0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : run_E %s %d THM 0.13/0.34 % Computer : n024.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 03:37:22 EDT 2022 0.13/0.34 % CPUTime : 0.19/0.49 Running higher-order on 8 cores theorem proving 0.19/0.49 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=120 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.19/0.49 # Version: 3.0pre003-ho 1.13/0.65 # Preprocessing class: HSLMSLSSLLLCHFA. 1.13/0.65 # Scheduled 8 strats onto 8 cores with 120 seconds (960 total) 1.13/0.65 # Starting ehoh_best5 with 120s (1) cores 1.13/0.65 # Starting almost_fo_3_lam with 120s (1) cores 1.13/0.65 # Starting new_bool_5 with 120s (1) cores 1.13/0.65 # Starting pre_casc_3 with 120s (1) cores 1.13/0.65 # Starting ho_unfolding_8 with 120s (1) cores 1.13/0.65 # Starting new_ho_10_cnf2 with 120s (1) cores 1.13/0.65 # Starting new_bool_3 with 120s (1) cores 1.13/0.65 # Starting new_ho_5 with 120s (1) cores 1.13/0.65 # new_bool_5 with pid 16817 completed with status 0 1.13/0.65 # Result found by new_bool_5 1.13/0.65 # Preprocessing class: HSLMSLSSLLLCHFA. 1.13/0.65 # Scheduled 8 strats onto 8 cores with 120 seconds (960 total) 1.13/0.65 # Starting ehoh_best5 with 120s (1) cores 1.13/0.65 # Starting almost_fo_3_lam with 120s (1) cores 1.13/0.65 # Starting new_bool_5 with 120s (1) cores 1.13/0.65 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 1.13/0.65 # ...ProofStateSinE()=171/377 1.13/0.65 # Search class: HGHSM-FSLM31-MHFMMSBN 1.13/0.65 # Scheduled 6 strats onto 1 cores with 120 seconds (120 total) 1.13/0.65 # Starting new_ho_10_cnf2 with 65s (1) cores 1.13/0.65 # new_ho_10_cnf2 with pid 16828 completed with status 0 1.13/0.65 # Result found by new_ho_10_cnf2 1.13/0.65 # Preprocessing class: HSLMSLSSLLLCHFA. 1.13/0.65 # Scheduled 8 strats onto 8 cores with 120 seconds (960 total) 1.13/0.65 # Starting ehoh_best5 with 120s (1) cores 1.13/0.65 # Starting almost_fo_3_lam with 120s (1) cores 1.13/0.65 # Starting new_bool_5 with 120s (1) cores 1.13/0.65 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 1.13/0.65 # ...ProofStateSinE()=171/377 1.13/0.65 # Search class: HGHSM-FSLM31-MHFMMSBN 1.13/0.65 # Scheduled 6 strats onto 1 cores with 120 seconds (120 total) 1.13/0.65 # Starting new_ho_10_cnf2 with 65s (1) cores 1.13/0.65 # Preprocessing time : 0.005 s 1.13/0.65 # Presaturation interreduction done 1.13/0.65 1.13/0.65 # Proof found! 1.13/0.65 # SZS status Theorem 1.13/0.65 # SZS output start CNFRefutation 1.13/0.65 thf(decl_22, type, in: $i > $i > $o). 1.13/0.65 thf(decl_23, type, exu: ($i > $o) > $o). 1.13/0.65 thf(decl_24, type, setextAx: $o). 1.13/0.65 thf(decl_25, type, emptyset: $i). 1.13/0.65 thf(decl_26, type, emptysetAx: $o). 1.13/0.65 thf(decl_27, type, setadjoin: $i > $i > $i). 1.13/0.65 thf(decl_28, type, setadjoinAx: $o). 1.13/0.65 thf(decl_29, type, powerset: $i > $i). 1.13/0.65 thf(decl_30, type, powersetAx: $o). 1.13/0.65 thf(decl_31, type, setunion: $i > $i). 1.13/0.65 thf(decl_32, type, setunionAx: $o). 1.13/0.65 thf(decl_33, type, omega: $i). 1.13/0.65 thf(decl_34, type, omega0Ax: $o). 1.13/0.65 thf(decl_35, type, omegaSAx: $o). 1.13/0.65 thf(decl_36, type, omegaIndAx: $o). 1.13/0.65 thf(decl_37, type, replAx: $o). 1.13/0.65 thf(decl_38, type, foundationAx: $o). 1.13/0.65 thf(decl_39, type, wellorderingAx: $o). 1.13/0.65 thf(decl_40, type, descr: ($i > $o) > $i). 1.13/0.65 thf(decl_41, type, descrp: $o). 1.13/0.65 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 1.13/0.65 thf(decl_43, type, dsetconstrI: $o). 1.13/0.65 thf(decl_44, type, dsetconstrEL: $o). 1.13/0.65 thf(decl_45, type, dsetconstrER: $o). 1.13/0.65 thf(decl_46, type, exuE1: $o). 1.13/0.65 thf(decl_47, type, prop2set: $o > $i). 1.13/0.65 thf(decl_48, type, prop2setE: $o). 1.13/0.65 thf(decl_49, type, emptysetE: $o). 1.13/0.65 thf(decl_50, type, emptysetimpfalse: $o). 1.13/0.65 thf(decl_51, type, notinemptyset: $o). 1.13/0.65 thf(decl_52, type, exuE3e: $o). 1.13/0.65 thf(decl_53, type, setext: $o). 1.13/0.65 thf(decl_54, type, emptyI: $o). 1.13/0.65 thf(decl_55, type, noeltsimpempty: $o). 1.13/0.65 thf(decl_56, type, setbeta: $o). 1.13/0.65 thf(decl_57, type, nonempty: $i > $o). 1.13/0.65 thf(decl_58, type, nonemptyE1: $o). 1.13/0.65 thf(decl_59, type, nonemptyI: $o). 1.13/0.65 thf(decl_60, type, nonemptyI1: $o). 1.13/0.65 thf(decl_61, type, setadjoinIL: $o). 1.13/0.65 thf(decl_62, type, emptyinunitempty: $o). 1.13/0.65 thf(decl_63, type, setadjoinIR: $o). 1.13/0.65 thf(decl_64, type, setadjoinE: $o). 1.13/0.65 thf(decl_65, type, setadjoinOr: $o). 1.13/0.65 thf(decl_66, type, setoftrueEq: $o). 1.13/0.65 thf(decl_67, type, powersetI: $o). 1.13/0.65 thf(decl_68, type, emptyinPowerset: $o). 1.13/0.65 thf(decl_69, type, emptyInPowerset: $o). 1.13/0.65 thf(decl_70, type, powersetE: $o). 1.13/0.65 thf(decl_71, type, setunionI: $o). 1.13/0.65 thf(decl_72, type, setunionE: $o). 1.13/0.65 thf(decl_73, type, subPowSU: $o). 1.13/0.65 thf(decl_74, type, exuE2: $o). 1.13/0.65 thf(decl_75, type, nonemptyImpWitness: $o). 1.13/0.65 thf(decl_76, type, uniqinunit: $o). 1.13/0.65 thf(decl_77, type, notinsingleton: $o). 1.13/0.65 thf(decl_78, type, eqinunit: $o). 1.13/0.65 thf(decl_79, type, singletonsswitch: $o). 1.13/0.65 thf(decl_80, type, upairsetE: $o). 1.13/0.65 thf(decl_81, type, upairsetIL: $o). 1.13/0.65 thf(decl_82, type, upairsetIR: $o). 1.13/0.65 thf(decl_83, type, emptyE1: $o). 1.13/0.65 thf(decl_84, type, vacuousDall: $o). 1.13/0.65 thf(decl_85, type, quantDeMorgan1: $o). 1.13/0.65 thf(decl_86, type, quantDeMorgan2: $o). 1.13/0.65 thf(decl_87, type, quantDeMorgan3: $o). 1.13/0.65 thf(decl_88, type, quantDeMorgan4: $o). 1.13/0.65 thf(decl_89, type, prop2setI: $o). 1.13/0.65 thf(decl_90, type, set2prop: $i > $o). 1.13/0.65 thf(decl_91, type, prop2set2propI: $o). 1.13/0.65 thf(decl_92, type, notdexE: $o). 1.13/0.65 thf(decl_93, type, notdallE: $o). 1.13/0.65 thf(decl_94, type, exuI1: $o). 1.13/0.65 thf(decl_95, type, exuI3: $o). 1.13/0.65 thf(decl_96, type, exuI2: $o). 1.13/0.65 thf(decl_97, type, inCongP: $o). 1.13/0.65 thf(decl_98, type, in__Cong: $o). 1.13/0.65 thf(decl_99, type, exuE3u: $o). 1.13/0.65 thf(decl_100, type, exu__Cong: $o). 1.13/0.65 thf(decl_101, type, emptyset__Cong: $o). 1.13/0.65 thf(decl_102, type, setadjoin__Cong: $o). 1.13/0.65 thf(decl_103, type, powerset__Cong: $o). 1.13/0.65 thf(decl_104, type, setunion__Cong: $o). 1.13/0.65 thf(decl_105, type, omega__Cong: $o). 1.13/0.65 thf(decl_106, type, exuEu: $o). 1.13/0.65 thf(decl_107, type, descr__Cong: $o). 1.13/0.65 thf(decl_108, type, dsetconstr__Cong: $o). 1.13/0.65 thf(decl_109, type, subset: $i > $i > $o). 1.13/0.65 thf(decl_110, type, disjoint: $i > $i > $o). 1.13/0.65 thf(decl_111, type, setsmeet: $i > $i > $o). 1.13/0.65 thf(decl_112, type, subsetI1: $o). 1.13/0.65 thf(decl_113, type, eqimpsubset2: $o). 1.13/0.65 thf(decl_114, type, eqimpsubset1: $o). 1.13/0.65 thf(decl_115, type, subsetI2: $o). 1.13/0.65 thf(decl_116, type, emptysetsubset: $o). 1.13/0.65 thf(decl_117, type, subsetE: $o). 1.13/0.65 thf(decl_118, type, subsetE2: $o). 1.13/0.65 thf(decl_119, type, notsubsetI: $o). 1.13/0.65 thf(decl_120, type, notequalI1: $o). 1.13/0.65 thf(decl_121, type, notequalI2: $o). 1.13/0.65 thf(decl_122, type, subsetRefl: $o). 1.13/0.65 thf(decl_123, type, subsetTrans: $o). 1.13/0.65 thf(decl_124, type, setadjoinSub: $o). 1.13/0.65 thf(decl_125, type, setadjoinSub2: $o). 1.13/0.65 thf(decl_126, type, subset2powerset: $o). 1.13/0.65 thf(decl_127, type, setextsub: $o). 1.13/0.65 thf(decl_128, type, subsetemptysetimpeq: $o). 1.13/0.65 thf(decl_129, type, powersetI1: $o). 1.13/0.65 thf(decl_130, type, powersetE1: $o). 1.13/0.65 thf(decl_131, type, inPowerset: $o). 1.13/0.65 thf(decl_132, type, powersetsubset: $o). 1.13/0.65 thf(decl_133, type, sepInPowerset: $o). 1.13/0.65 thf(decl_134, type, sepSubset: $o). 1.13/0.65 thf(decl_135, type, binunion: $i > $i > $i). 1.13/0.65 thf(decl_136, type, binunionIL: $o). 1.13/0.65 thf(decl_137, type, upairset2IR: $o). 1.13/0.65 thf(decl_138, type, binunionIR: $o). 1.13/0.65 thf(decl_139, type, binunionEcases: $o). 1.13/0.65 thf(decl_140, type, binunionE: $o). 1.13/0.65 thf(decl_141, type, binunionLsub: $o). 1.13/0.65 thf(decl_142, type, binunionRsub: $o). 1.13/0.65 thf(decl_143, type, binintersect: $i > $i > $i). 1.13/0.65 thf(decl_144, type, binintersectI: $o). 1.13/0.65 thf(decl_145, type, binintersectSubset5: $o). 1.13/0.65 thf(decl_146, type, binintersectEL: $o). 1.13/0.65 thf(decl_147, type, binintersectLsub: $o). 1.13/0.65 thf(decl_148, type, binintersectSubset2: $o). 1.13/0.65 thf(decl_149, type, binintersectSubset3: $o). 1.13/0.65 thf(decl_150, type, binintersectER: $o). 1.13/0.65 thf(decl_151, type, disjointsetsI1: $o). 1.13/0.65 thf(decl_152, type, binintersectRsub: $o). 1.13/0.65 thf(decl_153, type, binintersectSubset4: $o). 1.13/0.65 thf(decl_154, type, binintersectSubset1: $o). 1.13/0.65 thf(decl_155, type, bs114d: $o). 1.13/0.65 thf(decl_156, type, regular: $i > $o). 1.13/0.65 thf(decl_157, type, setminus: $i > $i > $i). 1.13/0.65 thf(decl_158, type, setminusI: $o). 1.13/0.65 thf(decl_159, type, setminusEL: $o). 1.13/0.65 thf(decl_160, type, setminusER: $o). 1.13/0.65 thf(decl_161, type, setminusSubset2: $o). 1.13/0.65 thf(decl_162, type, setminusERneg: $o). 1.13/0.65 thf(decl_163, type, setminusELneg: $o). 1.13/0.65 thf(decl_164, type, setminusILneg: $o). 1.13/0.65 thf(decl_165, type, setminusIRneg: $o). 1.13/0.65 thf(decl_166, type, setminusLsub: $o). 1.13/0.65 thf(decl_167, type, setminusSubset1: $o). 1.13/0.65 thf(decl_168, type, symdiff: $i > $i > $i). 1.13/0.65 thf(decl_169, type, symdiffE: $o). 1.13/0.65 thf(decl_170, type, symdiffI1: $o). 1.13/0.65 thf(decl_171, type, symdiffI2: $o). 1.13/0.65 thf(decl_172, type, symdiffIneg1: $o). 1.13/0.65 thf(decl_173, type, symdiffIneg2: $o). 1.13/0.65 thf(decl_174, type, iskpair: $i > $o). 1.13/0.65 thf(decl_175, type, secondinupair: $o). 1.13/0.65 thf(decl_176, type, setukpairIL: $o). 1.13/0.65 thf(decl_177, type, setukpairIR: $o). 1.13/0.65 thf(decl_178, type, kpairiskpair: $o). 1.13/0.65 thf(decl_179, type, kpair: $i > $i > $i). 1.13/0.65 thf(decl_180, type, kpairp: $o). 1.13/0.65 thf(decl_181, type, cartprod: $i > $i > $i). 1.13/0.65 thf(decl_182, type, singletonsubset: $o). 1.13/0.65 thf(decl_183, type, singletoninpowerset: $o). 1.13/0.65 thf(decl_184, type, singletoninpowunion: $o). 1.13/0.65 thf(decl_185, type, upairset2E: $o). 1.13/0.65 thf(decl_186, type, upairsubunion: $o). 1.13/0.65 thf(decl_187, type, upairinpowunion: $o). 1.13/0.65 thf(decl_188, type, ubforcartprodlem1: $o). 1.13/0.65 thf(decl_189, type, ubforcartprodlem2: $o). 1.13/0.65 thf(decl_190, type, ubforcartprodlem3: $o). 1.13/0.65 thf(decl_191, type, cartprodpairin: $o). 1.13/0.65 thf(decl_192, type, cartprodmempair1: $o). 1.13/0.65 thf(decl_193, type, cartprodmempair: $o). 1.13/0.65 thf(decl_194, type, setunionE2: $o). 1.13/0.65 thf(decl_195, type, setunionsingleton1: $o). 1.13/0.65 thf(decl_196, type, setunionsingleton2: $o). 1.13/0.65 thf(decl_197, type, setunionsingleton: $o). 1.13/0.65 thf(decl_198, type, singleton: $i > $o). 1.13/0.65 thf(decl_199, type, singletonprop: $o). 1.13/0.65 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 1.13/0.65 thf(decl_201, type, ex1E1: $o). 1.13/0.65 thf(decl_202, type, ex1I: $o). 1.13/0.65 thf(decl_203, type, ex1I2: $o). 1.13/0.65 thf(decl_204, type, singletonsuniq: $o). 1.13/0.65 thf(decl_205, type, atmost1p: $i > $o). 1.13/0.65 thf(decl_206, type, atleast2p: $i > $o). 1.13/0.65 thf(decl_207, type, atmost2p: $i > $o). 1.13/0.65 thf(decl_208, type, upairsetp: $i > $o). 1.13/0.65 thf(decl_209, type, setukpairinjL1: $o). 1.13/0.65 thf(decl_210, type, kfstsingleton: $o). 1.13/0.65 thf(decl_211, type, theprop: $o). 1.13/0.65 thf(decl_212, type, kfst: $i > $i). 1.13/0.65 thf(decl_213, type, kfstpairEq: $o). 1.13/0.65 thf(decl_214, type, cartprodfstin: $o). 1.13/0.65 thf(decl_215, type, setukpairinjL2: $o). 1.13/0.65 thf(decl_216, type, setukpairinjL: $o). 1.13/0.65 thf(decl_217, type, setukpairinjR11: $o). 1.13/0.65 thf(decl_218, type, setukpairinjR12: $o). 1.13/0.65 thf(decl_219, type, setukpairinjR1: $o). 1.13/0.65 thf(decl_220, type, upairequniteq: $o). 1.13/0.65 thf(decl_221, type, setukpairinjR2: $o). 1.13/0.65 thf(decl_222, type, epred1_0: $o). 1.13/0.65 thf(decl_223, type, esk1_2: $i > $i > $i). 1.13/0.65 thf(decl_224, type, esk2_2: $i > $i > $i). 1.13/0.65 thf(decl_225, type, esk3_2: $i > $i > $i). 1.13/0.65 thf(decl_226, type, esk4_1: $i > $i). 1.13/0.65 thf(decl_227, type, esk5_2: ($i > $i > $o) > $i > $i). 1.13/0.65 thf(decl_228, type, esk6_2: ($i > $i > $o) > $i > $i). 1.13/0.65 thf(decl_229, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 1.13/0.65 thf(decl_230, type, esk8_1: $i > $i). 1.13/0.65 thf(decl_231, type, esk9_1: ($i > $o) > $i). 1.13/0.65 thf(decl_232, type, esk10_1: ($i > $o) > $i). 1.13/0.65 thf(decl_233, type, esk11_2: $i > $i > $i). 1.13/0.65 thf(decl_234, type, esk12_2: $i > $i > $i). 1.13/0.65 thf(decl_235, type, esk13_1: $i > $i). 1.13/0.65 thf(decl_236, type, esk14_1: $i > $i). 1.13/0.65 thf(decl_237, type, esk15_1: $i > $i). 1.13/0.65 thf(decl_238, type, esk16_2: $i > $i > $i). 1.13/0.65 thf(decl_239, type, esk17_3: $i > $i > $o > $i). 1.13/0.65 thf(decl_240, type, esk18_1: ($i > $o) > $i). 1.13/0.65 thf(decl_241, type, esk19_1: $i > $i). 1.13/0.65 thf(decl_242, type, esk20_2: $i > ($i > $o) > $i). 1.13/0.65 thf(decl_243, type, esk21_2: $i > ($i > $o) > $i). 1.13/0.65 thf(decl_244, type, esk22_2: $i > ($i > $o) > $i). 1.13/0.65 thf(decl_245, type, esk23_2: $i > ($i > $o) > $i). 1.13/0.65 thf(decl_246, type, esk24_2: $i > ($i > $o) > $i). 1.13/0.65 thf(decl_247, type, esk25_2: $i > ($i > $o) > $i). 1.13/0.65 thf(decl_248, type, esk26_2: ($i > $o) > $i > $i). 1.13/0.65 thf(decl_249, type, esk27_1: ($i > $o) > $i). 1.13/0.65 thf(decl_250, type, esk28_1: ($i > $o) > $i). 1.13/0.65 thf(decl_251, type, esk29_2: ($i > $o) > $i > $i). 1.13/0.65 thf(decl_252, type, esk30_2: ($i > $o) > ($i > $o) > $i). 1.13/0.65 thf(decl_253, type, esk31_2: ($i > $o) > ($i > $o) > $i). 1.13/0.65 thf(decl_254, type, esk32_2: ($i > $o) > ($i > $o) > $i). 1.13/0.65 thf(decl_255, type, esk33_2: ($i > $o) > ($i > $o) > $i). 1.13/0.65 thf(decl_256, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 1.13/0.65 thf(decl_257, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 1.13/0.65 thf(decl_258, type, esk36_2: $i > $i > $i). 1.13/0.65 thf(decl_259, type, esk37_2: $i > $i > $i). 1.13/0.65 thf(decl_260, type, esk38_2: $i > $i > $i). 1.13/0.65 thf(decl_261, type, esk39_3: $i > $i > $i > $i). 1.13/0.65 thf(decl_262, type, esk40_3: $i > $i > $i > $i). 1.13/0.65 thf(decl_263, type, esk41_2: $i > $i > $i). 1.13/0.65 thf(decl_264, type, esk42_2: $i > ($i > $o) > $i). 1.13/0.65 thf(decl_265, type, esk43_2: $i > ($i > $o) > $i). 1.13/0.65 thf(decl_266, type, esk44_2: $i > ($i > $o) > $i). 1.13/0.65 thf(decl_267, type, esk45_3: $i > ($i > $o) > $i > $i). 1.13/0.65 thf(decl_268, type, esk46_2: $i > ($i > $o) > $i). 1.13/0.65 thf(decl_269, type, esk47_2: $i > ($i > $o) > $i). 1.13/0.65 thf(decl_270, type, esk48_0: $i). 1.13/0.65 thf(decl_271, type, esk49_0: $i). 1.13/0.65 thf(decl_272, type, esk50_0: $i). 1.13/0.65 thf(decl_273, type, esk51_0: $i). 1.13/0.65 thf(decl_274, type, esk52_1: $i > $i). 1.13/0.65 thf(decl_275, type, esk53_3: $i > $i > $i > $i). 1.13/0.65 thf(decl_276, type, esk54_2: $i > $i > $i). 1.13/0.65 thf(decl_277, type, esk55_2: $i > $i > $i). 1.13/0.65 thf(decl_278, type, esk56_2: $i > $i > $i). 1.13/0.65 thf(decl_279, type, epred2_1: $i > $i > $o). 1.13/0.65 thf(decl_280, type, epred3_0: $i > $o). 1.13/0.65 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exu__Cong)). 1.13/0.65 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI1)). 1.13/0.65 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyE1)). 1.13/0.65 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setoftrueEq)). 1.13/0.65 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI)). 1.13/0.65 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE1)). 1.13/0.65 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrER)). 1.13/0.65 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', replAx)). 1.13/0.65 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonprop)). 1.13/0.65 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1I)). 1.13/0.65 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1I2)). 1.13/0.65 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstsingleton)). 1.13/0.65 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1E1)). 1.13/0.65 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sepSubset)). 1.13/0.65 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sepInPowerset)). 1.13/0.65 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstr__Cong)). 1.13/0.65 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descr__Cong)). 1.13/0.65 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuEu)). 1.13/0.65 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE3u)). 1.13/0.65 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI2)). 1.13/0.65 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI3)). 1.13/0.65 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE2)). 1.13/0.65 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setbeta)). 1.13/0.65 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE3e)). 1.13/0.65 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrEL)). 1.13/0.65 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrI)). 1.13/0.65 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descrp)). 1.13/0.65 thf(setukpairinjR, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>(((omega0Ax)=>(((((foundationAx)=>(((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((((prop2setE)=>((((notinemptyset)=>((exuE3e)=>((setext)=>((((setbeta)=>(((((setadjoinIL)=>((emptyinunitempty)=>(((((((emptyinPowerset)=>((((setunionI)=>(((subPowSU)=>((exuE2)=>((((notinsingleton)=>((((((((vacuousDall)=>(((quantDeMorgan2)=>((quantDeMorgan3)=>((((((notdallE)=>(((exuI3)=>((exuI2)=>(((in__Cong)=>((exuE3u)=>(((emptyset__Cong)=>(((powerset__Cong)=>((((exuEu)=>((descr__Cong)=>((((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>(((subsetE)=>(((notsubsetI)=>((notequalI1)=>((((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>(((setextsub)=>((subsetemptysetimpeq)=>(((((powersetsubset)=>((((binunionIL)=>((upairset2IR)=>((binunionIR)=>(((((binunionRsub)=>(((((binintersectLsub)=>((binintersectSubset2)=>(((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>(((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>(((setminusELneg)=>(((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>(((((symdiffIneg1)=>((((setukpairIL)=>((setukpairIR)=>((((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((((cartprodpairin)=>(((cartprodmempair)=>((((((singletonprop)=>(((ex1I)=>((ex1I2)=>((((kfstsingleton)=>(((kfstpairEq)=>(((setukpairinjL2)=>((setukpairinjL)=>(((((upairequniteq)=>(![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))<=(setukpairinjR2)))<=(setukpairinjR1))<=(setukpairinjR12))<=(setukpairinjR11))))<=(cartprodfstin)))<=(theprop)))<=(setukpairinjL1))<=(singletonsuniq))))<=(ex1E1)))<=(setunionsingleton))<=(setunionsingleton2))<=(setunionsingleton1))<=(setunionE2)))<=(cartprodmempair1)))<=(ubforcartprodlem3))<=(ubforcartprodlem2)))))))))<=(kpairp))<=(kpairiskpair))))<=(secondinupair))<=(symdiffIneg2)))<=(symdiffI2))<=(symdiffI1))<=(symdiffE)))))<=(setminusILneg)))<=(setminusERneg))))))<=(bs114d)))))))<=(binintersectSubset3))))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI)))<=(binunionLsub))<=(binunionE))<=(binunionEcases)))))<=(sepSubset))<=(sepInPowerset)))<=(inPowerset))<=(powersetE1))<=(powersetI1))))<=(subset2powerset)))))<=(subsetRefl))<=(notequalI2))))<=(subsetE2)))<=(emptysetsubset)))))<=(subsetI1))<=(dsetconstr__Cong))))<=(omega__Cong))<=(setunion__Cong)))<=(setadjoin__Cong)))<=(exu__Cong))))<=(inCongP))))<=(exuI1)))<=(notdexE))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4))))<=(quantDeMorgan1)))<=(emptyE1))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch))<=(eqinunit)))<=(uniqinunit))<=(nonemptyImpWitness))))<=(setunionE)))<=(powersetE))<=(emptyInPowerset)))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR))))<=(nonemptyI1))<=(nonemptyI))<=(nonemptyE1)))<=(noeltsimpempty))<=(emptyI)))))<=(emptysetimpfalse))<=(emptysetE)))<=(exuE1))<=(dsetconstrER)))))<=(wellorderingAx)))<=(replAx))<=(omegaIndAx))<=(omegaSAx)))<=(setunionAx)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR)). 1.13/0.65 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinE)). 1.13/0.65 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIR)). 1.13/0.65 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionAx)). 1.13/0.65 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectLsub)). 1.13/0.65 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inCongP)). 1.13/0.65 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdexE)). 1.13/0.65 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset2)). 1.13/0.65 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setI)). 1.13/0.65 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan4)). 1.13/0.65 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectER)). 1.13/0.65 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan1)). 1.13/0.65 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', disjointsetsI1)). 1.13/0.65 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIR)). 1.13/0.65 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIL)). 1.13/0.65 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectRsub)). 1.13/0.65 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetE)). 1.13/0.65 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsswitch)). 1.13/0.65 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset4)). 1.13/0.65 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqinunit)). 1.13/0.65 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', uniqinunit)). 1.13/0.65 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset1)). 1.13/0.65 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyImpWitness)). 1.13/0.65 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusI)). 1.13/0.65 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionE)). 1.13/0.65 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE)). 1.13/0.65 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyInPowerset)). 1.13/0.65 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusEL)). 1.13/0.65 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI)). 1.13/0.65 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinOr)). 1.13/0.65 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusER)). 1.13/0.65 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI1)). 1.13/0.65 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset2)). 1.13/0.65 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyE1)). 1.13/0.65 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusELneg)). 1.13/0.65 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', noeltsimpempty)). 1.13/0.65 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyI)). 1.13/0.65 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusIRneg)). 1.13/0.65 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetimpfalse)). 1.13/0.65 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetE)). 1.13/0.65 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusLsub)). 1.13/0.65 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', wellorderingAx)). 1.13/0.65 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset1)). 1.13/0.65 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaIndAx)). 1.13/0.65 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaSAx)). 1.13/0.65 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg1)). 1.13/0.65 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairIL)). 1.13/0.65 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairIR)). 1.13/0.65 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsubset)). 1.13/0.65 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowerset)). 1.13/0.65 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowunion)). 1.13/0.65 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2E)). 1.13/0.65 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsubunion)). 1.13/0.65 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairinpowunion)). 1.13/0.65 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem1)). 1.13/0.65 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairin)). 1.13/0.65 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempair)). 1.13/0.65 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset5)). 1.13/0.65 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectI)). 1.13/0.65 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstpairEq)). 1.13/0.65 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL2)). 1.13/0.65 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL)). 1.13/0.65 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairequniteq)). 1.13/0.65 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR2)). 1.13/0.65 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR1)). 1.13/0.65 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR12)). 1.13/0.65 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR11)). 1.13/0.65 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodfstin)). 1.13/0.65 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', theprop)). 1.13/0.65 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL1)). 1.13/0.65 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsuniq)). 1.13/0.65 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton)). 1.13/0.65 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton2)). 1.13/0.65 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton1)). 1.13/0.65 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionE2)). 1.13/0.65 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempair1)). 1.13/0.65 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem3)). 1.13/0.65 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2IR)). 1.13/0.65 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem2)). 1.13/0.65 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairp)). 1.13/0.65 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairiskpair)). 1.13/0.65 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', secondinupair)). 1.13/0.65 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg2)). 1.13/0.65 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI2)). 1.13/0.65 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI1)). 1.13/0.65 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffE)). 1.13/0.65 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIR)). 1.13/0.65 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusILneg)). 1.13/0.65 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionRsub)). 1.13/0.65 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusERneg)). 1.13/0.65 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', bs114d)). 1.13/0.65 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset3)). 1.13/0.65 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectEL)). 1.13/0.65 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionLsub)). 1.13/0.65 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionE)). 1.13/0.65 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionEcases)). 1.13/0.65 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inPowerset)). 1.13/0.65 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE1)). 1.13/0.65 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI1)). 1.13/0.65 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subset2powerset)). 1.13/0.65 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetRefl)). 1.13/0.65 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI2)). 1.13/0.65 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE2)). 1.13/0.65 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetsubset)). 1.13/0.65 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI1)). 1.13/0.65 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega__Cong)). 1.13/0.65 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunion__Cong)). 1.13/0.65 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoin__Cong)). 1.13/0.65 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIL)). 1.13/0.65 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetsubset)). 1.13/0.65 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetemptysetimpeq)). 1.13/0.65 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextsub)). 1.13/0.65 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub2)). 1.13/0.65 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub)). 1.13/0.65 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetTrans)). 1.13/0.65 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI1)). 1.13/0.65 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notsubsetI)). 1.13/0.65 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE)). 1.13/0.65 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI2)). 1.13/0.65 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset1)). 1.13/0.65 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset2)). 1.13/0.65 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powerset__Cong)). 1.13/0.65 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyset__Cong)). 1.13/0.65 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', in__Cong)). 1.13/0.65 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdallE)). 1.13/0.65 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan3)). 1.13/0.65 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan2)). 1.13/0.65 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', vacuousDall)). 1.13/0.65 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinsingleton)). 1.13/0.65 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subPowSU)). 1.13/0.65 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionI)). 1.13/0.65 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinPowerset)). 1.13/0.65 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinunitempty)). 1.13/0.65 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIL)). 1.13/0.65 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setext)). 1.13/0.65 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinemptyset)). 1.13/0.65 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setE)). 1.13/0.65 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', foundationAx)). 1.13/0.65 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega0Ax)). 1.13/0.65 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetAx)). 1.13/0.65 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinAx)). 1.13/0.65 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetAx)). 1.13/0.65 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextAx)). 1.13/0.65 thf(kpair, axiom, ((kpair)=(^[X2:$i, X3:$i]:(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpair)). 1.13/0.65 thf(c_0_171, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 1.13/0.65 thf(c_0_172, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 1.13/0.65 thf(c_0_173, 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])). 1.13/0.65 thf(c_0_174, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 1.13/0.65 thf(c_0_175, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 1.13/0.65 thf(c_0_176, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 1.13/0.65 thf(c_0_177, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 1.13/0.65 thf(c_0_178, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 1.13/0.65 thf(c_0_179, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 1.13/0.65 thf(c_0_180, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 1.13/0.65 thf(c_0_181, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 1.13/0.65 thf(c_0_182, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 1.13/0.65 thf(c_0_183, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 1.13/0.65 thf(c_0_184, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 1.13/0.65 thf(c_0_185, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 1.13/0.65 thf(c_0_186, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 1.13/0.65 thf(c_0_187, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 1.13/0.65 thf(c_0_188, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 1.13/0.65 thf(c_0_189, 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])). 1.13/0.65 thf(c_0_190, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 1.13/0.65 thf(c_0_191, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 1.13/0.65 thf(c_0_192, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 1.13/0.65 thf(c_0_193, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 1.13/0.65 thf(c_0_194, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 1.13/0.65 thf(c_0_195, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 1.13/0.65 thf(c_0_196, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 1.13/0.65 thf(c_0_197, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 1.13/0.65 thf(c_0_198, plain, ((epred1_0)<=>![X920:$i]:(?[X921:$i]:((((![X922:$i]:(((in @ X922 @ X921)=>![X923:$i]:(((in @ X923 @ X922)=>(in @ X923 @ X920)))))&![X924:$i, X925:$i]:((((in @ X924 @ X920)&(in @ X925 @ X920))=>(![X926:$i]:(((in @ X926 @ X921)=>((in @ X924 @ X926)<=>(in @ X925 @ X926))))=>((X924)=(X925))))))&![X927:$i, X928:$i]:((((in @ X927 @ X921)&(in @ X928 @ X921))=>(![X929:$i]:(((in @ X929 @ X927)=>(in @ X929 @ X928)))|![X930:$i]:(((in @ X930 @ X928)=>(in @ X930 @ X927)))))))&![X931:$i]:(((![X932:$i]:(((in @ X932 @ X931)=>(in @ X932 @ X920)))&?[X933:$i]:((in @ X933 @ X931)))=>?[X934:$i, X935:$i]:(((((in @ X934 @ X921)&(in @ X935 @ X931))&~(?[X936:$i]:(((in @ X936 @ X934)&(in @ X936 @ X931)))))&![X937:$i]:(((in @ X937 @ X921)=>(![X938:$i]:(((in @ X938 @ X937)=>(in @ X938 @ X934)))|(in @ X935 @ X937)))))))))))), introduced(definition)). 1.13/0.65 thf(c_0_199, negated_conjecture, ~((![X489:$i, X490:$i]:((![X491:$i]:(((in @ X491 @ X489)<=>(in @ X491 @ X490)))=>((X489)=(X490))))=>(![X492:$i]:(~(in @ X492 @ emptyset))=>(![X493:$i, X494:$i, X495:$i]:(((in @ X495 @ (setadjoin @ X493 @ X494))<=>(((X495)=(X493))|(in @ X495 @ X494))))=>(![X496:$i, X497:$i]:(((in @ X497 @ (powerset @ X496))<=>![X498:$i]:(((in @ X498 @ X497)=>(in @ X498 @ X496)))))=>(![X949:$i, X950:$i]:(((in @ X950 @ (setunion @ X949))<=>?[X951:$i]:(((in @ X950 @ X951)&(in @ X951 @ X949)))))=>((in @ emptyset @ omega)=>(![X948:$i]:(((in @ X948 @ omega)=>(in @ (setadjoin @ X948 @ X948) @ omega)))=>(![X945:$i]:((((in @ emptyset @ X945)&![X946:$i]:((((in @ X946 @ omega)&(in @ X946 @ X945))=>(in @ (setadjoin @ X946 @ X946) @ X945))))=>![X947:$i]:(((in @ X947 @ omega)=>(in @ X947 @ X945)))))=>(![X939:$i > $i > $o, X940:$i]:((![X941:$i]:(((in @ X941 @ X940)=>(exu @ (^[Z0:$i]:((X939 @ X941 @ Z0))))))=>?[X942:$i]:(![X943:$i]:(((in @ X943 @ X942)<=>?[X944:$i]:(((in @ X944 @ X940)&(X939 @ X944 @ X943))))))))=>(![X499:$i]:((?[X500:$i]:((in @ X500 @ X499))=>?[X501:$i]:(((in @ X501 @ X499)&~(?[X502:$i]:(((in @ X502 @ X501)&(in @ X502 @ X499))))))))=>((epred1_0)=>(![X503:$i > $o]:(((exu @ (^[Z0:$i]:((X503 @ Z0))))=>(X503 @ (descr @ (^[Z0:$i]:((X503 @ Z0)))))))=>(![X504:$i, X505:$i > $o, X506:$i]:(((in @ X506 @ X504)=>((X505 @ X506)=>(in @ X506 @ (dsetconstr @ X504 @ (^[Z0:$i]:((X505 @ Z0))))))))=>(![X507:$i, X508:$i > $o, X509:$i]:(((in @ X509 @ (dsetconstr @ X507 @ (^[Z0:$i]:((X508 @ Z0)))))=>(in @ X509 @ X507)))=>(![X917:$i, X918:$i > $o, X919:$i]:(((in @ X919 @ (dsetconstr @ X917 @ (^[Z0:$i]:((X918 @ Z0)))))=>(X918 @ X919)))=>(![X914:$i > $o]:(((exu @ (^[Z0:$i]:((X914 @ Z0))))=>?[X915:$i]:(((X914 @ X915)&![X916:$i]:(((X914 @ X916)=>((X915)=(X916))))))))=>(![X510:$o, X511:$i]:(((in @ X511 @ (prop2set @ ((X510))))=>(X510)))=>(![X912:$i]:(((in @ X912 @ emptyset)=>![X913:$o]:((X913))))=>(![X911:$i]:(~(in @ X911 @ emptyset))=>(![X512:$i]:(~(in @ X512 @ emptyset))=>(![X513:$i > $o]:(((exu @ (^[Z0:$i]:((X513 @ Z0))))=>?[X514:$i]:((X513 @ X514))))=>(![X515:$i, X516:$i]:((![X517:$i]:(((in @ X517 @ X515)=>(in @ X517 @ X516)))=>(![X518:$i]:(((in @ X518 @ X516)=>(in @ X518 @ X515)))=>((X515)=(X516)))))=>(![X909:$i]:((![X910:$i]:(~(in @ X910 @ X909))=>((X909)=(emptyset))))=>(![X907:$i]:((![X908:$i]:(~(in @ X908 @ X907))=>((X907)=(emptyset))))=>(![X519:$i, X520:$i > $o, X521:$i]:(((in @ X521 @ X519)=>((in @ X521 @ (dsetconstr @ X519 @ (^[Z0:$i]:((X520 @ Z0)))))<=>(X520 @ X521))))=>(![X905:$i]:(((nonempty @ X905)=>?[X906:$i]:((in @ X906 @ X905))))=>(![X902:$i, X903:$i > $o, X904:$i]:(((in @ X904 @ X902)=>((X903 @ X904)=>(nonempty @ (dsetconstr @ X902 @ (^[Z0:$i]:((X903 @ Z0))))))))=>(![X900:$i]:((?[X901:$i]:((in @ X901 @ X900))=>(nonempty @ X900)))=>(![X522:$i, X523:$i]:((in @ X522 @ (setadjoin @ X522 @ X523)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X897:$i, X898:$i, X899:$i]:(((in @ X899 @ X898)=>(in @ X899 @ (setadjoin @ X897 @ X898))))=>(![X893:$i, X894:$i, X895:$i]:(((in @ X895 @ (setadjoin @ X893 @ X894))=>![X896:$o]:(((((X895)=(X893))=>(X896))=>(((in @ X895 @ X894)=>(X896))=>(X896))))))=>(![X890:$i, X891:$i, X892:$i]:(((in @ X892 @ (setadjoin @ X890 @ X891))=>(((X892)=(X890))|(in @ X892 @ X891))))=>(![X889:$i]:(((dsetconstr @ X889 @ (^[Z0:$i]:(($true))))=(X889)))=>(![X886:$i, X887:$i]:((![X888:$i]:(((in @ X888 @ X887)=>(in @ X888 @ X886)))=>(in @ X887 @ (powerset @ X886))))=>(![X524:$i]:((in @ emptyset @ (powerset @ X524)))=>(![X885:$i]:((in @ emptyset @ (powerset @ X885)))=>(![X882:$i, X883:$i, X884:$i]:(((in @ X883 @ (powerset @ X882))=>((in @ X884 @ X883)=>(in @ X884 @ X882))))=>(![X525:$i, X526:$i, X527:$i]:(((in @ X526 @ X527)=>((in @ X527 @ X525)=>(in @ X526 @ (setunion @ X525)))))=>(![X878:$i, X879:$i]:(((in @ X879 @ (setunion @ X878))=>![X880:$o]:((![X881:$i]:(((in @ X879 @ X881)=>((in @ X881 @ X878)=>(X880))))=>(X880)))))=>(![X528:$i, X529:$i]:(((in @ X529 @ X528)=>(in @ X529 @ (powerset @ (setunion @ X528)))))=>(![X530:$i > $o]:(((exu @ (^[Z0:$i]:((X530 @ Z0))))=>?[X531:$i]:(![X532:$i]:(((X530 @ X532)<=>((X532)=(X531)))))))=>(![X876:$i]:(((nonempty @ X876)=>?[X877:$i]:((in @ X877 @ X876))))=>(![X874:$i, X875:$i]:(((in @ X874 @ (setadjoin @ X875 @ emptyset))=>((X874)=(X875))))=>(![X533:$i, X534:$i]:((((X533)!=(X534))=>~(in @ X534 @ (setadjoin @ X533 @ emptyset))))=>(![X872:$i, X873:$i]:((((X872)=(X873))=>(in @ X872 @ (setadjoin @ X873 @ emptyset))))=>(![X870:$i, X871:$i]:(((in @ X870 @ (setadjoin @ X871 @ emptyset))=>(in @ X871 @ (setadjoin @ X870 @ emptyset))))=>(![X867:$i, X868:$i, X869:$i]:(((in @ X869 @ (setadjoin @ X867 @ (setadjoin @ X868 @ emptyset)))=>(((X869)=(X867))|((X869)=(X868)))))=>(![X865:$i, X866:$i]:((in @ X865 @ (setadjoin @ X865 @ (setadjoin @ X866 @ emptyset))))=>(![X863:$i, X864:$i]:((in @ X864 @ (setadjoin @ X863 @ (setadjoin @ X864 @ emptyset))))=>(![X860:$i, X861:$i > $o]:((?[X862:$i]:(((in @ X862 @ X860)&(X861 @ X862)))=>((dsetconstr @ X860 @ (^[Z0:$i]:((X861 @ Z0))))!=(emptyset))))=>(![X535:$i > $o, X536:$i]:(((in @ X536 @ emptyset)=>(X535 @ X536)))=>(![X856:$i, X857:$i > $o]:((~(![X858:$i]:(((in @ X858 @ X856)=>(X857 @ X858))))=>?[X859:$i]:(((in @ X859 @ X856)&~(X857 @ X859)))))=>(![X537:$i, X538:$i > $o]:((![X539:$i]:(((in @ X539 @ X537)=>~(X538 @ X539)))=>~(?[X540:$i]:(((in @ X540 @ X537)&(X538 @ X540))))))=>(![X541:$i, X542:$i > $o]:((~(?[X543:$i]:(((in @ X543 @ X541)&(X542 @ X543))))=>![X544:$i]:(((in @ X544 @ X541)=>~(X542 @ X544)))))=>(![X852:$i, X853:$i > $o]:((?[X854:$i]:(((in @ X854 @ X852)&~(X853 @ X854)))=>~(![X855:$i]:(((in @ X855 @ X852)=>(X853 @ X855))))))=>(![X851:$o]:(((X851)=>(in @ emptyset @ (prop2set @ ((X851))))))=>((prop2set2propI)=>(![X847:$i, X848:$i > $o]:((~(?[X849:$i]:(((in @ X849 @ X847)&(X848 @ X849))))=>![X850:$i]:(((in @ X850 @ X847)=>~(X848 @ X850)))))=>(![X545:$i, X546:$i > $o]:((~(![X547:$i]:(((in @ X547 @ X545)=>(X546 @ X547))))=>?[X548:$i]:(((in @ X548 @ X545)&~(X546 @ X548)))))=>(![X844:$i > $o]:((?[X845:$i]:(((X844 @ X845)&![X846:$i]:(((X844 @ X846)=>((X845)=(X846))))))=>(exu @ (^[Z0:$i]:((X844 @ Z0))))))=>(![X549:$i > $o]:((?[X550:$i]:((X549 @ X550))=>(![X551:$i, X552:$i]:(((X549 @ X551)=>((X549 @ X552)=>((X551)=(X552)))))=>(exu @ (^[Z0:$i]:((X549 @ Z0)))))))=>(![X553:$i > $o]:((?[X554:$i]:(![X555:$i]:(((X553 @ X555)<=>((X555)=(X554)))))=>(exu @ (^[Z0:$i]:((X553 @ Z0))))))=>(![X840:$i, X841:$i]:((((X840)=(X841))=>![X842:$i, X843:$i]:((((X842)=(X843))=>((in @ X842 @ X840)=>(in @ X843 @ X841))))))=>(![X556:$i, X557:$i]:((((X556)=(X557))=>![X558:$i, X559:$i]:((((X558)=(X559))=>((in @ X558 @ X556)<=>(in @ X559 @ X557))))))=>(![X560:$i > $o]:(((exu @ (^[Z0:$i]:((X560 @ Z0))))=>![X561:$i, X562:$i]:(((X560 @ X561)=>((X560 @ X562)=>((X561)=(X562)))))))=>(![X836:$i > $o, X837:$i > $o]:((![X838:$i, X839:$i]:((((X838)=(X839))=>((X836 @ X838)<=>(X837 @ X839))))=>((exu @ (^[Z0:$i]:((X836 @ Z0))))<=>(exu @ (^[Z0:$i]:((X837 @ Z0)))))))=>(((emptyset)=(emptyset))=>(![X832:$i, X833:$i]:((((X832)=(X833))=>![X834:$i, X835:$i]:((((X834)=(X835))=>((setadjoin @ X832 @ X834)=(setadjoin @ X833 @ X835))))))=>(![X563:$i, X564:$i]:((((X563)=(X564))=>((powerset @ X563)=(powerset @ X564))))=>(![X830:$i, X831:$i]:((((X830)=(X831))=>((setunion @ X830)=(setunion @ X831))))=>(((omega)=(omega))=>(![X565:$i > $o]:(((exu @ (^[Z0:$i]:((X565 @ Z0))))=>![X566:$i, X567:$i]:(((X565 @ X566)=>((X565 @ X567)=>((X566)=(X567)))))))=>(![X568:$i > $o, X569:$i > $o]:((![X570:$i, X571:$i]:((((X570)=(X571))=>((X568 @ X570)<=>(X569 @ X571))))=>((exu @ (^[Z0:$i]:((X568 @ Z0))))=>((exu @ (^[Z0:$i]:((X569 @ Z0))))=>((descr @ (^[Z0:$i]:((X568 @ Z0))))=(descr @ (^[Z0:$i]:((X569 @ Z0)))))))))=>(![X824:$i, X825:$i]:((((X824)=(X825))=>![X826:$i > $o, X827:$i > $o]:((![X828:$i]:(((in @ X828 @ X824)=>![X829:$i]:(((in @ X829 @ 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X815)=>((X814)!=(X815)))))=>(![X813:$i]:((subset @ X813 @ X813))=>(![X587:$i, X588:$i, X589:$i]:(((subset @ X587 @ X588)=>((subset @ X588 @ X589)=>(subset @ X587 @ X589))))=>(![X590:$i, X591:$i]:((subset @ X591 @ (setadjoin @ X590 @ X591)))=>(![X592:$i, X593:$i, X594:$i]:(((subset @ X592 @ X594)=>(subset @ X592 @ (setadjoin @ X593 @ X594))))=>(![X811:$i, X812:$i]:(((subset @ X811 @ X812)=>(in @ X811 @ (powerset @ X812))))=>(![X595:$i, X596:$i]:(((subset @ X595 @ X596)=>((subset @ X596 @ X595)=>((X595)=(X596)))))=>(![X597:$i]:(((subset @ X597 @ emptyset)=>((X597)=(emptyset))))=>(![X809:$i, X810:$i]:(((subset @ X810 @ X809)=>(in @ X810 @ (powerset @ X809))))=>(![X807:$i, X808:$i]:(((in @ X808 @ (powerset @ X807))=>(subset @ X808 @ X807)))=>(![X806:$i]:((in @ X806 @ (powerset @ X806)))=>(![X598:$i, X599:$i]:(((subset @ X598 @ X599)=>(subset @ (powerset @ X598) @ (powerset @ X599))))=>(![X804:$i, X805:$i > $o]:((in @ (dsetconstr @ X804 @ (^[Z0:$i]:((X805 @ Z0)))) @ (powerset @ 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setadjoinE]), setadjoinIR]), setunionAx]), c_0_171]), binintersectLsub]), inCongP]), c_0_172]), notdexE]), binintersectSubset2]), prop2setI]), quantDeMorgan4]), binintersectER]), quantDeMorgan1]), c_0_173]), disjointsetsI1]), upairsetIR]), upairsetIL]), binintersectRsub]), upairsetE]), singletonsswitch]), binintersectSubset4]), eqinunit]), uniqinunit]), binintersectSubset1]), nonemptyImpWitness]), setminusI]), setunionE]), powersetE]), emptyInPowerset]), setminusEL]), powersetI]), c_0_174]), setadjoinOr]), setminusER]), nonemptyI1]), setminusSubset2]), c_0_175]), nonemptyE1]), setminusELneg]), noeltsimpempty]), emptyI]), setminusIRneg]), emptysetimpfalse]), emptysetE]), c_0_176]), c_0_177]), setminusLsub]), wellorderingAx]), c_0_178]), setminusSubset1]), omegaIndAx]), omegaSAx]), symdiffIneg1]), setukpairIL]), setukpairIR]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), cartprodpairin]), cartprodmempair]), c_0_179]), binintersectSubset5]), binintersectI]), c_0_180]), c_0_181]), c_0_182]), kfstpairEq]), setukpairinjL2]), setukpairinjL]), upairequniteq]), setukpairinjR2]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), cartprodfstin]), theprop]), setukpairinjL1]), singletonsuniq]), c_0_183]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodmempair1]), ubforcartprodlem3]), upairset2IR]), ubforcartprodlem2]), kpairp]), kpairiskpair]), secondinupair]), symdiffIneg2]), symdiffI2]), symdiffI1]), symdiffE]), binunionIR]), setminusILneg]), binunionRsub]), setminusERneg]), bs114d]), binintersectSubset3]), binintersectEL]), binunionLsub]), binunionE]), binunionEcases]), c_0_184]), c_0_185]), inPowerset]), powersetE1]), powersetI1]), subset2powerset]), subsetRefl]), notequalI2]), subsetE2]), emptysetsubset]), subsetI1]), c_0_186]), omega__Cong]), setunion__Cong]), setadjoin__Cong]), binunionIL]), powersetsubset]), subsetemptysetimpeq]), setextsub]), setadjoinSub2]), setadjoinSub]), subsetTrans]), notequalI1]), notsubsetI]), subsetE]), subsetI2]), eqimpsubset1]), eqimpsubset2]), c_0_187]), c_0_188]), powerset__Cong]), emptyset__Cong]), c_0_189]), in__Cong]), c_0_190]), c_0_191]), notdallE]), quantDeMorgan3]), quantDeMorgan2]), vacuousDall]), notinsingleton]), c_0_192]), subPowSU]), setunionI]), emptyinPowerset]), emptyinunitempty]), setadjoinIL]), c_0_193]), setext]), c_0_194]), notinemptyset]), prop2setE]), c_0_195]), c_0_196]), c_0_197]), foundationAx]), omega0Ax]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_198])). 1.13/0.65 thf(c_0_200, plain, ![X952:$i, X953:$i]:(((kpair @ X952 @ X953)=(setadjoin @ (setadjoin @ X952 @ emptyset) @ (setadjoin @ (setadjoin @ X952 @ (setadjoin @ X953 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])])). 1.13/0.65 thf(c_0_201, negated_conjecture, ![X954:$i, X955:$i, X957:$i, X958:$i, X959:$i, X960:$i, X961:$i, X962:$i, X963:$i, X964:$i, X965:$i, X967:$i, X968:$i, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i, X976:$i, X977:$i > $i > $o, X978:$i, X981:$i, X983:$i, X984:$i, X985:$i, X986:$i, X988:$i, X989:$i > $o, X990:$i, X991:$i > $o, X992:$i, X993:$i, X994:$i > $o, X995:$i, X996:$i, X997:$i > $o, X998:$i, X999:$i > $o, X1001:$i, X1002:$o, X1003:$i, X1004:$i, X1005:$o, X1006:$i, X1007:$i, X1008:$i > $o, X1010:$i, X1011:$i, X1014:$i, X1016:$i, X1018:$i, X1019:$i > $o, X1020:$i, X1021:$i, X1023:$i, X1024:$i > $o, X1025:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$o, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$o, X1056:$i, X1057:$i, X1058:$i > $o, X1060:$i, X1061:$i, X1062:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1075:$i, X1076:$i, X1077:$i, X1078:$i, X1079:$i, X1080:$i > $o, X1081:$i, X1082:$i > $o, X1083:$i, X1084:$i, X1085:$i > $o, X1086:$i, X1088:$i, X1089:$i > $o, X1091:$i, X1092:$i, X1093:$i > $o, X1095:$i, X1096:$i, X1097:$i > $o, X1098:$i, X1100:$o, X1101:$i, X1102:$i > $o, X1104:$i, X1105:$i, X1106:$i > $o, X1107:$i, X1109:$i > $o, X1110:$i, X1112:$i > $o, X1113:$i, X1116:$i > $o, X1117:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i > $o, X1128:$i, X1129:$i, X1130:$i > $o, X1131:$i > $o, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i > $o, X1143:$i, X1144:$i, X1145:$i > $o, X1146:$i > $o, X1149:$i, X1150:$i, X1151:$i > $o, X1152:$i > $o, X1155:$i, X1156:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1165:$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, X1198:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i > $o, X1203:$i, X1204:$i > $o, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1216:$o, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1228:$i, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$i, X1264:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$o, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i > $o, X1359:$i, X1360:$i, X1361:$i > $o, X1363:$i, X1364:$i > $o, X1365:$i, X1367:$i, X1368:$i > $o, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i]:((((~(in @ (esk1_2 @ X954 @ X955) @ X954)|~(in @ (esk1_2 @ X954 @ X955) @ X955)|((X954)=(X955)))&((in @ (esk1_2 @ X954 @ X955) @ X954)|(in @ (esk1_2 @ X954 @ X955) @ X955)|((X954)=(X955))))&(~(in @ X957 @ emptyset)&(((~(in @ X960 @ (setadjoin @ X958 @ X959))|(((X960)=(X958))|(in @ X960 @ X959)))&((((X960)!=(X958))|(in @ X960 @ (setadjoin @ X958 @ X959)))&(~(in @ X960 @ X959)|(in @ X960 @ (setadjoin @ X958 @ X959)))))&(((~(in @ X962 @ (powerset @ X961))|(~(in @ X963 @ X962)|(in @ X963 @ X961)))&(((in @ (esk2_2 @ X964 @ X965) @ X965)|(in @ X965 @ (powerset @ X964)))&(~(in @ (esk2_2 @ X964 @ X965) @ X964)|(in @ X965 @ (powerset @ X964)))))&(((((in @ X968 @ (esk3_2 @ X967 @ X968))|~(in @ X968 @ (setunion @ X967)))&((in @ (esk3_2 @ X967 @ X968) @ X967)|~(in @ X968 @ (setunion @ X967))))&(~(in @ X971 @ X972)|~(in @ X972 @ X970)|(in @ X971 @ (setunion @ X970))))&((in @ emptyset @ omega)&((~(in @ X973 @ omega)|(in @ (setadjoin @ X973 @ X973) @ omega))&(((((in @ (esk4_1 @ X974) @ omega)|~(in @ emptyset @ X974)|(~(in @ X976 @ omega)|(in @ X976 @ X974)))&((in @ (esk4_1 @ X974) @ X974)|~(in @ emptyset @ X974)|(~(in @ X976 @ omega)|(in @ X976 @ X974))))&(~(in @ (setadjoin @ (esk4_1 @ X974) @ (esk4_1 @ X974)) @ X974)|~(in @ emptyset @ X974)|(~(in @ X976 @ omega)|(in @ X976 @ X974))))&((((((in @ (esk7_3 @ X977 @ X978 @ X981) @ X978)|~(in @ X981 @ (esk6_2 @ X977 @ X978))|(in @ (esk5_2 @ X977 @ X978) @ X978))&((X977 @ (esk7_3 @ X977 @ X978 @ X981) @ X981)|~(in @ X981 @ (esk6_2 @ X977 @ X978))|(in @ (esk5_2 @ X977 @ X978) @ X978)))&(~(in @ X984 @ X978)|~(X977 @ X984 @ X983)|(in @ X983 @ (esk6_2 @ X977 @ X978))|(in @ (esk5_2 @ X977 @ X978) @ X978)))&((((in @ (esk7_3 @ X977 @ X978 @ X981) @ X978)|~(in @ X981 @ (esk6_2 @ X977 @ X978))|~(exu @ (^[Z0:$i]:((X977 @ (esk5_2 @ X977 @ X978) @ Z0)))))&((X977 @ (esk7_3 @ X977 @ X978 @ X981) @ X981)|~(in @ X981 @ (esk6_2 @ X977 @ X978))|~(exu @ (^[Z0:$i]:((X977 @ (esk5_2 @ X977 @ X978) @ Z0))))))&(~(in @ X984 @ X978)|~(X977 @ X984 @ X983)|(in @ X983 @ (esk6_2 @ X977 @ X978))|~(exu @ (^[Z0:$i]:((X977 @ (esk5_2 @ X977 @ X978) @ Z0)))))))&((((in @ (esk8_1 @ X985) @ X985)|~(in @ X986 @ X985))&(~(in @ X988 @ (esk8_1 @ X985))|~(in @ X988 @ X985)|~(in @ X986 @ X985)))&((epred1_0)&((~(exu @ (^[Z0:$i]:((X989 @ Z0))))|(X989 @ (descr @ (^[Z0:$i]:((X989 @ Z0))))))&((~(in @ X992 @ X990)|(~(X991 @ X992)|(in @ X992 @ (dsetconstr @ X990 @ (^[Z0:$i]:((X991 @ Z0)))))))&((~(in @ X995 @ (dsetconstr @ X993 @ (^[Z0:$i]:((X994 @ Z0)))))|(in @ X995 @ X993))&((~(in @ X998 @ (dsetconstr @ X996 @ (^[Z0:$i]:((X997 @ Z0)))))|(X997 @ X998))&((((X999 @ (esk9_1 @ X999))|~(exu @ (^[Z0:$i]:((X999 @ Z0)))))&(~(X999 @ X1001)|((esk9_1 @ X999)=(X1001))|~(exu @ (^[Z0:$i]:((X999 @ Z0))))))&((~(in @ X1003 @ (prop2set @ ((X1002))))|(X1002))&((~(in @ X1004 @ emptyset)|(X1005))&(~(in @ X1006 @ emptyset)&(~(in @ X1007 @ emptyset)&((~(exu @ (^[Z0:$i]:((X1008 @ Z0))))|(X1008 @ (esk10_1 @ X1008)))&(((((in @ (esk12_2 @ X1010 @ X1011) @ X1011)|((X1010)=(X1011))|(in @ (esk11_2 @ X1010 @ X1011) @ X1010))&(~(in @ (esk12_2 @ X1010 @ X1011) @ X1010)|((X1010)=(X1011))|(in @ (esk11_2 @ X1010 @ X1011) @ X1010)))&(((in @ (esk12_2 @ X1010 @ X1011) @ X1011)|((X1010)=(X1011))|~(in @ (esk11_2 @ X1010 @ X1011) @ X1011))&(~(in @ (esk12_2 @ X1010 @ X1011) @ X1010)|((X1010)=(X1011))|~(in @ (esk11_2 @ X1010 @ X1011) @ X1011))))&(((in @ (esk13_1 @ X1014) @ X1014)|((X1014)=(emptyset)))&(((in @ (esk14_1 @ X1016) @ X1016)|((X1016)=(emptyset)))&(((~(in @ X1020 @ (dsetconstr @ X1018 @ (^[Z0:$i]:((X1019 @ Z0)))))|(X1019 @ X1020)|~(in @ X1020 @ X1018))&(~(X1019 @ X1020)|(in @ X1020 @ (dsetconstr @ X1018 @ (^[Z0:$i]:((X1019 @ Z0)))))|~(in @ X1020 @ X1018)))&((~(nonempty @ X1021)|(in @ (esk15_1 @ X1021) @ X1021))&((~(in @ X1025 @ X1023)|(~(X1024 @ X1025)|(nonempty @ (dsetconstr @ X1023 @ (^[Z0:$i]:((X1024 @ Z0)))))))&((~(in @ X1027 @ X1026)|(nonempty @ X1026))&((in @ X1028 @ (setadjoin @ X1028 @ X1029))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1032 @ X1031)|(in @ X1032 @ (setadjoin @ X1030 @ X1031)))&(((((in @ X1035 @ X1034)|(X1036)|((X1035)=(X1033))|~(in @ X1035 @ (setadjoin @ X1033 @ X1034)))&(~(X1036)|(X1036)|((X1035)=(X1033))|~(in @ X1035 @ (setadjoin @ X1033 @ X1034))))&(((in @ X1035 @ X1034)|(X1036)|~(X1036)|~(in @ X1035 @ (setadjoin @ X1033 @ X1034)))&(~(X1036)|(X1036)|~(X1036)|~(in @ X1035 @ (setadjoin @ X1033 @ X1034)))))&((~(in @ X1039 @ (setadjoin @ X1037 @ X1038))|(((X1039)=(X1037))|(in @ X1039 @ X1038)))&(((dsetconstr @ X1040 @ (^[Z0:$i]:(($true))))=(X1040))&((((in @ (esk16_2 @ X1041 @ X1042) @ X1042)|(in @ X1042 @ (powerset @ X1041)))&(~(in @ (esk16_2 @ X1041 @ X1042) @ X1041)|(in @ X1042 @ (powerset @ X1041))))&((in @ emptyset @ (powerset @ X1044))&((in @ emptyset @ (powerset @ X1045))&((~(in @ X1047 @ (powerset @ X1046))|(~(in @ X1048 @ X1047)|(in @ X1048 @ X1046)))&((~(in @ X1050 @ X1051)|(~(in @ X1051 @ X1049)|(in @ X1050 @ (setunion @ X1049))))&((((in @ X1053 @ (esk17_3 @ X1052 @ X1053 @ X1054))|(X1054)|~(in @ X1053 @ (setunion @ X1052)))&(((in @ (esk17_3 @ X1052 @ X1053 @ X1054) @ X1052)|(X1054)|~(in @ X1053 @ (setunion @ X1052)))&(~(X1054)|(X1054)|~(in @ X1053 @ (setunion @ X1052)))))&((~(in @ X1057 @ X1056)|(in @ X1057 @ (powerset @ (setunion @ X1056))))&(((~(X1058 @ X1060)|((X1060)=(esk18_1 @ X1058))|~(exu @ (^[Z0:$i]:((X1058 @ Z0)))))&(((X1061)!=(esk18_1 @ X1058))|(X1058 @ X1061)|~(exu @ (^[Z0:$i]:((X1058 @ Z0))))))&((~(nonempty @ X1062)|(in @ (esk19_1 @ X1062) @ X1062))&((~(in @ X1064 @ (setadjoin @ X1065 @ emptyset))|((X1064)=(X1065)))&((((X1066)=(X1067))|~(in @ X1067 @ (setadjoin @ X1066 @ emptyset)))&((((X1068)!=(X1069))|(in @ X1068 @ (setadjoin @ X1069 @ emptyset)))&((~(in @ X1070 @ (setadjoin @ X1071 @ emptyset))|(in @ X1071 @ (setadjoin @ X1070 @ emptyset)))&((~(in @ X1074 @ (setadjoin @ X1072 @ (setadjoin @ X1073 @ emptyset)))|(((X1074)=(X1072))|((X1074)=(X1073))))&((in @ X1075 @ (setadjoin @ X1075 @ (setadjoin @ X1076 @ emptyset)))&((in @ X1078 @ (setadjoin @ X1077 @ (setadjoin @ X1078 @ emptyset)))&((~(in @ X1081 @ X1079)|~(X1080 @ X1081)|((dsetconstr @ X1079 @ (^[Z0:$i]:((X1080 @ Z0))))!=(emptyset)))&((~(in @ X1083 @ emptyset)|(X1082 @ X1083))&((((in @ (esk20_2 @ X1084 @ X1085) @ X1084)|(~(in @ X1086 @ X1084)|(X1085 @ X1086)))&(~(X1085 @ (esk20_2 @ X1084 @ X1085))|(~(in @ X1086 @ X1084)|(X1085 @ X1086))))&((((in @ (esk21_2 @ X1088 @ X1089) @ X1088)|(~(in @ X1091 @ X1088)|~(X1089 @ X1091)))&((X1089 @ (esk21_2 @ X1088 @ X1089))|(~(in @ X1091 @ X1088)|~(X1089 @ X1091))))&((((in @ (esk22_2 @ X1092 @ X1093) @ X1092)|(~(in @ X1095 @ X1092)|~(X1093 @ X1095)))&((X1093 @ (esk22_2 @ X1092 @ X1093))|(~(in @ X1095 @ X1092)|~(X1093 @ X1095))))&((((in @ (esk23_2 @ X1096 @ X1097) @ X1096)|(~(in @ X1098 @ X1096)|(X1097 @ X1098)))&(~(X1097 @ (esk23_2 @ X1096 @ X1097))|(~(in @ X1098 @ X1096)|(X1097 @ X1098))))&((~(X1100)|(in @ emptyset @ (prop2set @ ((X1100)))))&((prop2set2propI)&((((in @ (esk24_2 @ X1101 @ X1102) @ X1101)|(~(in @ X1104 @ X1101)|~(X1102 @ X1104)))&((X1102 @ (esk24_2 @ X1101 @ X1102))|(~(in @ X1104 @ X1101)|~(X1102 @ X1104))))&((((in @ (esk25_2 @ X1105 @ X1106) @ X1105)|(~(in @ X1107 @ X1105)|(X1106 @ X1107)))&(~(X1106 @ (esk25_2 @ X1105 @ X1106))|(~(in @ X1107 @ X1105)|(X1106 @ X1107))))&((((X1109 @ (esk26_2 @ X1109 @ X1110))|~(X1109 @ X1110)|(exu @ (^[Z0:$i]:((X1109 @ Z0)))))&(((X1110)!=(esk26_2 @ X1109 @ X1110))|~(X1109 @ X1110)|(exu @ (^[Z0:$i]:((X1109 @ Z0))))))&((((X1112 @ (esk27_1 @ X1112))|(exu @ (^[Z0:$i]:((X1112 @ Z0))))|~(X1112 @ X1113))&(((X1112 @ (esk28_1 @ X1112))|(exu @ (^[Z0:$i]:((X1112 @ Z0))))|~(X1112 @ X1113))&(((esk27_1 @ X1112)!=(esk28_1 @ X1112))|(exu @ (^[Z0:$i]:((X1112 @ Z0))))|~(X1112 @ X1113))))&(((~(X1116 @ (esk29_2 @ X1116 @ X1117))|((esk29_2 @ X1116 @ X1117)!=(X1117))|(exu @ (^[Z0:$i]:((X1116 @ Z0)))))&((X1116 @ (esk29_2 @ X1116 @ X1117))|((esk29_2 @ X1116 @ X1117)=(X1117))|(exu @ (^[Z0:$i]:((X1116 @ Z0))))))&((((X1119)!=(X1120))|(((X1121)!=(X1122))|(~(in @ X1121 @ X1119)|(in @ X1122 @ X1120))))&(((~(in @ X1125 @ X1123)|(in @ X1126 @ X1124)|((X1125)!=(X1126))|((X1123)!=(X1124)))&(~(in @ X1126 @ X1124)|(in @ X1125 @ X1123)|((X1125)!=(X1126))|((X1123)!=(X1124))))&((~(exu @ (^[Z0:$i]:((X1127 @ Z0))))|(~(X1127 @ X1128)|(~(X1127 @ X1129)|((X1128)=(X1129)))))&((((~(exu @ (^[Z0:$i]:((X1130 @ Z0))))|(exu @ (^[Z0:$i]:((X1131 @ Z0))))|((esk30_2 @ X1130 @ X1131)=(esk31_2 @ X1130 @ X1131)))&(~(exu @ (^[Z0:$i]:((X1131 @ Z0))))|(exu @ (^[Z0:$i]:((X1130 @ Z0))))|((esk30_2 @ X1130 @ X1131)=(esk31_2 @ X1130 @ X1131))))&(((~(exu @ (^[Z0:$i]:((X1130 @ Z0))))|(exu @ (^[Z0:$i]:((X1131 @ Z0))))|(~(X1130 @ (esk30_2 @ X1130 @ X1131))|~(X1131 @ (esk31_2 @ X1130 @ X1131))))&(~(exu @ (^[Z0:$i]:((X1131 @ Z0))))|(exu @ (^[Z0:$i]:((X1130 @ Z0))))|(~(X1130 @ (esk30_2 @ X1130 @ X1131))|~(X1131 @ (esk31_2 @ X1130 @ X1131)))))&((~(exu @ (^[Z0:$i]:((X1130 @ Z0))))|(exu @ (^[Z0:$i]:((X1131 @ Z0))))|((X1130 @ (esk30_2 @ X1130 @ X1131))|(X1131 @ (esk31_2 @ X1130 @ X1131))))&(~(exu @ (^[Z0:$i]:((X1131 @ Z0))))|(exu @ (^[Z0:$i]:((X1130 @ Z0))))|((X1130 @ (esk30_2 @ X1130 @ X1131))|(X1131 @ (esk31_2 @ X1130 @ X1131)))))))&(((emptyset)=(emptyset))&((((X1134)!=(X1135))|(((X1136)!=(X1137))|((setadjoin @ X1134 @ X1136)=(setadjoin @ X1135 @ X1137))))&((((X1138)!=(X1139))|((powerset @ X1138)=(powerset @ X1139)))&((((X1140)!=(X1141))|((setunion @ X1140)=(setunion @ X1141)))&(((omega)=(omega))&((~(exu @ (^[Z0:$i]:((X1142 @ Z0))))|(~(X1142 @ X1143)|(~(X1142 @ X1144)|((X1143)=(X1144)))))&(((((esk32_2 @ X1145 @ X1146)=(esk33_2 @ X1145 @ X1146))|(~(exu @ (^[Z0:$i]:((X1145 @ Z0))))|(~(exu @ (^[Z0:$i]:((X1146 @ Z0))))|((descr @ (^[Z0:$i]:((X1145 @ Z0))))=(descr @ (^[Z0:$i]:((X1146 @ Z0))))))))&((~(X1145 @ (esk32_2 @ X1145 @ X1146))|~(X1146 @ (esk33_2 @ X1145 @ X1146))|(~(exu @ (^[Z0:$i]:((X1145 @ Z0))))|(~(exu @ (^[Z0:$i]:((X1146 @ Z0))))|((descr @ (^[Z0:$i]:((X1145 @ Z0))))=(descr @ (^[Z0:$i]:((X1146 @ Z0))))))))&((X1145 @ (esk32_2 @ X1145 @ X1146))|(X1146 @ (esk33_2 @ X1145 @ X1146))|(~(exu @ (^[Z0:$i]:((X1145 @ Z0))))|(~(exu @ (^[Z0:$i]:((X1146 @ Z0))))|((descr @ (^[Z0:$i]:((X1145 @ Z0))))=(descr @ (^[Z0:$i]:((X1146 @ Z0))))))))))&((((in @ (esk34_4 @ X1149 @ X1150 @ X1151 @ X1152) @ X1149)|((dsetconstr @ X1149 @ (^[Z0:$i]:((X1151 @ Z0))))=(dsetconstr @ X1150 @ (^[Z0:$i]:((X1152 @ Z0)))))|((X1149)!=(X1150)))&(((in @ (esk35_4 @ X1149 @ X1150 @ X1151 @ X1152) @ X1150)|((dsetconstr @ X1149 @ (^[Z0:$i]:((X1151 @ Z0))))=(dsetconstr @ X1150 @ (^[Z0:$i]:((X1152 @ Z0)))))|((X1149)!=(X1150)))&((((esk34_4 @ X1149 @ X1150 @ X1151 @ X1152)=(esk35_4 @ X1149 @ X1150 @ X1151 @ X1152))|((dsetconstr @ X1149 @ (^[Z0:$i]:((X1151 @ Z0))))=(dsetconstr @ X1150 @ (^[Z0:$i]:((X1152 @ Z0)))))|((X1149)!=(X1150)))&((~(X1151 @ (esk34_4 @ X1149 @ X1150 @ X1151 @ X1152))|~(X1152 @ (esk35_4 @ X1149 @ X1150 @ X1151 @ X1152))|((dsetconstr @ X1149 @ (^[Z0:$i]:((X1151 @ Z0))))=(dsetconstr @ X1150 @ (^[Z0:$i]:((X1152 @ Z0)))))|((X1149)!=(X1150)))&((X1151 @ (esk34_4 @ X1149 @ X1150 @ X1151 @ X1152))|(X1152 @ (esk35_4 @ X1149 @ X1150 @ X1151 @ X1152))|((dsetconstr @ X1149 @ (^[Z0:$i]:((X1151 @ Z0))))=(dsetconstr @ X1150 @ (^[Z0:$i]:((X1152 @ Z0)))))|((X1149)!=(X1150)))))))&((((in @ (esk36_2 @ X1155 @ X1156) @ X1155)|(subset @ X1155 @ X1156))&(~(in @ (esk36_2 @ X1155 @ X1156) @ X1156)|(subset @ X1155 @ X1156)))&((((X1158)!=(X1159))|(subset @ X1159 @ X1158))&((((X1160)!=(X1161))|(subset @ X1160 @ X1161))&((((in @ (esk37_2 @ X1162 @ X1163) @ X1162)|(subset @ X1162 @ X1163))&(~(in @ (esk37_2 @ X1162 @ X1163) @ X1163)|(subset @ X1162 @ X1163)))&((subset @ emptyset @ X1165)&((~(subset @ X1166 @ X1167)|(~(in @ X1168 @ X1166)|(in @ X1168 @ X1167)))&((~(subset @ X1169 @ X1170)|((in @ X1171 @ X1170)|~(in @ X1171 @ X1169)))&((~(in @ X1174 @ X1172)|((in @ X1174 @ X1173)|~(subset @ X1172 @ X1173)))&(((subset @ X1175 @ X1176)|((X1175)!=(X1176)))&((~(in @ X1179 @ X1177)|((in @ X1179 @ X1178)|((X1177)!=(X1178))))&((subset @ X1180 @ X1180)&((~(subset @ X1181 @ X1182)|(~(subset @ X1182 @ X1183)|(subset @ X1181 @ X1183)))&((subset @ X1185 @ (setadjoin @ X1184 @ X1185))&((~(subset @ X1186 @ X1188)|(subset @ X1186 @ (setadjoin @ X1187 @ X1188)))&((~(subset @ X1189 @ X1190)|(in @ X1189 @ (powerset @ X1190)))&((~(subset @ X1191 @ X1192)|(~(subset @ X1192 @ X1191)|((X1191)=(X1192))))&((~(subset @ X1193 @ emptyset)|((X1193)=(emptyset)))&((~(subset @ X1195 @ X1194)|(in @ X1195 @ (powerset @ X1194)))&((~(in @ X1197 @ (powerset @ X1196))|(subset @ X1197 @ X1196))&((in @ X1198 @ (powerset @ X1198))&((~(subset @ X1199 @ X1200)|(subset @ (powerset @ X1199) @ (powerset @ X1200)))&((in @ (dsetconstr @ X1201 @ (^[Z0:$i]:((X1202 @ Z0)))) @ (powerset @ X1201))&((subset @ (dsetconstr @ X1203 @ (^[Z0:$i]:((X1204 @ Z0)))) @ X1203)&((~(in @ X1207 @ X1205)|(in @ X1207 @ (binunion @ X1205 @ X1206)))&((in @ X1209 @ (setadjoin @ X1208 @ (setadjoin @ X1209 @ emptyset)))&((~(in @ X1212 @ X1211)|(in @ X1212 @ (binunion @ X1210 @ X1211)))&(((((in @ X1215 @ X1214)|(X1216)|(in @ X1215 @ X1213)|~(in @ X1215 @ (binunion @ X1213 @ X1214)))&(~(X1216)|(X1216)|(in @ X1215 @ X1213)|~(in @ X1215 @ (binunion @ X1213 @ X1214))))&(((in @ X1215 @ X1214)|(X1216)|~(X1216)|~(in @ X1215 @ (binunion @ X1213 @ X1214)))&(~(X1216)|(X1216)|~(X1216)|~(in @ X1215 @ (binunion @ X1213 @ X1214)))))&((~(in @ X1219 @ (binunion @ X1217 @ X1218))|((in @ X1219 @ X1217)|(in @ X1219 @ X1218)))&((subset @ X1220 @ (binunion @ X1220 @ X1221))&((subset @ X1223 @ (binunion @ X1222 @ X1223))&((~(in @ X1226 @ X1224)|(~(in @ X1226 @ X1225)|(in @ X1226 @ (binintersect @ X1224 @ X1225))))&((~(subset @ X1229 @ X1227)|(~(subset @ X1229 @ X1228)|(subset @ X1229 @ (binintersect @ X1227 @ X1228))))&((~(in @ X1232 @ (binintersect @ X1230 @ X1231))|(in @ X1232 @ X1230))&((subset @ (binintersect @ X1233 @ X1234) @ X1233)&((~(subset @ X1235 @ X1236)|((binintersect @ X1235 @ X1236)=(X1235)))&((((binintersect @ X1237 @ X1238)!=(X1238))|(subset @ X1238 @ X1237))&((~(in @ X1241 @ (binintersect @ X1239 @ X1240))|(in @ X1241 @ X1240))&((((in @ (esk38_2 @ X1242 @ X1243) @ X1242)|((binintersect @ X1242 @ X1243)=(emptyset)))&((in @ (esk38_2 @ X1242 @ X1243) @ X1243)|((binintersect @ X1242 @ X1243)=(emptyset))))&((subset @ (binintersect @ X1245 @ X1246) @ X1246)&((~(subset @ X1248 @ X1247)|((binintersect @ X1247 @ X1248)=(X1248)))&((((binintersect @ X1249 @ X1250)!=(X1249))|(subset @ X1249 @ X1250))&(((binintersect @ X1251 @ (binunion @ X1252 @ X1253))=(binunion @ (binintersect @ X1251 @ X1252) @ (binintersect @ X1251 @ X1253)))&((~(in @ X1256 @ X1254)|((in @ X1256 @ X1255)|(in @ X1256 @ (setminus @ X1254 @ X1255))))&((~(in @ X1259 @ (setminus @ X1257 @ X1258))|(in @ X1259 @ X1257))&((~(in @ X1262 @ (setminus @ X1260 @ X1261))|~(in @ X1262 @ X1261))&((~(subset @ X1263 @ X1264)|((setminus @ X1263 @ X1264)=(emptyset)))&(((in @ X1267 @ (setminus @ X1265 @ X1266))|(~(in @ X1267 @ X1265)|(in @ X1267 @ X1266)))&(((in @ X1270 @ (setminus @ X1268 @ X1269))|((in @ X1270 @ X1269)|~(in @ X1270 @ X1268)))&(((in @ X1273 @ X1271)|~(in @ X1273 @ (setminus @ X1271 @ X1272)))&((~(in @ X1276 @ X1275)|~(in @ X1276 @ (setminus @ X1274 @ X1275)))&((subset @ (setminus @ X1277 @ X1278) @ X1277)&((((setminus @ X1279 @ X1280)!=(emptyset))|(subset @ X1279 @ X1280))&((((~(in @ X1283 @ X1281)|(X1284)|(in @ X1283 @ X1281)|~(in @ X1283 @ (symdiff @ X1281 @ X1282)))&(((in @ X1283 @ X1282)|(X1284)|(in @ X1283 @ X1281)|~(in @ X1283 @ (symdiff @ X1281 @ X1282)))&(~(X1284)|(X1284)|(in @ X1283 @ X1281)|~(in @ X1283 @ (symdiff @ X1281 @ X1282)))))&(((~(in @ X1283 @ X1281)|(X1284)|~(in @ X1283 @ X1282)|~(in @ X1283 @ (symdiff @ X1281 @ X1282)))&(((in @ X1283 @ X1282)|(X1284)|~(in @ X1283 @ X1282)|~(in @ X1283 @ (symdiff @ X1281 @ X1282)))&(~(X1284)|(X1284)|~(in @ X1283 @ X1282)|~(in @ X1283 @ (symdiff @ X1281 @ X1282)))))&((~(in @ X1283 @ X1281)|(X1284)|~(X1284)|~(in @ X1283 @ (symdiff @ X1281 @ X1282)))&(((in @ X1283 @ X1282)|(X1284)|~(X1284)|~(in @ X1283 @ (symdiff @ X1281 @ X1282)))&(~(X1284)|(X1284)|~(X1284)|~(in @ X1283 @ (symdiff @ X1281 @ X1282)))))))&((~(in @ X1287 @ X1285)|((in @ X1287 @ X1286)|(in @ X1287 @ (symdiff @ X1285 @ X1286))))&(((in @ X1290 @ X1288)|(~(in @ X1290 @ X1289)|(in @ X1290 @ (symdiff @ X1288 @ X1289))))&((~(in @ X1293 @ X1291)|(~(in @ X1293 @ X1292)|~(in @ X1293 @ (symdiff @ X1291 @ X1292))))&(((in @ X1296 @ X1294)|((in @ X1296 @ X1295)|~(in @ X1296 @ (symdiff @ X1294 @ X1295))))&((in @ X1298 @ (setadjoin @ X1297 @ (setadjoin @ X1298 @ emptyset)))&((in @ X1299 @ (setunion @ (setadjoin @ (setadjoin @ X1299 @ emptyset) @ (setadjoin @ (setadjoin @ X1299 @ (setadjoin @ X1300 @ emptyset)) @ emptyset))))&((in @ X1302 @ (setunion @ (setadjoin @ (setadjoin @ X1301 @ emptyset) @ (setadjoin @ (setadjoin @ X1301 @ (setadjoin @ X1302 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1303 @ emptyset) @ (setadjoin @ (setadjoin @ X1303 @ (setadjoin @ X1304 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1305 @ X1306))&((~(in @ X1308 @ X1307)|(subset @ (setadjoin @ X1308 @ emptyset) @ X1307))&((~(in @ X1310 @ X1309)|(in @ (setadjoin @ X1310 @ emptyset) @ (powerset @ X1309)))&((~(in @ X1313 @ X1311)|(in @ (setadjoin @ X1313 @ emptyset) @ (powerset @ (binunion @ X1311 @ X1312))))&((~(in @ X1316 @ (setadjoin @ X1314 @ (setadjoin @ X1315 @ emptyset)))|(((X1316)=(X1314))|((X1316)=(X1315))))&((~(in @ X1319 @ X1317)|(~(in @ X1320 @ X1318)|(subset @ (setadjoin @ X1319 @ (setadjoin @ X1320 @ emptyset)) @ (binunion @ X1317 @ X1318))))&((~(in @ X1323 @ X1321)|(~(in @ X1324 @ X1322)|(in @ (setadjoin @ X1323 @ (setadjoin @ X1324 @ emptyset)) @ (powerset @ (binunion @ X1321 @ X1322)))))&((~(in @ X1327 @ X1325)|(~(in @ X1328 @ X1326)|(subset @ (setadjoin @ (setadjoin @ X1327 @ emptyset) @ (setadjoin @ (setadjoin @ X1327 @ (setadjoin @ X1328 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1325 @ X1326)))))&((~(in @ X1331 @ X1329)|(~(in @ X1332 @ X1330)|(in @ (setadjoin @ (setadjoin @ X1331 @ emptyset) @ (setadjoin @ (setadjoin @ X1331 @ (setadjoin @ X1332 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1329 @ X1330))))))&((~(in @ X1335 @ X1333)|(~(in @ X1336 @ X1334)|(in @ (kpair @ X1335 @ X1336) @ (powerset @ (powerset @ (binunion @ X1333 @ X1334))))))&((~(in @ X1339 @ X1337)|(~(in @ X1340 @ X1338)|(in @ (kpair @ X1339 @ X1340) @ (cartprod @ X1337 @ X1338))))&((((in @ (esk39_3 @ X1341 @ X1342 @ X1343) @ X1341)|~(in @ X1343 @ (cartprod @ X1341 @ X1342)))&(((in @ (esk40_3 @ X1341 @ X1342 @ X1343) @ X1342)|~(in @ X1343 @ (cartprod @ X1341 @ X1342)))&(((X1343)=(kpair @ (esk39_3 @ X1341 @ X1342 @ X1343) @ (esk40_3 @ X1341 @ X1342 @ X1343)))|~(in @ X1343 @ (cartprod @ X1341 @ X1342)))))&((~(in @ X1348 @ (cartprod @ X1346 @ X1347))|(iskpair @ X1348))&((((in @ (esk41_2 @ X1349 @ X1350) @ X1349)|~(in @ X1350 @ (setunion @ X1349)))&((in @ X1350 @ (esk41_2 @ X1349 @ X1350))|~(in @ X1350 @ (setunion @ X1349))))&((subset @ (setunion @ (setadjoin @ X1352 @ emptyset)) @ X1352)&((subset @ X1353 @ (setunion @ (setadjoin @ X1353 @ emptyset)))&(((setunion @ (setadjoin @ X1354 @ emptyset))=(X1354))&((((in @ (esk42_2 @ X1355 @ X1356) @ X1355)|(~(in @ X1359 @ X1355)|~(X1356 @ X1359)|(singleton @ (dsetconstr @ X1355 @ (^[Z0:$i]:((X1356 @ Z0)))))))&(((in @ (esk43_2 @ X1355 @ X1356) @ X1355)|(~(in @ X1359 @ X1355)|~(X1356 @ X1359)|(singleton @ (dsetconstr @ X1355 @ (^[Z0:$i]:((X1356 @ Z0)))))))&(((X1356 @ (esk42_2 @ X1355 @ X1356))|(~(in @ X1359 @ X1355)|~(X1356 @ X1359)|(singleton @ (dsetconstr @ X1355 @ (^[Z0:$i]:((X1356 @ Z0)))))))&(((X1356 @ (esk43_2 @ X1355 @ X1356))|(~(in @ X1359 @ X1355)|~(X1356 @ X1359)|(singleton @ (dsetconstr @ X1355 @ (^[Z0:$i]:((X1356 @ Z0)))))))&(((esk42_2 @ X1355 @ X1356)!=(esk43_2 @ X1355 @ X1356))|(~(in @ X1359 @ X1355)|~(X1356 @ X1359)|(singleton @ (dsetconstr @ X1355 @ (^[Z0:$i]:((X1356 @ Z0)))))))))))&((((in @ (esk44_2 @ X1360 @ X1361) @ X1360)|~(ex1 @ X1360 @ (^[Z0:$i]:((X1361 @ Z0)))))&((X1361 @ (esk44_2 @ X1360 @ X1361))|~(ex1 @ X1360 @ (^[Z0:$i]:((X1361 @ Z0))))))&((((in @ (esk45_3 @ X1363 @ X1364 @ X1365) @ X1363)|(ex1 @ X1363 @ (^[Z0:$i]:((X1364 @ Z0))))|~(X1364 @ X1365)|~(in @ X1365 @ X1363))&(((X1364 @ (esk45_3 @ X1363 @ X1364 @ X1365))|(ex1 @ X1363 @ (^[Z0:$i]:((X1364 @ Z0))))|~(X1364 @ X1365)|~(in @ X1365 @ X1363))&(((esk45_3 @ X1363 @ X1364 @ X1365)!=(X1365))|(ex1 @ X1363 @ (^[Z0:$i]:((X1364 @ Z0))))|~(X1364 @ X1365)|~(in @ X1365 @ X1363))))&((((in @ (esk46_2 @ X1367 @ X1368) @ X1367)|(~(in @ X1371 @ X1367)|~(X1368 @ X1371)|(ex1 @ X1367 @ (^[Z0:$i]:((X1368 @ Z0))))))&(((in @ (esk47_2 @ X1367 @ X1368) @ X1367)|(~(in @ X1371 @ X1367)|~(X1368 @ X1371)|(ex1 @ X1367 @ (^[Z0:$i]:((X1368 @ Z0))))))&(((X1368 @ (esk46_2 @ X1367 @ X1368))|(~(in @ X1371 @ X1367)|~(X1368 @ X1371)|(ex1 @ X1367 @ (^[Z0:$i]:((X1368 @ Z0))))))&(((X1368 @ (esk47_2 @ X1367 @ X1368))|(~(in @ X1371 @ X1367)|~(X1368 @ X1371)|(ex1 @ X1367 @ (^[Z0:$i]:((X1368 @ Z0))))))&(((esk46_2 @ X1367 @ X1368)!=(esk47_2 @ X1367 @ X1368))|(~(in @ X1371 @ X1367)|~(X1368 @ X1371)|(ex1 @ X1367 @ (^[Z0:$i]:((X1368 @ Z0))))))))))&((((setadjoin @ X1372 @ emptyset)!=(setadjoin @ X1373 @ emptyset))|((X1372)=(X1373)))&((~(in @ (setadjoin @ X1376 @ emptyset) @ (setadjoin @ (setadjoin @ X1374 @ emptyset) @ (setadjoin @ (setadjoin @ X1374 @ (setadjoin @ X1375 @ emptyset)) @ emptyset)))|((X1374)=(X1376)))&((~(iskpair @ X1377)|(singleton @ (dsetconstr @ (setunion @ X1377) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1377))))))&((~(singleton @ X1378)|(in @ (setunion @ X1378) @ X1378))&(((kfst @ (kpair @ X1379 @ X1380))=(X1379))&((~(in @ X1383 @ (cartprod @ X1381 @ X1382))|(in @ (kfst @ X1383) @ X1381))&((((setadjoin @ (setadjoin @ X1384 @ emptyset) @ (setadjoin @ (setadjoin @ X1384 @ (setadjoin @ X1385 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1386 @ emptyset) @ (setadjoin @ (setadjoin @ X1386 @ (setadjoin @ X1387 @ emptyset)) @ emptyset)))|((X1384)=(X1386)))&((((kpair @ X1388 @ X1389)!=(kpair @ X1390 @ X1391))|((X1388)=(X1390)))&((((X1392)!=(X1393))|((setadjoin @ X1392 @ (setadjoin @ X1393 @ emptyset))=(setadjoin @ X1392 @ emptyset)))&((((X1394)!=(X1395))|((setadjoin @ (setadjoin @ X1394 @ emptyset) @ (setadjoin @ (setadjoin @ X1394 @ (setadjoin @ X1395 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1394 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1396 @ emptyset) @ (setadjoin @ (setadjoin @ X1396 @ (setadjoin @ X1397 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1398 @ emptyset) @ (setadjoin @ (setadjoin @ X1398 @ (setadjoin @ X1399 @ emptyset)) @ emptyset)))|(((X1398)!=(X1399))|((X1397)=(X1399))))&((((setadjoin @ X1400 @ (setadjoin @ X1401 @ emptyset))!=(setadjoin @ X1402 @ emptyset))|((X1400)=(X1401)))&((((setadjoin @ (setadjoin @ X1403 @ emptyset) @ (setadjoin @ (setadjoin @ X1403 @ (setadjoin @ X1404 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1405 @ emptyset) @ (setadjoin @ (setadjoin @ X1405 @ (setadjoin @ X1406 @ emptyset)) @ emptyset)))|((X1404)=(X1406)))&(((kpair @ esk48_0 @ esk49_0)=(kpair @ esk50_0 @ esk51_0))&((esk49_0)!=(esk51_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[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_199])])])])])])). 1.13/0.65 thf(c_0_202, plain, ![X1411:$i, X1412:$i]:(((kpair @ X1411 @ X1412)=(setadjoin @ (setadjoin @ X1411 @ emptyset) @ (setadjoin @ (setadjoin @ X1411 @ (setadjoin @ X1412 @ emptyset)) @ emptyset)))), inference(variable_rename,[status(thm)],[c_0_200])). 1.13/0.65 thf(c_0_203, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_201])). 1.13/0.65 thf(c_0_204, negated_conjecture, ((kpair @ esk48_0 @ esk49_0)=(kpair @ esk50_0 @ esk51_0)), inference(split_conjunct,[status(thm)],[c_0_201])). 1.13/0.65 thf(c_0_205, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i]:((((X3)=(X5))|((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X4 @ (setadjoin @ X5 @ emptyset)) @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_201])). 1.13/0.65 thf(c_0_206, plain, ![X2:$i, X3:$i]:(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_202])). 1.13/0.65 thf(c_0_207, negated_conjecture, ((esk48_0)=(esk50_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203, c_0_204]), c_0_203])). 1.13/0.65 thf(c_0_208, negated_conjecture, ![X2:$i, X5:$i, X4:$i, X3:$i]:((((X2)=(X3))|((kpair @ X4 @ X2)!=(kpair @ X5 @ X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_205, c_0_206]), c_0_206])). 1.13/0.65 thf(c_0_209, negated_conjecture, ((kpair @ esk50_0 @ esk49_0)=(kpair @ esk50_0 @ esk51_0)), inference(rw,[status(thm)],[c_0_204, c_0_207])). 1.13/0.65 thf(c_0_210, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(esk49_0))|((kpair @ X3 @ X2)!=(kpair @ esk50_0 @ esk51_0)))), inference(spm,[status(thm)],[c_0_208, c_0_209])). 1.13/0.65 thf(c_0_211, negated_conjecture, ((esk49_0)!=(esk51_0)), inference(split_conjunct,[status(thm)],[c_0_201])). 1.13/0.65 thf(c_0_212, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_210]), c_0_211]), ['proof']). 1.13/0.65 # SZS output end CNFRefutation 1.13/0.65 # Parsed axioms : 377 1.13/0.65 # Removed by relevancy pruning/SinE : 206 1.13/0.65 # Initial clauses : 266 1.13/0.65 # Removed in clause preprocessing : 23 1.13/0.65 # Initial clauses in saturation : 243 1.13/0.65 # Processed clauses : 689 1.13/0.65 # ...of these trivial : 9 1.13/0.65 # ...subsumed : 135 1.13/0.65 # ...remaining for further processing : 545 1.13/0.65 # Other redundant clauses eliminated : 39 1.13/0.65 # Clauses deleted for lack of memory : 0 1.13/0.65 # Backward-subsumed : 3 1.13/0.65 # Backward-rewritten : 15 1.13/0.65 # Generated clauses : 5622 1.13/0.65 # ...of the previous two non-redundant : 5362 1.13/0.65 # ...aggressively subsumed : 0 1.13/0.65 # Contextual simplify-reflections : 0 1.13/0.65 # Paramodulations : 5577 1.13/0.65 # Factorizations : 2 1.13/0.65 # NegExts : 0 1.13/0.65 # Equation resolutions : 43 1.13/0.65 # Propositional unsat checks : 0 1.13/0.65 # Propositional check models : 0 1.13/0.65 # Propositional check unsatisfiable : 0 1.13/0.65 # Propositional clauses : 0 1.13/0.65 # Propositional clauses after purity: 0 1.13/0.65 # Propositional unsat core size : 0 1.13/0.65 # Propositional preprocessing time : 0.000 1.13/0.65 # Propositional encoding time : 0.000 1.13/0.65 # Propositional solver time : 0.000 1.13/0.65 # Success case prop preproc time : 0.000 1.13/0.65 # Success case prop encoding time : 0.000 1.13/0.65 # Success case prop solver time : 0.000 1.13/0.65 # Current number of processed clauses : 311 1.13/0.65 # Positive orientable unit clauses : 55 1.13/0.65 # Positive unorientable unit clauses: 1 1.13/0.65 # Negative unit clauses : 9 1.13/0.65 # Non-unit-clauses : 246 1.13/0.65 # Current number of unprocessed clauses: 5025 1.13/0.65 # ...number of literals in the above : 16637 1.13/0.65 # Current number of archived formulas : 0 1.13/0.65 # Current number of archived clauses : 221 1.13/0.65 # Clause-clause subsumption calls (NU) : 14407 1.13/0.65 # Rec. Clause-clause subsumption calls : 9215 1.13/0.65 # Non-unit clause-clause subsumptions : 90 1.13/0.65 # Unit Clause-clause subsumption calls : 189 1.13/0.65 # Rewrite failures with RHS unbound : 0 1.13/0.65 # BW rewrite match attempts : 42 1.13/0.65 # BW rewrite match successes : 12 1.13/0.65 # Condensation attempts : 689 1.13/0.65 # Condensation successes : 10 1.13/0.65 # Termbank termtop insertions : 108561 1.13/0.65 1.13/0.65 # ------------------------------------------------- 1.13/0.65 # User time : 0.125 s 1.13/0.65 # System time : 0.012 s 1.13/0.65 # Total time : 0.137 s 1.13/0.65 # Maximum resident set size: 5380 pages 1.13/0.66 EOF