0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.13 % Command : run_E %s %d THM 0.13/0.34 % Computer : n018.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Thu Jul 4 07:48:54 EDT 2024 0.13/0.35 % CPUTime : 0.21/0.49 Running higher-order theorem proving 0.21/0.53 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.gaOHU6xK3C/E---3.1_23436.p 1.08/0.65 # Version: 3.2.0-ho 1.08/0.65 # Preprocessing class: HSLMSLSSLLLCHFA. 1.08/0.65 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 1.08/0.65 # Starting ehoh_best5 with 180s (1) cores 1.08/0.65 # Starting almost_fo_3_lam with 180s (1) cores 1.08/0.65 # Starting new_bool_5 with 180s (1) cores 1.08/0.65 # Starting pre_casc_3 with 180s (1) cores 1.08/0.65 # Starting ho_unfolding_8 with 180s (1) cores 1.08/0.65 # Starting new_ho_10_cnf2 with 180s (1) cores 1.08/0.65 # Starting new_bool_3 with 180s (1) cores 1.08/0.65 # Starting new_ho_5 with 180s (1) cores 1.08/0.65 # new_bool_3 with pid 23549 completed with status 0 1.08/0.65 # Result found by new_bool_3 1.08/0.65 # Preprocessing class: HSLMSLSSLLLCHFA. 1.08/0.65 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 1.08/0.65 # Starting ehoh_best5 with 180s (1) cores 1.08/0.65 # Starting almost_fo_3_lam with 180s (1) cores 1.08/0.65 # Starting new_bool_5 with 180s (1) cores 1.08/0.65 # Starting pre_casc_3 with 180s (1) cores 1.08/0.65 # Starting ho_unfolding_8 with 180s (1) cores 1.08/0.65 # Starting new_ho_10_cnf2 with 180s (1) cores 1.08/0.65 # Starting new_bool_3 with 180s (1) cores 1.08/0.65 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 1.08/0.65 # Search class: HGHSM-FSLM31-MHFMMSBN 1.08/0.65 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 1.08/0.65 # Starting new_ho_10_cnf2 with 98s (1) cores 1.08/0.65 # new_ho_10_cnf2 with pid 23576 completed with status 0 1.08/0.65 # Result found by new_ho_10_cnf2 1.08/0.65 # Preprocessing class: HSLMSLSSLLLCHFA. 1.08/0.65 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 1.08/0.65 # Starting ehoh_best5 with 180s (1) cores 1.08/0.65 # Starting almost_fo_3_lam with 180s (1) cores 1.08/0.65 # Starting new_bool_5 with 180s (1) cores 1.08/0.65 # Starting pre_casc_3 with 180s (1) cores 1.08/0.65 # Starting ho_unfolding_8 with 180s (1) cores 1.08/0.65 # Starting new_ho_10_cnf2 with 180s (1) cores 1.08/0.65 # Starting new_bool_3 with 180s (1) cores 1.08/0.65 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 1.08/0.65 # Search class: HGHSM-FSLM31-MHFMMSBN 1.08/0.65 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 1.08/0.65 # Starting new_ho_10_cnf2 with 98s (1) cores 1.08/0.65 # Preprocessing time : 0.005 s 1.08/0.65 # Presaturation interreduction done 1.08/0.65 1.08/0.65 # Proof found! 1.08/0.65 # SZS status Theorem 1.08/0.65 # SZS output start CNFRefutation 1.08/0.65 thf(decl_22, type, in: $i > $i > $o). 1.08/0.65 thf(decl_23, type, exu: ($i > $o) > $o). 1.08/0.65 thf(decl_24, type, setextAx: $o). 1.08/0.65 thf(decl_25, type, emptyset: $i). 1.08/0.65 thf(decl_26, type, emptysetAx: $o). 1.08/0.65 thf(decl_27, type, setadjoin: $i > $i > $i). 1.08/0.65 thf(decl_28, type, setadjoinAx: $o). 1.08/0.65 thf(decl_29, type, powerset: $i > $i). 1.08/0.65 thf(decl_30, type, powersetAx: $o). 1.08/0.65 thf(decl_31, type, setunion: $i > $i). 1.08/0.65 thf(decl_32, type, setunionAx: $o). 1.08/0.65 thf(decl_33, type, omega: $i). 1.08/0.65 thf(decl_34, type, omega0Ax: $o). 1.08/0.65 thf(decl_35, type, omegaSAx: $o). 1.08/0.65 thf(decl_36, type, omegaIndAx: $o). 1.08/0.65 thf(decl_37, type, replAx: $o). 1.08/0.65 thf(decl_38, type, foundationAx: $o). 1.08/0.65 thf(decl_39, type, wellorderingAx: $o). 1.08/0.65 thf(decl_40, type, descr: ($i > $o) > $i). 1.08/0.65 thf(decl_41, type, descrp: $o). 1.08/0.65 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 1.08/0.65 thf(decl_43, type, dsetconstrI: $o). 1.08/0.65 thf(decl_44, type, dsetconstrEL: $o). 1.08/0.65 thf(decl_45, type, dsetconstrER: $o). 1.08/0.65 thf(decl_46, type, exuE1: $o). 1.08/0.65 thf(decl_47, type, prop2set: $o > $i). 1.08/0.65 thf(decl_48, type, prop2setE: $o). 1.08/0.65 thf(decl_49, type, emptysetE: $o). 1.08/0.65 thf(decl_50, type, emptysetimpfalse: $o). 1.08/0.65 thf(decl_51, type, notinemptyset: $o). 1.08/0.65 thf(decl_52, type, exuE3e: $o). 1.08/0.65 thf(decl_53, type, setext: $o). 1.08/0.65 thf(decl_54, type, emptyI: $o). 1.08/0.65 thf(decl_55, type, noeltsimpempty: $o). 1.08/0.65 thf(decl_56, type, setbeta: $o). 1.08/0.65 thf(decl_57, type, nonempty: $i > $o). 1.08/0.65 thf(decl_58, type, nonemptyE1: $o). 1.08/0.65 thf(decl_59, type, nonemptyI: $o). 1.08/0.65 thf(decl_60, type, nonemptyI1: $o). 1.08/0.65 thf(decl_61, type, setadjoinIL: $o). 1.08/0.65 thf(decl_62, type, emptyinunitempty: $o). 1.08/0.65 thf(decl_63, type, setadjoinIR: $o). 1.08/0.65 thf(decl_64, type, setadjoinE: $o). 1.08/0.65 thf(decl_65, type, setadjoinOr: $o). 1.08/0.65 thf(decl_66, type, setoftrueEq: $o). 1.08/0.65 thf(decl_67, type, powersetI: $o). 1.08/0.65 thf(decl_68, type, emptyinPowerset: $o). 1.08/0.65 thf(decl_69, type, emptyInPowerset: $o). 1.08/0.65 thf(decl_70, type, powersetE: $o). 1.08/0.65 thf(decl_71, type, setunionI: $o). 1.08/0.65 thf(decl_72, type, setunionE: $o). 1.08/0.65 thf(decl_73, type, subPowSU: $o). 1.08/0.65 thf(decl_74, type, exuE2: $o). 1.08/0.65 thf(decl_75, type, nonemptyImpWitness: $o). 1.08/0.65 thf(decl_76, type, uniqinunit: $o). 1.08/0.65 thf(decl_77, type, notinsingleton: $o). 1.08/0.65 thf(decl_78, type, eqinunit: $o). 1.08/0.65 thf(decl_79, type, singletonsswitch: $o). 1.08/0.65 thf(decl_80, type, upairsetE: $o). 1.08/0.65 thf(decl_81, type, upairsetIL: $o). 1.08/0.65 thf(decl_82, type, upairsetIR: $o). 1.08/0.65 thf(decl_83, type, emptyE1: $o). 1.08/0.65 thf(decl_84, type, vacuousDall: $o). 1.08/0.65 thf(decl_85, type, quantDeMorgan1: $o). 1.08/0.65 thf(decl_86, type, quantDeMorgan2: $o). 1.08/0.65 thf(decl_87, type, quantDeMorgan3: $o). 1.08/0.65 thf(decl_88, type, quantDeMorgan4: $o). 1.08/0.65 thf(decl_89, type, prop2setI: $o). 1.08/0.65 thf(decl_91, type, prop2set2propI: $o). 1.08/0.65 thf(decl_92, type, notdexE: $o). 1.08/0.65 thf(decl_93, type, notdallE: $o). 1.08/0.65 thf(decl_94, type, exuI1: $o). 1.08/0.65 thf(decl_95, type, exuI3: $o). 1.08/0.65 thf(decl_96, type, exuI2: $o). 1.08/0.65 thf(decl_97, type, inCongP: $o). 1.08/0.65 thf(decl_98, type, in__Cong: $o). 1.08/0.65 thf(decl_99, type, exuE3u: $o). 1.08/0.65 thf(decl_100, type, exu__Cong: $o). 1.08/0.65 thf(decl_101, type, emptyset__Cong: $o). 1.08/0.65 thf(decl_102, type, setadjoin__Cong: $o). 1.08/0.65 thf(decl_103, type, powerset__Cong: $o). 1.08/0.65 thf(decl_104, type, setunion__Cong: $o). 1.08/0.65 thf(decl_105, type, omega__Cong: $o). 1.08/0.65 thf(decl_106, type, exuEu: $o). 1.08/0.65 thf(decl_107, type, descr__Cong: $o). 1.08/0.65 thf(decl_108, type, dsetconstr__Cong: $o). 1.08/0.65 thf(decl_109, type, subset: $i > $i > $o). 1.08/0.65 thf(decl_112, type, subsetI1: $o). 1.08/0.65 thf(decl_113, type, eqimpsubset2: $o). 1.08/0.65 thf(decl_114, type, eqimpsubset1: $o). 1.08/0.65 thf(decl_115, type, subsetI2: $o). 1.08/0.65 thf(decl_116, type, emptysetsubset: $o). 1.08/0.65 thf(decl_117, type, subsetE: $o). 1.08/0.65 thf(decl_118, type, subsetE2: $o). 1.08/0.65 thf(decl_119, type, notsubsetI: $o). 1.08/0.65 thf(decl_120, type, notequalI1: $o). 1.08/0.65 thf(decl_121, type, notequalI2: $o). 1.08/0.65 thf(decl_122, type, subsetRefl: $o). 1.08/0.65 thf(decl_123, type, subsetTrans: $o). 1.08/0.65 thf(decl_124, type, setadjoinSub: $o). 1.08/0.65 thf(decl_125, type, setadjoinSub2: $o). 1.08/0.65 thf(decl_126, type, subset2powerset: $o). 1.08/0.65 thf(decl_127, type, setextsub: $o). 1.08/0.65 thf(decl_128, type, subsetemptysetimpeq: $o). 1.08/0.65 thf(decl_129, type, powersetI1: $o). 1.08/0.65 thf(decl_130, type, powersetE1: $o). 1.08/0.65 thf(decl_131, type, inPowerset: $o). 1.08/0.65 thf(decl_132, type, powersetsubset: $o). 1.08/0.65 thf(decl_133, type, sepInPowerset: $o). 1.08/0.65 thf(decl_134, type, sepSubset: $o). 1.08/0.65 thf(decl_135, type, binunion: $i > $i > $i). 1.08/0.65 thf(decl_136, type, binunionIL: $o). 1.08/0.65 thf(decl_137, type, upairset2IR: $o). 1.08/0.65 thf(decl_138, type, binunionIR: $o). 1.08/0.65 thf(decl_139, type, binunionEcases: $o). 1.08/0.65 thf(decl_140, type, binunionE: $o). 1.08/0.65 thf(decl_141, type, binunionLsub: $o). 1.08/0.65 thf(decl_142, type, binunionRsub: $o). 1.08/0.65 thf(decl_143, type, binintersect: $i > $i > $i). 1.08/0.65 thf(decl_144, type, binintersectI: $o). 1.08/0.65 thf(decl_145, type, binintersectSubset5: $o). 1.08/0.65 thf(decl_146, type, binintersectEL: $o). 1.08/0.65 thf(decl_147, type, binintersectLsub: $o). 1.08/0.65 thf(decl_148, type, binintersectSubset2: $o). 1.08/0.65 thf(decl_149, type, binintersectSubset3: $o). 1.08/0.65 thf(decl_150, type, binintersectER: $o). 1.08/0.65 thf(decl_151, type, disjointsetsI1: $o). 1.08/0.65 thf(decl_152, type, binintersectRsub: $o). 1.08/0.65 thf(decl_153, type, binintersectSubset4: $o). 1.08/0.65 thf(decl_154, type, binintersectSubset1: $o). 1.08/0.65 thf(decl_155, type, bs114d: $o). 1.08/0.65 thf(decl_157, type, setminus: $i > $i > $i). 1.08/0.65 thf(decl_158, type, setminusI: $o). 1.08/0.65 thf(decl_159, type, setminusEL: $o). 1.08/0.65 thf(decl_160, type, setminusER: $o). 1.08/0.65 thf(decl_161, type, setminusSubset2: $o). 1.08/0.65 thf(decl_162, type, setminusERneg: $o). 1.08/0.65 thf(decl_163, type, setminusELneg: $o). 1.08/0.65 thf(decl_164, type, setminusILneg: $o). 1.08/0.65 thf(decl_165, type, setminusIRneg: $o). 1.08/0.65 thf(decl_166, type, setminusLsub: $o). 1.08/0.65 thf(decl_167, type, setminusSubset1: $o). 1.08/0.65 thf(decl_168, type, symdiff: $i > $i > $i). 1.08/0.65 thf(decl_169, type, symdiffE: $o). 1.08/0.65 thf(decl_170, type, symdiffI1: $o). 1.08/0.65 thf(decl_171, type, symdiffI2: $o). 1.08/0.65 thf(decl_172, type, symdiffIneg1: $o). 1.08/0.65 thf(decl_173, type, symdiffIneg2: $o). 1.08/0.65 thf(decl_174, type, iskpair: $i > $o). 1.08/0.65 thf(decl_175, type, secondinupair: $o). 1.08/0.65 thf(decl_176, type, setukpairIL: $o). 1.08/0.65 thf(decl_177, type, setukpairIR: $o). 1.08/0.65 thf(decl_178, type, kpairiskpair: $o). 1.08/0.65 thf(decl_179, type, kpair: $i > $i > $i). 1.08/0.65 thf(decl_180, type, kpairp: $o). 1.08/0.65 thf(decl_181, type, cartprod: $i > $i > $i). 1.08/0.65 thf(decl_182, type, singletonsubset: $o). 1.08/0.65 thf(decl_183, type, singletoninpowerset: $o). 1.08/0.65 thf(decl_184, type, singletoninpowunion: $o). 1.08/0.65 thf(decl_185, type, upairset2E: $o). 1.08/0.65 thf(decl_186, type, upairsubunion: $o). 1.08/0.65 thf(decl_187, type, upairinpowunion: $o). 1.08/0.65 thf(decl_188, type, ubforcartprodlem1: $o). 1.08/0.65 thf(decl_189, type, ubforcartprodlem2: $o). 1.08/0.65 thf(decl_190, type, ubforcartprodlem3: $o). 1.08/0.65 thf(decl_191, type, cartprodpairin: $o). 1.08/0.65 thf(decl_192, type, cartprodmempair1: $o). 1.08/0.65 thf(decl_193, type, cartprodmempair: $o). 1.08/0.65 thf(decl_194, type, setunionE2: $o). 1.08/0.65 thf(decl_195, type, setunionsingleton1: $o). 1.08/0.65 thf(decl_196, type, setunionsingleton2: $o). 1.08/0.65 thf(decl_197, type, setunionsingleton: $o). 1.08/0.65 thf(decl_198, type, singleton: $i > $o). 1.08/0.65 thf(decl_199, type, singletonprop: $o). 1.08/0.65 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 1.08/0.65 thf(decl_201, type, ex1E1: $o). 1.08/0.65 thf(decl_202, type, ex1I: $o). 1.08/0.65 thf(decl_203, type, ex1I2: $o). 1.08/0.65 thf(decl_204, type, singletonsuniq: $o). 1.08/0.65 thf(decl_209, type, setukpairinjL1: $o). 1.08/0.65 thf(decl_210, type, kfstsingleton: $o). 1.08/0.65 thf(decl_211, type, theprop: $o). 1.08/0.65 thf(decl_212, type, kfst: $i > $i). 1.08/0.65 thf(decl_213, type, kfstpairEq: $o). 1.08/0.65 thf(decl_214, type, cartprodfstin: $o). 1.08/0.65 thf(decl_215, type, setukpairinjL2: $o). 1.08/0.65 thf(decl_216, type, setukpairinjL: $o). 1.08/0.65 thf(decl_217, type, setukpairinjR11: $o). 1.08/0.65 thf(decl_218, type, setukpairinjR12: $o). 1.08/0.65 thf(decl_219, type, setukpairinjR1: $o). 1.08/0.65 thf(decl_220, type, upairequniteq: $o). 1.08/0.65 thf(decl_221, type, setukpairinjR2: $o). 1.08/0.65 thf(decl_222, type, setukpairinjR: $o). 1.08/0.65 thf(decl_223, type, ksndsingleton: $o). 1.08/0.65 thf(decl_224, type, ksnd: $i > $i). 1.08/0.65 thf(decl_225, type, ksndpairEq: $o). 1.08/0.65 thf(decl_226, type, kpairsurjEq: $o). 1.08/0.65 thf(decl_227, type, cartprodsndin: $o). 1.08/0.65 thf(decl_228, type, cartprodpairmemEL: $o). 1.08/0.65 thf(decl_229, type, epred1_0: $o). 1.08/0.65 thf(decl_230, type, esk1_2: $i > $i > $i). 1.08/0.65 thf(decl_231, type, esk2_2: $i > $i > $i). 1.08/0.65 thf(decl_232, type, esk3_2: $i > $i > $i). 1.08/0.65 thf(decl_233, type, esk4_1: $i > $i). 1.08/0.65 thf(decl_234, type, esk5_2: ($i > $i > $o) > $i > $i). 1.08/0.65 thf(decl_235, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 1.08/0.65 thf(decl_236, type, esk7_2: ($i > $i > $o) > $i > $i). 1.08/0.65 thf(decl_237, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 1.08/0.65 thf(decl_238, type, esk9_1: $i > $i). 1.08/0.65 thf(decl_239, type, esk10_2: ($i > $o) > $i > $i). 1.08/0.65 thf(decl_240, type, esk11_2: ($i > $o) > $i > $i). 1.08/0.65 thf(decl_241, type, esk12_1: ($i > $o) > $i). 1.08/0.65 thf(decl_242, type, esk13_2: ($i > $o) > $i > $i). 1.08/0.65 thf(decl_243, type, esk14_1: ($i > $o) > $i). 1.08/0.65 thf(decl_244, type, esk15_2: $i > $i > $i). 1.08/0.65 thf(decl_245, type, esk16_2: $i > $i > $i). 1.08/0.65 thf(decl_246, type, esk17_1: $i > $i). 1.08/0.65 thf(decl_247, type, esk18_1: $i > $i). 1.08/0.65 thf(decl_248, type, esk19_1: $i > $i). 1.08/0.65 thf(decl_249, type, esk20_2: $i > $i > $i). 1.08/0.65 thf(decl_250, type, esk21_3: $i > $i > $o > $i). 1.08/0.65 thf(decl_251, type, esk22_2: ($i > $o) > $i > $i). 1.08/0.65 thf(decl_252, type, esk23_1: ($i > $o) > $i). 1.08/0.65 thf(decl_253, type, esk24_1: $i > $i). 1.08/0.65 thf(decl_254, type, esk25_2: $i > ($i > $o) > $i). 1.08/0.65 thf(decl_255, type, esk26_2: $i > ($i > $o) > $i). 1.08/0.65 thf(decl_256, type, esk27_2: $i > ($i > $o) > $i). 1.08/0.65 thf(decl_257, type, esk28_2: $i > ($i > $o) > $i). 1.08/0.65 thf(decl_258, type, esk29_2: $i > ($i > $o) > $i). 1.08/0.65 thf(decl_259, type, esk30_2: $i > ($i > $o) > $i). 1.08/0.65 thf(decl_260, type, esk31_2: ($i > $o) > $i > $i). 1.08/0.65 thf(decl_261, type, esk32_1: ($i > $o) > $i). 1.08/0.65 thf(decl_262, type, esk33_1: ($i > $o) > $i). 1.08/0.66 thf(decl_263, type, esk34_1: ($i > $o) > $i). 1.08/0.66 thf(decl_264, type, esk35_1: ($i > $o) > $i). 1.08/0.66 thf(decl_265, type, esk36_2: ($i > $o) > $i > $i). 1.08/0.66 thf(decl_266, type, esk37_1: ($i > $o) > $i). 1.08/0.66 thf(decl_267, type, esk38_2: ($i > $o) > $i > $i). 1.08/0.66 thf(decl_268, type, esk39_2: ($i > $o) > ($i > $o) > $i). 1.08/0.66 thf(decl_269, type, esk40_2: ($i > $o) > ($i > $o) > $i). 1.08/0.66 thf(decl_270, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 1.08/0.66 thf(decl_271, type, esk42_2: ($i > $o) > ($i > $o) > $i). 1.08/0.66 thf(decl_272, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 1.08/0.66 thf(decl_273, type, esk44_2: ($i > $o) > ($i > $o) > $i). 1.08/0.66 thf(decl_274, type, esk45_2: ($i > $o) > $i > $i). 1.08/0.66 thf(decl_275, type, esk46_2: ($i > $o) > ($i > $o) > $i). 1.08/0.66 thf(decl_276, type, esk47_2: ($i > $o) > ($i > $o) > $i). 1.08/0.66 thf(decl_277, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 1.08/0.66 thf(decl_278, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 1.08/0.66 thf(decl_279, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 1.08/0.66 thf(decl_280, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 1.08/0.66 thf(decl_281, type, esk52_2: $i > $i > $i). 1.08/0.66 thf(decl_282, type, esk53_2: $i > $i > $i). 1.08/0.66 thf(decl_283, type, esk54_2: $i > $i > $i). 1.08/0.66 thf(decl_284, type, esk55_3: $i > $i > $i > $i). 1.08/0.66 thf(decl_285, type, esk56_3: $i > $i > $i > $i). 1.08/0.66 thf(decl_286, type, esk57_2: $i > $i > $i). 1.08/0.66 thf(decl_287, type, esk58_2: $i > ($i > $o) > $i). 1.08/0.66 thf(decl_288, type, esk59_2: $i > ($i > $o) > $i). 1.08/0.66 thf(decl_289, type, esk60_2: $i > ($i > $o) > $i). 1.08/0.66 thf(decl_290, type, esk61_2: $i > ($i > $o) > $i). 1.08/0.66 thf(decl_291, type, esk62_3: $i > ($i > $o) > $i > $i). 1.08/0.66 thf(decl_292, type, esk63_3: $i > ($i > $o) > $i > $i). 1.08/0.66 thf(decl_293, type, esk64_2: $i > ($i > $o) > $i). 1.08/0.66 thf(decl_294, type, esk65_2: $i > ($i > $o) > $i). 1.08/0.66 thf(decl_295, type, esk66_2: $i > ($i > $o) > $i). 1.08/0.66 thf(decl_296, type, esk67_1: $i > $i). 1.08/0.66 thf(decl_297, type, esk68_1: $i > $i). 1.08/0.66 thf(decl_298, type, esk69_0: $i). 1.08/0.66 thf(decl_299, type, esk70_0: $i). 1.08/0.66 thf(decl_300, type, esk71_0: $i). 1.08/0.66 thf(decl_301, type, esk72_0: $i). 1.08/0.66 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', ex1)). 1.08/0.66 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', singleton)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', exuI1)). 1.08/0.66 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', exu)). 1.08/0.66 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', nonemptyI)). 1.08/0.66 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', nonempty)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', exuE1)). 1.08/0.66 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', replAx)). 1.08/0.66 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', kfstsingleton)). 1.08/0.66 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', ex1I2)). 1.08/0.66 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', ex1E1)). 1.08/0.66 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', ksndsingleton)). 1.08/0.66 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.gaOHU6xK3C/E---3.1_23436.p', ex1I)). 1.08/0.66 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', singletonprop)). 1.08/0.66 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', exu__Cong)). 1.08/0.66 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', exuE3u)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', exuI2)). 1.08/0.66 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', exuI3)). 1.08/0.66 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', descr__Cong)). 1.08/0.66 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', exuEu)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', exuE2)). 1.08/0.66 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', exuE3e)). 1.08/0.66 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', descrp)). 1.08/0.66 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', sepInPowerset)). 1.08/0.66 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', sepSubset)). 1.08/0.66 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setoftrueEq)). 1.08/0.66 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setbeta)). 1.08/0.66 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', dsetconstrER)). 1.08/0.66 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', dsetconstrI)). 1.08/0.66 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', theprop)). 1.08/0.66 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', dsetconstr__Cong)). 1.08/0.66 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.gaOHU6xK3C/E---3.1_23436.p', emptyE1)). 1.08/0.66 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', nonemptyImpWitness)). 1.08/0.66 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', nonemptyI1)). 1.08/0.66 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', nonemptyE1)). 1.08/0.66 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', dsetconstrEL)). 1.08/0.66 thf(cartprodpairmemER, conjecture, ((setextAx)=>(((setadjoinAx)=>((powersetAx)=>(((omega0Ax)=>(((((foundationAx)=>((wellorderingAx)=>((descrp)=>(((dsetconstrEL)=>((((((emptysetimpfalse)=>(((exuE3e)=>((setext)=>(((noeltsimpempty)=>(((nonemptyE1)=>(((nonemptyI1)=>((((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>(((powersetI)=>((emptyinPowerset)=>((((((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>(((eqinunit)=>((singletonsswitch)=>((((upairsetIR)=>((emptyE1)=>((vacuousDall)=>(((quantDeMorgan2)=>((quantDeMorgan3)=>((((prop2set2propI)=>(((((((inCongP)=>((in__Cong)=>((((emptyset__Cong)=>((((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>(((eqimpsubset1)=>(((((subsetE2)=>(((((subsetRefl)=>((subsetTrans)=>((((subset2powerset)=>((setextsub)=>((((powersetE1)=>((((sepInPowerset)=>((sepSubset)=>((binunionIL)=>(((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((((binintersectEL)=>((((((disjointsetsI1)=>((((binintersectSubset1)=>((bs114d)=>((((setminusER)=>((((setminusELneg)=>(((setminusIRneg)=>((((((((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>(((kpairiskpair)=>((kpairp)=>((singletonsubset)=>(((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>(((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((((ex1E1)=>((((singletonsuniq)=>((setukpairinjL1)=>((((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((((setukpairinjR1)=>((((setukpairinjR)=>((ksndsingleton)=>(((kpairsurjEq)=>((cartprodsndin)=>(![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))<=(cartprodpairmemEL))))<=(ksndpairEq))))<=(setukpairinjR2))<=(upairequniteq)))<=(setukpairinjR12))<=(setukpairinjR11))))))<=(theprop))<=(kfstsingleton))))<=(ex1I2))<=(ex1I)))<=(singletonprop))<=(setunionsingleton)))))))))<=(ubforcartprodlem2)))))))<=(singletoninpowerset)))))<=(setukpairIR)))))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1))<=(symdiffE))<=(setminusSubset1))<=(setminusLsub)))<=(setminusILneg)))<=(setminusERneg))<=(setminusSubset2)))<=(setminusEL))<=(setminusI))))<=(binintersectSubset4))<=(binintersectRsub)))<=(binintersectER))<=(binintersectSubset3))<=(binintersectSubset2))<=(binintersectLsub)))<=(binintersectSubset5))<=(binintersectI)))))))<=(upairset2IR)))))<=(powersetsubset))<=(inPowerset)))<=(powersetI1))<=(subsetemptysetimpeq))))<=(setadjoinSub2))<=(setadjoinSub))))<=(notequalI2))<=(notequalI1))<=(notsubsetI)))<=(subsetE))<=(emptysetsubset))<=(subsetI2)))<=(eqimpsubset2))))))))<=(powerset__Cong))<=(setadjoin__Cong)))<=(exu__Cong))<=(exuE3u))))<=(exuI2))<=(exuI3))<=(exuI1))<=(notdallE))<=(notdexE)))<=(prop2setI))<=(quantDeMorgan4))))<=(quantDeMorgan1)))))<=(upairsetIL))<=(upairsetE))))<=(notinsingleton))))))<=(setunionE))<=(setunionI))<=(powersetE))<=(emptyInPowerset))))<=(setoftrueEq)))))<=(emptyinunitempty))<=(setadjoinIL)))<=(nonemptyI)))<=(setbeta)))<=(emptyI))))<=(notinemptyset)))<=(emptysetE))<=(prop2setE))<=(exuE1))<=(dsetconstrER)))<=(dsetconstrI)))))<=(replAx))<=(omegaIndAx))<=(omegaSAx)))<=(setunionAx))))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', cartprodpairmemER)). 1.08/0.66 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', subsetRefl)). 1.08/0.66 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', emptysetE)). 1.08/0.66 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', emptysetAx)). 1.08/0.66 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', notdallE)). 1.08/0.66 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', notdexE)). 1.08/0.66 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setextsub)). 1.08/0.66 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', prop2setI)). 1.08/0.66 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', quantDeMorgan4)). 1.08/0.66 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', powersetE1)). 1.08/0.66 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', quantDeMorgan1)). 1.08/0.66 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', upairsetIL)). 1.08/0.66 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', upairsetE)). 1.08/0.66 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', notinsingleton)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', setunionE)). 1.08/0.66 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setunionI)). 1.08/0.66 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', powersetE)). 1.08/0.66 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', emptyInPowerset)). 1.08/0.66 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binunionIL)). 1.08/0.66 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', subsetE2)). 1.08/0.66 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', emptyinunitempty)). 1.08/0.66 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setadjoinIL)). 1.08/0.66 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binunionIR)). 1.08/0.66 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', emptyI)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', binunionEcases)). 1.08/0.66 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', notinemptyset)). 1.08/0.66 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', singletonsubset)). 1.08/0.66 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', prop2setE)). 1.08/0.66 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binunionE)). 1.08/0.66 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binunionLsub)). 1.08/0.66 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', omegaIndAx)). 1.08/0.66 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binunionRsub)). 1.08/0.66 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', omegaSAx)). 1.08/0.66 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setunionAx)). 1.08/0.66 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binintersectEL)). 1.08/0.66 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', disjointsetsI1)). 1.08/0.66 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binintersectSubset1)). 1.08/0.66 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', bs114d)). 1.08/0.66 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setminusER)). 1.08/0.66 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setminusELneg)). 1.08/0.66 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setminusIRneg)). 1.08/0.66 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', symdiffIneg2)). 1.08/0.66 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', secondinupair)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', setukpairIL)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', kpairiskpair)). 1.08/0.66 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', kpairp)). 1.08/0.66 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', singletoninpowunion)). 1.08/0.66 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', upairset2E)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', upairsubunion)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', upairinpowunion)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', ubforcartprodlem1)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', ubforcartprodlem3)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', cartprodpairin)). 1.08/0.66 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', cartprodmempair1)). 1.08/0.66 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', subsetTrans)). 1.08/0.66 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', cartprodmempair)). 1.08/0.66 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setunionE2)). 1.08/0.66 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setunionsingleton1)). 1.08/0.66 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setunionsingleton2)). 1.08/0.66 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', singletonsuniq)). 1.08/0.66 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setukpairinjL1)). 1.08/0.66 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', kfstpairEq)). 1.08/0.66 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', cartprodfstin)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', setukpairinjL2)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', setukpairinjL)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', setukpairinjR1)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', setukpairinjR)). 1.08/0.66 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', kpairsurjEq)). 1.08/0.66 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', cartprodsndin)). 1.08/0.66 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', cartprodpairmemEL)). 1.08/0.66 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', ksndpairEq)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', setukpairinjR2)). 1.08/0.66 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', upairequniteq)). 1.08/0.66 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setukpairinjR12)). 1.08/0.66 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setukpairinjR11)). 1.08/0.66 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setunionsingleton)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', ubforcartprodlem2)). 1.08/0.66 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', singletoninpowerset)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', setukpairIR)). 1.08/0.66 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', symdiffIneg1)). 1.08/0.66 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', symdiffI2)). 1.08/0.66 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', symdiffI1)). 1.08/0.66 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', symdiffE)). 1.08/0.66 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setminusSubset1)). 1.08/0.66 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setminusLsub)). 1.08/0.66 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setminusILneg)). 1.08/0.66 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setminusERneg)). 1.08/0.66 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setminusSubset2)). 1.08/0.66 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setminusEL)). 1.08/0.66 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setminusI)). 1.08/0.66 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binintersectSubset4)). 1.08/0.66 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binintersectRsub)). 1.08/0.66 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binintersectER)). 1.08/0.66 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binintersectSubset3)). 1.08/0.66 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binintersectSubset2)). 1.08/0.66 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binintersectLsub)). 1.08/0.66 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binintersectSubset5)). 1.08/0.66 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', binintersectI)). 1.08/0.66 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', upairset2IR)). 1.08/0.66 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', powersetsubset)). 1.08/0.66 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', inPowerset)). 1.08/0.66 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', powersetI1)). 1.08/0.66 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', subsetemptysetimpeq)). 1.08/0.66 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setadjoinSub2)). 1.08/0.66 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', subset2powerset)). 1.08/0.66 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setadjoinSub)). 1.08/0.66 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', notequalI2)). 1.08/0.66 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', notequalI1)). 1.08/0.66 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', notsubsetI)). 1.08/0.66 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', subsetE)). 1.08/0.66 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', emptysetsubset)). 1.08/0.66 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', subsetI2)). 1.08/0.66 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', eqimpsubset2)). 1.08/0.66 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', powerset__Cong)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', setadjoin__Cong)). 1.08/0.66 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', eqimpsubset1)). 1.08/0.66 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', subsetI1)). 1.08/0.66 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', omega__Cong)). 1.08/0.66 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setunion__Cong)). 1.08/0.66 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', emptyset__Cong)). 1.08/0.66 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', in__Cong)). 1.08/0.66 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', inCongP)). 1.08/0.66 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', quantDeMorgan3)). 1.08/0.66 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', quantDeMorgan2)). 1.08/0.66 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', vacuousDall)). 1.08/0.66 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', upairsetIR)). 1.08/0.66 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', singletonsswitch)). 1.08/0.66 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', eqinunit)). 1.08/0.66 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', uniqinunit)). 1.08/0.66 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', subPowSU)). 1.08/0.66 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', emptyinPowerset)). 1.08/0.66 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', powersetI)). 1.08/0.66 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setadjoinOr)). 1.08/0.66 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setadjoinE)). 1.08/0.66 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setadjoinIR)). 1.08/0.66 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', noeltsimpempty)). 1.08/0.66 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.gaOHU6xK3C/E---3.1_23436.p', setext)). 1.08/0.66 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', emptysetimpfalse)). 1.08/0.66 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', wellorderingAx)). 1.08/0.66 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', foundationAx)). 1.08/0.66 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', omega0Ax)). 1.08/0.66 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', powersetAx)). 1.08/0.66 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setadjoinAx)). 1.08/0.66 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.gaOHU6xK3C/E---3.1_23436.p', setextAx)). 1.08/0.66 thf(c_0_180, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X533:$i]:(((in @ X533 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X533 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])). 1.08/0.66 thf(c_0_181, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])). 1.08/0.66 thf(c_0_182, 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])). 1.08/0.66 thf(c_0_183, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 1.08/0.66 thf(c_0_184, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 1.08/0.66 thf(c_0_185, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 1.08/0.66 thf(c_0_186, 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])). 1.08/0.66 thf(c_0_187, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 1.08/0.66 thf(c_0_188, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 1.08/0.66 thf(c_0_189, plain, ((ex1I2)<=>![X4:$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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 1.08/0.66 thf(c_0_190, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X533:$i]:(((in @ X533 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X533 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_180, c_0_181])). 1.08/0.66 thf(c_0_191, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 1.08/0.66 thf(c_0_192, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 1.08/0.66 thf(c_0_193, plain, ((ex1I)<=>![X4:$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])). 1.08/0.66 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 1.08/0.66 thf(c_0_195, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 1.08/0.66 thf(c_0_196, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 1.08/0.66 thf(c_0_197, 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])). 1.08/0.66 thf(c_0_198, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 1.08/0.66 thf(c_0_199, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 1.08/0.66 thf(c_0_200, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 1.08/0.66 thf(c_0_201, 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])). 1.08/0.66 thf(c_0_202, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 1.08/0.66 thf(c_0_203, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 1.08/0.66 thf(c_0_204, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X514:$i]:((((X1 @ X514))&![X515:$i]:((((X1 @ X515))=>((X514)=(X515))))))))))), inference(apply_def,[status(thm)],[c_0_182, c_0_183])). 1.08/0.66 thf(c_0_205, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 1.08/0.66 thf(c_0_206, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 1.08/0.66 thf(c_0_207, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 1.08/0.66 thf(c_0_208, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_184, c_0_185])). 1.08/0.66 thf(c_0_209, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 1.08/0.66 thf(c_0_210, plain, ((exuE1)=(![X1:$i > $o]:(((?[X508:$i]:((((X1 @ X508))&![X509:$i]:((((X1 @ X509))=>((X508)=(X509)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_186, c_0_183])). 1.08/0.66 thf(c_0_211, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 1.08/0.66 thf(c_0_212, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 1.08/0.66 thf(c_0_213, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X504:$i]:((((X6 @ X2 @ X504))&![X505:$i]:((((X6 @ X2 @ X505))=>((X504)=(X505)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_187, c_0_183])). 1.08/0.66 thf(c_0_214, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X537:$i]:(((in @ X537 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X537 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_188, c_0_181])). 1.08/0.66 thf(c_0_215, 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)))=>(?[X536:$i]:(((in @ X536 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X536 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_189, c_0_190])). 1.08/0.66 thf(c_0_216, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X534:$i]:(((in @ X534 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X534 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_191, c_0_190])). 1.08/0.66 thf(c_0_217, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X539:$i]:(((in @ X539 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X539 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_192, c_0_181])). 1.08/0.66 thf(c_0_218, axiom, ((theprop)=(![X21:$i]:(((?[X538:$i]:(((in @ X538 @ X21)&((X21)=(setadjoin @ X538 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_181])). 1.08/0.66 thf(c_0_219, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X535:$i]:(((in @ X535 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X535 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_193, c_0_190])). 1.08/0.66 thf(c_0_220, 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)))=>(?[X532:$i]:(((in @ X532 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X532 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_194, c_0_181])). 1.08/0.66 thf(c_0_221, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X522:$i]:((((X1 @ X522))&![X523:$i]:((((X1 @ X523))=>((X522)=(X523)))))))<=>(?[X524:$i]:((((X17 @ X524))&![X525:$i]:((((X17 @ X525))=>((X524)=(X525)))))))))))), inference(apply_def,[status(thm)],[c_0_195, c_0_183])). 1.08/0.66 thf(c_0_222, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X520:$i]:((((X1 @ X520))&![X521:$i]:((((X1 @ X521))=>((X520)=(X521)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_196, c_0_183])). 1.08/0.66 thf(c_0_223, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X518:$i]:((((X1 @ X518))&![X519:$i]:((((X1 @ X519))=>((X518)=(X519))))))))))), inference(apply_def,[status(thm)],[c_0_197, c_0_183])). 1.08/0.66 thf(c_0_224, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X516:$i]:((((X1 @ X516))&![X517:$i]:((((X1 @ X517))=>((X516)=(X517)))))))))))), inference(apply_def,[status(thm)],[c_0_198, c_0_183])). 1.08/0.66 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 1.08/0.66 thf(c_0_226, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X528:$i]:((((X1 @ X528))&![X529:$i]:((((X1 @ X529))=>((X528)=(X529)))))))=>((?[X530:$i]:((((X17 @ X530))&![X531:$i]:((((X17 @ X531))=>((X530)=(X531)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_199, c_0_183])). 1.08/0.66 thf(c_0_227, plain, ((exuEu)=(![X1:$i > $o]:(((?[X526:$i]:((((X1 @ X526))&![X527:$i]:((((X1 @ X527))=>((X526)=(X527)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_200, c_0_183])). 1.08/0.66 thf(c_0_228, plain, ((emptyE1)<=>![X4:$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])). 1.08/0.66 thf(c_0_229, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_185])). 1.08/0.66 thf(c_0_230, plain, ((exuE2)=(![X1:$i > $o]:(((?[X512:$i]:((((X1 @ X512))&![X513:$i]:((((X1 @ X513))=>((X512)=(X513)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_201, c_0_183])). 1.08/0.66 thf(c_0_231, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_185])). 1.08/0.66 thf(c_0_232, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_185])). 1.08/0.66 thf(c_0_233, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X510:$i]:((((X1 @ X510))&![X511:$i]:((((X1 @ X511))=>((X510)=(X511)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_202, c_0_183])). 1.08/0.66 thf(c_0_234, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 1.08/0.66 thf(c_0_235, plain, ((descrp)=(![X1:$i > $o]:(((?[X506:$i]:((((X1 @ X506))&![X507:$i]:((((X1 @ X507))=>((X506)=(X507)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_203, c_0_183])). 1.08/0.66 thf(c_0_236, 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:$i]:(((in @ X571 @ X570)=>(in @ X571 @ X567)))|(in @ X568 @ X570)))))))))))), introduced(definition)). 1.08/0.66 thf(c_0_237, negated_conjecture, ~((![X540:$i, X541:$i]:((![X542:$i]:(((in @ X542 @ X540)<=>(in @ X542 @ X541)))=>((X540)=(X541))))=>(![X1052:$i]:(~(in @ X1052 @ emptyset))=>(![X543:$i, X544:$i, X545:$i]:(((in @ X545 @ (setadjoin @ X543 @ X544))<=>(((X545)=(X543))|(in @ X545 @ X544))))=>(![X546:$i, X547:$i]:(((in @ X547 @ (powerset @ X546))<=>![X548:$i]:(((in @ X548 @ X547)=>(in @ X548 @ X546)))))=>(![X1049:$i, X1050:$i]:(((in @ X1050 @ (setunion @ X1049))<=>?[X1051:$i]:(((in @ X1050 @ X1051)&(in @ X1051 @ X1049)))))=>((in @ emptyset @ omega)=>(![X1048:$i]:(((in @ X1048 @ omega)=>(in @ (setadjoin @ X1048 @ X1048) @ omega)))=>(![X1045:$i]:((((in @ emptyset @ X1045)&![X1046:$i]:((((in @ X1046 @ omega)&(in @ X1046 @ X1045))=>(in @ (setadjoin @ X1046 @ X1046) @ X1045))))=>![X1047:$i]:(((in @ X1047 @ omega)=>(in @ X1047 @ X1045)))))=>(![X1037:$i > $i > $o, X1038:$i]:((![X1039:$i]:(((in @ X1039 @ X1038)=>?[X1040:$i]:(((X1037 @ X1039 @ X1040)&![X1041:$i]:(((X1037 @ X1039 @ X1041)=>((X1040)=(X1041))))))))=>?[X1042:$i]:(![X1043:$i]:(((in @ X1043 @ X1042)<=>?[X1044:$i]:(((in @ X1044 @ X1038)&(X1037 @ X1044 @ X1043))))))))=>(![X549:$i]:((?[X550:$i]:((in @ X550 @ X549))=>?[X551:$i]:(((in @ X551 @ X549)&~(?[X552:$i]:(((in @ X552 @ X551)&(in @ X552 @ X549))))))))=>((epred1_0)=>(![X572:$i > $o]:((?[X573:$i]:(((X572 @ X573)&![X574:$i]:(((X572 @ X574)=>((X573)=(X574))))))=>(X572 @ (descr @ (^[Z0/* 17 */:$i]:(X572 @ Z0))))))=>(![X1034:$i, X1035:$i > $o, X1036:$i]:(((in @ X1036 @ X1034)=>((X1035 @ X1036)=>(in @ X1036 @ (dsetconstr @ X1034 @ X1035)))))=>(![X575:$i, X576:$i > $o, X577:$i]:(((in @ X577 @ (dsetconstr @ X575 @ X576))=>(in @ X577 @ X575)))=>(![X1031:$i, X1032:$i > $o, X1033:$i]:(((in @ X1033 @ (dsetconstr @ X1031 @ X1032))=>(X1032 @ X1033)))=>(![X1026:$i > $o]:((?[X1027:$i]:(((X1026 @ X1027)&![X1028:$i]:(((X1026 @ X1028)=>((X1027)=(X1028))))))=>?[X1029:$i]:(((X1026 @ X1029)&![X1030:$i]:(((X1026 @ X1030)=>((X1029)=(X1030))))))))=>(![X1024:$o, X1025:$i]:(((in @ X1025 @ (prop2set @ ((X1024))))=>(X1024)))=>(![X1022:$i]:(((in @ X1022 @ emptyset)=>![X1023:$o]:((X1023))))=>(![X578:$i]:(((in @ X578 @ emptyset)=>~($true)))=>(![X1021:$i]:(~(in @ X1021 @ emptyset))=>(![X579:$i > $o]:((?[X580:$i]:(((X579 @ X580)&![X581:$i]:(((X579 @ X581)=>((X580)=(X581))))))=>?[X582:$i]:((X579 @ X582))))=>(![X583:$i, X584:$i]:((![X585:$i]:(((in @ X585 @ X583)=>(in @ X585 @ X584)))=>(![X586:$i]:(((in @ X586 @ X584)=>(in @ X586 @ X583)))=>((X583)=(X584)))))=>(![X1019:$i]:((![X1020:$i]:(~(in @ X1020 @ X1019))=>((X1019)=(emptyset))))=>(![X587:$i]:((![X588:$i]:(~(in @ X588 @ X587))=>((X587)=(emptyset))))=>(![X1016:$i, X1017:$i > $o, X1018:$i]:(((in @ X1018 @ X1016)=>((in @ X1018 @ (dsetconstr @ X1016 @ X1017))<=>(X1017 @ X1018))))=>(![X589:$i]:((((X589)!=(emptyset))=>?[X590:$i]:((in @ X590 @ X589))))=>(![X1013:$i, X1014:$i > $o, X1015:$i]:(((in @ X1015 @ X1013)=>((X1014 @ X1015)=>((dsetconstr @ X1013 @ X1014)!=(emptyset)))))=>(![X591:$i]:((?[X592:$i]:((in @ X592 @ X591))=>((X591)!=(emptyset))))=>(![X1011:$i, X1012:$i]:((in @ X1011 @ (setadjoin @ X1011 @ X1012)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X593:$i, X594:$i, X595:$i]:(((in @ X595 @ X594)=>(in @ X595 @ (setadjoin @ X593 @ X594))))=>(![X596:$i, X597:$i, X598:$i]:(((in @ X598 @ (setadjoin @ X596 @ X597))=>![X599:$o]:(((((X598)=(X596))=>(X599))=>(((in @ X598 @ X597)=>(X599))=>(X599))))))=>(![X600:$i, X601:$i, X602:$i]:(((in @ X602 @ (setadjoin @ X600 @ X601))=>(((X602)=(X600))|(in @ X602 @ X601))))=>(![X1010:$i]:(((dsetconstr @ X1010 @ (^[Z0/* 1 */:$i]:($true)))=(X1010)))=>(![X603:$i, X604:$i]:((![X605:$i]:(((in @ X605 @ X604)=>(in @ X605 @ X603)))=>(in @ X604 @ (powerset @ X603))))=>(![X606:$i]:((in @ emptyset @ (powerset @ X606)))=>(![X1009:$i]:((in @ emptyset @ (powerset @ X1009)))=>(![X1006:$i, X1007:$i, X1008:$i]:(((in @ X1007 @ (powerset @ X1006))=>((in @ X1008 @ X1007)=>(in @ X1008 @ X1006))))=>(![X1003:$i, X1004:$i, X1005:$i]:(((in @ X1004 @ X1005)=>((in @ X1005 @ X1003)=>(in @ X1004 @ (setunion @ X1003)))))=>(![X999:$i, X1000:$i]:(((in @ X1000 @ (setunion @ X999))=>![X1001:$o]:((![X1002:$i]:(((in @ X1000 @ X1002)=>((in @ X1002 @ X999)=>(X1001))))=>(X1001)))))=>(![X607:$i, X608:$i]:(((in @ X608 @ X607)=>(in @ X608 @ (powerset @ (setunion @ X607)))))=>(![X609:$i > $o]:((?[X610:$i]:(((X609 @ X610)&![X611:$i]:(((X609 @ X611)=>((X610)=(X611))))))=>?[X612:$i]:(![X613:$i]:(((X609 @ X613)<=>((X613)=(X612)))))))=>(![X614:$i]:((((X614)!=(emptyset))=>?[X615:$i]:(((in @ X615 @ X614)&$true))))=>(![X616:$i, X617:$i]:(((in @ X616 @ (setadjoin @ X617 @ emptyset))=>((X616)=(X617))))=>(![X997:$i, X998:$i]:((((X997)!=(X998))=>~(in @ X998 @ (setadjoin @ X997 @ emptyset))))=>(![X618:$i, X619:$i]:((((X618)=(X619))=>(in @ X618 @ (setadjoin @ X619 @ emptyset))))=>(![X620:$i, X621:$i]:(((in @ X620 @ (setadjoin @ X621 @ emptyset))=>(in @ X621 @ (setadjoin @ X620 @ emptyset))))=>(![X994:$i, X995:$i, X996:$i]:(((in @ X996 @ (setadjoin @ X994 @ (setadjoin @ X995 @ emptyset)))=>(((X996)=(X994))|((X996)=(X995)))))=>(![X992:$i, X993:$i]:((in @ X992 @ (setadjoin @ X992 @ (setadjoin @ X993 @ emptyset))))=>(![X622:$i, X623:$i]:((in @ X623 @ (setadjoin @ X622 @ (setadjoin @ X623 @ emptyset))))=>(![X624:$i, X625:$i > $o]:((?[X626:$i]:(((in @ X626 @ X624)&(X625 @ X626)))=>(((dsetconstr @ X624 @ X625)=(emptyset))=>~($true))))=>(![X627:$i > $o, X628:$i]:(((in @ X628 @ emptyset)=>(X627 @ X628)))=>(![X988:$i, X989:$i > $o]:((~(![X990:$i]:(((in @ X990 @ X988)=>(X989 @ X990))))=>?[X991:$i]:(((in @ X991 @ X988)&~((X989 @ X991))))))=>(![X629:$i, X630:$i > $o]:((![X631:$i]:(((in @ X631 @ X629)=>~((X630 @ X631))))=>~(?[X632:$i]:(((in @ X632 @ X629)&(X630 @ X632))))))=>(![X633:$i, X634:$i > $o]:((~(?[X635:$i]:(((in @ X635 @ X633)&(X634 @ X635))))=>![X636:$i]:(((in @ X636 @ X633)=>~((X634 @ X636))))))=>(![X984:$i, X985:$i > $o]:((?[X986:$i]:(((in @ X986 @ X984)&~((X985 @ X986))))=>~(![X987:$i]:(((in @ X987 @ X984)=>(X985 @ X987))))))=>(![X983:$o]:(((X983)=>(in @ emptyset @ (prop2set @ ((X983))))))=>((prop2set2propI)=>(![X979:$i, X980:$i > $o]:((~(?[X981:$i]:(((in @ 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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(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cartprodpairmemER]), subsetRefl]), emptysetE]), emptysetAx]), c_0_204]), notdallE]), notdexE]), setextsub]), prop2setI]), quantDeMorgan4]), powersetE1]), quantDeMorgan1]), upairsetIL]), upairsetE]), c_0_205]), notinsingleton]), setunionE]), c_0_206]), setunionI]), powersetE]), emptyInPowerset]), binunionIL]), c_0_207]), subsetE2]), emptyinunitempty]), setadjoinIL]), binunionIR]), c_0_208]), c_0_209]), emptyI]), binunionEcases]), notinemptyset]), singletonsubset]), prop2setE]), binunionE]), c_0_210]), c_0_211]), c_0_212]), binunionLsub]), c_0_213]), omegaIndAx]), binunionRsub]), omegaSAx]), setunionAx]), binintersectEL]), disjointsetsI1]), binintersectSubset1]), bs114d]), setminusER]), setminusELneg]), setminusIRneg]), symdiffIneg2]), secondinupair]), setukpairIL]), kpairiskpair]), kpairp]), c_0_214]), c_0_215]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), subsetTrans]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), c_0_216]), singletonsuniq]), setukpairinjL1]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR1]), setukpairinjR]), c_0_217]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), ksndpairEq]), setukpairinjR2]), upairequniteq]), setukpairinjR12]), setukpairinjR11]), c_0_218]), c_0_219]), c_0_220]), setunionsingleton]), ubforcartprodlem2]), singletoninpowerset]), setukpairIR]), symdiffIneg1]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), setminusILneg]), setminusERneg]), setminusSubset2]), setminusEL]), setminusI]), binintersectSubset4]), binintersectRsub]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectSubset5]), binintersectI]), upairset2IR]), powersetsubset]), inPowerset]), powersetI1]), subsetemptysetimpeq]), setadjoinSub2]), subset2powerset]), setadjoinSub]), notequalI2]), notequalI1]), notsubsetI]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset2]), powerset__Cong]), setadjoin__Cong]), c_0_221]), c_0_222]), c_0_223]), c_0_224]), eqimpsubset1]), subsetI1]), c_0_225]), c_0_226]), c_0_227]), omega__Cong]), setunion__Cong]), emptyset__Cong]), in__Cong]), inCongP]), quantDeMorgan3]), quantDeMorgan2]), vacuousDall]), c_0_228]), upairsetIR]), singletonsswitch]), eqinunit]), uniqinunit]), c_0_229]), c_0_230]), subPowSU]), emptyinPowerset]), powersetI]), setadjoinOr]), setadjoinE]), setadjoinIR]), c_0_231]), c_0_232]), noeltsimpempty]), setext]), c_0_233]), emptysetimpfalse]), c_0_234]), c_0_235]), wellorderingAx]), foundationAx]), omega0Ax]), powersetAx]), setadjoinAx]), setextAx])])]), c_0_236])). 1.08/0.66 thf(c_0_238, negated_conjecture, ![X1053:$i, X1054:$i, X1056:$i, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i, X1064:$i, X1066:$i, X1067:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1075:$i, X1076:$i > $i > $o, X1077:$i, X1079:$i, X1082:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i, X1089:$i, X1090:$i > $o, X1091:$i, X1093:$i, X1094:$i > $o, X1095:$i, X1096:$i, X1097:$i > $o, X1098:$i, X1099:$i, X1100:$i > $o, X1101:$i, X1102:$i > $o, X1103:$i, X1106:$i, X1107:$o, X1108:$i, X1109:$i, X1110:$o, X1111:$i, X1112:$i, X1113:$i > $o, X1114:$i, X1117:$i, X1118:$i, X1121:$i, X1123:$i, X1125:$i, X1126:$i > $o, X1127:$i, X1128:$i, X1130:$i, X1131:$i > $o, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$o, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$o, X1163:$i, X1164:$i, X1165:$i > $o, X1166:$i, X1169:$i, X1170:$i, X1171:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i > $o, X1190:$i, X1191:$i > $o, X1192:$i, X1193:$i, X1194:$i > $o, X1195:$i, X1197:$i, X1198:$i > $o, X1200:$i, X1201:$i, X1202:$i > $o, X1204:$i, X1205:$i, X1206:$i > $o, X1207:$i, X1209:$o, X1210:$i, X1211:$i > $o, X1213:$i, X1214:$i, X1215:$i > $o, X1216:$i, X1218:$i > $o, X1219:$i, X1222:$i, X1223:$i > $o, X1224:$i, X1228:$i, X1229:$i > $o, X1230:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i > $o, X1243:$i, X1245:$i, X1246:$i, X1247:$i > $o, X1248:$i > $o, X1251:$i, X1254:$i, X1255:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$i, X1264:$i, X1265:$i, X1266:$i, X1267:$i > $o, X1268:$i, X1270:$i, X1271:$i, X1272:$i > $o, X1273:$i > $o, X1276:$i, X1278:$i, X1280:$i, X1281:$i, X1282:$i > $o, X1283:$i > $o, X1286:$i, X1287:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i > $o, X1334:$i, X1335:$i > $o, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1345:$i, X1346:$i, X1347:$o, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$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:$i, X1415:$o, X1416:$i, X1417:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, 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, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$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:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i > $o, X1490:$i, X1492:$i, X1493:$i > $o, X1494:$i, X1496:$i, X1497:$i > $o, X1498:$i, X1501:$i, X1502:$i > $o, X1505:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i]:((((~(in @ (esk1_2 @ X1053 @ X1054) @ X1053)|~(in @ (esk1_2 @ X1053 @ X1054) @ X1054)|((X1053)=(X1054)))&((in @ (esk1_2 @ X1053 @ X1054) @ X1053)|(in @ (esk1_2 @ X1053 @ X1054) @ X1054)|((X1053)=(X1054))))&(~(in @ X1056 @ emptyset)&(((~(in @ X1059 @ (setadjoin @ X1057 @ X1058))|(((X1059)=(X1057))|(in @ X1059 @ X1058)))&((((X1059)!=(X1057))|(in @ X1059 @ (setadjoin @ X1057 @ X1058)))&(~(in @ X1059 @ X1058)|(in @ X1059 @ (setadjoin @ X1057 @ X1058)))))&(((~(in @ X1061 @ (powerset @ X1060))|(~(in @ X1062 @ X1061)|(in @ X1062 @ X1060)))&(((in @ (esk2_2 @ X1063 @ X1064) @ X1064)|(in @ X1064 @ (powerset @ X1063)))&(~(in @ (esk2_2 @ X1063 @ X1064) @ X1063)|(in @ X1064 @ (powerset @ X1063)))))&(((((in @ X1067 @ (esk3_2 @ X1066 @ X1067))|~(in @ X1067 @ (setunion @ X1066)))&((in @ (esk3_2 @ X1066 @ X1067) @ X1066)|~(in @ X1067 @ (setunion @ X1066))))&(~(in @ X1070 @ X1071)|~(in @ X1071 @ X1069)|(in @ X1070 @ (setunion @ X1069))))&((in @ emptyset @ omega)&((~(in @ X1072 @ omega)|(in @ (setadjoin @ X1072 @ X1072) @ omega))&(((((in @ (esk4_1 @ X1073) @ omega)|~(in @ emptyset @ X1073)|(~(in @ X1075 @ omega)|(in @ X1075 @ X1073)))&((in @ (esk4_1 @ X1073) @ X1073)|~(in @ emptyset @ X1073)|(~(in @ X1075 @ omega)|(in @ X1075 @ X1073))))&(~(in @ (setadjoin @ (esk4_1 @ X1073) @ (esk4_1 @ X1073)) @ X1073)|~(in @ emptyset @ X1073)|(~(in @ X1075 @ omega)|(in @ X1075 @ X1073))))&((((((in @ (esk8_3 @ X1076 @ X1077 @ X1082) @ X1077)|~(in @ X1082 @ (esk7_2 @ X1076 @ X1077))|(in @ (esk5_2 @ X1076 @ X1077) @ X1077))&((X1076 @ (esk8_3 @ X1076 @ X1077 @ X1082) @ X1082)|~(in @ X1082 @ (esk7_2 @ X1076 @ X1077))|(in @ (esk5_2 @ X1076 @ X1077) @ X1077)))&(~(in @ X1085 @ X1077)|~(X1076 @ X1085 @ X1084)|(in @ X1084 @ (esk7_2 @ X1076 @ X1077))|(in @ (esk5_2 @ X1076 @ X1077) @ X1077)))&(((((in @ (esk8_3 @ X1076 @ X1077 @ X1082) @ X1077)|~(in @ X1082 @ (esk7_2 @ X1076 @ X1077))|((X1076 @ (esk5_2 @ X1076 @ X1077) @ (esk6_3 @ X1076 @ X1077 @ X1079))|~(X1076 @ (esk5_2 @ X1076 @ X1077) @ X1079)))&((X1076 @ (esk8_3 @ X1076 @ X1077 @ X1082) @ X1082)|~(in @ X1082 @ (esk7_2 @ X1076 @ X1077))|((X1076 @ (esk5_2 @ X1076 @ X1077) @ (esk6_3 @ X1076 @ X1077 @ X1079))|~(X1076 @ (esk5_2 @ X1076 @ X1077) @ X1079))))&(~(in @ X1085 @ X1077)|~(X1076 @ X1085 @ X1084)|(in @ X1084 @ (esk7_2 @ X1076 @ X1077))|((X1076 @ (esk5_2 @ X1076 @ X1077) @ (esk6_3 @ X1076 @ X1077 @ X1079))|~(X1076 @ (esk5_2 @ X1076 @ X1077) @ X1079))))&((((in @ (esk8_3 @ X1076 @ X1077 @ X1082) @ X1077)|~(in @ X1082 @ (esk7_2 @ X1076 @ X1077))|(((X1079)!=(esk6_3 @ X1076 @ X1077 @ X1079))|~(X1076 @ (esk5_2 @ X1076 @ X1077) @ X1079)))&((X1076 @ (esk8_3 @ X1076 @ X1077 @ X1082) @ X1082)|~(in @ X1082 @ (esk7_2 @ 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emptyset))))&((X1493 @ (esk61_2 @ X1492 @ X1493))|(~(in @ X1494 @ (dsetconstr @ X1492 @ X1493))|((dsetconstr @ X1492 @ X1493)!=(setadjoin @ X1494 @ emptyset)))))&(((((in @ (esk63_3 @ X1496 @ X1497 @ X1498) @ (dsetconstr @ X1496 @ X1497))|(in @ (esk62_3 @ X1496 @ X1497 @ X1498) @ X1496)|~(X1497 @ X1498)|~(in @ X1498 @ X1496))&(((dsetconstr @ X1496 @ X1497)=(setadjoin @ (esk63_3 @ X1496 @ X1497 @ X1498) @ emptyset))|(in @ (esk62_3 @ X1496 @ X1497 @ X1498) @ X1496)|~(X1497 @ X1498)|~(in @ X1498 @ X1496)))&((((in @ (esk63_3 @ X1496 @ X1497 @ X1498) @ (dsetconstr @ X1496 @ X1497))|(X1497 @ (esk62_3 @ X1496 @ X1497 @ X1498))|~(X1497 @ X1498)|~(in @ X1498 @ X1496))&(((dsetconstr @ X1496 @ X1497)=(setadjoin @ (esk63_3 @ X1496 @ X1497 @ X1498) @ emptyset))|(X1497 @ (esk62_3 @ X1496 @ X1497 @ X1498))|~(X1497 @ X1498)|~(in @ X1498 @ X1496)))&(((in @ (esk63_3 @ X1496 @ X1497 @ X1498) @ (dsetconstr @ X1496 @ X1497))|((esk62_3 @ X1496 @ X1497 @ X1498)!=(X1498))|~(X1497 @ X1498)|~(in @ X1498 @ X1496))&(((dsetconstr @ X1496 @ X1497)=(setadjoin @ (esk63_3 @ X1496 @ X1497 @ X1498) @ emptyset))|((esk62_3 @ X1496 @ X1497 @ X1498)!=(X1498))|~(X1497 @ X1498)|~(in @ X1498 @ X1496)))))&(((((in @ (esk66_2 @ X1501 @ X1502) @ (dsetconstr @ X1501 @ X1502))|(~(in @ X1505 @ X1501)|~(X1502 @ X1505))|(in @ (esk64_2 @ X1501 @ X1502) @ X1501))&(((dsetconstr @ X1501 @ X1502)=(setadjoin @ (esk66_2 @ X1501 @ X1502) @ emptyset))|(~(in @ X1505 @ X1501)|~(X1502 @ X1505))|(in @ (esk64_2 @ X1501 @ X1502) @ X1501)))&((((in @ (esk66_2 @ X1501 @ X1502) @ (dsetconstr @ X1501 @ X1502))|(~(in @ X1505 @ X1501)|~(X1502 @ X1505))|(in @ (esk65_2 @ X1501 @ X1502) @ X1501))&(((dsetconstr @ X1501 @ X1502)=(setadjoin @ (esk66_2 @ X1501 @ X1502) @ emptyset))|(~(in @ X1505 @ X1501)|~(X1502 @ X1505))|(in @ (esk65_2 @ X1501 @ X1502) @ X1501)))&((((in @ (esk66_2 @ X1501 @ X1502) @ (dsetconstr @ X1501 @ X1502))|(~(in @ X1505 @ X1501)|~(X1502 @ X1505))|(X1502 @ (esk64_2 @ X1501 @ X1502)))&(((dsetconstr @ X1501 @ X1502)=(setadjoin @ (esk66_2 @ X1501 @ X1502) @ emptyset))|(~(in @ X1505 @ X1501)|~(X1502 @ X1505))|(X1502 @ (esk64_2 @ X1501 @ X1502))))&((((in @ (esk66_2 @ X1501 @ X1502) @ (dsetconstr @ X1501 @ X1502))|(~(in @ X1505 @ X1501)|~(X1502 @ X1505))|(X1502 @ (esk65_2 @ X1501 @ X1502)))&(((dsetconstr @ X1501 @ X1502)=(setadjoin @ (esk66_2 @ X1501 @ X1502) @ emptyset))|(~(in @ X1505 @ X1501)|~(X1502 @ X1505))|(X1502 @ (esk65_2 @ X1501 @ X1502))))&(((in @ (esk66_2 @ X1501 @ X1502) @ (dsetconstr @ X1501 @ X1502))|(~(in @ X1505 @ X1501)|~(X1502 @ X1505))|((esk64_2 @ X1501 @ X1502)!=(esk65_2 @ X1501 @ X1502)))&(((dsetconstr @ X1501 @ X1502)=(setadjoin @ (esk66_2 @ X1501 @ X1502) @ emptyset))|(~(in @ X1505 @ X1501)|~(X1502 @ X1505))|((esk64_2 @ X1501 @ X1502)!=(esk65_2 @ X1501 @ X1502))))))))&((((setadjoin @ X1507 @ emptyset)!=(setadjoin @ X1508 @ emptyset))|((X1507)=(X1508)))&((~(in @ (setadjoin @ X1511 @ emptyset) @ (setadjoin @ (setadjoin @ X1509 @ emptyset) @ (setadjoin @ (setadjoin @ X1509 @ (setadjoin @ X1510 @ emptyset)) @ emptyset)))|((X1509)=(X1511)))&((((in @ (esk67_1 @ X1512) @ (dsetconstr @ (setunion @ X1512) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1512)))))|~(iskpair @ X1512))&(((dsetconstr @ (setunion @ X1512) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1512))))=(setadjoin @ (esk67_1 @ X1512) @ emptyset))|~(iskpair @ X1512)))&((~(in @ X1515 @ X1514)|((X1514)!=(setadjoin @ X1515 @ emptyset))|(in @ (setunion @ X1514) @ X1514))&(((kfst @ (kpair @ X1516 @ X1517))=(X1516))&((~(in @ X1520 @ (cartprod @ X1518 @ X1519))|(in @ (kfst @ X1520) @ X1518))&((((setadjoin @ (setadjoin @ X1521 @ emptyset) @ (setadjoin @ (setadjoin @ X1521 @ (setadjoin @ X1522 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1523 @ emptyset) @ (setadjoin @ (setadjoin @ X1523 @ (setadjoin @ X1524 @ emptyset)) @ emptyset)))|((X1521)=(X1523)))&((((kpair @ X1525 @ X1526)!=(kpair @ X1527 @ X1528))|((X1525)=(X1527)))&((((X1529)!=(X1530))|((setadjoin @ X1529 @ (setadjoin @ X1530 @ emptyset))=(setadjoin @ X1529 @ emptyset)))&((((X1531)!=(X1532))|((setadjoin @ (setadjoin @ X1531 @ emptyset) @ (setadjoin @ (setadjoin @ X1531 @ (setadjoin @ X1532 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1531 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1533 @ emptyset) @ (setadjoin @ (setadjoin @ X1533 @ (setadjoin @ X1534 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1535 @ emptyset) @ (setadjoin @ (setadjoin @ X1535 @ (setadjoin @ X1536 @ emptyset)) @ emptyset)))|(((X1535)!=(X1536))|((X1534)=(X1536))))&((((setadjoin @ X1537 @ (setadjoin @ X1538 @ emptyset))!=(setadjoin @ X1539 @ emptyset))|((X1537)=(X1538)))&((((setadjoin @ (setadjoin @ X1540 @ emptyset) @ (setadjoin @ (setadjoin @ X1540 @ (setadjoin @ X1541 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1542 @ emptyset) @ (setadjoin @ (setadjoin @ X1542 @ (setadjoin @ X1543 @ emptyset)) @ emptyset)))|((X1541)=(X1543)))&((((kpair @ X1544 @ X1545)!=(kpair @ X1546 @ X1547))|((X1545)=(X1547)))&((((in @ (esk68_1 @ X1548) @ (dsetconstr @ (setunion @ X1548) @ (^[Z0/* 3 */:$i]:(((X1548)=(kpair @ (kfst @ X1548) @ Z0))))))|~(iskpair @ X1548))&(((dsetconstr @ (setunion @ X1548) @ (^[Z0/* 3 */:$i]:(((X1548)=(kpair @ (kfst @ X1548) @ Z0)))))=(setadjoin @ (esk68_1 @ X1548) @ emptyset))|~(iskpair @ X1548)))&(((ksnd @ (kpair @ X1550 @ X1551))=(X1551))&((~(iskpair @ X1552)|((kpair @ (kfst @ X1552) @ (ksnd @ X1552))=(X1552)))&((~(in @ X1555 @ (cartprod @ X1553 @ X1554))|(in @ (ksnd @ X1555) @ X1554))&((~(in @ (kpair @ X1558 @ X1559) @ (cartprod @ X1556 @ X1557))|(in @ X1558 @ X1556))&((in @ (kpair @ esk71_0 @ esk72_0) @ (cartprod @ esk69_0 @ esk70_0))&~(in @ esk72_0 @ esk70_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_237])])])])])])])). 1.08/0.66 thf(c_0_239, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (ksnd @ X2) @ X4)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_238])). 1.08/0.66 thf(c_0_240, negated_conjecture, (in @ (kpair @ esk71_0 @ esk72_0) @ (cartprod @ esk69_0 @ esk70_0)), inference(split_conjunct,[status(thm)],[c_0_238])). 1.08/0.66 thf(c_0_241, negated_conjecture, ![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3))), inference(split_conjunct,[status(thm)],[c_0_238])). 1.08/0.66 thf(c_0_242, negated_conjecture, ~((in @ esk72_0 @ esk70_0)), inference(split_conjunct,[status(thm)],[c_0_238])). 1.08/0.66 thf(c_0_243, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239, c_0_240]), c_0_241]), c_0_242]), ['proof']). 1.08/0.66 # SZS output end CNFRefutation 1.08/0.66 # Parsed axioms : 388 1.08/0.66 # Removed by relevancy pruning/SinE : 208 1.08/0.66 # Initial clauses : 329 1.08/0.66 # Removed in clause preprocessing : 24 1.08/0.66 # Initial clauses in saturation : 305 1.08/0.66 # Processed clauses : 436 1.08/0.66 # ...of these trivial : 7 1.08/0.66 # ...subsumed : 41 1.08/0.66 # ...remaining for further processing : 388 1.08/0.66 # Other redundant clauses eliminated : 25 1.08/0.66 # Clauses deleted for lack of memory : 0 1.08/0.66 # Backward-subsumed : 0 1.08/0.66 # Backward-rewritten : 3 1.08/0.66 # Generated clauses : 376 1.08/0.66 # ...of the previous two non-redundant : 295 1.08/0.66 # ...aggressively subsumed : 0 1.08/0.66 # Contextual simplify-reflections : 0 1.08/0.66 # Paramodulations : 348 1.08/0.66 # Factorizations : 0 1.08/0.66 # NegExts : 0 1.08/0.66 # Equation resolutions : 28 1.08/0.66 # Disequality decompositions : 0 1.08/0.66 # Total rewrite steps : 105 1.08/0.66 # ...of those cached : 68 1.08/0.66 # Propositional unsat checks : 0 1.08/0.66 # Propositional check models : 0 1.08/0.66 # Propositional check unsatisfiable : 0 1.08/0.66 # Propositional clauses : 0 1.08/0.66 # Propositional clauses after purity: 0 1.08/0.66 # Propositional unsat core size : 0 1.08/0.66 # Propositional preprocessing time : 0.000 1.08/0.66 # Propositional encoding time : 0.000 1.08/0.66 # Propositional solver time : 0.000 1.08/0.66 # Success case prop preproc time : 0.000 1.08/0.66 # Success case prop encoding time : 0.000 1.08/0.66 # Success case prop solver time : 0.000 1.08/0.66 # Current number of processed clauses : 104 1.08/0.66 # Positive orientable unit clauses : 42 1.08/0.66 # Positive unorientable unit clauses: 0 1.08/0.66 # Negative unit clauses : 2 1.08/0.66 # Non-unit-clauses : 60 1.08/0.66 # Current number of unprocessed clauses: 413 1.08/0.66 # ...number of literals in the above : 1175 1.08/0.66 # Current number of archived formulas : 0 1.08/0.66 # Current number of archived clauses : 268 1.08/0.66 # Clause-clause subsumption calls (NU) : 11681 1.08/0.66 # Rec. Clause-clause subsumption calls : 5137 1.08/0.66 # Non-unit clause-clause subsumptions : 28 1.08/0.66 # Unit Clause-clause subsumption calls : 59 1.08/0.66 # Rewrite failures with RHS unbound : 0 1.08/0.66 # BW rewrite match attempts : 16 1.08/0.66 # BW rewrite match successes : 3 1.08/0.66 # Condensation attempts : 436 1.08/0.66 # Condensation successes : 4 1.08/0.66 # Termbank termtop insertions : 52578 1.08/0.66 # Search garbage collected termcells : 17072 1.08/0.66 1.08/0.66 # ------------------------------------------------- 1.08/0.66 # User time : 0.083 s 1.08/0.66 # System time : 0.008 s 1.08/0.66 # Total time : 0.091 s 1.08/0.66 # Maximum resident set size: 6044 pages 1.08/0.66 1.08/0.66 # ------------------------------------------------- 1.08/0.66 # User time : 0.090 s 1.08/0.66 # System time : 0.013 s 1.08/0.66 # Total time : 0.103 s 1.08/0.66 # Maximum resident set size: 2200 pages 1.08/0.66 % E---3.1 exiting 1.08/0.66 % E exiting 1.08/0.66 EOF