%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU654^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:53 AM UTC 2026
% Result : Theorem 53.87s 9.31s
% Output : CNFRefutation 53.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU654^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:09:05 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.23/0.27 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p
% 53.87/9.31 % Version: 3.5.1-ho
% 53.87/9.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 53.87/9.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 53.87/9.31 % Starting ehoh_best5 with 300s (1) cores
% 53.87/9.31 % Starting almost_fo_3_lam with 300s (1) cores
% 53.87/9.31 % Starting new_bool_5 with 300s (1) cores
% 53.87/9.31 % Starting pre_casc_3 with 300s (1) cores
% 53.87/9.31 % Starting ho_unfolding_8 with 300s (1) cores
% 53.87/9.31 % Starting new_ho_10_cnf2 with 300s (1) cores
% 53.87/9.31 % Starting new_bool_3 with 300s (1) cores
% 53.87/9.31 % Starting new_ho_5 with 300s (1) cores
% 53.87/9.31 % new_ho_5 with pid 1298930 completed with status 9
% 53.87/9.31 % almost_fo_3_lam with pid 1298924 completed with status 0
% 53.87/9.31 % Result found by almost_fo_3_lam
% 53.87/9.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 53.87/9.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 53.87/9.31 % Starting ehoh_best5 with 300s (1) cores
% 53.87/9.31 % Starting almost_fo_3_lam with 300s (1) cores
% 53.87/9.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 53.87/9.31 % No SInE strategy applied
% 53.87/9.31 % Search class: HGHSM-FSLM31-MHFMMSBN
% 53.87/9.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 53.87/9.31 % Starting SubtermCWHack with 28s (1) cores
% 53.87/9.31 % SubtermCWHack with pid 1298950 completed with status 0
% 53.87/9.31 % Result found by SubtermCWHack
% 53.87/9.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 53.87/9.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 53.87/9.31 % Starting ehoh_best5 with 300s (1) cores
% 53.87/9.31 % Starting almost_fo_3_lam with 300s (1) cores
% 53.87/9.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 53.87/9.31 % No SInE strategy applied
% 53.87/9.31 % Search class: HGHSM-FSLM31-MHFMMSBN
% 53.87/9.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 53.87/9.31 % Starting SubtermCWHack with 28s (1) cores
% 53.87/9.31 % Preprocessing time : 0.006 s
% 53.87/9.31
% 53.87/9.31 % Proof found!
% 53.87/9.31 % SZS status Theorem
% 53.87/9.31 % SZS output start CNFRefutation
% 53.87/9.31 thf(decl_23, type, in: $i > $i > $o).
% 53.87/9.31 thf(decl_24, type, exu: ($i > $o) > $o).
% 53.87/9.31 thf(decl_25, type, setextAx: $o).
% 53.87/9.31 thf(decl_26, type, emptyset: $i).
% 53.87/9.31 thf(decl_27, type, emptysetAx: $o).
% 53.87/9.31 thf(decl_28, type, setadjoin: $i > $i > $i).
% 53.87/9.31 thf(decl_29, type, setadjoinAx: $o).
% 53.87/9.31 thf(decl_30, type, powerset: $i > $i).
% 53.87/9.31 thf(decl_31, type, powersetAx: $o).
% 53.87/9.31 thf(decl_32, type, setunion: $i > $i).
% 53.87/9.31 thf(decl_33, type, setunionAx: $o).
% 53.87/9.31 thf(decl_34, type, omega: $i).
% 53.87/9.31 thf(decl_35, type, omega0Ax: $o).
% 53.87/9.31 thf(decl_36, type, omegaSAx: $o).
% 53.87/9.31 thf(decl_37, type, omegaIndAx: $o).
% 53.87/9.31 thf(decl_38, type, replAx: $o).
% 53.87/9.31 thf(decl_39, type, foundationAx: $o).
% 53.87/9.31 thf(decl_40, type, wellorderingAx: $o).
% 53.87/9.31 thf(decl_41, type, descr: ($i > $o) > $i).
% 53.87/9.31 thf(decl_42, type, descrp: $o).
% 53.87/9.31 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_44, type, dsetconstrI: $o).
% 53.87/9.31 thf(decl_45, type, dsetconstrEL: $o).
% 53.87/9.31 thf(decl_46, type, dsetconstrER: $o).
% 53.87/9.31 thf(decl_47, type, exuE1: $o).
% 53.87/9.31 thf(decl_48, type, prop2set: $o > $i).
% 53.87/9.31 thf(decl_49, type, prop2setE: $o).
% 53.87/9.31 thf(decl_50, type, emptysetE: $o).
% 53.87/9.31 thf(decl_51, type, emptysetimpfalse: $o).
% 53.87/9.31 thf(decl_52, type, notinemptyset: $o).
% 53.87/9.31 thf(decl_53, type, exuE3e: $o).
% 53.87/9.31 thf(decl_54, type, setext: $o).
% 53.87/9.31 thf(decl_55, type, emptyI: $o).
% 53.87/9.31 thf(decl_56, type, noeltsimpempty: $o).
% 53.87/9.31 thf(decl_57, type, setbeta: $o).
% 53.87/9.31 thf(decl_58, type, nonempty: $i > $o).
% 53.87/9.31 thf(decl_59, type, nonemptyE1: $o).
% 53.87/9.31 thf(decl_60, type, nonemptyI: $o).
% 53.87/9.31 thf(decl_61, type, nonemptyI1: $o).
% 53.87/9.31 thf(decl_62, type, setadjoinIL: $o).
% 53.87/9.31 thf(decl_63, type, emptyinunitempty: $o).
% 53.87/9.31 thf(decl_64, type, setadjoinIR: $o).
% 53.87/9.31 thf(decl_65, type, setadjoinE: $o).
% 53.87/9.31 thf(decl_66, type, setadjoinOr: $o).
% 53.87/9.31 thf(decl_67, type, setoftrueEq: $o).
% 53.87/9.31 thf(decl_68, type, powersetI: $o).
% 53.87/9.31 thf(decl_69, type, emptyinPowerset: $o).
% 53.87/9.31 thf(decl_70, type, emptyInPowerset: $o).
% 53.87/9.31 thf(decl_71, type, powersetE: $o).
% 53.87/9.31 thf(decl_72, type, setunionI: $o).
% 53.87/9.31 thf(decl_73, type, setunionE: $o).
% 53.87/9.31 thf(decl_74, type, subPowSU: $o).
% 53.87/9.31 thf(decl_75, type, exuE2: $o).
% 53.87/9.31 thf(decl_76, type, nonemptyImpWitness: $o).
% 53.87/9.31 thf(decl_77, type, uniqinunit: $o).
% 53.87/9.31 thf(decl_78, type, notinsingleton: $o).
% 53.87/9.31 thf(decl_79, type, eqinunit: $o).
% 53.87/9.31 thf(decl_80, type, singletonsswitch: $o).
% 53.87/9.31 thf(decl_81, type, upairsetE: $o).
% 53.87/9.31 thf(decl_82, type, upairsetIL: $o).
% 53.87/9.31 thf(decl_83, type, upairsetIR: $o).
% 53.87/9.31 thf(decl_84, type, emptyE1: $o).
% 53.87/9.31 thf(decl_85, type, vacuousDall: $o).
% 53.87/9.31 thf(decl_86, type, quantDeMorgan1: $o).
% 53.87/9.31 thf(decl_87, type, quantDeMorgan2: $o).
% 53.87/9.31 thf(decl_88, type, quantDeMorgan3: $o).
% 53.87/9.31 thf(decl_89, type, quantDeMorgan4: $o).
% 53.87/9.31 thf(decl_90, type, prop2setI: $o).
% 53.87/9.31 thf(decl_91, type, set2prop: $i > $o).
% 53.87/9.31 thf(decl_92, type, prop2set2propI: $o).
% 53.87/9.31 thf(decl_93, type, notdexE: $o).
% 53.87/9.31 thf(decl_94, type, notdallE: $o).
% 53.87/9.31 thf(decl_95, type, exuI1: $o).
% 53.87/9.31 thf(decl_96, type, exuI3: $o).
% 53.87/9.31 thf(decl_97, type, exuI2: $o).
% 53.87/9.31 thf(decl_98, type, inCongP: $o).
% 53.87/9.31 thf(decl_99, type, in__Cong: $o).
% 53.87/9.31 thf(decl_100, type, exuE3u: $o).
% 53.87/9.31 thf(decl_101, type, exu__Cong: $o).
% 53.87/9.31 thf(decl_102, type, emptyset__Cong: $o).
% 53.87/9.31 thf(decl_103, type, setadjoin__Cong: $o).
% 53.87/9.31 thf(decl_104, type, powerset__Cong: $o).
% 53.87/9.31 thf(decl_105, type, setunion__Cong: $o).
% 53.87/9.31 thf(decl_106, type, omega__Cong: $o).
% 53.87/9.31 thf(decl_107, type, exuEu: $o).
% 53.87/9.31 thf(decl_108, type, descr__Cong: $o).
% 53.87/9.31 thf(decl_109, type, dsetconstr__Cong: $o).
% 53.87/9.31 thf(decl_110, type, subset: $i > $i > $o).
% 53.87/9.31 thf(decl_113, type, subsetI1: $o).
% 53.87/9.31 thf(decl_114, type, eqimpsubset2: $o).
% 53.87/9.31 thf(decl_115, type, eqimpsubset1: $o).
% 53.87/9.31 thf(decl_116, type, subsetI2: $o).
% 53.87/9.31 thf(decl_117, type, emptysetsubset: $o).
% 53.87/9.31 thf(decl_118, type, subsetE: $o).
% 53.87/9.31 thf(decl_119, type, subsetE2: $o).
% 53.87/9.31 thf(decl_120, type, notsubsetI: $o).
% 53.87/9.31 thf(decl_121, type, notequalI1: $o).
% 53.87/9.31 thf(decl_122, type, notequalI2: $o).
% 53.87/9.31 thf(decl_123, type, subsetRefl: $o).
% 53.87/9.31 thf(decl_124, type, subsetTrans: $o).
% 53.87/9.31 thf(decl_125, type, setadjoinSub: $o).
% 53.87/9.31 thf(decl_126, type, setadjoinSub2: $o).
% 53.87/9.31 thf(decl_127, type, subset2powerset: $o).
% 53.87/9.31 thf(decl_128, type, setextsub: $o).
% 53.87/9.31 thf(decl_129, type, subsetemptysetimpeq: $o).
% 53.87/9.31 thf(decl_130, type, powersetI1: $o).
% 53.87/9.31 thf(decl_131, type, powersetE1: $o).
% 53.87/9.31 thf(decl_132, type, inPowerset: $o).
% 53.87/9.31 thf(decl_133, type, powersetsubset: $o).
% 53.87/9.31 thf(decl_134, type, sepInPowerset: $o).
% 53.87/9.31 thf(decl_135, type, sepSubset: $o).
% 53.87/9.31 thf(decl_136, type, binunion: $i > $i > $i).
% 53.87/9.31 thf(decl_137, type, binunionIL: $o).
% 53.87/9.31 thf(decl_138, type, upairset2IR: $o).
% 53.87/9.31 thf(decl_139, type, binunionIR: $o).
% 53.87/9.31 thf(decl_140, type, binunionEcases: $o).
% 53.87/9.31 thf(decl_141, type, binunionE: $o).
% 53.87/9.31 thf(decl_142, type, binunionLsub: $o).
% 53.87/9.31 thf(decl_143, type, binunionRsub: $o).
% 53.87/9.31 thf(decl_144, type, binintersect: $i > $i > $i).
% 53.87/9.31 thf(decl_145, type, binintersectI: $o).
% 53.87/9.31 thf(decl_146, type, binintersectSubset5: $o).
% 53.87/9.31 thf(decl_147, type, binintersectEL: $o).
% 53.87/9.31 thf(decl_148, type, binintersectLsub: $o).
% 53.87/9.31 thf(decl_149, type, binintersectSubset2: $o).
% 53.87/9.31 thf(decl_150, type, binintersectSubset3: $o).
% 53.87/9.31 thf(decl_151, type, binintersectER: $o).
% 53.87/9.31 thf(decl_152, type, disjointsetsI1: $o).
% 53.87/9.31 thf(decl_153, type, binintersectRsub: $o).
% 53.87/9.31 thf(decl_154, type, binintersectSubset4: $o).
% 53.87/9.31 thf(decl_155, type, binintersectSubset1: $o).
% 53.87/9.31 thf(decl_156, type, bs114d: $o).
% 53.87/9.31 thf(decl_158, type, setminus: $i > $i > $i).
% 53.87/9.31 thf(decl_159, type, setminusI: $o).
% 53.87/9.31 thf(decl_160, type, setminusEL: $o).
% 53.87/9.31 thf(decl_161, type, setminusER: $o).
% 53.87/9.31 thf(decl_162, type, setminusSubset2: $o).
% 53.87/9.31 thf(decl_163, type, setminusERneg: $o).
% 53.87/9.31 thf(decl_164, type, setminusELneg: $o).
% 53.87/9.31 thf(decl_165, type, setminusILneg: $o).
% 53.87/9.31 thf(decl_166, type, setminusIRneg: $o).
% 53.87/9.31 thf(decl_167, type, setminusLsub: $o).
% 53.87/9.31 thf(decl_168, type, setminusSubset1: $o).
% 53.87/9.31 thf(decl_169, type, symdiff: $i > $i > $i).
% 53.87/9.31 thf(decl_170, type, symdiffE: $o).
% 53.87/9.31 thf(decl_171, type, symdiffI1: $o).
% 53.87/9.31 thf(decl_172, type, symdiffI2: $o).
% 53.87/9.31 thf(decl_173, type, symdiffIneg1: $o).
% 53.87/9.31 thf(decl_174, type, symdiffIneg2: $o).
% 53.87/9.31 thf(decl_175, type, iskpair: $i > $o).
% 53.87/9.31 thf(decl_176, type, secondinupair: $o).
% 53.87/9.31 thf(decl_177, type, setukpairIL: $o).
% 53.87/9.31 thf(decl_178, type, setukpairIR: $o).
% 53.87/9.31 thf(decl_179, type, kpairiskpair: $o).
% 53.87/9.31 thf(decl_180, type, kpair: $i > $i > $i).
% 53.87/9.31 thf(decl_181, type, kpairp: $o).
% 53.87/9.31 thf(decl_182, type, cartprod: $i > $i > $i).
% 53.87/9.31 thf(decl_183, type, singletonsubset: $o).
% 53.87/9.31 thf(decl_184, type, singletoninpowerset: $o).
% 53.87/9.31 thf(decl_185, type, singletoninpowunion: $o).
% 53.87/9.31 thf(decl_186, type, upairset2E: $o).
% 53.87/9.31 thf(decl_187, type, upairsubunion: $o).
% 53.87/9.31 thf(decl_188, type, upairinpowunion: $o).
% 53.87/9.31 thf(decl_189, type, ubforcartprodlem1: $o).
% 53.87/9.31 thf(decl_190, type, ubforcartprodlem2: $o).
% 53.87/9.31 thf(decl_191, type, ubforcartprodlem3: $o).
% 53.87/9.31 thf(decl_192, type, cartprodpairin: $o).
% 53.87/9.31 thf(decl_193, type, cartprodmempair1: $o).
% 53.87/9.31 thf(decl_194, type, cartprodmempair: $o).
% 53.87/9.31 thf(decl_195, type, setunionE2: $o).
% 53.87/9.31 thf(decl_196, type, setunionsingleton1: $o).
% 53.87/9.31 thf(decl_197, type, setunionsingleton2: $o).
% 53.87/9.31 thf(decl_198, type, setunionsingleton: $o).
% 53.87/9.31 thf(decl_199, type, singleton: $i > $o).
% 53.87/9.31 thf(decl_200, type, singletonprop: $o).
% 53.87/9.31 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 53.87/9.31 thf(decl_202, type, ex1E1: $o).
% 53.87/9.31 thf(decl_203, type, ex1I: $o).
% 53.87/9.31 thf(decl_204, type, ex1I2: $o).
% 53.87/9.31 thf(decl_205, type, singletonsuniq: $o).
% 53.87/9.31 thf(decl_210, type, setukpairinjL1: $o).
% 53.87/9.31 thf(decl_211, type, kfstsingleton: $o).
% 53.87/9.31 thf(decl_212, type, theprop: $o).
% 53.87/9.31 thf(decl_213, type, kfst: $i > $i).
% 53.87/9.31 thf(decl_214, type, kfstpairEq: $o).
% 53.87/9.31 thf(decl_215, type, cartprodfstin: $o).
% 53.87/9.31 thf(decl_216, type, setukpairinjL2: $o).
% 53.87/9.31 thf(decl_217, type, setukpairinjL: $o).
% 53.87/9.31 thf(decl_218, type, setukpairinjR11: $o).
% 53.87/9.31 thf(decl_219, type, setukpairinjR12: $o).
% 53.87/9.31 thf(decl_220, type, setukpairinjR1: $o).
% 53.87/9.31 thf(decl_221, type, upairequniteq: $o).
% 53.87/9.31 thf(decl_222, type, setukpairinjR2: $o).
% 53.87/9.31 thf(decl_223, type, epred1_0: $o).
% 53.87/9.31 thf(decl_224, type, esk1_2: $i > $i > $i).
% 53.87/9.31 thf(decl_225, type, esk2_2: $i > $i > $i).
% 53.87/9.31 thf(decl_226, type, esk3_2: $i > $i > $i).
% 53.87/9.31 thf(decl_227, type, esk4_1: $i > $i).
% 53.87/9.31 thf(decl_228, type, esk5_2: ($i > $i > $o) > $i > $i).
% 53.87/9.31 thf(decl_229, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 53.87/9.31 thf(decl_230, type, esk7_2: ($i > $i > $o) > $i > $i).
% 53.87/9.31 thf(decl_231, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 53.87/9.31 thf(decl_232, type, esk9_1: $i > $i).
% 53.87/9.31 thf(decl_233, type, esk10_2: ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_234, type, esk11_2: ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_235, type, esk12_1: ($i > $o) > $i).
% 53.87/9.31 thf(decl_236, type, esk13_2: ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_237, type, esk14_1: ($i > $o) > $i).
% 53.87/9.31 thf(decl_238, type, esk15_2: $i > $i > $i).
% 53.87/9.31 thf(decl_239, type, esk16_2: $i > $i > $i).
% 53.87/9.31 thf(decl_240, type, esk17_1: $i > $i).
% 53.87/9.31 thf(decl_241, type, esk18_1: $i > $i).
% 53.87/9.31 thf(decl_242, type, esk19_1: $i > $i).
% 53.87/9.31 thf(decl_243, type, esk20_2: $i > $i > $i).
% 53.87/9.31 thf(decl_244, type, esk21_3: $i > $i > $o > $i).
% 53.87/9.31 thf(decl_245, type, esk22_2: ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_246, type, esk23_1: ($i > $o) > $i).
% 53.87/9.31 thf(decl_247, type, esk24_1: $i > $i).
% 53.87/9.31 thf(decl_248, type, esk25_2: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_249, type, esk26_2: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_250, type, esk27_2: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_251, type, esk28_2: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_252, type, esk29_2: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_253, type, esk30_2: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_254, type, esk31_2: ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_255, type, esk32_1: ($i > $o) > $i).
% 53.87/9.31 thf(decl_256, type, esk33_1: ($i > $o) > $i).
% 53.87/9.31 thf(decl_257, type, esk34_1: ($i > $o) > $i).
% 53.87/9.31 thf(decl_258, type, esk35_1: ($i > $o) > $i).
% 53.87/9.31 thf(decl_259, type, esk36_2: ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_260, type, esk37_1: ($i > $o) > $i).
% 53.87/9.31 thf(decl_261, type, esk38_2: ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_262, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 53.87/9.31 thf(decl_263, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 53.87/9.31 thf(decl_264, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_265, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 53.87/9.31 thf(decl_266, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_267, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 53.87/9.31 thf(decl_268, type, esk45_2: ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_269, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 53.87/9.31 thf(decl_270, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 53.87/9.31 thf(decl_271, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_272, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_273, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 53.87/9.31 thf(decl_274, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 53.87/9.31 thf(decl_275, type, esk52_2: $i > $i > $i).
% 53.87/9.31 thf(decl_276, type, esk53_2: $i > $i > $i).
% 53.87/9.31 thf(decl_277, type, esk54_2: $i > $i > $i).
% 53.87/9.31 thf(decl_278, type, esk55_2: $i > $i > $i).
% 53.87/9.31 thf(decl_279, type, esk56_2: $i > $i > $i).
% 53.87/9.31 thf(decl_280, type, esk57_2: $i > $i > $i).
% 53.87/9.31 thf(decl_281, type, esk58_2: $i > $i > $i).
% 53.87/9.31 thf(decl_282, type, esk59_3: $i > $i > $i > $i).
% 53.87/9.31 thf(decl_283, type, esk60_3: $i > $i > $i > $i).
% 53.87/9.31 thf(decl_284, type, esk61_3: $i > $i > $i > $i).
% 53.87/9.31 thf(decl_285, type, esk62_3: $i > $i > $i > $i).
% 53.87/9.31 thf(decl_286, type, esk63_2: $i > $i > $i).
% 53.87/9.31 thf(decl_287, type, esk64_2: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_288, type, esk65_2: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_289, type, esk66_2: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_290, type, esk67_2: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_291, type, esk68_3: $i > ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_292, type, esk69_3: $i > ($i > $o) > $i > $i).
% 53.87/9.31 thf(decl_293, type, esk70_2: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_294, type, esk71_2: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_295, type, esk72_2: $i > ($i > $o) > $i).
% 53.87/9.31 thf(decl_296, type, esk73_1: $i > $i).
% 53.87/9.31 thf(decl_297, type, esk74_0: $i).
% 53.87/9.31 thf(decl_298, type, esk75_0: $i).
% 53.87/9.31 thf(decl_299, type, esk76_0: $i).
% 53.87/9.31 thf(decl_300, type, esk77_0: $i).
% 53.87/9.31 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', ex1)).
% 53.87/9.31 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', singleton)).
% 53.87/9.31 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', replAx)).
% 53.87/9.31 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', exu)).
% 53.87/9.31 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', descrp)).
% 53.87/9.31 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', exuE1)).
% 53.87/9.31 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', exuE3e)).
% 53.87/9.31 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', nonempty)).
% 53.87/9.31 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', nonemptyI)).
% 53.87/9.31 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', exuE2)).
% 53.87/9.31 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', exuI1)).
% 53.87/9.31 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', exuI3)).
% 53.87/9.31 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', exuI2)).
% 53.87/9.31 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', exuE3u)).
% 53.87/9.31 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', exu__Cong)).
% 53.87/9.31 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', exuEu)).
% 53.87/9.31 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', descr__Cong)).
% 53.87/9.31 thf(iskpair, axiom, ((iskpair)=(^[X4:$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/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', iskpair)).
% 53.87/9.31 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', singletonprop)).
% 53.87/9.31 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', ex1E1)).
% 53.87/9.31 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', ex1I)).
% 53.87/9.31 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', ex1I2)).
% 53.87/9.31 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', kfstsingleton)).
% 53.87/9.31 thf(setukpairinjR, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((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)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setukpairinjR)).
% 53.87/9.31 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', dsetconstrI)).
% 53.87/9.31 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', dsetconstrEL)).
% 53.87/9.31 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', dsetconstrER)).
% 53.87/9.31 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setbeta)).
% 53.87/9.31 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', nonemptyE1)).
% 53.87/9.31 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', nonemptyI1)).
% 53.87/9.31 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setoftrueEq)).
% 53.87/9.31 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', nonemptyImpWitness)).
% 53.87/9.31 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', emptyE1)).
% 53.87/9.31 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', dsetconstr__Cong)).
% 53.87/9.31 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', sepInPowerset)).
% 53.87/9.31 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', sepSubset)).
% 53.87/9.31 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', kpairiskpair)).
% 53.87/9.31 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', kpairp)).
% 53.87/9.31 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', cartprodmempair)).
% 53.87/9.31 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', theprop)).
% 53.87/9.31 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setextAx)).
% 53.87/9.31 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', emptysetAx)).
% 53.87/9.31 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setadjoinAx)).
% 53.87/9.31 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', powersetAx)).
% 53.87/9.31 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setunionAx)).
% 53.87/9.31 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', omega0Ax)).
% 53.87/9.31 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', omegaSAx)).
% 53.87/9.31 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', omegaIndAx)).
% 53.87/9.31 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', foundationAx)).
% 53.87/9.31 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', wellorderingAx)).
% 53.87/9.31 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', prop2setE)).
% 53.87/9.31 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', emptysetE)).
% 53.87/9.31 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', emptysetimpfalse)).
% 53.87/9.31 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', notinemptyset)).
% 53.87/9.31 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setext)).
% 53.87/9.31 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', emptyI)).
% 53.87/9.31 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', noeltsimpempty)).
% 53.87/9.31 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setadjoinIL)).
% 53.87/9.31 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', emptyinunitempty)).
% 53.87/9.31 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setadjoinIR)).
% 53.87/9.31 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setadjoinE)).
% 53.87/9.31 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setadjoinOr)).
% 53.87/9.31 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', powersetI)).
% 53.87/9.31 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', emptyinPowerset)).
% 53.87/9.31 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', emptyInPowerset)).
% 53.87/9.31 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', powersetE)).
% 53.87/9.31 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setunionI)).
% 53.87/9.31 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setunionE)).
% 53.87/9.31 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', subPowSU)).
% 53.87/9.31 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', uniqinunit)).
% 53.87/9.31 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', notinsingleton)).
% 53.87/9.31 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', eqinunit)).
% 53.87/9.31 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', singletonsswitch)).
% 53.87/9.31 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', upairsetE)).
% 53.87/9.31 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', upairsetIL)).
% 53.87/9.31 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', upairsetIR)).
% 53.87/9.31 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', vacuousDall)).
% 53.87/9.31 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', quantDeMorgan1)).
% 53.87/9.31 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', quantDeMorgan2)).
% 53.87/9.31 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', quantDeMorgan3)).
% 53.87/9.31 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', quantDeMorgan4)).
% 53.87/9.31 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', prop2setI)).
% 53.87/9.31 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', prop2set2propI)).
% 53.87/9.31 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', notdexE)).
% 53.87/9.31 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', notdallE)).
% 53.87/9.31 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', inCongP)).
% 53.87/9.31 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', in__Cong)).
% 53.87/9.31 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', emptyset__Cong)).
% 53.87/9.31 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setadjoin__Cong)).
% 53.87/9.31 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', powerset__Cong)).
% 53.87/9.31 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setunion__Cong)).
% 53.87/9.31 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', omega__Cong)).
% 53.87/9.31 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', subsetI1)).
% 53.87/9.31 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', eqimpsubset2)).
% 53.87/9.31 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', eqimpsubset1)).
% 53.87/9.31 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', subsetI2)).
% 53.87/9.31 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', emptysetsubset)).
% 53.87/9.31 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', subsetE)).
% 53.87/9.31 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', subsetE2)).
% 53.87/9.31 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', notsubsetI)).
% 53.87/9.31 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', notequalI1)).
% 53.87/9.31 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', notequalI2)).
% 53.87/9.31 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', subsetRefl)).
% 53.87/9.31 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', subsetTrans)).
% 53.87/9.31 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setadjoinSub)).
% 53.87/9.31 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setadjoinSub2)).
% 53.87/9.31 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', subset2powerset)).
% 53.87/9.31 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setextsub)).
% 53.87/9.31 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', subsetemptysetimpeq)).
% 53.87/9.31 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', powersetI1)).
% 53.87/9.31 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', powersetE1)).
% 53.87/9.31 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', inPowerset)).
% 53.87/9.31 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', powersetsubset)).
% 53.87/9.31 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binunionIL)).
% 53.87/9.31 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', upairset2IR)).
% 53.87/9.31 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binunionIR)).
% 53.87/9.31 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binunionEcases)).
% 53.87/9.31 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binunionE)).
% 53.87/9.31 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binunionLsub)).
% 53.87/9.31 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binunionRsub)).
% 53.87/9.31 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binintersectI)).
% 53.87/9.31 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binintersectSubset5)).
% 53.87/9.31 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binintersectEL)).
% 53.87/9.31 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binintersectLsub)).
% 53.87/9.31 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binintersectSubset2)).
% 53.87/9.31 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binintersectSubset3)).
% 53.87/9.31 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binintersectER)).
% 53.87/9.31 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', disjointsetsI1)).
% 53.87/9.31 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binintersectRsub)).
% 53.87/9.31 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binintersectSubset4)).
% 53.87/9.31 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', binintersectSubset1)).
% 53.87/9.31 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', bs114d)).
% 53.87/9.31 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setminusI)).
% 53.87/9.31 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setminusEL)).
% 53.87/9.31 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setminusER)).
% 53.87/9.31 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setminusSubset2)).
% 53.87/9.31 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setminusERneg)).
% 53.87/9.31 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setminusELneg)).
% 53.87/9.31 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setminusILneg)).
% 53.87/9.31 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setminusIRneg)).
% 53.87/9.31 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setminusLsub)).
% 53.87/9.31 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setminusSubset1)).
% 53.87/9.31 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', symdiffE)).
% 53.87/9.31 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', symdiffI1)).
% 53.87/9.31 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', symdiffI2)).
% 53.87/9.31 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', symdiffIneg1)).
% 53.87/9.31 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', symdiffIneg2)).
% 53.87/9.31 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', secondinupair)).
% 53.87/9.31 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setukpairIL)).
% 53.87/9.31 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setukpairIR)).
% 53.87/9.31 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', singletonsubset)).
% 53.87/9.31 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', singletoninpowerset)).
% 53.87/9.31 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', singletoninpowunion)).
% 53.87/9.31 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', upairset2E)).
% 53.87/9.31 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', upairsubunion)).
% 53.87/9.31 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', upairinpowunion)).
% 53.87/9.31 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', ubforcartprodlem1)).
% 53.87/9.31 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', ubforcartprodlem2)).
% 53.87/9.31 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', ubforcartprodlem3)).
% 53.87/9.31 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', cartprodpairin)).
% 53.87/9.31 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', cartprodmempair1)).
% 53.87/9.31 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setunionE2)).
% 53.87/9.31 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setunionsingleton1)).
% 53.87/9.31 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setunionsingleton2)).
% 53.87/9.31 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setunionsingleton)).
% 53.87/9.31 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', singletonsuniq)).
% 53.87/9.31 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setukpairinjL1)).
% 53.87/9.31 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', kfstpairEq)).
% 53.87/9.31 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', cartprodfstin)).
% 53.87/9.31 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setukpairinjL2)).
% 53.87/9.31 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setukpairinjL)).
% 53.87/9.31 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setukpairinjR11)).
% 53.87/9.31 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setukpairinjR12)).
% 53.87/9.31 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setukpairinjR1)).
% 53.87/9.31 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', upairequniteq)).
% 53.87/9.31 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', setukpairinjR2)).
% 53.87/9.31 thf(kpair, axiom, ((kpair)=(^[X2:$i, X3:$i]:(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.am5aS9WgZe/E---3.1_1298887.p', kpair)).
% 53.87/9.31 thf(c_0_177, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X525:$i]:((((in @ X525 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X525 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 53.87/9.31 thf(c_0_178, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 53.87/9.31 thf(c_0_179, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 53.87/9.31 thf(c_0_180, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 53.87/9.31 thf(c_0_181, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 53.87/9.31 thf(c_0_182, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 53.87/9.31 thf(c_0_183, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 53.87/9.31 thf(c_0_184, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 53.87/9.31 thf(c_0_185, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 53.87/9.31 thf(c_0_186, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 53.87/9.31 thf(c_0_187, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 53.87/9.31 thf(c_0_188, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 53.87/9.31 thf(c_0_189, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 53.87/9.31 thf(c_0_190, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 53.87/9.31 thf(c_0_191, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 53.87/9.31 thf(c_0_192, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 53.87/9.31 thf(c_0_193, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 53.87/9.31 thf(c_0_194, plain, ((iskpair)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ (setunion @ Z0)))&(?[X3:$i]:((((in @ X3 @ (setunion @ Z0)))&(((Z0)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))))), inference(fof_simplification,[status(thm)],[iskpair])).
% 53.87/9.31 thf(c_0_195, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 53.87/9.31 thf(c_0_196, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 53.87/9.31 thf(c_0_197, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X525:$i]:((((in @ X525 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X525 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_177, c_0_178])).
% 53.87/9.31 thf(c_0_198, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 53.87/9.31 thf(c_0_199, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 53.87/9.31 thf(c_0_200, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 53.87/9.31 thf(c_0_201, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((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)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setukpairinjR])).
% 53.87/9.31 thf(c_0_202, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X490:$i]:(((((X6 @ X2 @ X490)))&(![X491:$i]:(((((X6 @ X2 @ X491)))=>(((X490)=(X491)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_179, c_0_180])).
% 53.87/9.31 thf(c_0_203, plain, ((descrp)=(![X1:$i > $o]:((((?[X492:$i]:(((((X1 @ X492)))&(![X493:$i]:(((((X1 @ X493)))=>(((X492)=(X493))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_181, c_0_180])).
% 53.87/9.31 thf(c_0_204, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 53.87/9.31 thf(c_0_205, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 53.87/9.31 thf(c_0_206, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 53.87/9.31 thf(c_0_207, plain, ((exuE1)=(![X1:$i > $o]:((((?[X494:$i]:(((((X1 @ X494)))&(![X495:$i]:(((((X1 @ X495)))=>(((X494)=(X495))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_182, c_0_180])).
% 53.87/9.31 thf(c_0_208, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X496:$i]:(((((X1 @ X496)))&(![X497:$i]:(((((X1 @ X497)))=>(((X496)=(X497))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_183, c_0_180])).
% 53.87/9.31 thf(c_0_209, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 53.87/9.31 thf(c_0_210, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_184])).
% 53.87/9.31 thf(c_0_211, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_185, c_0_184])).
% 53.87/9.31 thf(c_0_212, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_184])).
% 53.87/9.31 thf(c_0_213, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 53.87/9.31 thf(c_0_214, plain, ((exuE2)=(![X1:$i > $o]:((((?[X498:$i]:(((((X1 @ X498)))&(![X499:$i]:(((((X1 @ X499)))=>(((X498)=(X499))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_186, c_0_180])).
% 53.87/9.31 thf(c_0_215, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_184])).
% 53.87/9.31 thf(c_0_216, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 53.87/9.31 thf(c_0_217, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X500:$i]:(((((X1 @ X500)))&(![X501:$i]:(((((X1 @ X501)))=>(((X500)=(X501)))))))))))))), inference(apply_def,[status(thm)],[c_0_187, c_0_180])).
% 53.87/9.31 thf(c_0_218, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X502:$i]:(((((X1 @ X502)))&(![X503:$i]:(((((X1 @ X503)))=>(((X502)=(X503)))))))))))))))), inference(apply_def,[status(thm)],[c_0_188, c_0_180])).
% 53.87/9.31 thf(c_0_219, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X504:$i]:(((((X1 @ X504)))&(![X505:$i]:(((((X1 @ X505)))=>(((X504)=(X505)))))))))))))), inference(apply_def,[status(thm)],[c_0_189, c_0_180])).
% 53.87/9.31 thf(c_0_220, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X506:$i]:(((((X1 @ X506)))&(![X507:$i]:(((((X1 @ X507)))=>(((X506)=(X507))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_190, c_0_180])).
% 53.87/9.31 thf(c_0_221, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X508:$i]:(((((X1 @ X508)))&(![X509:$i]:(((((X1 @ X509)))=>(((X508)=(X509))))))))))<=>((?[X510:$i]:(((((X17 @ X510)))&(![X511:$i]:(((((X17 @ X511)))=>(((X510)=(X511)))))))))))))))), inference(apply_def,[status(thm)],[c_0_191, c_0_180])).
% 53.87/9.31 thf(c_0_222, plain, ((exuEu)=(![X1:$i > $o]:((((?[X512:$i]:(((((X1 @ X512)))&(![X513:$i]:(((((X1 @ X513)))=>(((X512)=(X513))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_192, c_0_180])).
% 53.87/9.31 thf(c_0_223, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X514:$i]:(((((X1 @ X514)))&(![X515:$i]:(((((X1 @ X515)))=>(((X514)=(X515))))))))))=>((((?[X516:$i]:(((((X17 @ X516)))&(![X517:$i]:(((((X17 @ X517)))=>(((X516)=(X517))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_193, c_0_180])).
% 53.87/9.31 thf(c_0_224, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 53.87/9.31 thf(c_0_225, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 53.87/9.31 thf(c_0_226, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 53.87/9.31 thf(c_0_227, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X518:$i]:((((in @ X518 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(?[X519:$i]:((((in @ X519 @ (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 @ X518 @ emptyset) @ (setadjoin @ (setadjoin @ X518 @ (setadjoin @ X519 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_194])).
% 53.87/9.31 thf(c_0_228, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X520:$i]:((((in @ X520 @ (setunion @ (kpair @ X2 @ X3))))&(?[X521:$i]:((((in @ X521 @ (setunion @ (kpair @ X2 @ X3))))&(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X520 @ emptyset) @ (setadjoin @ (setadjoin @ X520 @ (setadjoin @ X521 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_194])).
% 53.87/9.31 thf(c_0_229, axiom, ((cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:((((in @ X18 @ (cartprod @ X4 @ X5)))=>((?[X522:$i]:((((in @ X522 @ (setunion @ X18)))&(?[X523:$i]:((((in @ X523 @ (setunion @ X18)))&(((X18)=(setadjoin @ (setadjoin @ X522 @ emptyset) @ (setadjoin @ (setadjoin @ X522 @ (setadjoin @ X523 @ emptyset)) @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[cartprodmempair, c_0_194])).
% 53.87/9.31 thf(c_0_230, plain, ((singletonprop)=(![X4:$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)))))=>((?[X524:$i]:((((in @ X524 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X524 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_195, c_0_178])).
% 53.87/9.31 thf(c_0_231, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X526:$i]:((((in @ X526 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X526 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_196, c_0_197])).
% 53.87/9.31 thf(c_0_232, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X527:$i]:((((in @ X527 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X527 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_198, c_0_197])).
% 53.87/9.31 thf(c_0_233, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))))=>(((?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2)))))=>((?[X528:$i]:((((in @ X528 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X528 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_199, c_0_197])).
% 53.87/9.31 thf(c_0_234, plain, ((kfstsingleton)=(![X18:$i]:((((?[X529:$i]:((((in @ X529 @ (setunion @ X18)))&(?[X530:$i]:((((in @ X530 @ (setunion @ X18)))&(((X18)=(setadjoin @ (setadjoin @ X529 @ emptyset) @ (setadjoin @ (setadjoin @ X529 @ (setadjoin @ X530 @ emptyset)) @ emptyset)))))))))))=>((?[X531:$i]:((((in @ X531 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X531 @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_200, c_0_194]), c_0_178])).
% 53.87/9.31 thf(c_0_235, axiom, ((theprop)=(![X21:$i]:((((?[X532:$i]:((((in @ X532 @ X21))&(((X21)=(setadjoin @ X532 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_178])).
% 53.87/9.31 thf(c_0_236, plain, ((epred1_0)<=>![X562:$i]:(?[X563:$i]:((((![X564:$i]:(((in @ X564 @ X563)=>![X565:$i]:(((in @ X565 @ X564)=>(in @ X565 @ X562)))))&![X566:$i, X567:$i]:((((in @ X566 @ X562)&(in @ X567 @ X562))=>(![X568:$i]:(((in @ X568 @ X563)=>((in @ X566 @ X568)<=>(in @ X567 @ X568))))=>((X566)=(X567))))))&![X569:$i, X570:$i]:((((in @ X569 @ X563)&(in @ X570 @ X563))=>(![X571:$i]:(((in @ X571 @ X569)=>(in @ X571 @ X570)))|![X572:$i]:(((in @ X572 @ X570)=>(in @ X572 @ X569)))))))&![X573:$i]:(((![X574:$i]:(((in @ X574 @ X573)=>(in @ X574 @ X562)))&?[X575:$i]:((in @ X575 @ X573)))=>?[X576:$i, X577:$i]:(((((in @ X576 @ X563)&(in @ X577 @ X573))&~(?[X578:$i]:(((in @ X578 @ X576)&(in @ X578 @ X573)))))&![X579:$i]:(((in @ X579 @ X563)=>(![X580:$i]:(((in @ X580 @ X579)=>(in @ X580 @ X576)))|(in @ X577 @ X579)))))))))))), introduced(definition)).
% 53.87/9.31 thf(c_0_237, negated_conjecture, ~((![X533:$i, X534:$i]:((![X535:$i]:(((in @ X535 @ X533)<=>(in @ X535 @ X534)))=>((X533)=(X534))))=>(![X536:$i]:(~(in @ X536 @ emptyset))=>(![X537:$i, X538:$i, X539:$i]:(((in @ X539 @ (setadjoin @ X537 @ X538))<=>(((X539)=(X537))|(in @ X539 @ X538))))=>(![X540:$i, X541:$i]:(((in @ X541 @ (powerset @ X540))<=>![X542:$i]:(((in @ X542 @ X541)=>(in @ X542 @ X540)))))=>(![X543:$i, X544:$i]:(((in @ X544 @ (setunion @ X543))<=>?[X545:$i]:(((in @ X544 @ X545)&(in @ X545 @ X543)))))=>((in @ emptyset @ omega)=>(![X546:$i]:(((in @ X546 @ omega)=>(in @ (setadjoin @ X546 @ X546) @ omega)))=>(![X547:$i]:((((in @ emptyset @ X547)&![X548:$i]:((((in @ X548 @ omega)&(in @ X548 @ X547))=>(in @ (setadjoin @ X548 @ X548) @ X547))))=>![X549:$i]:(((in @ X549 @ omega)=>(in @ X549 @ X547)))))=>(![X550:$i > $i > $o, X551:$i]:((![X552:$i]:(((in @ X552 @ X551)=>?[X553:$i]:(((X550 @ X552 @ X553)&![X554:$i]:(((X550 @ X552 @ X554)=>((X553)=(X554))))))))=>?[X555:$i]:(![X556:$i]:(((in @ X556 @ X555)<=>?[X557:$i]:(((in @ X557 @ X551)&(X550 @ X557 @ X556))))))))=>(![X558:$i]:((?[X559:$i]:((in @ X559 @ X558))=>?[X560:$i]:(((in @ X560 @ X558)&~(?[X561:$i]:(((in @ X561 @ X560)&(in @ X561 @ X558))))))))=>((epred1_0)=>(![X581:$i > $o]:((?[X582:$i]:(((X581 @ X582)&![X583:$i]:(((X581 @ X583)=>((X582)=(X583))))))=>(X581 @ (descr @ (^[Z0:$i]:(X581 @ Z0))))))=>(![X584:$i, X585:$i > $o, X586:$i]:(((in @ X586 @ X584)=>((X585 @ X586)=>(in @ X586 @ (dsetconstr @ X584 @ X585)))))=>(![X587:$i, X588:$i > $o, X589:$i]:(((in @ X589 @ (dsetconstr @ X587 @ X588))=>(in @ X589 @ X587)))=>(![X590:$i, X591:$i > $o, X592:$i]:(((in @ X592 @ (dsetconstr @ X590 @ X591))=>(X591 @ X592)))=>(![X593:$i > $o]:((?[X594:$i]:(((X593 @ X594)&![X595:$i]:(((X593 @ X595)=>((X594)=(X595))))))=>?[X596:$i]:(((X593 @ X596)&![X597:$i]:(((X593 @ X597)=>((X596)=(X597))))))))=>(![X598:$o, X599:$i]:(((in @ X599 @ (prop2set @ ((X598))))=>(X598)))=>(![X600:$i]:(((in @ X600 @ emptyset)=>![X601:$o]:((X601))))=>(![X602:$i]:(((in @ X602 @ emptyset)=>~($true)))=>(![X603:$i]:(~(in @ X603 @ emptyset))=>(![X604:$i > $o]:((?[X605:$i]:(((X604 @ X605)&![X606:$i]:(((X604 @ X606)=>((X605)=(X606))))))=>?[X607:$i]:((X604 @ X607))))=>(![X608:$i, X609:$i]:((![X610:$i]:(((in @ X610 @ X608)=>(in @ X610 @ X609)))=>(![X611:$i]:(((in @ X611 @ X609)=>(in @ X611 @ X608)))=>((X608)=(X609)))))=>(![X612:$i]:((![X613:$i]:(~(in @ X613 @ X612))=>((X612)=(emptyset))))=>(![X614:$i]:((![X615:$i]:(~(in @ X615 @ X614))=>((X614)=(emptyset))))=>(![X616:$i, X617:$i > $o, X618:$i]:(((in @ X618 @ X616)=>((in @ X618 @ (dsetconstr @ X616 @ X617))<=>(X617 @ X618))))=>(![X619:$i]:((((X619)!=(emptyset))=>?[X620:$i]:((in @ X620 @ X619))))=>(![X621:$i, X622:$i > $o, X623:$i]:(((in @ X623 @ X621)=>((X622 @ X623)=>((dsetconstr @ X621 @ X622)!=(emptyset)))))=>(![X624:$i]:((?[X625:$i]:((in @ X625 @ X624))=>((X624)!=(emptyset))))=>(![X626:$i, X627:$i]:((in @ X626 @ (setadjoin @ X626 @ X627)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X628:$i, X629:$i, X630:$i]:(((in @ X630 @ X629)=>(in @ X630 @ (setadjoin @ X628 @ X629))))=>(![X631:$i, X632:$i, X633:$i]:(((in @ X633 @ (setadjoin @ X631 @ X632))=>![X634:$o]:(((((X633)=(X631))=>(X634))=>(((in @ X633 @ X632)=>(X634))=>(X634))))))=>(![X635:$i, X636:$i, X637:$i]:(((in @ X637 @ (setadjoin @ X635 @ X636))=>(((X637)=(X635))|(in @ X637 @ X636))))=>(![X638:$i]:(((dsetconstr @ X638 @ (^[Z0:$i]:($true)))=(X638)))=>(![X639:$i, X640:$i]:((![X641:$i]:(((in @ X641 @ X640)=>(in @ X641 @ X639)))=>(in @ X640 @ (powerset @ X639))))=>(![X642:$i]:((in @ emptyset @ (powerset @ X642)))=>(![X643:$i]:((in @ emptyset @ (powerset @ X643)))=>(![X644:$i, X645:$i, X646:$i]:(((in @ X645 @ (powerset @ X644))=>((in @ X646 @ X645)=>(in @ X646 @ X644))))=>(![X647:$i, X648:$i, X649:$i]:(((in @ X648 @ X649)=>((in @ X649 @ X647)=>(in @ X648 @ (setunion @ X647)))))=>(![X650:$i, X651:$i]:(((in @ X651 @ (setunion @ X650))=>![X652:$o]:((![X653:$i]:(((in @ X651 @ X653)=>((in @ X653 @ X650)=>(X652))))=>(X652)))))=>(![X654:$i, X655:$i]:(((in @ X655 @ X654)=>(in @ X655 @ (powerset @ (setunion @ X654)))))=>(![X656:$i > $o]:((?[X657:$i]:(((X656 @ X657)&![X658:$i]:(((X656 @ X658)=>((X657)=(X658))))))=>?[X659:$i]:(![X660:$i]:(((X656 @ X660)<=>((X660)=(X659)))))))=>(![X661:$i]:((((X661)!=(emptyset))=>?[X662:$i]:(((in @ X662 @ X661)&$true))))=>(![X663:$i, X664:$i]:(((in @ X663 @ (setadjoin @ X664 @ emptyset))=>((X663)=(X664))))=>(![X665:$i, X666:$i]:((((X665)!=(X666))=>~(in @ X666 @ (setadjoin @ X665 @ emptyset))))=>(![X667:$i, X668:$i]:((((X667)=(X668))=>(in @ X667 @ (setadjoin @ X668 @ emptyset))))=>(![X669:$i, X670:$i]:(((in @ X669 @ (setadjoin @ X670 @ emptyset))=>(in @ X670 @ (setadjoin @ X669 @ emptyset))))=>(![X671:$i, X672:$i, X673:$i]:(((in @ X673 @ (setadjoin @ X671 @ (setadjoin @ X672 @ emptyset)))=>(((X673)=(X671))|((X673)=(X672)))))=>(![X674:$i, X675:$i]:((in @ X674 @ (setadjoin @ X674 @ (setadjoin @ X675 @ emptyset))))=>(![X676:$i, X677:$i]:((in @ X677 @ (setadjoin @ X676 @ (setadjoin @ X677 @ emptyset))))=>(![X678:$i, X679:$i > $o]:((?[X680:$i]:(((in @ X680 @ X678)&(X679 @ X680)))=>(((dsetconstr @ X678 @ X679)=(emptyset))=>~($true))))=>(![X681:$i > $o, X682:$i]:(((in @ X682 @ emptyset)=>(X681 @ X682)))=>(![X683:$i, X684:$i > $o]:((~(![X685:$i]:(((in @ X685 @ X683)=>(X684 @ X685))))=>?[X686:$i]:(((in @ X686 @ X683)&~((X684 @ X686))))))=>(![X687:$i, X688:$i > $o]:((![X689:$i]:(((in @ X689 @ X687)=>~((X688 @ X689))))=>~(?[X690:$i]:(((in @ X690 @ X687)&(X688 @ X690))))))=>(![X691:$i, X692:$i > $o]:((~(?[X693:$i]:(((in @ X693 @ X691)&(X692 @ X693))))=>![X694:$i]:(((in @ X694 @ X691)=>~((X692 @ X694))))))=>(![X695:$i, X696:$i > $o]:((?[X697:$i]:(((in @ X697 @ X695)&~((X696 @ X697))))=>~(![X698:$i]:(((in @ X698 @ X695)=>(X696 @ X698))))))=>(![X699:$o]:(((X699)=>(in @ emptyset @ (prop2set @ ((X699))))))=>(![X700:$o]:(((X700)=>(set2prop @ (prop2set @ ((X700))))))=>(![X701:$i, X702:$i > $o]:((~(?[X703:$i]:(((in @ X703 @ X701)&(X702 @ X703))))=>![X704:$i]:(((in @ X704 @ X701)=>~((X702 @ X704))))))=>(![X705:$i, X706:$i > $o]:((~(![X707:$i]:(((in @ X707 @ X705)=>(X706 @ X707))))=>?[X708:$i]:(((in @ X708 @ X705)&~((X706 @ X708))))))=>(![X709:$i > $o]:((?[X710:$i]:(((X709 @ X710)&![X711:$i]:(((X709 @ X711)=>((X710)=(X711))))))=>?[X712:$i]:(((X709 @ X712)&![X713:$i]:(((X709 @ X713)=>((X712)=(X713))))))))=>(![X714:$i > $o]:((?[X715:$i]:((X714 @ X715))=>(![X716:$i, X717:$i]:(((X714 @ X716)=>((X714 @ X717)=>((X716)=(X717)))))=>?[X718:$i]:(((X714 @ X718)&![X719:$i]:(((X714 @ X719)=>((X718)=(X719)))))))))=>(![X720:$i > $o]:((?[X721:$i]:(![X722:$i]:(((X720 @ X722)<=>((X722)=(X721)))))=>?[X723:$i]:(((X720 @ X723)&![X724:$i]:(((X720 @ X724)=>((X723)=(X724))))))))=>(![X725:$i, X726:$i]:((((X725)=(X726))=>![X727:$i, X728:$i]:((((X727)=(X728))=>((in @ X727 @ X725)=>(in @ X728 @ X726))))))=>(![X729:$i, X730:$i]:((((X729)=(X730))=>![X731:$i, X732:$i]:((((X731)=(X732))=>((in @ X731 @ X729)<=>(in @ X732 @ X730))))))=>(![X733:$i > $o]:((?[X734:$i]:(((X733 @ X734)&![X735:$i]:(((X733 @ X735)=>((X734)=(X735))))))=>![X736:$i, X737:$i]:(((X733 @ X736)=>((X733 @ X737)=>((X736)=(X737)))))))=>(![X738:$i > $o, X739:$i > $o]:((![X740:$i, X741:$i]:((((X740)=(X741))=>((X738 @ X740)<=>(X739 @ X741))))=>(?[X742:$i]:(((X738 @ X742)&![X743:$i]:(((X738 @ X743)=>((X742)=(X743))))))<=>?[X744:$i]:(((X739 @ X744)&![X745:$i]:(((X739 @ X745)=>((X744)=(X745)))))))))=>(((emptyset)=(emptyset))=>(![X746:$i, X747:$i]:((((X746)=(X747))=>![X748:$i, X749:$i]:((((X748)=(X749))=>((setadjoin @ X746 @ X748)=(setadjoin @ X747 @ X749))))))=>(![X750:$i, X751:$i]:((((X750)=(X751))=>((powerset @ X750)=(powerset @ X751))))=>(![X752:$i, X753:$i]:((((X752)=(X753))=>((setunion @ X752)=(setunion @ X753))))=>(((omega)=(omega))=>(![X754:$i > $o]:((?[X755:$i]:(((X754 @ X755)&![X756:$i]:(((X754 @ X756)=>((X755)=(X756))))))=>![X757:$i, X758:$i]:(((X754 @ X757)=>((X754 @ X758)=>((X757)=(X758)))))))=>(![X759:$i > $o, X760:$i > $o]:((![X761:$i, X762:$i]:((((X761)=(X762))=>((X759 @ X761)<=>(X760 @ X762))))=>(?[X763:$i]:(((X759 @ X763)&![X764:$i]:(((X759 @ X764)=>((X763)=(X764))))))=>(?[X765:$i]:(((X760 @ X765)&![X766:$i]:(((X760 @ X766)=>((X765)=(X766))))))=>((descr @ X759)=(descr @ X760))))))=>(![X767:$i, X768:$i]:((((X767)=(X768))=>![X769:$i > $o, X770:$i > $o]:((![X771:$i]:(((in @ X771 @ X767)=>![X772:$i]:(((in @ X772 @ X768)=>(((X771)=(X772))=>((X769 @ X771)<=>(X770 @ X772)))))))=>((dsetconstr @ X767 @ X769)=(dsetconstr @ X768 @ X770))))))=>(![X773:$i, X774:$i]:((![X775:$i]:(((in @ X775 @ X773)=>(in @ X775 @ X774)))=>(subset @ X773 @ X774)))=>(![X776:$i, X777:$i]:((((X776)=(X777))=>(subset @ X777 @ X776)))=>(![X778:$i, X779:$i]:((((X778)=(X779))=>(subset @ X778 @ X779)))=>(![X780:$i, X781:$i]:((![X782:$i]:(((in @ X782 @ X780)=>(in @ X782 @ X781)))=>(subset @ X780 @ X781)))=>(![X783:$i]:((subset @ emptyset @ X783))=>(![X784:$i, X785:$i, X786:$i]:(((subset @ X784 @ X785)=>((in @ X786 @ X784)=>(in @ X786 @ X785))))=>(![X787:$i, X788:$i, X789:$i]:(((subset @ X787 @ X788)=>(~(in @ X789 @ X788)=>~(in @ X789 @ X787))))=>(![X790:$i, X791:$i, X792:$i]:(((in @ X792 @ X790)=>(~(in @ X792 @ X791)=>~(subset @ X790 @ X791))))=>(![X793:$i, X794:$i]:((~(subset @ X793 @ X794)=>((X793)!=(X794))))=>(![X795:$i, X796:$i, X797:$i]:(((in @ X797 @ X795)=>(~(in @ X797 @ X796)=>((X795)!=(X796)))))=>(![X798:$i]:((subset @ X798 @ X798))=>(![X799:$i, X800:$i, X801:$i]:(((subset @ X799 @ X800)=>((subset @ X800 @ X801)=>(subset @ X799 @ X801))))=>(![X802:$i, X803:$i]:((subset @ X803 @ (setadjoin @ X802 @ X803)))=>(![X804:$i, X805:$i, X806:$i]:(((subset @ X804 @ X806)=>(subset @ X804 @ (setadjoin @ X805 @ X806))))=>(![X807:$i, X808:$i]:(((subset @ X807 @ X808)=>(in @ X807 @ (powerset @ X808))))=>(![X809:$i, X810:$i]:(((subset @ X809 @ X810)=>((subset @ X810 @ X809)=>((X809)=(X810)))))=>(![X811:$i]:(((subset @ X811 @ emptyset)=>((X811)=(emptyset))))=>(![X812:$i, X813:$i]:(((subset @ X813 @ 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@ X1028 @ emptyset) @ (setadjoin @ (setadjoin @ X1028 @ (setadjoin @ X1029 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1030 @ emptyset) @ (setadjoin @ (setadjoin @ X1030 @ (setadjoin @ X1031 @ emptyset)) @ emptyset)))=>(((X1030)=(X1031))=>((X1029)=(X1031)))))=>(![X1032:$i, X1033:$i, X1034:$i]:((((setadjoin @ X1032 @ (setadjoin @ X1033 @ emptyset))=(setadjoin @ X1034 @ emptyset))=>((X1032)=(X1033))))=>(![X1035:$i, X1036:$i, X1037:$i, X1038:$i]:((((setadjoin @ (setadjoin @ X1035 @ emptyset) @ (setadjoin @ (setadjoin @ X1035 @ (setadjoin @ X1036 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1037 @ emptyset) @ (setadjoin @ (setadjoin @ X1037 @ (setadjoin @ X1038 @ emptyset)) @ emptyset)))=>((X1036)=(X1038))))=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_201, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_202]), foundationAx]), wellorderingAx]), c_0_203]), c_0_204]), c_0_205]), c_0_206]), c_0_207]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_208]), setext]), emptyI]), noeltsimpempty]), c_0_209]), c_0_210]), c_0_211]), c_0_212]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_213]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_214]), c_0_215]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_216]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_217]), c_0_218]), c_0_219]), inCongP]), in__Cong]), c_0_220]), c_0_221]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_222]), c_0_223]), c_0_224]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_225]), c_0_226]), 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_227]), c_0_228]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), c_0_229]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_230]), c_0_231]), c_0_232]), c_0_233]), singletonsuniq]), setukpairinjL1]), c_0_234]), c_0_235]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2])])]), c_0_236])).
% 53.87/9.31 thf(c_0_238, plain, ![X1039:$i, X1040:$i]:(((kpair @ X1039 @ X1040)=(setadjoin @ (setadjoin @ X1039 @ emptyset) @ (setadjoin @ (setadjoin @ X1039 @ (setadjoin @ X1040 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])])).
% 53.87/9.31 thf(c_0_239, negated_conjecture, ![X1043:$i, X1044:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1056:$i, X1057:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i, X1065:$i, X1066:$i > $i > $o, X1067:$i, X1069:$i, X1072:$i, X1074:$i, X1075:$i, X1076:$i, X1077:$i, X1079:$i, X1080:$i > $o, X1081:$i, X1083:$i, X1084:$i > $o, X1085:$i, X1086:$i, X1087:$i > $o, X1088:$i, X1089:$i, X1090:$i > $o, X1091:$i, X1092:$i > $o, X1093:$i, X1096:$i, X1097:$o, X1098:$i, X1099:$i, X1100:$o, X1101:$i, X1102:$i, X1103:$i > $o, X1104:$i, X1107:$i, X1108:$i, X1111:$i, X1113:$i, X1115:$i, X1116:$i > $o, X1117:$i, X1118:$i, X1120:$i, X1121:$i > $o, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$o, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$o, X1153:$i, X1154:$i, X1155:$i > $o, X1156:$i, X1159:$i, X1160:$i, X1161:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i > $o, X1180:$i, X1181:$i > $o, X1182:$i, X1183:$i, X1184:$i > $o, X1185:$i, X1187:$i, X1188:$i > $o, X1190:$i, X1191:$i, X1192:$i > $o, X1194:$i, X1195:$i, X1196:$i > $o, X1197:$i, X1199:$o, X1200:$o, X1201:$i, X1202:$i > $o, X1204:$i, X1205:$i, X1206:$i > $o, X1207:$i, X1209:$i > $o, X1210:$i, X1213:$i, X1214:$i > $o, X1215:$i, X1219:$i, X1220:$i > $o, X1221:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1228:$i, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i > $o, X1234:$i, X1236:$i, X1237:$i, X1238:$i > $o, X1239:$i > $o, X1242:$i, X1245:$i, X1246:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i > $o, X1259:$i, X1261:$i, X1262:$i, X1263:$i > $o, X1264:$i > $o, X1267:$i, X1269:$i, X1271:$i, X1272:$i, X1273:$i > $o, X1274:$i > $o, X1277:$i, X1278:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i > $o, X1325:$i, X1326:$i > $o, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$o, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$o, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1429:$i, X1430:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1472:$i, X1473:$i, X1474:$i, X1477:$i, X1478:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i > $o, X1487:$i, X1489:$i, X1490:$i > $o, X1491:$i, X1493:$i, X1494:$i > $o, X1495:$i, X1498:$i, X1499:$i > $o, X1502:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i]:((((~(in @ (esk1_2 @ X1043 @ X1044) @ X1043)|~(in @ (esk1_2 @ X1043 @ X1044) @ X1044)|((X1043)=(X1044)))&((in @ (esk1_2 @ X1043 @ X1044) @ X1043)|(in @ (esk1_2 @ X1043 @ X1044) @ X1044)|((X1043)=(X1044))))&(~(in @ X1046 @ emptyset)&(((~(in @ X1049 @ (setadjoin @ X1047 @ X1048))|(((X1049)=(X1047))|(in @ X1049 @ X1048)))&((((X1049)!=(X1047))|(in @ X1049 @ (setadjoin @ X1047 @ X1048)))&(~(in @ X1049 @ X1048)|(in @ X1049 @ (setadjoin @ X1047 @ X1048)))))&(((~(in @ X1051 @ (powerset @ X1050))|(~(in @ X1052 @ X1051)|(in @ X1052 @ X1050)))&(((in @ (esk2_2 @ X1053 @ X1054) @ X1054)|(in @ X1054 @ (powerset @ X1053)))&(~(in @ (esk2_2 @ X1053 @ X1054) @ X1053)|(in @ X1054 @ (powerset @ X1053)))))&(((((in @ X1057 @ (esk3_2 @ X1056 @ X1057))|~(in @ X1057 @ (setunion @ X1056)))&((in @ (esk3_2 @ X1056 @ X1057) @ X1056)|~(in @ X1057 @ (setunion @ X1056))))&(~(in @ X1060 @ X1061)|~(in @ X1061 @ X1059)|(in @ X1060 @ (setunion @ X1059))))&((in @ emptyset @ omega)&((~(in @ X1062 @ omega)|(in @ (setadjoin @ X1062 @ X1062) @ omega))&(((((in @ (esk4_1 @ X1063) @ omega)|~(in @ emptyset @ X1063)|(~(in @ X1065 @ omega)|(in @ X1065 @ X1063)))&((in @ (esk4_1 @ X1063) @ X1063)|~(in @ emptyset @ X1063)|(~(in @ X1065 @ omega)|(in @ X1065 @ X1063))))&(~(in @ (setadjoin @ (esk4_1 @ X1063) @ (esk4_1 @ X1063)) @ X1063)|~(in @ emptyset @ X1063)|(~(in @ X1065 @ omega)|(in @ X1065 @ X1063))))&((((((in @ (esk8_3 @ X1066 @ X1067 @ X1072) @ X1067)|~(in @ X1072 @ (esk7_2 @ X1066 @ X1067))|(in @ (esk5_2 @ X1066 @ X1067) @ X1067))&((X1066 @ (esk8_3 @ X1066 @ X1067 @ X1072) @ X1072)|~(in @ X1072 @ (esk7_2 @ X1066 @ X1067))|(in @ (esk5_2 @ X1066 @ X1067) @ X1067)))&(~(in @ X1075 @ X1067)|~(X1066 @ X1075 @ X1074)|(in @ X1074 @ (esk7_2 @ X1066 @ X1067))|(in @ (esk5_2 @ X1066 @ X1067) @ X1067)))&(((((in @ (esk8_3 @ X1066 @ X1067 @ X1072) @ X1067)|~(in @ X1072 @ (esk7_2 @ X1066 @ X1067))|((X1066 @ (esk5_2 @ X1066 @ X1067) @ (esk6_3 @ X1066 @ X1067 @ X1069))|~(X1066 @ (esk5_2 @ X1066 @ X1067) @ X1069)))&((X1066 @ (esk8_3 @ X1066 @ X1067 @ X1072) @ X1072)|~(in @ X1072 @ (esk7_2 @ X1066 @ X1067))|((X1066 @ (esk5_2 @ X1066 @ X1067) @ (esk6_3 @ X1066 @ X1067 @ X1069))|~(X1066 @ (esk5_2 @ X1066 @ X1067) @ X1069))))&(~(in @ X1075 @ X1067)|~(X1066 @ X1075 @ X1074)|(in @ X1074 @ (esk7_2 @ X1066 @ X1067))|((X1066 @ (esk5_2 @ X1066 @ X1067) @ (esk6_3 @ X1066 @ X1067 @ X1069))|~(X1066 @ (esk5_2 @ X1066 @ X1067) @ X1069))))&((((in @ (esk8_3 @ X1066 @ X1067 @ X1072) @ X1067)|~(in @ X1072 @ (esk7_2 @ X1066 @ X1067))|(((X1069)!=(esk6_3 @ X1066 @ X1067 @ X1069))|~(X1066 @ (esk5_2 @ X1066 @ X1067) @ X1069)))&((X1066 @ (esk8_3 @ X1066 @ X1067 @ X1072) @ X1072)|~(in @ X1072 @ (esk7_2 @ X1066 @ X1067))|(((X1069)!=(esk6_3 @ X1066 @ X1067 @ X1069))|~(X1066 @ (esk5_2 @ X1066 @ X1067) @ X1069))))&(~(in @ X1075 @ X1067)|~(X1066 @ X1075 @ X1074)|(in @ X1074 @ (esk7_2 @ X1066 @ X1067))|(((X1069)!=(esk6_3 @ X1066 @ X1067 @ X1069))|~(X1066 @ (esk5_2 @ X1066 @ X1067) @ X1069))))))&((((in @ (esk9_1 @ X1076) @ X1076)|~(in @ X1077 @ X1076))&(~(in @ X1079 @ (esk9_1 @ X1076))|~(in @ X1079 @ X1076)|~(in @ X1077 @ X1076)))&((epred1_0)&((((X1080 @ (esk10_2 @ X1080 @ X1081))|~(X1080 @ X1081)|(X1080 @ (descr @ X1080)))&(((X1081)!=(esk10_2 @ X1080 @ X1081))|~(X1080 @ X1081)|(X1080 @ (descr @ X1080))))&((~(in @ X1085 @ X1083)|(~(X1084 @ X1085)|(in @ X1085 @ (dsetconstr @ X1083 @ X1084))))&((~(in @ X1088 @ (dsetconstr @ X1086 @ X1087))|(in @ X1088 @ X1086))&((~(in @ X1091 @ (dsetconstr @ X1089 @ X1090))|(X1090 @ 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(esk65_2 @ X1483 @ X1484))))&(((in @ (esk66_2 @ X1483 @ X1484) @ (dsetconstr @ X1483 @ X1484))|(~(in @ X1487 @ X1483)|~(X1484 @ X1487))|((esk64_2 @ X1483 @ X1484)!=(esk65_2 @ X1483 @ X1484)))&(((dsetconstr @ X1483 @ X1484)=(setadjoin @ (esk66_2 @ X1483 @ X1484) @ emptyset))|(~(in @ X1487 @ X1483)|~(X1484 @ X1487))|((esk64_2 @ X1483 @ X1484)!=(esk65_2 @ X1483 @ X1484))))))))&((((in @ (esk67_2 @ X1489 @ X1490) @ X1489)|(~(in @ X1491 @ (dsetconstr @ X1489 @ X1490))|((dsetconstr @ X1489 @ X1490)!=(setadjoin @ X1491 @ emptyset))))&((X1490 @ (esk67_2 @ X1489 @ X1490))|(~(in @ X1491 @ (dsetconstr @ X1489 @ X1490))|((dsetconstr @ X1489 @ X1490)!=(setadjoin @ X1491 @ emptyset)))))&(((((in @ (esk69_3 @ X1493 @ X1494 @ X1495) @ (dsetconstr @ X1493 @ X1494))|(in @ (esk68_3 @ X1493 @ X1494 @ X1495) @ X1493)|~(X1494 @ X1495)|~(in @ X1495 @ X1493))&(((dsetconstr @ X1493 @ X1494)=(setadjoin @ (esk69_3 @ X1493 @ X1494 @ X1495) @ emptyset))|(in @ (esk68_3 @ X1493 @ X1494 @ X1495) @ X1493)|~(X1494 @ X1495)|~(in @ X1495 @ X1493)))&((((in @ (esk69_3 @ X1493 @ X1494 @ X1495) @ (dsetconstr @ X1493 @ X1494))|(X1494 @ (esk68_3 @ X1493 @ X1494 @ X1495))|~(X1494 @ X1495)|~(in @ X1495 @ X1493))&(((dsetconstr @ X1493 @ X1494)=(setadjoin @ (esk69_3 @ X1493 @ X1494 @ X1495) @ emptyset))|(X1494 @ (esk68_3 @ X1493 @ X1494 @ X1495))|~(X1494 @ X1495)|~(in @ X1495 @ X1493)))&(((in @ (esk69_3 @ X1493 @ X1494 @ X1495) @ (dsetconstr @ X1493 @ X1494))|((esk68_3 @ X1493 @ X1494 @ X1495)!=(X1495))|~(X1494 @ X1495)|~(in @ X1495 @ X1493))&(((dsetconstr @ X1493 @ X1494)=(setadjoin @ (esk69_3 @ X1493 @ X1494 @ X1495) @ emptyset))|((esk68_3 @ X1493 @ X1494 @ X1495)!=(X1495))|~(X1494 @ X1495)|~(in @ X1495 @ X1493)))))&(((((in @ (esk72_2 @ X1498 @ X1499) @ (dsetconstr @ X1498 @ X1499))|(~(in @ X1502 @ X1498)|~(X1499 @ X1502))|(in @ (esk70_2 @ X1498 @ X1499) @ X1498))&(((dsetconstr @ X1498 @ X1499)=(setadjoin @ (esk72_2 @ X1498 @ X1499) @ emptyset))|(~(in @ X1502 @ X1498)|~(X1499 @ X1502))|(in @ (esk70_2 @ X1498 @ X1499) @ X1498)))&((((in @ (esk72_2 @ X1498 @ X1499) @ (dsetconstr @ X1498 @ X1499))|(~(in @ X1502 @ X1498)|~(X1499 @ X1502))|(in @ (esk71_2 @ X1498 @ X1499) @ X1498))&(((dsetconstr @ X1498 @ X1499)=(setadjoin @ (esk72_2 @ X1498 @ X1499) @ emptyset))|(~(in @ X1502 @ X1498)|~(X1499 @ X1502))|(in @ (esk71_2 @ X1498 @ X1499) @ X1498)))&((((in @ (esk72_2 @ X1498 @ X1499) @ (dsetconstr @ X1498 @ X1499))|(~(in @ X1502 @ X1498)|~(X1499 @ X1502))|(X1499 @ (esk70_2 @ X1498 @ X1499)))&(((dsetconstr @ X1498 @ X1499)=(setadjoin @ (esk72_2 @ X1498 @ X1499) @ emptyset))|(~(in @ X1502 @ X1498)|~(X1499 @ X1502))|(X1499 @ (esk70_2 @ X1498 @ X1499))))&((((in @ (esk72_2 @ X1498 @ X1499) @ (dsetconstr @ X1498 @ X1499))|(~(in @ X1502 @ X1498)|~(X1499 @ X1502))|(X1499 @ (esk71_2 @ X1498 @ X1499)))&(((dsetconstr @ X1498 @ X1499)=(setadjoin @ (esk72_2 @ X1498 @ X1499) @ emptyset))|(~(in @ X1502 @ X1498)|~(X1499 @ X1502))|(X1499 @ (esk71_2 @ X1498 @ X1499))))&(((in @ (esk72_2 @ X1498 @ X1499) @ (dsetconstr @ X1498 @ X1499))|(~(in @ X1502 @ X1498)|~(X1499 @ X1502))|((esk70_2 @ X1498 @ X1499)!=(esk71_2 @ X1498 @ X1499)))&(((dsetconstr @ X1498 @ X1499)=(setadjoin @ (esk72_2 @ X1498 @ X1499) @ emptyset))|(~(in @ X1502 @ X1498)|~(X1499 @ X1502))|((esk70_2 @ X1498 @ X1499)!=(esk71_2 @ X1498 @ X1499))))))))&((((setadjoin @ X1504 @ emptyset)!=(setadjoin @ X1505 @ emptyset))|((X1504)=(X1505)))&((~(in @ (setadjoin @ X1508 @ emptyset) @ (setadjoin @ (setadjoin @ X1506 @ emptyset) @ (setadjoin @ (setadjoin @ X1506 @ (setadjoin @ X1507 @ emptyset)) @ emptyset)))|((X1506)=(X1508)))&((((in @ (esk73_1 @ X1509) @ (dsetconstr @ (setunion @ X1509) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1509)))))|(~(in @ X1510 @ (setunion @ X1509))|(~(in @ X1511 @ (setunion @ X1509))|((X1509)!=(setadjoin @ (setadjoin @ X1510 @ emptyset) @ (setadjoin @ (setadjoin @ X1510 @ (setadjoin @ X1511 @ emptyset)) @ emptyset))))))&(((dsetconstr @ (setunion @ X1509) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1509))))=(setadjoin @ (esk73_1 @ X1509) @ emptyset))|(~(in @ X1510 @ (setunion @ X1509))|(~(in @ X1511 @ (setunion @ X1509))|((X1509)!=(setadjoin @ (setadjoin @ X1510 @ emptyset) @ (setadjoin @ (setadjoin @ X1510 @ (setadjoin @ X1511 @ emptyset)) @ emptyset)))))))&((~(in @ X1514 @ X1513)|((X1513)!=(setadjoin @ X1514 @ emptyset))|(in @ (setunion @ X1513) @ X1513))&(((kfst @ (kpair @ X1515 @ X1516))=(X1515))&((~(in @ X1519 @ (cartprod @ X1517 @ X1518))|(in @ (kfst @ X1519) @ X1517))&((((setadjoin @ (setadjoin @ X1520 @ emptyset) @ (setadjoin @ (setadjoin @ X1520 @ (setadjoin @ X1521 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1522 @ emptyset) @ (setadjoin @ (setadjoin @ X1522 @ (setadjoin @ X1523 @ emptyset)) @ emptyset)))|((X1520)=(X1522)))&((((kpair @ X1524 @ X1525)!=(kpair @ X1526 @ X1527))|((X1524)=(X1526)))&((((X1528)!=(X1529))|((setadjoin @ X1528 @ (setadjoin @ X1529 @ emptyset))=(setadjoin @ X1528 @ emptyset)))&((((X1530)!=(X1531))|((setadjoin @ (setadjoin @ X1530 @ emptyset) @ (setadjoin @ (setadjoin @ X1530 @ (setadjoin @ X1531 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1530 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1532 @ emptyset) @ (setadjoin @ (setadjoin @ X1532 @ (setadjoin @ X1533 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1534 @ emptyset) @ (setadjoin @ (setadjoin @ X1534 @ (setadjoin @ X1535 @ emptyset)) @ emptyset)))|(((X1534)!=(X1535))|((X1533)=(X1535))))&((((setadjoin @ X1536 @ (setadjoin @ X1537 @ emptyset))!=(setadjoin @ X1538 @ emptyset))|((X1536)=(X1537)))&((((setadjoin @ (setadjoin @ X1539 @ emptyset) @ (setadjoin @ (setadjoin @ X1539 @ (setadjoin @ X1540 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1541 @ emptyset) @ (setadjoin @ (setadjoin @ X1541 @ (setadjoin @ X1542 @ emptyset)) @ emptyset)))|((X1540)=(X1542)))&(((kpair @ esk74_0 @ esk75_0)=(kpair @ esk76_0 @ esk77_0))&((esk75_0)!=(esk77_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_237])])])])])])])).
% 53.87/9.31 thf(c_0_240, plain, ![X1041:$i, X1042:$i]:(((kpair @ X1041 @ X1042)=(setadjoin @ (setadjoin @ X1041 @ emptyset) @ (setadjoin @ (setadjoin @ X1041 @ (setadjoin @ X1042 @ emptyset)) @ emptyset)))), inference(variable_rename,[status(thm)],[c_0_238])).
% 53.87/9.31 thf(c_0_241, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_239])).
% 53.87/9.31 thf(c_0_242, negated_conjecture, ((kpair @ esk74_0 @ esk75_0)=(kpair @ esk76_0 @ esk77_0)), inference(split_conjunct,[status(thm)],[c_0_239])).
% 53.87/9.31 thf(c_0_243, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i]:((((X3)=(X5))|((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X4 @ (setadjoin @ X5 @ emptyset)) @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_239])).
% 53.87/9.31 thf(c_0_244, plain, ![X2:$i, X3:$i]:(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_240])).
% 53.87/9.31 thf(c_0_245, negated_conjecture, ((esk74_0)=(esk76_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241, c_0_242]), c_0_241])).
% 53.87/9.31 thf(c_0_246, negated_conjecture, ![X2:$i, X5:$i, X4:$i, X3:$i]:((((X2)=(X3))|((kpair @ X4 @ X2)!=(kpair @ X5 @ X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_243, c_0_244]), c_0_244])).
% 53.87/9.31 thf(c_0_247, negated_conjecture, ((kpair @ esk76_0 @ esk75_0)=(kpair @ esk76_0 @ esk77_0)), inference(rw,[status(thm)],[c_0_242, c_0_245])).
% 53.87/9.31 thf(c_0_248, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(esk75_0))|((kpair @ X3 @ X2)!=(kpair @ esk76_0 @ esk77_0)))), inference(spm,[status(thm)],[c_0_246, c_0_247])).
% 53.87/9.31 thf(c_0_249, negated_conjecture, ((esk75_0)!=(esk77_0)), inference(split_conjunct,[status(thm)],[c_0_239])).
% 53.87/9.31 thf(c_0_250, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_248]), c_0_249]), ['proof']).
% 53.87/9.31 % SZS output end CNFRefutation
% 53.87/9.31 % Parsed axioms : 377
% 53.87/9.31 % Removed by relevancy pruning/SinE : 0
% 53.87/9.31 % Initial clauses : 529
% 53.87/9.31 % Removed in clause preprocessing : 224
% 53.87/9.31 % Initial clauses in saturation : 305
% 53.87/9.31 % Processed clauses : 19794
% 53.87/9.31 % ...of these trivial : 35
% 53.87/9.31 % ...subsumed : 16246
% 53.87/9.31 % ...remaining for further processing : 3513
% 53.87/9.31 % Other redundant clauses eliminated : 100
% 53.87/9.31 % Clauses deleted for lack of memory : 0
% 53.87/9.31 % Backward-subsumed : 227
% 53.87/9.31 % Backward-rewritten : 44
% 53.87/9.31 % Generated clauses : 469275
% 53.87/9.31 % ...of the previous two non-redundant : 426737
% 53.87/9.31 % ...aggressively subsumed : 0
% 53.87/9.31 % Contextual simplify-reflections : 7
% 53.87/9.31 % Paramodulations : 469169
% 53.87/9.31 % Factorizations : 2
% 53.87/9.31 % NegExts : 0
% 53.87/9.31 % Equation resolutions : 104
% 53.87/9.31 % Disequality decompositions : 0
% 53.87/9.31 % Total rewrite steps : 95471
% 53.87/9.31 % ...of those cached : 92996
% 53.87/9.31 % Propositional unsat checks : 0
% 53.87/9.31 % Propositional check models : 0
% 53.87/9.31 % Propositional check unsatisfiable : 0
% 53.87/9.31 % Propositional clauses : 0
% 53.87/9.31 % Propositional clauses after purity: 0
% 53.87/9.31 % Propositional unsat core size : 0
% 53.87/9.31 % Propositional preprocessing time : 0.000
% 53.87/9.31 % Propositional encoding time : 0.000
% 53.87/9.31 % Propositional solver time : 0.000
% 53.87/9.31 % Success case prop preproc time : 0.000
% 53.87/9.31 % Success case prop encoding time : 0.000
% 53.87/9.31 % Success case prop solver time : 0.000
% 53.87/9.31 % Current number of processed clauses : 3224
% 53.87/9.31 % Positive orientable unit clauses : 762
% 53.87/9.31 % Positive unorientable unit clauses: 0
% 53.87/9.31 % Negative unit clauses : 452
% 53.87/9.31 % Non-unit-clauses : 2010
% 53.87/9.31 % Current number of unprocessed clauses: 406561
% 53.87/9.31 % ...number of literals in the above : 1200760
% 53.87/9.31 % Current number of archived formulas : 0
% 53.87/9.31 % Current number of archived clauses : 271
% 53.87/9.31 % Clause-clause subsumption calls (NU) : 443395
% 53.87/9.31 % Rec. Clause-clause subsumption calls : 329255
% 53.87/9.31 % Non-unit clause-clause subsumptions : 12174
% 53.87/9.31 % Unit Clause-clause subsumption calls : 127887
% 53.87/9.31 % Rewrite failures with RHS unbound : 0
% 53.87/9.31 % BW rewrite match attempts : 5396
% 53.87/9.31 % BW rewrite match successes : 43
% 53.87/9.31 % Condensation attempts : 0
% 53.87/9.31 % Condensation successes : 0
% 53.87/9.31 % Termbank termtop insertions : 7949090
% 53.87/9.31 % Search garbage collected termcells : 16806
% 53.87/9.31
% 53.87/9.31 % -------------------------------------------------
% 53.87/9.31 % User time : 8.520 s
% 53.87/9.31 % System time : 0.305 s
% 53.87/9.31 % Total time : 8.825 s
% 53.87/9.31 % Maximum resident set size: 7556 pages
% 53.87/9.31
% 53.87/9.31 % -------------------------------------------------
% 53.87/9.31 % User time : 8.636 s
% 53.87/9.31 % System time : 0.355 s
% 53.87/9.31 % Total time : 8.991 s
% 53.87/9.31 % Maximum resident set size: 5120 pages
% 53.87/9.31 % E exiting
%------------------------------------------------------------------------------