0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : run_E %s %d THM 0.13/0.34 % Computer : n021.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 960 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Tue Aug 9 04:38:05 EDT 2022 0.13/0.35 % CPUTime : 0.20/0.49 Running higher-order on 8 cores theorem proving 0.20/0.49 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=120 /export/starexec/sandbox/benchmark/theBenchmark.p 0.20/0.50 # Version: 3.0pre003-ho 0.20/0.56 # Preprocessing class: HSLMSLSSLLLCHFA. 0.20/0.56 # Scheduled 8 strats onto 8 cores with 120 seconds (960 total) 0.20/0.56 # Starting ehoh_best5 with 120s (1) cores 0.20/0.56 # Starting almost_fo_3_lam with 120s (1) cores 0.20/0.56 # Starting new_bool_5 with 120s (1) cores 0.20/0.56 # Starting pre_casc_3 with 120s (1) cores 0.20/0.56 # Starting ho_unfolding_8 with 120s (1) cores 0.20/0.56 # Starting new_ho_10_cnf2 with 120s (1) cores 0.20/0.56 # Starting new_bool_3 with 120s (1) cores 0.20/0.56 # Starting new_ho_5 with 120s (1) cores 0.20/0.56 # new_bool_3 with pid 17963 completed with status 0 0.20/0.56 # Result found by new_bool_3 0.20/0.56 # Preprocessing class: HSLMSLSSLLLCHFA. 0.20/0.56 # Scheduled 8 strats onto 8 cores with 120 seconds (960 total) 0.20/0.56 # Starting ehoh_best5 with 120s (1) cores 0.20/0.56 # Starting almost_fo_3_lam with 120s (1) cores 0.20/0.56 # Starting new_bool_5 with 120s (1) cores 0.20/0.56 # Starting pre_casc_3 with 120s (1) cores 0.20/0.56 # Starting ho_unfolding_8 with 120s (1) cores 0.20/0.56 # Starting new_ho_10_cnf2 with 120s (1) cores 0.20/0.56 # Starting new_bool_3 with 120s (1) cores 0.20/0.56 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.20/0.56 # ...ProofStateSinE()=155/330 0.20/0.56 # Search class: HGHSM-FSLS31-MHFMMSBN 0.20/0.56 # Scheduled 5 strats onto 1 cores with 120 seconds (120 total) 0.20/0.56 # Starting pre_casc_7 with 73s (1) cores 0.20/0.56 # pre_casc_7 with pid 17967 completed with status 0 0.20/0.56 # Result found by pre_casc_7 0.20/0.56 # Preprocessing class: HSLMSLSSLLLCHFA. 0.20/0.56 # Scheduled 8 strats onto 8 cores with 120 seconds (960 total) 0.20/0.56 # Starting ehoh_best5 with 120s (1) cores 0.20/0.56 # Starting almost_fo_3_lam with 120s (1) cores 0.20/0.56 # Starting new_bool_5 with 120s (1) cores 0.20/0.56 # Starting pre_casc_3 with 120s (1) cores 0.20/0.56 # Starting ho_unfolding_8 with 120s (1) cores 0.20/0.56 # Starting new_ho_10_cnf2 with 120s (1) cores 0.20/0.56 # Starting new_bool_3 with 120s (1) cores 0.20/0.56 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.20/0.56 # ...ProofStateSinE()=155/330 0.20/0.56 # Search class: HGHSM-FSLS31-MHFMMSBN 0.20/0.56 # Scheduled 5 strats onto 1 cores with 120 seconds (120 total) 0.20/0.56 # Starting pre_casc_7 with 73s (1) cores 0.20/0.56 # Preprocessing time : 0.005 s 0.20/0.56 0.20/0.56 # Proof found! 0.20/0.56 # SZS status Theorem 0.20/0.56 # SZS output start CNFRefutation 0.20/0.56 thf(decl_22, type, in: $i > $i > $o). 0.20/0.56 thf(decl_23, type, exu: ($i > $o) > $o). 0.20/0.56 thf(decl_24, type, setextAx: $o). 0.20/0.56 thf(decl_25, type, emptyset: $i). 0.20/0.56 thf(decl_26, type, emptysetAx: $o). 0.20/0.56 thf(decl_27, type, setadjoin: $i > $i > $i). 0.20/0.56 thf(decl_28, type, setadjoinAx: $o). 0.20/0.56 thf(decl_29, type, powerset: $i > $i). 0.20/0.56 thf(decl_30, type, powersetAx: $o). 0.20/0.56 thf(decl_31, type, setunion: $i > $i). 0.20/0.56 thf(decl_32, type, setunionAx: $o). 0.20/0.56 thf(decl_33, type, omega: $i). 0.20/0.56 thf(decl_34, type, omega0Ax: $o). 0.20/0.56 thf(decl_35, type, omegaSAx: $o). 0.20/0.56 thf(decl_36, type, omegaIndAx: $o). 0.20/0.56 thf(decl_37, type, replAx: $o). 0.20/0.56 thf(decl_38, type, foundationAx: $o). 0.20/0.56 thf(decl_39, type, wellorderingAx: $o). 0.20/0.56 thf(decl_40, type, descr: ($i > $o) > $i). 0.20/0.56 thf(decl_41, type, descrp: $o). 0.20/0.56 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.20/0.56 thf(decl_43, type, dsetconstrI: $o). 0.20/0.56 thf(decl_44, type, dsetconstrEL: $o). 0.20/0.56 thf(decl_45, type, dsetconstrER: $o). 0.20/0.56 thf(decl_46, type, exuE1: $o). 0.20/0.56 thf(decl_47, type, prop2set: $o > $i). 0.20/0.56 thf(decl_48, type, prop2setE: $o). 0.20/0.56 thf(decl_49, type, emptysetE: $o). 0.20/0.56 thf(decl_50, type, emptysetimpfalse: $o). 0.20/0.56 thf(decl_51, type, notinemptyset: $o). 0.20/0.56 thf(decl_52, type, exuE3e: $o). 0.20/0.56 thf(decl_53, type, setext: $o). 0.20/0.56 thf(decl_54, type, emptyI: $o). 0.20/0.56 thf(decl_55, type, noeltsimpempty: $o). 0.20/0.56 thf(decl_56, type, setbeta: $o). 0.20/0.56 thf(decl_57, type, nonempty: $i > $o). 0.20/0.56 thf(decl_58, type, nonemptyE1: $o). 0.20/0.56 thf(decl_59, type, nonemptyI: $o). 0.20/0.56 thf(decl_60, type, nonemptyI1: $o). 0.20/0.56 thf(decl_61, type, setadjoinIL: $o). 0.20/0.56 thf(decl_62, type, emptyinunitempty: $o). 0.20/0.56 thf(decl_63, type, setadjoinIR: $o). 0.20/0.56 thf(decl_64, type, setadjoinE: $o). 0.20/0.56 thf(decl_65, type, setadjoinOr: $o). 0.20/0.56 thf(decl_66, type, setoftrueEq: $o). 0.20/0.56 thf(decl_67, type, powersetI: $o). 0.20/0.56 thf(decl_68, type, emptyinPowerset: $o). 0.20/0.56 thf(decl_69, type, emptyInPowerset: $o). 0.20/0.56 thf(decl_70, type, powersetE: $o). 0.20/0.56 thf(decl_71, type, setunionI: $o). 0.20/0.56 thf(decl_72, type, setunionE: $o). 0.20/0.56 thf(decl_73, type, subPowSU: $o). 0.20/0.56 thf(decl_74, type, exuE2: $o). 0.20/0.56 thf(decl_75, type, nonemptyImpWitness: $o). 0.20/0.56 thf(decl_76, type, uniqinunit: $o). 0.20/0.56 thf(decl_77, type, notinsingleton: $o). 0.20/0.56 thf(decl_78, type, eqinunit: $o). 0.20/0.56 thf(decl_79, type, singletonsswitch: $o). 0.20/0.56 thf(decl_80, type, upairsetE: $o). 0.20/0.56 thf(decl_81, type, upairsetIL: $o). 0.20/0.56 thf(decl_82, type, upairsetIR: $o). 0.20/0.56 thf(decl_83, type, emptyE1: $o). 0.20/0.56 thf(decl_84, type, vacuousDall: $o). 0.20/0.56 thf(decl_85, type, quantDeMorgan1: $o). 0.20/0.56 thf(decl_86, type, quantDeMorgan2: $o). 0.20/0.56 thf(decl_87, type, quantDeMorgan3: $o). 0.20/0.56 thf(decl_88, type, quantDeMorgan4: $o). 0.20/0.56 thf(decl_89, type, prop2setI: $o). 0.20/0.56 thf(decl_90, type, set2prop: $i > $o). 0.20/0.56 thf(decl_91, type, prop2set2propI: $o). 0.20/0.56 thf(decl_92, type, notdexE: $o). 0.20/0.56 thf(decl_93, type, notdallE: $o). 0.20/0.56 thf(decl_94, type, exuI1: $o). 0.20/0.56 thf(decl_95, type, exuI3: $o). 0.20/0.56 thf(decl_96, type, exuI2: $o). 0.20/0.56 thf(decl_97, type, inCongP: $o). 0.20/0.56 thf(decl_98, type, in__Cong: $o). 0.20/0.56 thf(decl_99, type, exuE3u: $o). 0.20/0.56 thf(decl_100, type, exu__Cong: $o). 0.20/0.56 thf(decl_101, type, emptyset__Cong: $o). 0.20/0.56 thf(decl_102, type, setadjoin__Cong: $o). 0.20/0.56 thf(decl_103, type, powerset__Cong: $o). 0.20/0.56 thf(decl_104, type, setunion__Cong: $o). 0.20/0.56 thf(decl_105, type, omega__Cong: $o). 0.20/0.56 thf(decl_106, type, exuEu: $o). 0.20/0.56 thf(decl_107, type, descr__Cong: $o). 0.20/0.56 thf(decl_108, type, dsetconstr__Cong: $o). 0.20/0.56 thf(decl_109, type, subset: $i > $i > $o). 0.20/0.56 thf(decl_110, type, disjoint: $i > $i > $o). 0.20/0.56 thf(decl_111, type, setsmeet: $i > $i > $o). 0.20/0.56 thf(decl_112, type, subsetI1: $o). 0.20/0.56 thf(decl_113, type, eqimpsubset2: $o). 0.20/0.56 thf(decl_114, type, eqimpsubset1: $o). 0.20/0.56 thf(decl_115, type, subsetI2: $o). 0.20/0.56 thf(decl_116, type, emptysetsubset: $o). 0.20/0.56 thf(decl_117, type, subsetE: $o). 0.20/0.56 thf(decl_118, type, subsetE2: $o). 0.20/0.56 thf(decl_119, type, notsubsetI: $o). 0.20/0.56 thf(decl_120, type, notequalI1: $o). 0.20/0.56 thf(decl_121, type, notequalI2: $o). 0.20/0.56 thf(decl_122, type, subsetRefl: $o). 0.20/0.56 thf(decl_123, type, subsetTrans: $o). 0.20/0.56 thf(decl_124, type, setadjoinSub: $o). 0.20/0.56 thf(decl_125, type, setadjoinSub2: $o). 0.20/0.56 thf(decl_126, type, subset2powerset: $o). 0.20/0.56 thf(decl_127, type, setextsub: $o). 0.20/0.56 thf(decl_128, type, subsetemptysetimpeq: $o). 0.20/0.56 thf(decl_129, type, powersetI1: $o). 0.20/0.56 thf(decl_130, type, powersetE1: $o). 0.20/0.56 thf(decl_131, type, inPowerset: $o). 0.20/0.56 thf(decl_132, type, powersetsubset: $o). 0.20/0.56 thf(decl_133, type, sepInPowerset: $o). 0.20/0.56 thf(decl_134, type, sepSubset: $o). 0.20/0.56 thf(decl_135, type, binunion: $i > $i > $i). 0.20/0.56 thf(decl_136, type, binunionIL: $o). 0.20/0.56 thf(decl_137, type, upairset2IR: $o). 0.20/0.56 thf(decl_138, type, binunionIR: $o). 0.20/0.56 thf(decl_139, type, binunionEcases: $o). 0.20/0.56 thf(decl_140, type, binunionE: $o). 0.20/0.56 thf(decl_141, type, binunionLsub: $o). 0.20/0.56 thf(decl_142, type, binunionRsub: $o). 0.20/0.56 thf(decl_143, type, binintersect: $i > $i > $i). 0.20/0.56 thf(decl_144, type, binintersectI: $o). 0.20/0.56 thf(decl_145, type, binintersectSubset5: $o). 0.20/0.56 thf(decl_146, type, binintersectEL: $o). 0.20/0.56 thf(decl_147, type, binintersectLsub: $o). 0.20/0.56 thf(decl_148, type, binintersectSubset2: $o). 0.20/0.56 thf(decl_149, type, binintersectSubset3: $o). 0.20/0.56 thf(decl_150, type, binintersectER: $o). 0.20/0.56 thf(decl_151, type, disjointsetsI1: $o). 0.20/0.56 thf(decl_152, type, binintersectRsub: $o). 0.20/0.56 thf(decl_153, type, binintersectSubset4: $o). 0.20/0.56 thf(decl_154, type, binintersectSubset1: $o). 0.20/0.56 thf(decl_155, type, bs114d: $o). 0.20/0.56 thf(decl_156, type, regular: $i > $o). 0.20/0.56 thf(decl_157, type, setminus: $i > $i > $i). 0.20/0.56 thf(decl_158, type, setminusI: $o). 0.20/0.56 thf(decl_159, type, setminusEL: $o). 0.20/0.56 thf(decl_160, type, setminusER: $o). 0.20/0.56 thf(decl_161, type, setminusSubset2: $o). 0.20/0.56 thf(decl_162, type, setminusERneg: $o). 0.20/0.56 thf(decl_163, type, setminusELneg: $o). 0.20/0.56 thf(decl_164, type, setminusILneg: $o). 0.20/0.56 thf(decl_165, type, setminusIRneg: $o). 0.20/0.56 thf(decl_166, type, setminusLsub: $o). 0.20/0.56 thf(decl_167, type, setminusSubset1: $o). 0.20/0.56 thf(decl_168, type, symdiff: $i > $i > $i). 0.20/0.56 thf(decl_169, type, symdiffE: $o). 0.20/0.56 thf(decl_170, type, symdiffI1: $o). 0.20/0.56 thf(decl_171, type, symdiffI2: $o). 0.20/0.56 thf(decl_172, type, symdiffIneg1: $o). 0.20/0.56 thf(decl_173, type, symdiffIneg2: $o). 0.20/0.56 thf(decl_174, type, iskpair: $i > $o). 0.20/0.56 thf(decl_175, type, secondinupair: $o). 0.20/0.56 thf(decl_176, type, setukpairIL: $o). 0.20/0.56 thf(decl_177, type, setukpairIR: $o). 0.20/0.56 thf(decl_178, type, kpairiskpair: $o). 0.20/0.56 thf(decl_179, type, kpair: $i > $i > $i). 0.20/0.56 thf(decl_180, type, kpairp: $o). 0.20/0.56 thf(decl_181, type, cartprod: $i > $i > $i). 0.20/0.56 thf(decl_182, type, singletonsubset: $o). 0.20/0.56 thf(decl_183, type, singletoninpowerset: $o). 0.20/0.56 thf(decl_184, type, singletoninpowunion: $o). 0.20/0.56 thf(decl_185, type, upairset2E: $o). 0.20/0.56 thf(decl_186, type, upairsubunion: $o). 0.20/0.56 thf(decl_187, type, upairinpowunion: $o). 0.20/0.56 thf(decl_188, type, ubforcartprodlem1: $o). 0.20/0.56 thf(decl_189, type, ubforcartprodlem2: $o). 0.20/0.56 thf(decl_190, type, ubforcartprodlem3: $o). 0.20/0.56 thf(decl_191, type, cartprodpairin: $o). 0.20/0.56 thf(decl_192, type, cartprodmempair1: $o). 0.20/0.56 thf(decl_193, type, cartprodmempair: $o). 0.20/0.56 thf(decl_194, type, setunionE2: $o). 0.20/0.56 thf(decl_195, type, setunionsingleton1: $o). 0.20/0.56 thf(decl_196, type, epred1_0: $o). 0.20/0.56 thf(decl_197, type, esk1_2: $i > $i > $i). 0.20/0.56 thf(decl_198, type, esk2_2: $i > $i > $i). 0.20/0.56 thf(decl_199, type, esk3_2: $i > $i > $i). 0.20/0.56 thf(decl_200, type, esk4_1: $i > $i). 0.20/0.56 thf(decl_201, type, esk5_2: ($i > $i > $o) > $i > $i). 0.20/0.56 thf(decl_202, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 0.20/0.56 thf(decl_203, type, esk7_2: ($i > $i > $o) > $i > $i). 0.20/0.56 thf(decl_204, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 0.20/0.56 thf(decl_205, type, esk9_1: $i > $i). 0.20/0.56 thf(decl_206, type, esk10_2: ($i > $o) > $i > $i). 0.20/0.56 thf(decl_207, type, esk11_2: ($i > $o) > $i > $i). 0.20/0.56 thf(decl_208, type, esk12_1: ($i > $o) > $i). 0.20/0.56 thf(decl_209, type, esk13_2: ($i > $o) > $i > $i). 0.20/0.56 thf(decl_210, type, esk14_1: ($i > $o) > $i). 0.20/0.56 thf(decl_211, type, esk15_2: $i > $i > $i). 0.20/0.56 thf(decl_212, type, esk16_2: $i > $i > $i). 0.20/0.56 thf(decl_213, type, esk17_1: $i > $i). 0.20/0.56 thf(decl_214, type, esk18_1: $i > $i). 0.20/0.56 thf(decl_215, type, esk19_1: $i > $i). 0.20/0.56 thf(decl_216, type, esk20_2: $i > $i > $i). 0.20/0.56 thf(decl_217, type, esk21_3: $i > $i > $o > $i). 0.20/0.56 thf(decl_218, type, esk22_2: ($i > $o) > $i > $i). 0.20/0.56 thf(decl_219, type, esk23_1: ($i > $o) > $i). 0.20/0.56 thf(decl_220, type, esk24_1: $i > $i). 0.20/0.56 thf(decl_221, type, esk25_2: $i > ($i > $o) > $i). 0.20/0.56 thf(decl_222, type, esk26_2: $i > ($i > $o) > $i). 0.20/0.56 thf(decl_223, type, esk27_2: $i > ($i > $o) > $i). 0.20/0.56 thf(decl_224, type, esk28_2: $i > ($i > $o) > $i). 0.20/0.56 thf(decl_225, type, esk29_2: $i > ($i > $o) > $i). 0.20/0.56 thf(decl_226, type, esk30_2: $i > ($i > $o) > $i). 0.20/0.56 thf(decl_227, type, esk31_2: ($i > $o) > $i > $i). 0.20/0.56 thf(decl_228, type, esk32_1: ($i > $o) > $i). 0.20/0.56 thf(decl_229, type, esk33_1: ($i > $o) > $i). 0.20/0.56 thf(decl_230, type, esk34_1: ($i > $o) > $i). 0.20/0.56 thf(decl_231, type, esk35_1: ($i > $o) > $i). 0.20/0.56 thf(decl_232, type, esk36_2: ($i > $o) > $i > $i). 0.20/0.56 thf(decl_233, type, esk37_1: ($i > $o) > $i). 0.20/0.56 thf(decl_234, type, esk38_2: ($i > $o) > $i > $i). 0.20/0.56 thf(decl_235, type, esk39_2: ($i > $o) > ($i > $o) > $i). 0.20/0.56 thf(decl_236, type, esk40_2: ($i > $o) > ($i > $o) > $i). 0.20/0.56 thf(decl_237, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 0.20/0.56 thf(decl_238, type, esk42_2: ($i > $o) > ($i > $o) > $i). 0.20/0.56 thf(decl_239, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 0.20/0.56 thf(decl_240, type, esk44_2: ($i > $o) > ($i > $o) > $i). 0.20/0.56 thf(decl_241, type, esk45_2: ($i > $o) > $i > $i). 0.20/0.56 thf(decl_242, type, esk46_2: ($i > $o) > ($i > $o) > $i). 0.20/0.56 thf(decl_243, type, esk47_2: ($i > $o) > ($i > $o) > $i). 0.20/0.56 thf(decl_244, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 0.20/0.56 thf(decl_245, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 0.20/0.56 thf(decl_246, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.20/0.56 thf(decl_247, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.20/0.56 thf(decl_248, type, esk52_2: $i > $i > $i). 0.20/0.56 thf(decl_249, type, esk53_2: $i > $i > $i). 0.20/0.56 thf(decl_250, type, esk54_2: $i > $i > $i). 0.20/0.56 thf(decl_251, type, esk55_2: $i > $i > $i). 0.20/0.56 thf(decl_252, type, esk56_2: $i > $i > $i). 0.20/0.56 thf(decl_253, type, esk57_2: $i > $i > $i). 0.20/0.56 thf(decl_254, type, esk58_2: $i > $i > $i). 0.20/0.56 thf(decl_255, type, esk59_3: $i > $i > $i > $i). 0.20/0.56 thf(decl_256, type, esk60_3: $i > $i > $i > $i). 0.20/0.56 thf(decl_257, type, esk61_3: $i > $i > $i > $i). 0.20/0.56 thf(decl_258, type, esk62_3: $i > $i > $i > $i). 0.20/0.56 thf(decl_259, type, esk63_2: $i > $i > $i). 0.20/0.56 thf(decl_260, type, esk64_0: $i). 0.20/0.56 thf(decl_261, type, esk65_1: $i > $i). 0.20/0.56 thf(decl_262, type, esk66_3: $i > $i > $i > $i). 0.20/0.56 thf(decl_263, type, esk67_2: $i > $i > $i). 0.20/0.56 thf(decl_264, type, esk68_2: $i > $i > $i). 0.20/0.56 thf(decl_265, type, esk69_2: $i > $i > $i). 0.20/0.56 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonempty)). 0.20/0.56 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE1)). 0.20/0.56 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu)). 0.20/0.56 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descrp)). 0.20/0.56 thf(kpair, axiom, ((kpair)=(^[X2:$i, X3:$i]:(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpair)). 0.20/0.56 thf(iskpair, axiom, ((iskpair)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ (setunion @ X4))&?[X3:$i]:(((in @ X3 @ (setunion @ X4))&((X4)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', iskpair)). 0.20/0.56 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descr__Cong)). 0.20/0.56 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuEu)). 0.20/0.56 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu__Cong)). 0.20/0.56 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3u)). 0.20/0.56 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI3)). 0.20/0.56 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI1)). 0.20/0.56 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI2)). 0.20/0.56 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE2)). 0.20/0.56 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI)). 0.20/0.56 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3e)). 0.20/0.56 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', replAx)). 0.20/0.56 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyImpWitness)). 0.20/0.56 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setbeta)). 0.20/0.56 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrI)). 0.20/0.56 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairin)). 0.20/0.56 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair)). 0.20/0.56 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair1)). 0.20/0.56 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem3)). 0.20/0.56 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairp)). 0.20/0.56 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairiskpair)). 0.20/0.56 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepSubset)). 0.20/0.56 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepInPowerset)). 0.20/0.56 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyE1)). 0.20/0.56 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstr__Cong)). 0.20/0.56 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setoftrueEq)). 0.20/0.56 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI1)). 0.20/0.56 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyE1)). 0.20/0.56 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrER)). 0.20/0.56 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrEL)). 0.20/0.56 thf(setunionsingleton2, conjecture, ((setextAx)=>((emptysetAx)=>((((setunionAx)=>(((omegaSAx)=>((omegaIndAx)=>((replAx)=>(((wellorderingAx)=>((((dsetconstrEL)=>((dsetconstrER)=>(((prop2setE)=>(((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((((((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((((((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>(((((setunionI)=>(((subPowSU)=>((exuE2)=>((((notinsingleton)=>((eqinunit)=>(((((((((((((prop2set2propI)=>((notdexE)=>((notdallE)=>((((exuI2)=>((inCongP)=>(((((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((((((dsetconstr__Cong)=>(((((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>(((subsetRefl)=>((((((((powersetI1)=>(((((((binunionIL)=>(((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>(((binintersectSubset5)=>((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((((binintersectSubset1)=>(((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>(((setminusIRneg)=>(((setminusSubset1)=>((((symdiffI2)=>(((symdiffIneg2)=>((secondinupair)=>(((setukpairIR)=>((((singletonsubset)=>((singletoninpowerset)=>(((upairset2E)=>((((ubforcartprodlem1)=>((ubforcartprodlem2)=>(((cartprodpairin)=>(((((setunionsingleton1)=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset)))))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1)))<=(ubforcartprodlem3))))<=(upairinpowunion))<=(upairsubunion)))<=(singletoninpowunion))))<=(kpairp))<=(kpairiskpair)))<=(setukpairIL))))<=(symdiffIneg1)))<=(symdiffI1))<=(symdiffE)))<=(setminusLsub)))<=(setminusILneg))))))))<=(bs114d)))<=(binintersectSubset4))<=(binintersectRsub))))))<=(binintersectLsub))))<=(binintersectI)))))))<=(upairset2IR)))<=(sepSubset))<=(sepInPowerset))<=(powersetsubset))<=(inPowerset))<=(powersetE1)))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset))<=(setadjoinSub2))<=(setadjoinSub))<=(subsetTrans)))<=(notequalI2))))))))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1)))<=(descr__Cong))<=(exuEu))<=(omega__Cong))<=(setunion__Cong)))))<=(exu__Cong))<=(exuE3u))<=(in__Cong))))<=(exuI3))<=(exuI1)))))<=(prop2setI))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall))<=(emptyE1))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch))))<=(uniqinunit))<=(nonemptyImpWitness))))<=(setunionE)))<=(powersetE))<=(emptyInPowerset))<=(emptyinPowerset)))))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty))<=(setadjoinIL)))))<=(setbeta))<=(noeltsimpempty))<=(emptyI))<=(setext)))))<=(emptysetE)))<=(exuE1))))<=(dsetconstrI))<=(descrp)))<=(foundationAx)))))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton2)). 0.20/0.56 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetAx)). 0.20/0.56 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinAx)). 0.20/0.56 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', uniqinunit)). 0.20/0.56 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE)). 0.20/0.56 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusER)). 0.20/0.56 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE)). 0.20/0.56 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyInPowerset)). 0.20/0.56 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset2)). 0.20/0.56 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinPowerset)). 0.20/0.56 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinE)). 0.20/0.56 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusERneg)). 0.20/0.56 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIR)). 0.20/0.56 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinunitempty)). 0.20/0.56 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusELneg)). 0.20/0.56 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIL)). 0.20/0.56 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusIRneg)). 0.20/0.56 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', noeltsimpempty)). 0.20/0.56 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyI)). 0.20/0.56 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset1)). 0.20/0.56 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setext)). 0.20/0.56 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI2)). 0.20/0.56 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetE)). 0.20/0.56 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg2)). 0.20/0.56 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', foundationAx)). 0.20/0.56 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega0Ax)). 0.20/0.56 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', secondinupair)). 0.20/0.56 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairIL)). 0.20/0.56 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairIR)). 0.20/0.56 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsubset)). 0.20/0.56 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletoninpowerset)). 0.20/0.56 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2E)). 0.20/0.56 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem1)). 0.20/0.56 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem2)). 0.20/0.56 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton1)). 0.20/0.56 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE2)). 0.20/0.56 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairinpowunion)). 0.20/0.56 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsubunion)). 0.20/0.56 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletoninpowunion)). 0.20/0.56 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setI)). 0.20/0.56 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan4)). 0.20/0.56 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg1)). 0.20/0.56 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI1)). 0.20/0.56 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffE)). 0.20/0.56 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusLsub)). 0.20/0.56 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusILneg)). 0.20/0.56 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', bs114d)). 0.20/0.56 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset4)). 0.20/0.56 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectRsub)). 0.20/0.56 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectLsub)). 0.20/0.56 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectI)). 0.20/0.56 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2IR)). 0.20/0.56 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetsubset)). 0.20/0.56 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inPowerset)). 0.20/0.56 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE1)). 0.20/0.56 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetemptysetimpeq)). 0.20/0.56 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextsub)). 0.20/0.56 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subset2powerset)). 0.20/0.56 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub2)). 0.20/0.56 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub)). 0.20/0.56 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetTrans)). 0.20/0.56 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset1)). 0.20/0.56 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI2)). 0.20/0.56 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset1)). 0.20/0.56 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset2)). 0.20/0.56 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI1)). 0.20/0.56 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega__Cong)). 0.20/0.56 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunion__Cong)). 0.20/0.56 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusI)). 0.20/0.56 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusEL)). 0.20/0.56 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', in__Cong)). 0.20/0.56 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan3)). 0.20/0.56 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan2)). 0.20/0.56 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan1)). 0.20/0.56 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', vacuousDall)). 0.20/0.56 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIR)). 0.20/0.56 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIL)). 0.20/0.56 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetE)). 0.20/0.56 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsswitch)). 0.20/0.56 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', disjointsetsI1)). 0.20/0.56 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectER)). 0.20/0.56 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset3)). 0.20/0.56 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset2)). 0.20/0.56 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectEL)). 0.20/0.56 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset5)). 0.20/0.56 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionRsub)). 0.20/0.56 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionLsub)). 0.20/0.56 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionE)). 0.20/0.56 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionEcases)). 0.20/0.56 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIR)). 0.20/0.56 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIL)). 0.20/0.56 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI1)). 0.20/0.56 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetRefl)). 0.20/0.56 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI1)). 0.20/0.56 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notsubsetI)). 0.20/0.56 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE2)). 0.20/0.56 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE)). 0.20/0.56 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetsubset)). 0.20/0.56 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI2)). 0.20/0.56 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powerset__Cong)). 0.20/0.56 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoin__Cong)). 0.20/0.56 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyset__Cong)). 0.20/0.56 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inCongP)). 0.20/0.56 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdallE)). 0.20/0.56 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdexE)). 0.20/0.56 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqinunit)). 0.20/0.56 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinsingleton)). 0.20/0.56 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subPowSU)). 0.20/0.56 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionI)). 0.20/0.56 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI)). 0.20/0.56 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinOr)). 0.20/0.56 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinemptyset)). 0.20/0.56 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetimpfalse)). 0.20/0.56 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setE)). 0.20/0.56 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', wellorderingAx)). 0.20/0.56 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaIndAx)). 0.20/0.56 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaSAx)). 0.20/0.56 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionAx)). 0.20/0.56 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetAx)). 0.20/0.56 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextAx)). 0.20/0.56 thf(c_0_155, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.20/0.56 thf(c_0_156, 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])). 0.20/0.56 thf(c_0_157, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.20/0.56 thf(c_0_158, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.20/0.56 thf(c_0_159, plain, ((kpair)=(^[Z0:$i, Z1:$i]:(setadjoin @ (setadjoin @ Z0 @ emptyset) @ (setadjoin @ (setadjoin @ Z0 @ (setadjoin @ Z1 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[kpair])). 0.20/0.56 thf(c_0_160, plain, ((iskpair)=(^[Z0:$i]:(?[X2:$i]:(((in @ X2 @ (setunion @ Z0))&?[X3:$i]:(((in @ X3 @ (setunion @ Z0))&((Z0)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))), inference(fof_simplification,[status(thm)],[iskpair])). 0.20/0.56 thf(c_0_161, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.20/0.56 thf(c_0_162, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.20/0.56 thf(c_0_163, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.20/0.56 thf(c_0_164, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 0.20/0.56 thf(c_0_165, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.20/0.56 thf(c_0_166, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 0.20/0.56 thf(c_0_167, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.20/0.56 thf(c_0_168, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.20/0.56 thf(c_0_169, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.20/0.56 thf(c_0_170, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.20/0.56 thf(c_0_171, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.20/0.56 thf(c_0_172, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_155])). 0.20/0.56 thf(c_0_173, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.20/0.56 thf(c_0_174, plain, ((exuE1)=(![X1:$i > $o]:(((?[X436:$i]:((((X1 @ X436))&![X437:$i]:((((X1 @ X437))=>((X436)=(X437)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_156, c_0_157])). 0.20/0.56 thf(c_0_175, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.20/0.56 thf(c_0_176, plain, ((descrp)=(![X1:$i > $o]:(((?[X434:$i]:((((X1 @ X434))&![X435:$i]:((((X1 @ X435))=>((X434)=(X435)))))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_158, c_0_157])). 0.20/0.56 thf(c_0_177, axiom, ((cartprodpairin)=(![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)) @ (cartprod @ X4 @ X5)))))))), inference(apply_def,[status(thm)],[cartprodpairin, c_0_159])). 0.20/0.56 thf(c_0_178, axiom, ((cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(?[X464:$i]:(((in @ X464 @ (setunion @ X18))&?[X465:$i]:(((in @ X465 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X464 @ emptyset) @ (setadjoin @ (setadjoin @ X464 @ (setadjoin @ X465 @ emptyset)) @ emptyset)))))))))))), inference(apply_def,[status(thm)],[cartprodmempair, c_0_160])). 0.20/0.56 thf(c_0_179, axiom, ((cartprodmempair1)=(![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[cartprodmempair1, c_0_159])). 0.20/0.56 thf(c_0_180, axiom, ((ubforcartprodlem3)=(![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)))))))))), inference(apply_def,[status(thm)],[ubforcartprodlem3, c_0_159])). 0.20/0.56 thf(c_0_181, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X462:$i]:(((in @ X462 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X463:$i]:(((in @ X463 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X462 @ emptyset) @ (setadjoin @ (setadjoin @ X462 @ (setadjoin @ X463 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[kpairp, c_0_160]), c_0_159])). 0.20/0.56 thf(c_0_182, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X460:$i]:(((in @ X460 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X461:$i]:(((in @ X461 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X460 @ emptyset) @ (setadjoin @ (setadjoin @ X460 @ (setadjoin @ X461 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_160])). 0.20/0.56 thf(c_0_183, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.20/0.56 thf(c_0_184, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.20/0.56 thf(c_0_185, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X456:$i]:((((X1 @ X456))&![X457:$i]:((((X1 @ X457))=>((X456)=(X457)))))))=>((?[X458:$i]:((((X17 @ X458))&![X459:$i]:((((X17 @ X459))=>((X458)=(X459)))))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_161, c_0_157])). 0.20/0.56 thf(c_0_186, plain, ((exuEu)=(![X1:$i > $o]:(((?[X454:$i]:((((X1 @ X454))&![X455:$i]:((((X1 @ X455))=>((X454)=(X455)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_162, c_0_157])). 0.20/0.56 thf(c_0_187, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X450:$i]:((((X1 @ X450))&![X451:$i]:((((X1 @ X451))=>((X450)=(X451)))))))<=>(?[X452:$i]:((((X17 @ X452))&![X453:$i]:((((X17 @ X453))=>((X452)=(X453)))))))))))), inference(apply_def,[status(thm)],[c_0_163, c_0_157])). 0.20/0.56 thf(c_0_188, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X448:$i]:((((X1 @ X448))&![X449:$i]:((((X1 @ X449))=>((X448)=(X449)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_164, c_0_157])). 0.20/0.56 thf(c_0_189, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X444:$i]:((((X1 @ X444))&![X445:$i]:((((X1 @ X445))=>((X444)=(X445)))))))))))), inference(apply_def,[status(thm)],[c_0_165, c_0_157])). 0.20/0.56 thf(c_0_190, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X442:$i]:((((X1 @ X442))&![X443:$i]:((((X1 @ X443))=>((X442)=(X443))))))))))), inference(apply_def,[status(thm)],[c_0_166, c_0_157])). 0.20/0.56 thf(c_0_191, plain, ((emptyE1)<=>![X4:$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])). 0.20/0.56 thf(c_0_192, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.20/0.56 thf(c_0_193, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X446:$i]:((((X1 @ X446))&![X447:$i]:((((X1 @ X447))=>((X446)=(X447))))))))))), inference(apply_def,[status(thm)],[c_0_167, c_0_157])). 0.20/0.56 thf(c_0_194, plain, ((exuE2)=(![X1:$i > $o]:(((?[X440:$i]:((((X1 @ X440))&![X441:$i]:((((X1 @ X441))=>((X440)=(X441)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_168, c_0_157])). 0.20/0.56 thf(c_0_195, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.20/0.56 thf(c_0_196, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_155])). 0.20/0.56 thf(c_0_197, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_169, c_0_155])). 0.20/0.56 thf(c_0_198, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_155])). 0.20/0.56 thf(c_0_199, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X438:$i]:((((X1 @ X438))&![X439:$i]:((((X1 @ X439))=>((X438)=(X439)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_170, c_0_157])). 0.20/0.56 thf(c_0_200, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.20/0.56 thf(c_0_201, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.20/0.56 thf(c_0_202, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X432:$i]:((((X6 @ X2 @ X432))&![X433:$i]:((((X6 @ X2 @ X433))=>((X432)=(X433)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_171, c_0_157])). 0.20/0.56 thf(c_0_203, plain, ((epred1_0)<=>![X485:$i]:(?[X486:$i]:((((![X487:$i]:(((in @ X487 @ X486)=>![X488:$i]:(((in @ X488 @ X487)=>(in @ X488 @ X485)))))&![X489:$i, X490:$i]:((((in @ X489 @ X485)&(in @ X490 @ X485))=>(![X491:$i]:(((in @ X491 @ X486)=>((in @ X489 @ X491)<=>(in @ X490 @ X491))))=>((X489)=(X490))))))&![X492:$i, X493:$i]:((((in @ X492 @ X486)&(in @ X493 @ X486))=>(![X494:$i]:(((in @ X494 @ X492)=>(in @ X494 @ X493)))|![X495:$i]:(((in @ X495 @ X493)=>(in @ X495 @ X492)))))))&![X496:$i]:(((![X497:$i]:(((in @ X497 @ X496)=>(in @ X497 @ X485)))&?[X498:$i]:((in @ X498 @ X496)))=>?[X499:$i, X500:$i]:(((((in @ X499 @ X486)&(in @ X500 @ X496))&~(?[X501:$i]:(((in @ X501 @ X499)&(in @ X501 @ X496)))))&![X502:$i]:(((in @ X502 @ X486)=>(![X503:$i]:(((in @ X503 @ X502)=>(in @ X503 @ X499)))|(in @ X500 @ X502)))))))))))), introduced(definition)). 0.20/0.56 thf(c_0_204, negated_conjecture, ~((![X466:$i, X467:$i]:((![X468:$i]:(((in @ X468 @ X466)<=>(in @ X468 @ X467)))=>((X466)=(X467))))=>(![X469:$i]:(~(in @ X469 @ emptyset))=>(![X906:$i, X907:$i, X908:$i]:(((in @ X908 @ (setadjoin @ X906 @ X907))<=>(((X908)=(X906))|(in @ X908 @ X907))))=>(![X903:$i, X904:$i]:(((in @ X904 @ (powerset @ X903))<=>![X905:$i]:(((in @ X905 @ X904)=>(in @ X905 @ X903)))))=>(![X470:$i, X471:$i]:(((in @ X471 @ (setunion @ X470))<=>?[X472:$i]:(((in @ X471 @ X472)&(in @ X472 @ X470)))))=>((in @ emptyset @ omega)=>(![X473:$i]:(((in @ X473 @ omega)=>(in @ (setadjoin @ X473 @ X473) @ omega)))=>(![X474:$i]:((((in @ emptyset @ X474)&![X475:$i]:((((in @ X475 @ omega)&(in @ X475 @ X474))=>(in @ (setadjoin @ X475 @ X475) @ X474))))=>![X476:$i]:(((in @ X476 @ omega)=>(in @ X476 @ X474)))))=>(![X477:$i > $i > $o, X478:$i]:((![X479:$i]:(((in @ X479 @ X478)=>?[X480:$i]:(((X477 @ X479 @ X480)&![X481:$i]:(((X477 @ X479 @ X481)=>((X480)=(X481))))))))=>?[X482:$i]:(![X483:$i]:(((in @ X483 @ X482)<=>?[X484:$i]:(((in @ X484 @ X478)&(X477 @ X484 @ X483))))))))=>(![X899:$i]:((?[X900:$i]:((in @ X900 @ X899))=>?[X901:$i]:(((in @ X901 @ X899)&~(?[X902:$i]:(((in @ X902 @ X901)&(in @ X902 @ X899))))))))=>((epred1_0)=>(![X896:$i > $o]:((?[X897:$i]:(((X896 @ X897)&![X898:$i]:(((X896 @ X898)=>((X897)=(X898))))))=>(X896 @ (descr @ (^[Z0:$i]:((X896 @ Z0)))))))=>(![X893:$i, X894:$i > $o, X895:$i]:(((in @ X895 @ X893)=>((X894 @ X895)=>(in @ X895 @ (dsetconstr @ X893 @ (^[Z0:$i]:((X894 @ Z0))))))))=>(![X504:$i, X505:$i > $o, X506:$i]:(((in @ X506 @ (dsetconstr @ X504 @ (^[Z0:$i]:((X505 @ Z0)))))=>(in @ X506 @ X504)))=>(![X507:$i, X508:$i > $o, X509:$i]:(((in @ X509 @ (dsetconstr @ X507 @ (^[Z0:$i]:((X508 @ Z0)))))=>(X508 @ X509)))=>(![X888:$i > $o]:((?[X889:$i]:(((X888 @ X889)&![X890:$i]:(((X888 @ X890)=>((X889)=(X890))))))=>?[X891:$i]:(((X888 @ X891)&![X892:$i]:(((X888 @ X892)=>((X891)=(X892))))))))=>(![X510:$o, X511:$i]:(((in @ X511 @ (prop2set @ ((X510))))=>(X510)))=>(![X886:$i]:(((in @ X886 @ emptyset)=>![X887:$o]:((X887))))=>(![X512:$i]:(~(in @ X512 @ emptyset))=>(![X513:$i]:(~(in @ X513 @ emptyset))=>(![X514:$i > $o]:((?[X515:$i]:(((X514 @ X515)&![X516:$i]:(((X514 @ X516)=>((X515)=(X516))))))=>?[X517:$i]:((X514 @ X517))))=>(![X882:$i, X883:$i]:((![X884:$i]:(((in @ X884 @ X882)=>(in @ X884 @ X883)))=>(![X885:$i]:(((in @ X885 @ X883)=>(in @ X885 @ X882)))=>((X882)=(X883)))))=>(![X880:$i]:((![X881:$i]:(~(in @ X881 @ X880))=>((X880)=(emptyset))))=>(![X878:$i]:((![X879:$i]:(~(in @ X879 @ X878))=>((X878)=(emptyset))))=>(![X875:$i, X876:$i > $o, X877:$i]:(((in @ X877 @ X875)=>((in @ X877 @ (dsetconstr @ X875 @ (^[Z0:$i]:((X876 @ Z0)))))<=>(X876 @ X877))))=>(![X518:$i]:((((X518)!=(emptyset))=>?[X519:$i]:((in @ X519 @ X518))))=>(![X520:$i, X521:$i > $o, X522:$i]:(((in @ X522 @ X520)=>((X521 @ X522)=>((dsetconstr @ X520 @ (^[Z0:$i]:((X521 @ Z0))))!=(emptyset)))))=>(![X523:$i]:((?[X524:$i]:((in @ X524 @ X523))=>((X523)!=(emptyset))))=>(![X873:$i, X874:$i]:((in @ X873 @ (setadjoin @ X873 @ X874)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X870:$i, X871:$i, X872:$i]:(((in @ X872 @ X871)=>(in @ X872 @ (setadjoin @ X870 @ X871))))=>(![X866:$i, X867:$i, X868:$i]:(((in @ X868 @ (setadjoin @ X866 @ X867))=>![X869:$o]:(((((X868)=(X866))=>(X869))=>(((in @ X868 @ X867)=>(X869))=>(X869))))))=>(![X525:$i, X526:$i, X527:$i]:(((in @ X527 @ (setadjoin @ X525 @ X526))=>(((X527)=(X525))|(in @ X527 @ X526))))=>(![X528:$i]:(((dsetconstr @ X528 @ (^[Z0:$i]:(($true))))=(X528)))=>(![X529:$i, X530:$i]:((![X531:$i]:(((in @ X531 @ X530)=>(in @ X531 @ X529)))=>(in @ X530 @ (powerset @ X529))))=>(![X865:$i]:((in @ emptyset @ (powerset @ X865)))=>(![X864:$i]:((in @ emptyset @ (powerset @ X864)))=>(![X861:$i, X862:$i, X863:$i]:(((in @ X862 @ (powerset @ X861))=>((in @ X863 @ X862)=>(in @ X863 @ X861))))=>(![X532:$i, X533:$i, X534:$i]:(((in @ X533 @ X534)=>((in @ X534 @ X532)=>(in @ X533 @ (setunion @ X532)))))=>(![X857:$i, X858:$i]:(((in @ X858 @ (setunion @ X857))=>![X859:$o]:((![X860:$i]:(((in @ X858 @ X860)=>((in @ X860 @ X857)=>(X859))))=>(X859)))))=>(![X535:$i, X536:$i]:(((in @ X536 @ X535)=>(in @ X536 @ (powerset @ (setunion @ X535)))))=>(![X537:$i > $o]:((?[X538:$i]:(((X537 @ X538)&![X539:$i]:(((X537 @ X539)=>((X538)=(X539))))))=>?[X540:$i]:(![X541:$i]:(((X537 @ X541)<=>((X541)=(X540)))))))=>(![X855:$i]:((((X855)!=(emptyset))=>?[X856:$i]:((in @ X856 @ X855))))=>(![X853:$i, X854:$i]:(((in @ X853 @ (setadjoin @ X854 @ emptyset))=>((X853)=(X854))))=>(![X542:$i, X543:$i]:((((X542)!=(X543))=>~(in @ X543 @ (setadjoin @ X542 @ emptyset))))=>(![X544:$i, X545:$i]:((((X544)=(X545))=>(in @ X544 @ (setadjoin @ X545 @ emptyset))))=>(![X851:$i, X852:$i]:(((in @ X851 @ (setadjoin @ X852 @ emptyset))=>(in @ X852 @ (setadjoin @ X851 @ emptyset))))=>(![X848:$i, X849:$i, X850:$i]:(((in @ X850 @ (setadjoin @ X848 @ (setadjoin @ X849 @ emptyset)))=>(((X850)=(X848))|((X850)=(X849)))))=>(![X846:$i, X847:$i]:((in @ X846 @ (setadjoin @ X846 @ (setadjoin @ X847 @ emptyset))))=>(![X844:$i, X845:$i]:((in @ X845 @ (setadjoin @ X844 @ (setadjoin @ X845 @ emptyset))))=>(![X841:$i, X842:$i > $o]:((?[X843:$i]:(((in @ X843 @ X841)&(X842 @ X843)))=>((dsetconstr @ X841 @ (^[Z0:$i]:((X842 @ Z0))))!=(emptyset))))=>(![X839:$i > $o, X840:$i]:(((in @ X840 @ emptyset)=>(X839 @ X840)))=>(![X835:$i, X836:$i > $o]:((~(![X837:$i]:(((in @ X837 @ X835)=>(X836 @ X837))))=>?[X838:$i]:(((in @ X838 @ X835)&~(X836 @ X838)))))=>(![X831:$i, X832:$i > $o]:((![X833:$i]:(((in @ X833 @ X831)=>~(X832 @ X833)))=>~(?[X834:$i]:(((in @ X834 @ X831)&(X832 @ X834))))))=>(![X827:$i, X828:$i > $o]:((~(?[X829:$i]:(((in @ X829 @ X827)&(X828 @ X829))))=>![X830:$i]:(((in @ X830 @ X827)=>~(X828 @ X830)))))=>(![X823:$i, X824:$i > $o]:((?[X825:$i]:(((in @ X825 @ X823)&~(X824 @ X825)))=>~(![X826:$i]:(((in @ X826 @ X823)=>(X824 @ X826))))))=>(![X822:$o]:(((X822)=>(in @ emptyset @ (prop2set @ ((X822))))))=>((prop2set2propI)=>(![X546:$i, X547:$i > $o]:((~(?[X548:$i]:(((in @ X548 @ X546)&(X547 @ X548))))=>![X549:$i]:(((in @ X549 @ X546)=>~(X547 @ X549)))))=>(![X550:$i, X551:$i > $o]:((~(![X552:$i]:(((in @ X552 @ X550)=>(X551 @ X552))))=>?[X553:$i]:(((in @ X553 @ X550)&~(X551 @ X553)))))=>(![X817:$i > $o]:((?[X818:$i]:(((X817 @ X818)&![X819:$i]:(((X817 @ X819)=>((X818)=(X819))))))=>?[X820:$i]:(((X817 @ X820)&![X821:$i]:(((X817 @ X821)=>((X820)=(X821))))))))=>(![X811:$i > $o]:((?[X812:$i]:((X811 @ X812))=>(![X813:$i, X814:$i]:(((X811 @ X813)=>((X811 @ X814)=>((X813)=(X814)))))=>?[X815:$i]:(((X811 @ X815)&![X816:$i]:(((X811 @ X816)=>((X815)=(X816)))))))))=>(![X554:$i > $o]:((?[X555:$i]:(![X556:$i]:(((X554 @ X556)<=>((X556)=(X555)))))=>?[X557:$i]:(((X554 @ X557)&![X558:$i]:(((X554 @ X558)=>((X557)=(X558))))))))=>(![X559:$i, X560:$i]:((((X559)=(X560))=>![X561:$i, X562:$i]:((((X561)=(X562))=>((in @ X561 @ X559)=>(in @ X562 @ X560))))))=>(![X807:$i, X808:$i]:((((X807)=(X808))=>![X809:$i, X810:$i]:((((X809)=(X810))=>((in @ X809 @ X807)<=>(in @ X810 @ X808))))))=>(![X802:$i > $o]:((?[X803:$i]:(((X802 @ X803)&![X804:$i]:(((X802 @ X804)=>((X803)=(X804))))))=>![X805:$i, X806:$i]:(((X802 @ X805)=>((X802 @ X806)=>((X805)=(X806)))))))=>(![X794:$i > $o, X795:$i > $o]:((![X796:$i, X797:$i]:((((X796)=(X797))=>((X794 @ X796)<=>(X795 @ X797))))=>(?[X798:$i]:(((X794 @ X798)&![X799:$i]:(((X794 @ X799)=>((X798)=(X799))))))<=>?[X800:$i]:(((X795 @ X800)&![X801:$i]:(((X795 @ X801)=>((X800)=(X801)))))))))=>(((emptyset)=(emptyset))=>(![X563:$i, X564:$i]:((((X563)=(X564))=>![X565:$i, X566:$i]:((((X565)=(X566))=>((setadjoin @ X563 @ X565)=(setadjoin @ X564 @ X566))))))=>(![X567:$i, X568:$i]:((((X567)=(X568))=>((powerset @ X567)=(powerset @ X568))))=>(![X792:$i, X793:$i]:((((X792)=(X793))=>((setunion @ X792)=(setunion @ X793))))=>(((omega)=(omega))=>(![X787:$i > $o]:((?[X788:$i]:(((X787 @ X788)&![X789:$i]:(((X787 @ X789)=>((X788)=(X789))))))=>![X790:$i, X791:$i]:(((X787 @ X790)=>((X787 @ X791)=>((X790)=(X791)))))))=>(![X779:$i > $o, X780:$i > $o]:((![X781:$i, X782:$i]:((((X781)=(X782))=>((X779 @ X781)<=>(X780 @ X782))))=>(?[X783:$i]:(((X779 @ X783)&![X784:$i]:(((X779 @ X784)=>((X783)=(X784))))))=>(?[X785:$i]:(((X780 @ X785)&![X786:$i]:(((X780 @ X786)=>((X785)=(X786))))))=>((descr @ (^[Z0:$i]:((X779 @ Z0))))=(descr @ (^[Z0:$i]:((X780 @ Z0)))))))))=>(![X569:$i, X570:$i]:((((X569)=(X570))=>![X571:$i > $o, X572:$i > $o]:((![X573:$i]:(((in @ X573 @ X569)=>![X574:$i]:(((in @ X574 @ X570)=>(((X573)=(X574))=>((X571 @ X573)<=>(X572 @ X574)))))))=>((dsetconstr @ X569 @ (^[Z0:$i]:((X571 @ Z0))))=(dsetconstr @ X570 @ 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powersetI]), c_0_195]), setadjoinOr]), c_0_196]), c_0_197]), c_0_198]), c_0_199]), notinemptyset]), emptysetimpfalse]), prop2setE]), c_0_200]), c_0_201]), wellorderingAx]), c_0_202]), omegaIndAx]), omegaSAx]), setunionAx]), emptysetAx]), setextAx])]), c_0_203])). 0.20/0.56 thf(c_0_205, negated_conjecture, ![X909:$i, X910:$i, X912:$i, X913:$i, X914:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$i, X920:$i, X922:$i, X923:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X931:$i, X932:$i > $i > $o, X933:$i, X935:$i, X938:$i, X940:$i, X941:$i, X942:$i, X943:$i, X945:$i, X946:$i > $o, X947:$i, X949:$i, X950:$i > $o, X951:$i, X952:$i, X953:$i > $o, X954:$i, X955:$i, X956:$i > $o, X957:$i, X958:$i > $o, X959:$i, X962:$i, X963:$o, X964:$i, X965:$i, X966:$o, X967:$i, X968:$i, X969:$i > $o, X970:$i, X973:$i, X974:$i, X977:$i, X979:$i, X981:$i, X982:$i > $o, X983:$i, X984:$i, X986:$i, X987:$i > $o, X988:$i, X989:$i, X990:$i, X991:$i, X992:$i, X993:$i, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i, X999:$o, X1000:$i, X1001:$i, X1002:$i, X1003:$i, X1004:$i, X1005:$i, X1007:$i, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$o, X1019:$i, X1020:$i, X1021:$i > $o, X1022:$i, X1025:$i, X1026:$i, X1027:$i, X1029:$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 > $o, X1046:$i, X1047:$i > $o, X1048:$i, X1049:$i, X1050:$i > $o, X1051:$i, X1053:$i, X1054:$i > $o, X1056:$i, X1057:$i, X1058:$i > $o, X1060:$i, X1061:$i, X1062:$i > $o, X1063:$i, X1065:$o, X1066:$i, X1067:$i > $o, X1069:$i, X1070:$i, X1071:$i > $o, X1072:$i, X1074:$i > $o, X1075:$i, X1078:$i, X1079:$i > $o, X1080:$i, X1084:$i, X1085:$i > $o, X1086:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i > $o, X1099:$i, X1101:$i, X1102:$i, X1103:$i > $o, X1104:$i > $o, X1107:$i, X1110:$i, X1111:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i > $o, X1124:$i, X1126:$i, X1127:$i, X1128:$i > $o, X1129:$i > $o, X1132:$i, X1134:$i, X1136:$i, X1137:$i, X1138:$i > $o, X1139:$i > $o, X1142:$i, X1143:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i > $o, X1190:$i, X1191:$i > $o, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$o, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1228:$i, X1229:$i, X1230:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$i, X1264:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$o, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1294:$i, X1295:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, 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X1211)|(~(in @ X1213 @ X1212)|(in @ X1213 @ (binintersect @ X1211 @ X1212))))&((~(subset @ X1216 @ X1214)|(~(subset @ X1216 @ X1215)|(subset @ X1216 @ (binintersect @ X1214 @ X1215))))&((~(in @ X1219 @ (binintersect @ X1217 @ X1218))|(in @ X1219 @ X1217))&((subset @ (binintersect @ X1220 @ X1221) @ X1220)&((~(subset @ X1222 @ X1223)|((binintersect @ X1222 @ X1223)=(X1222)))&((((binintersect @ X1224 @ X1225)!=(X1225))|(subset @ X1225 @ X1224))&((~(in @ X1228 @ (binintersect @ X1226 @ X1227))|(in @ X1228 @ X1227))&((((in @ (esk54_2 @ X1229 @ X1230) @ X1229)|((binintersect @ X1229 @ X1230)=(emptyset)))&((in @ (esk54_2 @ X1229 @ X1230) @ X1230)|((binintersect @ X1229 @ X1230)=(emptyset))))&((subset @ (binintersect @ X1232 @ X1233) @ X1233)&((~(subset @ X1235 @ X1234)|((binintersect @ X1234 @ X1235)=(X1235)))&((((binintersect @ X1236 @ X1237)!=(X1236))|(subset @ X1236 @ X1237))&(((binintersect @ X1238 @ (binunion @ X1239 @ X1240))=(binunion @ (binintersect @ X1238 @ X1239) @ (binintersect @ X1238 @ X1240)))&((~(in @ X1243 @ X1241)|((in @ X1243 @ X1242)|(in @ X1243 @ (setminus @ X1241 @ X1242))))&((~(in @ X1246 @ (setminus @ X1244 @ X1245))|(in @ X1246 @ X1244))&((~(in @ X1249 @ (setminus @ X1247 @ X1248))|~(in @ X1249 @ X1248))&((~(subset @ X1250 @ X1251)|((setminus @ X1250 @ X1251)=(emptyset)))&(((in @ X1254 @ (setminus @ X1252 @ X1253))|(~(in @ X1254 @ X1252)|(in @ X1254 @ X1253)))&(((in @ X1257 @ (setminus @ X1255 @ X1256))|((in @ X1257 @ X1256)|~(in @ X1257 @ X1255)))&(((in @ X1260 @ X1258)|~(in @ X1260 @ (setminus @ X1258 @ X1259)))&((~(in @ X1263 @ X1262)|~(in @ X1263 @ (setminus @ X1261 @ X1262)))&((subset @ (setminus @ X1264 @ X1265) @ X1264)&((((setminus @ X1266 @ X1267)!=(emptyset))|(subset @ X1266 @ X1267))&((((~(in @ X1270 @ X1268)|(X1271)|(in @ X1270 @ X1268)|~(in @ X1270 @ (symdiff @ X1268 @ X1269)))&(((in @ X1270 @ X1269)|(X1271)|(in @ X1270 @ X1268)|~(in @ X1270 @ (symdiff @ X1268 @ X1269)))&(~(X1271)|(X1271)|(in @ X1270 @ X1268)|~(in @ X1270 @ (symdiff @ X1268 @ X1269)))))&(((~(in @ X1270 @ X1268)|(X1271)|~(in @ X1270 @ X1269)|~(in @ X1270 @ (symdiff @ X1268 @ X1269)))&(((in @ X1270 @ X1269)|(X1271)|~(in @ X1270 @ X1269)|~(in @ X1270 @ (symdiff @ X1268 @ X1269)))&(~(X1271)|(X1271)|~(in @ X1270 @ X1269)|~(in @ X1270 @ (symdiff @ X1268 @ X1269)))))&((~(in @ X1270 @ X1268)|(X1271)|~(X1271)|~(in @ X1270 @ (symdiff @ X1268 @ X1269)))&(((in @ X1270 @ X1269)|(X1271)|~(X1271)|~(in @ X1270 @ (symdiff @ X1268 @ X1269)))&(~(X1271)|(X1271)|~(X1271)|~(in @ X1270 @ (symdiff @ X1268 @ X1269)))))))&((~(in @ X1274 @ X1272)|((in @ X1274 @ X1273)|(in @ X1274 @ (symdiff @ X1272 @ X1273))))&(((in @ X1277 @ X1275)|(~(in @ X1277 @ X1276)|(in @ X1277 @ (symdiff @ X1275 @ X1276))))&((~(in @ X1280 @ X1278)|(~(in @ X1280 @ X1279)|~(in @ X1280 @ (symdiff @ X1278 @ X1279))))&(((in @ X1283 @ X1281)|((in @ X1283 @ X1282)|~(in @ X1283 @ (symdiff @ X1281 @ X1282))))&((in @ X1285 @ (setadjoin @ X1284 @ (setadjoin @ X1285 @ emptyset)))&((in @ X1286 @ (setunion @ (setadjoin @ (setadjoin @ X1286 @ emptyset) @ (setadjoin @ (setadjoin @ X1286 @ (setadjoin @ X1287 @ emptyset)) @ emptyset))))&((in @ X1289 @ (setunion @ (setadjoin @ (setadjoin @ X1288 @ emptyset) @ (setadjoin @ (setadjoin @ X1288 @ (setadjoin @ X1289 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1290 @ X1291) @ (setunion @ (setadjoin @ (setadjoin @ X1290 @ emptyset) @ (setadjoin @ (setadjoin @ X1290 @ (setadjoin @ X1291 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1290 @ X1291) @ (setunion @ (setadjoin @ (setadjoin @ X1290 @ emptyset) @ (setadjoin @ (setadjoin @ X1290 @ (setadjoin @ X1291 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1290 @ emptyset) @ (setadjoin @ (setadjoin @ X1290 @ (setadjoin @ X1291 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1290 @ X1291) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1290 @ X1291) @ (setadjoin @ (esk56_2 @ X1290 @ X1291) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1294 @ X1295) @ (setunion @ (setadjoin @ (setadjoin @ X1294 @ emptyset) @ (setadjoin @ (setadjoin @ X1294 @ (setadjoin @ X1295 @ emptyset)) @ emptyset))))&((in @ (esk58_2 @ X1294 @ X1295) @ (setunion @ (setadjoin @ (setadjoin @ X1294 @ emptyset) @ (setadjoin @ (setadjoin @ X1294 @ (setadjoin @ X1295 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1294 @ emptyset) @ (setadjoin @ (setadjoin @ X1294 @ (setadjoin @ X1295 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk57_2 @ X1294 @ X1295) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1294 @ X1295) @ (setadjoin @ (esk58_2 @ X1294 @ X1295) @ emptyset)) @ emptyset)))))&((~(in @ X1299 @ X1298)|(subset @ (setadjoin @ X1299 @ emptyset) @ X1298))&((~(in @ X1301 @ X1300)|(in @ (setadjoin @ X1301 @ emptyset) @ (powerset @ X1300)))&((~(in @ X1304 @ X1302)|(in @ (setadjoin @ X1304 @ emptyset) @ (powerset @ (binunion @ X1302 @ X1303))))&((~(in @ X1307 @ (setadjoin @ X1305 @ (setadjoin @ X1306 @ emptyset)))|(((X1307)=(X1305))|((X1307)=(X1306))))&((~(in @ X1310 @ X1308)|(~(in @ X1311 @ X1309)|(subset @ (setadjoin @ X1310 @ (setadjoin @ X1311 @ emptyset)) @ (binunion @ X1308 @ X1309))))&((~(in @ X1314 @ X1312)|(~(in @ X1315 @ X1313)|(in @ (setadjoin @ X1314 @ (setadjoin @ X1315 @ emptyset)) @ (powerset @ (binunion @ X1312 @ X1313)))))&((~(in @ X1318 @ X1316)|(~(in @ X1319 @ X1317)|(subset @ (setadjoin @ (setadjoin @ X1318 @ emptyset) @ (setadjoin @ (setadjoin @ X1318 @ (setadjoin @ X1319 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1316 @ X1317)))))&((~(in @ X1322 @ X1320)|(~(in @ X1323 @ X1321)|(in @ (setadjoin @ (setadjoin @ X1322 @ emptyset) @ (setadjoin @ (setadjoin @ X1322 @ (setadjoin @ X1323 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1320 @ X1321))))))&((~(in @ X1326 @ X1324)|(~(in @ X1327 @ X1325)|(in @ (setadjoin @ (setadjoin @ X1326 @ emptyset) @ (setadjoin @ (setadjoin @ X1326 @ (setadjoin @ X1327 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1324 @ X1325))))))&((~(in @ X1330 @ X1328)|(~(in @ X1331 @ X1329)|(in @ (setadjoin @ (setadjoin @ X1330 @ emptyset) @ (setadjoin @ (setadjoin @ X1330 @ (setadjoin @ X1331 @ emptyset)) @ emptyset)) @ (cartprod @ X1328 @ X1329))))&((((in @ (esk59_3 @ X1332 @ X1333 @ X1334) @ X1332)|~(in @ X1334 @ (cartprod @ X1332 @ X1333)))&(((in @ (esk60_3 @ X1332 @ X1333 @ X1334) @ X1333)|~(in @ X1334 @ (cartprod @ X1332 @ X1333)))&(((X1334)=(setadjoin @ (setadjoin @ (esk59_3 @ X1332 @ X1333 @ X1334) @ emptyset) @ (setadjoin @ (setadjoin @ (esk59_3 @ X1332 @ X1333 @ X1334) @ (setadjoin @ (esk60_3 @ X1332 @ X1333 @ X1334) @ emptyset)) @ emptyset)))|~(in @ X1334 @ (cartprod @ X1332 @ X1333)))))&((((in @ (esk61_3 @ X1337 @ X1338 @ X1339) @ (setunion @ X1339))|~(in @ X1339 @ (cartprod @ X1337 @ X1338)))&(((in @ (esk62_3 @ X1337 @ X1338 @ X1339) @ (setunion @ X1339))|~(in @ X1339 @ (cartprod @ X1337 @ X1338)))&(((X1339)=(setadjoin @ (setadjoin @ (esk61_3 @ X1337 @ X1338 @ X1339) @ emptyset) @ (setadjoin @ (setadjoin @ (esk61_3 @ X1337 @ X1338 @ X1339) @ (setadjoin @ (esk62_3 @ X1337 @ X1338 @ X1339) @ emptyset)) @ emptyset)))|~(in @ X1339 @ (cartprod @ X1337 @ X1338)))))&((((in @ (esk63_2 @ X1342 @ X1343) @ X1342)|~(in @ X1343 @ (setunion @ X1342)))&((in @ X1343 @ (esk63_2 @ X1342 @ X1343))|~(in @ X1343 @ (setunion @ X1342))))&((subset @ (setunion @ (setadjoin @ X1345 @ emptyset)) @ X1345)&~(subset @ esk64_0 @ (setunion @ (setadjoin @ esk64_0 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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_204])])])])])])). 0.20/0.56 thf(c_0_206, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X2 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_205])). 0.20/0.56 thf(c_0_207, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ (setunion @ X3)))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_205])). 0.20/0.56 thf(c_0_208, negated_conjecture, ~((subset @ esk64_0 @ (setunion @ (setadjoin @ esk64_0 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_205])). 0.20/0.56 thf(c_0_209, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ (setunion @ X3))|~((in @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_206, c_0_207])). 0.20/0.56 thf(c_0_210, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_205])). 0.20/0.56 thf(c_0_211, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208, c_0_209]), c_0_210])]), ['proof']). 0.20/0.56 # SZS output end CNFRefutation 0.20/0.56 # Parsed axioms : 330 0.20/0.56 # Removed by relevancy pruning/SinE : 175 0.20/0.56 # Initial clauses : 282 0.20/0.56 # Removed in clause preprocessing : 23 0.20/0.56 # Initial clauses in saturation : 259 0.20/0.56 # Processed clauses : 201 0.20/0.56 # ...of these trivial : 6 0.20/0.56 # ...subsumed : 64 0.20/0.56 # ...remaining for further processing : 131 0.20/0.56 # Other redundant clauses eliminated : 15 0.20/0.56 # Clauses deleted for lack of memory : 0 0.20/0.56 # Backward-subsumed : 2 0.20/0.56 # Backward-rewritten : 2 0.20/0.56 # Generated clauses : 494 0.20/0.56 # ...of the previous two non-redundant : 369 0.20/0.56 # ...aggressively subsumed : 0 0.20/0.56 # Contextual simplify-reflections : 0 0.20/0.56 # Paramodulations : 478 0.20/0.56 # Factorizations : 0 0.20/0.56 # NegExts : 0 0.20/0.56 # Equation resolutions : 15 0.20/0.56 # Propositional unsat checks : 0 0.20/0.56 # Propositional check models : 0 0.20/0.56 # Propositional check unsatisfiable : 0 0.20/0.56 # Propositional clauses : 0 0.20/0.56 # Propositional clauses after purity: 0 0.20/0.56 # Propositional unsat core size : 0 0.20/0.56 # Propositional preprocessing time : 0.000 0.20/0.56 # Propositional encoding time : 0.000 0.20/0.56 # Propositional solver time : 0.000 0.20/0.56 # Success case prop preproc time : 0.000 0.20/0.56 # Success case prop encoding time : 0.000 0.20/0.56 # Success case prop solver time : 0.000 0.20/0.56 # Current number of processed clauses : 121 0.20/0.56 # Positive orientable unit clauses : 34 0.20/0.56 # Positive unorientable unit clauses: 0 0.20/0.56 # Negative unit clauses : 8 0.20/0.56 # Non-unit-clauses : 79 0.20/0.56 # Current number of unprocessed clauses: 424 0.20/0.56 # ...number of literals in the above : 1261 0.20/0.56 # Current number of archived formulas : 0 0.20/0.56 # Current number of archived clauses : 4 0.20/0.56 # Clause-clause subsumption calls (NU) : 372 0.20/0.56 # Rec. Clause-clause subsumption calls : 336 0.20/0.56 # Non-unit clause-clause subsumptions : 53 0.20/0.56 # Unit Clause-clause subsumption calls : 94 0.20/0.56 # Rewrite failures with RHS unbound : 0 0.20/0.56 # BW rewrite match attempts : 7 0.20/0.56 # BW rewrite match successes : 2 0.20/0.56 # Condensation attempts : 201 0.20/0.56 # Condensation successes : 3 0.20/0.56 # Termbank termtop insertions : 40077 0.20/0.56 0.20/0.56 # ------------------------------------------------- 0.20/0.56 # User time : 0.049 s 0.20/0.56 # System time : 0.008 s 0.20/0.56 # Total time : 0.057 s 0.20/0.56 # Maximum resident set size: 5344 pages 0.20/0.57 0.20/0.57 # ------------------------------------------------- 0.20/0.57 # User time : 0.056 s 0.20/0.57 # System time : 0.012 s 0.20/0.57 # Total time : 0.068 s 0.20/0.57 # Maximum resident set size: 2108 pages 0.20/0.57 EOF