12)). 0.56/0.60 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setukpairinjR11)). 0.56/0.60 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setukpairinjL)). 0.56/0.60 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', cartprodfstin)). 0.56/0.60 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', kfstpairEq)). 0.56/0.60 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setunionsingleton)). 0.56/0.60 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', cartprodmempair1)). 0.56/0.60 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', cartprodpairin)). 0.56/0.60 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', ubforcartprodlem3)). 0.56/0.60 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', upairsubunion)). 0.56/0.60 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', upairset2E)). 0.56/0.60 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', singletoninpowerset)). 0.56/0.60 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/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setukpairIR)). 0.56/0.60 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/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setukpairIL)). 0.56/0.60 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', symdiffIneg1)). 0.56/0.60 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', symdiffI2)). 0.56/0.60 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', symdiffI1)). 0.56/0.60 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', symdiffE)). 0.56/0.60 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setminusSubset1)). 0.56/0.60 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setminusIRneg)). 0.56/0.60 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setminusELneg)). 0.56/0.60 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setminusER)). 0.56/0.60 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setminusI)). 0.56/0.60 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binintersectSubset4)). 0.56/0.60 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binintersectER)). 0.56/0.60 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binintersectSubset3)). 0.56/0.60 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binunionRsub)). 0.56/0.60 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binunionLsub)). 0.56/0.60 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/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binunionEcases)). 0.56/0.60 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', binunionIR)). 0.56/0.60 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', upairset2IR)). 0.56/0.60 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', powersetsubset)). 0.56/0.60 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', inPowerset)). 0.56/0.60 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', powersetE1)). 0.56/0.60 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setadjoinSub2)). 0.56/0.60 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', notequalI1)). 0.56/0.60 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', subsetE2)). 0.56/0.60 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', subsetI2)). 0.56/0.60 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', subsetI1)). 0.56/0.60 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', omega__Cong)). 0.56/0.60 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setunion__Cong)). 0.56/0.60 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', powerset__Cong)). 0.56/0.60 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', emptyset__Cong)). 0.56/0.60 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/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', in__Cong)). 0.56/0.60 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', notdallE)). 0.56/0.60 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', notdexE)). 0.56/0.60 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', quantDeMorgan4)). 0.56/0.60 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', upairsetIR)). 0.56/0.60 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', subsetE)). 0.56/0.60 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', emptysetsubset)). 0.56/0.60 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', eqimpsubset1)). 0.56/0.60 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', eqimpsubset2)). 0.56/0.60 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setadjoin__Cong)). 0.56/0.60 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', inCongP)). 0.56/0.60 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', prop2set2propI)). 0.56/0.60 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', prop2setI)). 0.56/0.60 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', quantDeMorgan3)). 0.56/0.60 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', quantDeMorgan2)). 0.56/0.60 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', quantDeMorgan1)). 0.56/0.60 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', vacuousDall)). 0.56/0.60 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', upairsetIL)). 0.56/0.60 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', upairsetE)). 0.56/0.60 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', uniqinunit)). 0.56/0.60 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setunionI)). 0.56/0.60 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', emptyinPowerset)). 0.56/0.60 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setadjoinOr)). 0.56/0.60 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setadjoinIL)). 0.56/0.60 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/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setext)). 0.56/0.60 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', notinemptyset)). 0.56/0.60 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', emptysetE)). 0.56/0.60 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', wellorderingAx)). 0.56/0.60 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', omegaIndAx)). 0.56/0.60 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', omegaSAx)). 0.56/0.60 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', omega0Ax)). 0.56/0.60 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setunionAx)). 0.56/0.60 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', powersetAx)). 0.56/0.60 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', setadjoinAx)). 0.56/0.60 thf(kpair, axiom, ((kpair)=(^[X2:$i, X3:$i]:(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.SC6GVQBgbD/E---3.1_5182.p', kpair)). 0.56/0.60 thf(c_0_180, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X529:$i]:(((in @ X529 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X529 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])). 0.56/0.60 thf(c_0_181, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])). 0.56/0.60 thf(c_0_182, 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])). 0.56/0.60 thf(c_0_183, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.56/0.60 thf(c_0_184, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.56/0.60 thf(c_0_185, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.56/0.60 thf(c_0_186, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.56/0.60 thf(c_0_187, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.56/0.60 thf(c_0_188, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.56/0.60 thf(c_0_189, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.56/0.60 thf(c_0_190, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 0.56/0.60 thf(c_0_191, plain, ((iskpair)=(^[Z0/* 5 */:$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])). 0.56/0.60 thf(c_0_192, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 0.56/0.60 thf(c_0_193, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X529:$i]:(((in @ X529 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X529 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_180, c_0_181])). 0.56/0.60 thf(c_0_194, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 0.56/0.60 thf(c_0_195, plain, ((ex1I)<=>![X4:$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])). 0.56/0.60 thf(c_0_196, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 0.56/0.60 thf(c_0_197, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 0.56/0.60 thf(c_0_198, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.56/0.60 thf(c_0_199, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.56/0.60 thf(c_0_200, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.56/0.60 thf(c_0_201, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.56/0.60 thf(c_0_202, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.56/0.60 thf(c_0_203, 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])). 0.56/0.60 thf(c_0_204, 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])). 0.56/0.60 thf(c_0_205, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.56/0.60 thf(c_0_206, plain, ((exuE2)=(![X1:$i > $o]:(((?[X502:$i]:((((X1 @ X502))&![X503:$i]:((((X1 @ X503))=>((X502)=(X503)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_182, c_0_183])). 0.56/0.60 thf(c_0_207, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_184, c_0_185])). 0.56/0.60 thf(c_0_208, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X500:$i]:((((X1 @ X500))&![X501:$i]:((((X1 @ X501))=>((X500)=(X501)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_186, c_0_183])). 0.56/0.60 thf(c_0_209, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.56/0.60 thf(c_0_210, plain, ((exuE1)=(![X1:$i > $o]:(((?[X498:$i]:((((X1 @ X498))&![X499:$i]:((((X1 @ X499))=>((X498)=(X499)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_187, c_0_183])). 0.56/0.60 thf(c_0_211, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.56/0.60 thf(c_0_212, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.56/0.60 thf(c_0_213, plain, ((descrp)=(![X1:$i > $o]:(((?[X496:$i]:((((X1 @ X496))&![X497:$i]:((((X1 @ X497))=>((X496)=(X497)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_188, c_0_183])). 0.56/0.60 thf(c_0_214, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X494:$i]:((((X6 @ X2 @ X494))&![X495:$i]:((((X6 @ X2 @ X495))=>((X494)=(X495)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_189, c_0_183])). 0.56/0.60 thf(c_0_215, plain, ((kfstsingleton)=(![X18:$i]:(((?[X533:$i]:(((in @ X533 @ (setunion @ X18))&?[X534:$i]:(((in @ X534 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X533 @ emptyset) @ (setadjoin @ (setadjoin @ X533 @ (setadjoin @ X534 @ emptyset)) @ emptyset))))))))=>(?[X535:$i]:(((in @ X535 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X535 @ emptyset))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_190, c_0_191]), c_0_181])). 0.56/0.60 thf(c_0_216, 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)))=>(?[X532:$i]:(((in @ X532 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X532 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_192, c_0_193])). 0.56/0.60 thf(c_0_217, plain, ((singletonprop)=(![X4:$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)))=>(?[X528:$i]:(((in @ X528 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X528 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_194, c_0_181])). 0.56/0.60 thf(c_0_218, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X531:$i]:(((in @ X531 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X531 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_195, c_0_193])). 0.56/0.60 thf(c_0_219, axiom, ((theprop)=(![X21:$i]:(((?[X536:$i]:(((in @ X536 @ X21)&((X21)=(setadjoin @ X536 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_181])). 0.56/0.60 thf(c_0_220, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X524:$i]:(((in @ X524 @ (setunion @ (kpair @ X2 @ X3)))&?[X525:$i]:(((in @ X525 @ (setunion @ (kpair @ X2 @ X3)))&((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X524 @ emptyset) @ (setadjoin @ (setadjoin @ X524 @ (setadjoin @ X525 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_191])). 0.56/0.60 thf(c_0_221, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X522:$i]:(((in @ X522 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X523:$i]:(((in @ X523 @ (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 @ X522 @ emptyset) @ (setadjoin @ (setadjoin @ X522 @ (setadjoin @ X523 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_191])). 0.56/0.60 thf(c_0_222, plain, ((ksndsingleton)=(![X18:$i]:(((?[X537:$i]:(((in @ X537 @ (setunion @ X18))&?[X538:$i]:(((in @ X538 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X537 @ emptyset) @ (setadjoin @ (setadjoin @ X537 @ (setadjoin @ X538 @ emptyset)) @ emptyset))))))))=>(?[X539:$i]:(((in @ X539 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X539 @ emptyset))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_196, c_0_191]), c_0_181])). 0.56/0.60 thf(c_0_223, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X530:$i]:(((in @ X530 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X530 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_197, c_0_193])). 0.56/0.60 thf(c_0_224, axiom, ((cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(?[X526:$i]:(((in @ X526 @ (setunion @ X18))&?[X527:$i]:(((in @ X527 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X526 @ emptyset) @ (setadjoin @ (setadjoin @ X526 @ (setadjoin @ X527 @ emptyset)) @ emptyset)))))))))))), inference(apply_def,[status(thm)],[cartprodmempair, c_0_191])). 0.56/0.60 thf(c_0_225, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.56/0.60 thf(c_0_226, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X518:$i]:((((X1 @ X518))&![X519:$i]:((((X1 @ X519))=>((X518)=(X519)))))))=>((?[X520:$i]:((((X17 @ X520))&![X521:$i]:((((X17 @ X521))=>((X520)=(X521)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_198, c_0_183])). 0.56/0.60 thf(c_0_227, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X512:$i]:((((X1 @ X512))&![X513:$i]:((((X1 @ X513))=>((X512)=(X513)))))))<=>(?[X514:$i]:((((X17 @ X514))&![X515:$i]:((((X17 @ X515))=>((X514)=(X515)))))))))))), inference(apply_def,[status(thm)],[c_0_199, c_0_183])). 0.56/0.60 thf(c_0_228, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X508:$i]:((((X1 @ X508))&![X509:$i]:((((X1 @ X509))=>((X508)=(X509))))))))))), inference(apply_def,[status(thm)],[c_0_200, c_0_183])). 0.56/0.60 thf(c_0_229, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X506:$i]:((((X1 @ X506))&![X507:$i]:((((X1 @ X507))=>((X506)=(X507)))))))))))), inference(apply_def,[status(thm)],[c_0_201, c_0_183])). 0.56/0.60 thf(c_0_230, 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])). 0.56/0.60 thf(c_0_231, plain, ((exuEu)=(![X1:$i > $o]:(((?[X516:$i]:((((X1 @ X516))&![X517:$i]:((((X1 @ X517))=>((X516)=(X517)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_202, c_0_183])). 0.56/0.60 thf(c_0_232, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X510:$i]:((((X1 @ X510))&![X511:$i]:((((X1 @ X511))=>((X510)=(X511)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_203, c_0_183])). 0.56/0.60 thf(c_0_233, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X504:$i]:((((X1 @ X504))&![X505:$i]:((((X1 @ X505))=>((X504)=(X505))))))))))), inference(apply_def,[status(thm)],[c_0_204, c_0_183])). 0.56/0.60 thf(c_0_234, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_185])). 0.56/0.60 thf(c_0_235, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.56/0.60 thf(c_0_236, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_185])). 0.56/0.60 thf(c_0_237, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_185])). 0.56/0.60 thf(c_0_238, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.56/0.60 thf(c_0_239, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.56/0.60 thf(c_0_240, plain, ((epred1_0)<=>![X553:$i]:(?[X554:$i]:((((![X555:$i]:(((in @ X555 @ X554)=>![X556:$i]:(((in @ X556 @ X555)=>(in @ X556 @ X553)))))&![X557:$i, X558:$i]:((((in @ X557 @ X553)&(in @ X558 @ X553))=>(![X559:$i]:(((in @ X559 @ X554)=>((in @ X557 @ X559)<=>(in @ X558 @ X559))))=>((X557)=(X558))))))&![X560:$i, X561:$i]:((((in @ X560 @ X554)&(in @ X561 @ X554))=>(![X562:$i]:(((in @ X562 @ X560)=>(in @ X562 @ X561)))|![X563:$i]:(((in @ X563 @ X561)=>(in @ X563 @ X560)))))))&![X564:$i]:(((![X565:$i]:(((in @ X565 @ X564)=>(in @ X565 @ X553)))&?[X566:$i]:((in @ X566 @ X564)))=>?[X567:$i, X568:$i]:(((((in @ X567 @ X554)&(in @ X568 @ X564))&~(?[X569:$i]:(((in @ X569 @ X567)&(in @ X569 @ X564)))))&![X570:$i]:(((in @ X570 @ X554)=>(![X571:$i]:(((in @ X571 @ X570)=>(in @ X571 @ X567)))|(in @ X568 @ X570)))))))))))), introduced(definition)). 0.56/0.60 thf(c_0_241, negated_conjecture, ~((![X1055:$i, X1056:$i]:((![X1057:$i]:(((in @ X1057 @ X1055)<=>(in @ X1057 @ X1056)))=>((X1055)=(X1056))))=>(![X1054:$i]:(~(in @ X1054 @ emptyset))=>(![X540:$i, X541:$i, X542:$i]:(((in @ X542 @ (setadjoin @ X540 @ X541))<=>(((X542)=(X540))|(in @ X542 @ X541))))=>(![X543:$i, X544:$i]:(((in @ X544 @ (powerset @ X543))<=>![X545:$i]:(((in @ X545 @ X544)=>(in @ X545 @ X543)))))=>(![X546:$i, X547:$i]:(((in @ X547 @ (setunion @ X546))<=>?[X548:$i]:(((in @ X547 @ X548)&(in @ X548 @ X546)))))=>((in @ emptyset @ omega)=>(![X549:$i]:(((in @ X549 @ omega)=>(in @ (setadjoin @ X549 @ X549) @ omega)))=>(![X550:$i]:((((in @ emptyset @ X550)&![X551:$i]:((((in @ X551 @ omega)&(in @ X551 @ X550))=>(in @ (setadjoin @ X551 @ X551) @ X550))))=>![X552:$i]:(((in @ X552 @ omega)=>(in @ X552 @ X550)))))=>(![X1046:$i > $i > $o, X1047:$i]:((![X1048:$i]:(((in @ X1048 @ X1047)=>?[X1049:$i]:(((X1046 @ X1048 @ X1049)&![X1050:$i]:(((X1046 @ X1048 @ X1050)=>((X1049)=(X1050))))))))=>?[X1051:$i]:(![X1052:$i]:(((in @ X1052 @ X1051)<=>?[X1053:$i]:(((in @ X1053 @ X1047)&(X1046 @ X1053 @ X1052))))))))=>(![X1042:$i]:((?[X1043:$i]:((in @ X1043 @ X1042))=>?[X1044:$i]:(((in @ X1044 @ X1042)&~(?[X1045:$i]:(((in @ X1045 @ X1044)&(in @ X1045 @ X1042))))))))=>((epred1_0)=>(![X1039:$i > $o]:((?[X1040:$i]:(((X1039 @ X1040)&![X1041:$i]:(((X1039 @ X1041)=>((X1040)=(X1041))))))=>(X1039 @ (descr @ (^[Z0/* 17 */:$i]:(X1039 @ Z0))))))=>(![X1036:$i, X1037:$i > $o, X1038:$i]:(((in @ X1038 @ X1036)=>((X1037 @ X1038)=>(in @ X1038 @ (dsetconstr @ X1036 @ X1037)))))=>(![X572:$i, X573:$i > $o, X574:$i]:(((in @ X574 @ (dsetconstr @ X572 @ X573))=>(in @ X574 @ X572)))=>(![X1033:$i, X1034:$i > $o, X1035:$i]:(((in @ X1035 @ (dsetconstr @ X1033 @ X1034))=>(X1034 @ X1035)))=>(![X1028:$i > $o]:((?[X1029:$i]:(((X1028 @ X1029)&![X1030:$i]:(((X1028 @ X1030)=>((X1029)=(X1030))))))=>?[X1031:$i]:(((X1028 @ X1031)&![X1032:$i]:(((X1028 @ X1032)=>((X1031)=(X1032))))))))=>(![X1026:$o, X1027:$i]:(((in @ X1027 @ (prop2set @ ((X1026))))=>(X1026)))=>(![X575:$i]:(((in @ X575 @ emptyset)=>![X576:$o]:((X576))))=>(![X1025:$i]:(((in @ X1025 @ emptyset)=>~($true)))=>(![X577:$i]:(~(in @ X577 @ emptyset))=>(![X1021:$i > $o]:((?[X1022:$i]:(((X1021 @ X1022)&![X1023:$i]:(((X1021 @ X1023)=>((X1022)=(X1023))))))=>?[X1024:$i]:((X1021 @ X1024))))=>(![X578:$i, X579:$i]:((![X580:$i]:(((in @ X580 @ X578)=>(in @ X580 @ X579)))=>(![X581:$i]:(((in @ X581 @ X579)=>(in @ X581 @ X578)))=>((X578)=(X579)))))=>(![X1019:$i]:((![X1020:$i]:(~(in @ X1020 @ X1019))=>((X1019)=(emptyset))))=>(![X1017:$i]:((![X1018:$i]:(~(in @ X1018 @ X1017))=>((X1017)=(emptyset))))=>(![X582:$i, X583:$i > $o, X584:$i]:(((in @ X584 @ X582)=>((in @ X584 @ (dsetconstr @ X582 @ X583))<=>(X583 @ X584))))=>(![X585:$i]:((((X585)!=(emptyset))=>?[X586:$i]:((in @ X586 @ X585))))=>(![X1014:$i, X1015:$i > $o, X1016:$i]:(((in @ X1016 @ X1014)=>((X1015 @ X1016)=>((dsetconstr @ X1014 @ X1015)!=(emptyset)))))=>(![X587:$i]:((?[X588:$i]:((in @ X588 @ X587))=>((X587)!=(emptyset))))=>(![X589:$i, X590:$i]:((in @ X589 @ (setadjoin @ X589 @ X590)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1011:$i, X1012:$i, X1013:$i]:(((in @ X1013 @ X1012)=>(in @ X1013 @ (setadjoin @ X1011 @ X1012))))=>(![X1007:$i, X1008:$i, X1009:$i]:(((in @ X1009 @ (setadjoin @ X1007 @ X1008))=>![X1010:$o]:(((((X1009)=(X1007))=>(X1010))=>(((in @ X1009 @ X1008)=>(X1010))=>(X1010))))))=>(![X591:$i, X592:$i, X593:$i]:(((in @ X593 @ (setadjoin @ X591 @ X592))=>(((X593)=(X591))|(in @ X593 @ X592))))=>(![X594:$i]:(((dsetconstr @ X594 @ (^[Z0/* 1 */:$i]:($true)))=(X594)))=>(![X1004:$i, X1005:$i]:((![X1006:$i]:(((in @ X1006 @ X1005)=>(in @ X1006 @ X1004)))=>(in @ X1005 @ (powerset @ X1004))))=>(![X595:$i]:((in @ emptyset @ (powerset @ X595)))=>(![X1003:$i]:((in @ emptyset @ (powerset @ X1003)))=>(![X1000:$i, X1001:$i, X1002:$i]:(((in @ X1001 @ (powerset @ X1000))=>((in @ X1002 @ X1001)=>(in @ X1002 @ X1000))))=>(![X596:$i, X597:$i, X598:$i]:(((in @ X597 @ X598)=>((in @ X598 @ X596)=>(in @ X597 @ (setunion @ X596)))))=>(![X996:$i, X997:$i]:(((in @ X997 @ (setunion @ X996))=>![X998:$o]:((![X999:$i]:(((in @ X997 @ X999)=>((in @ X999 @ X996)=>(X998))))=>(X998)))))=>(![X994:$i, X995:$i]:(((in @ X995 @ X994)=>(in @ X995 @ (powerset @ (setunion @ X994)))))=>(![X989:$i > $o]:((?[X990:$i]:(((X989 @ X990)&![X991:$i]:(((X989 @ X991)=>((X990)=(X991))))))=>?[X992:$i]:(![X993:$i]:(((X989 @ X993)<=>((X993)=(X992)))))))=>(![X599:$i]:((((X599)!=(emptyset))=>?[X600:$i]:(((in @ X600 @ X599)&$true))))=>(![X601:$i, X602:$i]:(((in @ X601 @ (setadjoin @ X602 @ emptyset))=>((X601)=(X602))))=>(![X987:$i, X988:$i]:((((X987)!=(X988))=>~(in @ X988 @ (setadjoin @ X987 @ emptyset))))=>(![X985:$i, X986:$i]:((((X985)=(X986))=>(in @ X985 @ (setadjoin @ X986 @ emptyset))))=>(![X983:$i, X984:$i]:(((in 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(setunion @ X813) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X813))))=(setadjoin @ X816 @ emptyset))))))=>(![X771:$i]:((?[X772:$i]:(((in @ X772 @ X771)&((X771)=(setadjoin @ X772 @ emptyset))))=>(in @ (setunion @ X771) @ X771)))=>(![X811:$i, X812:$i]:(((kfst @ (kpair @ X811 @ X812))=(X811)))=>(![X808:$i, X809:$i, X810:$i]:(((in @ X810 @ (cartprod @ X808 @ X809))=>(in @ (kfst @ X810) @ X808)))=>(![X773:$i, X774:$i, X775:$i, X776:$i]:((((setadjoin @ (setadjoin @ X773 @ emptyset) @ (setadjoin @ (setadjoin @ X773 @ (setadjoin @ X774 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X775 @ emptyset) @ (setadjoin @ (setadjoin @ X775 @ (setadjoin @ X776 @ emptyset)) @ emptyset)))=>((X773)=(X775))))=>(![X804:$i, X805:$i, X806:$i, X807:$i]:((((kpair @ X804 @ X805)=(kpair @ X806 @ X807))=>((X804)=(X806))))=>(![X802:$i, X803:$i]:((((X802)=(X803))=>((setadjoin @ X802 @ (setadjoin @ X803 @ emptyset))=(setadjoin @ X802 @ emptyset))))=>(![X800:$i, X801:$i]:((((X800)=(X801))=>((setadjoin @ (setadjoin @ X800 @ emptyset) @ (setadjoin @ (setadjoin @ X800 @ (setadjoin @ X801 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X800 @ emptyset) @ emptyset))))=>(![X777:$i, X778:$i, X779:$i, X780:$i]:((((setadjoin @ (setadjoin @ X777 @ emptyset) @ (setadjoin @ (setadjoin @ X777 @ (setadjoin @ X778 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X779 @ emptyset) @ (setadjoin @ (setadjoin @ X779 @ (setadjoin @ X780 @ emptyset)) @ emptyset)))=>(((X779)=(X780))=>((X778)=(X780)))))=>(![X781:$i, X782:$i, X783:$i]:((((setadjoin @ X781 @ (setadjoin @ X782 @ emptyset))=(setadjoin @ X783 @ emptyset))=>((X781)=(X782))))=>(![X784:$i, X785:$i, X786:$i, X787:$i]:((((setadjoin @ (setadjoin @ X784 @ emptyset) @ (setadjoin @ (setadjoin @ X784 @ (setadjoin @ X785 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X786 @ emptyset) @ (setadjoin @ (setadjoin @ X786 @ (setadjoin @ X787 @ emptyset)) @ emptyset)))=>((X785)=(X787))))=>(![X788:$i, X789:$i, X790:$i, X791:$i]:((((kpair @ X788 @ X789)=(kpair @ X790 @ X791))=>((X789)=(X791))))=>(![X796:$i]:((?[X797:$i]:(((in @ X797 @ (setunion @ X796))&?[X798:$i]:(((in @ X798 @ (setunion @ X796))&((X796)=(setadjoin @ (setadjoin @ X797 @ emptyset) @ (setadjoin @ (setadjoin @ X797 @ (setadjoin @ X798 @ emptyset)) @ emptyset)))))))=>?[X799:$i]:(((in @ X799 @ (dsetconstr @ (setunion @ X796) @ (^[Z0/* 3 */:$i]:(((X796)=(kpair @ (kfst @ X796) @ Z0))))))&((dsetconstr @ (setunion @ X796) @ (^[Z0/* 3 */:$i]:(((X796)=(kpair @ (kfst @ X796) @ Z0)))))=(setadjoin @ X799 @ emptyset))))))=>(![X794:$i, X795:$i]:(((ksnd @ (kpair @ X794 @ X795))=(X795)))=>![X18:$i]:((?[X792:$i]:(((in @ X792 @ (setunion @ X18))&?[X793:$i]:(((in @ X793 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X792 @ emptyset) @ (setadjoin @ (setadjoin @ X792 @ (setadjoin @ X793 @ emptyset)) @ emptyset)))))))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[kpairsurjEq]), notequalI2]), c_0_205]), setextAx]), singletonsswitch]), eqinunit]), notinsingleton]), setadjoinSub]), c_0_206]), subPowSU]), subset2powerset]), setunionE]), powersetE]), emptyInPowerset]), setextsub]), powersetI]), setadjoinE]), subsetemptysetimpeq]), setadjoinIR]), emptyinunitempty]), c_0_207]), powersetI1]), noeltsimpempty]), notsubsetI]), emptyI]), c_0_208]), c_0_209]), emptysetimpfalse]), prop2setE]), c_0_210]), c_0_211]), c_0_212]), setminusLsub]), c_0_213]), binunionIL]), foundationAx]), c_0_214]), emptysetAx]), binunionE]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), disjointsetsI1]), binintersectRsub]), binintersectSubset1]), bs114d]), setminusEL]), setminusSubset2]), setminusERneg]), setminusILneg]), c_0_215]), c_0_216]), symdiffIneg2]), secondinupair]), singletonsubset]), singletoninpowunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), subsetRefl]), setunionE2]), setunionsingleton1]), subsetTrans]), setunionsingleton2]), c_0_217]), c_0_218]), singletonsuniq]), setukpairinjL1]), c_0_219]), setukpairinjL2]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_220]), c_0_221]), c_0_191]), ksndpairEq]), c_0_222]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), cartprodfstin]), kfstpairEq]), c_0_223]), setunionsingleton]), c_0_224]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), upairsubunion]), upairset2E]), singletoninpowerset]), setukpairIR]), setukpairIL]), symdiffIneg1]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setminusIRneg]), setminusELneg]), setminusER]), setminusI]), binintersectSubset4]), binintersectER]), binintersectSubset3]), binunionRsub]), binunionLsub]), binunionEcases]), binunionIR]), upairset2IR]), powersetsubset]), inPowerset]), powersetE1]), setadjoinSub2]), notequalI1]), subsetE2]), subsetI2]), subsetI1]), c_0_225]), c_0_226]), omega__Cong]), setunion__Cong]), powerset__Cong]), emptyset__Cong]), c_0_227]), in__Cong]), c_0_228]), c_0_229]), notdallE]), notdexE]), quantDeMorgan4]), c_0_230]), upairsetIR]), subsetE]), emptysetsubset]), eqimpsubset1]), eqimpsubset2]), c_0_231]), setadjoin__Cong]), c_0_232]), inCongP]), c_0_233]), prop2set2propI]), prop2setI]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), upairsetIL]), upairsetE]), uniqinunit]), c_0_234]), setunionI]), emptyinPowerset]), c_0_235]), setadjoinOr]), setadjoinIL]), c_0_236]), c_0_237]), c_0_238]), setext]), notinemptyset]), emptysetE]), c_0_239]), wellorderingAx]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx])])]), c_0_240])). 0.56/0.60 thf(c_0_242, plain, ![X1058:$i, X1059:$i]:(((kpair @ X1058 @ X1059)=(setadjoin @ (setadjoin @ X1058 @ emptyset) @ (setadjoin @ (setadjoin @ X1058 @ (setadjoin @ X1059 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])])). 0.56/0.60 thf(c_0_243, negated_conjecture, ![X1060:$i, X1061:$i, X1063:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1073:$i, X1074:$i, X1076:$i, X1077:$i, X1078:$i, X1079:$i, X1080:$i, X1082:$i, X1083:$i > $i > $o, X1084:$i, X1086:$i, X1089:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1096:$i, X1097:$i > $o, X1098:$i, X1100:$i, X1101:$i > $o, X1102:$i, X1103:$i, X1104:$i > $o, X1105:$i, X1106:$i, X1107:$i > $o, X1108:$i, X1109:$i > $o, X1110:$i, X1113:$i, X1114:$o, X1115:$i, X1116:$i, X1117:$o, X1118:$i, X1119:$i, X1120:$i > $o, X1121:$i, X1124:$i, X1125:$i, X1128:$i, X1130:$i, X1132:$i, X1133:$i > $o, X1134:$i, X1135:$i, X1137:$i, X1138:$i > $o, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$o, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$o, X1170:$i, X1171:$i, X1172:$i > $o, X1173:$i, X1176:$i, X1177:$i, X1178:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i > $o, X1197:$i, X1198:$i > $o, X1199:$i, X1200:$i, X1201:$i > $o, X1202:$i, X1204:$i, X1205:$i > $o, X1207:$i, X1208:$i, X1209:$i > $o, X1211:$i, X1212:$i, X1213:$i > $o, X1214:$i, X1216:$o, X1217:$o, X1218:$i, X1219:$i > $o, X1221:$i, X1222:$i, X1223:$i > $o, X1224:$i, X1226:$i > $o, X1227:$i, X1230:$i, X1231:$i > $o, X1232:$i, X1236:$i, X1237:$i > $o, X1238:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i > $o, X1251:$i, X1253:$i, X1254:$i, X1255:$i > $o, X1256:$i > $o, X1259:$i, X1262:$i, X1263:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i > $o, X1276:$i, X1278:$i, X1279:$i, X1280:$i > $o, X1281:$i > $o, X1284:$i, X1286:$i, X1288:$i, X1289:$i, X1290:$i > $o, X1291:$i > $o, X1294:$i, X1295:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1304:$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:$i, X1324:$i, 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 > $o, X1342:$i, X1343:$i > $o, X1344:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$o, X1356:$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, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$o, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1446:$i, X1447:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1489:$i, X1490:$i, X1491:$i, X1494:$i, X1495:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i > $o, X1504:$i, X1506:$i, X1507:$i > $o, 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X1438 @ (setadjoin @ X1439 @ emptyset)) @ emptyset))))&((in @ X1441 @ (setunion @ (setadjoin @ (setadjoin @ X1440 @ emptyset) @ (setadjoin @ (setadjoin @ X1440 @ (setadjoin @ X1441 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1442 @ X1443) @ (setunion @ (setadjoin @ (setadjoin @ X1442 @ emptyset) @ (setadjoin @ (setadjoin @ X1442 @ (setadjoin @ X1443 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1442 @ X1443) @ (setunion @ (setadjoin @ (setadjoin @ X1442 @ emptyset) @ (setadjoin @ (setadjoin @ X1442 @ (setadjoin @ X1443 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1442 @ emptyset) @ (setadjoin @ (setadjoin @ X1442 @ (setadjoin @ X1443 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1442 @ X1443) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1442 @ X1443) @ (setadjoin @ (esk56_2 @ X1442 @ X1443) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1446 @ X1447) @ (setunion @ (kpair @ X1446 @ X1447)))&((in @ (esk58_2 @ X1446 @ X1447) @ (setunion @ (kpair @ X1446 @ X1447)))&((kpair @ X1446 @ X1447)=(setadjoin @ (setadjoin @ (esk57_2 @ X1446 @ X1447) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1446 @ X1447) @ (setadjoin @ (esk58_2 @ X1446 @ X1447) @ emptyset)) @ emptyset)))))&((~(in @ X1451 @ X1450)|(subset @ (setadjoin @ X1451 @ emptyset) @ X1450))&((~(in @ X1453 @ X1452)|(in @ (setadjoin @ X1453 @ emptyset) @ (powerset @ X1452)))&((~(in @ X1456 @ X1454)|(in @ (setadjoin @ X1456 @ emptyset) @ (powerset @ (binunion @ X1454 @ X1455))))&((~(in @ X1459 @ (setadjoin @ X1457 @ (setadjoin @ X1458 @ emptyset)))|(((X1459)=(X1457))|((X1459)=(X1458))))&((~(in @ X1462 @ X1460)|(~(in @ X1463 @ X1461)|(subset @ (setadjoin @ X1462 @ (setadjoin @ X1463 @ emptyset)) @ (binunion @ X1460 @ X1461))))&((~(in @ X1466 @ X1464)|(~(in @ X1467 @ X1465)|(in @ (setadjoin @ X1466 @ (setadjoin @ X1467 @ emptyset)) @ (powerset @ (binunion @ X1464 @ X1465)))))&((~(in @ X1470 @ X1468)|(~(in @ X1471 @ X1469)|(subset @ (setadjoin @ (setadjoin @ X1470 @ emptyset) @ (setadjoin @ (setadjoin @ X1470 @ (setadjoin @ X1471 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1468 @ X1469)))))&((~(in @ X1474 @ X1472)|(~(in @ X1475 @ X1473)|(in @ (setadjoin @ (setadjoin @ X1474 @ emptyset) @ (setadjoin @ (setadjoin @ X1474 @ (setadjoin @ X1475 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1472 @ X1473))))))&((~(in @ X1478 @ X1476)|(~(in @ X1479 @ X1477)|(in @ (kpair @ X1478 @ X1479) @ (powerset @ (powerset @ (binunion @ X1476 @ X1477))))))&((~(in @ X1482 @ X1480)|(~(in @ X1483 @ X1481)|(in @ (kpair @ X1482 @ X1483) @ (cartprod @ X1480 @ X1481))))&((((in @ (esk59_3 @ X1484 @ X1485 @ X1486) @ X1484)|~(in @ X1486 @ (cartprod @ X1484 @ X1485)))&(((in @ (esk60_3 @ X1484 @ X1485 @ X1486) @ X1485)|~(in @ X1486 @ (cartprod @ X1484 @ X1485)))&(((X1486)=(kpair @ (esk59_3 @ X1484 @ X1485 @ X1486) @ (esk60_3 @ X1484 @ X1485 @ X1486)))|~(in @ X1486 @ (cartprod @ X1484 @ X1485)))))&((((in @ (esk61_3 @ X1489 @ X1490 @ X1491) @ (setunion @ X1491))|~(in @ X1491 @ (cartprod @ X1489 @ X1490)))&(((in @ (esk62_3 @ X1489 @ X1490 @ X1491) @ (setunion @ X1491))|~(in @ X1491 @ (cartprod @ X1489 @ X1490)))&(((X1491)=(setadjoin @ (setadjoin @ (esk61_3 @ X1489 @ X1490 @ X1491) @ emptyset) @ (setadjoin @ (setadjoin @ (esk61_3 @ X1489 @ X1490 @ X1491) @ (setadjoin @ (esk62_3 @ X1489 @ X1490 @ X1491) @ emptyset)) @ emptyset)))|~(in @ X1491 @ (cartprod @ X1489 @ X1490)))))&((((in @ (esk63_2 @ X1494 @ X1495) @ X1494)|~(in @ X1495 @ (setunion @ X1494)))&((in @ X1495 @ (esk63_2 @ X1494 @ X1495))|~(in @ X1495 @ (setunion @ X1494))))&((subset @ (setunion @ (setadjoin @ X1497 @ emptyset)) @ X1497)&((subset @ X1498 @ (setunion @ (setadjoin @ X1498 @ emptyset)))&(((setunion @ (setadjoin @ X1499 @ emptyset))=(X1499))&(((((in @ (esk66_2 @ X1500 @ X1501) @ (dsetconstr @ X1500 @ X1501))|(~(in @ X1504 @ X1500)|~(X1501 @ X1504))|(in @ (esk64_2 @ X1500 @ X1501) @ X1500))&(((dsetconstr @ X1500 @ X1501)=(setadjoin @ (esk66_2 @ X1500 @ X1501) @ emptyset))|(~(in @ X1504 @ X1500)|~(X1501 @ X1504))|(in @ (esk64_2 @ X1500 @ X1501) @ X1500)))&((((in @ (esk66_2 @ X1500 @ X1501) @ (dsetconstr @ X1500 @ X1501))|(~(in @ X1504 @ X1500)|~(X1501 @ X1504))|(in @ (esk65_2 @ X1500 @ X1501) @ X1500))&(((dsetconstr @ X1500 @ X1501)=(setadjoin @ (esk66_2 @ X1500 @ X1501) @ emptyset))|(~(in @ X1504 @ X1500)|~(X1501 @ X1504))|(in @ (esk65_2 @ X1500 @ X1501) @ X1500)))&((((in @ (esk66_2 @ X1500 @ X1501) @ (dsetconstr @ X1500 @ X1501))|(~(in @ X1504 @ X1500)|~(X1501 @ X1504))|(X1501 @ (esk64_2 @ X1500 @ X1501)))&(((dsetconstr @ X1500 @ X1501)=(setadjoin @ (esk66_2 @ X1500 @ X1501) @ emptyset))|(~(in @ X1504 @ X1500)|~(X1501 @ X1504))|(X1501 @ (esk64_2 @ X1500 @ X1501))))&((((in @ (esk66_2 @ X1500 @ X1501) @ (dsetconstr @ X1500 @ X1501))|(~(in @ X1504 @ X1500)|~(X1501 @ X1504))|(X1501 @ (esk65_2 @ X1500 @ X1501)))&(((dsetconstr @ X1500 @ X1501)=(setadjoin @ (esk66_2 @ X1500 @ X1501) @ emptyset))|(~(in @ X1504 @ X1500)|~(X1501 @ X1504))|(X1501 @ (esk65_2 @ X1500 @ X1501))))&(((in @ (esk66_2 @ X1500 @ X1501) @ (dsetconstr @ X1500 @ X1501))|(~(in @ X1504 @ X1500)|~(X1501 @ X1504))|((esk64_2 @ X1500 @ X1501)!=(esk65_2 @ X1500 @ X1501)))&(((dsetconstr @ X1500 @ X1501)=(setadjoin @ (esk66_2 @ X1500 @ X1501) @ emptyset))|(~(in @ X1504 @ X1500)|~(X1501 @ X1504))|((esk64_2 @ X1500 @ X1501)!=(esk65_2 @ X1500 @ X1501))))))))&((((in @ (esk67_2 @ X1506 @ X1507) @ X1506)|(~(in @ X1508 @ (dsetconstr @ X1506 @ X1507))|((dsetconstr @ X1506 @ X1507)!=(setadjoin @ X1508 @ emptyset))))&((X1507 @ (esk67_2 @ X1506 @ X1507))|(~(in @ X1508 @ (dsetconstr @ X1506 @ X1507))|((dsetconstr @ X1506 @ X1507)!=(setadjoin @ X1508 @ emptyset)))))&(((((in @ (esk69_3 @ X1510 @ X1511 @ X1512) @ (dsetconstr @ X1510 @ X1511))|(in @ (esk68_3 @ X1510 @ X1511 @ X1512) @ X1510)|~(X1511 @ X1512)|~(in @ X1512 @ X1510))&(((dsetconstr @ X1510 @ X1511)=(setadjoin @ (esk69_3 @ X1510 @ X1511 @ X1512) @ emptyset))|(in @ (esk68_3 @ X1510 @ X1511 @ X1512) @ X1510)|~(X1511 @ X1512)|~(in @ X1512 @ X1510)))&((((in @ (esk69_3 @ X1510 @ X1511 @ X1512) @ (dsetconstr @ X1510 @ X1511))|(X1511 @ (esk68_3 @ X1510 @ X1511 @ X1512))|~(X1511 @ X1512)|~(in @ X1512 @ X1510))&(((dsetconstr @ X1510 @ X1511)=(setadjoin @ (esk69_3 @ X1510 @ X1511 @ X1512) @ emptyset))|(X1511 @ (esk68_3 @ X1510 @ X1511 @ X1512))|~(X1511 @ X1512)|~(in @ X1512 @ X1510)))&(((in @ (esk69_3 @ X1510 @ X1511 @ X1512) @ (dsetconstr @ X1510 @ X1511))|((esk68_3 @ X1510 @ X1511 @ X1512)!=(X1512))|~(X1511 @ X1512)|~(in @ X1512 @ X1510))&(((dsetconstr @ X1510 @ X1511)=(setadjoin @ (esk69_3 @ X1510 @ X1511 @ X1512) @ emptyset))|((esk68_3 @ X1510 @ X1511 @ X1512)!=(X1512))|~(X1511 @ X1512)|~(in @ X1512 @ X1510)))))&(((((in @ (esk72_2 @ X1515 @ X1516) @ (dsetconstr @ X1515 @ X1516))|(~(in @ X1519 @ X1515)|~(X1516 @ X1519))|(in @ (esk70_2 @ X1515 @ X1516) @ X1515))&(((dsetconstr @ X1515 @ X1516)=(setadjoin @ (esk72_2 @ X1515 @ X1516) @ emptyset))|(~(in @ X1519 @ X1515)|~(X1516 @ X1519))|(in @ (esk70_2 @ X1515 @ X1516) @ X1515)))&((((in @ (esk72_2 @ X1515 @ X1516) @ (dsetconstr @ X1515 @ X1516))|(~(in @ X1519 @ X1515)|~(X1516 @ X1519))|(in @ (esk71_2 @ X1515 @ X1516) @ X1515))&(((dsetconstr @ X1515 @ X1516)=(setadjoin @ (esk72_2 @ X1515 @ X1516) @ emptyset))|(~(in @ X1519 @ X1515)|~(X1516 @ X1519))|(in @ (esk71_2 @ X1515 @ X1516) @ X1515)))&((((in @ (esk72_2 @ X1515 @ X1516) @ (dsetconstr @ X1515 @ X1516))|(~(in @ X1519 @ X1515)|~(X1516 @ X1519))|(X1516 @ (esk70_2 @ X1515 @ X1516)))&(((dsetconstr @ X1515 @ X1516)=(setadjoin @ (esk72_2 @ X1515 @ X1516) @ emptyset))|(~(in @ X1519 @ X1515)|~(X1516 @ X1519))|(X1516 @ (esk70_2 @ X1515 @ X1516))))&((((in @ (esk72_2 @ X1515 @ X1516) @ (dsetconstr @ X1515 @ X1516))|(~(in @ X1519 @ X1515)|~(X1516 @ X1519))|(X1516 @ (esk71_2 @ X1515 @ X1516)))&(((dsetconstr @ X1515 @ X1516)=(setadjoin @ (esk72_2 @ X1515 @ X1516) @ emptyset))|(~(in @ X1519 @ X1515)|~(X1516 @ X1519))|(X1516 @ (esk71_2 @ X1515 @ X1516))))&(((in @ (esk72_2 @ X1515 @ X1516) @ (dsetconstr @ X1515 @ X1516))|(~(in @ X1519 @ X1515)|~(X1516 @ X1519))|((esk70_2 @ X1515 @ X1516)!=(esk71_2 @ X1515 @ X1516)))&(((dsetconstr @ X1515 @ X1516)=(setadjoin @ (esk72_2 @ X1515 @ X1516) @ emptyset))|(~(in @ X1519 @ X1515)|~(X1516 @ X1519))|((esk70_2 @ X1515 @ X1516)!=(esk71_2 @ X1515 @ X1516))))))))&((((setadjoin @ X1521 @ emptyset)!=(setadjoin @ X1522 @ emptyset))|((X1521)=(X1522)))&((~(in @ (setadjoin @ X1525 @ emptyset) @ (setadjoin @ (setadjoin @ X1523 @ emptyset) @ (setadjoin @ (setadjoin @ X1523 @ (setadjoin @ X1524 @ emptyset)) @ emptyset)))|((X1523)=(X1525)))&((((in @ (esk73_1 @ X1526) @ (dsetconstr @ (setunion @ X1526) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1526)))))|(~(in @ X1527 @ (setunion @ X1526))|(~(in @ X1528 @ (setunion @ X1526))|((X1526)!=(setadjoin @ (setadjoin @ X1527 @ emptyset) @ (setadjoin @ (setadjoin @ X1527 @ (setadjoin @ X1528 @ emptyset)) @ emptyset))))))&(((dsetconstr @ (setunion @ X1526) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1526))))=(setadjoin @ (esk73_1 @ X1526) @ emptyset))|(~(in @ X1527 @ (setunion @ X1526))|(~(in @ X1528 @ (setunion @ X1526))|((X1526)!=(setadjoin @ (setadjoin @ X1527 @ emptyset) @ (setadjoin @ (setadjoin @ X1527 @ (setadjoin @ X1528 @ emptyset)) @ emptyset)))))))&((~(in @ X1531 @ X1530)|((X1530)!=(setadjoin @ X1531 @ emptyset))|(in @ (setunion @ X1530) @ X1530))&(((kfst @ (kpair @ X1532 @ X1533))=(X1532))&((~(in @ X1536 @ (cartprod @ X1534 @ X1535))|(in @ (kfst @ X1536) @ X1534))&((((setadjoin @ (setadjoin @ X1537 @ emptyset) @ (setadjoin @ (setadjoin @ X1537 @ (setadjoin @ X1538 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1539 @ emptyset) @ (setadjoin @ (setadjoin @ X1539 @ (setadjoin @ X1540 @ emptyset)) @ emptyset)))|((X1537)=(X1539)))&((((kpair @ X1541 @ X1542)!=(kpair @ X1543 @ X1544))|((X1541)=(X1543)))&((((X1545)!=(X1546))|((setadjoin @ X1545 @ (setadjoin @ X1546 @ emptyset))=(setadjoin @ X1545 @ emptyset)))&((((X1547)!=(X1548))|((setadjoin @ (setadjoin @ X1547 @ emptyset) @ (setadjoin @ (setadjoin @ X1547 @ (setadjoin @ X1548 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1547 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1549 @ emptyset) @ (setadjoin @ (setadjoin @ X1549 @ (setadjoin @ X1550 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1551 @ emptyset) @ (setadjoin @ (setadjoin @ X1551 @ (setadjoin @ X1552 @ emptyset)) @ emptyset)))|(((X1551)!=(X1552))|((X1550)=(X1552))))&((((setadjoin @ X1553 @ (setadjoin @ X1554 @ emptyset))!=(setadjoin @ X1555 @ emptyset))|((X1553)=(X1554)))&((((setadjoin @ (setadjoin @ X1556 @ emptyset) @ (setadjoin @ (setadjoin @ X1556 @ (setadjoin @ X1557 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1558 @ emptyset) @ (setadjoin @ (setadjoin @ X1558 @ (setadjoin @ X1559 @ emptyset)) @ emptyset)))|((X1557)=(X1559)))&((((kpair @ X1560 @ X1561)!=(kpair @ X1562 @ X1563))|((X1561)=(X1563)))&((((in @ (esk74_1 @ X1564) @ (dsetconstr @ (setunion @ X1564) @ (^[Z0/* 3 */:$i]:(((X1564)=(kpair @ (kfst @ X1564) @ Z0))))))|(~(in @ X1565 @ (setunion @ X1564))|(~(in @ X1566 @ (setunion @ X1564))|((X1564)!=(setadjoin @ (setadjoin @ X1565 @ emptyset) @ (setadjoin @ (setadjoin @ X1565 @ (setadjoin @ X1566 @ emptyset)) @ emptyset))))))&(((dsetconstr @ (setunion @ X1564) @ (^[Z0/* 3 */:$i]:(((X1564)=(kpair @ (kfst @ X1564) @ Z0)))))=(setadjoin @ (esk74_1 @ X1564) @ emptyset))|(~(in @ X1565 @ (setunion @ X1564))|(~(in @ X1566 @ (setunion @ X1564))|((X1564)!=(setadjoin @ (setadjoin @ X1565 @ emptyset) @ (setadjoin @ (setadjoin @ X1565 @ (setadjoin @ X1566 @ emptyset)) @ emptyset)))))))&(((ksnd @ (kpair @ X1568 @ X1569))=(X1569))&(((in @ esk76_0 @ (setunion @ esk75_0))&((in @ esk77_0 @ (setunion @ esk75_0))&((esk75_0)=(setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset)))))&((kpair @ (kfst @ esk75_0) @ (ksnd @ esk75_0))!=(esk75_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_241])])])])])])])). 0.56/0.60 thf(c_0_244, plain, ![X1573:$i, X1574:$i]:(((kpair @ X1573 @ X1574)=(setadjoin @ (setadjoin @ X1573 @ emptyset) @ (setadjoin @ (setadjoin @ X1573 @ (setadjoin @ X1574 @ emptyset)) @ emptyset)))), inference(variable_rename,[status(thm)],[c_0_242])). 0.56/0.60 thf(c_0_245, negated_conjecture, ((esk75_0)=(setadjoin @ (setadjoin @ esk76_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk76_0 @ (setadjoin @ esk77_0 @ emptyset)) @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_243])). 0.56/0.60 thf(c_0_246, plain, ![X2:$i, X3:$i]:(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_244])). 0.56/0.60 thf(c_0_247, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_243])). 0.56/0.60 thf(c_0_248, negated_conjecture, ((kpair @ esk76_0 @ esk77_0)=(esk75_0)), inference(rw,[status(thm)],[c_0_245, c_0_246])). 0.56/0.60 thf(c_0_249, negated_conjecture, ((kpair @ (kfst @ esk75_0) @ (ksnd @ esk75_0))!=(esk75_0)), inference(split_conjunct,[status(thm)],[c_0_243])). 0.56/0.60 thf(c_0_250, negated_conjecture, ((kfst @ esk75_0)=(esk76_0)), inference(spm,[status(thm)],[c_0_247, c_0_248])). 0.56/0.60 thf(c_0_251, negated_conjecture, ![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3))), inference(split_conjunct,[status(thm)],[c_0_243])). 0.56/0.60 thf(c_0_252, negated_conjecture, ((kpair @ esk76_0 @ (ksnd @ esk75_0))!=(esk75_0)), inference(rw,[status(thm)],[c_0_249, c_0_250])). 0.56/0.60 thf(c_0_253, negated_conjecture, ((ksnd @ esk75_0)=(esk77_0)), inference(spm,[status(thm)],[c_0_251, c_0_248])). 0.56/0.60 thf(c_0_254, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_252, c_0_253]), c_0_248])]), ['proof']). 0.56/0.60 # SZS output end CNFRefutation 0.56/0.60 # Parsed axioms : 384 0.56/0.60 # Removed by relevancy pruning/SinE : 204 0.56/0.60 # Initial clauses : 341 0.56/0.60 # Removed in clause preprocessing : 25 0.56/0.60 # Initial clauses in saturation : 316 0.56/0.60 # Processed clauses : 361 0.56/0.60 # ...of these trivial : 6 0.56/0.60 # ...subsumed : 29 0.56/0.60 # ...remaining for further processing : 326 0.56/0.60 # Other redundant clauses eliminated : 21 0.56/0.60 # Clauses deleted for lack of memory : 0 0.56/0.60 # Backward-subsumed : 0 0.56/0.60 # Backward-rewritten : 5 0.56/0.60 # Generated clauses : 24 0.56/0.60 # ...of the previous two non-redundant : 20 0.56/0.60 # ...aggressively subsumed : 0 0.56/0.60 # Contextual simplify-reflections : 0 0.56/0.60 # Paramodulations : 3 0.56/0.60 # Factorizations : 0 0.56/0.60 # NegExts : 0 0.56/0.60 # Equation resolutions : 21 0.56/0.60 # Disequality decompositions : 0 0.56/0.60 # Total rewrite steps : 55 0.56/0.60 # ...of those cached : 34 0.56/0.60 # Propositional unsat checks : 0 0.56/0.60 # Propositional check models : 0 0.56/0.60 # Propositional check unsatisfiable : 0 0.56/0.60 # Propositional clauses : 0 0.56/0.60 # Propositional clauses after purity: 0 0.56/0.60 # Propositional unsat core size : 0 0.56/0.60 # Propositional preprocessing time : 0.000 0.56/0.60 # Propositional encoding time : 0.000 0.56/0.60 # Propositional solver time : 0.000 0.56/0.60 # Success case prop preproc time : 0.000 0.56/0.60 # Success case prop encoding time : 0.000 0.56/0.60 # Success case prop solver time : 0.000 0.56/0.60 # Current number of processed clauses : 27 0.56/0.60 # Positive orientable unit clauses : 19 0.56/0.60 # Positive unorientable unit clauses: 0 0.56/0.60 # Negative unit clauses : 2 0.56/0.60 # Non-unit-clauses : 6 0.56/0.60 # Current number of unprocessed clauses: 249 0.56/0.60 # ...number of literals in the above : 807 0.56/0.60 # Current number of archived formulas : 0 0.56/0.60 # Current number of archived clauses : 279 0.56/0.60 # Clause-clause subsumption calls (NU) : 12182 0.56/0.60 # Rec. Clause-clause subsumption calls : 5175 0.56/0.60 # Non-unit clause-clause subsumptions : 27 0.56/0.60 # Unit Clause-clause subsumption calls : 71 0.56/0.60 # Rewrite failures with RHS unbound : 0 0.56/0.60 # BW rewrite match attempts : 26 0.56/0.60 # BW rewrite match successes : 5 0.56/0.60 # Condensation attempts : 361 0.56/0.60 # Condensation successes : 3 0.56/0.60 # Termbank termtop insertions : 50006 0.56/0.60 # Search garbage collected termcells : 17314 0.56/0.60 0.56/0.60 # ------------------------------------------------- 0.56/0.60 # User time : 0.063 s 0.56/0.60 # System time : 0.013 s 0.56/0.60 # Total time : 0.077 s 0.56/0.60 # Maximum resident set size: 6132 pages 0.56/0.60 0.56/0.60 # ------------------------------------------------- 0.56/0.60 # User time : 0.072 s 0.56/0.60 # System time : 0.017 s 0.56/0.60 # Total time : 0.089 s 0.56/0.60 # Maximum resident set size: 2196 pages 0.56/0.60 % E---3.1 exiting 0.56/0.60 % E exiting 0.56/0.60 EOF