0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.10/0.37 % Computer : n002.cluster.edu 0.10/0.37 % Model : x86_64 x86_64 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.37 % Memory : 8046.5625MB 0.10/0.37 % OS : Linux 6.8.0-71-generic 0.10/0.37 % CPULimit : 1440 0.10/0.37 % WCLimit : 180 0.10/0.37 % DateTime : Mon Jul 27 14:34:43 UTC 2026 0.10/0.37 % CPUTime : 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.10/0.41 Running higher-order theorem proving 0.19/0.46 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.TXhKssAo14/E---3.1_3430301.p 554.07/73.77 % Version: 3.5.1-ho 554.07/73.77 % Preprocessing class: HSLMSLSSLLLCHFA. 554.07/73.77 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 554.07/73.77 % Starting ehoh_best5 with 180s (1) cores 554.07/73.77 % Starting almost_fo_3_lam with 180s (1) cores 554.07/73.77 % Starting new_bool_5 with 180s (1) cores 554.07/73.77 % Starting pre_casc_3 with 180s (1) cores 554.07/73.77 % Starting ho_unfolding_8 with 180s (1) cores 554.07/73.77 % Starting new_ho_10_cnf2 with 180s (1) cores 554.07/73.77 % Starting new_bool_3 with 180s (1) cores 554.07/73.77 % Starting new_ho_5 with 180s (1) cores 554.07/73.77 % new_bool_5 with pid 3430316 completed with status 0 554.07/73.77 % Result found by new_bool_5 554.07/73.77 % Preprocessing class: HSLMSLSSLLLCHFA. 554.07/73.77 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 554.07/73.77 % Starting ehoh_best5 with 180s (1) cores 554.07/73.77 % Starting almost_fo_3_lam with 180s (1) cores 554.07/73.77 % Starting new_bool_5 with 180s (1) cores 554.07/73.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)) 554.07/73.77 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 554.07/73.77 % Search class: HGHSM-FSLM32-MHFMMSBN 554.07/73.77 % Scheduled 11 strats onto 1 cores with 180 seconds (180 total) 554.07/73.77 % Starting SubtermCWHack with 17s (1) cores 554.07/73.77 % SubtermCWHack with pid 3430322 completed with status 8 554.07/73.77 % Starting new_bool_5 with 19s (1) cores 554.07/73.77 % new_bool_5 with pid 3430331 completed with status 8 554.07/73.77 % Starting new_bool_6 with 17s (1) cores 554.07/73.77 % new_bool_6 with pid 3430339 completed with status 8 554.07/73.77 % Starting additional_ho_3 with 17s (1) cores 554.07/73.77 % additional_ho_3 with pid 3430343 completed with status 8 554.07/73.77 % Starting pre_casc_3 with 17s (1) cores 554.07/73.77 % pre_casc_3 with pid 3430352 completed with status 0 554.07/73.77 % Result found by pre_casc_3 554.07/73.77 % Preprocessing class: HSLMSLSSLLLCHFA. 554.07/73.77 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 554.07/73.77 % Starting ehoh_best5 with 180s (1) cores 554.07/73.77 % Starting almost_fo_3_lam with 180s (1) cores 554.07/73.77 % Starting new_bool_5 with 180s (1) cores 554.07/73.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)) 554.07/73.77 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 554.07/73.77 % Search class: HGHSM-FSLM32-MHFMMSBN 554.07/73.77 % Scheduled 11 strats onto 1 cores with 180 seconds (180 total) 554.07/73.77 % Starting SubtermCWHack with 17s (1) cores 554.07/73.77 % SubtermCWHack with pid 3430322 completed with status 8 554.07/73.77 % Starting new_bool_5 with 19s (1) cores 554.07/73.77 % new_bool_5 with pid 3430331 completed with status 8 554.07/73.77 % Starting new_bool_6 with 17s (1) cores 554.07/73.77 % new_bool_6 with pid 3430339 completed with status 8 554.07/73.77 % Starting additional_ho_3 with 17s (1) cores 554.07/73.77 % additional_ho_3 with pid 3430343 completed with status 8 554.07/73.77 % Starting pre_casc_3 with 17s (1) cores 554.07/73.77 % Preprocessing time : 0.009 s 554.07/73.77 % Presaturation interreduction done 554.07/73.77 554.07/73.77 % Proof found! 554.07/73.77 % SZS status Theorem 554.07/73.77 % SZS output start CNFRefutation 554.07/73.77 thf(decl_23, type, in: $i > $i > $o). 554.07/73.77 thf(decl_24, type, exu: ($i > $o) > $o). 554.07/73.77 thf(decl_25, type, setextAx: $o). 554.07/73.77 thf(decl_26, type, emptyset: $i). 554.07/73.77 thf(decl_27, type, emptysetAx: $o). 554.07/73.77 thf(decl_28, type, setadjoin: $i > $i > $i). 554.07/73.77 thf(decl_29, type, setadjoinAx: $o). 554.07/73.77 thf(decl_30, type, powerset: $i > $i). 554.07/73.77 thf(decl_31, type, powersetAx: $o). 554.07/73.77 thf(decl_32, type, setunion: $i > $i). 554.07/73.77 thf(decl_33, type, setunionAx: $o). 554.07/73.77 thf(decl_34, type, omega: $i). 554.07/73.77 thf(decl_35, type, omega0Ax: $o). 554.07/73.77 thf(decl_36, type, omegaSAx: $o). 554.07/73.77 thf(decl_37, type, omegaIndAx: $o). 554.07/73.77 thf(decl_38, type, replAx: $o). 554.07/73.77 thf(decl_39, type, foundationAx: $o). 554.07/73.77 thf(decl_40, type, wellorderingAx: $o). 554.07/73.77 thf(decl_41, type, descr: ($i > $o) > $i). 554.07/73.77 thf(decl_42, type, descrp: $o). 554.07/73.77 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 554.07/73.77 thf(decl_44, type, dsetconstrI: $o). 554.07/73.77 thf(decl_45, type, dsetconstrEL: $o). 554.07/73.77 thf(decl_46, type, dsetconstrER: $o). 554.07/73.77 thf(decl_47, type, exuE1: $o). 554.07/73.77 thf(decl_48, type, prop2set: $o > $i). 554.07/73.77 thf(decl_49, type, prop2setE: $o). 554.07/73.77 thf(decl_50, type, emptysetE: $o). 554.07/73.77 thf(decl_51, type, emptysetimpfalse: $o). 554.07/73.77 thf(decl_52, type, notinemptyset: $o). 554.07/73.77 thf(decl_53, type, exuE3e: $o). 554.07/73.77 thf(decl_54, type, setext: $o). 554.07/73.77 thf(decl_55, type, emptyI: $o). 554.07/73.77 thf(decl_56, type, noeltsimpempty: $o). 554.07/73.77 thf(decl_57, type, setbeta: $o). 554.07/73.77 thf(decl_58, type, nonempty: $i > $o). 554.07/73.77 thf(decl_59, type, nonemptyE1: $o). 554.07/73.77 thf(decl_60, type, nonemptyI: $o). 554.07/73.77 thf(decl_61, type, nonemptyI1: $o). 554.07/73.77 thf(decl_62, type, setadjoinIL: $o). 554.07/73.77 thf(decl_63, type, emptyinunitempty: $o). 554.07/73.77 thf(decl_64, type, setadjoinIR: $o). 554.07/73.77 thf(decl_65, type, setadjoinE: $o). 554.07/73.77 thf(decl_66, type, setadjoinOr: $o). 554.07/73.77 thf(decl_67, type, setoftrueEq: $o). 554.07/73.77 thf(decl_68, type, powersetI: $o). 554.07/73.77 thf(decl_69, type, emptyinPowerset: $o). 554.07/73.77 thf(decl_70, type, emptyInPowerset: $o). 554.07/73.77 thf(decl_71, type, powersetE: $o). 554.07/73.77 thf(decl_72, type, setunionI: $o). 554.07/73.77 thf(decl_73, type, setunionE: $o). 554.07/73.77 thf(decl_74, type, subPowSU: $o). 554.07/73.77 thf(decl_75, type, exuE2: $o). 554.07/73.77 thf(decl_76, type, nonemptyImpWitness: $o). 554.07/73.77 thf(decl_77, type, uniqinunit: $o). 554.07/73.77 thf(decl_78, type, notinsingleton: $o). 554.07/73.77 thf(decl_79, type, eqinunit: $o). 554.07/73.77 thf(decl_80, type, singletonsswitch: $o). 554.07/73.77 thf(decl_81, type, upairsetE: $o). 554.07/73.77 thf(decl_82, type, upairsetIL: $o). 554.07/73.77 thf(decl_83, type, upairsetIR: $o). 554.07/73.77 thf(decl_84, type, emptyE1: $o). 554.07/73.77 thf(decl_85, type, vacuousDall: $o). 554.07/73.77 thf(decl_86, type, quantDeMorgan1: $o). 554.07/73.77 thf(decl_87, type, quantDeMorgan2: $o). 554.07/73.77 thf(decl_88, type, quantDeMorgan3: $o). 554.07/73.77 thf(decl_89, type, quantDeMorgan4: $o). 554.07/73.77 thf(decl_90, type, prop2setI: $o). 554.07/73.77 thf(decl_92, type, prop2set2propI: $o). 554.07/73.77 thf(decl_93, type, notdexE: $o). 554.07/73.77 thf(decl_94, type, notdallE: $o). 554.07/73.77 thf(decl_95, type, exuI1: $o). 554.07/73.77 thf(decl_96, type, exuI3: $o). 554.07/73.77 thf(decl_97, type, exuI2: $o). 554.07/73.77 thf(decl_98, type, inCongP: $o). 554.07/73.77 thf(decl_99, type, in__Cong: $o). 554.07/73.77 thf(decl_100, type, exuE3u: $o). 554.07/73.77 thf(decl_101, type, exu__Cong: $o). 554.07/73.77 thf(decl_102, type, emptyset__Cong: $o). 554.07/73.77 thf(decl_103, type, setadjoin__Cong: $o). 554.07/73.77 thf(decl_104, type, powerset__Cong: $o). 554.07/73.77 thf(decl_105, type, setunion__Cong: $o). 554.07/73.77 thf(decl_106, type, omega__Cong: $o). 554.07/73.77 thf(decl_107, type, exuEu: $o). 554.07/73.77 thf(decl_108, type, descr__Cong: $o). 554.07/73.77 thf(decl_109, type, dsetconstr__Cong: $o). 554.07/73.77 thf(decl_110, type, subset: $i > $i > $o). 554.07/73.77 thf(decl_113, type, subsetI1: $o). 554.07/73.77 thf(decl_114, type, eqimpsubset2: $o). 554.07/73.77 thf(decl_115, type, eqimpsubset1: $o). 554.07/73.77 thf(decl_116, type, subsetI2: $o). 554.07/73.77 thf(decl_117, type, emptysetsubset: $o). 554.07/73.77 thf(decl_118, type, subsetE: $o). 554.07/73.77 thf(decl_119, type, subsetE2: $o). 554.07/73.77 thf(decl_120, type, notsubsetI: $o). 554.07/73.77 thf(decl_121, type, notequalI1: $o). 554.07/73.77 thf(decl_122, type, notequalI2: $o). 554.07/73.77 thf(decl_123, type, subsetRefl: $o). 554.07/73.77 thf(decl_124, type, subsetTrans: $o). 554.07/73.77 thf(decl_125, type, setadjoinSub: $o). 554.07/73.77 thf(decl_126, type, setadjoinSub2: $o). 554.07/73.77 thf(decl_127, type, subset2powerset: $o). 554.07/73.77 thf(decl_128, type, setextsub: $o). 554.07/73.77 thf(decl_129, type, subsetemptysetimpeq: $o). 554.07/73.77 thf(decl_130, type, powersetI1: $o). 554.07/73.77 thf(decl_131, type, powersetE1: $o). 554.07/73.77 thf(decl_132, type, inPowerset: $o). 554.07/73.77 thf(decl_133, type, powersetsubset: $o). 554.07/73.77 thf(decl_134, type, sepInPowerset: $o). 554.07/73.77 thf(decl_135, type, sepSubset: $o). 554.07/73.77 thf(decl_136, type, binunion: $i > $i > $i). 554.07/73.77 thf(decl_137, type, binunionIL: $o). 554.07/73.77 thf(decl_138, type, upairset2IR: $o). 554.07/73.77 thf(decl_139, type, binunionIR: $o). 554.07/73.77 thf(decl_140, type, binunionEcases: $o). 554.07/73.77 thf(decl_141, type, binunionE: $o). 554.07/73.77 thf(decl_142, type, binunionLsub: $o). 554.07/73.77 thf(decl_143, type, binunionRsub: $o). 554.07/73.77 thf(decl_144, type, binintersect: $i > $i > $i). 554.07/73.77 thf(decl_145, type, binintersectI: $o). 554.07/73.77 thf(decl_146, type, binintersectSubset5: $o). 554.07/73.77 thf(decl_147, type, binintersectEL: $o). 554.07/73.77 thf(decl_148, type, binintersectLsub: $o). 554.07/73.77 thf(decl_149, type, binintersectSubset2: $o). 554.07/73.77 thf(decl_150, type, binintersectSubset3: $o). 554.07/73.77 thf(decl_151, type, binintersectER: $o). 554.07/73.77 thf(decl_152, type, disjointsetsI1: $o). 554.07/73.77 thf(decl_153, type, binintersectRsub: $o). 554.07/73.77 thf(decl_154, type, binintersectSubset4: $o). 554.07/73.77 thf(decl_155, type, binintersectSubset1: $o). 554.07/73.77 thf(decl_156, type, bs114d: $o). 554.07/73.77 thf(decl_158, type, setminus: $i > $i > $i). 554.07/73.77 thf(decl_159, type, setminusI: $o). 554.07/73.77 thf(decl_160, type, setminusEL: $o). 554.07/73.77 thf(decl_161, type, setminusER: $o). 554.07/73.77 thf(decl_162, type, setminusSubset2: $o). 554.07/73.77 thf(decl_163, type, setminusERneg: $o). 554.07/73.77 thf(decl_164, type, setminusELneg: $o). 554.07/73.77 thf(decl_165, type, setminusILneg: $o). 554.07/73.77 thf(decl_166, type, setminusIRneg: $o). 554.07/73.77 thf(decl_167, type, setminusLsub: $o). 554.07/73.77 thf(decl_168, type, setminusSubset1: $o). 554.07/73.77 thf(decl_169, type, symdiff: $i > $i > $i). 554.07/73.77 thf(decl_170, type, symdiffE: $o). 554.07/73.77 thf(decl_171, type, symdiffI1: $o). 554.07/73.77 thf(decl_172, type, symdiffI2: $o). 554.07/73.77 thf(decl_173, type, symdiffIneg1: $o). 554.07/73.77 thf(decl_174, type, symdiffIneg2: $o). 554.07/73.77 thf(decl_175, type, iskpair: $i > $o). 554.07/73.77 thf(decl_176, type, secondinupair: $o). 554.07/73.77 thf(decl_177, type, setukpairIL: $o). 554.07/73.77 thf(decl_178, type, setukpairIR: $o). 554.07/73.77 thf(decl_179, type, kpairiskpair: $o). 554.07/73.77 thf(decl_180, type, kpair: $i > $i > $i). 554.07/73.77 thf(decl_181, type, kpairp: $o). 554.07/73.77 thf(decl_182, type, cartprod: $i > $i > $i). 554.07/73.77 thf(decl_183, type, singletonsubset: $o). 554.07/73.77 thf(decl_184, type, singletoninpowerset: $o). 554.07/73.77 thf(decl_185, type, singletoninpowunion: $o). 554.07/73.77 thf(decl_186, type, upairset2E: $o). 554.07/73.77 thf(decl_187, type, upairsubunion: $o). 554.07/73.77 thf(decl_188, type, upairinpowunion: $o). 554.07/73.77 thf(decl_189, type, ubforcartprodlem1: $o). 554.07/73.77 thf(decl_190, type, ubforcartprodlem2: $o). 554.07/73.77 thf(decl_191, type, ubforcartprodlem3: $o). 554.07/73.77 thf(decl_192, type, cartprodpairin: $o). 554.07/73.77 thf(decl_193, type, cartprodmempair1: $o). 554.07/73.77 thf(decl_194, type, cartprodmempair: $o). 554.07/73.77 thf(decl_195, type, setunionE2: $o). 554.07/73.77 thf(decl_196, type, setunionsingleton1: $o). 554.07/73.77 thf(decl_197, type, setunionsingleton2: $o). 554.07/73.77 thf(decl_198, type, setunionsingleton: $o). 554.07/73.77 thf(decl_199, type, singleton: $i > $o). 554.07/73.77 thf(decl_200, type, singletonprop: $o). 554.07/73.77 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 554.07/73.77 thf(decl_202, type, ex1E1: $o). 554.07/73.77 thf(decl_203, type, ex1I: $o). 554.07/73.77 thf(decl_204, type, ex1I2: $o). 554.07/73.77 thf(decl_205, type, singletonsuniq: $o). 554.07/73.77 thf(decl_210, type, setukpairinjL1: $o). 554.07/73.77 thf(decl_211, type, kfstsingleton: $o). 554.07/73.77 thf(decl_212, type, theprop: $o). 554.07/73.77 thf(decl_213, type, kfst: $i > $i). 554.07/73.77 thf(decl_214, type, kfstpairEq: $o). 554.07/73.77 thf(decl_215, type, cartprodfstin: $o). 554.07/73.77 thf(decl_216, type, setukpairinjL2: $o). 554.07/73.77 thf(decl_217, type, setukpairinjL: $o). 554.07/73.77 thf(decl_218, type, setukpairinjR11: $o). 554.07/73.77 thf(decl_219, type, setukpairinjR12: $o). 554.07/73.77 thf(decl_220, type, setukpairinjR1: $o). 554.07/73.77 thf(decl_221, type, upairequniteq: $o). 554.07/73.77 thf(decl_222, type, setukpairinjR2: $o). 554.07/73.77 thf(decl_223, type, setukpairinjR: $o). 554.07/73.77 thf(decl_224, type, ksndsingleton: $o). 554.07/73.77 thf(decl_225, type, ksnd: $i > $i). 554.07/73.77 thf(decl_226, type, ksndpairEq: $o). 554.07/73.77 thf(decl_227, type, kpairsurjEq: $o). 554.07/73.77 thf(decl_228, type, cartprodsndin: $o). 554.07/73.77 thf(decl_229, type, cartprodpairmemEL: $o). 554.07/73.77 thf(decl_230, type, cartprodpairmemER: $o). 554.07/73.77 thf(decl_231, type, cartprodmempaircEq: $o). 554.07/73.77 thf(decl_232, type, cartprodfstpairEq: $o). 554.07/73.77 thf(decl_233, type, cartprodsndpairEq: $o). 554.07/73.77 thf(decl_234, type, cartprodpairsurjEq: $o). 554.07/73.77 thf(decl_235, type, breln: $i > $i > $i > $o). 554.07/73.77 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 554.07/73.77 thf(decl_237, type, dpsetconstrI: $o). 554.07/73.77 thf(decl_238, type, dpsetconstrSub: $o). 554.07/73.77 thf(decl_239, type, setOfPairsIsBReln: $o). 554.07/73.77 thf(decl_240, type, dpsetconstrERa: $o). 554.07/73.77 thf(decl_241, type, dpsetconstrEL1: $o). 554.07/73.77 thf(decl_242, type, dpsetconstrEL2: $o). 554.07/73.77 thf(decl_243, type, dpsetconstrER: $o). 554.07/73.77 thf(decl_244, type, func: $i > $i > $i > $o). 554.07/73.77 thf(decl_245, type, funcSet: $i > $i > $i). 554.07/73.77 thf(decl_246, type, funcImageSingleton: $o). 554.07/73.77 thf(decl_247, type, apProp: $o). 554.07/73.77 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 554.07/73.77 thf(decl_249, type, app: $o). 554.07/73.77 thf(decl_250, type, infuncsetfunc: $o). 554.07/73.77 thf(decl_251, type, ap2p: $o). 554.07/73.77 thf(decl_252, type, funcinfuncset: $o). 554.07/73.77 thf(decl_253, type, lamProp: $o). 554.07/73.77 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 554.07/73.77 thf(decl_255, type, lamp: $o). 554.07/73.77 thf(decl_256, type, lam2p: $o). 554.07/73.77 thf(decl_257, type, brelnall1: $o). 554.07/73.77 thf(decl_258, type, brelnall2: $o). 554.07/73.77 thf(decl_259, type, ex1E2: $o). 554.07/73.77 thf(decl_260, type, funcGraphProp1: $o). 554.07/73.77 thf(decl_261, type, funcGraphProp3: $o). 554.07/73.77 thf(decl_262, type, funcGraphProp2: $o). 554.07/73.77 thf(decl_263, type, funcextLem: $o). 554.07/73.77 thf(decl_264, type, funcGraphProp4: $o). 554.07/73.77 thf(decl_265, type, subbreln: $o). 554.07/73.77 thf(decl_266, type, eqbreln: $o). 554.07/73.77 thf(decl_267, type, funcext: $o). 554.07/73.77 thf(decl_268, type, funcext2: $o). 554.07/73.77 thf(decl_269, type, ap2apEq1: $o). 554.07/73.77 thf(decl_270, type, ap2apEq2: $o). 554.07/73.77 thf(decl_271, type, beta1: $o). 554.07/73.77 thf(decl_272, type, eta1: $o). 554.07/73.77 thf(decl_273, type, lam2lamEq: $o). 554.07/73.77 thf(decl_274, type, beta2: $o). 554.07/73.77 thf(decl_275, type, eta2: $o). 554.07/73.77 thf(decl_276, type, iffalseProp1: $o). 554.07/73.77 thf(decl_277, type, iffalseProp2: $o). 554.07/73.77 thf(decl_278, type, iftrueProp1: $o). 554.07/73.77 thf(decl_279, type, iftrueProp2: $o). 554.07/73.77 thf(decl_280, type, ifSingleton: $o). 554.07/73.77 thf(decl_281, type, if: $i > $o > $i > $i > $i). 554.07/73.77 thf(decl_282, type, ifp: $o). 554.07/73.77 thf(decl_283, type, theeq: $o). 554.07/73.77 thf(decl_284, type, iftrue: $o). 554.07/73.77 thf(decl_285, type, iffalse: $o). 554.07/73.77 thf(decl_286, type, iftrueorfalse: $o). 554.07/73.77 thf(decl_287, type, binintersectT_lem: $o). 554.07/73.77 thf(decl_288, type, epred1_0: $o). 554.07/73.77 thf(decl_289, type, esk1_2: $i > $i > $i). 554.07/73.77 thf(decl_290, type, esk2_2: $i > $i > $i). 554.07/73.77 thf(decl_291, type, esk3_2: $i > $i > $i). 554.07/73.77 thf(decl_292, type, esk4_1: $i > $i). 554.07/73.77 thf(decl_293, type, esk5_2: ($i > $i > $o) > $i > $i). 554.07/73.77 thf(decl_294, type, esk6_2: ($i > $i > $o) > $i > $i). 554.07/73.77 thf(decl_295, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 554.07/73.77 thf(decl_296, type, esk8_1: $i > $i). 554.07/73.77 thf(decl_297, type, esk9_1: ($i > $o) > $i). 554.07/73.77 thf(decl_298, type, esk10_1: ($i > $o) > $i). 554.07/73.77 thf(decl_299, type, esk11_2: $i > $i > $i). 554.07/73.77 thf(decl_300, type, esk12_2: $i > $i > $i). 554.07/73.77 thf(decl_301, type, esk13_1: $i > $i). 554.07/73.77 thf(decl_302, type, esk14_1: $i > $i). 554.07/73.77 thf(decl_303, type, esk15_1: $i > $i). 554.07/73.77 thf(decl_304, type, esk16_2: $i > $i > $i). 554.07/73.77 thf(decl_305, type, esk17_3: $i > $i > $o > $i). 554.07/73.77 thf(decl_306, type, esk18_1: ($i > $o) > $i). 554.07/73.77 thf(decl_307, type, esk19_1: $i > $i). 554.07/73.77 thf(decl_308, type, esk20_2: $i > ($i > $o) > $i). 554.07/73.77 thf(decl_309, type, esk21_2: $i > ($i > $o) > $i). 554.07/73.77 thf(decl_310, type, esk22_2: $i > ($i > $o) > $i). 554.07/73.77 thf(decl_311, type, esk23_2: $i > ($i > $o) > $i). 554.07/73.77 thf(decl_312, type, esk24_2: $i > ($i > $o) > $i). 554.07/73.77 thf(decl_313, type, esk25_2: $i > ($i > $o) > $i). 554.07/73.77 thf(decl_314, type, esk26_2: ($i > $o) > $i > $i). 554.07/73.77 thf(decl_315, type, esk27_1: ($i > $o) > $i). 554.07/73.77 thf(decl_316, type, esk28_1: ($i > $o) > $i). 554.07/73.77 thf(decl_317, type, esk29_2: ($i > $o) > $i > $i). 554.07/73.77 thf(decl_318, type, esk30_2: ($i > $o) > ($i > $o) > $i). 554.07/73.77 thf(decl_319, type, esk31_2: ($i > $o) > ($i > $o) > $i). 554.07/73.77 thf(decl_320, type, esk32_2: ($i > $o) > ($i > $o) > $i). 554.07/73.77 thf(decl_321, type, esk33_2: ($i > $o) > ($i > $o) > $i). 554.07/73.77 thf(decl_322, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 554.07/73.77 thf(decl_323, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 554.07/73.77 thf(decl_324, type, esk36_2: $i > $i > $i). 554.07/73.77 thf(decl_325, type, esk37_2: $i > $i > $i). 554.07/73.77 thf(decl_326, type, esk38_2: $i > $i > $i). 554.07/73.77 thf(decl_327, type, esk39_3: $i > $i > $i > $i). 554.07/73.77 thf(decl_328, type, esk40_3: $i > $i > $i > $i). 554.07/73.77 thf(decl_329, type, esk41_2: $i > $i > $i). 554.07/73.77 thf(decl_330, type, esk42_2: $i > ($i > $o) > $i). 554.07/73.77 thf(decl_331, type, esk43_2: $i > ($i > $o) > $i). 554.07/73.77 thf(decl_332, type, esk44_2: $i > ($i > $o) > $i). 554.07/73.77 thf(decl_333, type, esk45_3: $i > ($i > $o) > $i > $i). 554.07/73.77 thf(decl_334, type, esk46_2: $i > ($i > $o) > $i). 554.07/73.77 thf(decl_335, type, esk47_2: $i > ($i > $o) > $i). 554.07/73.77 thf(decl_336, type, esk48_3: $i > $i > ($i > $i) > $i). 554.07/73.77 thf(decl_337, type, esk49_3: $i > $i > ($i > $i) > $i). 554.07/73.77 thf(decl_338, type, esk50_3: $i > $i > ($i > $i) > $i). 554.07/73.77 thf(decl_339, type, esk51_4: $i > $i > $i > ($i > $o) > $i). 554.07/73.77 thf(decl_340, type, esk52_4: $i > $i > $i > ($i > $o) > $i). 554.07/73.77 thf(decl_341, type, esk53_4: $i > $i > $i > ($i > $o) > $i). 554.07/73.77 thf(decl_342, type, esk54_4: $i > $i > $i > ($i > $o) > $i). 554.07/73.77 thf(decl_343, type, esk55_4: $i > $i > $i > $i > $i). 554.07/73.77 thf(decl_344, type, esk56_4: $i > $i > $i > $i > $i). 554.07/73.77 thf(decl_345, type, esk57_4: $i > $i > $i > $i > $i). 554.07/73.77 thf(decl_346, type, esk58_4: $i > $i > $i > $i > $i). 554.07/73.77 thf(decl_347, type, esk59_4: $i > $i > $i > $i > $i). 554.07/73.77 thf(decl_348, type, esk60_4: $i > $i > $i > $i > $i). 554.07/73.77 thf(decl_349, type, esk61_4: $i > $i > $i > $i > $i). 554.07/73.77 thf(decl_350, type, esk62_4: $i > $i > $i > $i > $i). 554.07/73.77 thf(decl_351, type, esk63_4: $i > $i > $i > $i > $i). 554.07/73.77 thf(decl_352, type, esk64_3: $i > $i > ($i > $i) > $i). 554.07/73.77 thf(decl_353, type, esk65_3: $i > $i > ($i > $i) > $i). 554.07/73.77 thf(decl_354, type, esk66_3: $i > $i > ($i > $i) > $i). 554.07/73.77 thf(decl_355, type, esk67_0: $i). 554.07/73.77 thf(decl_356, type, esk68_0: $i). 554.07/73.77 thf(decl_357, type, esk69_0: $i). 554.07/73.77 thf(binunionT_lem, conjecture, (((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((((omegaSAx)=>((((((descrp)=>(((dsetconstrEL)=>((((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>(((exuE3e)=>((((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>(((setadjoinIR)=>(((((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>(((setunionE)=>((subPowSU)=>((((((eqinunit)=>((((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>(((notdexE)=>((notdallE)=>((exuI1)=>(((((in__Cong)=>(((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((((exuEu)=>(((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>(((((subsetTrans)=>(((setadjoinSub2)=>((subset2powerset)=>(((((powersetE1)=>((inPowerset)=>((powersetsubset)=>(((sepSubset)=>((((binunionIR)=>((binunionEcases)=>((((binunionRsub)=>((((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>(((((binintersectSubset1)=>((bs114d)=>(((setminusEL)=>((((((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>(((symdiffE)=>((symdiffI1)=>(((symdiffIneg1)=>((symdiffIneg2)=>(((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((((singletoninpowerset)=>(((((((ubforcartprodlem2)=>(((((cartprodmempair)=>(((setunionsingleton1)=>(((setunionsingleton)=>((((ex1I)=>(((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>(((kfstpairEq)=>((cartprodfstin)=>(((setukpairinjL)=>((((setukpairinjR1)=>(((((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>(((((cartprodmempaircEq)=>((((((dpsetconstrSub)=>((setOfPairsIsBReln)=>(((dpsetconstrEL1)=>(((((apProp)=>(((infuncsetfunc)=>((((lamProp)=>((lamp)=>(((brelnall1)=>((((((((funcGraphProp4)=>((((funcext)=>(((ap2apEq1)=>(((beta1)=>(((((eta2)=>((((iftrueProp1)=>((((ifp)=>((theeq)=>(((iffalse)=>((iftrueorfalse)=>(![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ (binunion @ X21 @ X48) @ (powerset @ X4))<=(in @ X48 @ (powerset @ X4))))))<=(binintersectT_lem))))<=(iftrue))))<=(ifSingleton))<=(iftrueProp2)))<=(iffalseProp2))<=(iffalseProp1)))<=(beta2))<=(lam2lamEq))<=(eta1)))<=(ap2apEq2)))<=(funcext2)))<=(eqbreln))<=(subbreln)))<=(funcextLem))<=(funcGraphProp2))<=(funcGraphProp3))<=(funcGraphProp1))<=(ex1E2))<=(brelnall2)))<=(lam2p))))<=(funcinfuncset))<=(ap2p)))<=(app)))<=(funcImageSingleton))<=(dpsetconstrER))<=(dpsetconstrEL2)))<=(dpsetconstrERa))))<=(dpsetconstrI))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq)))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin)))))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq)))<=(setukpairinjR12))<=(setukpairinjR11)))<=(setukpairinjL2))))<=(theprop)))))<=(ex1I2)))<=(ex1E1))<=(singletonprop)))<=(setunionsingleton2)))<=(setunionE2)))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3)))<=(ubforcartprodlem1))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp)))))<=(secondinupair))))<=(symdiffI2))))<=(setminusSubset1)))))<=(setminusELneg))<=(setminusERneg))<=(setminusSubset2))<=(setminusER)))<=(setminusI))))<=(binintersectSubset4))<=(binintersectRsub))<=(disjointsetsI1)))))<=(binintersectLsub)))<=(binintersectSubset5))<=(binintersectI)))<=(binunionLsub))<=(binunionE))))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset)))))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub))))<=(setadjoinSub)))<=(subsetRefl))<=(notequalI2))<=(notequalI1))))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1)))))<=(descr__Cong)))<=(omega__Cong))<=(setunion__Cong))))))<=(exuE3u)))<=(inCongP))<=(exuI2))<=(exuI3)))))<=(prop2set2propI)))))<=(quantDeMorgan2))<=(quantDeMorgan1))))))<=(upairsetE))<=(singletonsswitch)))<=(notinsingleton))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))))<=(setunionI))))))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE)))<=(emptyinunitempty))))))))<=(emptyI))<=(setext)))<=(notinemptyset)))))<=(exuE1))<=(dsetconstrER)))<=(dsetconstrI)))<=(wellorderingAx))<=(foundationAx))<=(replAx))<=(omegaIndAx)))<=(omega0Ax))<=(setunionAx)))))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binunionT_lem)). 554.07/73.77 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', sepInPowerset)). 554.07/73.77 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', descr__Cong)). 554.07/73.77 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', exuE3u)). 554.07/73.77 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.TXhKssAo14/E---3.1_3430301.p', exuI2)). 554.07/73.77 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', exuI3)). 554.07/73.77 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', exuE2)). 554.07/73.77 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setoftrueEq)). 554.07/73.77 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', sepSubset)). 554.07/73.77 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.TXhKssAo14/E---3.1_3430301.p', exuE1)). 554.07/73.77 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', dsetconstrER)). 554.07/73.77 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', dsetconstrI)). 554.07/73.77 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', replAx)). 554.07/73.77 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.TXhKssAo14/E---3.1_3430301.p', ex1I)). 554.07/73.77 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.TXhKssAo14/E---3.1_3430301.p', ksndsingleton)). 554.07/73.77 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.TXhKssAo14/E---3.1_3430301.p', kfstsingleton)). 554.07/73.77 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', lamProp)). 554.07/73.77 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', apProp)). 554.07/73.77 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', dpsetconstrEL1)). 554.07/73.77 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setOfPairsIsBReln)). 554.07/73.77 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', dpsetconstrSub)). 554.07/73.77 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', lamp)). 554.07/73.77 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', iftrueProp1)). 554.07/73.77 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', eta2)). 554.07/73.77 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', beta1)). 554.07/73.77 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', iftrueProp2)). 554.07/73.77 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', ifSingleton)). 554.07/73.77 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', iffalseProp2)). 554.07/73.77 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', eta1)). 554.07/73.77 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', lam2lamEq)). 554.07/73.77 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', beta2)). 554.07/73.77 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', iffalseProp1)). 554.07/73.77 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', lam2p)). 554.07/73.77 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', ex1E2)). 554.07/73.77 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', dpsetconstrI)). 554.07/73.77 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', dpsetconstrERa)). 554.07/73.77 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', dpsetconstrEL2)). 554.07/73.77 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', dpsetconstrER)). 554.07/73.77 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', funcImageSingleton)). 554.07/73.77 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', singletonprop)). 554.07/73.77 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', ex1E1)). 554.07/73.77 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', ex1I2)). 554.07/73.77 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', dsetconstr__Cong)). 554.07/73.77 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', exuEu)). 554.07/73.77 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', exu__Cong)). 554.07/73.77 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', exuI1)). 554.07/73.77 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.TXhKssAo14/E---3.1_3430301.p', emptyE1)). 554.07/73.77 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', nonemptyI)). 554.07/73.77 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setbeta)). 554.07/73.77 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', exuE3e)). 554.07/73.77 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', dsetconstrEL)). 554.07/73.77 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', descrp)). 554.07/73.77 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binunionIL)). 554.07/73.77 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binunionLsub)). 554.07/73.77 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binunionE)). 554.07/73.77 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', powersetI1)). 554.07/73.77 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', subsetemptysetimpeq)). 554.07/73.77 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setextsub)). 554.07/73.77 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setadjoinSub)). 554.07/73.77 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', subsetRefl)). 554.07/73.77 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', notequalI2)). 554.07/73.77 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', notequalI1)). 554.07/73.77 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', subsetE)). 554.07/73.77 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setadjoinSub2)). 554.07/73.77 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', subsetI2)). 554.07/73.77 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', subsetTrans)). 554.07/73.77 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', eqimpsubset1)). 554.07/73.77 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', notsubsetI)). 554.07/73.77 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', subsetE2)). 554.07/73.77 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', omega__Cong)). 554.07/73.77 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', emptysetsubset)). 554.07/73.77 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setunion__Cong)). 554.07/73.77 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', eqimpsubset2)). 554.07/73.77 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', inCongP)). 554.07/73.77 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', subsetI1)). 554.07/73.77 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', subset2powerset)). 554.07/73.77 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', quantDeMorgan2)). 554.07/73.77 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', quantDeMorgan1)). 554.07/73.77 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', upairsetE)). 554.07/73.77 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', singletonsswitch)). 554.07/73.77 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', notinsingleton)). 554.07/73.77 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', uniqinunit)). 554.07/73.77 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', nonemptyImpWitness)). 554.07/73.77 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setunionI)). 554.07/73.77 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setadjoinOr)). 554.07/73.77 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setadjoinE)). 554.07/73.77 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binunionRsub)). 554.07/73.77 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', emptyinunitempty)). 554.07/73.77 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binunionEcases)). 554.07/73.77 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', emptyI)). 554.07/73.77 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binunionIR)). 554.07/73.77 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.TXhKssAo14/E---3.1_3430301.p', setext)). 554.07/73.77 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', notinemptyset)). 554.07/73.77 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', powersetsubset)). 554.07/73.77 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', inPowerset)). 554.07/73.77 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', powersetE1)). 554.07/73.77 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binintersectEL)). 554.07/73.77 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.TXhKssAo14/E---3.1_3430301.p', wellorderingAx)). 554.07/73.77 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.TXhKssAo14/E---3.1_3430301.p', foundationAx)). 554.07/73.77 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', omegaIndAx)). 554.07/73.77 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', omega0Ax)). 554.07/73.77 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setunionAx)). 554.07/73.77 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setextAx)). 554.07/73.77 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setminusILneg)). 554.07/73.77 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setminusEL)). 554.07/73.77 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', bs114d)). 554.07/73.77 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binintersectSubset1)). 554.07/73.77 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binintersectER)). 554.07/73.77 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binintersectSubset3)). 554.07/73.77 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binintersectSubset2)). 554.07/73.77 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setminusIRneg)). 554.07/73.77 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.TXhKssAo14/E---3.1_3430301.p', setukpairIR)). 554.07/73.77 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.TXhKssAo14/E---3.1_3430301.p', setukpairIL)). 554.07/73.77 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', symdiffIneg2)). 554.07/73.77 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', symdiffIneg1)). 554.07/73.77 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', symdiffI1)). 554.07/73.77 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', symdiffE)). 554.07/73.77 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setminusLsub)). 554.07/73.77 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', kpairiskpair)). 554.07/73.77 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', singletonsuniq)). 554.07/73.77 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setunionsingleton)). 554.07/73.77 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setunionsingleton1)). 554.07/73.77 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', cartprodmempair)). 554.07/73.77 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.TXhKssAo14/E---3.1_3430301.p', ubforcartprodlem2)). 554.07/73.77 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', singletoninpowerset)). 554.07/73.77 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setukpairinjL1)). 554.07/73.77 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', ksndpairEq)). 554.07/73.77 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setukpairinjR1)). 554.07/73.77 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setukpairinjL)). 554.07/73.77 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', cartprodfstin)). 554.07/73.77 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', kfstpairEq)). 554.07/73.77 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', kpairsurjEq)). 554.07/73.77 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', infuncsetfunc)). 554.07/73.77 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', cartprodmempaircEq)). 554.07/73.77 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', ap2apEq1)). 554.07/73.77 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', funcext)). 554.07/73.77 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', funcGraphProp4)). 554.07/73.77 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', brelnall1)). 554.07/73.77 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', ifp)). 554.07/73.77 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', iftrue)). 554.07/73.77 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binintersectT_lem)). 554.07/73.77 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', iftrueorfalse)). 554.07/73.77 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', iffalse)). 554.07/73.77 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', theeq)). 554.07/73.78 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', eqbreln)). 554.07/73.78 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', funcext2)). 554.07/73.78 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', ap2apEq2)). 554.07/73.78 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', subbreln)). 554.07/73.78 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', brelnall2)). 554.07/73.78 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', funcGraphProp1)). 554.07/73.78 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', funcGraphProp3)). 554.07/73.78 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', funcGraphProp2)). 554.07/73.78 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', funcextLem)). 554.07/73.78 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', funcinfuncset)). 554.07/73.78 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', app)). 554.07/73.78 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', ap2p)). 554.07/73.78 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', cartprodpairsurjEq)). 554.07/73.78 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.TXhKssAo14/E---3.1_3430301.p', setukpairinjR2)). 554.07/73.78 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.TXhKssAo14/E---3.1_3430301.p', setukpairinjR)). 554.07/73.78 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', cartprodsndin)). 554.07/73.78 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', cartprodpairmemEL)). 554.07/73.78 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', cartprodpairmemER)). 554.07/73.78 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', cartprodfstpairEq)). 554.07/73.78 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', cartprodsndpairEq)). 554.07/73.78 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', upairequniteq)). 554.07/73.78 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', theprop)). 554.07/73.78 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setukpairinjL2)). 554.07/73.78 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setukpairinjR11)). 554.07/73.78 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setukpairinjR12)). 554.07/73.78 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setunionsingleton2)). 554.07/73.78 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.TXhKssAo14/E---3.1_3430301.p', upairsubunion)). 554.07/73.78 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.TXhKssAo14/E---3.1_3430301.p', upairinpowunion)). 554.07/73.78 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.TXhKssAo14/E---3.1_3430301.p', ubforcartprodlem1)). 554.07/73.78 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.TXhKssAo14/E---3.1_3430301.p', ubforcartprodlem3)). 554.07/73.78 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.TXhKssAo14/E---3.1_3430301.p', cartprodpairin)). 554.07/73.78 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', cartprodmempair1)). 554.07/73.78 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setunionE2)). 554.07/73.78 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', upairset2E)). 554.07/73.78 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setminusELneg)). 554.07/73.78 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setminusSubset1)). 554.07/73.78 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', symdiffI2)). 554.07/73.78 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', secondinupair)). 554.07/73.78 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', kpairp)). 554.07/73.78 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', singletonsubset)). 554.07/73.78 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', singletoninpowunion)). 554.07/73.78 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setminusERneg)). 554.07/73.78 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binintersectLsub)). 554.07/73.78 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', disjointsetsI1)). 554.07/73.78 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binintersectRsub)). 554.07/73.78 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binintersectSubset4)). 554.07/73.78 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setminusI)). 554.07/73.78 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setminusER)). 554.07/73.78 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setminusSubset2)). 554.07/73.78 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binintersectSubset5)). 554.07/73.78 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', binintersectI)). 554.07/73.78 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', upairset2IR)). 554.07/73.78 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', powerset__Cong)). 554.07/73.78 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.TXhKssAo14/E---3.1_3430301.p', setadjoin__Cong)). 554.07/73.78 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', emptyset__Cong)). 554.07/73.78 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.TXhKssAo14/E---3.1_3430301.p', in__Cong)). 554.07/73.78 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', notdallE)). 554.07/73.78 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', notdexE)). 554.07/73.78 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', prop2setI)). 554.07/73.78 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', quantDeMorgan4)). 554.07/73.78 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', quantDeMorgan3)). 554.07/73.78 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', vacuousDall)). 554.07/73.78 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', upairsetIR)). 554.07/73.78 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', upairsetIL)). 554.07/73.78 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', eqinunit)). 554.07/73.78 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', subPowSU)). 554.07/73.78 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.TXhKssAo14/E---3.1_3430301.p', setunionE)). 554.07/73.78 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', powersetE)). 554.07/73.78 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', emptyInPowerset)). 554.07/73.78 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', emptyinPowerset)). 554.07/73.78 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', powersetI)). 554.07/73.78 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setadjoinIR)). 554.07/73.78 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setadjoinIL)). 554.07/73.78 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', nonemptyI1)). 554.07/73.78 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', nonemptyE1)). 554.07/73.78 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', noeltsimpempty)). 554.07/73.78 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', emptysetimpfalse)). 554.07/73.78 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', emptysetE)). 554.07/73.78 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', prop2setE)). 554.07/73.78 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', omegaSAx)). 554.07/73.78 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', powersetAx)). 554.07/73.78 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', setadjoinAx)). 554.07/73.78 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.TXhKssAo14/E---3.1_3430301.p', emptysetAx)). 554.07/73.78 thf(c_0_227, negated_conjecture, ~((((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((((omegaSAx)=>((((((descrp)=>(((dsetconstrEL)=>((((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>(((exuE3e)=>((((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>(((setadjoinIR)=>(((((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>(((setunionE)=>((subPowSU)=>((((((eqinunit)=>((((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>(((notdexE)=>((notdallE)=>((exuI1)=>(((((in__Cong)=>(((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((((exuEu)=>(((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>(((((subsetTrans)=>(((setadjoinSub2)=>((subset2powerset)=>(((((powersetE1)=>((inPowerset)=>((powersetsubset)=>(((sepSubset)=>((((binunionIR)=>((binunionEcases)=>((((binunionRsub)=>((((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>(((((binintersectSubset1)=>((bs114d)=>(((setminusEL)=>((((((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>(((symdiffE)=>((symdiffI1)=>(((symdiffIneg1)=>((symdiffIneg2)=>(((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((((singletoninpowerset)=>(((((((ubforcartprodlem2)=>(((((cartprodmempair)=>(((setunionsingleton1)=>(((setunionsingleton)=>((((ex1I)=>(((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>(((kfstpairEq)=>((cartprodfstin)=>(((setukpairinjL)=>((((setukpairinjR1)=>(((((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>(((((cartprodmempaircEq)=>((((((dpsetconstrSub)=>((setOfPairsIsBReln)=>(((dpsetconstrEL1)=>(((((apProp)=>(((infuncsetfunc)=>((((lamProp)=>((lamp)=>(((brelnall1)=>((((((((funcGraphProp4)=>((((funcext)=>(((ap2apEq1)=>(((beta1)=>(((((eta2)=>((((iftrueProp1)=>((((ifp)=>((theeq)=>(((iffalse)=>((iftrueorfalse)=>(![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ (binunion @ X21 @ X48) @ (powerset @ X4))<=(in @ X48 @ (powerset @ X4))))))<=(binintersectT_lem))))<=(iftrue))))<=(ifSingleton))<=(iftrueProp2)))<=(iffalseProp2))<=(iffalseProp1)))<=(beta2))<=(lam2lamEq))<=(eta1)))<=(ap2apEq2)))<=(funcext2)))<=(eqbreln))<=(subbreln)))<=(funcextLem))<=(funcGraphProp2))<=(funcGraphProp3))<=(funcGraphProp1))<=(ex1E2))<=(brelnall2)))<=(lam2p))))<=(funcinfuncset))<=(ap2p)))<=(app)))<=(funcImageSingleton))<=(dpsetconstrER))<=(dpsetconstrEL2)))<=(dpsetconstrERa))))<=(dpsetconstrI))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq)))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin)))))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq)))<=(setukpairinjR12))<=(setukpairinjR11)))<=(setukpairinjL2))))<=(theprop)))))<=(ex1I2)))<=(ex1E1))<=(singletonprop)))<=(setunionsingleton2)))<=(setunionE2)))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3)))<=(ubforcartprodlem1))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp)))))<=(secondinupair))))<=(symdiffI2))))<=(setminusSubset1)))))<=(setminusELneg))<=(setminusERneg))<=(setminusSubset2))<=(setminusER)))<=(setminusI))))<=(binintersectSubset4))<=(binintersectRsub))<=(disjointsetsI1)))))<=(binintersectLsub)))<=(binintersectSubset5))<=(binintersectI)))<=(binunionLsub))<=(binunionE))))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset)))))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub))))<=(setadjoinSub)))<=(subsetRefl))<=(notequalI2))<=(notequalI1))))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1)))))<=(descr__Cong)))<=(omega__Cong))<=(setunion__Cong))))))<=(exuE3u)))<=(inCongP))<=(exuI2))<=(exuI3)))))<=(prop2set2propI)))))<=(quantDeMorgan2))<=(quantDeMorgan1))))))<=(upairsetE))<=(singletonsswitch)))<=(notinsingleton))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))))<=(setunionI))))))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE)))<=(emptyinunitempty))))))))<=(emptyI))<=(setext)))<=(notinemptyset)))))<=(exuE1))<=(dsetconstrER)))<=(dsetconstrI)))<=(wellorderingAx))<=(foundationAx))<=(replAx))<=(omegaIndAx)))<=(omega0Ax))<=(setunionAx)))))<=(setextAx))), inference(assume_negation,[status(cth)],[binunionT_lem])). 554.07/73.78 thf(c_0_228, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 554.07/73.78 thf(c_0_229, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 554.07/73.78 thf(c_0_230, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 554.07/73.78 thf(c_0_231, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 554.07/73.78 thf(c_0_232, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 554.07/73.78 thf(c_0_233, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 554.07/73.78 thf(c_0_234, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 554.07/73.78 thf(c_0_235, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 554.07/73.78 thf(c_0_236, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 554.07/73.78 thf(c_0_237, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 554.07/73.78 thf(c_0_238, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 554.07/73.78 thf(c_0_239, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 554.07/73.78 thf(c_0_240, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 554.07/73.78 thf(c_0_241, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 554.07/73.78 thf(c_0_242, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 554.07/73.78 thf(c_0_243, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])). 554.07/73.78 thf(c_0_244, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 554.07/73.78 thf(c_0_245, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 554.07/73.78 thf(c_0_246, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 554.07/73.78 thf(c_0_247, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 554.07/73.78 thf(c_0_248, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 554.07/73.78 thf(c_0_249, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 554.07/73.78 thf(c_0_250, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 554.07/73.78 thf(c_0_251, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])). 554.07/73.78 thf(c_0_252, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 554.07/73.78 thf(c_0_253, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 554.07/73.78 thf(c_0_254, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])). 554.07/73.78 thf(c_0_255, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 554.07/73.78 thf(c_0_256, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])). 554.07/73.78 thf(c_0_257, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])). 554.07/73.78 thf(c_0_258, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 554.07/73.78 thf(c_0_259, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 554.07/73.78 thf(c_0_260, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])). 554.07/73.78 thf(c_0_261, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 554.07/73.78 thf(c_0_262, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 554.07/73.78 thf(c_0_263, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 554.07/73.78 thf(c_0_264, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 554.07/73.78 thf(c_0_265, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 554.07/73.78 thf(c_0_266, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 554.07/73.78 thf(c_0_267, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 554.07/73.78 thf(c_0_268, plain, ((ex1I2)<=>![X4:$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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 554.07/73.78 thf(c_0_269, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 554.07/73.78 thf(c_0_270, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 554.07/73.78 thf(c_0_271, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 554.07/73.78 thf(c_0_272, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 554.07/73.78 thf(c_0_273, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 554.07/73.78 thf(c_0_274, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 554.07/73.78 thf(c_0_275, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 554.07/73.78 thf(c_0_276, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 554.07/73.78 thf(c_0_277, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 554.07/73.78 thf(c_0_278, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 554.07/73.78 thf(c_0_279, plain, ((epred1_0)<=>![X1410:$i]:(?[X1411:$i]:((((![X1412:$i]:(((in @ X1412 @ X1411)=>![X1413:$i]:(((in @ X1413 @ X1412)=>(in @ X1413 @ X1410)))))&![X1414:$i, X1415:$i]:((((in @ X1414 @ X1410)&(in @ X1415 @ X1410))=>(![X1416:$i]:(((in @ X1416 @ X1411)=>((in @ X1414 @ X1416)<=>(in @ X1415 @ X1416))))=>((X1414)=(X1415))))))&![X1417:$i, X1418:$i]:((((in @ X1417 @ X1411)&(in @ X1418 @ X1411))=>(![X1419:$i]:(((in @ X1419 @ X1417)=>(in @ X1419 @ X1418)))|![X1420:$i]:(((in @ X1420 @ X1418)=>(in @ X1420 @ X1417)))))))&![X1421:$i]:(((![X1422:$i]:(((in @ X1422 @ X1421)=>(in @ X1422 @ X1410)))&?[X1423:$i]:((in @ X1423 @ X1421)))=>?[X1424:$i, X1425:$i]:(((((in @ X1424 @ X1411)&(in @ X1425 @ X1421))&~(?[X1426:$i]:(((in @ X1426 @ X1424)&(in @ X1426 @ X1421)))))&![X1427:$i]:(((in @ X1427 @ X1411)=>(![X1428:$i]:(((in @ X1428 @ X1427)=>(in @ X1428 @ X1424)))|(in @ X1425 @ X1427)))))))))))), introduced(definition)). 554.07/73.78 thf(c_0_280, negated_conjecture, ~((![X1445:$i, X1446:$i]:((![X1447:$i]:(((in @ X1447 @ X1445)<=>(in @ X1447 @ X1446)))=>((X1445)=(X1446))))=>(![X750:$i]:(~(in @ X750 @ emptyset))=>(![X751:$i, X752:$i, X753:$i]:(((in @ X753 @ (setadjoin @ X751 @ X752))<=>(((X753)=(X751))|(in @ X753 @ X752))))=>(![X754:$i, X755:$i]:(((in @ X755 @ (powerset @ X754))<=>![X756:$i]:(((in @ X756 @ X755)=>(in @ X756 @ X754)))))=>(![X1442:$i, X1443:$i]:(((in @ X1443 @ (setunion @ X1442))<=>?[X1444:$i]:(((in @ X1443 @ X1444)&(in @ X1444 @ X1442)))))=>((in @ emptyset @ omega)=>(![X757:$i]:(((in @ X757 @ omega)=>(in @ (setadjoin @ X757 @ X757) @ omega)))=>(![X1439:$i]:((((in @ emptyset @ X1439)&![X1440:$i]:((((in @ X1440 @ omega)&(in @ X1440 @ X1439))=>(in @ (setadjoin @ X1440 @ X1440) @ X1439))))=>![X1441:$i]:(((in @ X1441 @ omega)=>(in @ X1441 @ X1439)))))=>(![X1433:$i > $i > $o, X1434:$i]:((![X1435:$i]:(((in @ X1435 @ X1434)=>(exu @ (X1433 @ X1435))))=>?[X1436:$i]:(![X1437:$i]:(((in @ X1437 @ X1436)<=>?[X1438:$i]:(((in @ X1438 @ X1434)&(X1433 @ X1438 @ X1437))))))))=>(![X1429:$i]:((?[X1430:$i]:((in @ X1430 @ X1429))=>?[X1431:$i]:(((in @ X1431 @ X1429)&~(?[X1432:$i]:(((in @ X1432 @ X1431)&(in @ X1432 @ X1429))))))))=>((epred1_0)=>(![X758:$i > $o]:(((exu @ X758)=>(X758 @ (descr @ (^[Z0:$i]:(X758 @ Z0))))))=>(![X1407:$i, X1408:$i > $o, X1409:$i]:(((in @ X1409 @ X1407)=>((X1408 @ X1409)=>(in @ X1409 @ (dsetconstr @ X1407 @ X1408)))))=>(![X759:$i, X760:$i > $o, X761:$i]:(((in @ X761 @ (dsetconstr @ X759 @ X760))=>(in @ X761 @ X759)))=>(![X1404:$i, X1405:$i > $o, X1406:$i]:(((in @ X1406 @ (dsetconstr @ X1404 @ X1405))=>(X1405 @ X1406)))=>(![X1401:$i > $o]:(((exu @ X1401)=>?[X1402:$i]:(((X1401 @ X1402)&![X1403:$i]:(((X1401 @ X1403)=>((X1402)=(X1403))))))))=>(![X762:$o, X763:$i]:(((in @ X763 @ (prop2set @ ((X762))))=>(X762)))=>(![X764:$i]:(((in @ X764 @ emptyset)=>![X765:$o]:((X765))))=>(![X766:$i]:(((in @ X766 @ emptyset)=>~($true)))=>(![X1400:$i]:(~(in @ X1400 @ emptyset))=>(![X767:$i > $o]:(((exu @ X767)=>?[X768:$i]:((X767 @ X768))))=>(![X1396:$i, X1397:$i]:((![X1398:$i]:(((in @ X1398 @ X1396)=>(in @ X1398 @ X1397)))=>(![X1399:$i]:(((in @ X1399 @ X1397)=>(in @ X1399 @ X1396)))=>((X1396)=(X1397)))))=>(![X1394:$i]:((![X1395:$i]:(~(in @ X1395 @ X1394))=>((X1394)=(emptyset))))=>(![X769:$i]:((![X770:$i]:(~(in @ X770 @ X769))=>((X769)=(emptyset))))=>(![X771:$i, X772:$i > $o, X773:$i]:(((in @ X773 @ X771)=>((in @ X773 @ (dsetconstr @ X771 @ X772))<=>(X772 @ X773))))=>(![X774:$i]:(((nonempty @ X774)=>?[X775:$i]:((in @ X775 @ X774))))=>(![X776:$i, X777:$i > $o, X778:$i]:(((in @ X778 @ X776)=>((X777 @ X778)=>(nonempty @ (dsetconstr @ X776 @ X777)))))=>(![X779:$i]:((?[X780:$i]:((in @ X780 @ X779))=>(nonempty @ X779)))=>(![X781:$i, X782:$i]:((in @ X781 @ (setadjoin @ X781 @ X782)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X783:$i, X784:$i, X785:$i]:(((in @ X785 @ X784)=>(in @ X785 @ (setadjoin @ X783 @ X784))))=>(![X1390:$i, X1391:$i, X1392:$i]:(((in @ X1392 @ (setadjoin @ X1390 @ X1391))=>![X1393:$o]:(((((X1392)=(X1390))=>(X1393))=>(((in @ X1392 @ X1391)=>(X1393))=>(X1393))))))=>(![X1387:$i, X1388:$i, X1389:$i]:(((in @ X1389 @ (setadjoin @ X1387 @ X1388))=>(((X1389)=(X1387))|(in @ X1389 @ X1388))))=>(![X1386:$i]:(((dsetconstr @ X1386 @ (^[Z0:$i]:($true)))=(X1386)))=>(![X786:$i, X787:$i]:((![X788:$i]:(((in @ X788 @ X787)=>(in @ X788 @ X786)))=>(in @ X787 @ (powerset @ X786))))=>(![X789:$i]:((in @ emptyset @ (powerset @ X789)))=>(![X790:$i]:((in @ emptyset @ (powerset @ X790)))=>(![X791:$i, X792:$i, X793:$i]:(((in @ X792 @ (powerset @ X791))=>((in @ X793 @ X792)=>(in @ X793 @ X791))))=>(![X1383:$i, X1384:$i, X1385:$i]:(((in @ X1384 @ X1385)=>((in @ X1385 @ X1383)=>(in @ X1384 @ (setunion @ X1383)))))=>(![X794:$i, X795:$i]:(((in @ X795 @ (setunion @ X794))=>![X796:$o]:((![X797:$i]:(((in @ X795 @ X797)=>((in @ X797 @ X794)=>(X796))))=>(X796)))))=>(![X798:$i, X799:$i]:(((in @ X799 @ X798)=>(in @ X799 @ (powerset @ (setunion @ X798)))))=>(![X1380:$i > $o]:(((exu @ X1380)=>?[X1381:$i]:(![X1382:$i]:(((X1380 @ X1382)<=>((X1382)=(X1381)))))))=>(![X1378:$i]:(((nonempty @ X1378)=>?[X1379:$i]:(((in @ X1379 @ X1378)&$true))))=>(![X1376:$i, X1377:$i]:(((in @ X1376 @ (setadjoin @ X1377 @ emptyset))=>((X1376)=(X1377))))=>(![X1374:$i, X1375:$i]:((((X1374)!=(X1375))=>~(in @ X1375 @ (setadjoin @ X1374 @ emptyset))))=>(![X800:$i, X801:$i]:((((X800)=(X801))=>(in @ X800 @ (setadjoin @ X801 @ emptyset))))=>(![X1372:$i, X1373:$i]:(((in @ X1372 @ (setadjoin @ X1373 @ emptyset))=>(in @ X1373 @ (setadjoin @ X1372 @ emptyset))))=>(![X1369:$i, X1370:$i, X1371:$i]:(((in @ X1371 @ (setadjoin @ X1369 @ (setadjoin @ X1370 @ emptyset)))=>(((X1371)=(X1369))|((X1371)=(X1370)))))=>(![X802:$i, X803:$i]:((in @ X802 @ (setadjoin @ X802 @ (setadjoin @ X803 @ emptyset))))=>(![X804:$i, X805:$i]:((in @ X805 @ (setadjoin @ X804 @ (setadjoin @ X805 @ emptyset))))=>(![X806:$i, X807:$i > $o]:((?[X808:$i]:(((in @ X808 @ X806)&(X807 @ X808)))=>(((dsetconstr @ X806 @ X807)=(emptyset))=>~($true))))=>(![X809:$i > $o, X810:$i]:(((in @ X810 @ emptyset)=>(X809 @ X810)))=>(![X1365:$i, X1366:$i > $o]:((~(![X1367:$i]:(((in @ X1367 @ X1365)=>(X1366 @ X1367))))=>?[X1368:$i]:(((in @ X1368 @ X1365)&~((X1366 @ X1368))))))=>(![X1361:$i, X1362:$i > $o]:((![X1363:$i]:(((in @ X1363 @ X1361)=>~((X1362 @ X1363))))=>~(?[X1364:$i]:(((in @ X1364 @ X1361)&(X1362 @ X1364))))))=>(![X811:$i, X812:$i > $o]:((~(?[X813:$i]:(((in @ X813 @ X811)&(X812 @ X813))))=>![X814:$i]:(((in @ X814 @ X811)=>~((X812 @ X814))))))=>(![X815:$i, X816:$i > $o]:((?[X817:$i]:(((in @ X817 @ X815)&~((X816 @ X817))))=>~(![X818:$i]:(((in @ X818 @ X815)=>(X816 @ X818))))))=>(![X819:$o]:(((X819)=>(in @ emptyset @ (prop2set @ ((X819))))))=>((prop2set2propI)=>(![X820:$i, X821:$i > $o]:((~(?[X822:$i]:(((in @ X822 @ X820)&(X821 @ X822))))=>![X823:$i]:(((in @ X823 @ X820)=>~((X821 @ X823))))))=>(![X824:$i, X825:$i > $o]:((~(![X826:$i]:(((in @ X826 @ X824)=>(X825 @ X826))))=>?[X827:$i]:(((in @ X827 @ X824)&~((X825 @ X827))))))=>(![X828:$i > $o]:((?[X829:$i]:(((X828 @ X829)&![X830:$i]:(((X828 @ X830)=>((X829)=(X830))))))=>(exu @ X828)))=>(![X1357:$i > $o]:((?[X1358:$i]:((X1357 @ X1358))=>(![X1359:$i, X1360:$i]:(((X1357 @ X1359)=>((X1357 @ X1360)=>((X1359)=(X1360)))))=>(exu @ X1357))))=>(![X1354:$i > $o]:((?[X1355:$i]:(![X1356:$i]:(((X1354 @ X1356)<=>((X1356)=(X1355)))))=>(exu @ X1354)))=>(![X1350:$i, X1351:$i]:((((X1350)=(X1351))=>![X1352:$i, X1353:$i]:((((X1352)=(X1353))=>((in @ X1352 @ X1350)=>(in @ X1353 @ X1351))))))=>(![X831:$i, X832:$i]:((((X831)=(X832))=>![X833:$i, X834:$i]:((((X833)=(X834))=>((in @ X833 @ X831)<=>(in @ X834 @ X832))))))=>(![X1347:$i > $o]:(((exu @ X1347)=>![X1348:$i, X1349:$i]:(((X1347 @ X1348)=>((X1347 @ X1349)=>((X1348)=(X1349)))))))=>(![X835:$i > $o, X836:$i > $o]:((![X837:$i, X838:$i]:((((X837)=(X838))=>((X835 @ X837)<=>(X836 @ X838))))=>((exu @ X835)<=>(exu @ X836))))=>(((emptyset)=(emptyset))=>(![X839:$i, X840:$i]:((((X839)=(X840))=>![X841:$i, X842:$i]:((((X841)=(X842))=>((setadjoin @ X839 @ X841)=(setadjoin @ X840 @ X842))))))=>(![X843:$i, X844:$i]:((((X843)=(X844))=>((powerset @ X843)=(powerset @ X844))))=>(![X1345:$i, X1346:$i]:((((X1345)=(X1346))=>((setunion @ X1345)=(setunion @ X1346))))=>(((omega)=(omega))=>(![X845:$i > $o]:(((exu @ X845)=>![X846:$i, X847:$i]:(((X845 @ X846)=>((X845 @ X847)=>((X846)=(X847)))))))=>(![X1341:$i > $o, X1342:$i > $o]:((![X1343:$i, X1344:$i]:((((X1343)=(X1344))=>((X1341 @ X1343)<=>(X1342 @ X1344))))=>((exu @ X1341)=>((exu @ X1342)=>((descr @ X1341)=(descr @ X1342))))))=>(![X848:$i, X849:$i]:((((X848)=(X849))=>![X850:$i > $o, X851:$i > $o]:((![X852:$i]:(((in @ X852 @ X848)=>![X853:$i]:(((in @ X853 @ X849)=>(((X852)=(X853))=>((X850 @ X852)<=>(X851 @ X853)))))))=>((dsetconstr @ X848 @ X850)=(dsetconstr @ X849 @ X851))))))=>(![X854:$i, X855:$i]:((![X856:$i]:(((in @ X856 @ X854)=>(in @ X856 @ X855)))=>(subset @ X854 @ X855)))=>(![X857:$i, X858:$i]:((((X857)=(X858))=>(subset @ X858 @ X857)))=>(![X1339:$i, X1340:$i]:((((X1339)=(X1340))=>(subset @ X1339 @ X1340)))=>(![X1336:$i, X1337:$i]:((![X1338:$i]:(((in @ X1338 @ X1336)=>(in @ X1338 @ X1337)))=>(subset @ X1336 @ X1337)))=>(![X859:$i]:((subset @ emptyset @ X859))=>(![X1333:$i, X1334:$i, X1335:$i]:(((subset @ X1333 @ X1334)=>((in @ X1335 @ X1333)=>(in @ X1335 @ X1334))))=>(![X860:$i, X861:$i, X862:$i]:(((subset @ X860 @ X861)=>(~(in @ X862 @ X861)=>~(in @ X862 @ X860))))=>(![X863:$i, X864:$i, X865:$i]:(((in @ X865 @ X863)=>(~(in @ X865 @ X864)=>~(subset @ X863 @ X864))))=>(![X1331:$i, X1332:$i]:((~(subset @ X1331 @ X1332)=>((X1331)!=(X1332))))=>(![X1328:$i, X1329:$i, X1330:$i]:(((in @ X1330 @ X1328)=>(~(in @ X1330 @ X1329)=>((X1328)!=(X1329)))))=>(![X1327:$i]:((subset @ X1327 @ X1327))=>(![X866:$i, X867:$i, X868:$i]:(((subset @ X866 @ X867)=>((subset @ X867 @ X868)=>(subset @ X866 @ X868))))=>(![X1325:$i, X1326:$i]:((subset @ X1326 @ (setadjoin @ X1325 @ X1326)))=>(![X869:$i, X870:$i, X871:$i]:(((subset @ X869 @ X871)=>(subset @ X869 @ (setadjoin @ X870 @ X871))))=>(![X872:$i, X873:$i]:(((subset @ X872 @ X873)=>(in @ X872 @ (powerset @ X873))))=>(![X1323:$i, X1324:$i]:(((subset @ X1323 @ X1324)=>((subset @ X1324 @ X1323)=>((X1323)=(X1324)))))=>(![X1322:$i]:(((subset @ X1322 @ emptyset)=>((X1322)=(emptyset))))=>(![X1320:$i, X1321:$i]:(((subset @ X1321 @ X1320)=>(in @ X1321 @ (powerset @ X1320))))=>(![X874:$i, X875:$i]:(((in @ X875 @ (powerset @ X874))=>(subset @ X875 @ X874)))=>(![X876:$i]:((in @ X876 @ (powerset @ X876)))=>(![X877:$i, X878:$i]:(((subset @ X877 @ X878)=>(subset @ (powerset @ X877) @ (powerset @ X878))))=>(![X1318:$i, X1319:$i > $o]:((in @ (dsetconstr @ X1318 @ X1319) @ (powerset @ X1318)))=>(![X879:$i, X880:$i > $o]:((subset @ (dsetconstr @ X879 @ X880) @ X879))=>(![X1315:$i, X1316:$i, X1317:$i]:(((in @ X1317 @ X1315)=>(in @ X1317 @ (binunion @ X1315 @ X1316))))=>(![X1313:$i, X1314:$i]:((in @ X1314 @ (setadjoin @ X1313 @ (setadjoin @ X1314 @ emptyset))))=>(![X881:$i, X882:$i, X883:$i]:(((in @ X883 @ X882)=>(in @ X883 @ (binunion @ X881 @ X882))))=>(![X884:$i, X885:$i, X886:$i, X887:$o]:(((in @ X886 @ (binunion @ X884 @ X885))=>(((in @ X886 @ X884)=>(X887))=>(((in @ X886 @ X885)=>(X887))=>(X887)))))=>(![X1310:$i, X1311:$i, X1312:$i]:(((in @ X1312 @ (binunion @ X1310 @ X1311))=>((in @ X1312 @ X1310)|(in @ X1312 @ X1311))))=>(![X1308:$i, X1309:$i]:((subset @ X1308 @ (binunion @ X1308 @ X1309)))=>(![X888:$i, X889:$i]:((subset @ X889 @ (binunion @ X888 @ X889)))=>(![X1305:$i, X1306:$i, X1307:$i]:(((in @ X1307 @ X1305)=>((in @ X1307 @ X1306)=>(in @ X1307 @ (binintersect @ X1305 @ X1306)))))=>(![X1302:$i, X1303:$i, X1304:$i]:(((subset @ X1304 @ X1302)=>((subset @ X1304 @ X1303)=>(subset @ X1304 @ (binintersect @ X1302 @ X1303)))))=>(![X890:$i, X891:$i, X892:$i]:(((in @ X892 @ (binintersect @ X890 @ X891))=>(in @ X892 @ X890)))=>(![X1300:$i, X1301:$i]:((subset @ (binintersect @ X1300 @ X1301) @ X1300))=>(![X893:$i, X894:$i]:(((subset @ X893 @ X894)=>((binintersect @ X893 @ X894)=(X893))))=>(![X895:$i, X896:$i]:((((binintersect @ X895 @ X896)=(X896))=>(subset @ X896 @ X895)))=>(![X897:$i, X898:$i, X899:$i]:(((in @ X899 @ (binintersect @ X897 @ X898))=>(in @ X899 @ X898)))=>(![X1297:$i, X1298:$i]:((~(?[X1299:$i]:(((in @ X1299 @ X1297)&(in @ X1299 @ X1298))))=>((binintersect @ X1297 @ X1298)=(emptyset))))=>(![X1295:$i, X1296:$i]:((subset @ (binintersect @ X1295 @ X1296) @ X1296))=>(![X1293:$i, X1294:$i]:(((subset @ X1294 @ X1293)=>((binintersect @ X1293 @ X1294)=(X1294))))=>(![X900:$i, X901:$i]:((((binintersect @ X900 @ X901)=(X900))=>(subset @ X900 @ X901)))=>(![X902:$i, X903:$i, X904:$i]:(((binintersect @ X902 @ (binunion @ X903 @ X904))=(binunion @ (binintersect @ X902 @ X903) @ (binintersect @ X902 @ X904))))=>(![X1290:$i, X1291:$i, X1292:$i]:(((in @ X1292 @ X1290)=>(~(in @ X1292 @ X1291)=>(in @ X1292 @ (setminus @ X1290 @ X1291)))))=>(![X905:$i, X906:$i, X907:$i]:(((in @ X907 @ (setminus @ X905 @ X906))=>(in @ X907 @ X905)))=>(![X1287:$i, X1288:$i, X1289:$i]:(((in @ X1289 @ (setminus @ X1287 @ X1288))=>~(in @ X1289 @ X1288)))=>(![X1285:$i, X1286:$i]:(((subset @ X1285 @ X1286)=>((setminus @ X1285 @ X1286)=(emptyset))))=>(![X1282:$i, X1283:$i, X1284:$i]:((~(in @ X1284 @ (setminus @ X1282 @ X1283))=>((in @ X1284 @ X1282)=>(in @ X1284 @ X1283))))=>(![X1279:$i, X1280:$i, X1281:$i]:((~(in @ X1281 @ (setminus @ X1279 @ X1280))=>(~(in @ X1281 @ X1280)=>~(in @ X1281 @ X1279))))=>(![X908:$i, X909:$i, X910:$i]:((~(in @ X910 @ X908)=>~(in @ X910 @ (setminus @ X908 @ X909))))=>(![X911:$i, X912:$i, X913:$i]:(((in @ X913 @ X912)=>~(in @ X913 @ (setminus @ X911 @ X912))))=>(![X914:$i, X915:$i]:((subset @ (setminus @ X914 @ X915) @ X914))=>(![X1277:$i, X1278:$i]:((((setminus @ X1277 @ X1278)=(emptyset))=>(subset @ X1277 @ X1278)))=>(![X916:$i, X917:$i, X918:$i]:(((in @ X918 @ (symdiff @ X916 @ X917))=>![X919:$o]:((((in @ X918 @ X916)=>(~(in @ X918 @ 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X1074)))=>![X1077:$i]:(((in @ X1077 @ X1073)=>((ap @ X1073 @ X1074 @ (lam @ X1073 @ X1074 @ X1075) @ X1077)=(X1075 @ X1077))))))=>(![X1029:$i, X1030:$i, X1031:$i]:(((in @ X1031 @ (funcSet @ X1029 @ X1030))=>((lam @ X1029 @ X1030 @ (ap @ X1029 @ X1030 @ X1031))=(X1031))))=>(![X1069:$i, X1070:$o, X1071:$i]:(((in @ X1071 @ X1069)=>![X1072:$i]:(((in @ X1072 @ X1069)=>(~(X1070)=>(in @ X1072 @ (dsetconstr @ X1069 @ (^[Z0:$i]:((((((X1070))&(((Z0)=(X1071)))))|(((~((X1070)))&(((Z0)=(X1072)))))))))))))))=>(![X1065:$i, X1066:$o, X1067:$i]:(((in @ X1067 @ X1065)=>![X1068:$i]:(((in @ X1068 @ X1065)=>(~(X1066)=>((dsetconstr @ X1065 @ (^[Z0:$i]:((((((X1066))&(((Z0)=(X1067)))))|(((~((X1066)))&(((Z0)=(X1068)))))))))=(setadjoin @ X1068 @ emptyset)))))))=>(![X1032:$i, X1033:$o, X1034:$i]:(((in @ X1034 @ X1032)=>![X1035:$i]:(((in @ X1035 @ X1032)=>((X1033)=>(in @ X1034 @ (dsetconstr @ X1032 @ (^[Z0:$i]:((((((X1033))&(((Z0)=(X1034)))))|(((~((X1033)))&(((Z0)=(X1035)))))))))))))))=>(![X1061:$i, X1062:$o, 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c_0_228]), binunionIL]), binunionLsub]), binunionE]), powersetI1]), subsetemptysetimpeq]), setextsub]), setadjoinSub]), subsetRefl]), notequalI2]), notequalI1]), subsetE]), setadjoinSub2]), subsetI2]), subsetTrans]), eqimpsubset1]), notsubsetI]), c_0_229]), subsetE2]), omega__Cong]), emptysetsubset]), setunion__Cong]), eqimpsubset2]), c_0_230]), inCongP]), subsetI1]), c_0_231]), subset2powerset]), c_0_232]), quantDeMorgan2]), quantDeMorgan1]), upairsetE]), singletonsswitch]), notinsingleton]), uniqinunit]), nonemptyImpWitness]), c_0_233]), setunionI]), c_0_234]), setadjoinOr]), setadjoinE]), binunionRsub]), emptyinunitempty]), binunionEcases]), emptyI]), binunionIR]), setext]), c_0_235]), notinemptyset]), powersetsubset]), c_0_236]), inPowerset]), c_0_237]), powersetE1]), c_0_238]), binintersectEL]), wellorderingAx]), foundationAx]), c_0_239]), omegaIndAx]), omega0Ax]), setunionAx]), setextAx]), setminusILneg]), setminusEL]), bs114d]), binintersectSubset1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), setminusIRneg]), setukpairIR]), setukpairIL]), symdiffIneg2]), symdiffIneg1]), symdiffI1]), symdiffE]), setminusLsub]), kpairiskpair]), singletonsuniq]), c_0_240]), setunionsingleton]), setunionsingleton1]), cartprodmempair]), ubforcartprodlem2]), singletoninpowerset]), setukpairinjL1]), ksndpairEq]), c_0_241]), setukpairinjR1]), setukpairinjL]), cartprodfstin]), kfstpairEq]), c_0_242]), kpairsurjEq]), c_0_243]), infuncsetfunc]), c_0_244]), c_0_245]), c_0_246]), c_0_247]), cartprodmempaircEq]), c_0_248]), c_0_249]), c_0_250]), c_0_251]), ap2apEq1]), funcext]), funcGraphProp4]), brelnall1]), ifp]), c_0_252]), c_0_253]), iftrue]), binintersectT_lem]), iftrueorfalse]), iffalse]), theeq]), c_0_254]), eqbreln]), funcext2]), ap2apEq2]), c_0_255]), c_0_256]), c_0_257]), c_0_258]), subbreln]), c_0_259]), brelnall2]), c_0_260]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcinfuncset]), c_0_261]), c_0_262]), c_0_263]), c_0_264]), c_0_265]), app]), ap2p]), cartprodpairsurjEq]), setukpairinjR2]), setukpairinjR]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodfstpairEq]), cartprodsndpairEq]), upairequniteq]), c_0_266]), c_0_267]), c_0_268]), theprop]), setukpairinjL2]), setukpairinjR11]), setukpairinjR12]), setunionsingleton2]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), setunionE2]), upairset2E]), setminusELneg]), setminusSubset1]), symdiffI2]), secondinupair]), kpairp]), singletonsubset]), singletoninpowunion]), setminusERneg]), binintersectLsub]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), setminusI]), setminusER]), setminusSubset2]), binintersectSubset5]), binintersectI]), upairset2IR]), c_0_269]), c_0_270]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_271]), in__Cong]), c_0_272]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), vacuousDall]), c_0_273]), upairsetIR]), upairsetIL]), eqinunit]), subPowSU]), setunionE]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), setadjoinIR]), setadjoinIL]), nonemptyI1]), c_0_274]), nonemptyE1]), c_0_275]), noeltsimpempty]), c_0_276]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_277]), c_0_278]), omegaSAx]), powersetAx]), setadjoinAx]), emptysetAx])])]), c_0_279])). 554.07/73.78 thf(c_0_281, negated_conjecture, ![X1448:$i, X1449:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1461:$i, X1462:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1470:$i, X1471:$i > $i > $o, X1472:$i, X1475:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1482:$i, X1483:$i > $o, X1484:$i, X1485:$i > $o, X1486:$i, X1487:$i, X1488:$i > $o, X1489:$i, X1490:$i, X1491:$i > $o, X1492:$i, X1493:$i > $o, X1495:$i, X1496:$o, X1497:$i, X1498:$i, X1499:$o, X1500:$i, X1501:$i, X1502:$i > $o, X1504:$i, X1505:$i, X1508:$i, X1510:$i, X1512:$i, X1513:$i > $o, X1514:$i, X1515:$i, X1517:$i, X1518:$i > $o, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$o, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$o, X1550:$i, X1551:$i, X1552:$i > $o, X1554:$i, X1555:$i, X1556:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i > $o, X1575:$i, X1576:$i > $o, X1577:$i, X1578:$i, X1579:$i > $o, X1580:$i, X1582:$i, X1583:$i > $o, X1585:$i, X1586:$i, X1587:$i > $o, X1589:$i, X1590:$i, X1591:$i > $o, X1592:$i, X1594:$o, X1595:$i, X1596:$i > $o, X1598:$i, X1599:$i, X1600:$i > $o, X1601:$i, X1603:$i > $o, X1604:$i, X1606:$i > $o, X1607:$i, X1610:$i > $o, X1611:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i > $o, X1622:$i, X1623:$i, X1624:$i > $o, X1625:$i > $o, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i > $o, X1637:$i, X1638:$i, X1639:$i > $o, X1640:$i > $o, X1643:$i, X1644:$i, X1645:$i > $o, X1646:$i > $o, X1649:$i, X1650:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i > $o, X1697:$i, X1698:$i > $o, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$o, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$o, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i > $o, X1853:$i, X1854:$i, X1855:$i > $o, X1857:$i, X1858:$i > $o, X1859:$i, X1861:$i, X1862:$i > $o, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i > $i > $o, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i > $i > $o, X1943:$i, X1944:$i, X1945:$i > $i > $o, X1946:$i, X1947:$i, X1948:$i > $i > $o, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i > $i > $o, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i > $i > $o, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i > $i > $o, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i > $i, X1992:$i, X1993:$i, X1994:$i > $i, X1996:$i, X1997:$i, X1998:$i > $i, X2000:$i, X2001:$i, X2002:$i, X2003:$i > $o, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i > $o, X2013:$i, X2014:$i, X2015:$i > $o, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i > $i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i > $i, X2087:$i, X2088:$i, X2089:$i > $i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$o, X2097:$i, X2098:$i, X2099:$i, X2100:$o, X2101:$i, X2102:$i, X2103:$i, X2104:$o, X2105:$i, X2106:$i, X2107:$i, X2108:$o, X2109:$i, X2110:$i, X2111:$i, X2112:$o, X2113:$i, X2114:$i, X2115:$i, X2116:$o, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$o, X2123:$i, X2124:$i, X2125:$i, X2126:$o, X2127:$i, X2128:$i, X2129:$i, X2130:$o, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i]:((((~(in @ (esk1_2 @ X1448 @ X1449) @ 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X1985 @ X1986 @ X1987)|(in @ X1987 @ (funcSet @ X1985 @ X1986)))&((((in @ (esk48_3 @ X1988 @ X1989 @ X1990) @ X1988)|(func @ X1988 @ X1989 @ (dpsetconstr @ X1988 @ X1989 @ (^[Z0:$i]:($eq @ (X1990 @ Z0))))))&(~(in @ (X1990 @ (esk48_3 @ X1988 @ X1989 @ X1990)) @ X1989)|(func @ X1988 @ X1989 @ (dpsetconstr @ X1988 @ X1989 @ (^[Z0:$i]:($eq @ (X1990 @ Z0)))))))&((((in @ (esk49_3 @ X1992 @ X1993 @ X1994) @ X1992)|(func @ X1992 @ X1993 @ (lam @ X1992 @ X1993 @ X1994)))&(~(in @ (X1994 @ (esk49_3 @ X1992 @ X1993 @ X1994)) @ X1993)|(func @ X1992 @ X1993 @ (lam @ X1992 @ X1993 @ X1994))))&((((in @ (esk50_3 @ X1996 @ X1997 @ X1998) @ X1996)|(in @ (lam @ X1996 @ X1997 @ X1998) @ (funcSet @ X1996 @ X1997)))&(~(in @ (X1998 @ (esk50_3 @ X1996 @ X1997 @ X1998)) @ X1997)|(in @ (lam @ X1996 @ X1997 @ X1998) @ (funcSet @ X1996 @ X1997))))&((((in @ (esk51_4 @ X2000 @ X2001 @ X2002 @ X2003) @ X2000)|(~(in @ X2006 @ X2002)|(X2003 @ X2006))|~(breln @ X2000 @ X2001 @ X2002))&(((in @ (esk52_4 @ X2000 @ X2001 @ X2002 @ X2003) @ X2001)|(~(in @ X2006 @ X2002)|(X2003 @ X2006))|~(breln @ X2000 @ X2001 @ X2002))&(((in @ (kpair @ (esk51_4 @ X2000 @ X2001 @ X2002 @ X2003) @ (esk52_4 @ X2000 @ X2001 @ X2002 @ X2003)) @ X2002)|(~(in @ X2006 @ X2002)|(X2003 @ X2006))|~(breln @ X2000 @ X2001 @ X2002))&(~(X2003 @ (kpair @ (esk51_4 @ X2000 @ X2001 @ X2002 @ X2003) @ (esk52_4 @ X2000 @ X2001 @ X2002 @ X2003)))|(~(in @ X2006 @ X2002)|(X2003 @ X2006))|~(breln @ X2000 @ X2001 @ X2002)))))&((((in @ (esk53_4 @ X2007 @ X2008 @ X2009 @ X2010) @ X2007)|(~(in @ X2013 @ X2009)|(X2010 @ X2013))|~(breln @ X2007 @ X2008 @ X2009))&(((in @ (esk54_4 @ X2007 @ X2008 @ X2009 @ X2010) @ X2008)|(~(in @ X2013 @ X2009)|(X2010 @ X2013))|~(breln @ X2007 @ X2008 @ X2009))&(((in @ (kpair @ (esk53_4 @ X2007 @ X2008 @ X2009 @ X2010) @ (esk54_4 @ X2007 @ X2008 @ X2009 @ X2010)) @ X2009)|(~(in @ X2013 @ X2009)|(X2010 @ X2013))|~(breln @ X2007 @ X2008 @ X2009))&(~(X2010 @ (kpair @ (esk53_4 @ X2007 @ X2008 @ X2009 @ X2010) @ (esk54_4 @ X2007 @ X2008 @ X2009 @ X2010)))|(~(in @ X2013 @ X2009)|(X2010 @ X2013))|~(breln @ X2007 @ X2008 @ X2009)))))&((~(ex1 @ X2014 @ X2015)|(~(in @ X2016 @ X2014)|(~(in @ X2017 @ X2014)|(~(X2015 @ X2016)|(~(X2015 @ X2017)|((X2016)=(X2017)))))))&((~(func @ X2018 @ X2019 @ X2020)|(~(in @ X2021 @ X2018)|(in @ (kpair @ X2021 @ (ap @ X2018 @ X2019 @ X2020 @ X2021)) @ X2020)))&((~(in @ X2024 @ (funcSet @ X2022 @ X2023))|(~(in @ X2025 @ X2022)|(in @ (kpair @ X2025 @ (ap @ X2022 @ X2023 @ X2024 @ X2025)) @ X2024)))&((~(func @ X2026 @ X2027 @ X2028)|(~(in @ X2029 @ X2026)|(~(in @ X2030 @ X2027)|(~(in @ (kpair @ X2029 @ X2030) @ X2028)|((ap @ X2026 @ X2027 @ X2028 @ X2029)=(X2030))))))&((((in @ (esk55_4 @ X2031 @ X2032 @ X2033 @ X2034) @ X2031)|(~(in @ X2036 @ X2031)|(~(in @ X2037 @ X2032)|(~(in @ (kpair @ X2036 @ X2037) @ X2034)|(in @ (kpair @ X2036 @ X2037) @ X2033))))|~(func @ X2031 @ X2032 @ X2034)|~(func @ X2031 @ X2032 @ X2033))&(((ap @ X2031 @ X2032 @ X2033 @ (esk55_4 @ X2031 @ X2032 @ X2033 @ X2034))!=(ap @ X2031 @ X2032 @ X2034 @ (esk55_4 @ X2031 @ X2032 @ X2033 @ X2034)))|(~(in @ X2036 @ X2031)|(~(in @ X2037 @ X2032)|(~(in @ (kpair @ X2036 @ X2037) @ X2034)|(in @ (kpair @ X2036 @ X2037) @ X2033))))|~(func @ X2031 @ X2032 @ X2034)|~(func @ X2031 @ X2032 @ X2033)))&((~(in @ X2040 @ (funcSet @ X2038 @ X2039))|(~(in @ X2041 @ X2038)|(~(in @ X2042 @ X2039)|(~(in @ (kpair @ X2041 @ X2042) @ X2040)|((ap @ X2038 @ X2039 @ X2040 @ X2041)=(X2042))))))&((((in @ (esk56_4 @ X2043 @ X2044 @ X2045 @ X2046) @ X2043)|(subset @ X2045 @ X2046)|~(breln @ X2043 @ X2044 @ X2046)|~(breln @ X2043 @ X2044 @ X2045))&(((in @ (esk57_4 @ X2043 @ X2044 @ X2045 @ X2046) @ X2044)|(subset @ X2045 @ X2046)|~(breln @ X2043 @ X2044 @ X2046)|~(breln @ X2043 @ X2044 @ X2045))&(((in @ (kpair @ (esk56_4 @ X2043 @ X2044 @ X2045 @ X2046) @ (esk57_4 @ X2043 @ X2044 @ X2045 @ X2046)) @ X2045)|(subset @ X2045 @ X2046)|~(breln @ X2043 @ X2044 @ X2046)|~(breln @ X2043 @ X2044 @ X2045))&(~(in @ (kpair @ (esk56_4 @ X2043 @ X2044 @ X2045 @ X2046) @ (esk57_4 @ X2043 @ X2044 @ X2045 @ X2046)) @ X2046)|(subset @ X2045 @ X2046)|~(breln @ X2043 @ X2044 @ X2046)|~(breln @ X2043 @ X2044 @ X2045)))))&(((((in @ (esk60_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2049)|((X2051)=(X2052))|(in @ (esk58_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2049)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051))&(((in @ (esk61_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2050)|((X2051)=(X2052))|(in @ (esk58_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2049)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051))&(((in @ (kpair @ (esk60_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk61_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2052)|((X2051)=(X2052))|(in @ (esk58_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2049)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051))&(~(in @ (kpair @ (esk60_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk61_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2051)|((X2051)=(X2052))|(in @ (esk58_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2049)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051)))))&((((in @ (esk60_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2049)|((X2051)=(X2052))|(in @ (esk59_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2050)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051))&(((in @ (esk61_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2050)|((X2051)=(X2052))|(in @ (esk59_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2050)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051))&(((in @ (kpair @ (esk60_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk61_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2052)|((X2051)=(X2052))|(in @ (esk59_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2050)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051))&(~(in @ (kpair @ (esk60_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk61_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2051)|((X2051)=(X2052))|(in @ (esk59_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2050)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051)))))&((((in @ (esk60_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2049)|((X2051)=(X2052))|(in @ (kpair @ (esk58_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk59_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2051)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051))&(((in @ (esk61_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2050)|((X2051)=(X2052))|(in @ (kpair @ (esk58_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk59_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2051)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051))&(((in @ (kpair @ (esk60_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk61_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2052)|((X2051)=(X2052))|(in @ (kpair @ (esk58_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk59_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2051)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051))&(~(in @ (kpair @ (esk60_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk61_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2051)|((X2051)=(X2052))|(in @ (kpair @ (esk58_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk59_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2051)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051)))))&(((in @ (esk60_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2049)|((X2051)=(X2052))|~(in @ (kpair @ (esk58_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk59_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2052)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051))&(((in @ (esk61_4 @ X2049 @ X2050 @ X2051 @ X2052) @ X2050)|((X2051)=(X2052))|~(in @ (kpair @ (esk58_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk59_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2052)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051))&(((in @ (kpair @ (esk60_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk61_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2052)|((X2051)=(X2052))|~(in @ (kpair @ (esk58_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk59_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2052)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051))&(~(in @ (kpair @ (esk60_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk61_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2051)|((X2051)=(X2052))|~(in @ (kpair @ (esk58_4 @ X2049 @ X2050 @ X2051 @ X2052) @ (esk59_4 @ X2049 @ X2050 @ X2051 @ X2052)) @ X2052)|~(breln @ X2049 @ X2050 @ X2052)|~(breln @ X2049 @ X2050 @ X2051))))))))&((((in @ (esk62_4 @ X2057 @ X2058 @ X2059 @ X2060) @ X2057)|((X2059)=(X2060))|~(func @ X2057 @ X2058 @ X2060)|~(func @ X2057 @ X2058 @ X2059))&(((ap @ X2057 @ X2058 @ X2059 @ (esk62_4 @ X2057 @ X2058 @ X2059 @ X2060))!=(ap @ X2057 @ X2058 @ X2060 @ (esk62_4 @ X2057 @ X2058 @ X2059 @ X2060)))|((X2059)=(X2060))|~(func @ X2057 @ X2058 @ X2060)|~(func @ X2057 @ X2058 @ X2059)))&((((in @ (esk63_4 @ X2062 @ X2063 @ X2064 @ X2065) @ X2062)|((X2064)=(X2065))|~(in @ X2065 @ (funcSet @ X2062 @ X2063))|~(in @ X2064 @ (funcSet @ X2062 @ X2063)))&(((ap @ X2062 @ X2063 @ X2064 @ (esk63_4 @ X2062 @ X2063 @ X2064 @ X2065))!=(ap @ X2062 @ X2063 @ X2065 @ (esk63_4 @ X2062 @ X2063 @ X2064 @ X2065)))|((X2064)=(X2065))|~(in @ X2065 @ (funcSet @ X2062 @ X2063))|~(in @ X2064 @ (funcSet @ X2062 @ X2063))))&((~(in @ X2069 @ (funcSet @ X2067 @ X2068))|(~(in @ X2070 @ X2067)|((ap @ X2067 @ X2068 @ X2069 @ X2070)=(ap @ X2067 @ X2068 @ X2069 @ X2070))))&((~(func @ X2071 @ X2072 @ X2073)|(~(in @ X2074 @ X2071)|((ap @ X2071 @ X2072 @ X2073 @ X2074)=(ap @ X2071 @ X2072 @ X2073 @ X2074))))&((((in @ (esk64_3 @ X2075 @ X2076 @ X2077) @ X2075)|(~(in @ X2079 @ X2075)|((ap @ X2075 @ X2076 @ (lam @ X2075 @ X2076 @ X2077) @ X2079)=(X2077 @ X2079))))&(~(in @ (X2077 @ (esk64_3 @ X2075 @ X2076 @ X2077)) @ X2076)|(~(in @ X2079 @ X2075)|((ap @ X2075 @ X2076 @ (lam @ X2075 @ X2076 @ X2077) @ X2079)=(X2077 @ X2079)))))&((~(func @ X2080 @ X2081 @ X2082)|((lam @ X2080 @ X2081 @ (ap @ X2080 @ X2081 @ X2082))=(X2082)))&((((in @ (esk65_3 @ X2083 @ X2084 @ X2085) @ X2083)|((lam @ X2083 @ X2084 @ X2085)=(lam @ X2083 @ X2084 @ X2085)))&(~(in @ (X2085 @ (esk65_3 @ X2083 @ X2084 @ X2085)) @ X2084)|((lam @ X2083 @ X2084 @ X2085)=(lam @ X2083 @ X2084 @ X2085))))&((((in @ (esk66_3 @ X2087 @ X2088 @ X2089) @ X2087)|(~(in @ X2091 @ X2087)|((ap @ X2087 @ X2088 @ (lam @ X2087 @ X2088 @ X2089) @ X2091)=(X2089 @ X2091))))&(~(in @ (X2089 @ (esk66_3 @ X2087 @ X2088 @ X2089)) @ X2088)|(~(in @ X2091 @ X2087)|((ap @ X2087 @ X2088 @ (lam @ X2087 @ X2088 @ X2089) @ X2091)=(X2089 @ X2091)))))&((~(in @ X2094 @ (funcSet @ X2092 @ X2093))|((lam @ X2092 @ X2093 @ (ap @ X2092 @ X2093 @ X2094))=(X2094)))&((~(in @ X2097 @ X2095)|(~(in @ X2098 @ X2095)|((X2096)|(in @ X2098 @ (dsetconstr @ X2095 @ (^[Z0:$i]:((((((X2096))&(((Z0)=(X2097)))))|(((~((X2096)))&(((Z0)=(X2098)))))))))))))&((~(in @ X2101 @ X2099)|(~(in @ X2102 @ X2099)|((X2100)|((dsetconstr @ X2099 @ (^[Z0:$i]:((((((X2100))&(((Z0)=(X2101)))))|(((~((X2100)))&(((Z0)=(X2102)))))))))=(setadjoin @ X2102 @ emptyset)))))&((~(in @ X2105 @ X2103)|(~(in @ X2106 @ X2103)|(~(X2104)|(in @ X2105 @ (dsetconstr @ X2103 @ (^[Z0:$i]:((((((X2104))&(((Z0)=(X2105)))))|(((~((X2104)))&(((Z0)=(X2106)))))))))))))&((~(in @ X2109 @ X2107)|(~(in @ X2110 @ X2107)|(~(X2108)|((dsetconstr @ X2107 @ (^[Z0:$i]:((((((X2108))&(((Z0)=(X2109)))))|(((~((X2108)))&(((Z0)=(X2110)))))))))=(setadjoin @ X2109 @ emptyset)))))&((~(in @ X2113 @ X2111)|(~(in @ X2114 @ X2111)|(singleton @ (dsetconstr @ X2111 @ (^[Z0:$i]:((((((X2112))&(((Z0)=(X2113)))))|(((~((X2112)))&(((Z0)=(X2114))))))))))))&((~(in @ X2117 @ X2115)|(~(in @ X2118 @ X2115)|(in @ (if @ X2115 @ ((X2116)) @ X2117 @ X2118) @ X2115)))&((~(singleton @ X2119)|(~(in @ X2120 @ X2119)|((setunion @ X2119)=(X2120))))&((~(in @ X2123 @ X2121)|(~(in @ X2124 @ X2121)|(~(X2122)|((if @ X2121 @ ((X2122)) @ X2123 @ X2124)=(X2123)))))&((~(in @ X2127 @ X2125)|(~(in @ X2128 @ X2125)|((X2126)|((if @ X2125 @ ((X2126)) @ X2127 @ X2128)=(X2128)))))&((~(in @ X2131 @ X2129)|(~(in @ X2132 @ X2129)|(in @ (if @ X2129 @ ((X2130)) @ X2131 @ X2132) @ (setadjoin @ X2131 @ (setadjoin @ X2132 @ emptyset)))))&((~(in @ X2134 @ (powerset @ X2133))|(~(in @ X2135 @ (powerset @ X2133))|(in @ (binintersect @ X2134 @ X2135) @ (powerset @ X2133))))&((in @ esk68_0 @ (powerset @ esk67_0))&((in @ esk69_0 @ (powerset @ esk67_0))&~(in @ (binunion @ esk68_0 @ esk69_0) @ (powerset @ esk67_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_280])])])])])])])). 554.07/73.78 thf(c_0_282, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X2 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_281])). 554.07/73.78 thf(c_0_283, negated_conjecture, (in @ esk69_0 @ (powerset @ esk67_0)), inference(split_conjunct,[status(thm)],[c_0_281])). 554.07/73.78 thf(c_0_284, negated_conjecture, ![X2:$i, X3:$i]:((((binintersect @ X3 @ X2)=(X2))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_281])). 554.07/73.78 thf(c_0_285, negated_conjecture, (subset @ esk69_0 @ esk67_0), inference(spm,[status(thm)],[c_0_282, c_0_283])). 554.07/73.78 thf(c_0_286, negated_conjecture, (in @ esk68_0 @ (powerset @ esk67_0)), inference(split_conjunct,[status(thm)],[c_0_281])). 554.07/73.78 thf(c_0_287, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((binintersect @ X2 @ (binunion @ X3 @ X4))=(binunion @ (binintersect @ X2 @ X3) @ (binintersect @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_281])). 554.07/73.78 thf(c_0_288, negated_conjecture, ((binintersect @ esk67_0 @ esk69_0)=(esk69_0)), inference(spm,[status(thm)],[c_0_284, c_0_285])). 554.07/73.78 thf(c_0_289, negated_conjecture, (subset @ esk68_0 @ esk67_0), inference(spm,[status(thm)],[c_0_282, c_0_286])). 554.07/73.78 thf(c_0_290, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_281])). 554.07/73.78 thf(c_0_291, negated_conjecture, ![X3:$i, X2:$i]:((subset @ (binintersect @ X2 @ X3) @ X2)), inference(split_conjunct,[status(thm)],[c_0_281])). 554.07/73.78 thf(c_0_292, negated_conjecture, ![X2:$i]:(((binunion @ (binintersect @ esk67_0 @ X2) @ esk69_0)=(binintersect @ esk67_0 @ (binunion @ X2 @ esk69_0)))), inference(spm,[status(thm)],[c_0_287, c_0_288])). 554.07/73.78 thf(c_0_293, negated_conjecture, ((binintersect @ esk67_0 @ esk68_0)=(esk68_0)), inference(spm,[status(thm)],[c_0_284, c_0_289])). 554.07/73.78 thf(c_0_294, negated_conjecture, ![X3:$i, X2:$i]:((in @ (binintersect @ X2 @ X3) @ (powerset @ X2))), inference(spm,[status(thm)],[c_0_290, c_0_291])). 554.07/73.78 thf(c_0_295, negated_conjecture, ((binintersect @ esk67_0 @ (binunion @ esk68_0 @ esk69_0))=(binunion @ esk68_0 @ esk69_0)), inference(spm,[status(thm)],[c_0_292, c_0_293])). 554.07/73.78 thf(c_0_296, negated_conjecture, ~((in @ (binunion @ esk68_0 @ esk69_0) @ (powerset @ esk67_0))), inference(split_conjunct,[status(thm)],[c_0_281])). 554.07/73.78 thf(c_0_297, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_294, c_0_295]), c_0_296]), ['proof']). 554.07/73.78 % SZS output end CNFRefutation 554.07/73.78 % Parsed axioms : 497 554.07/73.78 % Removed by relevancy pruning/SinE : 270 554.07/73.78 % Initial clauses : 375 554.07/73.78 % Removed in clause preprocessing : 34 554.07/73.78 % Initial clauses in saturation : 341 554.07/73.78 % Processed clauses : 4492 554.07/73.78 % ...of these trivial : 130 554.07/73.78 % ...subsumed : 2230 554.07/73.78 % ...remaining for further processing : 2132 554.07/73.78 % Other redundant clauses eliminated : 45 554.07/73.78 % Clauses deleted for lack of memory : 0 554.07/73.78 % Backward-subsumed : 43 554.07/73.78 % Backward-rewritten : 13 554.07/73.78 % Generated clauses : 29474 554.07/73.78 % ...of the previous two non-redundant : 25956 554.07/73.78 % ...aggressively subsumed : 0 554.07/73.78 % Contextual simplify-reflections : 2 554.07/73.78 % Paramodulations : 29342 554.07/73.78 % Factorizations : 2 554.07/73.78 % NegExts : 2 554.07/73.78 % Equation resolutions : 54 554.07/73.78 % Disequality decompositions : 0 554.07/73.78 % Total rewrite steps : 4067 554.07/73.78 % ...of those cached : 3262 554.07/73.78 % Propositional unsat checks : 0 554.07/73.78 % Propositional check models : 0 554.07/73.78 % Propositional check unsatisfiable : 0 554.07/73.78 % Propositional clauses : 0 554.07/73.78 % Propositional clauses after purity: 0 554.07/73.78 % Propositional unsat core size : 0 554.07/73.78 % Propositional preprocessing time : 0.000 554.07/73.78 % Propositional encoding time : 0.000 554.07/73.78 % Propositional solver time : 0.000 554.07/73.78 % Success case prop preproc time : 0.000 554.07/73.78 % Success case prop encoding time : 0.000 554.07/73.78 % Success case prop solver time : 0.000 554.07/73.78 % Current number of processed clauses : 1756 554.07/73.78 % Positive orientable unit clauses : 374 554.07/73.78 % Positive unorientable unit clauses: 0 554.07/73.78 % Negative unit clauses : 233 554.07/73.78 % Non-unit-clauses : 1149 554.07/73.78 % Current number of unprocessed clauses: 22055 554.07/73.78 % ...number of literals in the above : 51856 554.07/73.78 % Current number of archived formulas : 0 554.07/73.78 % Current number of archived clauses : 360 554.07/73.78 % Clause-clause subsumption calls (NU) : 162593 554.07/73.78 % Rec. Clause-clause subsumption calls : 121654 554.07/73.78 % Non-unit clause-clause subsumptions : 1068 554.07/73.78 % Unit Clause-clause subsumption calls : 54923 554.07/73.78 % Rewrite failures with RHS unbound : 0 554.07/73.78 % BW rewrite match attempts : 214 554.07/73.78 % BW rewrite match successes : 15 554.07/73.78 % Condensation attempts : 4492 554.07/73.78 % Condensation successes : 5 554.07/73.78 % Termbank termtop insertions : 484539 554.07/73.78 % Search garbage collected termcells : 22100 554.07/73.78 554.07/73.78 % ------------------------------------------------- 554.07/73.78 % User time : 68.891 s 554.07/73.78 % System time : 2.223 s 554.07/73.78 % Total time : 71.114 s 554.07/73.78 % Maximum resident set size: 9032 pages 554.07/73.78 554.07/73.78 % ------------------------------------------------- 554.07/73.78 % User time : 68.908 s 554.07/73.78 % System time : 2.234 s 554.07/73.78 % Total time : 71.142 s 554.07/73.78 % Maximum resident set size: 5632 pages 554.07/73.78 % E exiting 554.07/73.78 EOF