0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.15 % Command : run_E %s %d THM 0.14/0.36 % Computer : n011.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 960 0.14/0.36 % WCLimit : 120 0.14/0.36 % DateTime : Tue Aug 9 02:53:51 EDT 2022 0.14/0.36 % CPUTime : 0.21/0.51 Running higher-order on 8 cores theorem proving 0.21/0.51 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 0.21/0.51 # Version: 3.0pre003-ho 0.21/0.57 # Preprocessing class: HSLMSLSSLLLCHFA. 0.21/0.57 # Scheduled 8 strats onto 8 cores with 120 seconds (960 total) 0.21/0.57 # Starting ehoh_best5 with 120s (1) cores 0.21/0.57 # Starting almost_fo_3_lam with 120s (1) cores 0.21/0.57 # Starting new_bool_5 with 120s (1) cores 0.21/0.57 # Starting pre_casc_3 with 120s (1) cores 0.21/0.57 # Starting ho_unfolding_8 with 120s (1) cores 0.21/0.57 # Starting new_ho_10_cnf2 with 120s (1) cores 0.21/0.57 # Starting new_bool_3 with 120s (1) cores 0.21/0.57 # Starting new_ho_5 with 120s (1) cores 0.21/0.57 # new_bool_5 with pid 29622 completed with status 0 0.21/0.57 # Result found by new_bool_5 0.21/0.57 # Preprocessing class: HSLMSLSSLLLCHFA. 0.21/0.57 # Scheduled 8 strats onto 8 cores with 120 seconds (960 total) 0.21/0.57 # Starting ehoh_best5 with 120s (1) cores 0.21/0.57 # Starting almost_fo_3_lam with 120s (1) cores 0.21/0.57 # Starting new_bool_5 with 120s (1) cores 0.21/0.57 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 0.21/0.57 # ...ProofStateSinE()=146/319 0.21/0.57 # Search class: HGHSM-FSLM31-MHFMMSBN 0.21/0.57 # Scheduled 6 strats onto 1 cores with 120 seconds (120 total) 0.21/0.57 # Starting new_ho_10_cnf2 with 65s (1) cores 0.21/0.57 # new_ho_10_cnf2 with pid 29628 completed with status 0 0.21/0.57 # Result found by new_ho_10_cnf2 0.21/0.57 # Preprocessing class: HSLMSLSSLLLCHFA. 0.21/0.57 # Scheduled 8 strats onto 8 cores with 120 seconds (960 total) 0.21/0.57 # Starting ehoh_best5 with 120s (1) cores 0.21/0.57 # Starting almost_fo_3_lam with 120s (1) cores 0.21/0.57 # Starting new_bool_5 with 120s (1) cores 0.21/0.57 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 0.21/0.57 # ...ProofStateSinE()=146/319 0.21/0.57 # Search class: HGHSM-FSLM31-MHFMMSBN 0.21/0.57 # Scheduled 6 strats onto 1 cores with 120 seconds (120 total) 0.21/0.57 # Starting new_ho_10_cnf2 with 65s (1) cores 0.21/0.57 # Preprocessing time : 0.002 s 0.21/0.57 # Presaturation interreduction done 0.21/0.57 0.21/0.57 # Proof found! 0.21/0.57 # SZS status Theorem 0.21/0.57 # SZS output start CNFRefutation 0.21/0.57 thf(decl_22, type, in: $i > $i > $o). 0.21/0.57 thf(decl_23, type, exu: ($i > $o) > $o). 0.21/0.57 thf(decl_24, type, setextAx: $o). 0.21/0.57 thf(decl_25, type, emptyset: $i). 0.21/0.57 thf(decl_26, type, emptysetAx: $o). 0.21/0.57 thf(decl_27, type, setadjoin: $i > $i > $i). 0.21/0.57 thf(decl_28, type, setadjoinAx: $o). 0.21/0.57 thf(decl_29, type, powerset: $i > $i). 0.21/0.57 thf(decl_30, type, powersetAx: $o). 0.21/0.57 thf(decl_31, type, setunion: $i > $i). 0.21/0.57 thf(decl_32, type, setunionAx: $o). 0.21/0.57 thf(decl_33, type, omega: $i). 0.21/0.57 thf(decl_34, type, omega0Ax: $o). 0.21/0.57 thf(decl_35, type, omegaSAx: $o). 0.21/0.57 thf(decl_36, type, omegaIndAx: $o). 0.21/0.57 thf(decl_37, type, replAx: $o). 0.21/0.57 thf(decl_38, type, foundationAx: $o). 0.21/0.57 thf(decl_39, type, wellorderingAx: $o). 0.21/0.57 thf(decl_40, type, descr: ($i > $o) > $i). 0.21/0.57 thf(decl_41, type, descrp: $o). 0.21/0.57 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.21/0.57 thf(decl_43, type, dsetconstrI: $o). 0.21/0.57 thf(decl_44, type, dsetconstrEL: $o). 0.21/0.57 thf(decl_45, type, dsetconstrER: $o). 0.21/0.57 thf(decl_46, type, exuE1: $o). 0.21/0.57 thf(decl_47, type, prop2set: $o > $i). 0.21/0.57 thf(decl_48, type, prop2setE: $o). 0.21/0.57 thf(decl_49, type, emptysetE: $o). 0.21/0.57 thf(decl_50, type, emptysetimpfalse: $o). 0.21/0.57 thf(decl_51, type, notinemptyset: $o). 0.21/0.57 thf(decl_52, type, exuE3e: $o). 0.21/0.57 thf(decl_53, type, setext: $o). 0.21/0.57 thf(decl_54, type, emptyI: $o). 0.21/0.57 thf(decl_55, type, noeltsimpempty: $o). 0.21/0.57 thf(decl_56, type, setbeta: $o). 0.21/0.57 thf(decl_57, type, nonempty: $i > $o). 0.21/0.57 thf(decl_58, type, nonemptyE1: $o). 0.21/0.57 thf(decl_59, type, nonemptyI: $o). 0.21/0.57 thf(decl_60, type, nonemptyI1: $o). 0.21/0.57 thf(decl_61, type, setadjoinIL: $o). 0.21/0.57 thf(decl_62, type, emptyinunitempty: $o). 0.21/0.57 thf(decl_63, type, setadjoinIR: $o). 0.21/0.57 thf(decl_64, type, setadjoinE: $o). 0.21/0.57 thf(decl_65, type, setadjoinOr: $o). 0.21/0.57 thf(decl_66, type, setoftrueEq: $o). 0.21/0.57 thf(decl_67, type, powersetI: $o). 0.21/0.57 thf(decl_68, type, emptyinPowerset: $o). 0.21/0.57 thf(decl_69, type, emptyInPowerset: $o). 0.21/0.57 thf(decl_70, type, powersetE: $o). 0.21/0.57 thf(decl_71, type, setunionI: $o). 0.21/0.57 thf(decl_72, type, setunionE: $o). 0.21/0.57 thf(decl_73, type, subPowSU: $o). 0.21/0.57 thf(decl_74, type, exuE2: $o). 0.21/0.57 thf(decl_75, type, nonemptyImpWitness: $o). 0.21/0.57 thf(decl_76, type, uniqinunit: $o). 0.21/0.57 thf(decl_77, type, notinsingleton: $o). 0.21/0.57 thf(decl_78, type, eqinunit: $o). 0.21/0.57 thf(decl_79, type, singletonsswitch: $o). 0.21/0.57 thf(decl_80, type, upairsetE: $o). 0.21/0.57 thf(decl_81, type, upairsetIL: $o). 0.21/0.57 thf(decl_82, type, upairsetIR: $o). 0.21/0.57 thf(decl_83, type, emptyE1: $o). 0.21/0.57 thf(decl_84, type, vacuousDall: $o). 0.21/0.57 thf(decl_85, type, quantDeMorgan1: $o). 0.21/0.57 thf(decl_86, type, quantDeMorgan2: $o). 0.21/0.57 thf(decl_87, type, quantDeMorgan3: $o). 0.21/0.57 thf(decl_88, type, quantDeMorgan4: $o). 0.21/0.57 thf(decl_89, type, prop2setI: $o). 0.21/0.57 thf(decl_90, type, set2prop: $i > $o). 0.21/0.57 thf(decl_91, type, prop2set2propI: $o). 0.21/0.57 thf(decl_92, type, notdexE: $o). 0.21/0.57 thf(decl_93, type, notdallE: $o). 0.21/0.57 thf(decl_94, type, exuI1: $o). 0.21/0.57 thf(decl_95, type, exuI3: $o). 0.21/0.57 thf(decl_96, type, exuI2: $o). 0.21/0.57 thf(decl_97, type, inCongP: $o). 0.21/0.57 thf(decl_98, type, in__Cong: $o). 0.21/0.57 thf(decl_99, type, exuE3u: $o). 0.21/0.57 thf(decl_100, type, exu__Cong: $o). 0.21/0.57 thf(decl_101, type, emptyset__Cong: $o). 0.21/0.57 thf(decl_102, type, setadjoin__Cong: $o). 0.21/0.57 thf(decl_103, type, powerset__Cong: $o). 0.21/0.57 thf(decl_104, type, setunion__Cong: $o). 0.21/0.57 thf(decl_105, type, omega__Cong: $o). 0.21/0.57 thf(decl_106, type, exuEu: $o). 0.21/0.57 thf(decl_107, type, descr__Cong: $o). 0.21/0.57 thf(decl_108, type, dsetconstr__Cong: $o). 0.21/0.57 thf(decl_109, type, subset: $i > $i > $o). 0.21/0.57 thf(decl_110, type, disjoint: $i > $i > $o). 0.21/0.57 thf(decl_111, type, setsmeet: $i > $i > $o). 0.21/0.57 thf(decl_112, type, subsetI1: $o). 0.21/0.57 thf(decl_113, type, eqimpsubset2: $o). 0.21/0.57 thf(decl_114, type, eqimpsubset1: $o). 0.21/0.57 thf(decl_115, type, subsetI2: $o). 0.21/0.57 thf(decl_116, type, emptysetsubset: $o). 0.21/0.57 thf(decl_117, type, subsetE: $o). 0.21/0.57 thf(decl_118, type, subsetE2: $o). 0.21/0.57 thf(decl_119, type, notsubsetI: $o). 0.21/0.57 thf(decl_120, type, notequalI1: $o). 0.21/0.57 thf(decl_121, type, notequalI2: $o). 0.21/0.57 thf(decl_122, type, subsetRefl: $o). 0.21/0.57 thf(decl_123, type, subsetTrans: $o). 0.21/0.57 thf(decl_124, type, setadjoinSub: $o). 0.21/0.57 thf(decl_125, type, setadjoinSub2: $o). 0.21/0.57 thf(decl_126, type, subset2powerset: $o). 0.21/0.57 thf(decl_127, type, setextsub: $o). 0.21/0.57 thf(decl_128, type, subsetemptysetimpeq: $o). 0.21/0.57 thf(decl_129, type, powersetI1: $o). 0.21/0.57 thf(decl_130, type, powersetE1: $o). 0.21/0.57 thf(decl_131, type, inPowerset: $o). 0.21/0.57 thf(decl_132, type, powersetsubset: $o). 0.21/0.57 thf(decl_133, type, sepInPowerset: $o). 0.21/0.57 thf(decl_134, type, sepSubset: $o). 0.21/0.57 thf(decl_135, type, binunion: $i > $i > $i). 0.21/0.57 thf(decl_136, type, binunionIL: $o). 0.21/0.57 thf(decl_137, type, upairset2IR: $o). 0.21/0.57 thf(decl_138, type, binunionIR: $o). 0.21/0.57 thf(decl_139, type, binunionEcases: $o). 0.21/0.57 thf(decl_140, type, binunionE: $o). 0.21/0.57 thf(decl_141, type, binunionLsub: $o). 0.21/0.57 thf(decl_142, type, binunionRsub: $o). 0.21/0.57 thf(decl_143, type, binintersect: $i > $i > $i). 0.21/0.57 thf(decl_144, type, binintersectI: $o). 0.21/0.57 thf(decl_145, type, binintersectSubset5: $o). 0.21/0.57 thf(decl_146, type, binintersectEL: $o). 0.21/0.57 thf(decl_147, type, binintersectLsub: $o). 0.21/0.57 thf(decl_148, type, binintersectSubset2: $o). 0.21/0.57 thf(decl_149, type, binintersectSubset3: $o). 0.21/0.57 thf(decl_150, type, binintersectER: $o). 0.21/0.57 thf(decl_151, type, disjointsetsI1: $o). 0.21/0.57 thf(decl_152, type, binintersectRsub: $o). 0.21/0.57 thf(decl_153, type, binintersectSubset4: $o). 0.21/0.57 thf(decl_154, type, binintersectSubset1: $o). 0.21/0.57 thf(decl_155, type, bs114d: $o). 0.21/0.57 thf(decl_156, type, regular: $i > $o). 0.21/0.57 thf(decl_157, type, setminus: $i > $i > $i). 0.21/0.57 thf(decl_158, type, setminusI: $o). 0.21/0.57 thf(decl_159, type, setminusEL: $o). 0.21/0.57 thf(decl_160, type, setminusER: $o). 0.21/0.57 thf(decl_161, type, setminusSubset2: $o). 0.21/0.57 thf(decl_162, type, setminusERneg: $o). 0.21/0.57 thf(decl_163, type, setminusELneg: $o). 0.21/0.57 thf(decl_164, type, setminusILneg: $o). 0.21/0.57 thf(decl_165, type, setminusIRneg: $o). 0.21/0.57 thf(decl_166, type, setminusLsub: $o). 0.21/0.57 thf(decl_167, type, setminusSubset1: $o). 0.21/0.57 thf(decl_168, type, symdiff: $i > $i > $i). 0.21/0.57 thf(decl_169, type, symdiffE: $o). 0.21/0.57 thf(decl_170, type, symdiffI1: $o). 0.21/0.57 thf(decl_171, type, symdiffI2: $o). 0.21/0.57 thf(decl_172, type, symdiffIneg1: $o). 0.21/0.57 thf(decl_173, type, symdiffIneg2: $o). 0.21/0.57 thf(decl_174, type, iskpair: $i > $o). 0.21/0.57 thf(decl_175, type, secondinupair: $o). 0.21/0.57 thf(decl_176, type, setukpairIL: $o). 0.21/0.57 thf(decl_177, type, setukpairIR: $o). 0.21/0.57 thf(decl_178, type, kpairiskpair: $o). 0.21/0.57 thf(decl_179, type, kpair: $i > $i > $i). 0.21/0.57 thf(decl_180, type, kpairp: $o). 0.21/0.57 thf(decl_181, type, cartprod: $i > $i > $i). 0.21/0.57 thf(decl_182, type, singletonsubset: $o). 0.21/0.57 thf(decl_183, type, singletoninpowerset: $o). 0.21/0.57 thf(decl_184, type, singletoninpowunion: $o). 0.21/0.57 thf(decl_185, type, upairset2E: $o). 0.21/0.57 thf(decl_186, type, upairsubunion: $o). 0.21/0.57 thf(decl_187, type, upairinpowunion: $o). 0.21/0.57 thf(decl_188, type, ubforcartprodlem1: $o). 0.21/0.57 thf(decl_189, type, ubforcartprodlem2: $o). 0.21/0.57 thf(decl_190, type, epred1_0: $o). 0.21/0.57 thf(decl_191, type, esk1_2: $i > $i > $i). 0.21/0.57 thf(decl_192, type, esk2_2: $i > $i > $i). 0.21/0.57 thf(decl_193, type, esk3_2: $i > $i > $i). 0.21/0.57 thf(decl_194, type, esk4_1: $i > $i). 0.21/0.57 thf(decl_195, type, esk5_2: ($i > $i > $o) > $i > $i). 0.21/0.57 thf(decl_196, type, esk6_2: ($i > $i > $o) > $i > $i). 0.21/0.57 thf(decl_197, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 0.21/0.57 thf(decl_198, type, esk8_1: $i > $i). 0.21/0.57 thf(decl_199, type, esk9_1: ($i > $o) > $i). 0.21/0.57 thf(decl_200, type, esk10_1: ($i > $o) > $i). 0.21/0.57 thf(decl_201, type, esk11_2: $i > $i > $i). 0.21/0.57 thf(decl_202, type, esk12_2: $i > $i > $i). 0.21/0.57 thf(decl_203, type, esk13_1: $i > $i). 0.21/0.57 thf(decl_204, type, esk14_1: $i > $i). 0.21/0.57 thf(decl_205, type, esk15_1: $i > $i). 0.21/0.57 thf(decl_206, type, esk16_2: $i > $i > $i). 0.21/0.57 thf(decl_207, type, esk17_3: $i > $i > $o > $i). 0.21/0.57 thf(decl_208, type, esk18_1: ($i > $o) > $i). 0.21/0.57 thf(decl_209, type, esk19_1: $i > $i). 0.21/0.57 thf(decl_210, type, esk20_2: $i > ($i > $o) > $i). 0.21/0.57 thf(decl_211, type, esk21_2: $i > ($i > $o) > $i). 0.21/0.57 thf(decl_212, type, esk22_2: $i > ($i > $o) > $i). 0.21/0.57 thf(decl_213, type, esk23_2: $i > ($i > $o) > $i). 0.21/0.57 thf(decl_214, type, esk24_2: $i > ($i > $o) > $i). 0.21/0.57 thf(decl_215, type, esk25_2: $i > ($i > $o) > $i). 0.21/0.57 thf(decl_216, type, esk26_2: ($i > $o) > $i > $i). 0.21/0.57 thf(decl_217, type, esk27_1: ($i > $o) > $i). 0.21/0.57 thf(decl_218, type, esk28_1: ($i > $o) > $i). 0.21/0.57 thf(decl_219, type, esk29_2: ($i > $o) > $i > $i). 0.21/0.57 thf(decl_220, type, esk30_2: ($i > $o) > ($i > $o) > $i). 0.21/0.57 thf(decl_221, type, esk31_2: ($i > $o) > ($i > $o) > $i). 0.21/0.57 thf(decl_222, type, esk32_2: ($i > $o) > ($i > $o) > $i). 0.21/0.57 thf(decl_223, type, esk33_2: ($i > $o) > ($i > $o) > $i). 0.21/0.57 thf(decl_224, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.21/0.57 thf(decl_225, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.21/0.57 thf(decl_226, type, esk36_2: $i > $i > $i). 0.21/0.57 thf(decl_227, type, esk37_2: $i > $i > $i). 0.21/0.57 thf(decl_228, type, esk38_2: $i > $i > $i). 0.21/0.57 thf(decl_229, type, esk39_0: $i). 0.21/0.57 thf(decl_230, type, esk40_0: $i). 0.21/0.57 thf(decl_231, type, esk41_0: $i). 0.21/0.57 thf(decl_232, type, esk42_0: $i). 0.21/0.57 thf(decl_233, type, esk43_1: $i > $i). 0.21/0.57 thf(decl_234, type, esk44_3: $i > $i > $i > $i). 0.21/0.57 thf(decl_235, type, esk45_2: $i > $i > $i). 0.21/0.57 thf(decl_236, type, esk46_2: $i > $i > $i). 0.21/0.57 thf(decl_237, type, esk47_2: $i > $i > $i). 0.21/0.57 thf(decl_238, type, epred2_0: $i > $o). 0.21/0.57 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrEL)). 0.21/0.57 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descrp)). 0.21/0.57 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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)). 0.21/0.57 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)). 0.21/0.57 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setbeta)). 0.21/0.57 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE3e)). 0.21/0.57 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrER)). 0.21/0.57 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', replAx)). 0.21/0.57 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sepInPowerset)). 0.21/0.57 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)). 0.21/0.57 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descr__Cong)). 0.21/0.57 thf(exuEu, axiom, ((exuEu)<=>![X1:$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)). 0.21/0.57 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exu__Cong)). 0.21/0.57 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI3)). 0.21/0.57 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstr__Cong)). 0.21/0.57 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$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)). 0.21/0.57 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)). 0.21/0.57 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)). 0.21/0.57 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setoftrueEq)). 0.21/0.57 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI)). 0.21/0.57 thf(exuE1, axiom, ((exuE1)<=>![X1:$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)). 0.21/0.57 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrI)). 0.21/0.57 thf(ubforcartprodlem3, conjecture, ((setextAx)=>((emptysetAx)=>((((((omegaSAx)=>((((foundationAx)=>((wellorderingAx)=>(((dsetconstrI)=>((((exuE1)=>((((emptysetimpfalse)=>((notinemptyset)=>(((setext)=>(((noeltsimpempty)=>(((nonemptyE1)=>((nonemptyI)=>((((emptyinunitempty)=>(((((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>(((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((((upairsetIL)=>((upairsetIR)=>(((((quantDeMorgan2)=>(((((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>(((exuI2)=>(((in__Cong)=>((exuE3u)=>(((((((omega__Cong)=>((((dsetconstr__Cong)=>(((eqimpsubset2)=>(((((subsetE)=>((((notequalI1)=>(((((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((((powersetE1)=>((inPowerset)=>((((sepSubset)=>((binunionIL)=>(((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((((((binintersectSubset2)=>(((binintersectER)=>(((binintersectRsub)=>((binintersectSubset4)=>(((((setminusEL)=>((((setminusERneg)=>(((((setminusLsub)=>(((symdiffE)=>(((symdiffI2)=>(((symdiffIneg2)=>((((setukpairIR)=>(((kpairp)=>(((singletoninpowerset)=>((singletoninpowunion)=>((((upairinpowunion)=>((ubforcartprodlem1)=>(![X4:$i, X5:$i, X2:$i]:((![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))<=(in @ X2 @ X4)))<=(ubforcartprodlem2))))<=(upairsubunion))<=(upairset2E))))<=(singletonsubset)))<=(kpairiskpair)))<=(setukpairIL))<=(secondinupair)))<=(symdiffIneg1)))<=(symdiffI1)))<=(setminusSubset1)))<=(setminusIRneg))<=(setminusILneg))<=(setminusELneg)))<=(setminusSubset2))<=(setminusER)))<=(setminusI))<=(bs114d))<=(binintersectSubset1))))<=(disjointsetsI1)))<=(binintersectSubset3)))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI)))))))<=(upairset2IR))))<=(sepInPowerset))<=(powersetsubset))))<=(powersetI1))<=(subsetemptysetimpeq))))))<=(subsetTrans))<=(subsetRefl))<=(notequalI2)))<=(notsubsetI))<=(subsetE2)))<=(emptysetsubset))<=(subsetI2))<=(eqimpsubset1)))<=(subsetI1)))<=(descr__Cong))<=(exuEu)))<=(setunion__Cong))<=(powerset__Cong))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong))))<=(inCongP)))<=(exuI3))))))<=(prop2setI))<=(quantDeMorgan4))<=(quantDeMorgan3)))<=(quantDeMorgan1))<=(vacuousDall))<=(emptyE1))))<=(upairsetE))<=(singletonsswitch)))))<=(nonemptyImpWitness))<=(exuE2))))))<=(emptyInPowerset)))))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR)))<=(setadjoinIL))<=(nonemptyI1))))<=(setbeta)))<=(emptyI)))<=(exuE3e))))<=(emptysetE))<=(prop2setE)))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp))))<=(replAx))<=(omegaIndAx)))<=(omega0Ax))<=(setunionAx))<=(powersetAx))<=(setadjoinAx)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem3)). 0.21/0.57 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinAx)). 0.21/0.57 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan4)). 0.21/0.57 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIL)). 0.21/0.57 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan3)). 0.21/0.57 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan1)). 0.21/0.57 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', vacuousDall)). 0.21/0.57 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIR)). 0.21/0.57 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetE)). 0.21/0.57 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)). 0.21/0.57 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)). 0.21/0.57 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyImpWitness)). 0.21/0.57 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionE)). 0.21/0.57 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyInPowerset)). 0.21/0.57 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionLsub)). 0.21/0.57 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinOr)). 0.21/0.57 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)). 0.21/0.57 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionRsub)). 0.21/0.57 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIR)). 0.21/0.57 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIL)). 0.21/0.57 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset2)). 0.21/0.57 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI1)). 0.21/0.57 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectER)). 0.21/0.57 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyI)). 0.21/0.57 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectRsub)). 0.21/0.57 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetE)). 0.21/0.57 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setE)). 0.21/0.57 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset4)). 0.21/0.57 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusEL)). 0.21/0.57 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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)). 0.21/0.57 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega0Ax)). 0.21/0.57 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusERneg)). 0.21/0.57 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionAx)). 0.21/0.57 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetAx)). 0.21/0.57 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusLsub)). 0.21/0.57 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffE)). 0.21/0.57 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI2)). 0.21/0.57 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg2)). 0.21/0.57 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairIR)). 0.21/0.57 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairp)). 0.21/0.57 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowerset)). 0.21/0.57 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowunion)). 0.21/0.57 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)). 0.21/0.57 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)). 0.21/0.57 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)). 0.21/0.57 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)). 0.21/0.57 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2E)). 0.21/0.57 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsubset)). 0.21/0.57 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairiskpair)). 0.21/0.57 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairIL)). 0.21/0.57 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powerset__Cong)). 0.21/0.57 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoin__Cong)). 0.21/0.57 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', secondinupair)). 0.21/0.57 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg1)). 0.21/0.57 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI1)). 0.21/0.57 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset1)). 0.21/0.57 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusIRneg)). 0.21/0.57 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusILneg)). 0.21/0.57 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusELneg)). 0.21/0.57 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset2)). 0.21/0.57 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusER)). 0.21/0.57 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusI)). 0.21/0.57 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', bs114d)). 0.21/0.57 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset1)). 0.21/0.57 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', disjointsetsI1)). 0.21/0.57 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset3)). 0.21/0.57 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectLsub)). 0.21/0.57 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectEL)). 0.21/0.57 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset5)). 0.21/0.57 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectI)). 0.21/0.57 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2IR)). 0.21/0.57 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetsubset)). 0.21/0.57 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI1)). 0.21/0.57 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE1)). 0.21/0.57 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetemptysetimpeq)). 0.21/0.57 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetTrans)). 0.21/0.57 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetRefl)). 0.21/0.57 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI2)). 0.21/0.57 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notsubsetI)). 0.21/0.57 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE2)). 0.21/0.57 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetsubset)). 0.21/0.57 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI2)). 0.21/0.57 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset1)). 0.21/0.57 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inPowerset)). 0.21/0.57 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI1)). 0.21/0.57 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunion__Cong)). 0.21/0.57 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyset__Cong)). 0.21/0.57 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inCongP)). 0.21/0.57 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setI)). 0.21/0.57 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextsub)). 0.21/0.57 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subset2powerset)). 0.21/0.57 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub2)). 0.21/0.57 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub)). 0.21/0.57 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI1)). 0.21/0.57 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE)). 0.21/0.57 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset2)). 0.21/0.57 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega__Cong)). 0.21/0.57 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)). 0.21/0.57 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdallE)). 0.21/0.57 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdexE)). 0.21/0.57 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan2)). 0.21/0.57 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIR)). 0.21/0.57 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIL)). 0.21/0.57 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqinunit)). 0.21/0.57 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinsingleton)). 0.21/0.57 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', uniqinunit)). 0.21/0.57 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subPowSU)). 0.21/0.57 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionE)). 0.21/0.57 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionI)). 0.21/0.57 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE)). 0.21/0.57 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinPowerset)). 0.21/0.57 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI)). 0.21/0.57 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinunitempty)). 0.21/0.57 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyE1)). 0.21/0.57 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', noeltsimpempty)). 0.21/0.57 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setext)). 0.21/0.57 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinemptyset)). 0.21/0.57 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetimpfalse)). 0.21/0.57 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', wellorderingAx)). 0.21/0.57 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', foundationAx)). 0.21/0.57 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaSAx)). 0.21/0.57 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetAx)). 0.21/0.57 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextAx)). 0.21/0.57 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)). 0.21/0.57 thf(c_0_146, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.21/0.57 thf(c_0_147, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.21/0.57 thf(c_0_148, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 0.21/0.57 thf(c_0_149, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.21/0.57 thf(c_0_150, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.21/0.57 thf(c_0_151, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.21/0.57 thf(c_0_152, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.21/0.57 thf(c_0_153, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.21/0.57 thf(c_0_154, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.21/0.57 thf(c_0_155, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.21/0.57 thf(c_0_156, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.21/0.57 thf(c_0_157, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.21/0.57 thf(c_0_158, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.21/0.57 thf(c_0_159, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.21/0.57 thf(c_0_160, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.21/0.57 thf(c_0_161, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 0.21/0.57 thf(c_0_162, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.21/0.57 thf(c_0_163, 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])). 0.21/0.57 thf(c_0_164, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.21/0.57 thf(c_0_165, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.21/0.57 thf(c_0_166, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.21/0.57 thf(c_0_167, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.21/0.57 thf(c_0_168, plain, ((epred1_0)<=>![X423:$i]:(?[X424:$i]:((((![X425:$i]:(((in @ X425 @ X424)=>![X426:$i]:(((in @ X426 @ X425)=>(in @ X426 @ X423)))))&![X427:$i, X428:$i]:((((in @ X427 @ X423)&(in @ X428 @ X423))=>(![X429:$i]:(((in @ X429 @ X424)=>((in @ X427 @ X429)<=>(in @ X428 @ X429))))=>((X427)=(X428))))))&![X430:$i, X431:$i]:((((in @ X430 @ X424)&(in @ X431 @ X424))=>(![X432:$i]:(((in @ X432 @ X430)=>(in @ X432 @ X431)))|![X433:$i]:(((in @ X433 @ X431)=>(in @ X433 @ X430)))))))&![X434:$i]:(((![X435:$i]:(((in @ X435 @ X434)=>(in @ X435 @ X423)))&?[X436:$i]:((in @ X436 @ X434)))=>?[X437:$i, X438:$i]:(((((in @ X437 @ X424)&(in @ X438 @ X434))&~(?[X439:$i]:(((in @ X439 @ X437)&(in @ X439 @ X434)))))&![X440:$i]:(((in @ X440 @ X424)=>(![X441:$i]:(((in @ X441 @ X440)=>(in @ X441 @ X437)))|(in @ X438 @ X440)))))))))))), introduced(definition)). 0.21/0.57 thf(c_0_169, negated_conjecture, ~((![X414:$i, X415:$i]:((![X416:$i]:(((in @ X416 @ X414)<=>(in @ X416 @ X415)))=>((X414)=(X415))))=>(![X417:$i]:(~(in @ X417 @ emptyset))=>(![X800:$i, X801:$i, X802:$i]:(((in @ X802 @ (setadjoin @ X800 @ X801))<=>(((X802)=(X800))|(in @ X802 @ X801))))=>(![X797:$i, X798:$i]:(((in @ X798 @ (powerset @ X797))<=>![X799:$i]:(((in @ X799 @ X798)=>(in @ X799 @ X797)))))=>(![X794:$i, X795:$i]:(((in @ X795 @ (setunion @ X794))<=>?[X796:$i]:(((in @ X795 @ X796)&(in @ X796 @ X794)))))=>((in @ emptyset @ omega)=>(![X418:$i]:(((in @ X418 @ omega)=>(in @ (setadjoin @ X418 @ X418) @ omega)))=>(![X791:$i]:((((in @ emptyset @ X791)&![X792:$i]:((((in @ X792 @ omega)&(in @ X792 @ X791))=>(in @ (setadjoin @ X792 @ X792) @ X791))))=>![X793:$i]:(((in @ X793 @ omega)=>(in @ X793 @ X791)))))=>(![X785:$i > $i > $o, X786:$i]:((![X787:$i]:(((in @ X787 @ X786)=>(exu @ (^[Z0:$i]:((X785 @ X787 @ Z0))))))=>?[X788:$i]:(![X789:$i]:(((in @ X789 @ X788)<=>?[X790:$i]:(((in @ X790 @ X786)&(X785 @ X790 @ X789))))))))=>(![X419:$i]:((?[X420:$i]:((in @ X420 @ X419))=>?[X421:$i]:(((in @ X421 @ X419)&~(?[X422:$i]:(((in @ X422 @ X421)&(in @ X422 @ X419))))))))=>((epred1_0)=>(![X784:$i > $o]:(((exu @ (^[Z0:$i]:((X784 @ Z0))))=>(X784 @ (descr @ (^[Z0:$i]:((X784 @ Z0)))))))=>(![X442:$i, X443:$i > $o, X444:$i]:(((in @ X444 @ X442)=>((X443 @ X444)=>(in @ X444 @ (dsetconstr @ X442 @ (^[Z0:$i]:((X443 @ Z0))))))))=>(![X781:$i, X782:$i > $o, X783:$i]:(((in @ X783 @ (dsetconstr @ X781 @ (^[Z0:$i]:((X782 @ Z0)))))=>(in @ X783 @ X781)))=>(![X778:$i, X779:$i > $o, X780:$i]:(((in @ X780 @ (dsetconstr @ X778 @ (^[Z0:$i]:((X779 @ Z0)))))=>(X779 @ X780)))=>(![X445:$i > $o]:(((exu @ (^[Z0:$i]:((X445 @ Z0))))=>?[X446:$i]:(((X445 @ X446)&![X447:$i]:(((X445 @ X447)=>((X446)=(X447))))))))=>(![X776:$o, X777:$i]:(((in @ X777 @ (prop2set @ ((X776))))=>(X776)))=>(![X774:$i]:(((in @ X774 @ emptyset)=>![X775:$o]:((X775))))=>(![X448:$i]:(~(in @ X448 @ emptyset))=>(![X449:$i]:(~(in @ X449 @ emptyset))=>(![X772:$i > $o]:(((exu @ (^[Z0:$i]:((X772 @ Z0))))=>?[X773:$i]:((X772 @ X773))))=>(![X450:$i, X451:$i]:((![X452:$i]:(((in @ X452 @ X450)=>(in @ X452 @ X451)))=>(![X453:$i]:(((in @ X453 @ X451)=>(in @ X453 @ X450)))=>((X450)=(X451)))))=>(![X770:$i]:((![X771:$i]:(~(in @ X771 @ X770))=>((X770)=(emptyset))))=>(![X454:$i]:((![X455:$i]:(~(in @ X455 @ X454))=>((X454)=(emptyset))))=>(![X767:$i, X768:$i > $o, X769:$i]:(((in @ X769 @ X767)=>((in @ X769 @ (dsetconstr @ X767 @ (^[Z0:$i]:((X768 @ Z0)))))<=>(X768 @ X769))))=>(![X456:$i]:(((nonempty @ X456)=>?[X457:$i]:((in @ X457 @ X456))))=>(![X458:$i, X459:$i > $o, X460:$i]:(((in @ X460 @ X458)=>((X459 @ X460)=>(nonempty @ (dsetconstr @ X458 @ (^[Z0:$i]:((X459 @ Z0))))))))=>(![X765:$i]:((?[X766:$i]:((in @ X766 @ X765))=>(nonempty @ X765)))=>(![X763:$i, X764:$i]:((in @ X763 @ (setadjoin @ X763 @ X764)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X760:$i, X761:$i, X762:$i]:(((in @ X762 @ X761)=>(in @ X762 @ (setadjoin @ X760 @ X761))))=>(![X756:$i, X757:$i, X758:$i]:(((in @ X758 @ (setadjoin @ X756 @ X757))=>![X759:$o]:(((((X758)=(X756))=>(X759))=>(((in @ X758 @ X757)=>(X759))=>(X759))))))=>(![X753:$i, X754:$i, X755:$i]:(((in @ X755 @ (setadjoin @ X753 @ X754))=>(((X755)=(X753))|(in @ X755 @ X754))))=>(![X461:$i]:(((dsetconstr @ X461 @ (^[Z0:$i]:(($true))))=(X461)))=>(![X462:$i, X463:$i]:((![X464:$i]:(((in @ X464 @ X463)=>(in @ X464 @ X462)))=>(in @ X463 @ (powerset @ X462))))=>(![X465:$i]:((in @ emptyset @ (powerset @ X465)))=>(![X752:$i]:((in @ emptyset @ (powerset @ X752)))=>(![X466:$i, X467:$i, X468:$i]:(((in @ X467 @ (powerset @ X466))=>((in @ X468 @ X467)=>(in @ X468 @ X466))))=>(![X469:$i, X470:$i, X471:$i]:(((in @ X470 @ X471)=>((in @ X471 @ X469)=>(in @ X470 @ (setunion @ X469)))))=>(![X472:$i, X473:$i]:(((in @ X473 @ (setunion @ X472))=>![X474:$o]:((![X475:$i]:(((in @ X473 @ X475)=>((in @ X475 @ X472)=>(X474))))=>(X474)))))=>(![X476:$i, X477:$i]:(((in @ X477 @ X476)=>(in @ X477 @ (powerset @ (setunion @ X476)))))=>(![X749:$i > $o]:(((exu @ (^[Z0:$i]:((X749 @ Z0))))=>?[X750:$i]:(![X751:$i]:(((X749 @ X751)<=>((X751)=(X750)))))))=>(![X747:$i]:(((nonempty @ X747)=>?[X748:$i]:((in @ X748 @ X747))))=>(![X478:$i, X479:$i]:(((in @ X478 @ (setadjoin @ X479 @ emptyset))=>((X478)=(X479))))=>(![X480:$i, X481:$i]:((((X480)!=(X481))=>~(in @ X481 @ (setadjoin @ X480 @ emptyset))))=>(![X482:$i, X483:$i]:((((X482)=(X483))=>(in @ X482 @ (setadjoin @ X483 @ emptyset))))=>(![X745:$i, X746:$i]:(((in @ X745 @ (setadjoin @ X746 @ emptyset))=>(in @ X746 @ (setadjoin @ X745 @ emptyset))))=>(![X742:$i, X743:$i, X744:$i]:(((in @ X744 @ (setadjoin @ X742 @ (setadjoin @ X743 @ emptyset)))=>(((X744)=(X742))|((X744)=(X743)))))=>(![X484:$i, X485:$i]:((in @ X484 @ (setadjoin @ X484 @ (setadjoin @ X485 @ emptyset))))=>(![X486:$i, X487:$i]:((in @ X487 @ (setadjoin @ X486 @ (setadjoin @ X487 @ emptyset))))=>(![X739:$i, X740:$i > $o]:((?[X741:$i]:(((in @ X741 @ X739)&(X740 @ X741)))=>((dsetconstr @ X739 @ (^[Z0:$i]:((X740 @ Z0))))!=(emptyset))))=>(![X737:$i > $o, X738:$i]:(((in @ X738 @ emptyset)=>(X737 @ X738)))=>(![X733:$i, X734:$i > $o]:((~(![X735:$i]:(((in @ X735 @ X733)=>(X734 @ X735))))=>?[X736:$i]:(((in @ X736 @ X733)&~(X734 @ X736)))))=>(![X488:$i, X489:$i > $o]:((![X490:$i]:(((in @ X490 @ X488)=>~(X489 @ X490)))=>~(?[X491:$i]:(((in @ X491 @ X488)&(X489 @ X491))))))=>(![X729:$i, X730:$i > $o]:((~(?[X731:$i]:(((in @ X731 @ X729)&(X730 @ X731))))=>![X732:$i]:(((in @ X732 @ X729)=>~(X730 @ X732)))))=>(![X725:$i, X726:$i > $o]:((?[X727:$i]:(((in @ X727 @ X725)&~(X726 @ X727)))=>~(![X728:$i]:(((in @ X728 @ X725)=>(X726 @ X728))))))=>(![X724:$o]:(((X724)=>(in @ emptyset @ (prop2set @ ((X724))))))=>((prop2set2propI)=>(![X492:$i, X493:$i > $o]:((~(?[X494:$i]:(((in @ X494 @ X492)&(X493 @ X494))))=>![X495:$i]:(((in @ X495 @ X492)=>~(X493 @ X495)))))=>(![X496:$i, X497:$i > $o]:((~(![X498:$i]:(((in @ X498 @ X496)=>(X497 @ X498))))=>?[X499:$i]:(((in @ X499 @ X496)&~(X497 @ X499)))))=>(![X500:$i > $o]:((?[X501:$i]:(((X500 @ X501)&![X502:$i]:(((X500 @ X502)=>((X501)=(X502))))))=>(exu @ (^[Z0:$i]:((X500 @ Z0))))))=>(![X720:$i > $o]:((?[X721:$i]:((X720 @ X721))=>(![X722:$i, X723:$i]:(((X720 @ X722)=>((X720 @ X723)=>((X722)=(X723)))))=>(exu @ (^[Z0:$i]:((X720 @ Z0)))))))=>(![X503:$i > $o]:((?[X504:$i]:(![X505:$i]:(((X503 @ X505)<=>((X505)=(X504)))))=>(exu @ (^[Z0:$i]:((X503 @ Z0))))))=>(![X716:$i, X717:$i]:((((X716)=(X717))=>![X718:$i, X719:$i]:((((X718)=(X719))=>((in @ X718 @ X716)=>(in @ X719 @ X717))))))=>(![X506:$i, X507:$i]:((((X506)=(X507))=>![X508:$i, X509:$i]:((((X508)=(X509))=>((in @ X508 @ X506)<=>(in @ X509 @ X507))))))=>(![X510:$i > $o]:(((exu @ (^[Z0:$i]:((X510 @ Z0))))=>![X511:$i, X512:$i]:(((X510 @ X511)=>((X510 @ X512)=>((X511)=(X512)))))))=>(![X712:$i > $o, X713:$i > $o]:((![X714:$i, X715:$i]:((((X714)=(X715))=>((X712 @ X714)<=>(X713 @ X715))))=>((exu @ (^[Z0:$i]:((X712 @ Z0))))<=>(exu @ (^[Z0:$i]:((X713 @ Z0)))))))=>(((emptyset)=(emptyset))=>(![X708:$i, X709:$i]:((((X708)=(X709))=>![X710:$i, X711:$i]:((((X710)=(X711))=>((setadjoin @ X708 @ X710)=(setadjoin @ X709 @ X711))))))=>(![X706:$i, X707:$i]:((((X706)=(X707))=>((powerset @ X706)=(powerset @ X707))))=>(![X704:$i, X705:$i]:((((X704)=(X705))=>((setunion @ X704)=(setunion @ X705))))=>(((omega)=(omega))=>(![X701:$i > $o]:(((exu @ (^[Z0:$i]:((X701 @ Z0))))=>![X702:$i, X703:$i]:(((X701 @ X702)=>((X701 @ X703)=>((X702)=(X703)))))))=>(![X697:$i > $o, X698:$i > $o]:((![X699:$i, X700:$i]:((((X699)=(X700))=>((X697 @ X699)<=>(X698 @ X700))))=>((exu @ (^[Z0:$i]:((X697 @ Z0))))=>((exu @ (^[Z0:$i]:((X698 @ Z0))))=>((descr @ (^[Z0:$i]:((X697 @ Z0))))=(descr @ (^[Z0:$i]:((X698 @ Z0)))))))))=>(![X513:$i, X514:$i]:((((X513)=(X514))=>![X515:$i > $o, X516:$i > $o]:((![X517:$i]:(((in @ X517 @ X513)=>![X518:$i]:(((in @ X518 @ X514)=>(((X517)=(X518))=>((X515 @ X517)<=>(X516 @ X518)))))))=>((dsetconstr @ X513 @ (^[Z0:$i]:((X515 @ Z0))))=(dsetconstr @ X514 @ (^[Z0:$i]:((X516 @ Z0)))))))))=>(![X694:$i, X695:$i]:((![X696:$i]:(((in @ X696 @ X694)=>(in @ X696 @ X695)))=>(subset @ X694 @ X695)))=>(![X519:$i, X520:$i]:((((X519)=(X520))=>(subset @ X520 @ X519)))=>(![X692:$i, X693:$i]:((((X692)=(X693))=>(subset @ X692 @ X693)))=>(![X689:$i, X690:$i]:((![X691:$i]:(((in @ X691 @ X689)=>(in @ X691 @ X690)))=>(subset @ X689 @ X690)))=>(![X688:$i]:((subset @ emptyset @ X688))=>(![X521:$i, X522:$i, X523:$i]:(((subset @ X521 @ X522)=>((in @ X523 @ X521)=>(in @ X523 @ X522))))=>(![X685:$i, X686:$i, X687:$i]:(((subset @ X685 @ X686)=>(~(in @ X687 @ X686)=>~(in @ X687 @ X685))))=>(![X682:$i, X683:$i, X684:$i]:(((in @ X684 @ X682)=>(~(in @ X684 @ X683)=>~(subset @ X682 @ X683))))=>(![X524:$i, X525:$i]:((~(subset @ X524 @ X525)=>((X524)!=(X525))))=>(![X679:$i, X680:$i, X681:$i]:(((in @ X681 @ X679)=>(~(in @ X681 @ X680)=>((X679)!=(X680)))))=>(![X678:$i]:((subset @ X678 @ X678))=>(![X675:$i, X676:$i, X677:$i]:(((subset @ X675 @ X676)=>((subset @ X676 @ X677)=>(subset @ X675 @ X677))))=>(![X526:$i, X527:$i]:((subset @ X527 @ (setadjoin @ X526 @ X527)))=>(![X528:$i, X529:$i, X530:$i]:(((subset @ X528 @ X530)=>(subset @ X528 @ (setadjoin @ X529 @ X530))))=>(![X531:$i, X532:$i]:(((subset @ X531 @ X532)=>(in @ X531 @ (powerset @ X532))))=>(![X533:$i, X534:$i]:(((subset @ X533 @ X534)=>((subset @ X534 @ X533)=>((X533)=(X534)))))=>(![X674:$i]:(((subset @ X674 @ emptyset)=>((X674)=(emptyset))))=>(![X672:$i, X673:$i]:(((subset @ X673 @ X672)=>(in @ X673 @ (powerset @ X672))))=>(![X535:$i, X536:$i]:(((in @ X536 @ (powerset @ X535))=>(subset @ X536 @ X535)))=>(![X537:$i]:((in @ X537 @ (powerset @ X537)))=>(![X670:$i, X671:$i]:(((subset @ X670 @ X671)=>(subset @ (powerset @ X670) @ (powerset @ X671))))=>(![X668:$i, X669:$i > $o]:((in @ (dsetconstr @ X668 @ (^[Z0:$i]:((X669 @ Z0)))) @ (powerset @ X668)))=>(![X538:$i, X539:$i > $o]:((subset @ (dsetconstr @ X538 @ (^[Z0:$i]:((X539 @ Z0)))) @ X538))=>(![X540:$i, X541:$i, X542:$i]:(((in @ X542 @ X540)=>(in @ X542 @ (binunion @ X540 @ X541))))=>(![X666:$i, X667:$i]:((in @ X667 @ (setadjoin @ X666 @ (setadjoin @ X667 @ emptyset))))=>(![X543:$i, X544:$i, X545:$i]:(((in @ X545 @ X544)=>(in @ X545 @ (binunion @ X543 @ X544))))=>(![X546:$i, X547:$i, X548:$i, X549:$o]:(((in @ X548 @ (binunion @ X546 @ X547))=>(((in @ X548 @ X546)=>(X549))=>(((in @ X548 @ X547)=>(X549))=>(X549)))))=>(![X550:$i, X551:$i, X552:$i]:(((in @ X552 @ (binunion @ X550 @ X551))=>((in @ X552 @ X550)|(in @ X552 @ X551))))=>(![X553:$i, X554:$i]:((subset @ X553 @ (binunion @ X553 @ X554)))=>(![X555:$i, X556:$i]:((subset @ X556 @ (binunion @ X555 @ X556)))=>(![X663:$i, X664:$i, X665:$i]:(((in @ X665 @ X663)=>((in @ X665 @ X664)=>(in @ X665 @ (binintersect @ X663 @ X664)))))=>(![X660:$i, X661:$i, X662:$i]:(((subset @ X662 @ X660)=>((subset @ X662 @ X661)=>(subset @ X662 @ (binintersect @ X660 @ X661)))))=>(![X657:$i, X658:$i, X659:$i]:(((in @ X659 @ (binintersect @ X657 @ X658))=>(in @ X659 @ X657)))=>(![X655:$i, X656:$i]:((subset @ (binintersect @ X655 @ X656) @ X655))=>(![X557:$i, X558:$i]:(((subset @ X557 @ X558)=>((binintersect @ X557 @ X558)=(X557))))=>(![X653:$i, X654:$i]:((((binintersect @ X653 @ X654)=(X654))=>(subset @ X654 @ X653)))=>(![X559:$i, X560:$i, X561:$i]:(((in @ X561 @ (binintersect @ X559 @ X560))=>(in @ X561 @ X560)))=>(![X650:$i, X651:$i]:((~(?[X652:$i]:(((in @ X652 @ X650)&(in @ X652 @ X651))))=>((binintersect @ X650 @ X651)=(emptyset))))=>(![X562:$i, X563:$i]:((subset @ (binintersect @ X562 @ X563) @ X563))=>(![X564:$i, X565:$i]:(((subset @ X565 @ X564)=>((binintersect @ X564 @ X565)=(X565))))=>(![X648:$i, X649:$i]:((((binintersect @ X648 @ X649)=(X648))=>(subset @ X648 @ X649)))=>(![X645:$i, X646:$i, X647:$i]:(((binintersect @ X645 @ (binunion @ X646 @ X647))=(binunion @ (binintersect @ X645 @ X646) @ (binintersect @ X645 @ X647))))=>(![X642:$i, X643:$i, X644:$i]:(((in @ X644 @ X642)=>(~(in @ X644 @ X643)=>(in @ X644 @ (setminus @ X642 @ X643)))))=>(![X566:$i, X567:$i, X568:$i]:(((in @ X568 @ (setminus @ X566 @ X567))=>(in @ X568 @ X566)))=>(![X639:$i, X640:$i, X641:$i]:(((in @ X641 @ (setminus @ X639 @ X640))=>~(in @ X641 @ X640)))=>(![X637:$i, X638:$i]:(((subset @ X637 @ X638)=>((setminus @ X637 @ X638)=(emptyset))))=>(![X569:$i, X570:$i, X571:$i]:((~(in @ X571 @ (setminus @ X569 @ X570))=>((in @ X571 @ X569)=>(in @ X571 @ X570))))=>(![X634:$i, X635:$i, X636:$i]:((~(in @ X636 @ (setminus @ X634 @ X635))=>(~(in @ X636 @ X635)=>~(in @ X636 @ X634))))=>(![X631:$i, X632:$i, X633:$i]:((~(in @ X633 @ X631)=>~(in @ X633 @ (setminus @ X631 @ X632))))=>(![X628:$i, X629:$i, X630:$i]:(((in @ X630 @ X629)=>~(in @ X630 @ (setminus @ X628 @ X629))))=>(![X572:$i, X573:$i]:((subset @ (setminus @ X572 @ X573) @ X572))=>(![X626:$i, X627:$i]:((((setminus @ X626 @ X627)=(emptyset))=>(subset @ X626 @ X627)))=>(![X574:$i, X575:$i, X576:$i]:(((in @ X576 @ (symdiff @ X574 @ X575))=>![X577:$o]:((((in @ X576 @ X574)=>(~(in @ X576 @ X575)=>(X577)))=>((~(in @ X576 @ X574)=>((in @ X576 @ X575)=>(X577)))=>(X577))))))=>(![X623:$i, X624:$i, X625:$i]:(((in @ X625 @ X623)=>(~(in @ X625 @ X624)=>(in @ X625 @ (symdiff @ X623 @ X624)))))=>(![X578:$i, X579:$i, X580:$i]:((~(in @ X580 @ X578)=>((in @ X580 @ X579)=>(in @ X580 @ (symdiff @ X578 @ X579)))))=>(![X620:$i, X621:$i, X622:$i]:(((in @ X622 @ X620)=>((in @ X622 @ X621)=>~(in @ X622 @ (symdiff @ X620 @ X621)))))=>(![X581:$i, X582:$i, X583:$i]:((~(in @ X583 @ X581)=>(~(in @ X583 @ X582)=>~(in @ X583 @ (symdiff @ X581 @ X582)))))=>(![X618:$i, X619:$i]:((in @ X619 @ (setadjoin @ X618 @ (setadjoin @ X619 @ emptyset))))=>(![X616:$i, X617:$i]:((in @ X616 @ (setunion @ (setadjoin @ (setadjoin @ X616 @ emptyset) @ (setadjoin @ (setadjoin @ X616 @ (setadjoin @ X617 @ emptyset)) @ emptyset)))))=>(![X584:$i, X585:$i]:((in @ X585 @ (setunion @ (setadjoin @ (setadjoin @ X584 @ emptyset) @ (setadjoin @ (setadjoin @ X584 @ (setadjoin @ X585 @ emptyset)) @ emptyset)))))=>(![X614:$i, X615:$i]:((iskpair @ (setadjoin @ (setadjoin @ X614 @ emptyset) @ (setadjoin @ (setadjoin @ X614 @ (setadjoin @ X615 @ emptyset)) @ emptyset))))=>(![X586:$i, X587:$i]:((iskpair @ (kpair @ X586 @ X587)))=>(![X612:$i, X613:$i]:(((in @ X613 @ X612)=>(subset @ (setadjoin @ X613 @ emptyset) @ X612)))=>(![X588:$i, X589:$i]:(((in @ X589 @ X588)=>(in @ (setadjoin @ X589 @ emptyset) @ (powerset @ X588))))=>(![X590:$i, X591:$i, X592:$i]:(((in @ X592 @ X590)=>(in @ (setadjoin @ X592 @ emptyset) @ (powerset @ (binunion @ X590 @ X591)))))=>(![X609:$i, X610:$i, X611:$i]:(((in @ X611 @ (setadjoin @ X609 @ (setadjoin @ X610 @ emptyset)))=>(((X611)=(X609))|((X611)=(X610)))))=>(![X605:$i, X606:$i, X607:$i]:(((in @ X607 @ X605)=>![X608:$i]:(((in @ X608 @ X606)=>(subset @ (setadjoin @ X607 @ (setadjoin @ X608 @ emptyset)) @ (binunion @ X605 @ X606))))))=>(![X593:$i, X594:$i, X595:$i]:(((in @ X595 @ X593)=>![X596:$i]:(((in @ X596 @ X594)=>(in @ (setadjoin @ X595 @ (setadjoin @ X596 @ emptyset)) @ (powerset @ (binunion @ X593 @ X594)))))))=>(![X597:$i, X598:$i, X599:$i]:(((in @ X599 @ X597)=>![X600:$i]:(((in @ X600 @ X598)=>(subset @ (setadjoin @ (setadjoin @ X599 @ emptyset) @ (setadjoin @ (setadjoin @ X599 @ (setadjoin @ X600 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X597 @ X598)))))))=>(![X601:$i, X602:$i, X603:$i]:(((in @ X603 @ X601)=>![X604:$i]:(((in @ X604 @ X602)=>(in @ (setadjoin @ (setadjoin @ X603 @ emptyset) @ (setadjoin @ (setadjoin @ X603 @ (setadjoin @ X604 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X601 @ X602))))))))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[ubforcartprodlem3]), c_0_146]), c_0_147]), setadjoinAx]), quantDeMorgan4]), binunionIL]), quantDeMorgan3]), quantDeMorgan1]), vacuousDall]), binunionIR]), c_0_148]), upairsetE]), binunionEcases]), singletonsswitch]), nonemptyImpWitness]), binunionE]), c_0_149]), emptyInPowerset]), binunionLsub]), setadjoinOr]), setadjoinE]), binunionRsub]), setadjoinIR]), setadjoinIL]), binintersectSubset2]), nonemptyI1]), binintersectER]), c_0_150]), emptyI]), c_0_151]), binintersectRsub]), emptysetE]), prop2setE]), c_0_152]), binintersectSubset4]), c_0_153]), setminusEL]), omegaIndAx]), omega0Ax]), setminusERneg]), setunionAx]), powersetAx]), setminusLsub]), symdiffE]), symdiffI2]), symdiffIneg2]), setukpairIR]), kpairp]), singletoninpowerset]), singletoninpowunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), upairsubunion]), upairset2E]), singletonsubset]), kpairiskpair]), setukpairIL]), powerset__Cong]), setadjoin__Cong]), secondinupair]), symdiffIneg1]), symdiffI1]), setminusSubset1]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusSubset2]), setminusER]), setminusI]), bs114d]), binintersectSubset1]), disjointsetsI1]), binintersectSubset3]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), upairset2IR]), c_0_154]), powersetsubset]), powersetI1]), powersetE1]), subsetemptysetimpeq]), subsetTrans]), subsetRefl]), notequalI2]), notsubsetI]), subsetE2]), emptysetsubset]), subsetI2]), eqimpsubset1]), inPowerset]), c_0_155]), subsetI1]), c_0_156]), c_0_157]), setunion__Cong]), emptyset__Cong]), c_0_158]), inCongP]), c_0_159]), prop2setI]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), notequalI1]), subsetE]), eqimpsubset2]), c_0_160]), omega__Cong]), c_0_161]), in__Cong]), c_0_162]), c_0_163]), notdallE]), notdexE]), quantDeMorgan2]), upairsetIR]), upairsetIL]), eqinunit]), notinsingleton]), uniqinunit]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyinPowerset]), powersetI]), c_0_164]), emptyinunitempty]), c_0_165]), nonemptyE1]), noeltsimpempty]), setext]), notinemptyset]), emptysetimpfalse]), c_0_166]), c_0_167]), wellorderingAx]), foundationAx]), omegaSAx]), emptysetAx]), setextAx])]), c_0_168])). 0.21/0.57 thf(c_0_170, plain, ![X803:$i, X804:$i]:(((kpair @ X803 @ X804)=(setadjoin @ (setadjoin @ X803 @ emptyset) @ (setadjoin @ (setadjoin @ X803 @ (setadjoin @ X804 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])])). 0.21/0.57 thf(c_0_171, negated_conjecture, ![X805:$i, X806:$i, X808:$i, X809:$i, X810:$i, X811:$i, X812:$i, X813:$i, X814:$i, X815:$i, X816:$i, X818:$i, X819:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$i, X827:$i, X828:$i > $i > $o, X829:$i, X832:$i, X834:$i, X835:$i, X836:$i, X837:$i, X839:$i, X840:$i > $o, X841:$i, X842:$i > $o, X843:$i, X844:$i, X845:$i > $o, X846:$i, X847:$i, X848:$i > $o, X849:$i, X850:$i > $o, X852:$i, X853:$o, X854:$i, X855:$i, X856:$o, X857:$i, X858:$i, X859:$i > $o, X861:$i, X862:$i, X865:$i, X867:$i, X869:$i, X870:$i > $o, X871:$i, X872:$i, X874:$i, X875:$i > $o, X876:$i, X877:$i, X878:$i, X879:$i, X880:$i, X881:$i, X882:$i, X883:$i, X884:$i, X885:$i, X886:$i, X887:$o, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X895:$i, X896:$i, X897:$i, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X904:$i, X905:$o, X907:$i, X908:$i, X909:$i > $o, X911:$i, X912:$i, X913:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$i, X920:$i, X921:$i, X922:$i, X923:$i, X924:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i > $o, X932:$i, X933:$i > $o, X934:$i, X935:$i, X936:$i > $o, X937:$i, X939:$i, X940:$i > $o, X942:$i, X943:$i, X944:$i > $o, X946:$i, X947:$i, X948:$i > $o, X949:$i, X951:$o, X952:$i, X953:$i > $o, X955:$i, X956:$i, X957:$i > $o, X958:$i, X960:$i > $o, X961:$i, X963:$i > $o, X964:$i, X967:$i > $o, X968:$i, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i, X977:$i, X978:$i > $o, X979:$i, X980:$i, X981:$i > $o, X982:$i > $o, X985:$i, X986:$i, X987:$i, X988:$i, X989:$i, X990:$i, X991:$i, X992:$i, X993:$i > $o, X994:$i, X995:$i, X996:$i > $o, X997:$i > $o, X1000:$i, X1001:$i, X1002:$i > $o, X1003:$i > $o, X1006:$i, X1007:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i, X1014:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i > $o, X1054:$i, X1055:$i > $o, X1056:$i, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$o, X1068:$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, X1081:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$o, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i]:((((~(in @ (esk1_2 @ X805 @ X806) @ X805)|~(in @ (esk1_2 @ X805 @ X806) @ X806)|((X805)=(X806)))&((in @ (esk1_2 @ X805 @ X806) @ X805)|(in @ (esk1_2 @ X805 @ X806) @ X806)|((X805)=(X806))))&(~(in @ X808 @ emptyset)&(((~(in @ X811 @ (setadjoin @ X809 @ X810))|(((X811)=(X809))|(in @ X811 @ X810)))&((((X811)!=(X809))|(in @ X811 @ (setadjoin @ X809 @ X810)))&(~(in @ X811 @ X810)|(in @ X811 @ (setadjoin @ X809 @ X810)))))&(((~(in @ X813 @ (powerset @ X812))|(~(in @ X814 @ X813)|(in @ X814 @ X812)))&(((in @ (esk2_2 @ X815 @ X816) @ X816)|(in @ X816 @ (powerset @ X815)))&(~(in @ (esk2_2 @ X815 @ X816) @ X815)|(in @ X816 @ (powerset @ X815)))))&(((((in @ X819 @ (esk3_2 @ X818 @ X819))|~(in @ X819 @ (setunion @ X818)))&((in @ (esk3_2 @ X818 @ X819) @ X818)|~(in @ X819 @ (setunion @ X818))))&(~(in @ X822 @ X823)|~(in @ X823 @ X821)|(in @ X822 @ (setunion @ X821))))&((in @ emptyset @ omega)&((~(in @ X824 @ omega)|(in @ (setadjoin @ X824 @ X824) @ omega))&(((((in @ (esk4_1 @ X825) @ omega)|~(in @ emptyset @ X825)|(~(in @ X827 @ omega)|(in @ X827 @ X825)))&((in @ (esk4_1 @ X825) @ X825)|~(in @ emptyset @ X825)|(~(in @ X827 @ omega)|(in @ X827 @ X825))))&(~(in @ (setadjoin @ (esk4_1 @ X825) @ (esk4_1 @ X825)) @ X825)|~(in @ emptyset @ X825)|(~(in @ X827 @ omega)|(in @ X827 @ X825))))&((((((in @ (esk7_3 @ X828 @ X829 @ X832) @ X829)|~(in @ X832 @ (esk6_2 @ X828 @ X829))|(in @ (esk5_2 @ X828 @ X829) @ X829))&((X828 @ (esk7_3 @ X828 @ X829 @ X832) @ X832)|~(in @ X832 @ (esk6_2 @ X828 @ X829))|(in @ (esk5_2 @ X828 @ X829) @ X829)))&(~(in @ X835 @ X829)|~(X828 @ X835 @ X834)|(in @ X834 @ (esk6_2 @ X828 @ X829))|(in @ (esk5_2 @ X828 @ X829) @ X829)))&((((in @ (esk7_3 @ X828 @ X829 @ X832) @ X829)|~(in @ X832 @ (esk6_2 @ X828 @ X829))|~(exu @ (^[Z0:$i]:((X828 @ (esk5_2 @ X828 @ X829) @ Z0)))))&((X828 @ (esk7_3 @ X828 @ X829 @ X832) @ X832)|~(in @ X832 @ (esk6_2 @ X828 @ X829))|~(exu @ (^[Z0:$i]:((X828 @ (esk5_2 @ X828 @ X829) @ Z0))))))&(~(in @ X835 @ X829)|~(X828 @ X835 @ X834)|(in @ X834 @ (esk6_2 @ X828 @ X829))|~(exu @ (^[Z0:$i]:((X828 @ (esk5_2 @ X828 @ X829) @ Z0)))))))&((((in @ (esk8_1 @ X836) @ X836)|~(in @ X837 @ X836))&(~(in @ X839 @ (esk8_1 @ X836))|~(in @ X839 @ X836)|~(in @ X837 @ X836)))&((epred1_0)&((~(exu @ (^[Z0:$i]:((X840 @ Z0))))|(X840 @ (descr @ (^[Z0:$i]:((X840 @ Z0))))))&((~(in @ X843 @ X841)|(~(X842 @ X843)|(in @ X843 @ (dsetconstr @ X841 @ (^[Z0:$i]:((X842 @ Z0)))))))&((~(in @ X846 @ (dsetconstr @ X844 @ (^[Z0:$i]:((X845 @ Z0)))))|(in @ X846 @ X844))&((~(in @ X849 @ (dsetconstr @ X847 @ (^[Z0:$i]:((X848 @ Z0)))))|(X848 @ X849))&((((X850 @ (esk9_1 @ X850))|~(exu @ (^[Z0:$i]:((X850 @ Z0)))))&(~(X850 @ X852)|((esk9_1 @ X850)=(X852))|~(exu @ (^[Z0:$i]:((X850 @ Z0))))))&((~(in @ X854 @ (prop2set @ ((X853))))|(X853))&((~(in @ X855 @ emptyset)|(X856))&(~(in @ X857 @ emptyset)&(~(in @ X858 @ emptyset)&((~(exu @ (^[Z0:$i]:((X859 @ Z0))))|(X859 @ (esk10_1 @ X859)))&(((((in @ (esk12_2 @ X861 @ X862) @ X862)|((X861)=(X862))|(in @ (esk11_2 @ X861 @ X862) @ X861))&(~(in @ (esk12_2 @ X861 @ X862) @ X861)|((X861)=(X862))|(in @ (esk11_2 @ X861 @ X862) @ X861)))&(((in @ (esk12_2 @ X861 @ X862) @ X862)|((X861)=(X862))|~(in @ (esk11_2 @ X861 @ X862) @ X862))&(~(in @ (esk12_2 @ X861 @ X862) @ X861)|((X861)=(X862))|~(in @ (esk11_2 @ X861 @ X862) @ X862))))&(((in @ (esk13_1 @ X865) @ X865)|((X865)=(emptyset)))&(((in @ (esk14_1 @ X867) @ X867)|((X867)=(emptyset)))&(((~(in @ X871 @ (dsetconstr @ X869 @ (^[Z0:$i]:((X870 @ Z0)))))|(X870 @ X871)|~(in @ X871 @ X869))&(~(X870 @ X871)|(in @ X871 @ (dsetconstr @ X869 @ (^[Z0:$i]:((X870 @ Z0)))))|~(in @ X871 @ X869)))&((~(nonempty @ X872)|(in @ (esk15_1 @ X872) @ X872))&((~(in @ X876 @ X874)|(~(X875 @ X876)|(nonempty @ (dsetconstr @ X874 @ (^[Z0:$i]:((X875 @ Z0)))))))&((~(in @ X878 @ X877)|(nonempty @ X877))&((in @ X879 @ (setadjoin @ X879 @ X880))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X883 @ X882)|(in @ X883 @ (setadjoin @ X881 @ X882)))&(((((in @ X886 @ X885)|(X887)|((X886)=(X884))|~(in @ X886 @ (setadjoin @ X884 @ X885)))&(~(X887)|(X887)|((X886)=(X884))|~(in @ X886 @ (setadjoin @ X884 @ X885))))&(((in @ X886 @ X885)|(X887)|~(X887)|~(in @ X886 @ (setadjoin @ X884 @ X885)))&(~(X887)|(X887)|~(X887)|~(in @ X886 @ (setadjoin @ X884 @ X885)))))&((~(in @ X890 @ (setadjoin @ X888 @ X889))|(((X890)=(X888))|(in @ X890 @ X889)))&(((dsetconstr @ X891 @ (^[Z0:$i]:(($true))))=(X891))&((((in @ (esk16_2 @ X892 @ X893) @ X893)|(in @ X893 @ (powerset @ X892)))&(~(in @ (esk16_2 @ X892 @ X893) @ X892)|(in @ X893 @ (powerset @ X892))))&((in @ emptyset @ (powerset @ X895))&((in @ emptyset @ (powerset @ X896))&((~(in @ X898 @ (powerset @ X897))|(~(in @ X899 @ X898)|(in @ X899 @ X897)))&((~(in @ X901 @ X902)|(~(in @ X902 @ X900)|(in @ X901 @ (setunion @ X900))))&((((in @ X904 @ (esk17_3 @ X903 @ X904 @ X905))|(X905)|~(in @ X904 @ (setunion @ X903)))&(((in @ (esk17_3 @ X903 @ X904 @ X905) @ X903)|(X905)|~(in @ X904 @ (setunion @ X903)))&(~(X905)|(X905)|~(in @ X904 @ (setunion @ X903)))))&((~(in @ X908 @ X907)|(in @ X908 @ (powerset @ (setunion @ X907))))&(((~(X909 @ X911)|((X911)=(esk18_1 @ X909))|~(exu @ (^[Z0:$i]:((X909 @ Z0)))))&(((X912)!=(esk18_1 @ X909))|(X909 @ X912)|~(exu @ (^[Z0:$i]:((X909 @ Z0))))))&((~(nonempty @ X913)|(in @ (esk19_1 @ X913) @ X913))&((~(in @ X915 @ (setadjoin @ X916 @ emptyset))|((X915)=(X916)))&((((X917)=(X918))|~(in @ X918 @ (setadjoin @ X917 @ emptyset)))&((((X919)!=(X920))|(in @ X919 @ (setadjoin @ X920 @ emptyset)))&((~(in @ X921 @ (setadjoin @ X922 @ emptyset))|(in @ X922 @ (setadjoin @ X921 @ emptyset)))&((~(in @ X925 @ (setadjoin @ X923 @ (setadjoin @ X924 @ emptyset)))|(((X925)=(X923))|((X925)=(X924))))&((in @ X926 @ (setadjoin @ X926 @ (setadjoin @ X927 @ emptyset)))&((in @ X929 @ (setadjoin @ X928 @ (setadjoin @ X929 @ emptyset)))&((~(in @ X932 @ X930)|~(X931 @ X932)|((dsetconstr @ X930 @ (^[Z0:$i]:((X931 @ Z0))))!=(emptyset)))&((~(in @ X934 @ emptyset)|(X933 @ X934))&((((in @ (esk20_2 @ X935 @ X936) @ X935)|(~(in @ X937 @ X935)|(X936 @ X937)))&(~(X936 @ (esk20_2 @ X935 @ X936))|(~(in @ X937 @ X935)|(X936 @ X937))))&((((in @ (esk21_2 @ X939 @ X940) @ X939)|(~(in @ X942 @ X939)|~(X940 @ X942)))&((X940 @ (esk21_2 @ X939 @ X940))|(~(in @ X942 @ X939)|~(X940 @ X942))))&((((in @ (esk22_2 @ X943 @ X944) @ X943)|(~(in @ X946 @ X943)|~(X944 @ X946)))&((X944 @ (esk22_2 @ X943 @ X944))|(~(in @ X946 @ X943)|~(X944 @ X946))))&((((in @ (esk23_2 @ X947 @ X948) @ X947)|(~(in @ X949 @ X947)|(X948 @ X949)))&(~(X948 @ (esk23_2 @ X947 @ X948))|(~(in @ X949 @ X947)|(X948 @ X949))))&((~(X951)|(in @ emptyset @ (prop2set @ ((X951)))))&((prop2set2propI)&((((in @ (esk24_2 @ X952 @ X953) @ X952)|(~(in @ X955 @ X952)|~(X953 @ X955)))&((X953 @ (esk24_2 @ X952 @ X953))|(~(in @ X955 @ X952)|~(X953 @ X955))))&((((in @ (esk25_2 @ X956 @ X957) @ X956)|(~(in @ X958 @ X956)|(X957 @ X958)))&(~(X957 @ (esk25_2 @ X956 @ X957))|(~(in @ X958 @ X956)|(X957 @ X958))))&((((X960 @ (esk26_2 @ X960 @ X961))|~(X960 @ X961)|(exu @ (^[Z0:$i]:((X960 @ Z0)))))&(((X961)!=(esk26_2 @ X960 @ X961))|~(X960 @ X961)|(exu @ (^[Z0:$i]:((X960 @ Z0))))))&((((X963 @ (esk27_1 @ X963))|(exu @ (^[Z0:$i]:((X963 @ Z0))))|~(X963 @ X964))&(((X963 @ (esk28_1 @ X963))|(exu @ (^[Z0:$i]:((X963 @ Z0))))|~(X963 @ X964))&(((esk27_1 @ X963)!=(esk28_1 @ X963))|(exu @ (^[Z0:$i]:((X963 @ Z0))))|~(X963 @ X964))))&(((~(X967 @ (esk29_2 @ X967 @ X968))|((esk29_2 @ X967 @ X968)!=(X968))|(exu @ (^[Z0:$i]:((X967 @ Z0)))))&((X967 @ (esk29_2 @ X967 @ X968))|((esk29_2 @ X967 @ X968)=(X968))|(exu @ (^[Z0:$i]:((X967 @ Z0))))))&((((X970)!=(X971))|(((X972)!=(X973))|(~(in @ X972 @ X970)|(in @ X973 @ X971))))&(((~(in @ X976 @ X974)|(in @ X977 @ X975)|((X976)!=(X977))|((X974)!=(X975)))&(~(in @ X977 @ X975)|(in @ X976 @ X974)|((X976)!=(X977))|((X974)!=(X975))))&((~(exu @ (^[Z0:$i]:((X978 @ Z0))))|(~(X978 @ X979)|(~(X978 @ X980)|((X979)=(X980)))))&((((~(exu @ (^[Z0:$i]:((X981 @ Z0))))|(exu @ (^[Z0:$i]:((X982 @ Z0))))|((esk30_2 @ X981 @ X982)=(esk31_2 @ X981 @ X982)))&(~(exu @ (^[Z0:$i]:((X982 @ Z0))))|(exu @ (^[Z0:$i]:((X981 @ Z0))))|((esk30_2 @ X981 @ X982)=(esk31_2 @ X981 @ X982))))&(((~(exu @ (^[Z0:$i]:((X981 @ Z0))))|(exu @ (^[Z0:$i]:((X982 @ Z0))))|(~(X981 @ (esk30_2 @ X981 @ X982))|~(X982 @ (esk31_2 @ X981 @ X982))))&(~(exu @ (^[Z0:$i]:((X982 @ Z0))))|(exu @ (^[Z0:$i]:((X981 @ Z0))))|(~(X981 @ (esk30_2 @ X981 @ X982))|~(X982 @ (esk31_2 @ X981 @ X982)))))&((~(exu @ (^[Z0:$i]:((X981 @ Z0))))|(exu @ (^[Z0:$i]:((X982 @ Z0))))|((X981 @ (esk30_2 @ X981 @ X982))|(X982 @ (esk31_2 @ X981 @ X982))))&(~(exu @ (^[Z0:$i]:((X982 @ Z0))))|(exu @ (^[Z0:$i]:((X981 @ Z0))))|((X981 @ (esk30_2 @ X981 @ X982))|(X982 @ (esk31_2 @ X981 @ X982)))))))&(((emptyset)=(emptyset))&((((X985)!=(X986))|(((X987)!=(X988))|((setadjoin @ X985 @ X987)=(setadjoin @ X986 @ X988))))&((((X989)!=(X990))|((powerset @ X989)=(powerset @ X990)))&((((X991)!=(X992))|((setunion @ X991)=(setunion @ X992)))&(((omega)=(omega))&((~(exu @ (^[Z0:$i]:((X993 @ Z0))))|(~(X993 @ X994)|(~(X993 @ X995)|((X994)=(X995)))))&(((((esk32_2 @ X996 @ X997)=(esk33_2 @ X996 @ X997))|(~(exu @ (^[Z0:$i]:((X996 @ Z0))))|(~(exu @ (^[Z0:$i]:((X997 @ Z0))))|((descr @ (^[Z0:$i]:((X996 @ Z0))))=(descr @ (^[Z0:$i]:((X997 @ Z0))))))))&((~(X996 @ (esk32_2 @ X996 @ X997))|~(X997 @ (esk33_2 @ X996 @ X997))|(~(exu @ (^[Z0:$i]:((X996 @ Z0))))|(~(exu @ (^[Z0:$i]:((X997 @ Z0))))|((descr @ (^[Z0:$i]:((X996 @ Z0))))=(descr @ (^[Z0:$i]:((X997 @ Z0))))))))&((X996 @ (esk32_2 @ X996 @ X997))|(X997 @ (esk33_2 @ X996 @ X997))|(~(exu @ (^[Z0:$i]:((X996 @ Z0))))|(~(exu @ (^[Z0:$i]:((X997 @ Z0))))|((descr @ (^[Z0:$i]:((X996 @ Z0))))=(descr @ (^[Z0:$i]:((X997 @ Z0))))))))))&((((in @ (esk34_4 @ X1000 @ X1001 @ X1002 @ X1003) @ X1000)|((dsetconstr @ X1000 @ (^[Z0:$i]:((X1002 @ Z0))))=(dsetconstr @ X1001 @ (^[Z0:$i]:((X1003 @ Z0)))))|((X1000)!=(X1001)))&(((in @ (esk35_4 @ X1000 @ X1001 @ X1002 @ X1003) @ X1001)|((dsetconstr @ X1000 @ (^[Z0:$i]:((X1002 @ Z0))))=(dsetconstr @ X1001 @ (^[Z0:$i]:((X1003 @ Z0)))))|((X1000)!=(X1001)))&((((esk34_4 @ X1000 @ X1001 @ X1002 @ X1003)=(esk35_4 @ X1000 @ X1001 @ X1002 @ X1003))|((dsetconstr @ X1000 @ (^[Z0:$i]:((X1002 @ Z0))))=(dsetconstr @ X1001 @ (^[Z0:$i]:((X1003 @ Z0)))))|((X1000)!=(X1001)))&((~(X1002 @ (esk34_4 @ X1000 @ X1001 @ X1002 @ X1003))|~(X1003 @ (esk35_4 @ X1000 @ X1001 @ X1002 @ X1003))|((dsetconstr @ X1000 @ (^[Z0:$i]:((X1002 @ Z0))))=(dsetconstr @ X1001 @ (^[Z0:$i]:((X1003 @ Z0)))))|((X1000)!=(X1001)))&((X1002 @ (esk34_4 @ X1000 @ X1001 @ X1002 @ X1003))|(X1003 @ (esk35_4 @ X1000 @ X1001 @ X1002 @ X1003))|((dsetconstr @ X1000 @ (^[Z0:$i]:((X1002 @ Z0))))=(dsetconstr @ X1001 @ (^[Z0:$i]:((X1003 @ Z0)))))|((X1000)!=(X1001)))))))&((((in @ (esk36_2 @ X1006 @ X1007) @ X1006)|(subset @ X1006 @ X1007))&(~(in @ (esk36_2 @ X1006 @ X1007) @ X1007)|(subset @ X1006 @ X1007)))&((((X1009)!=(X1010))|(subset @ X1010 @ X1009))&((((X1011)!=(X1012))|(subset @ X1011 @ X1012))&((((in @ (esk37_2 @ X1013 @ X1014) @ X1013)|(subset @ X1013 @ X1014))&(~(in @ (esk37_2 @ X1013 @ X1014) @ X1014)|(subset @ X1013 @ X1014)))&((subset @ emptyset @ X1016)&((~(subset @ X1017 @ X1018)|(~(in @ X1019 @ X1017)|(in @ X1019 @ X1018)))&((~(subset @ X1020 @ X1021)|((in @ X1022 @ X1021)|~(in @ X1022 @ X1020)))&((~(in @ X1025 @ X1023)|((in @ X1025 @ X1024)|~(subset @ X1023 @ X1024)))&(((subset @ X1026 @ X1027)|((X1026)!=(X1027)))&((~(in @ X1030 @ X1028)|((in @ X1030 @ X1029)|((X1028)!=(X1029))))&((subset @ X1031 @ X1031)&((~(subset @ X1032 @ X1033)|(~(subset @ X1033 @ X1034)|(subset @ X1032 @ X1034)))&((subset @ X1036 @ (setadjoin @ X1035 @ X1036))&((~(subset @ X1037 @ X1039)|(subset @ X1037 @ (setadjoin @ X1038 @ X1039)))&((~(subset @ X1040 @ X1041)|(in @ X1040 @ (powerset @ X1041)))&((~(subset @ X1042 @ X1043)|(~(subset @ X1043 @ X1042)|((X1042)=(X1043))))&((~(subset @ X1044 @ emptyset)|((X1044)=(emptyset)))&((~(subset @ X1046 @ X1045)|(in @ X1046 @ (powerset @ X1045)))&((~(in @ X1048 @ (powerset @ X1047))|(subset @ X1048 @ X1047))&((in @ X1049 @ (powerset @ X1049))&((~(subset @ X1050 @ X1051)|(subset @ (powerset @ X1050) @ (powerset @ X1051)))&((in @ (dsetconstr @ X1052 @ (^[Z0:$i]:((X1053 @ Z0)))) @ (powerset @ X1052))&((subset @ (dsetconstr @ X1054 @ (^[Z0:$i]:((X1055 @ Z0)))) @ X1054)&((~(in @ X1058 @ X1056)|(in @ X1058 @ (binunion @ X1056 @ X1057)))&((in @ X1060 @ (setadjoin @ X1059 @ (setadjoin @ X1060 @ emptyset)))&((~(in @ X1063 @ X1062)|(in @ X1063 @ (binunion @ X1061 @ X1062)))&(((((in @ X1066 @ X1065)|(X1067)|(in @ X1066 @ X1064)|~(in @ X1066 @ (binunion @ X1064 @ X1065)))&(~(X1067)|(X1067)|(in @ X1066 @ X1064)|~(in @ X1066 @ (binunion @ X1064 @ X1065))))&(((in @ X1066 @ X1065)|(X1067)|~(X1067)|~(in @ X1066 @ (binunion @ X1064 @ X1065)))&(~(X1067)|(X1067)|~(X1067)|~(in @ X1066 @ (binunion @ X1064 @ X1065)))))&((~(in @ X1070 @ (binunion @ X1068 @ X1069))|((in @ X1070 @ X1068)|(in @ X1070 @ X1069)))&((subset @ X1071 @ (binunion @ X1071 @ X1072))&((subset @ X1074 @ (binunion @ X1073 @ X1074))&((~(in @ X1077 @ X1075)|(~(in @ X1077 @ X1076)|(in @ X1077 @ (binintersect @ X1075 @ X1076))))&((~(subset @ X1080 @ X1078)|(~(subset @ X1080 @ X1079)|(subset @ X1080 @ (binintersect @ X1078 @ X1079))))&((~(in @ X1083 @ (binintersect @ X1081 @ X1082))|(in @ X1083 @ X1081))&((subset @ (binintersect @ X1084 @ X1085) @ X1084)&((~(subset @ X1086 @ X1087)|((binintersect @ X1086 @ X1087)=(X1086)))&((((binintersect @ X1088 @ X1089)!=(X1089))|(subset @ X1089 @ X1088))&((~(in @ X1092 @ (binintersect @ X1090 @ X1091))|(in @ X1092 @ X1091))&((((in @ (esk38_2 @ X1093 @ X1094) @ X1093)|((binintersect @ X1093 @ X1094)=(emptyset)))&((in @ (esk38_2 @ X1093 @ X1094) @ X1094)|((binintersect @ X1093 @ X1094)=(emptyset))))&((subset @ (binintersect @ X1096 @ X1097) @ X1097)&((~(subset @ X1099 @ X1098)|((binintersect @ X1098 @ X1099)=(X1099)))&((((binintersect @ X1100 @ X1101)!=(X1100))|(subset @ X1100 @ X1101))&(((binintersect @ X1102 @ (binunion @ X1103 @ X1104))=(binunion @ (binintersect @ X1102 @ X1103) @ (binintersect @ X1102 @ X1104)))&((~(in @ X1107 @ X1105)|((in @ X1107 @ X1106)|(in @ X1107 @ (setminus @ X1105 @ X1106))))&((~(in @ X1110 @ (setminus @ X1108 @ X1109))|(in @ X1110 @ X1108))&((~(in @ X1113 @ (setminus @ X1111 @ X1112))|~(in @ X1113 @ X1112))&((~(subset @ X1114 @ X1115)|((setminus @ X1114 @ X1115)=(emptyset)))&(((in @ X1118 @ (setminus @ X1116 @ X1117))|(~(in @ X1118 @ X1116)|(in @ X1118 @ X1117)))&(((in @ X1121 @ (setminus @ X1119 @ X1120))|((in @ X1121 @ X1120)|~(in @ X1121 @ X1119)))&(((in @ X1124 @ X1122)|~(in @ X1124 @ (setminus @ X1122 @ X1123)))&((~(in @ X1127 @ X1126)|~(in @ X1127 @ (setminus @ X1125 @ X1126)))&((subset @ (setminus @ X1128 @ X1129) @ X1128)&((((setminus @ X1130 @ X1131)!=(emptyset))|(subset @ X1130 @ X1131))&((((~(in @ X1134 @ X1132)|(X1135)|(in @ X1134 @ X1132)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))&(((in @ X1134 @ X1133)|(X1135)|(in @ X1134 @ X1132)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))&(~(X1135)|(X1135)|(in @ X1134 @ X1132)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))))&(((~(in @ X1134 @ X1132)|(X1135)|~(in @ X1134 @ X1133)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))&(((in @ X1134 @ X1133)|(X1135)|~(in @ X1134 @ X1133)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))&(~(X1135)|(X1135)|~(in @ X1134 @ X1133)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))))&((~(in @ X1134 @ X1132)|(X1135)|~(X1135)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))&(((in @ X1134 @ X1133)|(X1135)|~(X1135)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))&(~(X1135)|(X1135)|~(X1135)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))))))&((~(in @ X1138 @ X1136)|((in @ X1138 @ X1137)|(in @ X1138 @ (symdiff @ X1136 @ X1137))))&(((in @ X1141 @ X1139)|(~(in @ X1141 @ X1140)|(in @ X1141 @ (symdiff @ X1139 @ X1140))))&((~(in @ X1144 @ X1142)|(~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143))))&(((in @ X1147 @ X1145)|((in @ X1147 @ X1146)|~(in @ X1147 @ (symdiff @ X1145 @ X1146))))&((in @ X1149 @ (setadjoin @ X1148 @ (setadjoin @ X1149 @ emptyset)))&((in @ X1150 @ (setunion @ (setadjoin @ (setadjoin @ X1150 @ emptyset) @ (setadjoin @ (setadjoin @ X1150 @ (setadjoin @ X1151 @ emptyset)) @ emptyset))))&((in @ X1153 @ (setunion @ (setadjoin @ (setadjoin @ X1152 @ emptyset) @ (setadjoin @ (setadjoin @ X1152 @ (setadjoin @ X1153 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1154 @ emptyset) @ (setadjoin @ (setadjoin @ X1154 @ (setadjoin @ X1155 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1156 @ X1157))&((~(in @ X1159 @ X1158)|(subset @ (setadjoin @ X1159 @ emptyset) @ X1158))&((~(in @ X1161 @ X1160)|(in @ (setadjoin @ X1161 @ emptyset) @ (powerset @ X1160)))&((~(in @ X1164 @ X1162)|(in @ (setadjoin @ X1164 @ emptyset) @ (powerset @ (binunion @ X1162 @ X1163))))&((~(in @ X1167 @ (setadjoin @ X1165 @ (setadjoin @ X1166 @ emptyset)))|(((X1167)=(X1165))|((X1167)=(X1166))))&((~(in @ X1170 @ X1168)|(~(in @ X1171 @ X1169)|(subset @ (setadjoin @ X1170 @ (setadjoin @ X1171 @ emptyset)) @ (binunion @ X1168 @ X1169))))&((~(in @ X1174 @ X1172)|(~(in @ X1175 @ X1173)|(in @ (setadjoin @ X1174 @ (setadjoin @ X1175 @ emptyset)) @ (powerset @ (binunion @ X1172 @ X1173)))))&((~(in @ X1178 @ X1176)|(~(in @ X1179 @ X1177)|(subset @ (setadjoin @ (setadjoin @ X1178 @ emptyset) @ (setadjoin @ (setadjoin @ X1178 @ (setadjoin @ X1179 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1176 @ X1177)))))&((~(in @ X1182 @ X1180)|(~(in @ X1183 @ X1181)|(in @ (setadjoin @ (setadjoin @ X1182 @ emptyset) @ (setadjoin @ (setadjoin @ X1182 @ (setadjoin @ X1183 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1180 @ X1181))))))&((in @ esk41_0 @ esk39_0)&((in @ esk42_0 @ esk40_0)&~(in @ (kpair @ esk41_0 @ esk42_0) @ (powerset @ (powerset @ (binunion @ esk39_0 @ esk40_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_169])])])])])])). 0.21/0.57 thf(c_0_172, plain, ![X1188:$i, X1189:$i]:(((kpair @ X1188 @ X1189)=(setadjoin @ (setadjoin @ X1188 @ emptyset) @ (setadjoin @ (setadjoin @ X1188 @ (setadjoin @ X1189 @ emptyset)) @ emptyset)))), inference(variable_rename,[status(thm)],[c_0_170])). 0.21/0.57 thf(c_0_173, negated_conjecture, ~((in @ (kpair @ esk41_0 @ esk42_0) @ (powerset @ (powerset @ (binunion @ esk39_0 @ esk40_0))))), inference(split_conjunct,[status(thm)],[c_0_171])). 0.21/0.57 thf(c_0_174, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_171])). 0.21/0.57 thf(c_0_175, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i]:(((subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X3 @ X5)))|~((in @ X2 @ X3))|~((in @ X4 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_171])). 0.21/0.57 thf(c_0_176, 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_172])). 0.21/0.57 thf(c_0_177, negated_conjecture, ~((subset @ (kpair @ esk41_0 @ esk42_0) @ (powerset @ (binunion @ esk39_0 @ esk40_0)))), inference(spm,[status(thm)],[c_0_173, c_0_174])). 0.21/0.57 thf(c_0_178, negated_conjecture, ![X3:$i, X2:$i, X5:$i, X4:$i]:(((subset @ (kpair @ X2 @ X3) @ (powerset @ (binunion @ X4 @ X5)))|~((in @ X3 @ X5))|~((in @ X2 @ X4)))), inference(rw,[status(thm)],[c_0_175, c_0_176])). 0.21/0.57 thf(c_0_179, negated_conjecture, (in @ esk42_0 @ esk40_0), inference(split_conjunct,[status(thm)],[c_0_171])). 0.21/0.57 thf(c_0_180, negated_conjecture, (in @ esk41_0 @ esk39_0), inference(split_conjunct,[status(thm)],[c_0_171])). 0.21/0.57 thf(c_0_181, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177, c_0_178]), c_0_179]), c_0_180])]), ['proof']). 0.21/0.57 # SZS output end CNFRefutation 0.21/0.57 # Parsed axioms : 319 0.21/0.57 # Removed by relevancy pruning/SinE : 173 0.21/0.57 # Initial clauses : 226 0.21/0.57 # Removed in clause preprocessing : 23 0.21/0.57 # Initial clauses in saturation : 203 0.21/0.57 # Processed clauses : 416 0.21/0.57 # ...of these trivial : 7 0.21/0.57 # ...subsumed : 49 0.21/0.57 # ...remaining for further processing : 360 0.21/0.57 # Other redundant clauses eliminated : 16 0.21/0.57 # Clauses deleted for lack of memory : 0 0.21/0.57 # Backward-subsumed : 0 0.21/0.57 # Backward-rewritten : 5 0.21/0.57 # Generated clauses : 1619 0.21/0.57 # ...of the previous two non-redundant : 1484 0.21/0.57 # ...aggressively subsumed : 0 0.21/0.57 # Contextual simplify-reflections : 0 0.21/0.57 # Paramodulations : 1603 0.21/0.57 # Factorizations : 0 0.21/0.57 # NegExts : 0 0.21/0.57 # Equation resolutions : 16 0.21/0.57 # Propositional unsat checks : 0 0.21/0.57 # Propositional check models : 0 0.21/0.57 # Propositional check unsatisfiable : 0 0.21/0.57 # Propositional clauses : 0 0.21/0.57 # Propositional clauses after purity: 0 0.21/0.57 # Propositional unsat core size : 0 0.21/0.57 # Propositional preprocessing time : 0.000 0.21/0.57 # Propositional encoding time : 0.000 0.21/0.57 # Propositional solver time : 0.000 0.21/0.57 # Success case prop preproc time : 0.000 0.21/0.57 # Success case prop encoding time : 0.000 0.21/0.57 # Success case prop solver time : 0.000 0.21/0.57 # Current number of processed clauses : 176 0.21/0.57 # Positive orientable unit clauses : 42 0.21/0.57 # Positive unorientable unit clauses: 0 0.21/0.57 # Negative unit clauses : 4 0.21/0.57 # Non-unit-clauses : 130 0.21/0.57 # Current number of unprocessed clauses: 1424 0.21/0.57 # ...number of literals in the above : 3896 0.21/0.57 # Current number of archived formulas : 0 0.21/0.57 # Current number of archived clauses : 173 0.21/0.57 # Clause-clause subsumption calls (NU) : 4446 0.21/0.57 # Rec. Clause-clause subsumption calls : 2814 0.21/0.57 # Non-unit clause-clause subsumptions : 33 0.21/0.57 # Unit Clause-clause subsumption calls : 53 0.21/0.57 # Rewrite failures with RHS unbound : 0 0.21/0.57 # BW rewrite match attempts : 19 0.21/0.57 # BW rewrite match successes : 4 0.21/0.57 # Condensation attempts : 416 0.21/0.57 # Condensation successes : 4 0.21/0.57 # Termbank termtop insertions : 50548 0.21/0.57 0.21/0.57 # ------------------------------------------------- 0.21/0.57 # User time : 0.039 s 0.21/0.57 # System time : 0.010 s 0.21/0.57 # Total time : 0.049 s 0.21/0.57 # Maximum resident set size: 4884 pages 0.21/0.57 0.21/0.57 # ------------------------------------------------- 0.21/0.57 # User time : 0.045 s 0.21/0.57 # System time : 0.014 s 0.21/0.57 # Total time : 0.059 s 0.21/0.57 # Maximum resident set size: 2076 pages 0.21/0.58 EOF