0.05/0.11 % Problem : Vampire---4.8_27808 : TPTP v0.0.0. Released v0.0.0. 0.05/0.11 % Command : run_E %s %d THM 0.11/0.30 % Computer : n002.cluster.edu 0.11/0.30 % Model : x86_64 x86_64 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.30 % Memory : 8042.1875MB 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.30 % CPULimit : 1440 0.11/0.30 % WCLimit : 180 0.11/0.30 % DateTime : Mon Jul 3 13:06:07 EDT 2023 0.11/0.30 % CPUTime : 0.15/0.43 Running higher-order theorem provingRunning: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808 0.15/0.43 # Version: 3.1pre001-ho 1041.76/141.13 # Preprocessing class: HSLMSLSSLLLCHSA. 1041.76/141.13 # Scheduled 5 strats onto 8 cores with 180 seconds (1440 total) 1041.76/141.13 # Starting ho_unfolding_5 with 720s (4) cores 1041.76/141.13 # Starting pre_casc_3 with 180s (1) cores 1041.76/141.13 # Starting new_ho_10_cnf2 with 180s (1) cores 1041.76/141.13 # Starting full_lambda_10 with 180s (1) cores 1041.76/141.13 # Starting ehoh_best_nonlift_rwall with 180s (1) cores 1041.76/141.13 # ho_unfolding_5 with pid 27986 completed with status 0 1041.76/141.13 # Result found by ho_unfolding_5 1041.76/141.13 # Preprocessing class: HSLMSLSSLLLCHSA. 1041.76/141.13 # Scheduled 5 strats onto 8 cores with 180 seconds (1440 total) 1041.76/141.13 # Starting ho_unfolding_5 with 720s (4) cores 1041.76/141.13 # No SInE strategy applied 1041.76/141.13 # Search class: HGHSM-FSLM31-MHSMMSBN 1041.76/141.13 # Scheduled 6 strats onto 4 cores with 720 seconds (720 total) 1041.76/141.13 # Starting new_ho_10_cnf2 with 376s (1) cores 1041.76/141.13 # Starting ho_unfolding_5 with 73s (1) cores 1041.76/141.13 # Starting new_bool_3 with 65s (1) cores 1041.76/141.13 # Starting ho_unfolding_7 with 65s (1) cores 1041.76/141.13 # new_bool_3 with pid 27993 completed with status 7 1041.76/141.13 # Starting ehoh_best_nonlift_rwall with 65s (1) cores 1041.76/141.13 # ho_unfolding_7 with pid 27994 completed with status 7 1041.76/141.13 # Starting pre_casc_3 with 76s (1) cores 1041.76/141.13 # ho_unfolding_5 with pid 27992 completed with status 7 1041.76/141.13 # ehoh_best_nonlift_rwall with pid 28696 completed with status 7 1041.76/141.13 # new_ho_10_cnf2 with pid 27991 completed with status 0 1041.76/141.13 # Result found by new_ho_10_cnf2 1041.76/141.13 # Preprocessing class: HSLMSLSSLLLCHSA. 1041.76/141.13 # Scheduled 5 strats onto 8 cores with 180 seconds (1440 total) 1041.76/141.13 # Starting ho_unfolding_5 with 720s (4) cores 1041.76/141.13 # No SInE strategy applied 1041.76/141.13 # Search class: HGHSM-FSLM31-MHSMMSBN 1041.76/141.13 # Scheduled 6 strats onto 4 cores with 720 seconds (720 total) 1041.76/141.13 # Starting new_ho_10_cnf2 with 376s (1) cores 1041.76/141.13 # Preprocessing time : 0.003 s 1041.76/141.13 # Presaturation interreduction done 1041.76/141.13 1041.76/141.13 # Proof found! 1041.76/141.13 # SZS status Theorem 1041.76/141.13 # SZS output start CNFRefutation 1041.76/141.13 thf(decl_22, type, in: $i > $i > $o). 1041.76/141.13 thf(decl_23, type, exu: ($i > $o) > $o). 1041.76/141.13 thf(decl_24, type, setextAx: $o). 1041.76/141.13 thf(decl_25, type, emptyset: $i). 1041.76/141.13 thf(decl_26, type, emptysetAx: $o). 1041.76/141.13 thf(decl_27, type, setadjoin: $i > $i > $i). 1041.76/141.13 thf(decl_28, type, setadjoinAx: $o). 1041.76/141.13 thf(decl_29, type, powerset: $i > $i). 1041.76/141.13 thf(decl_30, type, powersetAx: $o). 1041.76/141.13 thf(decl_31, type, setunion: $i > $i). 1041.76/141.13 thf(decl_32, type, setunionAx: $o). 1041.76/141.13 thf(decl_33, type, omega: $i). 1041.76/141.13 thf(decl_34, type, omega0Ax: $o). 1041.76/141.13 thf(decl_35, type, omegaSAx: $o). 1041.76/141.13 thf(decl_36, type, omegaIndAx: $o). 1041.76/141.13 thf(decl_37, type, replAx: $o). 1041.76/141.13 thf(decl_38, type, foundationAx: $o). 1041.76/141.13 thf(decl_39, type, wellorderingAx: $o). 1041.76/141.13 thf(decl_40, type, descr: ($i > $o) > $i). 1041.76/141.13 thf(decl_41, type, descrp: $o). 1041.76/141.13 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 1041.76/141.13 thf(decl_43, type, dsetconstrI: $o). 1041.76/141.13 thf(decl_44, type, dsetconstrEL: $o). 1041.76/141.13 thf(decl_45, type, dsetconstrER: $o). 1041.76/141.13 thf(decl_46, type, exuE1: $o). 1041.76/141.13 thf(decl_47, type, prop2set: $o > $i). 1041.76/141.13 thf(decl_48, type, prop2setE: $o). 1041.76/141.13 thf(decl_49, type, emptysetE: $o). 1041.76/141.13 thf(decl_50, type, emptysetimpfalse: $o). 1041.76/141.13 thf(decl_51, type, notinemptyset: $o). 1041.76/141.13 thf(decl_52, type, exuE3e: $o). 1041.76/141.13 thf(decl_53, type, setext: $o). 1041.76/141.13 thf(decl_54, type, emptyI: $o). 1041.76/141.13 thf(decl_55, type, noeltsimpempty: $o). 1041.76/141.13 thf(decl_56, type, setbeta: $o). 1041.76/141.13 thf(decl_57, type, nonempty: $i > $o). 1041.76/141.13 thf(decl_58, type, nonemptyE1: $o). 1041.76/141.13 thf(decl_59, type, nonemptyI: $o). 1041.76/141.13 thf(decl_60, type, nonemptyI1: $o). 1041.76/141.13 thf(decl_61, type, setadjoinIL: $o). 1041.76/141.13 thf(decl_62, type, emptyinunitempty: $o). 1041.76/141.13 thf(decl_63, type, setadjoinIR: $o). 1041.76/141.13 thf(decl_64, type, setadjoinE: $o). 1041.76/141.13 thf(decl_65, type, setadjoinOr: $o). 1041.76/141.13 thf(decl_66, type, setoftrueEq: $o). 1041.76/141.13 thf(decl_67, type, powersetI: $o). 1041.76/141.13 thf(decl_68, type, emptyinPowerset: $o). 1041.76/141.13 thf(decl_69, type, emptyInPowerset: $o). 1041.76/141.13 thf(decl_70, type, powersetE: $o). 1041.76/141.13 thf(decl_71, type, setunionI: $o). 1041.76/141.13 thf(decl_72, type, setunionE: $o). 1041.76/141.13 thf(decl_73, type, subPowSU: $o). 1041.76/141.13 thf(decl_74, type, exuE2: $o). 1041.76/141.13 thf(decl_75, type, nonemptyImpWitness: $o). 1041.76/141.13 thf(decl_76, type, uniqinunit: $o). 1041.76/141.13 thf(decl_77, type, notinsingleton: $o). 1041.76/141.13 thf(decl_78, type, eqinunit: $o). 1041.76/141.13 thf(decl_79, type, singletonsswitch: $o). 1041.76/141.13 thf(decl_80, type, upairsetE: $o). 1041.76/141.13 thf(decl_81, type, upairsetIL: $o). 1041.76/141.13 thf(decl_82, type, upairsetIR: $o). 1041.76/141.13 thf(decl_83, type, emptyE1: $o). 1041.76/141.13 thf(decl_84, type, vacuousDall: $o). 1041.76/141.13 thf(decl_85, type, quantDeMorgan1: $o). 1041.76/141.13 thf(decl_86, type, quantDeMorgan2: $o). 1041.76/141.13 thf(decl_87, type, quantDeMorgan3: $o). 1041.76/141.13 thf(decl_88, type, quantDeMorgan4: $o). 1041.76/141.13 thf(decl_89, type, prop2setI: $o). 1041.76/141.13 thf(decl_90, type, set2prop: $i > $o). 1041.76/141.13 thf(decl_91, type, prop2set2propI: $o). 1041.76/141.13 thf(decl_92, type, notdexE: $o). 1041.76/141.13 thf(decl_93, type, notdallE: $o). 1041.76/141.13 thf(decl_94, type, exuI1: $o). 1041.76/141.13 thf(decl_95, type, exuI3: $o). 1041.76/141.13 thf(decl_96, type, exuI2: $o). 1041.76/141.13 thf(decl_97, type, inCongP: $o). 1041.76/141.13 thf(decl_98, type, in__Cong: $o). 1041.76/141.13 thf(decl_99, type, exuE3u: $o). 1041.76/141.13 thf(decl_100, type, exu__Cong: $o). 1041.76/141.13 thf(decl_101, type, emptyset__Cong: $o). 1041.76/141.13 thf(decl_102, type, setadjoin__Cong: $o). 1041.76/141.13 thf(decl_103, type, powerset__Cong: $o). 1041.76/141.13 thf(decl_104, type, setunion__Cong: $o). 1041.76/141.13 thf(decl_105, type, omega__Cong: $o). 1041.76/141.13 thf(decl_106, type, exuEu: $o). 1041.76/141.13 thf(decl_107, type, descr__Cong: $o). 1041.76/141.13 thf(decl_108, type, dsetconstr__Cong: $o). 1041.76/141.13 thf(decl_109, type, subset: $i > $i > $o). 1041.76/141.13 thf(decl_112, type, subsetI1: $o). 1041.76/141.13 thf(decl_113, type, eqimpsubset2: $o). 1041.76/141.13 thf(decl_114, type, eqimpsubset1: $o). 1041.76/141.13 thf(decl_115, type, subsetI2: $o). 1041.76/141.13 thf(decl_116, type, emptysetsubset: $o). 1041.76/141.13 thf(decl_117, type, subsetE: $o). 1041.76/141.13 thf(decl_118, type, subsetE2: $o). 1041.76/141.13 thf(decl_119, type, notsubsetI: $o). 1041.76/141.13 thf(decl_120, type, notequalI1: $o). 1041.76/141.13 thf(decl_121, type, notequalI2: $o). 1041.76/141.13 thf(decl_122, type, subsetRefl: $o). 1041.76/141.13 thf(decl_123, type, subsetTrans: $o). 1041.76/141.13 thf(decl_124, type, setadjoinSub: $o). 1041.76/141.13 thf(decl_125, type, setadjoinSub2: $o). 1041.76/141.13 thf(decl_126, type, subset2powerset: $o). 1041.76/141.13 thf(decl_127, type, setextsub: $o). 1041.76/141.13 thf(decl_128, type, subsetemptysetimpeq: $o). 1041.76/141.13 thf(decl_129, type, powersetI1: $o). 1041.76/141.13 thf(decl_130, type, powersetE1: $o). 1041.76/141.13 thf(decl_131, type, inPowerset: $o). 1041.76/141.13 thf(decl_132, type, powersetsubset: $o). 1041.76/141.13 thf(decl_133, type, sepInPowerset: $o). 1041.76/141.13 thf(decl_134, type, sepSubset: $o). 1041.76/141.13 thf(decl_135, type, binunion: $i > $i > $i). 1041.76/141.13 thf(decl_136, type, binunionIL: $o). 1041.76/141.13 thf(decl_137, type, upairset2IR: $o). 1041.76/141.13 thf(decl_138, type, binunionIR: $o). 1041.76/141.13 thf(decl_139, type, binunionEcases: $o). 1041.76/141.13 thf(decl_140, type, binunionE: $o). 1041.76/141.13 thf(decl_141, type, binunionLsub: $o). 1041.76/141.13 thf(decl_142, type, binunionRsub: $o). 1041.76/141.13 thf(decl_143, type, binintersect: $i > $i > $i). 1041.76/141.13 thf(decl_144, type, binintersectI: $o). 1041.76/141.13 thf(decl_145, type, binintersectSubset5: $o). 1041.76/141.13 thf(decl_146, type, binintersectEL: $o). 1041.76/141.13 thf(decl_147, type, binintersectLsub: $o). 1041.76/141.13 thf(decl_148, type, binintersectSubset2: $o). 1041.76/141.13 thf(decl_149, type, binintersectSubset3: $o). 1041.76/141.13 thf(decl_150, type, binintersectER: $o). 1041.76/141.13 thf(decl_151, type, disjointsetsI1: $o). 1041.76/141.13 thf(decl_152, type, binintersectRsub: $o). 1041.76/141.13 thf(decl_153, type, binintersectSubset4: $o). 1041.76/141.13 thf(decl_154, type, binintersectSubset1: $o). 1041.76/141.13 thf(decl_155, type, bs114d: $o). 1041.76/141.13 thf(decl_157, type, setminus: $i > $i > $i). 1041.76/141.13 thf(decl_158, type, setminusI: $o). 1041.76/141.13 thf(decl_159, type, setminusEL: $o). 1041.76/141.13 thf(decl_160, type, setminusER: $o). 1041.76/141.13 thf(decl_161, type, setminusSubset2: $o). 1041.76/141.13 thf(decl_162, type, setminusERneg: $o). 1041.76/141.13 thf(decl_163, type, setminusELneg: $o). 1041.76/141.13 thf(decl_164, type, setminusILneg: $o). 1041.76/141.13 thf(decl_165, type, setminusIRneg: $o). 1041.76/141.13 thf(decl_166, type, setminusLsub: $o). 1041.76/141.13 thf(decl_167, type, setminusSubset1: $o). 1041.76/141.13 thf(decl_168, type, symdiff: $i > $i > $i). 1041.76/141.13 thf(decl_169, type, symdiffE: $o). 1041.76/141.13 thf(decl_170, type, symdiffI1: $o). 1041.76/141.13 thf(decl_171, type, symdiffI2: $o). 1041.76/141.13 thf(decl_172, type, symdiffIneg1: $o). 1041.76/141.13 thf(decl_173, type, symdiffIneg2: $o). 1041.76/141.13 thf(decl_174, type, iskpair: $i > $o). 1041.76/141.13 thf(decl_175, type, secondinupair: $o). 1041.76/141.13 thf(decl_176, type, setukpairIL: $o). 1041.76/141.13 thf(decl_177, type, setukpairIR: $o). 1041.76/141.13 thf(decl_178, type, kpairiskpair: $o). 1041.76/141.13 thf(decl_179, type, kpair: $i > $i > $i). 1041.76/141.13 thf(decl_180, type, kpairp: $o). 1041.76/141.13 thf(decl_181, type, cartprod: $i > $i > $i). 1041.76/141.13 thf(decl_182, type, singletonsubset: $o). 1041.76/141.13 thf(decl_183, type, singletoninpowerset: $o). 1041.76/141.13 thf(decl_184, type, singletoninpowunion: $o). 1041.76/141.13 thf(decl_185, type, upairset2E: $o). 1041.76/141.13 thf(decl_186, type, upairsubunion: $o). 1041.76/141.13 thf(decl_187, type, upairinpowunion: $o). 1041.76/141.13 thf(decl_188, type, ubforcartprodlem1: $o). 1041.76/141.13 thf(decl_189, type, ubforcartprodlem2: $o). 1041.76/141.13 thf(decl_190, type, ubforcartprodlem3: $o). 1041.76/141.13 thf(decl_191, type, cartprodpairin: $o). 1041.76/141.13 thf(decl_192, type, cartprodmempair1: $o). 1041.76/141.13 thf(decl_193, type, cartprodmempair: $o). 1041.76/141.13 thf(decl_194, type, setunionE2: $o). 1041.76/141.13 thf(decl_195, type, setunionsingleton1: $o). 1041.76/141.13 thf(decl_196, type, setunionsingleton2: $o). 1041.76/141.13 thf(decl_197, type, setunionsingleton: $o). 1041.76/141.13 thf(decl_198, type, singleton: $i > $o). 1041.76/141.13 thf(decl_199, type, singletonprop: $o). 1041.76/141.13 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 1041.76/141.13 thf(decl_201, type, ex1E1: $o). 1041.76/141.13 thf(decl_202, type, ex1I: $o). 1041.76/141.13 thf(decl_203, type, epred1_0: $o). 1041.76/141.13 thf(decl_204, type, esk1_2: $i > $i > $i). 1041.76/141.13 thf(decl_205, type, esk2_2: $i > $i > $i). 1041.76/141.13 thf(decl_206, type, esk3_2: $i > $i > $i). 1041.76/141.13 thf(decl_207, type, esk4_1: $i > $i). 1041.76/141.13 thf(decl_208, type, esk5_2: ($i > $i > $o) > $i > $i). 1041.76/141.13 thf(decl_209, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 1041.76/141.13 thf(decl_210, type, esk7_2: ($i > $i > $o) > $i > $i). 1041.76/141.13 thf(decl_211, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 1041.76/141.13 thf(decl_212, type, esk9_1: $i > $i). 1041.76/141.13 thf(decl_213, type, esk10_2: ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_214, type, esk11_2: ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_215, type, esk12_1: ($i > $o) > $i). 1041.76/141.13 thf(decl_216, type, esk13_2: ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_217, type, esk14_1: ($i > $o) > $i). 1041.76/141.13 thf(decl_218, type, esk15_2: $i > $i > $i). 1041.76/141.13 thf(decl_219, type, esk16_2: $i > $i > $i). 1041.76/141.13 thf(decl_220, type, esk17_1: $i > $i). 1041.76/141.13 thf(decl_221, type, esk18_1: $i > $i). 1041.76/141.13 thf(decl_222, type, esk19_1: $i > $i). 1041.76/141.13 thf(decl_223, type, esk20_2: $i > $i > $i). 1041.76/141.13 thf(decl_224, type, esk21_3: $i > $i > $o > $i). 1041.76/141.13 thf(decl_225, type, esk22_2: ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_226, type, esk23_1: ($i > $o) > $i). 1041.76/141.13 thf(decl_227, type, esk24_1: $i > $i). 1041.76/141.13 thf(decl_228, type, esk25_2: $i > ($i > $o) > $i). 1041.76/141.13 thf(decl_229, type, esk26_2: $i > ($i > $o) > $i). 1041.76/141.13 thf(decl_230, type, esk27_2: $i > ($i > $o) > $i). 1041.76/141.13 thf(decl_231, type, esk28_2: $i > ($i > $o) > $i). 1041.76/141.13 thf(decl_232, type, esk29_2: $i > ($i > $o) > $i). 1041.76/141.13 thf(decl_233, type, esk30_2: $i > ($i > $o) > $i). 1041.76/141.13 thf(decl_234, type, esk31_2: ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_235, type, esk32_1: ($i > $o) > $i). 1041.76/141.13 thf(decl_236, type, esk33_1: ($i > $o) > $i). 1041.76/141.13 thf(decl_237, type, esk34_1: ($i > $o) > $i). 1041.76/141.13 thf(decl_238, type, esk35_1: ($i > $o) > $i). 1041.76/141.13 thf(decl_239, type, esk36_2: ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_240, type, esk37_1: ($i > $o) > $i). 1041.76/141.13 thf(decl_241, type, esk38_2: ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_242, type, esk39_2: ($i > $o) > ($i > $o) > $i). 1041.76/141.13 thf(decl_243, type, esk40_2: ($i > $o) > ($i > $o) > $i). 1041.76/141.13 thf(decl_244, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_245, type, esk42_2: ($i > $o) > ($i > $o) > $i). 1041.76/141.13 thf(decl_246, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_247, type, esk44_2: ($i > $o) > ($i > $o) > $i). 1041.76/141.13 thf(decl_248, type, esk45_2: ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_249, type, esk46_2: ($i > $o) > ($i > $o) > $i). 1041.76/141.13 thf(decl_250, type, esk47_2: ($i > $o) > ($i > $o) > $i). 1041.76/141.13 thf(decl_251, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_252, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_253, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 1041.76/141.13 thf(decl_254, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 1041.76/141.13 thf(decl_255, type, esk52_2: $i > $i > $i). 1041.76/141.13 thf(decl_256, type, esk53_2: $i > $i > $i). 1041.76/141.13 thf(decl_257, type, esk54_2: $i > $i > $i). 1041.76/141.13 thf(decl_258, type, esk55_2: $i > $i > $i). 1041.76/141.13 thf(decl_259, type, esk56_2: $i > $i > $i). 1041.76/141.13 thf(decl_260, type, esk57_2: $i > $i > $i). 1041.76/141.13 thf(decl_261, type, esk58_2: $i > $i > $i). 1041.76/141.13 thf(decl_262, type, esk59_3: $i > $i > $i > $i). 1041.76/141.13 thf(decl_263, type, esk60_3: $i > $i > $i > $i). 1041.76/141.13 thf(decl_264, type, esk61_3: $i > $i > $i > $i). 1041.76/141.13 thf(decl_265, type, esk62_3: $i > $i > $i > $i). 1041.76/141.13 thf(decl_266, type, esk63_2: $i > $i > $i). 1041.76/141.13 thf(decl_267, type, esk64_2: $i > ($i > $o) > $i). 1041.76/141.13 thf(decl_268, type, esk65_2: $i > ($i > $o) > $i). 1041.76/141.13 thf(decl_269, type, esk66_2: $i > ($i > $o) > $i). 1041.76/141.13 thf(decl_270, type, esk67_2: $i > ($i > $o) > $i). 1041.76/141.13 thf(decl_271, type, esk68_3: $i > ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_272, type, esk69_3: $i > ($i > $o) > $i > $i). 1041.76/141.13 thf(decl_273, type, esk70_0: $i). 1041.76/141.13 thf(decl_274, type, epred2_0: $i > $o). 1041.76/141.13 thf(decl_275, type, esk71_0: $i). 1041.76/141.13 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', ex1)). 1041.76/141.13 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', singleton)). 1041.76/141.13 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', replAx)). 1041.76/141.13 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', exu)). 1041.76/141.13 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', descrp)). 1041.76/141.13 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', exuE1)). 1041.76/141.13 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', exuE3e)). 1041.76/141.13 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', nonempty)). 1041.76/141.13 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', nonemptyI)). 1041.76/141.13 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', exuE2)). 1041.76/141.13 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', exuI1)). 1041.76/141.13 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', exuI3)). 1041.76/141.13 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', exuI2)). 1041.76/141.13 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', exuE3u)). 1041.76/141.13 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', exu__Cong)). 1041.76/141.13 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', exuEu)). 1041.76/141.13 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', descr__Cong)). 1041.76/141.13 thf(iskpair, axiom, ((iskpair)=(^[X4:$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/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', iskpair)). 1041.76/141.13 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', singletonprop)). 1041.76/141.13 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', ex1E1)). 1041.76/141.13 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', ex1I)). 1041.76/141.13 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', dsetconstrI)). 1041.76/141.13 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', dsetconstrEL)). 1041.76/141.13 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', dsetconstrER)). 1041.76/141.13 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setbeta)). 1041.76/141.13 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', nonemptyE1)). 1041.76/141.13 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', nonemptyI1)). 1041.76/141.13 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setoftrueEq)). 1041.76/141.13 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', nonemptyImpWitness)). 1041.76/141.13 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', emptyE1)). 1041.76/141.13 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', dsetconstr__Cong)). 1041.76/141.13 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', sepInPowerset)). 1041.76/141.13 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', sepSubset)). 1041.76/141.13 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', kpairiskpair)). 1041.76/141.13 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', kpairp)). 1041.76/141.13 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', cartprodmempair)). 1041.76/141.13 thf(ex1I2, conjecture, (((emptysetAx)=>(((powersetAx)=>((((((replAx)=>(((wellorderingAx)=>(((dsetconstrI)=>((dsetconstrEL)=>(((exuE1)=>(((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>(((noeltsimpempty)=>(((((nonemptyI1)=>(((((((setoftrueEq)=>(((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>(((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((((quantDeMorgan1)=>((quantDeMorgan2)=>((((prop2setI)=>((((notdallE)=>((exuI1)=>((exuI3)=>((((in__Cong)=>(((exu__Cong)=>(((((setunion__Cong)=>((omega__Cong)=>(((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>(((((subsetE)=>(((notsubsetI)=>((((subsetRefl)=>(((setadjoinSub)=>((((setextsub)=>(((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>(((((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>(((((binintersectSubset2)=>(((binintersectER)=>(((binintersectRsub)=>((binintersectSubset4)=>((((setminusI)=>((setminusEL)=>(((setminusSubset2)=>((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>(((((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>(((((singletonsubset)=>((singletoninpowerset)=>(((((upairinpowunion)=>((ubforcartprodlem1)=>((((((cartprodmempair)=>(((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>(((ex1E1)=>(![X4:$i, X1:$i > $o]:((((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))<=?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))<=![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))<=(ex1I)))<=(singletonprop)))))<=(setunionE2)))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3))<=(ubforcartprodlem2))))<=(upairsubunion))<=(upairset2E))<=(singletoninpowunion))))<=(kpairp))<=(kpairiskpair))<=(setukpairIR))))))))<=(symdiffE))<=(setminusSubset1))<=(setminusLsub))))<=(setminusELneg))))<=(setminusER))))<=(bs114d))<=(binintersectSubset1))))<=(disjointsetsI1)))<=(binintersectSubset3)))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))))))))<=(upairset2IR))<=(binunionIL))<=(sepSubset)))))))<=(subsetemptysetimpeq)))<=(subset2powerset))<=(setadjoinSub2)))<=(subsetTrans)))<=(notequalI2))<=(notequalI1)))<=(subsetE2)))<=(emptysetsubset))<=(subsetI2))<=(eqimpsubset1))))))<=(exuEu))))<=(powerset__Cong))<=(setadjoin__Cong))<=(emptyset__Cong)))<=(exuE3u)))<=(inCongP))<=(exuI2)))))<=(notdexE))<=(prop2set2propI)))<=(quantDeMorgan4))<=(quantDeMorgan3))))<=(vacuousDall))<=(emptyE1)))))))<=(notinsingleton))))))<=(setunionE))<=(setunionI)))))<=(powersetI)))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty))<=(setadjoinIL)))<=(nonemptyI))<=(nonemptyE1))<=(setbeta)))<=(emptyI)))))))<=(prop2setE)))<=(dsetconstrER))))<=(descrp)))<=(foundationAx)))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax))<=(setunionAx)))<=(setadjoinAx)))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', ex1I2)). 1041.76/141.13 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setextAx)). 1041.76/141.13 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', emptysetAx)). 1041.76/141.13 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setadjoinAx)). 1041.76/141.13 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', powersetAx)). 1041.76/141.13 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setunionAx)). 1041.76/141.13 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', omega0Ax)). 1041.76/141.13 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', omegaSAx)). 1041.76/141.13 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', omegaIndAx)). 1041.76/141.13 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', foundationAx)). 1041.76/141.13 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', wellorderingAx)). 1041.76/141.13 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', prop2setE)). 1041.76/141.13 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', emptysetE)). 1041.76/141.13 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', emptysetimpfalse)). 1041.76/141.13 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', notinemptyset)). 1041.76/141.13 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setext)). 1041.76/141.13 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', emptyI)). 1041.76/141.13 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', noeltsimpempty)). 1041.76/141.13 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setadjoinIL)). 1041.76/141.13 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', emptyinunitempty)). 1041.76/141.13 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setadjoinIR)). 1041.76/141.13 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setadjoinE)). 1041.76/141.13 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setadjoinOr)). 1041.76/141.13 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', powersetI)). 1041.76/141.13 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', emptyinPowerset)). 1041.76/141.13 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', emptyInPowerset)). 1041.76/141.13 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', powersetE)). 1041.76/141.13 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setunionI)). 1041.76/141.13 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setunionE)). 1041.76/141.13 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', subPowSU)). 1041.76/141.13 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', uniqinunit)). 1041.76/141.13 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', notinsingleton)). 1041.76/141.13 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', eqinunit)). 1041.76/141.13 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', singletonsswitch)). 1041.76/141.13 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', upairsetE)). 1041.76/141.13 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', upairsetIL)). 1041.76/141.13 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', upairsetIR)). 1041.76/141.13 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', vacuousDall)). 1041.76/141.13 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', quantDeMorgan1)). 1041.76/141.13 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', quantDeMorgan2)). 1041.76/141.13 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', quantDeMorgan3)). 1041.76/141.13 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', quantDeMorgan4)). 1041.76/141.13 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', prop2setI)). 1041.76/141.13 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', prop2set2propI)). 1041.76/141.13 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', notdexE)). 1041.76/141.13 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', notdallE)). 1041.76/141.13 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', inCongP)). 1041.76/141.13 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', in__Cong)). 1041.76/141.13 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', emptyset__Cong)). 1041.76/141.13 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setadjoin__Cong)). 1041.76/141.13 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', powerset__Cong)). 1041.76/141.13 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setunion__Cong)). 1041.76/141.13 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', omega__Cong)). 1041.76/141.13 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', subsetI1)). 1041.76/141.13 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', eqimpsubset2)). 1041.76/141.13 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', eqimpsubset1)). 1041.76/141.13 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', subsetI2)). 1041.76/141.13 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', emptysetsubset)). 1041.76/141.13 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', subsetE)). 1041.76/141.13 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', subsetE2)). 1041.76/141.13 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', notsubsetI)). 1041.76/141.13 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', notequalI1)). 1041.76/141.13 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', notequalI2)). 1041.76/141.13 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', subsetRefl)). 1041.76/141.13 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', subsetTrans)). 1041.76/141.13 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setadjoinSub)). 1041.76/141.13 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setadjoinSub2)). 1041.76/141.13 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', subset2powerset)). 1041.76/141.13 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setextsub)). 1041.76/141.13 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', subsetemptysetimpeq)). 1041.76/141.13 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', powersetI1)). 1041.76/141.13 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', powersetE1)). 1041.76/141.13 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', inPowerset)). 1041.76/141.13 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', powersetsubset)). 1041.76/141.13 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binunionIL)). 1041.76/141.13 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', upairset2IR)). 1041.76/141.13 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binunionIR)). 1041.76/141.13 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binunionEcases)). 1041.76/141.13 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binunionE)). 1041.76/141.13 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binunionLsub)). 1041.76/141.13 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binunionRsub)). 1041.76/141.13 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binintersectI)). 1041.76/141.13 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binintersectSubset5)). 1041.76/141.13 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binintersectEL)). 1041.76/141.13 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binintersectLsub)). 1041.76/141.13 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binintersectSubset2)). 1041.76/141.13 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binintersectSubset3)). 1041.76/141.13 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binintersectER)). 1041.76/141.13 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', disjointsetsI1)). 1041.76/141.13 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binintersectRsub)). 1041.76/141.13 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binintersectSubset4)). 1041.76/141.13 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', binintersectSubset1)). 1041.76/141.13 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', bs114d)). 1041.76/141.13 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setminusI)). 1041.76/141.13 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setminusEL)). 1041.76/141.13 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setminusER)). 1041.76/141.13 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setminusSubset2)). 1041.76/141.13 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setminusERneg)). 1041.76/141.13 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setminusELneg)). 1041.76/141.13 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setminusILneg)). 1041.76/141.13 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setminusIRneg)). 1041.76/141.13 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setminusLsub)). 1041.76/141.13 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setminusSubset1)). 1041.76/141.13 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', symdiffE)). 1041.76/141.13 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', symdiffI1)). 1041.76/141.13 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', symdiffI2)). 1041.76/141.13 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', symdiffIneg1)). 1041.76/141.13 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', symdiffIneg2)). 1041.76/141.13 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', secondinupair)). 1041.76/141.13 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setukpairIL)). 1041.76/141.13 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setukpairIR)). 1041.76/141.13 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', singletonsubset)). 1041.76/141.13 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', singletoninpowerset)). 1041.76/141.13 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', singletoninpowunion)). 1041.76/141.13 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', upairset2E)). 1041.76/141.13 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', upairsubunion)). 1041.76/141.13 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', upairinpowunion)). 1041.76/141.13 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', ubforcartprodlem1)). 1041.76/141.13 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', ubforcartprodlem2)). 1041.76/141.13 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', ubforcartprodlem3)). 1041.76/141.13 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', cartprodpairin)). 1041.76/141.13 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', cartprodmempair1)). 1041.76/141.13 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setunionE2)). 1041.76/141.13 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setunionsingleton1)). 1041.76/141.13 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setunionsingleton2)). 1041.76/141.13 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.vrKGNuHfIy/Vampire---4.8_27808', setunionsingleton)). 1041.76/141.13 thf(c_0_162, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X486:$i]:(((in @ X486 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X486 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])). 1041.76/141.13 thf(c_0_163, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])). 1041.76/141.13 thf(c_0_164, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 1041.76/141.13 thf(c_0_165, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 1041.76/141.13 thf(c_0_166, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 1041.76/141.13 thf(c_0_167, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 1041.76/141.13 thf(c_0_168, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 1041.76/141.13 thf(c_0_169, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 1041.76/141.13 thf(c_0_170, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 1041.76/141.13 thf(c_0_171, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 1041.76/141.13 thf(c_0_172, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 1041.76/141.13 thf(c_0_173, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 1041.76/141.13 thf(c_0_174, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 1041.76/141.13 thf(c_0_175, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 1041.76/141.13 thf(c_0_176, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 1041.76/141.13 thf(c_0_177, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 1041.76/141.13 thf(c_0_178, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 1041.76/141.13 thf(c_0_179, plain, ((iskpair)=(^[Z0/* 5 */:$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])). 1041.76/141.13 thf(c_0_180, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 1041.76/141.13 thf(c_0_181, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 1041.76/141.13 thf(c_0_182, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X486:$i]:(((in @ X486 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X486 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_162, c_0_163])). 1041.76/141.13 thf(c_0_183, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 1041.76/141.13 thf(c_0_184, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X451:$i]:((((X6 @ X2 @ X451))&![X452:$i]:((((X6 @ X2 @ X452))=>((X451)=(X452)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_164, c_0_165])). 1041.76/141.13 thf(c_0_185, plain, ((descrp)=(![X1:$i > $o]:(((?[X453:$i]:((((X1 @ X453))&![X454:$i]:((((X1 @ X454))=>((X453)=(X454)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_166, c_0_165])). 1041.76/141.13 thf(c_0_186, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 1041.76/141.13 thf(c_0_187, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 1041.76/141.13 thf(c_0_188, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 1041.76/141.13 thf(c_0_189, plain, ((exuE1)=(![X1:$i > $o]:(((?[X455:$i]:((((X1 @ X455))&![X456:$i]:((((X1 @ X456))=>((X455)=(X456)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_167, c_0_165])). 1041.76/141.13 thf(c_0_190, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X457:$i]:((((X1 @ X457))&![X458:$i]:((((X1 @ X458))=>((X457)=(X458)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_168, c_0_165])). 1041.76/141.13 thf(c_0_191, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 1041.76/141.13 thf(c_0_192, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_169])). 1041.76/141.13 thf(c_0_193, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_170, c_0_169])). 1041.76/141.13 thf(c_0_194, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_169])). 1041.76/141.13 thf(c_0_195, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 1041.76/141.13 thf(c_0_196, plain, ((exuE2)=(![X1:$i > $o]:(((?[X459:$i]:((((X1 @ X459))&![X460:$i]:((((X1 @ X460))=>((X459)=(X460)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_171, c_0_165])). 1041.76/141.13 thf(c_0_197, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_169])). 1041.76/141.13 thf(c_0_198, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 1041.76/141.13 thf(c_0_199, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X461:$i]:((((X1 @ X461))&![X462:$i]:((((X1 @ X462))=>((X461)=(X462))))))))))), inference(apply_def,[status(thm)],[c_0_172, c_0_165])). 1041.76/141.13 thf(c_0_200, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X463:$i]:((((X1 @ X463))&![X464:$i]:((((X1 @ X464))=>((X463)=(X464)))))))))))), inference(apply_def,[status(thm)],[c_0_173, c_0_165])). 1041.76/141.13 thf(c_0_201, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X465:$i]:((((X1 @ X465))&![X466:$i]:((((X1 @ X466))=>((X465)=(X466))))))))))), inference(apply_def,[status(thm)],[c_0_174, c_0_165])). 1041.76/141.13 thf(c_0_202, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X467:$i]:((((X1 @ X467))&![X468:$i]:((((X1 @ X468))=>((X467)=(X468)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_175, c_0_165])). 1041.76/141.13 thf(c_0_203, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X469:$i]:((((X1 @ X469))&![X470:$i]:((((X1 @ X470))=>((X469)=(X470)))))))<=>(?[X471:$i]:((((X17 @ X471))&![X472:$i]:((((X17 @ X472))=>((X471)=(X472)))))))))))), inference(apply_def,[status(thm)],[c_0_176, c_0_165])). 1041.76/141.13 thf(c_0_204, plain, ((exuEu)=(![X1:$i > $o]:(((?[X473:$i]:((((X1 @ X473))&![X474:$i]:((((X1 @ X474))=>((X473)=(X474)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_177, c_0_165])). 1041.76/141.13 thf(c_0_205, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X475:$i]:((((X1 @ X475))&![X476:$i]:((((X1 @ X476))=>((X475)=(X476)))))))=>((?[X477:$i]:((((X17 @ X477))&![X478:$i]:((((X17 @ X478))=>((X477)=(X478)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_178, c_0_165])). 1041.76/141.13 thf(c_0_206, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 1041.76/141.13 thf(c_0_207, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 1041.76/141.13 thf(c_0_208, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 1041.76/141.13 thf(c_0_209, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X479:$i]:(((in @ X479 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X480:$i]:(((in @ X480 @ (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 @ X479 @ emptyset) @ (setadjoin @ (setadjoin @ X479 @ (setadjoin @ X480 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_179])). 1041.76/141.13 thf(c_0_210, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X481:$i]:(((in @ X481 @ (setunion @ (kpair @ X2 @ X3)))&?[X482:$i]:(((in @ X482 @ (setunion @ (kpair @ X2 @ X3)))&((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X481 @ emptyset) @ (setadjoin @ (setadjoin @ X481 @ (setadjoin @ X482 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_179])). 1041.76/141.13 thf(c_0_211, axiom, ((cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(?[X483:$i]:(((in @ X483 @ (setunion @ X18))&?[X484:$i]:(((in @ X484 @ (setunion @ X18))&((X18)=(setadjoin @ (setadjoin @ X483 @ emptyset) @ (setadjoin @ (setadjoin @ X483 @ (setadjoin @ X484 @ emptyset)) @ emptyset)))))))))))), inference(apply_def,[status(thm)],[cartprodmempair, c_0_179])). 1041.76/141.13 thf(c_0_212, plain, ((singletonprop)=(![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(?[X485:$i]:(((in @ X485 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X485 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_180, c_0_163])). 1041.76/141.13 thf(c_0_213, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X487:$i]:(((in @ X487 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X487 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_181, c_0_182])). 1041.76/141.13 thf(c_0_214, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X488:$i]:(((in @ X488 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X488 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_183, c_0_182])). 1041.76/141.13 thf(c_0_215, plain, ((epred1_0)<=>![X501:$i]:(?[X502:$i]:((((![X503:$i]:(((in @ X503 @ X502)=>![X504:$i]:(((in @ X504 @ X503)=>(in @ X504 @ X501)))))&![X505:$i, X506:$i]:((((in @ X505 @ X501)&(in @ X506 @ X501))=>(![X507:$i]:(((in @ X507 @ X502)=>((in @ X505 @ X507)<=>(in @ X506 @ X507))))=>((X505)=(X506))))))&![X508:$i, X509:$i]:((((in @ X508 @ X502)&(in @ X509 @ X502))=>(![X510:$i]:(((in @ X510 @ X508)=>(in @ X510 @ X509)))|![X511:$i]:(((in @ X511 @ X509)=>(in @ X511 @ X508)))))))&![X512:$i]:(((![X513:$i]:(((in @ X513 @ X512)=>(in @ X513 @ X501)))&?[X514:$i]:((in @ X514 @ X512)))=>?[X515:$i, X516:$i]:(((((in @ X515 @ X502)&(in @ X516 @ X512))&~(?[X517:$i]:(((in @ X517 @ X515)&(in @ X517 @ X512)))))&![X518:$i]:(((in @ X518 @ X502)=>(![X519:$i]:(((in @ X519 @ X518)=>(in @ X519 @ X515)))|(in @ X516 @ X518)))))))))))), introduced(definition)). 1041.76/141.13 thf(c_0_216, negated_conjecture, ~((![X948:$i, X949:$i]:((![X950:$i]:(((in @ X950 @ X948)<=>(in @ X950 @ X949)))=>((X948)=(X949))))=>(![X489:$i]:(~(in @ X489 @ emptyset))=>(![X945:$i, X946:$i, X947:$i]:(((in @ X947 @ (setadjoin @ X945 @ X946))<=>(((X947)=(X945))|(in @ X947 @ X946))))=>(![X490:$i, X491:$i]:(((in @ X491 @ (powerset @ X490))<=>![X492:$i]:(((in @ X492 @ X491)=>(in @ X492 @ X490)))))=>(![X942:$i, X943:$i]:(((in @ X943 @ (setunion @ X942))<=>?[X944:$i]:(((in @ X943 @ X944)&(in @ X944 @ X942)))))=>((in @ emptyset @ omega)=>(![X941:$i]:(((in @ X941 @ omega)=>(in @ (setadjoin @ X941 @ X941) @ omega)))=>(![X938:$i]:((((in @ emptyset @ X938)&![X939:$i]:((((in @ X939 @ omega)&(in @ X939 @ X938))=>(in @ (setadjoin @ X939 @ X939) @ X938))))=>![X940:$i]:(((in @ X940 @ omega)=>(in @ X940 @ X938)))))=>(![X493:$i > $i > $o, X494:$i]:((![X495:$i]:(((in @ X495 @ X494)=>?[X496:$i]:(((X493 @ X495 @ X496)&![X497:$i]:(((X493 @ X495 @ X497)=>((X496)=(X497))))))))=>?[X498:$i]:(![X499:$i]:(((in @ X499 @ X498)<=>?[X500:$i]:(((in @ X500 @ X494)&(X493 @ X500 @ X499))))))))=>(![X934:$i]:((?[X935:$i]:((in @ X935 @ X934))=>?[X936:$i]:(((in @ X936 @ X934)&~(?[X937:$i]:(((in @ X937 @ X936)&(in @ X937 @ X934))))))))=>((epred1_0)=>(![X931:$i > $o]:((?[X932:$i]:(((X931 @ X932)&![X933:$i]:(((X931 @ X933)=>((X932)=(X933))))))=>(X931 @ (descr @ (^[Z0/* 3 */:$i]:((X931 @ Z0)))))))=>(![X520:$i, X521:$i > $o, X522:$i]:(((in @ X522 @ X520)=>((X521 @ X522)=>(in @ X522 @ (dsetconstr @ X520 @ (^[Z0/* 3 */:$i]:((X521 @ Z0))))))))=>(![X523:$i, X524:$i > $o, X525:$i]:(((in @ X525 @ (dsetconstr @ X523 @ (^[Z0/* 3 */:$i]:((X524 @ Z0)))))=>(in @ X525 @ X523)))=>(![X928:$i, X929:$i > $o, X930:$i]:(((in @ X930 @ (dsetconstr @ X928 @ (^[Z0/* 3 */:$i]:((X929 @ Z0)))))=>(X929 @ X930)))=>(![X526:$i > $o]:((?[X527:$i]:(((X526 @ X527)&![X528:$i]:(((X526 @ X528)=>((X527)=(X528))))))=>?[X529:$i]:(((X526 @ X529)&![X530:$i]:(((X526 @ X530)=>((X529)=(X530))))))))=>(![X926:$o, X927:$i]:(((in @ X927 @ (prop2set @ ((X926))))=>(X926)))=>(![X531:$i]:(((in @ X531 @ emptyset)=>![X532:$o]:((X532))))=>(![X533:$i]:(~(in @ X533 @ emptyset))=>(![X534:$i]:(~(in @ X534 @ emptyset))=>(![X535:$i > $o]:((?[X536:$i]:(((X535 @ X536)&![X537:$i]:(((X535 @ X537)=>((X536)=(X537))))))=>?[X538:$i]:((X535 @ X538))))=>(![X539:$i, X540:$i]:((![X541:$i]:(((in @ X541 @ X539)=>(in @ X541 @ X540)))=>(![X542:$i]:(((in @ X542 @ X540)=>(in @ X542 @ X539)))=>((X539)=(X540)))))=>(![X924:$i]:((![X925:$i]:(~(in @ X925 @ X924))=>((X924)=(emptyset))))=>(![X543:$i]:((![X544:$i]:(~(in @ X544 @ X543))=>((X543)=(emptyset))))=>(![X921:$i, X922:$i > $o, X923:$i]:(((in @ X923 @ X921)=>((in @ X923 @ (dsetconstr @ X921 @ (^[Z0/* 3 */:$i]:((X922 @ Z0)))))<=>(X922 @ X923))))=>(![X919:$i]:((((X919)!=(emptyset))=>?[X920:$i]:((in @ X920 @ X919))))=>(![X916:$i, X917:$i > $o, X918:$i]:(((in @ X918 @ X916)=>((X917 @ X918)=>((dsetconstr @ X916 @ (^[Z0/* 3 */:$i]:((X917 @ Z0))))!=(emptyset)))))=>(![X545:$i]:((?[X546:$i]:((in @ X546 @ X545))=>((X545)!=(emptyset))))=>(![X914:$i, X915:$i]:((in @ X914 @ (setadjoin @ X914 @ X915)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X911:$i, X912:$i, X913:$i]:(((in @ X913 @ X912)=>(in @ X913 @ (setadjoin @ X911 @ X912))))=>(![X907:$i, X908:$i, X909:$i]:(((in @ X909 @ (setadjoin @ X907 @ X908))=>![X910:$o]:(((((X909)=(X907))=>(X910))=>(((in @ X909 @ X908)=>(X910))=>(X910))))))=>(![X904:$i, X905:$i, X906:$i]:(((in @ X906 @ (setadjoin @ X904 @ X905))=>(((X906)=(X904))|(in @ X906 @ X905))))=>(![X547:$i]:(((dsetconstr @ X547 @ (^[Z0/* 3 */:$i]:(($true))))=(X547)))=>(![X901:$i, X902:$i]:((![X903:$i]:(((in @ X903 @ X902)=>(in @ X903 @ X901)))=>(in @ X902 @ (powerset @ X901))))=>(![X548:$i]:((in @ emptyset @ (powerset @ X548)))=>(![X549:$i]:((in @ emptyset @ (powerset @ X549)))=>(![X550:$i, X551:$i, X552:$i]:(((in @ X551 @ (powerset @ X550))=>((in @ X552 @ X551)=>(in @ X552 @ X550))))=>(![X898:$i, X899:$i, X900:$i]:(((in @ X899 @ X900)=>((in @ X900 @ X898)=>(in @ X899 @ (setunion @ X898)))))=>(![X894:$i, X895:$i]:(((in @ X895 @ (setunion @ X894))=>![X896:$o]:((![X897:$i]:(((in @ X895 @ X897)=>((in @ X897 @ X894)=>(X896))))=>(X896)))))=>(![X553:$i, X554:$i]:(((in @ X554 @ X553)=>(in @ X554 @ (powerset @ (setunion @ X553)))))=>(![X555:$i > $o]:((?[X556:$i]:(((X555 @ X556)&![X557:$i]:(((X555 @ X557)=>((X556)=(X557))))))=>?[X558:$i]:(![X559:$i]:(((X555 @ X559)<=>((X559)=(X558)))))))=>(![X560:$i]:((((X560)!=(emptyset))=>?[X561:$i]:((in @ X561 @ X560))))=>(![X562:$i, X563:$i]:(((in @ X562 @ (setadjoin @ X563 @ emptyset))=>((X562)=(X563))))=>(![X892:$i, X893:$i]:((((X892)!=(X893))=>~(in @ X893 @ (setadjoin @ X892 @ emptyset))))=>(![X564:$i, X565:$i]:((((X564)=(X565))=>(in @ X564 @ (setadjoin @ X565 @ emptyset))))=>(![X566:$i, X567:$i]:(((in @ X566 @ (setadjoin @ X567 @ emptyset))=>(in @ X567 @ (setadjoin @ X566 @ emptyset))))=>(![X568:$i, X569:$i, X570:$i]:(((in @ X570 @ (setadjoin @ X568 @ (setadjoin @ X569 @ emptyset)))=>(((X570)=(X568))|((X570)=(X569)))))=>(![X571:$i, X572:$i]:((in @ X571 @ (setadjoin @ X571 @ (setadjoin @ X572 @ emptyset))))=>(![X573:$i, X574:$i]:((in @ X574 @ (setadjoin @ 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@ X782 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X783 @ emptyset) @ (setadjoin @ (setadjoin @ X783 @ (setadjoin @ X784 @ emptyset)) @ emptyset))))))))=>(![X777:$i, X778:$i]:(?[X779:$i]:(((in @ X779 @ (setunion @ (kpair @ X777 @ X778)))&?[X780:$i]:(((in @ X780 @ (setunion @ (kpair @ X777 @ X778)))&((kpair @ X777 @ X778)=(setadjoin @ (setadjoin @ X779 @ emptyset) @ (setadjoin @ (setadjoin @ X779 @ (setadjoin @ X780 @ emptyset)) @ emptyset))))))))=>(![X711:$i, X712:$i]:(((in @ X712 @ X711)=>(subset @ (setadjoin @ X712 @ emptyset) @ X711)))=>(![X713:$i, X714:$i]:(((in @ X714 @ X713)=>(in @ (setadjoin @ X714 @ emptyset) @ (powerset @ X713))))=>(![X774:$i, X775:$i, X776:$i]:(((in @ X776 @ X774)=>(in @ (setadjoin @ X776 @ emptyset) @ (powerset @ (binunion @ X774 @ X775)))))=>(![X771:$i, X772:$i, X773:$i]:(((in @ X773 @ (setadjoin @ X771 @ (setadjoin @ X772 @ emptyset)))=>(((X773)=(X771))|((X773)=(X772)))))=>(![X767:$i, X768:$i, X769:$i]:(((in @ X769 @ X767)=>![X770:$i]:(((in @ X770 @ X768)=>(subset @ (setadjoin @ X769 @ (setadjoin @ X770 @ emptyset)) @ (binunion @ X767 @ X768))))))=>(![X715:$i, X716:$i, X717:$i]:(((in @ X717 @ X715)=>![X718:$i]:(((in @ X718 @ X716)=>(in @ (setadjoin @ X717 @ (setadjoin @ X718 @ emptyset)) @ (powerset @ (binunion @ X715 @ X716)))))))=>(![X719:$i, X720:$i, X721:$i]:(((in @ X721 @ X719)=>![X722:$i]:(((in @ X722 @ X720)=>(subset @ (setadjoin @ (setadjoin @ X721 @ emptyset) @ (setadjoin @ (setadjoin @ X721 @ (setadjoin @ X722 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X719 @ X720)))))))=>(![X763:$i, X764:$i, X765:$i]:(((in @ X765 @ X763)=>![X766:$i]:(((in @ X766 @ X764)=>(in @ (setadjoin @ (setadjoin @ X765 @ emptyset) @ (setadjoin @ (setadjoin @ X765 @ (setadjoin @ X766 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X763 @ X764))))))))=>(![X759:$i, X760:$i, X761:$i]:(((in @ X761 @ X759)=>![X762:$i]:(((in @ X762 @ X760)=>(in @ (kpair @ X761 @ X762) @ (powerset @ (powerset @ (binunion @ X759 @ X760))))))))=>(![X755:$i, X756:$i, X757:$i]:(((in @ X757 @ X755)=>![X758:$i]:(((in @ X758 @ X756)=>(in @ (kpair @ X757 @ X758) @ (cartprod @ X755 @ X756))))))=>(![X750:$i, X751:$i, X752:$i]:(((in @ X752 @ (cartprod @ X750 @ X751))=>?[X753:$i]:(((in @ X753 @ X750)&?[X754:$i]:(((in @ X754 @ X751)&((X752)=(kpair @ X753 @ X754))))))))=>(![X723:$i, X724:$i, X725:$i]:(((in @ X725 @ (cartprod @ X723 @ X724))=>?[X726:$i]:(((in @ X726 @ (setunion @ X725))&?[X727:$i]:(((in @ X727 @ (setunion @ X725))&((X725)=(setadjoin @ (setadjoin @ X726 @ emptyset) @ (setadjoin @ (setadjoin @ X726 @ (setadjoin @ X727 @ emptyset)) @ emptyset)))))))))=>(![X747:$i, X748:$i]:(((in @ X748 @ (setunion @ X747))=>?[X749:$i]:(((in @ X749 @ X747)&(in @ X748 @ X749)))))=>(![X728:$i]:((subset @ (setunion @ (setadjoin @ X728 @ emptyset)) @ X728))=>(![X729:$i]:((subset @ X729 @ (setunion @ (setadjoin @ X729 @ emptyset))))=>(![X730:$i]:(((setunion @ (setadjoin @ X730 @ emptyset))=(X730)))=>(![X741:$i, X742:$i > $o]:((![X743:$i]:(((in @ X743 @ X741)=>![X744:$i]:(((in @ X744 @ X741)=>((X742 @ X743)=>((X742 @ X744)=>((X743)=(X744))))))))=>(?[X745:$i]:(((in @ X745 @ X741)&(X742 @ X745)))=>?[X746:$i]:(((in @ X746 @ (dsetconstr @ X741 @ (^[Z0/* 3 */:$i]:((X742 @ Z0)))))&((dsetconstr @ X741 @ (^[Z0/* 3 */:$i]:((X742 @ Z0))))=(setadjoin @ X746 @ emptyset)))))))=>(![X731:$i, X732:$i > $o]:((?[X733:$i]:(((in @ X733 @ (dsetconstr @ X731 @ (^[Z0/* 3 */:$i]:((X732 @ Z0)))))&((dsetconstr @ X731 @ (^[Z0/* 3 */:$i]:((X732 @ Z0))))=(setadjoin @ X733 @ emptyset))))=>?[X734:$i]:(((in @ X734 @ X731)&(X732 @ X734)))))=>(![X736:$i, X737:$i > $o, X738:$i]:(((in @ X738 @ X736)=>((X737 @ X738)=>(![X739:$i]:(((in @ X739 @ X736)=>((X737 @ X739)=>((X739)=(X738)))))=>?[X740:$i]:(((in @ X740 @ (dsetconstr @ X736 @ (^[Z0/* 3 */:$i]:((X737 @ Z0)))))&((dsetconstr @ X736 @ (^[Z0/* 3 */:$i]:((X737 @ Z0))))=(setadjoin @ X740 @ emptyset))))))))=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>?[X735:$i]:(((in @ X735 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X735 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[ex1I2])]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_184]), foundationAx]), wellorderingAx]), c_0_185]), c_0_186]), c_0_187]), c_0_188]), c_0_189]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_190]), setext]), emptyI]), noeltsimpempty]), c_0_191]), c_0_192]), c_0_193]), c_0_194]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_195]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_196]), c_0_197]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_198]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_199]), c_0_200]), c_0_201]), inCongP]), in__Cong]), c_0_202]), c_0_203]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_204]), c_0_205]), c_0_206]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_207]), c_0_208]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), c_0_209]), c_0_210]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), c_0_211]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_212]), c_0_182]), c_0_213]), c_0_214])]), c_0_215])). 1041.76/141.13 thf(c_0_217, negated_conjecture, ![X955:$i, X956:$i, X958:$i, X959:$i, X960:$i, X961:$i, X962:$i, X963:$i, X964:$i, X965:$i, X966:$i, X968:$i, X969:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X977:$i, X978:$i > $i > $o, X979:$i, X981:$i, X984:$i, X986:$i, X987:$i, X988:$i, X989:$i, X991:$i, X992:$i > $o, X993:$i, X995:$i, X996:$i > $o, X997:$i, X998:$i, X999:$i > $o, X1000:$i, X1001:$i, X1002:$i > $o, X1003:$i, X1004:$i > $o, X1005:$i, X1008:$i, X1009:$o, X1010:$i, X1011:$i, X1012:$o, X1013:$i, X1014:$i, X1015:$i > $o, X1016:$i, X1019:$i, X1020:$i, X1023:$i, X1025:$i, X1027:$i, X1028:$i > $o, X1029:$i, X1030:$i, X1032:$i, X1033:$i > $o, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$o, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1053:$i, X1054:$i, X1055:$i, X1056:$i, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$o, X1065:$i, X1066:$i, X1067:$i > $o, X1068:$i, X1071:$i, X1072:$i, X1073:$i, X1075:$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 > $o, X1092:$i, X1093:$i > $o, X1094:$i, X1095:$i, X1096:$i > $o, X1097:$i, X1099:$i, X1100:$i > $o, X1102:$i, X1103:$i, X1104:$i > $o, X1106:$i, X1107:$i, X1108:$i > $o, X1109:$i, X1111:$o, X1112:$o, X1113:$i, X1114:$i > $o, X1116:$i, X1117:$i, X1118:$i > $o, X1119:$i, X1121:$i > $o, X1122:$i, X1125:$i, X1126:$i > $o, X1127:$i, X1131:$i, X1132:$i > $o, X1133:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i > $o, X1146:$i, X1148:$i, X1149:$i, X1150:$i > $o, X1151:$i > $o, X1154:$i, X1157:$i, X1158:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i > $o, X1171:$i, X1173:$i, X1174:$i, X1175:$i > $o, X1176:$i > $o, X1179:$i, X1181:$i, X1183:$i, X1184:$i, X1185:$i > $o, X1186:$i > $o, X1189:$i, X1190:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, 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:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i > $o, X1237:$i, X1238:$i > $o, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$o, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$i, X1264:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, 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:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$o, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1341:$i, X1342:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, 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X1316)))&(~(X1318)|(X1318)|~(in @ X1317 @ X1316)|~(in @ X1317 @ (symdiff @ X1315 @ X1316)))))&((~(in @ X1317 @ X1315)|(X1318)|~(X1318)|~(in @ X1317 @ (symdiff @ X1315 @ X1316)))&(((in @ X1317 @ X1316)|(X1318)|~(X1318)|~(in @ X1317 @ (symdiff @ X1315 @ X1316)))&(~(X1318)|(X1318)|~(X1318)|~(in @ X1317 @ (symdiff @ X1315 @ X1316)))))))&((~(in @ X1321 @ X1319)|((in @ X1321 @ X1320)|(in @ X1321 @ (symdiff @ X1319 @ X1320))))&(((in @ X1324 @ X1322)|(~(in @ X1324 @ X1323)|(in @ X1324 @ (symdiff @ X1322 @ X1323))))&((~(in @ X1327 @ X1325)|(~(in @ X1327 @ X1326)|~(in @ X1327 @ (symdiff @ X1325 @ X1326))))&(((in @ X1330 @ X1328)|((in @ X1330 @ X1329)|~(in @ X1330 @ (symdiff @ X1328 @ X1329))))&((in @ X1332 @ (setadjoin @ X1331 @ (setadjoin @ X1332 @ emptyset)))&((in @ X1333 @ (setunion @ (setadjoin @ (setadjoin @ X1333 @ emptyset) @ (setadjoin @ (setadjoin @ X1333 @ (setadjoin @ X1334 @ emptyset)) @ emptyset))))&((in @ X1336 @ (setunion @ (setadjoin @ (setadjoin @ X1335 @ emptyset) @ (setadjoin @ (setadjoin @ X1335 @ (setadjoin @ X1336 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1337 @ X1338) @ (setunion @ (setadjoin @ (setadjoin @ X1337 @ emptyset) @ (setadjoin @ (setadjoin @ X1337 @ (setadjoin @ X1338 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1337 @ X1338) @ (setunion @ (setadjoin @ (setadjoin @ X1337 @ emptyset) @ (setadjoin @ (setadjoin @ X1337 @ (setadjoin @ X1338 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1337 @ emptyset) @ (setadjoin @ (setadjoin @ X1337 @ (setadjoin @ X1338 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1337 @ X1338) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1337 @ X1338) @ (setadjoin @ (esk56_2 @ X1337 @ X1338) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1341 @ X1342) @ (setunion @ (kpair @ X1341 @ X1342)))&((in @ (esk58_2 @ X1341 @ X1342) @ (setunion @ (kpair @ X1341 @ X1342)))&((kpair @ X1341 @ X1342)=(setadjoin @ (setadjoin @ (esk57_2 @ X1341 @ X1342) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1341 @ X1342) @ (setadjoin @ (esk58_2 @ X1341 @ X1342) @ emptyset)) @ emptyset)))))&((~(in @ X1346 @ X1345)|(subset @ (setadjoin @ X1346 @ emptyset) @ X1345))&((~(in @ X1348 @ X1347)|(in @ (setadjoin @ X1348 @ emptyset) @ (powerset @ X1347)))&((~(in @ X1351 @ X1349)|(in @ (setadjoin @ X1351 @ emptyset) @ (powerset @ (binunion @ X1349 @ X1350))))&((~(in @ X1354 @ (setadjoin @ X1352 @ (setadjoin @ X1353 @ emptyset)))|(((X1354)=(X1352))|((X1354)=(X1353))))&((~(in @ X1357 @ X1355)|(~(in @ X1358 @ X1356)|(subset @ (setadjoin @ X1357 @ (setadjoin @ X1358 @ emptyset)) @ (binunion @ X1355 @ X1356))))&((~(in @ X1361 @ X1359)|(~(in @ X1362 @ X1360)|(in @ (setadjoin @ X1361 @ (setadjoin @ X1362 @ emptyset)) @ (powerset @ (binunion @ X1359 @ X1360)))))&((~(in @ X1365 @ X1363)|(~(in @ X1366 @ X1364)|(subset @ (setadjoin @ (setadjoin @ X1365 @ emptyset) @ (setadjoin @ (setadjoin @ X1365 @ (setadjoin @ X1366 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1363 @ X1364)))))&((~(in @ X1369 @ X1367)|(~(in @ X1370 @ X1368)|(in @ (setadjoin @ (setadjoin @ X1369 @ emptyset) @ (setadjoin @ (setadjoin @ X1369 @ (setadjoin @ X1370 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1367 @ X1368))))))&((~(in @ X1373 @ X1371)|(~(in @ X1374 @ X1372)|(in @ (kpair @ X1373 @ X1374) @ (powerset @ (powerset @ (binunion @ X1371 @ X1372))))))&((~(in @ X1377 @ X1375)|(~(in @ X1378 @ X1376)|(in @ (kpair @ X1377 @ X1378) @ (cartprod @ X1375 @ X1376))))&((((in @ (esk59_3 @ X1379 @ X1380 @ X1381) @ X1379)|~(in @ X1381 @ (cartprod @ X1379 @ X1380)))&(((in @ (esk60_3 @ X1379 @ X1380 @ X1381) @ X1380)|~(in @ X1381 @ (cartprod @ X1379 @ X1380)))&(((X1381)=(kpair @ (esk59_3 @ X1379 @ X1380 @ X1381) @ (esk60_3 @ X1379 @ X1380 @ X1381)))|~(in @ X1381 @ (cartprod @ X1379 @ X1380)))))&((((in @ (esk61_3 @ X1384 @ X1385 @ X1386) @ (setunion @ X1386))|~(in @ X1386 @ (cartprod @ X1384 @ X1385)))&(((in @ (esk62_3 @ X1384 @ X1385 @ X1386) @ (setunion @ X1386))|~(in @ X1386 @ (cartprod @ X1384 @ X1385)))&(((X1386)=(setadjoin @ (setadjoin @ (esk61_3 @ X1384 @ X1385 @ X1386) @ emptyset) @ (setadjoin @ (setadjoin @ (esk61_3 @ X1384 @ X1385 @ X1386) @ (setadjoin @ (esk62_3 @ X1384 @ X1385 @ X1386) @ emptyset)) @ emptyset)))|~(in @ X1386 @ (cartprod @ X1384 @ X1385)))))&((((in @ (esk63_2 @ X1389 @ X1390) @ X1389)|~(in @ X1390 @ (setunion @ X1389)))&((in @ X1390 @ (esk63_2 @ X1389 @ X1390))|~(in @ X1390 @ (setunion @ X1389))))&((subset @ (setunion @ (setadjoin @ X1392 @ emptyset)) @ X1392)&((subset @ X1393 @ (setunion @ (setadjoin @ X1393 @ emptyset)))&(((setunion @ (setadjoin @ X1394 @ emptyset))=(X1394))&(((((in @ (esk66_2 @ X1395 @ X1396) @ (dsetconstr @ X1395 @ (^[Z0/* 3 */:$i]:((X1396 @ Z0)))))|(~(in @ X1399 @ X1395)|~(X1396 @ X1399))|(in @ (esk64_2 @ X1395 @ X1396) @ X1395))&(((dsetconstr @ X1395 @ (^[Z0/* 3 */:$i]:((X1396 @ Z0))))=(setadjoin @ (esk66_2 @ X1395 @ X1396) @ emptyset))|(~(in @ X1399 @ X1395)|~(X1396 @ X1399))|(in @ (esk64_2 @ X1395 @ X1396) @ X1395)))&((((in @ (esk66_2 @ X1395 @ X1396) @ (dsetconstr @ X1395 @ (^[Z0/* 3 */:$i]:((X1396 @ Z0)))))|(~(in @ X1399 @ X1395)|~(X1396 @ X1399))|(in @ (esk65_2 @ X1395 @ X1396) @ X1395))&(((dsetconstr @ X1395 @ (^[Z0/* 3 */:$i]:((X1396 @ Z0))))=(setadjoin @ (esk66_2 @ X1395 @ X1396) @ emptyset))|(~(in @ X1399 @ X1395)|~(X1396 @ X1399))|(in @ (esk65_2 @ X1395 @ X1396) @ X1395)))&((((in @ (esk66_2 @ X1395 @ X1396) @ (dsetconstr @ X1395 @ (^[Z0/* 3 */:$i]:((X1396 @ Z0)))))|(~(in @ X1399 @ X1395)|~(X1396 @ X1399))|(X1396 @ (esk64_2 @ X1395 @ X1396)))&(((dsetconstr @ X1395 @ (^[Z0/* 3 */:$i]:((X1396 @ Z0))))=(setadjoin @ (esk66_2 @ X1395 @ X1396) @ emptyset))|(~(in @ X1399 @ X1395)|~(X1396 @ X1399))|(X1396 @ (esk64_2 @ X1395 @ X1396))))&((((in @ (esk66_2 @ X1395 @ X1396) @ (dsetconstr @ X1395 @ (^[Z0/* 3 */:$i]:((X1396 @ Z0)))))|(~(in @ X1399 @ X1395)|~(X1396 @ X1399))|(X1396 @ (esk65_2 @ X1395 @ X1396)))&(((dsetconstr @ X1395 @ (^[Z0/* 3 */:$i]:((X1396 @ Z0))))=(setadjoin @ (esk66_2 @ X1395 @ X1396) @ emptyset))|(~(in @ X1399 @ X1395)|~(X1396 @ X1399))|(X1396 @ (esk65_2 @ X1395 @ X1396))))&(((in @ (esk66_2 @ X1395 @ X1396) @ (dsetconstr @ X1395 @ (^[Z0/* 3 */:$i]:((X1396 @ Z0)))))|(~(in @ X1399 @ X1395)|~(X1396 @ X1399))|((esk64_2 @ X1395 @ X1396)!=(esk65_2 @ X1395 @ X1396)))&(((dsetconstr @ X1395 @ (^[Z0/* 3 */:$i]:((X1396 @ Z0))))=(setadjoin @ (esk66_2 @ X1395 @ X1396) @ emptyset))|(~(in @ X1399 @ X1395)|~(X1396 @ X1399))|((esk64_2 @ X1395 @ X1396)!=(esk65_2 @ X1395 @ X1396))))))))&((((in @ (esk67_2 @ X1401 @ X1402) @ X1401)|(~(in @ X1403 @ (dsetconstr @ X1401 @ (^[Z0/* 3 */:$i]:((X1402 @ Z0)))))|((dsetconstr @ X1401 @ (^[Z0/* 3 */:$i]:((X1402 @ Z0))))!=(setadjoin @ X1403 @ emptyset))))&((X1402 @ (esk67_2 @ X1401 @ X1402))|(~(in @ X1403 @ (dsetconstr @ X1401 @ (^[Z0/* 3 */:$i]:((X1402 @ Z0)))))|((dsetconstr @ X1401 @ (^[Z0/* 3 */:$i]:((X1402 @ Z0))))!=(setadjoin @ X1403 @ emptyset)))))&(((((in @ (esk69_3 @ X1405 @ X1406 @ X1407) @ (dsetconstr @ X1405 @ (^[Z0/* 3 */:$i]:((X1406 @ Z0)))))|(in @ (esk68_3 @ X1405 @ X1406 @ X1407) @ X1405)|~(X1406 @ X1407)|~(in @ X1407 @ X1405))&(((dsetconstr @ X1405 @ (^[Z0/* 3 */:$i]:((X1406 @ Z0))))=(setadjoin @ (esk69_3 @ X1405 @ X1406 @ X1407) @ emptyset))|(in @ (esk68_3 @ X1405 @ X1406 @ X1407) @ X1405)|~(X1406 @ X1407)|~(in @ X1407 @ X1405)))&((((in @ (esk69_3 @ X1405 @ X1406 @ X1407) @ (dsetconstr @ X1405 @ (^[Z0/* 3 */:$i]:((X1406 @ Z0)))))|(X1406 @ (esk68_3 @ X1405 @ X1406 @ X1407))|~(X1406 @ X1407)|~(in @ X1407 @ X1405))&(((dsetconstr @ X1405 @ (^[Z0/* 3 */:$i]:((X1406 @ Z0))))=(setadjoin @ (esk69_3 @ X1405 @ X1406 @ X1407) @ emptyset))|(X1406 @ (esk68_3 @ X1405 @ X1406 @ X1407))|~(X1406 @ X1407)|~(in @ X1407 @ X1405)))&(((in @ (esk69_3 @ X1405 @ X1406 @ X1407) @ (dsetconstr @ X1405 @ (^[Z0/* 3 */:$i]:((X1406 @ Z0)))))|((esk68_3 @ X1405 @ X1406 @ X1407)!=(X1407))|~(X1406 @ X1407)|~(in @ X1407 @ X1405))&(((dsetconstr @ X1405 @ (^[Z0/* 3 */:$i]:((X1406 @ Z0))))=(setadjoin @ (esk69_3 @ X1405 @ X1406 @ X1407) @ emptyset))|((esk68_3 @ X1405 @ X1406 @ X1407)!=(X1407))|~(X1406 @ X1407)|~(in @ X1407 @ X1405)))))&((~(in @ X1412 @ esk70_0)|(~(in @ X1413 @ esk70_0)|(~(epred2_0 @ X1412)|(~(epred2_0 @ X1413)|((X1412)=(X1413))))))&(((in @ esk71_0 @ esk70_0)&(epred2_0 @ esk71_0))&(~(in @ X1415 @ (dsetconstr @ esk70_0 @ (^[Z0/* 3 */:$i]:((epred2_0 @ Z0)))))|((dsetconstr @ esk70_0 @ (^[Z0/* 3 */:$i]:((epred2_0 @ Z0))))!=(setadjoin @ X1415 @ 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_216])])])])])])). 1041.76/141.13 thf(c_0_218, negated_conjecture, ![X2:$i, X3:$i]:((((X2)=(X3))|~((in @ X2 @ esk70_0))|~((in @ X3 @ esk70_0))|~((epred2_0 @ X2))|~((epred2_0 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_217])). 1041.76/141.13 thf(c_0_219, negated_conjecture, (in @ esk71_0 @ esk70_0), inference(split_conjunct,[status(thm)],[c_0_217])). 1041.76/141.13 thf(c_0_220, negated_conjecture, (epred2_0 @ esk71_0), inference(split_conjunct,[status(thm)],[c_0_217])). 1041.76/141.13 thf(c_0_221, negated_conjecture, ![X2:$i]:((~((in @ X2 @ (dsetconstr @ esk70_0 @ epred2_0)))|((dsetconstr @ esk70_0 @ epred2_0)!=(setadjoin @ X2 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_217])). 1041.76/141.13 thf(c_0_222, negated_conjecture, ![X1:$i > $o, X3:$i, X2:$i]:(((in @ (esk69_3 @ X2 @ X1 @ X3) @ (dsetconstr @ X2 @ X1))|(in @ (esk68_3 @ X2 @ X1 @ X3) @ X2)|~((X1 @ X3))|~((in @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_217])). 1041.76/141.13 thf(c_0_223, negated_conjecture, ![X1:$i > $o, X3:$i, X2:$i]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk69_3 @ X2 @ X1 @ X3) @ emptyset))|(in @ (esk68_3 @ X2 @ X1 @ X3) @ X2)|~((X1 @ X3))|~((in @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_217])). 1041.76/141.13 thf(c_0_224, negated_conjecture, ![X1:$i > $o, X3:$i, X2:$i]:(((in @ (esk69_3 @ X2 @ X1 @ X3) @ (dsetconstr @ X2 @ X1))|(X1 @ (esk68_3 @ X2 @ X1 @ X3))|~((X1 @ X3))|~((in @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_217])). 1041.76/141.13 thf(c_0_225, negated_conjecture, ![X1:$i > $o, X3:$i, X2:$i]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk69_3 @ X2 @ X1 @ X3) @ emptyset))|(X1 @ (esk68_3 @ X2 @ X1 @ X3))|~((X1 @ X3))|~((in @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_217])). 1041.76/141.13 thf(c_0_226, negated_conjecture, ![X1:$i > $o, X3:$i, X2:$i]:(((in @ (esk69_3 @ X2 @ X1 @ X3) @ (dsetconstr @ X2 @ X1))|((esk68_3 @ X2 @ X1 @ X3)!=(X3))|~((X1 @ X3))|~((in @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_217])). 1041.76/141.13 thf(c_0_227, negated_conjecture, ![X1:$i > $o, X3:$i, X2:$i]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk69_3 @ X2 @ X1 @ X3) @ emptyset))|((esk68_3 @ X2 @ X1 @ X3)!=(X3))|~((X1 @ X3))|~((in @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_217])). 1041.76/141.13 thf(c_0_228, negated_conjecture, ![X2:$i]:((((X2)=(esk71_0))|~((in @ X2 @ esk70_0))|~((epred2_0 @ X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218, c_0_219]), c_0_220])])). 1041.76/141.13 thf(c_0_229, negated_conjecture, ![X2:$i]:(((in @ (esk68_3 @ esk70_0 @ epred2_0 @ X2) @ esk70_0)|~((in @ X2 @ esk70_0))|~((epred2_0 @ X2)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_221, c_0_222]), c_0_223])). 1041.76/141.13 thf(c_0_230, negated_conjecture, ![X2:$i]:(((epred2_0 @ (esk68_3 @ esk70_0 @ epred2_0 @ X2))|~((in @ X2 @ esk70_0))|~((epred2_0 @ X2)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_221, c_0_224]), c_0_225])). 1041.76/141.13 thf(c_0_231, negated_conjecture, ![X2:$i]:((((esk68_3 @ esk70_0 @ epred2_0 @ X2)!=(X2))|~((in @ X2 @ esk70_0))|~((epred2_0 @ X2)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_221, c_0_226]), c_0_227])). 1041.76/141.13 thf(c_0_232, negated_conjecture, ![X2:$i]:((((esk68_3 @ esk70_0 @ epred2_0 @ X2)=(esk71_0))|~((in @ X2 @ esk70_0))|~((epred2_0 @ X2)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_228, c_0_229]), c_0_230])). 1041.76/141.13 thf(c_0_233, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_231, c_0_232])]), c_0_219]), c_0_220])]), ['proof']). 1041.76/141.13 # SZS output end CNFRefutation 1041.76/141.13 # Parsed axioms : 344 1041.76/141.13 # Removed by relevancy pruning/SinE : 0 1041.76/141.13 # Initial clauses : 488 1041.76/141.13 # Removed in clause preprocessing : 205 1041.76/141.13 # Initial clauses in saturation : 283 1041.76/141.13 # Processed clauses : 13696 1041.76/141.13 # ...of these trivial : 140 1041.76/141.13 # ...subsumed : 5421 1041.76/141.13 # ...remaining for further processing : 8135 1041.76/141.13 # Other redundant clauses eliminated : 1122 1041.76/141.13 # Clauses deleted for lack of memory : 103166 1041.76/141.13 # Backward-subsumed : 148 1041.76/141.13 # Backward-rewritten : 243 1041.76/141.13 # Generated clauses : 4616358 1041.76/141.13 # ...of the previous two non-redundant : 4604376 1041.76/141.13 # ...aggressively subsumed : 0 1041.76/141.13 # Contextual simplify-reflections : 36 1041.76/141.13 # Paramodulations : 4615099 1041.76/141.13 # Factorizations : 137 1041.76/141.13 # NegExts : 0 1041.76/141.13 # Equation resolutions : 1122 1041.76/141.13 # Total rewrite steps : 38639 1041.76/141.13 # Propositional unsat checks : 0 1041.76/141.13 # Propositional check models : 0 1041.76/141.13 # Propositional check unsatisfiable : 0 1041.76/141.13 # Propositional clauses : 0 1041.76/141.13 # Propositional clauses after purity: 0 1041.76/141.13 # Propositional unsat core size : 0 1041.76/141.13 # Propositional preprocessing time : 0.000 1041.76/141.13 # Propositional encoding time : 0.000 1041.76/141.13 # Propositional solver time : 0.000 1041.76/141.13 # Success case prop preproc time : 0.000 1041.76/141.13 # Success case prop encoding time : 0.000 1041.76/141.13 # Success case prop solver time : 0.000 1041.76/141.13 # Current number of processed clauses : 7486 1041.76/141.13 # Positive orientable unit clauses : 137 1041.76/141.13 # Positive unorientable unit clauses: 0 1041.76/141.13 # Negative unit clauses : 302 1041.76/141.13 # Non-unit-clauses : 7047 1041.76/141.13 # Current number of unprocessed clauses: 1830473 1041.76/141.13 # ...number of literals in the above : 9517255 1041.76/141.13 # Current number of archived formulas : 0 1041.76/141.13 # Current number of archived clauses : 637 1041.76/141.13 # Clause-clause subsumption calls (NU) : 4938328 1041.76/141.13 # Rec. Clause-clause subsumption calls : 979990 1041.76/141.13 # Non-unit clause-clause subsumptions : 3484 1041.76/141.13 # Unit Clause-clause subsumption calls : 183531 1041.76/141.13 # Rewrite failures with RHS unbound : 0 1041.76/141.13 # BW rewrite match attempts : 83 1041.76/141.13 # BW rewrite match successes : 41 1041.76/141.13 # Condensation attempts : 13696 1041.76/141.13 # Condensation successes : 153 1041.76/141.13 # Termbank termtop insertions : 153541431 1041.76/141.13 1041.76/141.13 # ------------------------------------------------- 1041.76/141.13 # User time : 400.949 s 1041.76/141.13 # System time : 7.521 s 1041.76/141.13 # Total time : 408.470 s 1041.76/141.13 # Maximum resident set size: 5384 pages 1042.35/141.28 1042.35/141.28 # ------------------------------------------------- 1042.35/141.28 # User time : 473.396 s 1042.35/141.28 # System time : 9.025 s 1042.35/141.28 # Total time : 482.421 s 1042.35/141.28 # Maximum resident set size: 2204 pages 1042.35/141.28 % E---3.1 exiting 1042.35/141.28 EOF