0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.12/0.38 % Computer : n022.cluster.edu 0.12/0.38 % Model : x86_64 x86_64 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.38 % Memory : 8046.5625MB 0.12/0.38 % OS : Linux 6.8.0-71-generic 0.12/0.38 % CPULimit : 1440 0.12/0.38 % WCLimit : 180 0.12/0.38 % DateTime : Mon Jul 27 13:14:43 UTC 2026 0.12/0.38 % CPUTime : 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.12/0.43 Running higher-order theorem proving 0.20/0.47 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.xAI4abZFRc/E---3.1_941405.p 237.80/32.54 % Version: 3.5.1-ho 237.80/32.54 % Preprocessing class: HSLMSLSSLLLCHFA. 237.80/32.54 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 237.80/32.54 % Starting ehoh_best5 with 180s (1) cores 237.80/32.54 % Starting almost_fo_3_lam with 180s (1) cores 237.80/32.54 % Starting new_bool_5 with 180s (1) cores 237.80/32.54 % Starting pre_casc_3 with 180s (1) cores 237.80/32.54 % Starting ho_unfolding_8 with 180s (1) cores 237.80/32.54 % Starting new_ho_10_cnf2 with 180s (1) cores 237.80/32.54 % Starting new_bool_3 with 180s (1) cores 237.80/32.54 % Starting new_ho_5 with 180s (1) cores 237.80/32.54 % new_bool_5 with pid 941420 completed with status 0 237.80/32.54 % Result found by new_bool_5 237.80/32.54 % Preprocessing class: HSLMSLSSLLLCHFA. 237.80/32.54 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 237.80/32.54 % Starting ehoh_best5 with 180s (1) cores 237.80/32.54 % Starting almost_fo_3_lam with 180s (1) cores 237.80/32.54 % Starting new_bool_5 with 180s (1) cores 237.80/32.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)) 237.80/32.54 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 237.80/32.54 % Search class: HGHSM-FSLM31-MHFMMSBN 237.80/32.54 % Scheduled 7 strats onto 1 cores with 180 seconds (180 total) 237.80/32.54 % Starting SubtermCWHack with 17s (1) cores 237.80/32.54 % SubtermCWHack with pid 941433 completed with status 8 237.80/32.54 % Starting new_bool_5 with 19s (1) cores 237.80/32.54 % new_bool_5 with pid 941836 completed with status 0 237.80/32.54 % Result found by new_bool_5 237.80/32.54 % Preprocessing class: HSLMSLSSLLLCHFA. 237.80/32.54 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 237.80/32.54 % Starting ehoh_best5 with 180s (1) cores 237.80/32.54 % Starting almost_fo_3_lam with 180s (1) cores 237.80/32.54 % Starting new_bool_5 with 180s (1) cores 237.80/32.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)) 237.80/32.54 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 237.80/32.54 % Search class: HGHSM-FSLM31-MHFMMSBN 237.80/32.54 % Scheduled 7 strats onto 1 cores with 180 seconds (180 total) 237.80/32.54 % Starting SubtermCWHack with 17s (1) cores 237.80/32.54 % SubtermCWHack with pid 941433 completed with status 8 237.80/32.54 % Starting new_bool_5 with 19s (1) cores 237.80/32.54 % Preprocessing time : 0.005 s 237.80/32.54 % Presaturation interreduction done 237.80/32.54 237.80/32.54 % Proof found! 237.80/32.54 % SZS status Theorem 237.80/32.54 % SZS output start CNFRefutation 237.80/32.54 thf(decl_23, type, in: $i > $i > $o). 237.80/32.54 thf(decl_24, type, exu: ($i > $o) > $o). 237.80/32.54 thf(decl_25, type, setextAx: $o). 237.80/32.54 thf(decl_26, type, emptyset: $i). 237.80/32.54 thf(decl_27, type, emptysetAx: $o). 237.80/32.54 thf(decl_28, type, setadjoin: $i > $i > $i). 237.80/32.54 thf(decl_29, type, setadjoinAx: $o). 237.80/32.54 thf(decl_30, type, powerset: $i > $i). 237.80/32.54 thf(decl_31, type, powersetAx: $o). 237.80/32.54 thf(decl_32, type, setunion: $i > $i). 237.80/32.54 thf(decl_33, type, setunionAx: $o). 237.80/32.54 thf(decl_34, type, omega: $i). 237.80/32.54 thf(decl_35, type, omega0Ax: $o). 237.80/32.54 thf(decl_36, type, omegaSAx: $o). 237.80/32.54 thf(decl_37, type, omegaIndAx: $o). 237.80/32.54 thf(decl_38, type, replAx: $o). 237.80/32.54 thf(decl_39, type, foundationAx: $o). 237.80/32.54 thf(decl_40, type, wellorderingAx: $o). 237.80/32.54 thf(decl_41, type, descr: ($i > $o) > $i). 237.80/32.54 thf(decl_42, type, descrp: $o). 237.80/32.54 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 237.80/32.54 thf(decl_44, type, dsetconstrI: $o). 237.80/32.54 thf(decl_45, type, dsetconstrEL: $o). 237.80/32.54 thf(decl_46, type, dsetconstrER: $o). 237.80/32.54 thf(decl_47, type, exuE1: $o). 237.80/32.54 thf(decl_48, type, prop2set: $o > $i). 237.80/32.54 thf(decl_49, type, prop2setE: $o). 237.80/32.54 thf(decl_50, type, emptysetE: $o). 237.80/32.54 thf(decl_51, type, emptysetimpfalse: $o). 237.80/32.54 thf(decl_52, type, notinemptyset: $o). 237.80/32.54 thf(decl_53, type, exuE3e: $o). 237.80/32.54 thf(decl_54, type, setext: $o). 237.80/32.54 thf(decl_55, type, emptyI: $o). 237.80/32.54 thf(decl_56, type, noeltsimpempty: $o). 237.80/32.54 thf(decl_57, type, setbeta: $o). 237.80/32.54 thf(decl_58, type, nonempty: $i > $o). 237.80/32.54 thf(decl_59, type, nonemptyE1: $o). 237.80/32.54 thf(decl_60, type, nonemptyI: $o). 237.80/32.54 thf(decl_61, type, nonemptyI1: $o). 237.80/32.54 thf(decl_62, type, setadjoinIL: $o). 237.80/32.54 thf(decl_63, type, emptyinunitempty: $o). 237.80/32.54 thf(decl_64, type, setadjoinIR: $o). 237.80/32.54 thf(decl_65, type, setadjoinE: $o). 237.80/32.54 thf(decl_66, type, setadjoinOr: $o). 237.80/32.54 thf(decl_67, type, setoftrueEq: $o). 237.80/32.54 thf(decl_68, type, powersetI: $o). 237.80/32.54 thf(decl_69, type, emptyinPowerset: $o). 237.80/32.54 thf(decl_70, type, emptyInPowerset: $o). 237.80/32.54 thf(decl_71, type, powersetE: $o). 237.80/32.54 thf(decl_72, type, setunionI: $o). 237.80/32.54 thf(decl_73, type, setunionE: $o). 237.80/32.54 thf(decl_74, type, subPowSU: $o). 237.80/32.54 thf(decl_75, type, exuE2: $o). 237.80/32.54 thf(decl_76, type, nonemptyImpWitness: $o). 237.80/32.54 thf(decl_77, type, uniqinunit: $o). 237.80/32.54 thf(decl_78, type, notinsingleton: $o). 237.80/32.54 thf(decl_79, type, eqinunit: $o). 237.80/32.54 thf(decl_80, type, singletonsswitch: $o). 237.80/32.54 thf(decl_81, type, upairsetE: $o). 237.80/32.54 thf(decl_82, type, upairsetIL: $o). 237.80/32.54 thf(decl_83, type, upairsetIR: $o). 237.80/32.54 thf(decl_84, type, emptyE1: $o). 237.80/32.54 thf(decl_85, type, vacuousDall: $o). 237.80/32.54 thf(decl_86, type, quantDeMorgan1: $o). 237.80/32.54 thf(decl_87, type, quantDeMorgan2: $o). 237.80/32.54 thf(decl_88, type, quantDeMorgan3: $o). 237.80/32.54 thf(decl_89, type, quantDeMorgan4: $o). 237.80/32.54 thf(decl_90, type, prop2setI: $o). 237.80/32.54 thf(decl_92, type, prop2set2propI: $o). 237.80/32.54 thf(decl_93, type, notdexE: $o). 237.80/32.54 thf(decl_94, type, notdallE: $o). 237.80/32.54 thf(decl_95, type, exuI1: $o). 237.80/32.54 thf(decl_96, type, exuI3: $o). 237.80/32.54 thf(decl_97, type, exuI2: $o). 237.80/32.54 thf(decl_98, type, inCongP: $o). 237.80/32.54 thf(decl_99, type, in__Cong: $o). 237.80/32.54 thf(decl_100, type, exuE3u: $o). 237.80/32.54 thf(decl_101, type, exu__Cong: $o). 237.80/32.54 thf(decl_102, type, emptyset__Cong: $o). 237.80/32.54 thf(decl_103, type, setadjoin__Cong: $o). 237.80/32.54 thf(decl_104, type, powerset__Cong: $o). 237.80/32.54 thf(decl_105, type, setunion__Cong: $o). 237.80/32.54 thf(decl_106, type, omega__Cong: $o). 237.80/32.54 thf(decl_107, type, exuEu: $o). 237.80/32.54 thf(decl_108, type, descr__Cong: $o). 237.80/32.54 thf(decl_109, type, dsetconstr__Cong: $o). 237.80/32.54 thf(decl_110, type, subset: $i > $i > $o). 237.80/32.54 thf(decl_113, type, subsetI1: $o). 237.80/32.54 thf(decl_114, type, eqimpsubset2: $o). 237.80/32.54 thf(decl_115, type, eqimpsubset1: $o). 237.80/32.54 thf(decl_116, type, subsetI2: $o). 237.80/32.54 thf(decl_117, type, emptysetsubset: $o). 237.80/32.54 thf(decl_118, type, subsetE: $o). 237.80/32.54 thf(decl_119, type, subsetE2: $o). 237.80/32.54 thf(decl_120, type, notsubsetI: $o). 237.80/32.54 thf(decl_121, type, notequalI1: $o). 237.80/32.54 thf(decl_122, type, notequalI2: $o). 237.80/32.54 thf(decl_123, type, subsetRefl: $o). 237.80/32.54 thf(decl_124, type, subsetTrans: $o). 237.80/32.54 thf(decl_125, type, setadjoinSub: $o). 237.80/32.54 thf(decl_126, type, setadjoinSub2: $o). 237.80/32.54 thf(decl_127, type, subset2powerset: $o). 237.80/32.54 thf(decl_128, type, setextsub: $o). 237.80/32.54 thf(decl_129, type, subsetemptysetimpeq: $o). 237.80/32.54 thf(decl_130, type, powersetI1: $o). 237.80/32.54 thf(decl_131, type, powersetE1: $o). 237.80/32.54 thf(decl_132, type, inPowerset: $o). 237.80/32.54 thf(decl_133, type, powersetsubset: $o). 237.80/32.54 thf(decl_134, type, sepInPowerset: $o). 237.80/32.54 thf(decl_135, type, sepSubset: $o). 237.80/32.54 thf(decl_136, type, binunion: $i > $i > $i). 237.80/32.54 thf(decl_137, type, binunionIL: $o). 237.80/32.54 thf(decl_138, type, upairset2IR: $o). 237.80/32.54 thf(decl_139, type, binunionIR: $o). 237.80/32.54 thf(decl_140, type, binunionEcases: $o). 237.80/32.54 thf(decl_141, type, binunionE: $o). 237.80/32.54 thf(decl_142, type, binunionLsub: $o). 237.80/32.54 thf(decl_143, type, binunionRsub: $o). 237.80/32.54 thf(decl_144, type, binintersect: $i > $i > $i). 237.80/32.54 thf(decl_145, type, binintersectI: $o). 237.80/32.54 thf(decl_146, type, binintersectSubset5: $o). 237.80/32.54 thf(decl_147, type, binintersectEL: $o). 237.80/32.54 thf(decl_148, type, binintersectLsub: $o). 237.80/32.54 thf(decl_149, type, binintersectSubset2: $o). 237.80/32.54 thf(decl_150, type, binintersectSubset3: $o). 237.80/32.54 thf(decl_151, type, binintersectER: $o). 237.80/32.54 thf(decl_152, type, disjointsetsI1: $o). 237.80/32.54 thf(decl_153, type, binintersectRsub: $o). 237.80/32.54 thf(decl_154, type, binintersectSubset4: $o). 237.80/32.54 thf(decl_155, type, binintersectSubset1: $o). 237.80/32.54 thf(decl_156, type, bs114d: $o). 237.80/32.54 thf(decl_158, type, setminus: $i > $i > $i). 237.80/32.54 thf(decl_159, type, setminusI: $o). 237.80/32.54 thf(decl_160, type, setminusEL: $o). 237.80/32.55 thf(decl_161, type, setminusER: $o). 237.80/32.55 thf(decl_162, type, setminusSubset2: $o). 237.80/32.55 thf(decl_163, type, setminusERneg: $o). 237.80/32.55 thf(decl_164, type, setminusELneg: $o). 237.80/32.55 thf(decl_165, type, setminusILneg: $o). 237.80/32.55 thf(decl_166, type, setminusIRneg: $o). 237.80/32.55 thf(decl_167, type, setminusLsub: $o). 237.80/32.55 thf(decl_168, type, setminusSubset1: $o). 237.80/32.55 thf(decl_169, type, symdiff: $i > $i > $i). 237.80/32.55 thf(decl_170, type, symdiffE: $o). 237.80/32.55 thf(decl_171, type, symdiffI1: $o). 237.80/32.55 thf(decl_172, type, symdiffI2: $o). 237.80/32.55 thf(decl_173, type, symdiffIneg1: $o). 237.80/32.55 thf(decl_174, type, symdiffIneg2: $o). 237.80/32.55 thf(decl_175, type, iskpair: $i > $o). 237.80/32.55 thf(decl_176, type, secondinupair: $o). 237.80/32.55 thf(decl_177, type, setukpairIL: $o). 237.80/32.55 thf(decl_178, type, setukpairIR: $o). 237.80/32.55 thf(decl_179, type, kpairiskpair: $o). 237.80/32.55 thf(decl_180, type, kpair: $i > $i > $i). 237.80/32.55 thf(decl_181, type, kpairp: $o). 237.80/32.55 thf(decl_182, type, cartprod: $i > $i > $i). 237.80/32.55 thf(decl_183, type, singletonsubset: $o). 237.80/32.55 thf(decl_184, type, singletoninpowerset: $o). 237.80/32.55 thf(decl_185, type, singletoninpowunion: $o). 237.80/32.55 thf(decl_186, type, upairset2E: $o). 237.80/32.55 thf(decl_187, type, upairsubunion: $o). 237.80/32.55 thf(decl_188, type, upairinpowunion: $o). 237.80/32.55 thf(decl_189, type, ubforcartprodlem1: $o). 237.80/32.55 thf(decl_190, type, ubforcartprodlem2: $o). 237.80/32.55 thf(decl_191, type, ubforcartprodlem3: $o). 237.80/32.55 thf(decl_192, type, epred1_0: $o). 237.80/32.55 thf(decl_193, type, esk1_2: $i > $i > $i). 237.80/32.55 thf(decl_194, type, esk2_2: $i > $i > $i). 237.80/32.55 thf(decl_195, type, esk3_2: $i > $i > $i). 237.80/32.55 thf(decl_196, type, esk4_1: $i > $i). 237.80/32.55 thf(decl_197, type, esk5_2: ($i > $i > $o) > $i > $i). 237.80/32.55 thf(decl_198, type, esk6_2: ($i > $i > $o) > $i > $i). 237.80/32.55 thf(decl_199, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 237.80/32.55 thf(decl_200, type, esk8_1: $i > $i). 237.80/32.55 thf(decl_201, type, esk9_1: ($i > $o) > $i). 237.80/32.55 thf(decl_202, type, esk10_1: ($i > $o) > $i). 237.80/32.55 thf(decl_203, type, esk11_2: $i > $i > $i). 237.80/32.55 thf(decl_204, type, esk12_2: $i > $i > $i). 237.80/32.55 thf(decl_205, type, esk13_1: $i > $i). 237.80/32.55 thf(decl_206, type, esk14_1: $i > $i). 237.80/32.55 thf(decl_207, type, esk15_1: $i > $i). 237.80/32.55 thf(decl_208, type, esk16_2: $i > $i > $i). 237.80/32.55 thf(decl_209, type, esk17_3: $i > $i > $o > $i). 237.80/32.55 thf(decl_210, type, esk18_1: ($i > $o) > $i). 237.80/32.55 thf(decl_211, type, esk19_1: $i > $i). 237.80/32.55 thf(decl_212, type, esk20_2: $i > ($i > $o) > $i). 237.80/32.55 thf(decl_213, type, esk21_2: $i > ($i > $o) > $i). 237.80/32.55 thf(decl_214, type, esk22_2: $i > ($i > $o) > $i). 237.80/32.55 thf(decl_215, type, esk23_2: $i > ($i > $o) > $i). 237.80/32.55 thf(decl_216, type, esk24_2: $i > ($i > $o) > $i). 237.80/32.55 thf(decl_217, type, esk25_2: $i > ($i > $o) > $i). 237.80/32.55 thf(decl_218, type, esk26_2: ($i > $o) > $i > $i). 237.80/32.55 thf(decl_219, type, esk27_1: ($i > $o) > $i). 237.80/32.55 thf(decl_220, type, esk28_1: ($i > $o) > $i). 237.80/32.55 thf(decl_221, type, esk29_2: ($i > $o) > $i > $i). 237.80/32.55 thf(decl_222, type, esk30_2: ($i > $o) > ($i > $o) > $i). 237.80/32.55 thf(decl_223, type, esk31_2: ($i > $o) > ($i > $o) > $i). 237.80/32.55 thf(decl_224, type, esk32_2: ($i > $o) > ($i > $o) > $i). 237.80/32.55 thf(decl_225, type, esk33_2: ($i > $o) > ($i > $o) > $i). 237.80/32.55 thf(decl_226, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 237.80/32.55 thf(decl_227, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 237.80/32.55 thf(decl_228, type, esk36_2: $i > $i > $i). 237.80/32.55 thf(decl_229, type, esk37_2: $i > $i > $i). 237.80/32.55 thf(decl_230, type, esk38_2: $i > $i > $i). 237.80/32.55 thf(decl_231, type, esk39_0: $i). 237.80/32.55 thf(decl_232, type, esk40_0: $i). 237.80/32.55 thf(decl_233, type, esk41_0: $i). 237.80/32.55 thf(decl_234, type, esk42_0: $i). 237.80/32.55 thf(decl_241, type, epred3_2: $i > $i > $i > $o). 237.80/32.55 thf(decl_242, type, esk48_3: $i > $i > $i > $i). 237.80/32.55 thf(decl_243, type, esk49_3: $i > $i > $i > $i). 237.80/32.55 thf(cartprodpairin, conjecture, ((setextAx)=>((emptysetAx)=>((((setunionAx)=>((((((foundationAx)=>((wellorderingAx)=>(((((dsetconstrER)=>((exuE1)=>(((emptysetE)=>(((((setext)=>((emptyI)=>(((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((((emptyinunitempty)=>((((setadjoinOr)=>((setoftrueEq)=>((((emptyInPowerset)=>(((setunionI)=>((setunionE)=>(((((uniqinunit)=>((notinsingleton)=>((((upairsetE)=>(((upairsetIR)=>((((quantDeMorgan1)=>((((((prop2set2propI)=>((((exuI1)=>(((exuI2)=>((((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((((((exuEu)=>((((subsetI1)=>((eqimpsubset2)=>((((emptysetsubset)=>((subsetE)=>(((notsubsetI)=>(((notequalI2)=>((((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>(((subsetemptysetimpeq)=>((powersetI1)=>((((((((upairset2IR)=>((((binunionE)=>((binunionLsub)=>(((binintersectI)=>(((binintersectEL)=>(((((binintersectER)=>((((binintersectSubset4)=>((binintersectSubset1)=>((((setminusEL)=>(((setminusSubset2)=>((setminusERneg)=>((((setminusIRneg)=>((setminusLsub)=>(((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>(((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>(((ubforcartprodlem2)=>((ubforcartprodlem3)=>![X4:$i, X5:$i, X2:$i]:((![X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))<=(in @ X3 @ X5)))<=(in @ X2 @ X4)))))<=(ubforcartprodlem1))))))))<=(kpairp))<=(kpairiskpair)))))<=(symdiffIneg2))))))<=(setminusSubset1))))<=(setminusILneg))<=(setminusELneg))))<=(setminusER)))<=(setminusI))<=(bs114d))))<=(binintersectRsub))<=(disjointsetsI1)))<=(binintersectSubset3))<=(binintersectSubset2))<=(binintersectLsub)))<=(binintersectSubset5)))<=(binunionRsub))))<=(binunionEcases))<=(binunionIR)))<=(binunionIL))<=(sepSubset))<=(sepInPowerset))<=(powersetsubset))<=(inPowerset))<=(powersetE1))))<=(setextsub)))))<=(subsetTrans))<=(subsetRefl)))<=(notequalI1)))<=(subsetE2))))<=(subsetI2))<=(eqimpsubset1))))<=(dsetconstr__Cong))<=(descr__Cong)))<=(omega__Cong))<=(setunion__Cong))<=(powerset__Cong))<=(setadjoin__Cong)))))<=(in__Cong))<=(inCongP)))<=(exuI3)))<=(notdallE))<=(notdexE)))<=(prop2setI))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2)))<=(vacuousDall))<=(emptyE1)))<=(upairsetIL)))<=(singletonsswitch))<=(eqinunit))))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU))))<=(powersetE)))<=(emptyinPowerset))<=(powersetI))))<=(setadjoinE))<=(setadjoinIR)))<=(setadjoinIL))<=(nonemptyI1)))))<=(noeltsimpempty))))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE))))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp))))<=(replAx))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', cartprodpairin)). 237.80/32.55 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.xAI4abZFRc/E---3.1_941405.p', emptyE1)). 237.80/32.55 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.xAI4abZFRc/E---3.1_941405.p', exuE2)). 237.80/32.55 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.xAI4abZFRc/E---3.1_941405.p', exuEu)). 237.80/32.55 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', exuE3e)). 237.80/32.55 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', exu__Cong)). 237.80/32.55 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', exuE3u)). 237.80/32.55 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', dsetconstrEL)). 237.80/32.55 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', dsetconstrI)). 237.80/32.55 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', descrp)). 237.80/32.55 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', replAx)). 237.80/32.55 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', sepSubset)). 237.80/32.55 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', sepInPowerset)). 237.80/32.55 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', descr__Cong)). 237.80/32.55 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', dsetconstr__Cong)). 237.80/32.55 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', exuI3)). 237.80/32.55 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', exuI2)). 237.80/32.55 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.xAI4abZFRc/E---3.1_941405.p', exuI1)). 237.80/32.55 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setoftrueEq)). 237.80/32.55 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', nonemptyI)). 237.80/32.55 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setbeta)). 237.80/32.55 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', exuE1)). 237.80/32.55 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', dsetconstrER)). 237.80/32.55 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', singletonsswitch)). 237.80/32.55 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', quantDeMorgan2)). 237.80/32.55 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', vacuousDall)). 237.80/32.55 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', upairsetIL)). 237.80/32.55 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', eqinunit)). 237.80/32.55 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', nonemptyImpWitness)). 237.80/32.55 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', subPowSU)). 237.80/32.55 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', powersetE)). 237.80/32.55 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', emptyinPowerset)). 237.80/32.55 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', powersetI)). 237.80/32.55 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.xAI4abZFRc/E---3.1_941405.p', setadjoinE)). 237.80/32.55 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', emptysetsubset)). 237.80/32.55 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setadjoinIR)). 237.80/32.55 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', eqimpsubset2)). 237.80/32.55 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setadjoinIL)). 237.80/32.55 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', subsetI1)). 237.80/32.55 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', nonemptyI1)). 237.80/32.55 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', noeltsimpempty)). 237.80/32.55 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', emptyset__Cong)). 237.80/32.55 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', notinemptyset)). 237.80/32.55 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', emptysetimpfalse)). 237.80/32.55 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', prop2setE)). 237.80/32.55 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', subsetE)). 237.80/32.55 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.xAI4abZFRc/E---3.1_941405.p', omegaIndAx)). 237.80/32.55 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', omegaSAx)). 237.80/32.55 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', omega0Ax)). 237.80/32.55 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', powersetAx)). 237.80/32.55 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setadjoinAx)). 237.80/32.55 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', powersetI1)). 237.80/32.55 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', subsetemptysetimpeq)). 237.80/32.55 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', subset2powerset)). 237.80/32.55 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setadjoinSub2)). 237.80/32.55 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setadjoinSub)). 237.80/32.55 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', notequalI2)). 237.80/32.55 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', notsubsetI)). 237.80/32.55 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', upairset2IR)). 237.80/32.55 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binintersectSubset1)). 237.80/32.55 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binintersectSubset4)). 237.80/32.55 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binintersectER)). 237.80/32.55 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binintersectEL)). 237.80/32.55 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binintersectI)). 237.80/32.55 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binunionLsub)). 237.80/32.55 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binunionE)). 237.80/32.55 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setminusEL)). 237.80/32.55 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binunionIL)). 237.80/32.55 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binunionIR)). 237.80/32.55 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.xAI4abZFRc/E---3.1_941405.p', binunionEcases)). 237.80/32.55 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binunionRsub)). 237.80/32.55 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binintersectSubset5)). 237.80/32.55 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', symdiffI2)). 237.80/32.55 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', symdiffI1)). 237.80/32.55 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', symdiffE)). 237.80/32.55 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setminusLsub)). 237.80/32.55 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setminusIRneg)). 237.80/32.55 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setminusERneg)). 237.80/32.55 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setminusSubset2)). 237.80/32.55 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', symdiffIneg1)). 237.80/32.55 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', upairset2E)). 237.80/32.55 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', singletoninpowunion)). 237.80/32.55 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', singletoninpowerset)). 237.80/32.55 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', singletonsubset)). 237.80/32.55 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.xAI4abZFRc/E---3.1_941405.p', setukpairIR)). 237.80/32.55 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.xAI4abZFRc/E---3.1_941405.p', setukpairIL)). 237.80/32.55 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', secondinupair)). 237.80/32.55 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.xAI4abZFRc/E---3.1_941405.p', upairsubunion)). 237.80/32.55 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', symdiffIneg2)). 237.80/32.55 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', kpairiskpair)). 237.80/32.55 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', kpairp)). 237.80/32.55 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', ubforcartprodlem1)). 237.80/32.55 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', ubforcartprodlem3)). 237.80/32.55 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', ubforcartprodlem2)). 237.80/32.55 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', upairinpowunion)). 237.80/32.55 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setminusSubset1)). 237.80/32.55 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', disjointsetsI1)). 237.80/32.55 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binintersectRsub)). 237.80/32.55 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', bs114d)). 237.80/32.55 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setminusI)). 237.80/32.55 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setminusER)). 237.80/32.55 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setminusELneg)). 237.80/32.55 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setminusILneg)). 237.80/32.55 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binintersectSubset3)). 237.80/32.55 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binintersectLsub)). 237.80/32.55 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', binintersectSubset2)). 237.80/32.55 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', subsetRefl)). 237.80/32.55 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', subsetTrans)). 237.80/32.55 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setextsub)). 237.80/32.55 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', powersetE1)). 237.80/32.55 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', inPowerset)). 237.80/32.55 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', powersetsubset)). 237.80/32.55 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', notequalI1)). 237.80/32.55 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setunion__Cong)). 237.80/32.55 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', omega__Cong)). 237.80/32.55 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', eqimpsubset1)). 237.80/32.55 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', subsetI2)). 237.80/32.55 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', subsetE2)). 237.80/32.55 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', powerset__Cong)). 237.80/32.55 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', prop2setI)). 237.80/32.55 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', notdexE)). 237.80/32.55 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', notdallE)). 237.80/32.55 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', inCongP)). 237.80/32.55 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', in__Cong)). 237.80/32.55 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setadjoin__Cong)). 237.80/32.55 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', quantDeMorgan3)). 237.80/32.55 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', quantDeMorgan4)). 237.80/32.55 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', quantDeMorgan1)). 237.80/32.55 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', upairsetIR)). 237.80/32.55 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', upairsetE)). 237.80/32.55 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', notinsingleton)). 237.80/32.55 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', uniqinunit)). 237.80/32.55 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.xAI4abZFRc/E---3.1_941405.p', setunionE)). 237.80/32.55 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setunionI)). 237.80/32.55 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', emptyInPowerset)). 237.80/32.55 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setadjoinOr)). 237.80/32.55 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', emptyinunitempty)). 237.80/32.55 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', nonemptyE1)). 237.80/32.55 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', emptyI)). 237.80/32.55 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setext)). 237.80/32.55 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', emptysetE)). 237.80/32.55 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.xAI4abZFRc/E---3.1_941405.p', wellorderingAx)). 237.80/32.55 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.xAI4abZFRc/E---3.1_941405.p', foundationAx)). 237.80/32.55 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setunionAx)). 237.80/32.55 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', emptysetAx)). 237.80/32.55 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', setextAx)). 237.80/32.55 thf(cartprod, axiom, ((cartprod)=(^[X4:$i, X5:$i]:(dsetconstr @ (powerset @ (powerset @ (binunion @ X4 @ X5))) @ (^[X2:$i]:(?[X3:$i]:((((in @ X3 @ X4))&(?[X14:$i]:((((in @ X14 @ X5))&(((X2)=(kpair @ X3 @ X14))))))))))))), file('/export/starexec/sandbox/tmp/tmp.xAI4abZFRc/E---3.1_941405.p', cartprod)). 237.80/32.55 thf(c_0_147, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((((setunionAx)=>((((((foundationAx)=>((wellorderingAx)=>(((((dsetconstrER)=>((exuE1)=>(((emptysetE)=>(((((setext)=>((emptyI)=>(((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((((emptyinunitempty)=>((((setadjoinOr)=>((setoftrueEq)=>((((emptyInPowerset)=>(((setunionI)=>((setunionE)=>(((((uniqinunit)=>((notinsingleton)=>((((upairsetE)=>(((upairsetIR)=>((((quantDeMorgan1)=>((((((prop2set2propI)=>((((exuI1)=>(((exuI2)=>((((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((((((exuEu)=>((((subsetI1)=>((eqimpsubset2)=>((((emptysetsubset)=>((subsetE)=>(((notsubsetI)=>(((notequalI2)=>((((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>(((subsetemptysetimpeq)=>((powersetI1)=>((((((((upairset2IR)=>((((binunionE)=>((binunionLsub)=>(((binintersectI)=>(((binintersectEL)=>(((((binintersectER)=>((((binintersectSubset4)=>((binintersectSubset1)=>((((setminusEL)=>(((setminusSubset2)=>((setminusERneg)=>((((setminusIRneg)=>((setminusLsub)=>(((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>(((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>(((ubforcartprodlem2)=>((ubforcartprodlem3)=>![X4:$i, X5:$i, X2:$i]:((![X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))<=(in @ X3 @ X5)))<=(in @ X2 @ X4)))))<=(ubforcartprodlem1))))))))<=(kpairp))<=(kpairiskpair)))))<=(symdiffIneg2))))))<=(setminusSubset1))))<=(setminusILneg))<=(setminusELneg))))<=(setminusER)))<=(setminusI))<=(bs114d))))<=(binintersectRsub))<=(disjointsetsI1)))<=(binintersectSubset3))<=(binintersectSubset2))<=(binintersectLsub)))<=(binintersectSubset5)))<=(binunionRsub))))<=(binunionEcases))<=(binunionIR)))<=(binunionIL))<=(sepSubset))<=(sepInPowerset))<=(powersetsubset))<=(inPowerset))<=(powersetE1))))<=(setextsub)))))<=(subsetTrans))<=(subsetRefl)))<=(notequalI1)))<=(subsetE2))))<=(subsetI2))<=(eqimpsubset1))))<=(dsetconstr__Cong))<=(descr__Cong)))<=(omega__Cong))<=(setunion__Cong))<=(powerset__Cong))<=(setadjoin__Cong)))))<=(in__Cong))<=(inCongP)))<=(exuI3)))<=(notdallE))<=(notdexE)))<=(prop2setI))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2)))<=(vacuousDall))<=(emptyE1)))<=(upairsetIL)))<=(singletonsswitch))<=(eqinunit))))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU))))<=(powersetE)))<=(emptyinPowerset))<=(powersetI))))<=(setadjoinE))<=(setadjoinIR)))<=(setadjoinIL))<=(nonemptyI1)))))<=(noeltsimpempty))))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE))))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp))))<=(replAx))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx))))), inference(assume_negation,[status(cth)],[cartprodpairin])). 237.80/32.55 thf(c_0_148, 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])). 237.80/32.55 thf(c_0_149, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 237.80/32.55 thf(c_0_150, 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])). 237.80/32.55 thf(c_0_151, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 237.80/32.55 thf(c_0_152, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 237.80/32.55 thf(c_0_153, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 237.80/32.55 thf(c_0_154, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 237.80/32.55 thf(c_0_155, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 237.80/32.55 thf(c_0_156, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 237.80/32.55 thf(c_0_157, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 237.80/32.55 thf(c_0_158, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 237.80/32.55 thf(c_0_159, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 237.80/32.55 thf(c_0_160, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 237.80/32.55 thf(c_0_161, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 237.80/32.55 thf(c_0_162, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 237.80/32.55 thf(c_0_163, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 237.80/32.55 thf(c_0_164, 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])). 237.80/32.55 thf(c_0_165, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 237.80/32.55 thf(c_0_166, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 237.80/32.55 thf(c_0_167, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 237.80/32.55 thf(c_0_168, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 237.80/32.55 thf(c_0_169, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 237.80/32.55 thf(c_0_170, plain, ((epred1_0)<=>![X429:$i]:(?[X430:$i]:((((![X431:$i]:(((in @ X431 @ X430)=>![X432:$i]:(((in @ X432 @ X431)=>(in @ X432 @ X429)))))&![X433:$i, X434:$i]:((((in @ X433 @ X429)&(in @ X434 @ X429))=>(![X435:$i]:(((in @ X435 @ X430)=>((in @ X433 @ X435)<=>(in @ X434 @ X435))))=>((X433)=(X434))))))&![X436:$i, X437:$i]:((((in @ X436 @ X430)&(in @ X437 @ X430))=>(![X438:$i]:(((in @ X438 @ X436)=>(in @ X438 @ X437)))|![X439:$i]:(((in @ X439 @ X437)=>(in @ X439 @ X436)))))))&![X440:$i]:(((![X441:$i]:(((in @ X441 @ X440)=>(in @ X441 @ X429)))&?[X442:$i]:((in @ X442 @ X440)))=>?[X443:$i, X444:$i]:(((((in @ X443 @ X430)&(in @ X444 @ X440))&~(?[X445:$i]:(((in @ X445 @ X443)&(in @ X445 @ X440)))))&![X446:$i]:(((in @ X446 @ X430)=>(![X447:$i]:(((in @ X447 @ X446)=>(in @ X447 @ X443)))|(in @ X444 @ X446)))))))))))), introduced(definition)). 237.80/32.55 thf(c_0_171, negated_conjecture, ~((![X418:$i, X419:$i]:((![X420:$i]:(((in @ X420 @ X418)<=>(in @ X420 @ X419)))=>((X418)=(X419))))=>(![X421:$i]:(~(in @ X421 @ emptyset))=>(![X808:$i, X809:$i, X810:$i]:(((in @ X810 @ (setadjoin @ X808 @ X809))<=>(((X810)=(X808))|(in @ X810 @ X809))))=>(![X805:$i, X806:$i]:(((in @ X806 @ (powerset @ X805))<=>![X807:$i]:(((in @ X807 @ X806)=>(in @ X807 @ X805)))))=>(![X422:$i, X423:$i]:(((in @ X423 @ (setunion @ X422))<=>?[X424:$i]:(((in @ X423 @ X424)&(in @ X424 @ X422)))))=>((in @ emptyset @ omega)=>(![X804:$i]:(((in @ X804 @ omega)=>(in @ (setadjoin @ X804 @ X804) @ omega)))=>(![X801:$i]:((((in @ emptyset @ X801)&![X802:$i]:((((in @ X802 @ omega)&(in @ X802 @ X801))=>(in @ (setadjoin @ X802 @ X802) @ X801))))=>![X803:$i]:(((in @ X803 @ omega)=>(in @ X803 @ X801)))))=>(![X795:$i > $i > $o, X796:$i]:((![X797:$i]:(((in @ X797 @ X796)=>(exu @ (X795 @ X797))))=>?[X798:$i]:(![X799:$i]:(((in @ X799 @ X798)<=>?[X800:$i]:(((in @ X800 @ X796)&(X795 @ X800 @ X799))))))))=>(![X425:$i]:((?[X426:$i]:((in @ X426 @ X425))=>?[X427:$i]:(((in @ X427 @ X425)&~(?[X428:$i]:(((in @ X428 @ X427)&(in @ X428 @ X425))))))))=>((epred1_0)=>(![X794:$i > $o]:(((exu @ X794)=>(X794 @ (descr @ (^[Z0:$i]:(X794 @ Z0))))))=>(![X791:$i, X792:$i > $o, X793:$i]:(((in @ X793 @ X791)=>((X792 @ X793)=>(in @ X793 @ (dsetconstr @ X791 @ X792)))))=>(![X788:$i, X789:$i > $o, X790:$i]:(((in @ X790 @ (dsetconstr @ X788 @ X789))=>(in @ X790 @ X788)))=>(![X448:$i, X449:$i > $o, X450:$i]:(((in @ X450 @ (dsetconstr @ X448 @ X449))=>(X449 @ X450)))=>(![X451:$i > $o]:(((exu @ X451)=>?[X452:$i]:(((X451 @ X452)&![X453:$i]:(((X451 @ X453)=>((X452)=(X453))))))))=>(![X786:$o, X787:$i]:(((in @ X787 @ (prop2set @ ((X786))))=>(X786)))=>(![X454:$i]:(((in @ X454 @ emptyset)=>![X455:$o]:((X455))))=>(![X785:$i]:(((in @ X785 @ emptyset)=>~($true)))=>(![X784:$i]:(~(in @ X784 @ emptyset))=>(![X782:$i > $o]:(((exu @ X782)=>?[X783:$i]:((X782 @ X783))))=>(![X456:$i, X457:$i]:((![X458:$i]:(((in @ X458 @ X456)=>(in @ X458 @ X457)))=>(![X459:$i]:(((in @ X459 @ X457)=>(in @ X459 @ X456)))=>((X456)=(X457)))))=>(![X460:$i]:((![X461:$i]:(~(in @ X461 @ X460))=>((X460)=(emptyset))))=>(![X780:$i]:((![X781:$i]:(~(in @ X781 @ X780))=>((X780)=(emptyset))))=>(![X462:$i, X463:$i > $o, X464:$i]:(((in @ X464 @ X462)=>((in @ X464 @ (dsetconstr @ X462 @ X463))<=>(X463 @ X464))))=>(![X465:$i]:(((nonempty @ X465)=>?[X466:$i]:((in @ X466 @ X465))))=>(![X467:$i, X468:$i > $o, X469:$i]:(((in @ X469 @ X467)=>((X468 @ X469)=>(nonempty @ (dsetconstr @ X467 @ X468)))))=>(![X778:$i]:((?[X779:$i]:((in @ X779 @ X778))=>(nonempty @ X778)))=>(![X776:$i, X777:$i]:((in @ X776 @ (setadjoin @ X776 @ X777)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X773:$i, X774:$i, X775:$i]:(((in @ X775 @ X774)=>(in @ X775 @ (setadjoin @ X773 @ X774))))=>(![X769:$i, X770:$i, X771:$i]:(((in @ X771 @ (setadjoin @ X769 @ X770))=>![X772:$o]:(((((X771)=(X769))=>(X772))=>(((in @ X771 @ X770)=>(X772))=>(X772))))))=>(![X470:$i, X471:$i, X472:$i]:(((in @ X472 @ (setadjoin @ X470 @ X471))=>(((X472)=(X470))|(in @ X472 @ X471))))=>(![X473:$i]:(((dsetconstr @ X473 @ (^[Z0:$i]:($true)))=(X473)))=>(![X766:$i, X767:$i]:((![X768:$i]:(((in @ X768 @ X767)=>(in @ X768 @ X766)))=>(in @ X767 @ (powerset @ X766))))=>(![X765:$i]:((in @ emptyset @ (powerset @ X765)))=>(![X474:$i]:((in @ emptyset @ (powerset @ X474)))=>(![X762:$i, X763:$i, X764:$i]:(((in @ X763 @ (powerset @ X762))=>((in @ X764 @ X763)=>(in @ X764 @ X762))))=>(![X475:$i, X476:$i, X477:$i]:(((in @ X476 @ X477)=>((in @ X477 @ X475)=>(in @ X476 @ (setunion @ X475)))))=>(![X478:$i, X479:$i]:(((in @ X479 @ (setunion @ X478))=>![X480:$o]:((![X481:$i]:(((in @ X479 @ X481)=>((in @ X481 @ X478)=>(X480))))=>(X480)))))=>(![X760:$i, X761:$i]:(((in @ X761 @ X760)=>(in @ X761 @ (powerset @ (setunion @ X760)))))=>(![X757:$i > $o]:(((exu @ X757)=>?[X758:$i]:(![X759:$i]:(((X757 @ X759)<=>((X759)=(X758)))))))=>(![X755:$i]:(((nonempty @ X755)=>?[X756:$i]:(((in @ X756 @ X755)&$true))))=>(![X482:$i, X483:$i]:(((in @ X482 @ (setadjoin @ X483 @ emptyset))=>((X482)=(X483))))=>(![X484:$i, X485:$i]:((((X484)!=(X485))=>~(in @ X485 @ (setadjoin @ X484 @ emptyset))))=>(![X753:$i, X754:$i]:((((X753)=(X754))=>(in @ X753 @ (setadjoin @ X754 @ emptyset))))=>(![X751:$i, X752:$i]:(((in @ X751 @ (setadjoin @ X752 @ emptyset))=>(in @ X752 @ (setadjoin @ X751 @ emptyset))))=>(![X486:$i, X487:$i, X488:$i]:(((in @ X488 @ (setadjoin @ X486 @ (setadjoin @ X487 @ emptyset)))=>(((X488)=(X486))|((X488)=(X487)))))=>(![X749:$i, X750:$i]:((in @ X749 @ (setadjoin @ X749 @ (setadjoin @ X750 @ emptyset))))=>(![X489:$i, X490:$i]:((in @ X490 @ (setadjoin @ X489 @ (setadjoin @ X490 @ emptyset))))=>(![X746:$i, X747:$i > $o]:((?[X748:$i]:(((in @ X748 @ X746)&(X747 @ X748)))=>(((dsetconstr @ X746 @ X747)=(emptyset))=>~($true))))=>(![X744:$i > $o, X745:$i]:(((in @ X745 @ emptyset)=>(X744 @ X745)))=>(![X491:$i, X492:$i > $o]:((~(![X493:$i]:(((in @ X493 @ X491)=>(X492 @ X493))))=>?[X494:$i]:(((in @ X494 @ X491)&~((X492 @ X494))))))=>(![X740:$i, X741:$i > $o]:((![X742:$i]:(((in @ X742 @ X740)=>~((X741 @ X742))))=>~(?[X743:$i]:(((in @ X743 @ X740)&(X741 @ X743))))))=>(![X736:$i, X737:$i > $o]:((~(?[X738:$i]:(((in @ X738 @ X736)&(X737 @ X738))))=>![X739:$i]:(((in @ X739 @ X736)=>~((X737 @ X739))))))=>(![X732:$i, X733:$i > $o]:((?[X734:$i]:(((in @ X734 @ X732)&~((X733 @ X734))))=>~(![X735:$i]:(((in @ X735 @ X732)=>(X733 @ X735))))))=>(![X731:$o]:(((X731)=>(in @ emptyset @ (prop2set @ ((X731))))))=>((prop2set2propI)=>(![X727:$i, X728:$i > $o]:((~(?[X729:$i]:(((in @ X729 @ X727)&(X728 @ X729))))=>![X730:$i]:(((in @ X730 @ X727)=>~((X728 @ X730))))))=>(![X723:$i, X724:$i > $o]:((~(![X725:$i]:(((in @ X725 @ X723)=>(X724 @ X725))))=>?[X726:$i]:(((in @ X726 @ X723)&~((X724 @ X726))))))=>(![X495:$i > $o]:((?[X496:$i]:(((X495 @ X496)&![X497:$i]:(((X495 @ X497)=>((X496)=(X497))))))=>(exu @ X495)))=>(![X719:$i > $o]:((?[X720:$i]:((X719 @ X720))=>(![X721:$i, X722:$i]:(((X719 @ X721)=>((X719 @ X722)=>((X721)=(X722)))))=>(exu @ X719))))=>(![X498:$i > $o]:((?[X499:$i]:(![X500:$i]:(((X498 @ X500)<=>((X500)=(X499)))))=>(exu @ X498)))=>(![X715:$i, X716:$i]:((((X715)=(X716))=>![X717:$i, X718:$i]:((((X717)=(X718))=>((in @ X717 @ X715)=>(in @ X718 @ X716))))))=>(![X711:$i, X712:$i]:((((X711)=(X712))=>![X713:$i, X714:$i]:((((X713)=(X714))=>((in @ X713 @ X711)<=>(in @ X714 @ X712))))))=>(![X501:$i > $o]:(((exu @ X501)=>![X502:$i, X503:$i]:(((X501 @ X502)=>((X501 @ X503)=>((X502)=(X503)))))))=>(![X504:$i > $o, X505:$i > $o]:((![X506:$i, X507:$i]:((((X506)=(X507))=>((X504 @ X506)<=>(X505 @ X507))))=>((exu @ X504)<=>(exu @ X505))))=>(((emptyset)=(emptyset))=>(![X707:$i, X708:$i]:((((X707)=(X708))=>![X709:$i, X710:$i]:((((X709)=(X710))=>((setadjoin @ X707 @ X709)=(setadjoin @ X708 @ X710))))))=>(![X705:$i, X706:$i]:((((X705)=(X706))=>((powerset @ X705)=(powerset @ X706))))=>(![X703:$i, X704:$i]:((((X703)=(X704))=>((setunion @ X703)=(setunion @ X704))))=>(((omega)=(omega))=>(![X508:$i > $o]:(((exu @ X508)=>![X509:$i, X510:$i]:(((X508 @ X509)=>((X508 @ X510)=>((X509)=(X510)))))))=>(![X699:$i > $o, X700:$i > $o]:((![X701:$i, X702:$i]:((((X701)=(X702))=>((X699 @ X701)<=>(X700 @ X702))))=>((exu @ X699)=>((exu @ X700)=>((descr @ X699)=(descr @ X700))))))=>(![X693:$i, X694:$i]:((((X693)=(X694))=>![X695:$i > $o, X696:$i > $o]:((![X697:$i]:(((in @ X697 @ X693)=>![X698:$i]:(((in @ X698 @ X694)=>(((X697)=(X698))=>((X695 @ X697)<=>(X696 @ X698)))))))=>((dsetconstr @ X693 @ X695)=(dsetconstr @ X694 @ X696))))))=>(![X511:$i, X512:$i]:((![X513:$i]:(((in @ X513 @ X511)=>(in @ X513 @ X512)))=>(subset @ X511 @ X512)))=>(![X514:$i, X515:$i]:((((X514)=(X515))=>(subset @ X515 @ X514)))=>(![X691:$i, X692:$i]:((((X691)=(X692))=>(subset @ X691 @ X692)))=>(![X688:$i, X689:$i]:((![X690:$i]:(((in @ X690 @ X688)=>(in @ X690 @ X689)))=>(subset @ X688 @ X689)))=>(![X516:$i]:((subset @ emptyset @ X516))=>(![X517:$i, X518:$i, X519:$i]:(((subset @ X517 @ X518)=>((in @ X519 @ X517)=>(in @ X519 @ X518))))=>(![X685:$i, X686:$i, X687:$i]:(((subset @ X685 @ X686)=>(~(in @ X687 @ X686)=>~(in @ X687 @ X685))))=>(![X520:$i, X521:$i, X522:$i]:(((in @ X522 @ X520)=>(~(in @ X522 @ X521)=>~(subset @ X520 @ X521))))=>(![X683:$i, X684:$i]:((~(subset @ X683 @ X684)=>((X683)!=(X684))))=>(![X523:$i, X524:$i, X525:$i]:(((in @ X525 @ X523)=>(~(in @ X525 @ X524)=>((X523)!=(X524)))))=>(![X682:$i]:((subset @ X682 @ X682))=>(![X679:$i, X680:$i, X681:$i]:(((subset @ X679 @ X680)=>((subset @ X680 @ X681)=>(subset @ X679 @ X681))))=>(![X526:$i, X527:$i]:((subset @ X527 @ (setadjoin @ X526 @ X527)))=>(![X528:$i, X529:$i, X530:$i]:(((subset @ X528 @ X530)=>(subset @ X528 @ (setadjoin @ X529 @ X530))))=>(![X531:$i, X532:$i]:(((subset @ X531 @ X532)=>(in @ X531 @ (powerset @ X532))))=>(![X677:$i, X678:$i]:(((subset @ X677 @ X678)=>((subset @ X678 @ X677)=>((X677)=(X678)))))=>(![X533:$i]:(((subset @ X533 @ emptyset)=>((X533)=(emptyset))))=>(![X534:$i, X535:$i]:(((subset @ X535 @ X534)=>(in @ X535 @ (powerset @ X534))))=>(![X675:$i, X676:$i]:(((in @ X676 @ (powerset @ X675))=>(subset @ X676 @ X675)))=>(![X674:$i]:((in @ X674 @ (powerset @ X674)))=>(![X672:$i, X673:$i]:(((subset @ X672 @ X673)=>(subset @ (powerset @ X672) @ (powerset @ X673))))=>(![X670:$i, X671:$i > $o]:((in @ (dsetconstr @ X670 @ X671) @ (powerset @ X670)))=>(![X668:$i, X669:$i > $o]:((subset @ (dsetconstr @ X668 @ X669) @ X668))=>(![X665:$i, X666:$i, X667:$i]:(((in @ X667 @ X665)=>(in @ X667 @ (binunion @ X665 @ X666))))=>(![X536:$i, X537:$i]:((in @ X537 @ (setadjoin @ X536 @ (setadjoin @ X537 @ emptyset))))=>(![X662:$i, X663:$i, X664:$i]:(((in @ X664 @ X663)=>(in @ X664 @ (binunion @ X662 @ X663))))=>(![X658:$i, X659:$i, X660:$i, X661:$o]:(((in @ X660 @ (binunion @ X658 @ X659))=>(((in @ X660 @ X658)=>(X661))=>(((in @ X660 @ X659)=>(X661))=>(X661)))))=>(![X538:$i, X539:$i, X540:$i]:(((in @ X540 @ (binunion @ X538 @ X539))=>((in @ X540 @ X538)|(in @ X540 @ X539))))=>(![X541:$i, X542:$i]:((subset @ X541 @ (binunion @ X541 @ X542)))=>(![X656:$i, X657:$i]:((subset @ X657 @ (binunion @ X656 @ X657)))=>(![X543:$i, X544:$i, X545:$i]:(((in @ X545 @ X543)=>((in @ X545 @ X544)=>(in @ X545 @ (binintersect @ X543 @ X544)))))=>(![X653:$i, X654:$i, X655:$i]:(((subset @ X655 @ X653)=>((subset @ X655 @ X654)=>(subset @ X655 @ (binintersect @ X653 @ X654)))))=>(![X546:$i, X547:$i, X548:$i]:(((in @ X548 @ (binintersect @ X546 @ X547))=>(in @ X548 @ X546)))=>(![X651:$i, X652:$i]:((subset @ (binintersect @ X651 @ X652) @ X651))=>(![X649:$i, X650:$i]:(((subset @ X649 @ X650)=>((binintersect @ X649 @ X650)=(X649))))=>(![X647:$i, X648:$i]:((((binintersect @ X647 @ X648)=(X648))=>(subset @ X648 @ X647)))=>(![X549:$i, X550:$i, X551:$i]:(((in @ X551 @ (binintersect @ X549 @ X550))=>(in @ X551 @ X550)))=>(![X644:$i, X645:$i]:((~(?[X646:$i]:(((in @ X646 @ X644)&(in @ X646 @ X645))))=>((binintersect @ X644 @ X645)=(emptyset))))=>(![X642:$i, X643:$i]:((subset @ (binintersect @ X642 @ X643) @ X643))=>(![X552:$i, X553:$i]:(((subset @ X553 @ X552)=>((binintersect @ X552 @ X553)=(X553))))=>(![X554:$i, X555:$i]:((((binintersect @ X554 @ X555)=(X554))=>(subset @ X554 @ X555)))=>(![X639:$i, X640:$i, X641:$i]:(((binintersect @ X639 @ (binunion @ X640 @ X641))=(binunion @ (binintersect @ X639 @ X640) @ (binintersect @ X639 @ X641))))=>(![X636:$i, X637:$i, X638:$i]:(((in @ X638 @ X636)=>(~(in @ X638 @ X637)=>(in @ X638 @ (setminus @ X636 @ X637)))))=>(![X556:$i, X557:$i, X558:$i]:(((in @ X558 @ (setminus @ X556 @ X557))=>(in @ X558 @ X556)))=>(![X633:$i, X634:$i, X635:$i]:(((in @ X635 @ (setminus @ X633 @ X634))=>~(in @ X635 @ X634)))=>(![X559:$i, X560:$i]:(((subset @ X559 @ X560)=>((setminus @ X559 @ X560)=(emptyset))))=>(![X561:$i, X562:$i, X563:$i]:((~(in @ X563 @ (setminus @ X561 @ X562))=>((in @ X563 @ X561)=>(in @ X563 @ X562))))=>(![X630:$i, X631:$i, X632:$i]:((~(in @ X632 @ (setminus @ X630 @ X631))=>(~(in @ X632 @ X631)=>~(in @ X632 @ X630))))=>(![X627:$i, X628:$i, X629:$i]:((~(in @ X629 @ X627)=>~(in @ X629 @ (setminus @ X627 @ X628))))=>(![X564:$i, X565:$i, X566:$i]:(((in @ X566 @ X565)=>~(in @ X566 @ (setminus @ X564 @ X565))))=>(![X567:$i, X568:$i]:((subset @ (setminus @ X567 @ X568) @ X567))=>(![X625:$i, X626:$i]:((((setminus @ X625 @ X626)=(emptyset))=>(subset @ X625 @ X626)))=>(![X569:$i, X570:$i, X571:$i]:(((in @ X571 @ (symdiff @ X569 @ X570))=>![X572:$o]:((((in @ X571 @ X569)=>(~(in @ X571 @ X570)=>(X572)))=>((~(in @ X571 @ X569)=>((in @ X571 @ X570)=>(X572)))=>(X572))))))=>(![X573:$i, X574:$i, X575:$i]:(((in @ X575 @ X573)=>(~(in @ X575 @ X574)=>(in @ X575 @ (symdiff @ X573 @ X574)))))=>(![X576:$i, X577:$i, X578:$i]:((~(in @ X578 @ X576)=>((in @ X578 @ X577)=>(in @ X578 @ (symdiff @ X576 @ X577)))))=>(![X579:$i, X580:$i, X581:$i]:(((in @ X581 @ X579)=>((in @ X581 @ X580)=>~(in @ X581 @ (symdiff @ X579 @ X580)))))=>(![X622:$i, X623:$i, X624:$i]:((~(in @ X624 @ X622)=>(~(in @ X624 @ X623)=>~(in @ X624 @ (symdiff @ X622 @ X623)))))=>(![X582:$i, X583:$i]:((in @ X583 @ (setadjoin @ X582 @ (setadjoin @ X583 @ emptyset))))=>(![X584:$i, X585:$i]:((in @ X584 @ (setunion @ (setadjoin @ (setadjoin @ X584 @ emptyset) @ (setadjoin @ (setadjoin @ X584 @ (setadjoin @ X585 @ emptyset)) @ emptyset)))))=>(![X586:$i, X587:$i]:((in @ X587 @ (setunion @ (setadjoin @ (setadjoin @ X586 @ emptyset) @ (setadjoin @ (setadjoin @ X586 @ (setadjoin @ X587 @ emptyset)) @ emptyset)))))=>(![X620:$i, X621:$i]:((iskpair @ (setadjoin @ (setadjoin @ X620 @ emptyset) @ (setadjoin @ (setadjoin @ X620 @ (setadjoin @ X621 @ emptyset)) @ emptyset))))=>(![X618:$i, X619:$i]:((iskpair @ (kpair @ X618 @ X619)))=>(![X588:$i, X589:$i]:(((in @ X589 @ X588)=>(subset @ (setadjoin @ X589 @ emptyset) @ X588)))=>(![X590:$i, X591:$i]:(((in @ X591 @ X590)=>(in @ (setadjoin @ X591 @ emptyset) @ (powerset @ X590))))=>(![X592:$i, X593:$i, X594:$i]:(((in @ X594 @ X592)=>(in @ (setadjoin @ X594 @ emptyset) @ (powerset @ (binunion @ X592 @ X593)))))=>(![X595:$i, X596:$i, X597:$i]:(((in @ X597 @ (setadjoin @ X595 @ (setadjoin @ X596 @ emptyset)))=>(((X597)=(X595))|((X597)=(X596)))))=>(![X598:$i, X599:$i, X600:$i]:(((in @ X600 @ X598)=>![X601:$i]:(((in @ X601 @ X599)=>(subset @ (setadjoin @ X600 @ (setadjoin @ X601 @ emptyset)) @ (binunion @ X598 @ X599))))))=>(![X602:$i, X603:$i, X604:$i]:(((in @ X604 @ X602)=>![X605:$i]:(((in @ X605 @ X603)=>(in @ (setadjoin @ X604 @ (setadjoin @ X605 @ emptyset)) @ (powerset @ (binunion @ X602 @ X603)))))))=>(![X614:$i, X615:$i, X616:$i]:(((in @ X616 @ X614)=>![X617:$i]:(((in @ X617 @ X615)=>(subset @ (setadjoin @ (setadjoin @ X616 @ emptyset) @ (setadjoin @ (setadjoin @ X616 @ (setadjoin @ X617 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X614 @ X615)))))))=>(![X606:$i, X607:$i, X608:$i]:(((in @ X608 @ X606)=>![X609:$i]:(((in @ X609 @ X607)=>(in @ (setadjoin @ (setadjoin @ X608 @ emptyset) @ (setadjoin @ (setadjoin @ X608 @ (setadjoin @ X609 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X606 @ X607))))))))=>(![X610:$i, X611:$i, X612:$i]:(((in @ X612 @ X610)=>![X613:$i]:(((in @ X613 @ X611)=>(in @ (kpair @ X612 @ X613) @ (powerset @ (powerset @ (binunion @ X610 @ X611))))))))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_147, singletonsswitch]), c_0_148]), quantDeMorgan2]), vacuousDall]), upairsetIL]), eqinunit]), nonemptyImpWitness]), c_0_149]), subPowSU]), powersetE]), emptyinPowerset]), powersetI]), setadjoinE]), emptysetsubset]), setadjoinIR]), eqimpsubset2]), setadjoinIL]), subsetI1]), nonemptyI1]), c_0_150]), noeltsimpempty]), emptyset__Cong]), c_0_151]), c_0_152]), notinemptyset]), emptysetimpfalse]), c_0_153]), prop2setE]), subsetE]), c_0_154]), c_0_155]), c_0_156]), c_0_157]), omegaIndAx]), omegaSAx]), omega0Ax]), powersetAx]), setadjoinAx]), powersetI1]), subsetemptysetimpeq]), subset2powerset]), setadjoinSub2]), setadjoinSub]), notequalI2]), notsubsetI]), upairset2IR]), binintersectSubset1]), binintersectSubset4]), binintersectER]), binintersectEL]), binintersectI]), binunionLsub]), binunionE]), setminusEL]), binunionIL]), binunionIR]), binunionEcases]), binunionRsub]), binintersectSubset5]), symdiffI2]), symdiffI1]), symdiffE]), setminusLsub]), setminusIRneg]), setminusERneg]), setminusSubset2]), symdiffIneg1]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), setukpairIR]), setukpairIL]), secondinupair]), upairsubunion]), symdiffIneg2]), kpairiskpair]), kpairp]), ubforcartprodlem1]), ubforcartprodlem3]), ubforcartprodlem2]), upairinpowunion]), setminusSubset1]), disjointsetsI1]), binintersectRsub]), bs114d]), setminusI]), setminusER]), setminusELneg]), setminusILneg]), binintersectSubset3]), binintersectLsub]), binintersectSubset2]), c_0_158]), subsetRefl]), subsetTrans]), setextsub]), powersetE1]), inPowerset]), powersetsubset]), c_0_159]), notequalI1]), setunion__Cong]), omega__Cong]), c_0_160]), c_0_161]), eqimpsubset1]), subsetI2]), subsetE2]), powerset__Cong]), prop2setI]), notdexE]), notdallE]), c_0_162]), inCongP]), in__Cong]), setadjoin__Cong]), quantDeMorgan3]), quantDeMorgan4]), c_0_163]), c_0_164]), quantDeMorgan1]), upairsetIR]), upairsetE]), notinsingleton]), uniqinunit]), setunionE]), setunionI]), emptyInPowerset]), c_0_165]), setadjoinOr]), emptyinunitempty]), c_0_166]), nonemptyE1]), c_0_167]), emptyI]), setext]), emptysetE]), c_0_168]), c_0_169]), wellorderingAx]), foundationAx]), setunionAx]), emptysetAx]), setextAx])])]), c_0_170])). 237.80/32.55 thf(c_0_172, plain, ![X811:$i, X812:$i]:(((cartprod @ X811 @ X812)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X811 @ X812))) @ (^[Z0:$i]:(?[X3:$i]:((((in @ X3 @ X811))&(?[X14:$i]:((((in @ X14 @ X812))&(((Z0)=(kpair @ X3 @ X14))))))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[cartprod])])). 237.80/32.55 thf(c_0_173, negated_conjecture, ![X815:$i, X816:$i, X818:$i, X819:$i, X820:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$i, X826:$i, X828:$i, X829:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i, X837:$i, X838:$i > $i > $o, X839:$i, X842:$i, X844:$i, X845:$i, X846:$i, X847:$i, X849:$i, X850:$i > $o, X851:$i, X852:$i > $o, X853:$i, X854:$i, X855:$i > $o, X856:$i, X857:$i, X858:$i > $o, X859:$i, X860:$i > $o, X862:$i, X863:$o, X864:$i, X865:$i, X866:$o, X867:$i, X868:$i, X869:$i > $o, X871:$i, X872:$i, X875:$i, X877:$i, X879:$i, X880:$i > $o, X881:$i, X882:$i, X884:$i, X885:$i > $o, X886:$i, X887:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$o, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X912:$i, X913:$i, X914:$i, X915:$o, X917:$i, X918:$i, X919:$i > $o, X921:$i, X922:$i, X923:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i, X932:$i, X933:$i, X934:$i, X935:$i, X936:$i, X937:$i, X938:$i, X939:$i, X940:$i, X941:$i > $o, X942:$i, X943:$i > $o, X944:$i, X945:$i, X946:$i > $o, X947:$i, X949:$i, X950:$i > $o, X952:$i, X953:$i, X954:$i > $o, X956:$i, X957:$i, X958:$i > $o, X959:$i, X961:$o, X962:$i, X963:$i > $o, X965:$i, X966:$i, X967:$i > $o, X968:$i, X970:$i > $o, X971:$i, X973:$i > $o, X974:$i, X977:$i > $o, X978:$i, X980:$i, X981:$i, X982:$i, X983:$i, X984:$i, X985:$i, X986:$i, X987:$i, X988:$i > $o, X989:$i, X990:$i, X991:$i > $o, X992:$i > $o, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i > $o, X1004:$i, X1005:$i, X1006:$i > $o, X1007:$i > $o, X1010:$i, X1011:$i, X1012:$i > $o, X1013:$i > $o, X1016:$i, X1017:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1055:$i, X1056:$i, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i > $o, X1064:$i, X1065:$i > $o, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1075:$i, X1076:$i, X1077:$o, X1078:$i, X1079:$i, X1080:$i, X1081:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$o, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i]:((((~(in @ (esk1_2 @ X815 @ X816) @ X815)|~(in @ (esk1_2 @ X815 @ X816) @ X816)|((X815)=(X816)))&((in @ (esk1_2 @ X815 @ X816) @ X815)|(in @ (esk1_2 @ X815 @ X816) @ X816)|((X815)=(X816))))&(~(in @ X818 @ emptyset)&(((~(in @ X821 @ (setadjoin @ X819 @ X820))|(((X821)=(X819))|(in @ X821 @ X820)))&((((X821)!=(X819))|(in @ X821 @ (setadjoin @ X819 @ X820)))&(~(in @ X821 @ X820)|(in @ X821 @ (setadjoin @ X819 @ X820)))))&(((~(in @ X823 @ (powerset @ X822))|(~(in @ X824 @ X823)|(in @ X824 @ X822)))&(((in @ (esk2_2 @ X825 @ X826) @ X826)|(in @ X826 @ (powerset @ X825)))&(~(in @ (esk2_2 @ X825 @ X826) @ X825)|(in @ X826 @ (powerset @ X825)))))&(((((in @ X829 @ (esk3_2 @ X828 @ X829))|~(in @ X829 @ (setunion @ X828)))&((in @ (esk3_2 @ X828 @ X829) @ X828)|~(in @ X829 @ (setunion @ X828))))&(~(in @ X832 @ X833)|~(in @ X833 @ X831)|(in @ X832 @ (setunion @ X831))))&((in @ emptyset @ omega)&((~(in @ X834 @ omega)|(in @ (setadjoin @ X834 @ X834) @ omega))&(((((in @ (esk4_1 @ X835) @ omega)|~(in @ emptyset @ X835)|(~(in @ X837 @ omega)|(in @ X837 @ X835)))&((in @ (esk4_1 @ X835) @ X835)|~(in @ emptyset @ X835)|(~(in @ X837 @ omega)|(in @ X837 @ X835))))&(~(in @ (setadjoin @ (esk4_1 @ X835) @ (esk4_1 @ X835)) @ X835)|~(in @ emptyset @ X835)|(~(in @ X837 @ omega)|(in @ X837 @ X835))))&((((((in @ (esk7_3 @ X838 @ X839 @ X842) @ X839)|~(in @ X842 @ (esk6_2 @ X838 @ X839))|(in @ (esk5_2 @ X838 @ X839) @ X839))&((X838 @ (esk7_3 @ X838 @ X839 @ X842) @ X842)|~(in @ X842 @ (esk6_2 @ X838 @ X839))|(in @ (esk5_2 @ X838 @ X839) @ X839)))&(~(in @ X845 @ X839)|~(X838 @ X845 @ X844)|(in @ X844 @ (esk6_2 @ X838 @ X839))|(in @ (esk5_2 @ X838 @ X839) @ X839)))&((((in @ (esk7_3 @ X838 @ X839 @ X842) @ X839)|~(in @ X842 @ (esk6_2 @ X838 @ X839))|~(exu @ (X838 @ (esk5_2 @ X838 @ X839))))&((X838 @ (esk7_3 @ X838 @ X839 @ X842) @ X842)|~(in @ X842 @ (esk6_2 @ 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X871)|((X871)=(X872))|(in @ (esk11_2 @ X871 @ X872) @ X871)))&(((in @ (esk12_2 @ X871 @ X872) @ X872)|((X871)=(X872))|~(in @ (esk11_2 @ X871 @ X872) @ X872))&(~(in @ (esk12_2 @ X871 @ X872) @ X871)|((X871)=(X872))|~(in @ (esk11_2 @ X871 @ X872) @ X872))))&(((in @ (esk13_1 @ X875) @ X875)|((X875)=(emptyset)))&(((in @ (esk14_1 @ X877) @ X877)|((X877)=(emptyset)))&(((~(in @ X881 @ (dsetconstr @ X879 @ X880))|(X880 @ X881)|~(in @ X881 @ X879))&(~(X880 @ X881)|(in @ X881 @ (dsetconstr @ X879 @ X880))|~(in @ X881 @ X879)))&((~(nonempty @ X882)|(in @ (esk15_1 @ X882) @ X882))&((~(in @ X886 @ X884)|(~(X885 @ X886)|(nonempty @ (dsetconstr @ X884 @ X885))))&((~(in @ X888 @ X887)|(nonempty @ X887))&((in @ X889 @ (setadjoin @ X889 @ X890))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X893 @ X892)|(in @ X893 @ (setadjoin @ X891 @ X892)))&(((((in @ X896 @ X895)|(X897)|((X896)=(X894))|~(in @ X896 @ (setadjoin @ X894 @ X895)))&(~(X897)|(X897)|((X896)=(X894))|~(in @ X896 @ (setadjoin @ X894 @ X895))))&(((in @ X896 @ X895)|(X897)|~(X897)|~(in @ X896 @ (setadjoin @ X894 @ X895)))&(~(X897)|(X897)|~(X897)|~(in @ X896 @ (setadjoin @ X894 @ X895)))))&((~(in @ X900 @ (setadjoin @ X898 @ X899))|(((X900)=(X898))|(in @ X900 @ X899)))&(((dsetconstr @ X901 @ (^[Z0:$i]:($true)))=(X901))&((((in @ (esk16_2 @ X902 @ X903) @ X903)|(in @ X903 @ (powerset @ X902)))&(~(in @ (esk16_2 @ X902 @ X903) @ X902)|(in @ X903 @ (powerset @ X902))))&((in @ emptyset @ (powerset @ X905))&((in @ emptyset @ (powerset @ X906))&((~(in @ X908 @ (powerset @ X907))|(~(in @ X909 @ X908)|(in @ X909 @ X907)))&((~(in @ X911 @ X912)|(~(in @ X912 @ X910)|(in @ X911 @ (setunion @ X910))))&((((in @ X914 @ (esk17_3 @ X913 @ X914 @ X915))|(X915)|~(in @ X914 @ (setunion @ X913)))&(((in @ (esk17_3 @ X913 @ X914 @ X915) @ X913)|(X915)|~(in @ X914 @ (setunion @ X913)))&(~(X915)|(X915)|~(in @ X914 @ (setunion @ X913)))))&((~(in @ X918 @ X917)|(in @ X918 @ (powerset @ (setunion @ X917))))&(((~(X919 @ X921)|((X921)=(esk18_1 @ X919))|~(exu @ X919))&(((X922)!=(esk18_1 @ X919))|(X919 @ X922)|~(exu @ X919)))&((((in @ (esk19_1 @ X923) @ X923)|~(nonempty @ X923))&(($true)|~(nonempty @ X923)))&((~(in @ X925 @ (setadjoin @ X926 @ emptyset))|((X925)=(X926)))&((((X927)=(X928))|~(in @ X928 @ (setadjoin @ X927 @ emptyset)))&((((X929)!=(X930))|(in @ X929 @ (setadjoin @ X930 @ emptyset)))&((~(in @ X931 @ (setadjoin @ X932 @ emptyset))|(in @ X932 @ (setadjoin @ X931 @ emptyset)))&((~(in @ X935 @ (setadjoin @ X933 @ (setadjoin @ X934 @ emptyset)))|(((X935)=(X933))|((X935)=(X934))))&((in @ X936 @ (setadjoin @ X936 @ (setadjoin @ X937 @ emptyset)))&((in @ X939 @ (setadjoin @ X938 @ (setadjoin @ X939 @ emptyset)))&((~(in @ X942 @ X940)|~(X941 @ X942)|(((dsetconstr @ X940 @ X941)!=(emptyset))|~($true)))&((~(in @ X944 @ emptyset)|(X943 @ X944))&((((in @ (esk20_2 @ X945 @ X946) @ X945)|(~(in @ X947 @ X945)|(X946 @ X947)))&(~(X946 @ (esk20_2 @ X945 @ X946))|(~(in @ X947 @ X945)|(X946 @ X947))))&((((in @ (esk21_2 @ X949 @ X950) @ X949)|(~(in @ X952 @ X949)|~(X950 @ X952)))&((X950 @ (esk21_2 @ X949 @ X950))|(~(in @ X952 @ X949)|~(X950 @ X952))))&((((in @ (esk22_2 @ X953 @ X954) @ X953)|(~(in @ X956 @ X953)|~(X954 @ X956)))&((X954 @ (esk22_2 @ X953 @ X954))|(~(in @ X956 @ X953)|~(X954 @ X956))))&((((in @ (esk23_2 @ X957 @ X958) @ X957)|(~(in @ X959 @ X957)|(X958 @ X959)))&(~(X958 @ (esk23_2 @ X957 @ X958))|(~(in @ X959 @ X957)|(X958 @ X959))))&((~(X961)|(in @ emptyset @ (prop2set @ ((X961)))))&((prop2set2propI)&((((in @ (esk24_2 @ X962 @ X963) @ X962)|(~(in @ X965 @ X962)|~(X963 @ X965)))&((X963 @ (esk24_2 @ X962 @ X963))|(~(in @ X965 @ X962)|~(X963 @ X965))))&((((in @ (esk25_2 @ X966 @ X967) @ X966)|(~(in @ X968 @ X966)|(X967 @ X968)))&(~(X967 @ (esk25_2 @ X966 @ X967))|(~(in @ X968 @ X966)|(X967 @ X968))))&((((X970 @ (esk26_2 @ X970 @ X971))|~(X970 @ X971)|(exu @ X970))&(((X971)!=(esk26_2 @ X970 @ X971))|~(X970 @ X971)|(exu @ X970)))&((((X973 @ (esk27_1 @ X973))|(exu @ X973)|~(X973 @ X974))&(((X973 @ (esk28_1 @ X973))|(exu @ X973)|~(X973 @ X974))&(((esk27_1 @ X973)!=(esk28_1 @ X973))|(exu @ X973)|~(X973 @ X974))))&(((~(X977 @ (esk29_2 @ X977 @ X978))|((esk29_2 @ X977 @ X978)!=(X978))|(exu @ X977))&((X977 @ (esk29_2 @ X977 @ X978))|((esk29_2 @ X977 @ X978)=(X978))|(exu @ X977)))&((((X980)!=(X981))|(((X982)!=(X983))|(~(in @ X982 @ X980)|(in @ X983 @ X981))))&(((~(in @ X986 @ X984)|(in @ X987 @ X985)|((X986)!=(X987))|((X984)!=(X985)))&(~(in @ X987 @ X985)|(in @ X986 @ X984)|((X986)!=(X987))|((X984)!=(X985))))&((~(exu @ X988)|(~(X988 @ X989)|(~(X988 @ X990)|((X989)=(X990)))))&((((~(exu @ X991)|(exu @ X992)|((esk30_2 @ X991 @ X992)=(esk31_2 @ X991 @ X992)))&(~(exu @ X992)|(exu @ X991)|((esk30_2 @ X991 @ X992)=(esk31_2 @ X991 @ X992))))&(((~(exu @ X991)|(exu @ X992)|(~(X991 @ (esk30_2 @ X991 @ X992))|~(X992 @ (esk31_2 @ X991 @ X992))))&(~(exu @ X992)|(exu @ X991)|(~(X991 @ (esk30_2 @ X991 @ X992))|~(X992 @ (esk31_2 @ X991 @ X992)))))&((~(exu @ X991)|(exu @ X992)|((X991 @ (esk30_2 @ X991 @ X992))|(X992 @ (esk31_2 @ X991 @ X992))))&(~(exu @ X992)|(exu @ X991)|((X991 @ (esk30_2 @ X991 @ X992))|(X992 @ (esk31_2 @ X991 @ X992)))))))&(((emptyset)=(emptyset))&((((X995)!=(X996))|(((X997)!=(X998))|((setadjoin @ X995 @ X997)=(setadjoin @ X996 @ X998))))&((((X999)!=(X1000))|((powerset @ X999)=(powerset @ X1000)))&((((X1001)!=(X1002))|((setunion @ X1001)=(setunion @ X1002)))&(((omega)=(omega))&((~(exu @ X1003)|(~(X1003 @ X1004)|(~(X1003 @ X1005)|((X1004)=(X1005)))))&(((((esk32_2 @ X1006 @ X1007)=(esk33_2 @ X1006 @ X1007))|(~(exu @ X1006)|(~(exu @ X1007)|((descr @ X1006)=(descr @ X1007)))))&((~(X1006 @ (esk32_2 @ X1006 @ X1007))|~(X1007 @ (esk33_2 @ X1006 @ X1007))|(~(exu @ X1006)|(~(exu @ X1007)|((descr @ X1006)=(descr @ X1007)))))&((X1006 @ (esk32_2 @ X1006 @ X1007))|(X1007 @ (esk33_2 @ X1006 @ X1007))|(~(exu @ X1006)|(~(exu @ X1007)|((descr @ X1006)=(descr @ X1007)))))))&((((in @ (esk34_4 @ X1010 @ X1011 @ X1012 @ X1013) @ X1010)|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))&(((in @ (esk35_4 @ X1010 @ X1011 @ X1012 @ X1013) @ X1011)|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))&((((esk34_4 @ X1010 @ X1011 @ X1012 @ X1013)=(esk35_4 @ X1010 @ X1011 @ X1012 @ X1013))|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))&((~(X1012 @ (esk34_4 @ X1010 @ X1011 @ X1012 @ X1013))|~(X1013 @ (esk35_4 @ X1010 @ X1011 @ X1012 @ X1013))|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))&((X1012 @ (esk34_4 @ X1010 @ X1011 @ X1012 @ X1013))|(X1013 @ (esk35_4 @ X1010 @ X1011 @ X1012 @ X1013))|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))))))&((((in @ (esk36_2 @ X1016 @ X1017) @ X1016)|(subset @ X1016 @ X1017))&(~(in @ (esk36_2 @ X1016 @ X1017) @ X1017)|(subset @ X1016 @ X1017)))&((((X1019)!=(X1020))|(subset @ X1020 @ X1019))&((((X1021)!=(X1022))|(subset @ X1021 @ X1022))&((((in @ (esk37_2 @ X1023 @ X1024) @ X1023)|(subset @ X1023 @ X1024))&(~(in @ (esk37_2 @ X1023 @ X1024) @ X1024)|(subset @ X1023 @ X1024)))&((subset @ emptyset @ X1026)&((~(subset @ X1027 @ X1028)|(~(in @ X1029 @ X1027)|(in @ X1029 @ X1028)))&((~(subset @ X1030 @ X1031)|((in @ X1032 @ X1031)|~(in @ X1032 @ X1030)))&((~(in @ X1035 @ X1033)|((in @ X1035 @ X1034)|~(subset @ X1033 @ X1034)))&(((subset @ X1036 @ X1037)|((X1036)!=(X1037)))&((~(in @ X1040 @ X1038)|((in @ X1040 @ X1039)|((X1038)!=(X1039))))&((subset @ X1041 @ X1041)&((~(subset @ X1042 @ X1043)|(~(subset @ X1043 @ X1044)|(subset @ X1042 @ X1044)))&((subset @ X1046 @ (setadjoin @ X1045 @ X1046))&((~(subset @ X1047 @ X1049)|(subset @ X1047 @ (setadjoin @ X1048 @ X1049)))&((~(subset @ X1050 @ X1051)|(in @ X1050 @ (powerset @ X1051)))&((~(subset @ X1052 @ X1053)|(~(subset @ X1053 @ X1052)|((X1052)=(X1053))))&((~(subset @ X1054 @ emptyset)|((X1054)=(emptyset)))&((~(subset @ X1056 @ X1055)|(in @ X1056 @ (powerset @ X1055)))&((~(in @ X1058 @ (powerset @ X1057))|(subset @ X1058 @ X1057))&((in @ X1059 @ (powerset @ X1059))&((~(subset @ X1060 @ X1061)|(subset @ (powerset @ X1060) @ (powerset @ X1061)))&((in @ (dsetconstr @ X1062 @ X1063) @ (powerset @ X1062))&((subset @ (dsetconstr @ X1064 @ X1065) @ X1064)&((~(in @ X1068 @ X1066)|(in @ X1068 @ (binunion @ X1066 @ X1067)))&((in @ X1070 @ (setadjoin @ X1069 @ (setadjoin @ X1070 @ emptyset)))&((~(in @ X1073 @ X1072)|(in @ X1073 @ (binunion @ X1071 @ X1072)))&(((((in @ X1076 @ X1075)|(X1077)|(in @ X1076 @ X1074)|~(in @ X1076 @ (binunion @ X1074 @ X1075)))&(~(X1077)|(X1077)|(in @ X1076 @ X1074)|~(in @ X1076 @ (binunion @ X1074 @ X1075))))&(((in @ X1076 @ X1075)|(X1077)|~(X1077)|~(in @ X1076 @ (binunion @ X1074 @ X1075)))&(~(X1077)|(X1077)|~(X1077)|~(in @ X1076 @ (binunion @ X1074 @ X1075)))))&((~(in @ X1080 @ (binunion @ X1078 @ X1079))|((in @ X1080 @ X1078)|(in @ X1080 @ X1079)))&((subset @ X1081 @ (binunion @ X1081 @ X1082))&((subset @ X1084 @ (binunion @ X1083 @ X1084))&((~(in @ X1087 @ X1085)|(~(in @ X1087 @ X1086)|(in @ X1087 @ (binintersect @ X1085 @ X1086))))&((~(subset @ X1090 @ X1088)|(~(subset @ X1090 @ X1089)|(subset @ X1090 @ (binintersect @ X1088 @ X1089))))&((~(in @ X1093 @ (binintersect @ X1091 @ X1092))|(in @ X1093 @ X1091))&((subset @ (binintersect @ X1094 @ X1095) @ X1094)&((~(subset @ X1096 @ X1097)|((binintersect @ X1096 @ X1097)=(X1096)))&((((binintersect @ X1098 @ X1099)!=(X1099))|(subset @ X1099 @ X1098))&((~(in @ X1102 @ (binintersect @ X1100 @ X1101))|(in @ X1102 @ X1101))&((((in @ (esk38_2 @ X1103 @ X1104) @ X1103)|((binintersect @ X1103 @ X1104)=(emptyset)))&((in @ (esk38_2 @ X1103 @ X1104) @ X1104)|((binintersect @ X1103 @ X1104)=(emptyset))))&((subset @ (binintersect @ X1106 @ X1107) @ X1107)&((~(subset @ X1109 @ X1108)|((binintersect @ X1108 @ X1109)=(X1109)))&((((binintersect @ X1110 @ X1111)!=(X1110))|(subset @ X1110 @ X1111))&(((binintersect @ X1112 @ (binunion @ X1113 @ X1114))=(binunion @ (binintersect @ X1112 @ X1113) @ (binintersect @ X1112 @ X1114)))&((~(in @ X1117 @ X1115)|((in @ X1117 @ X1116)|(in @ X1117 @ (setminus @ X1115 @ X1116))))&((~(in @ X1120 @ (setminus @ X1118 @ X1119))|(in @ X1120 @ X1118))&((~(in @ X1123 @ (setminus @ X1121 @ X1122))|~(in @ X1123 @ X1122))&((~(subset @ X1124 @ X1125)|((setminus @ X1124 @ X1125)=(emptyset)))&(((in @ X1128 @ (setminus @ X1126 @ X1127))|(~(in @ X1128 @ X1126)|(in @ X1128 @ X1127)))&(((in @ X1131 @ (setminus @ X1129 @ X1130))|((in @ X1131 @ X1130)|~(in @ X1131 @ X1129)))&(((in @ X1134 @ X1132)|~(in @ X1134 @ (setminus @ X1132 @ X1133)))&((~(in @ X1137 @ X1136)|~(in @ X1137 @ (setminus @ X1135 @ X1136)))&((subset @ (setminus @ X1138 @ X1139) @ X1138)&((((setminus @ X1140 @ X1141)!=(emptyset))|(subset @ X1140 @ X1141))&((((~(in @ X1144 @ X1142)|(X1145)|(in @ X1144 @ X1142)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(((in @ X1144 @ X1143)|(X1145)|(in @ X1144 @ X1142)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(~(X1145)|(X1145)|(in @ X1144 @ X1142)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))))&(((~(in @ X1144 @ X1142)|(X1145)|~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(((in @ X1144 @ X1143)|(X1145)|~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(~(X1145)|(X1145)|~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))))&((~(in @ X1144 @ X1142)|(X1145)|~(X1145)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(((in @ X1144 @ X1143)|(X1145)|~(X1145)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(~(X1145)|(X1145)|~(X1145)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))))))&((~(in @ X1148 @ X1146)|((in @ X1148 @ X1147)|(in @ X1148 @ (symdiff @ X1146 @ X1147))))&(((in @ X1151 @ X1149)|(~(in @ X1151 @ X1150)|(in @ X1151 @ (symdiff @ X1149 @ X1150))))&((~(in @ X1154 @ X1152)|(~(in @ X1154 @ X1153)|~(in @ X1154 @ (symdiff @ X1152 @ X1153))))&(((in @ X1157 @ X1155)|((in @ X1157 @ X1156)|~(in @ X1157 @ (symdiff @ X1155 @ X1156))))&((in @ X1159 @ (setadjoin @ X1158 @ (setadjoin @ X1159 @ emptyset)))&((in @ X1160 @ (setunion @ (setadjoin @ (setadjoin @ X1160 @ emptyset) @ (setadjoin @ (setadjoin @ X1160 @ (setadjoin @ X1161 @ emptyset)) @ emptyset))))&((in @ X1163 @ (setunion @ (setadjoin @ (setadjoin @ X1162 @ emptyset) @ (setadjoin @ (setadjoin @ X1162 @ (setadjoin @ X1163 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1164 @ emptyset) @ (setadjoin @ (setadjoin @ X1164 @ (setadjoin @ X1165 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1166 @ X1167))&((~(in @ X1169 @ X1168)|(subset @ (setadjoin @ X1169 @ emptyset) @ X1168))&((~(in @ X1171 @ X1170)|(in @ (setadjoin @ X1171 @ emptyset) @ (powerset @ X1170)))&((~(in @ X1174 @ X1172)|(in @ (setadjoin @ X1174 @ emptyset) @ (powerset @ (binunion @ X1172 @ X1173))))&((~(in @ X1177 @ (setadjoin @ X1175 @ (setadjoin @ X1176 @ emptyset)))|(((X1177)=(X1175))|((X1177)=(X1176))))&((~(in @ X1180 @ X1178)|(~(in @ X1181 @ X1179)|(subset @ (setadjoin @ X1180 @ (setadjoin @ X1181 @ emptyset)) @ (binunion @ X1178 @ X1179))))&((~(in @ X1184 @ X1182)|(~(in @ X1185 @ X1183)|(in @ (setadjoin @ X1184 @ (setadjoin @ X1185 @ emptyset)) @ (powerset @ (binunion @ X1182 @ X1183)))))&((~(in @ X1188 @ X1186)|(~(in @ X1189 @ X1187)|(subset @ (setadjoin @ (setadjoin @ X1188 @ emptyset) @ (setadjoin @ (setadjoin @ X1188 @ (setadjoin @ X1189 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1186 @ X1187)))))&((~(in @ X1192 @ X1190)|(~(in @ X1193 @ X1191)|(in @ (setadjoin @ (setadjoin @ X1192 @ emptyset) @ (setadjoin @ (setadjoin @ X1192 @ (setadjoin @ X1193 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1190 @ X1191))))))&((~(in @ X1196 @ X1194)|(~(in @ X1197 @ X1195)|(in @ (kpair @ X1196 @ X1197) @ (powerset @ (powerset @ (binunion @ X1194 @ X1195))))))&((in @ esk41_0 @ esk39_0)&((in @ esk42_0 @ esk40_0)&~(in @ (kpair @ esk41_0 @ esk42_0) @ (cartprod @ esk39_0 @ esk40_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_171])])])])])])])). 237.80/32.55 thf(c_0_174, plain, ![X1202:$i, X1203:$i]:(((cartprod @ X1202 @ X1203)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X1202 @ X1203))) @ (^[Z0:$i]:(?[X3:$i]:((((in @ X3 @ X1202))&(?[X14:$i]:((((in @ X14 @ X1203))&(((Z0)=(kpair @ X3 @ X14))))))))))))), inference(variable_rename,[status(thm)],[c_0_172])). 237.80/32.55 thf(c_0_175, plain, ![X1228:$i, X2:$i, X3:$i]:(((epred3_2 @ X3 @ X2 @ X1228)<=>?[X1226:$i]:(((in @ X1226 @ X2)&?[X1227:$i]:(((in @ X1227 @ X3)&((X1228)=(kpair @ X1226 @ X1227)))))))), introduced(definition)). 237.80/32.55 thf(c_0_176, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((X1 @ X2))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_173])). 237.80/32.55 thf(c_0_177, plain, ![X3:$i, X2:$i]:(((cartprod @ X2 @ X3)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X2 @ X3))) @ (epred3_2 @ X3 @ X2)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_174]), c_0_175])). 237.80/32.55 thf(c_0_178, negated_conjecture, ~((in @ (kpair @ esk41_0 @ esk42_0) @ (cartprod @ esk39_0 @ esk40_0))), inference(split_conjunct,[status(thm)],[c_0_173])). 237.80/32.55 thf(c_0_179, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X2 @ (cartprod @ X3 @ X4))|~((in @ X2 @ (powerset @ (powerset @ (binunion @ X3 @ X4)))))|~((epred3_2 @ X4 @ X3 @ X2)))), inference(spm,[status(thm)],[c_0_176, c_0_177])). 237.80/32.55 thf(c_0_180, plain, ![X1230:$i, X1231:$i, X1232:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i]:(((((in @ (esk48_3 @ X1230 @ X1231 @ X1232) @ X1231)|~(epred3_2 @ X1232 @ X1231 @ X1230))&(((in @ (esk49_3 @ X1230 @ X1231 @ X1232) @ X1232)|~(epred3_2 @ X1232 @ X1231 @ X1230))&(((X1230)=(kpair @ (esk48_3 @ X1230 @ X1231 @ X1232) @ (esk49_3 @ X1230 @ X1231 @ X1232)))|~(epred3_2 @ X1232 @ X1231 @ X1230))))&(~(in @ X1238 @ X1236)|(~(in @ X1239 @ X1237)|((X1235)!=(kpair @ X1238 @ X1239)))|(epred3_2 @ X1237 @ X1236 @ X1235)))), 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)],[])])])])])])])). 237.80/32.55 thf(c_0_181, negated_conjecture, (~((in @ (kpair @ esk41_0 @ esk42_0) @ (powerset @ (powerset @ (binunion @ esk39_0 @ esk40_0)))))|~((epred3_2 @ esk40_0 @ esk39_0 @ (kpair @ esk41_0 @ esk42_0)))), inference(spm,[status(thm)],[c_0_178, c_0_179])). 237.80/32.55 thf(c_0_182, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i]:(((in @ (kpair @ X2 @ X4) @ (powerset @ (powerset @ (binunion @ X3 @ X5))))|~((in @ X2 @ X3))|~((in @ X4 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_173])). 237.80/32.55 thf(c_0_183, negated_conjecture, (in @ esk42_0 @ esk40_0), inference(split_conjunct,[status(thm)],[c_0_173])). 237.80/32.55 thf(c_0_184, negated_conjecture, (in @ esk41_0 @ esk39_0), inference(split_conjunct,[status(thm)],[c_0_173])). 237.80/32.55 thf(c_0_185, plain, ![X7:$i, X3:$i, X2:$i, X5:$i, X4:$i]:(((epred3_2 @ X5 @ X3 @ X7)|~((in @ X2 @ X3))|~((in @ X4 @ X5))|((X7)!=(kpair @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_180])). 237.80/32.55 thf(c_0_186, negated_conjecture, ~((epred3_2 @ esk40_0 @ esk39_0 @ (kpair @ esk41_0 @ esk42_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181, c_0_182]), c_0_183]), c_0_184])])). 237.80/32.55 thf(c_0_187, plain, ![X2:$i, X5:$i, X4:$i, X3:$i]:(((epred3_2 @ X2 @ X3 @ (kpair @ X4 @ X5))|~((in @ X5 @ X2))|~((in @ X4 @ X3)))), inference(er,[status(thm)],[c_0_185])). 237.80/32.55 thf(c_0_188, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186, c_0_187]), c_0_183]), c_0_184])]), ['proof']). 237.80/32.55 % SZS output end CNFRefutation 237.80/32.55 % Parsed axioms : 321 237.80/32.55 % Removed by relevancy pruning/SinE : 173 237.80/32.55 % Initial clauses : 234 237.80/32.55 % Removed in clause preprocessing : 25 237.80/32.55 % Initial clauses in saturation : 209 237.80/32.55 % Processed clauses : 4727 237.80/32.55 % ...of these trivial : 118 237.80/32.55 % ...subsumed : 1554 237.80/32.55 % ...remaining for further processing : 3055 237.80/32.55 % Other redundant clauses eliminated : 91 237.80/32.55 % Clauses deleted for lack of memory : 0 237.80/32.55 % Backward-subsumed : 439 237.80/32.55 % Backward-rewritten : 47 237.80/32.55 % Generated clauses : 497219 237.80/32.55 % ...of the previous two non-redundant : 492801 237.80/32.55 % ...aggressively subsumed : 0 237.80/32.55 % Contextual simplify-reflections : 10 237.80/32.55 % Paramodulations : 497004 237.80/32.55 % Factorizations : 110 237.80/32.55 % NegExts : 1 237.80/32.55 % Equation resolutions : 91 237.80/32.55 % Disequality decompositions : 0 237.80/32.55 % Total rewrite steps : 9001 237.80/32.55 % ...of those cached : 8020 237.80/32.55 % Propositional unsat checks : 0 237.80/32.55 % Propositional check models : 0 237.80/32.55 % Propositional check unsatisfiable : 0 237.80/32.55 % Propositional clauses : 0 237.80/32.55 % Propositional clauses after purity: 0 237.80/32.55 % Propositional unsat core size : 0 237.80/32.55 % Propositional preprocessing time : 0.000 237.80/32.55 % Propositional encoding time : 0.000 237.80/32.55 % Propositional solver time : 0.000 237.80/32.55 % Success case prop preproc time : 0.000 237.80/32.55 % Success case prop encoding time : 0.000 237.80/32.55 % Success case prop solver time : 0.000 237.80/32.55 % Current number of processed clauses : 2373 237.80/32.55 % Positive orientable unit clauses : 171 237.80/32.55 % Positive unorientable unit clauses: 0 237.80/32.55 % Negative unit clauses : 125 237.80/32.55 % Non-unit-clauses : 2077 237.80/32.55 % Current number of unprocessed clauses: 486876 237.80/32.55 % ...number of literals in the above : 2114451 237.80/32.55 % Current number of archived formulas : 0 237.80/32.55 % Current number of archived clauses : 670 237.80/32.55 % Clause-clause subsumption calls (NU) : 593562 237.80/32.55 % Rec. Clause-clause subsumption calls : 302516 237.80/32.55 % Non-unit clause-clause subsumptions : 710 237.80/32.55 % Unit Clause-clause subsumption calls : 21444 237.80/32.55 % Rewrite failures with RHS unbound : 0 237.80/32.55 % BW rewrite match attempts : 270 237.80/32.55 % BW rewrite match successes : 44 237.80/32.55 % Condensation attempts : 4727 237.80/32.55 % Condensation successes : 26 237.80/32.55 % Termbank termtop insertions : 9985349 237.80/32.55 % Search garbage collected termcells : 12948 237.80/32.55 237.80/32.55 % ------------------------------------------------- 237.80/32.55 % User time : 30.705 s 237.80/32.55 % System time : 0.963 s 237.80/32.55 % Total time : 31.668 s 237.80/32.55 % Maximum resident set size: 6508 pages 237.80/32.55 237.80/32.55 % ------------------------------------------------- 237.80/32.55 % User time : 30.717 s 237.80/32.55 % System time : 0.969 s 237.80/32.55 % Total time : 31.686 s 237.80/32.55 % Maximum resident set size: 4864 pages 237.80/32.55 % E exiting 237.80/32.55 EOF