%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU642^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:27:02 AM UTC 2026
% Result : Theorem 172.84s 29.76s
% Output : CNFRefutation 172.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU642^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n013.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 14:01:21 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p
% 172.84/29.76 % Version: 3.5.1-ho
% 172.84/29.76 % Preprocessing class: HSLMSLSSLLLCHFA.
% 172.84/29.76 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 172.84/29.76 % Starting ehoh_best5 with 300s (1) cores
% 172.84/29.76 % Starting almost_fo_3_lam with 300s (1) cores
% 172.84/29.76 % Starting new_bool_5 with 300s (1) cores
% 172.84/29.76 % Starting pre_casc_3 with 300s (1) cores
% 172.84/29.76 % Starting ho_unfolding_8 with 300s (1) cores
% 172.84/29.76 % Starting new_ho_10_cnf2 with 300s (1) cores
% 172.84/29.76 % Starting new_bool_3 with 300s (1) cores
% 172.84/29.76 % Starting new_ho_5 with 300s (1) cores
% 172.84/29.76 % new_ho_5 with pid 2166859 completed with status 9
% 172.84/29.76 % ho_unfolding_8 with pid 2166856 completed with status 0
% 172.84/29.76 % Result found by ho_unfolding_8
% 172.84/29.76 % Preprocessing class: HSLMSLSSLLLCHFA.
% 172.84/29.76 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 172.84/29.76 % Starting ehoh_best5 with 300s (1) cores
% 172.84/29.76 % Starting almost_fo_3_lam with 300s (1) cores
% 172.84/29.76 % Starting new_bool_5 with 300s (1) cores
% 172.84/29.76 % Starting pre_casc_3 with 300s (1) cores
% 172.84/29.76 % Starting ho_unfolding_8 with 300s (1) cores
% 172.84/29.76 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 172.84/29.76 % No SInE strategy applied
% 172.84/29.76 % Search class: HGHSM-FSLM31-MHFMMSBN
% 172.84/29.76 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 172.84/29.76 % Starting SubtermCWHack with 28s (1) cores
% 172.84/29.76 % SubtermCWHack with pid 2166870 completed with status 8
% 172.84/29.76 % Starting ho_unfolding_8 with 31s (1) cores
% 172.84/29.76 % ho_unfolding_8 with pid 2166885 completed with status 0
% 172.84/29.76 % Result found by ho_unfolding_8
% 172.84/29.76 % Preprocessing class: HSLMSLSSLLLCHFA.
% 172.84/29.76 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 172.84/29.76 % Starting ehoh_best5 with 300s (1) cores
% 172.84/29.76 % Starting almost_fo_3_lam with 300s (1) cores
% 172.84/29.76 % Starting new_bool_5 with 300s (1) cores
% 172.84/29.76 % Starting pre_casc_3 with 300s (1) cores
% 172.84/29.76 % Starting ho_unfolding_8 with 300s (1) cores
% 172.84/29.76 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 172.84/29.76 % No SInE strategy applied
% 172.84/29.76 % Search class: HGHSM-FSLM31-MHFMMSBN
% 172.84/29.76 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 172.84/29.76 % Starting SubtermCWHack with 28s (1) cores
% 172.84/29.76 % SubtermCWHack with pid 2166870 completed with status 8
% 172.84/29.76 % Starting ho_unfolding_8 with 31s (1) cores
% 172.84/29.76 % Preprocessing time : 0.214 s
% 172.84/29.76 % Presaturation interreduction done
% 172.84/29.76
% 172.84/29.76 % Proof found!
% 172.84/29.76 % SZS status Theorem
% 172.84/29.76 % SZS output start CNFRefutation
% 172.84/29.76 thf(decl_23, type, in: $i > $i > $o).
% 172.84/29.76 thf(decl_24, type, exu: ($i > $o) > $o).
% 172.84/29.76 thf(decl_25, type, setextAx: $o).
% 172.84/29.76 thf(decl_26, type, emptyset: $i).
% 172.84/29.76 thf(decl_27, type, emptysetAx: $o).
% 172.84/29.76 thf(decl_28, type, setadjoin: $i > $i > $i).
% 172.84/29.76 thf(decl_29, type, setadjoinAx: $o).
% 172.84/29.76 thf(decl_30, type, powerset: $i > $i).
% 172.84/29.76 thf(decl_31, type, powersetAx: $o).
% 172.84/29.76 thf(decl_32, type, setunion: $i > $i).
% 172.84/29.76 thf(decl_33, type, setunionAx: $o).
% 172.84/29.76 thf(decl_34, type, omega: $i).
% 172.84/29.76 thf(decl_35, type, omega0Ax: $o).
% 172.84/29.76 thf(decl_36, type, omegaSAx: $o).
% 172.84/29.76 thf(decl_37, type, omegaIndAx: $o).
% 172.84/29.76 thf(decl_38, type, replAx: $o).
% 172.84/29.76 thf(decl_39, type, foundationAx: $o).
% 172.84/29.76 thf(decl_40, type, wellorderingAx: $o).
% 172.84/29.76 thf(decl_41, type, descr: ($i > $o) > $i).
% 172.84/29.76 thf(decl_42, type, descrp: $o).
% 172.84/29.76 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_44, type, dsetconstrI: $o).
% 172.84/29.76 thf(decl_45, type, dsetconstrEL: $o).
% 172.84/29.76 thf(decl_46, type, dsetconstrER: $o).
% 172.84/29.76 thf(decl_47, type, exuE1: $o).
% 172.84/29.76 thf(decl_48, type, prop2set: $o > $i).
% 172.84/29.76 thf(decl_49, type, prop2setE: $o).
% 172.84/29.76 thf(decl_50, type, emptysetE: $o).
% 172.84/29.76 thf(decl_51, type, emptysetimpfalse: $o).
% 172.84/29.76 thf(decl_52, type, notinemptyset: $o).
% 172.84/29.76 thf(decl_53, type, exuE3e: $o).
% 172.84/29.76 thf(decl_54, type, setext: $o).
% 172.84/29.76 thf(decl_55, type, emptyI: $o).
% 172.84/29.76 thf(decl_56, type, noeltsimpempty: $o).
% 172.84/29.76 thf(decl_57, type, setbeta: $o).
% 172.84/29.76 thf(decl_58, type, nonempty: $i > $o).
% 172.84/29.76 thf(decl_59, type, nonemptyE1: $o).
% 172.84/29.76 thf(decl_60, type, nonemptyI: $o).
% 172.84/29.76 thf(decl_61, type, nonemptyI1: $o).
% 172.84/29.76 thf(decl_62, type, setadjoinIL: $o).
% 172.84/29.76 thf(decl_63, type, emptyinunitempty: $o).
% 172.84/29.76 thf(decl_64, type, setadjoinIR: $o).
% 172.84/29.76 thf(decl_65, type, setadjoinE: $o).
% 172.84/29.76 thf(decl_66, type, setadjoinOr: $o).
% 172.84/29.76 thf(decl_67, type, setoftrueEq: $o).
% 172.84/29.76 thf(decl_68, type, powersetI: $o).
% 172.84/29.76 thf(decl_69, type, emptyinPowerset: $o).
% 172.84/29.76 thf(decl_70, type, emptyInPowerset: $o).
% 172.84/29.76 thf(decl_71, type, powersetE: $o).
% 172.84/29.76 thf(decl_72, type, setunionI: $o).
% 172.84/29.76 thf(decl_73, type, setunionE: $o).
% 172.84/29.76 thf(decl_74, type, subPowSU: $o).
% 172.84/29.76 thf(decl_75, type, exuE2: $o).
% 172.84/29.76 thf(decl_76, type, nonemptyImpWitness: $o).
% 172.84/29.76 thf(decl_77, type, uniqinunit: $o).
% 172.84/29.76 thf(decl_78, type, notinsingleton: $o).
% 172.84/29.76 thf(decl_79, type, eqinunit: $o).
% 172.84/29.76 thf(decl_80, type, singletonsswitch: $o).
% 172.84/29.76 thf(decl_81, type, upairsetE: $o).
% 172.84/29.76 thf(decl_82, type, upairsetIL: $o).
% 172.84/29.76 thf(decl_83, type, upairsetIR: $o).
% 172.84/29.76 thf(decl_84, type, emptyE1: $o).
% 172.84/29.76 thf(decl_85, type, vacuousDall: $o).
% 172.84/29.76 thf(decl_86, type, quantDeMorgan1: $o).
% 172.84/29.76 thf(decl_87, type, quantDeMorgan2: $o).
% 172.84/29.76 thf(decl_88, type, quantDeMorgan3: $o).
% 172.84/29.76 thf(decl_89, type, quantDeMorgan4: $o).
% 172.84/29.76 thf(decl_90, type, prop2setI: $o).
% 172.84/29.76 thf(decl_91, type, set2prop: $i > $o).
% 172.84/29.76 thf(decl_92, type, prop2set2propI: $o).
% 172.84/29.76 thf(decl_93, type, notdexE: $o).
% 172.84/29.76 thf(decl_94, type, notdallE: $o).
% 172.84/29.76 thf(decl_95, type, exuI1: $o).
% 172.84/29.76 thf(decl_96, type, exuI3: $o).
% 172.84/29.76 thf(decl_97, type, exuI2: $o).
% 172.84/29.76 thf(decl_98, type, inCongP: $o).
% 172.84/29.76 thf(decl_99, type, in__Cong: $o).
% 172.84/29.76 thf(decl_100, type, exuE3u: $o).
% 172.84/29.76 thf(decl_101, type, exu__Cong: $o).
% 172.84/29.76 thf(decl_102, type, emptyset__Cong: $o).
% 172.84/29.76 thf(decl_103, type, setadjoin__Cong: $o).
% 172.84/29.76 thf(decl_104, type, powerset__Cong: $o).
% 172.84/29.76 thf(decl_105, type, setunion__Cong: $o).
% 172.84/29.76 thf(decl_106, type, omega__Cong: $o).
% 172.84/29.76 thf(decl_107, type, exuEu: $o).
% 172.84/29.76 thf(decl_108, type, descr__Cong: $o).
% 172.84/29.76 thf(decl_109, type, dsetconstr__Cong: $o).
% 172.84/29.76 thf(decl_110, type, subset: $i > $i > $o).
% 172.84/29.76 thf(decl_113, type, subsetI1: $o).
% 172.84/29.76 thf(decl_114, type, eqimpsubset2: $o).
% 172.84/29.76 thf(decl_115, type, eqimpsubset1: $o).
% 172.84/29.76 thf(decl_116, type, subsetI2: $o).
% 172.84/29.76 thf(decl_117, type, emptysetsubset: $o).
% 172.84/29.76 thf(decl_118, type, subsetE: $o).
% 172.84/29.76 thf(decl_119, type, subsetE2: $o).
% 172.84/29.76 thf(decl_120, type, notsubsetI: $o).
% 172.84/29.76 thf(decl_121, type, notequalI1: $o).
% 172.84/29.76 thf(decl_122, type, notequalI2: $o).
% 172.84/29.76 thf(decl_123, type, subsetRefl: $o).
% 172.84/29.76 thf(decl_124, type, subsetTrans: $o).
% 172.84/29.76 thf(decl_125, type, setadjoinSub: $o).
% 172.84/29.76 thf(decl_126, type, setadjoinSub2: $o).
% 172.84/29.76 thf(decl_127, type, subset2powerset: $o).
% 172.84/29.76 thf(decl_128, type, setextsub: $o).
% 172.84/29.76 thf(decl_129, type, subsetemptysetimpeq: $o).
% 172.84/29.76 thf(decl_130, type, powersetI1: $o).
% 172.84/29.76 thf(decl_131, type, powersetE1: $o).
% 172.84/29.76 thf(decl_132, type, inPowerset: $o).
% 172.84/29.76 thf(decl_133, type, powersetsubset: $o).
% 172.84/29.76 thf(decl_134, type, sepInPowerset: $o).
% 172.84/29.76 thf(decl_135, type, sepSubset: $o).
% 172.84/29.76 thf(decl_136, type, binunion: $i > $i > $i).
% 172.84/29.76 thf(decl_137, type, binunionIL: $o).
% 172.84/29.76 thf(decl_138, type, upairset2IR: $o).
% 172.84/29.76 thf(decl_139, type, binunionIR: $o).
% 172.84/29.76 thf(decl_140, type, binunionEcases: $o).
% 172.84/29.76 thf(decl_141, type, binunionE: $o).
% 172.84/29.76 thf(decl_142, type, binunionLsub: $o).
% 172.84/29.76 thf(decl_143, type, binunionRsub: $o).
% 172.84/29.76 thf(decl_144, type, binintersect: $i > $i > $i).
% 172.84/29.76 thf(decl_145, type, binintersectI: $o).
% 172.84/29.76 thf(decl_146, type, binintersectSubset5: $o).
% 172.84/29.76 thf(decl_147, type, binintersectEL: $o).
% 172.84/29.76 thf(decl_148, type, binintersectLsub: $o).
% 172.84/29.76 thf(decl_149, type, binintersectSubset2: $o).
% 172.84/29.76 thf(decl_150, type, binintersectSubset3: $o).
% 172.84/29.76 thf(decl_151, type, binintersectER: $o).
% 172.84/29.76 thf(decl_152, type, disjointsetsI1: $o).
% 172.84/29.76 thf(decl_153, type, binintersectRsub: $o).
% 172.84/29.76 thf(decl_154, type, binintersectSubset4: $o).
% 172.84/29.76 thf(decl_155, type, binintersectSubset1: $o).
% 172.84/29.76 thf(decl_156, type, bs114d: $o).
% 172.84/29.76 thf(decl_158, type, setminus: $i > $i > $i).
% 172.84/29.76 thf(decl_159, type, setminusI: $o).
% 172.84/29.76 thf(decl_160, type, setminusEL: $o).
% 172.84/29.76 thf(decl_161, type, setminusER: $o).
% 172.84/29.76 thf(decl_162, type, setminusSubset2: $o).
% 172.84/29.76 thf(decl_163, type, setminusERneg: $o).
% 172.84/29.76 thf(decl_164, type, setminusELneg: $o).
% 172.84/29.76 thf(decl_165, type, setminusILneg: $o).
% 172.84/29.76 thf(decl_166, type, setminusIRneg: $o).
% 172.84/29.76 thf(decl_167, type, setminusLsub: $o).
% 172.84/29.76 thf(decl_168, type, setminusSubset1: $o).
% 172.84/29.76 thf(decl_169, type, symdiff: $i > $i > $i).
% 172.84/29.76 thf(decl_170, type, symdiffE: $o).
% 172.84/29.76 thf(decl_171, type, symdiffI1: $o).
% 172.84/29.76 thf(decl_172, type, symdiffI2: $o).
% 172.84/29.76 thf(decl_173, type, symdiffIneg1: $o).
% 172.84/29.76 thf(decl_174, type, symdiffIneg2: $o).
% 172.84/29.76 thf(decl_175, type, iskpair: $i > $o).
% 172.84/29.76 thf(decl_176, type, secondinupair: $o).
% 172.84/29.76 thf(decl_177, type, setukpairIL: $o).
% 172.84/29.76 thf(decl_178, type, setukpairIR: $o).
% 172.84/29.76 thf(decl_179, type, kpairiskpair: $o).
% 172.84/29.76 thf(decl_180, type, kpair: $i > $i > $i).
% 172.84/29.76 thf(decl_181, type, kpairp: $o).
% 172.84/29.76 thf(decl_182, type, cartprod: $i > $i > $i).
% 172.84/29.76 thf(decl_183, type, singletonsubset: $o).
% 172.84/29.76 thf(decl_184, type, singletoninpowerset: $o).
% 172.84/29.76 thf(decl_185, type, singletoninpowunion: $o).
% 172.84/29.76 thf(decl_186, type, upairset2E: $o).
% 172.84/29.76 thf(decl_187, type, upairsubunion: $o).
% 172.84/29.76 thf(decl_188, type, upairinpowunion: $o).
% 172.84/29.76 thf(decl_189, type, ubforcartprodlem1: $o).
% 172.84/29.76 thf(decl_190, type, ubforcartprodlem2: $o).
% 172.84/29.76 thf(decl_191, type, ubforcartprodlem3: $o).
% 172.84/29.76 thf(decl_192, type, cartprodpairin: $o).
% 172.84/29.76 thf(decl_193, type, cartprodmempair1: $o).
% 172.84/29.76 thf(decl_194, type, cartprodmempair: $o).
% 172.84/29.76 thf(decl_195, type, setunionE2: $o).
% 172.84/29.76 thf(decl_196, type, setunionsingleton1: $o).
% 172.84/29.76 thf(decl_197, type, setunionsingleton2: $o).
% 172.84/29.76 thf(decl_198, type, setunionsingleton: $o).
% 172.84/29.76 thf(decl_199, type, singleton: $i > $o).
% 172.84/29.76 thf(decl_200, type, singletonprop: $o).
% 172.84/29.76 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 172.84/29.76 thf(decl_202, type, ex1E1: $o).
% 172.84/29.76 thf(decl_203, type, ex1I: $o).
% 172.84/29.76 thf(decl_204, type, ex1I2: $o).
% 172.84/29.76 thf(decl_205, type, singletonsuniq: $o).
% 172.84/29.76 thf(decl_210, type, epred1_0: $o).
% 172.84/29.76 thf(decl_211, type, esk1_2: $i > $i > $i).
% 172.84/29.76 thf(decl_212, type, esk2_2: $i > $i > $i).
% 172.84/29.76 thf(decl_213, type, esk3_2: $i > $i > $i).
% 172.84/29.76 thf(decl_214, type, esk4_1: $i > $i).
% 172.84/29.76 thf(decl_215, type, esk5_2: ($i > $i > $o) > $i > $i).
% 172.84/29.76 thf(decl_216, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 172.84/29.76 thf(decl_217, type, esk7_2: ($i > $i > $o) > $i > $i).
% 172.84/29.76 thf(decl_218, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 172.84/29.76 thf(decl_219, type, esk9_1: $i > $i).
% 172.84/29.76 thf(decl_220, type, esk10_2: ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_221, type, esk11_2: ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_222, type, esk12_1: ($i > $o) > $i).
% 172.84/29.76 thf(decl_223, type, esk13_2: ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_224, type, esk14_1: ($i > $o) > $i).
% 172.84/29.76 thf(decl_225, type, esk15_2: $i > $i > $i).
% 172.84/29.76 thf(decl_226, type, esk16_2: $i > $i > $i).
% 172.84/29.76 thf(decl_227, type, esk17_1: $i > $i).
% 172.84/29.76 thf(decl_228, type, esk18_1: $i > $i).
% 172.84/29.76 thf(decl_229, type, esk19_1: $i > $i).
% 172.84/29.76 thf(decl_230, type, esk20_2: $i > $i > $i).
% 172.84/29.76 thf(decl_231, type, esk21_3: $i > $i > $o > $i).
% 172.84/29.76 thf(decl_232, type, esk22_2: ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_233, type, esk23_1: ($i > $o) > $i).
% 172.84/29.76 thf(decl_234, type, esk24_1: $i > $i).
% 172.84/29.76 thf(decl_235, type, esk25_2: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_236, type, esk26_2: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_237, type, esk27_2: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_238, type, esk28_2: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_239, type, esk29_2: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_240, type, esk30_2: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_241, type, esk31_2: ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_242, type, esk32_1: ($i > $o) > $i).
% 172.84/29.76 thf(decl_243, type, esk33_1: ($i > $o) > $i).
% 172.84/29.76 thf(decl_244, type, esk34_1: ($i > $o) > $i).
% 172.84/29.76 thf(decl_245, type, esk35_1: ($i > $o) > $i).
% 172.84/29.76 thf(decl_246, type, esk36_2: ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_247, type, esk37_1: ($i > $o) > $i).
% 172.84/29.76 thf(decl_248, type, esk38_2: ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_249, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 172.84/29.76 thf(decl_250, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 172.84/29.76 thf(decl_251, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_252, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 172.84/29.76 thf(decl_253, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_254, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 172.84/29.76 thf(decl_255, type, esk45_2: ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_256, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 172.84/29.76 thf(decl_257, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 172.84/29.76 thf(decl_258, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_259, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_260, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 172.84/29.76 thf(decl_261, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 172.84/29.76 thf(decl_262, type, esk52_2: $i > $i > $i).
% 172.84/29.76 thf(decl_263, type, esk53_2: $i > $i > $i).
% 172.84/29.76 thf(decl_264, type, esk54_2: $i > $i > $i).
% 172.84/29.76 thf(decl_265, type, esk55_2: $i > $i > $i).
% 172.84/29.76 thf(decl_266, type, esk56_2: $i > $i > $i).
% 172.84/29.76 thf(decl_267, type, esk57_2: $i > $i > $i).
% 172.84/29.76 thf(decl_268, type, esk58_2: $i > $i > $i).
% 172.84/29.76 thf(decl_269, type, esk59_3: $i > $i > $i > $i).
% 172.84/29.76 thf(decl_270, type, esk60_3: $i > $i > $i > $i).
% 172.84/29.76 thf(decl_271, type, esk61_3: $i > $i > $i > $i).
% 172.84/29.76 thf(decl_272, type, esk62_3: $i > $i > $i > $i).
% 172.84/29.76 thf(decl_273, type, esk63_2: $i > $i > $i).
% 172.84/29.76 thf(decl_274, type, esk64_2: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_275, type, esk65_2: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_276, type, esk66_2: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_277, type, esk67_2: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_278, type, esk68_3: $i > ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_279, type, esk69_3: $i > ($i > $o) > $i > $i).
% 172.84/29.76 thf(decl_280, type, esk70_2: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_281, type, esk71_2: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_282, type, esk72_2: $i > ($i > $o) > $i).
% 172.84/29.76 thf(decl_283, type, esk73_0: $i).
% 172.84/29.76 thf(decl_284, type, esk74_0: $i).
% 172.84/29.76 thf(decl_285, type, esk75_0: $i).
% 172.84/29.76 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', ex1)).
% 172.84/29.76 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', singleton)).
% 172.84/29.76 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', replAx)).
% 172.84/29.76 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', exu)).
% 172.84/29.76 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', descrp)).
% 172.84/29.76 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', exuE1)).
% 172.84/29.76 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', exuE3e)).
% 172.84/29.76 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', nonempty)).
% 172.84/29.76 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', nonemptyI)).
% 172.84/29.76 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', exuE2)).
% 172.84/29.76 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', exuI1)).
% 172.84/29.76 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', exuI3)).
% 172.84/29.76 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', exuI2)).
% 172.84/29.76 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', exuE3u)).
% 172.84/29.76 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', exu__Cong)).
% 172.84/29.76 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', exuEu)).
% 172.84/29.76 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', descr__Cong)).
% 172.84/29.76 thf(iskpair, axiom, ((iskpair)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ (setunion @ X4)))&(?[X3:$i]:((((in @ X3 @ (setunion @ X4)))&(((X4)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', iskpair)).
% 172.84/29.76 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', singletonprop)).
% 172.84/29.76 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', ex1E1)).
% 172.84/29.76 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', ex1I)).
% 172.84/29.76 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/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', ex1I2)).
% 172.84/29.76 thf(setukpairinjL1, 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)=>![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/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setukpairinjL1)).
% 172.84/29.76 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', dsetconstrI)).
% 172.84/29.76 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', dsetconstrEL)).
% 172.84/29.76 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', dsetconstrER)).
% 172.84/29.76 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setbeta)).
% 172.84/29.76 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', nonemptyE1)).
% 172.84/29.76 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', nonemptyI1)).
% 172.84/29.76 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setoftrueEq)).
% 172.84/29.76 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', nonemptyImpWitness)).
% 172.84/29.76 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', emptyE1)).
% 172.84/29.76 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', dsetconstr__Cong)).
% 172.84/29.76 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', sepInPowerset)).
% 172.84/29.76 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', sepSubset)).
% 172.84/29.76 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', kpairiskpair)).
% 172.84/29.76 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', kpairp)).
% 172.84/29.76 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', cartprodmempair)).
% 172.84/29.76 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setextAx)).
% 172.84/29.76 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', emptysetAx)).
% 172.84/29.76 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setadjoinAx)).
% 172.84/29.76 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', powersetAx)).
% 172.84/29.76 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setunionAx)).
% 172.84/29.76 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', omega0Ax)).
% 172.84/29.76 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', omegaSAx)).
% 172.84/29.76 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', omegaIndAx)).
% 172.84/29.76 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', foundationAx)).
% 172.84/29.76 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', wellorderingAx)).
% 172.84/29.76 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', prop2setE)).
% 172.84/29.76 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', emptysetE)).
% 172.84/29.76 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', emptysetimpfalse)).
% 172.84/29.76 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', notinemptyset)).
% 172.84/29.76 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setext)).
% 172.84/29.76 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', emptyI)).
% 172.84/29.76 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', noeltsimpempty)).
% 172.84/29.76 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setadjoinIL)).
% 172.84/29.76 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', emptyinunitempty)).
% 172.84/29.76 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setadjoinIR)).
% 172.84/29.76 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setadjoinE)).
% 172.84/29.76 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setadjoinOr)).
% 172.84/29.76 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', powersetI)).
% 172.84/29.76 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', emptyinPowerset)).
% 172.84/29.76 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', emptyInPowerset)).
% 172.84/29.76 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', powersetE)).
% 172.84/29.76 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setunionI)).
% 172.84/29.76 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setunionE)).
% 172.84/29.76 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', subPowSU)).
% 172.84/29.76 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', uniqinunit)).
% 172.84/29.76 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', notinsingleton)).
% 172.84/29.76 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', eqinunit)).
% 172.84/29.76 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', singletonsswitch)).
% 172.84/29.76 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', upairsetE)).
% 172.84/29.76 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', upairsetIL)).
% 172.84/29.76 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', upairsetIR)).
% 172.84/29.76 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', vacuousDall)).
% 172.84/29.76 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', quantDeMorgan1)).
% 172.84/29.76 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', quantDeMorgan2)).
% 172.84/29.76 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', quantDeMorgan3)).
% 172.84/29.76 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', quantDeMorgan4)).
% 172.84/29.76 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', prop2setI)).
% 172.84/29.76 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', prop2set2propI)).
% 172.84/29.76 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', notdexE)).
% 172.84/29.76 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', notdallE)).
% 172.84/29.76 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', inCongP)).
% 172.84/29.76 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', in__Cong)).
% 172.84/29.76 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', emptyset__Cong)).
% 172.84/29.76 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setadjoin__Cong)).
% 172.84/29.76 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', powerset__Cong)).
% 172.84/29.76 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setunion__Cong)).
% 172.84/29.76 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', omega__Cong)).
% 172.84/29.76 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', subsetI1)).
% 172.84/29.76 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', eqimpsubset2)).
% 172.84/29.76 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', eqimpsubset1)).
% 172.84/29.76 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', subsetI2)).
% 172.84/29.76 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', emptysetsubset)).
% 172.84/29.76 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', subsetE)).
% 172.84/29.76 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', subsetE2)).
% 172.84/29.76 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', notsubsetI)).
% 172.84/29.76 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', notequalI1)).
% 172.84/29.76 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', notequalI2)).
% 172.84/29.76 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', subsetRefl)).
% 172.84/29.76 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', subsetTrans)).
% 172.84/29.76 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setadjoinSub)).
% 172.84/29.76 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setadjoinSub2)).
% 172.84/29.76 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', subset2powerset)).
% 172.84/29.76 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setextsub)).
% 172.84/29.76 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', subsetemptysetimpeq)).
% 172.84/29.76 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', powersetI1)).
% 172.84/29.76 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', powersetE1)).
% 172.84/29.76 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', inPowerset)).
% 172.84/29.76 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', powersetsubset)).
% 172.84/29.76 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binunionIL)).
% 172.84/29.76 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', upairset2IR)).
% 172.84/29.76 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binunionIR)).
% 172.84/29.76 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binunionEcases)).
% 172.84/29.76 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binunionE)).
% 172.84/29.76 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binunionLsub)).
% 172.84/29.76 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binunionRsub)).
% 172.84/29.76 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binintersectI)).
% 172.84/29.76 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binintersectSubset5)).
% 172.84/29.76 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binintersectEL)).
% 172.84/29.76 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binintersectLsub)).
% 172.84/29.76 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binintersectSubset2)).
% 172.84/29.76 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binintersectSubset3)).
% 172.84/29.76 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binintersectER)).
% 172.84/29.76 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', disjointsetsI1)).
% 172.84/29.76 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binintersectRsub)).
% 172.84/29.76 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binintersectSubset4)).
% 172.84/29.76 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', binintersectSubset1)).
% 172.84/29.76 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', bs114d)).
% 172.84/29.76 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setminusI)).
% 172.84/29.76 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setminusEL)).
% 172.84/29.76 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setminusER)).
% 172.84/29.76 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setminusSubset2)).
% 172.84/29.76 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setminusERneg)).
% 172.84/29.76 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setminusELneg)).
% 172.84/29.76 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setminusILneg)).
% 172.84/29.76 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setminusIRneg)).
% 172.84/29.76 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setminusLsub)).
% 172.84/29.76 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setminusSubset1)).
% 172.84/29.76 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', symdiffE)).
% 172.84/29.76 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', symdiffI1)).
% 172.84/29.76 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', symdiffI2)).
% 172.84/29.76 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', symdiffIneg1)).
% 172.84/29.76 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', symdiffIneg2)).
% 172.84/29.76 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', secondinupair)).
% 172.84/29.76 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setukpairIL)).
% 172.84/29.76 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setukpairIR)).
% 172.84/29.76 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', singletonsubset)).
% 172.84/29.76 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', singletoninpowerset)).
% 172.84/29.76 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', singletoninpowunion)).
% 172.84/29.76 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', upairset2E)).
% 172.84/29.76 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', upairsubunion)).
% 172.84/29.76 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', upairinpowunion)).
% 172.84/29.76 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', ubforcartprodlem1)).
% 172.84/29.76 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', ubforcartprodlem2)).
% 172.84/29.76 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', ubforcartprodlem3)).
% 172.84/29.76 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', cartprodpairin)).
% 172.84/29.76 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', cartprodmempair1)).
% 172.84/29.76 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setunionE2)).
% 172.84/29.76 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setunionsingleton1)).
% 172.84/29.76 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setunionsingleton2)).
% 172.84/29.76 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', setunionsingleton)).
% 172.84/29.76 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.qq76pFyKqn/E---3.1_2166839.p', singletonsuniq)).
% 172.84/29.76 thf(c_0_164, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X491:$i]:((((in @ X491 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X491 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 172.84/29.76 thf(c_0_165, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 172.84/29.76 thf(c_0_166, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 172.84/29.76 thf(c_0_167, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 172.84/29.76 thf(c_0_168, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 172.84/29.76 thf(c_0_169, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 172.84/29.76 thf(c_0_170, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 172.84/29.76 thf(c_0_171, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 172.84/29.76 thf(c_0_172, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 172.84/29.76 thf(c_0_173, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 172.84/29.76 thf(c_0_174, 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])).
% 172.84/29.76 thf(c_0_175, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 172.84/29.76 thf(c_0_176, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 172.84/29.76 thf(c_0_177, 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])).
% 172.84/29.76 thf(c_0_178, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 172.84/29.76 thf(c_0_179, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 172.84/29.76 thf(c_0_180, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 172.84/29.76 thf(c_0_181, plain, ((iskpair)=(^[Z0:$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])).
% 172.84/29.76 thf(c_0_182, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 172.84/29.76 thf(c_0_183, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 172.84/29.76 thf(c_0_184, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X491:$i]:((((in @ X491 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X491 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_164, c_0_165])).
% 172.84/29.76 thf(c_0_185, 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])).
% 172.84/29.76 thf(c_0_186, 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])).
% 172.84/29.76 thf(c_0_187, 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)=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setukpairinjL1])).
% 172.84/29.76 thf(c_0_188, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X456:$i]:(((((X6 @ X2 @ X456)))&(![X457:$i]:(((((X6 @ X2 @ X457)))=>(((X456)=(X457)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_166, c_0_167])).
% 172.84/29.76 thf(c_0_189, plain, ((descrp)=(![X1:$i > $o]:((((?[X458:$i]:(((((X1 @ X458)))&(![X459:$i]:(((((X1 @ X459)))=>(((X458)=(X459))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_168, c_0_167])).
% 172.84/29.76 thf(c_0_190, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 172.84/29.76 thf(c_0_191, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 172.84/29.76 thf(c_0_192, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 172.84/29.76 thf(c_0_193, plain, ((exuE1)=(![X1:$i > $o]:((((?[X460:$i]:(((((X1 @ X460)))&(![X461:$i]:(((((X1 @ X461)))=>(((X460)=(X461))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_169, c_0_167])).
% 172.84/29.76 thf(c_0_194, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X462:$i]:(((((X1 @ X462)))&(![X463:$i]:(((((X1 @ X463)))=>(((X462)=(X463))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_170, c_0_167])).
% 172.84/29.76 thf(c_0_195, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 172.84/29.76 thf(c_0_196, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_171])).
% 172.84/29.76 thf(c_0_197, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_172, c_0_171])).
% 172.84/29.76 thf(c_0_198, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_171])).
% 172.84/29.76 thf(c_0_199, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 172.84/29.76 thf(c_0_200, plain, ((exuE2)=(![X1:$i > $o]:((((?[X464:$i]:(((((X1 @ X464)))&(![X465:$i]:(((((X1 @ X465)))=>(((X464)=(X465))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_173, c_0_167])).
% 172.84/29.76 thf(c_0_201, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_171])).
% 172.84/29.76 thf(c_0_202, 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])).
% 172.84/29.76 thf(c_0_203, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X466:$i]:(((((X1 @ X466)))&(![X467:$i]:(((((X1 @ X467)))=>(((X466)=(X467)))))))))))))), inference(apply_def,[status(thm)],[c_0_174, c_0_167])).
% 172.84/29.76 thf(c_0_204, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X468:$i]:(((((X1 @ X468)))&(![X469:$i]:(((((X1 @ X469)))=>(((X468)=(X469)))))))))))))))), inference(apply_def,[status(thm)],[c_0_175, c_0_167])).
% 172.84/29.76 thf(c_0_205, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X470:$i]:(((((X1 @ X470)))&(![X471:$i]:(((((X1 @ X471)))=>(((X470)=(X471)))))))))))))), inference(apply_def,[status(thm)],[c_0_176, c_0_167])).
% 172.84/29.76 thf(c_0_206, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X472:$i]:(((((X1 @ X472)))&(![X473:$i]:(((((X1 @ X473)))=>(((X472)=(X473))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_177, c_0_167])).
% 172.84/29.76 thf(c_0_207, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X474:$i]:(((((X1 @ X474)))&(![X475:$i]:(((((X1 @ X475)))=>(((X474)=(X475))))))))))<=>((?[X476:$i]:(((((X17 @ X476)))&(![X477:$i]:(((((X17 @ X477)))=>(((X476)=(X477)))))))))))))))), inference(apply_def,[status(thm)],[c_0_178, c_0_167])).
% 172.84/29.76 thf(c_0_208, plain, ((exuEu)=(![X1:$i > $o]:((((?[X478:$i]:(((((X1 @ X478)))&(![X479:$i]:(((((X1 @ X479)))=>(((X478)=(X479))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_179, c_0_167])).
% 172.84/29.76 thf(c_0_209, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X480:$i]:(((((X1 @ X480)))&(![X481:$i]:(((((X1 @ X481)))=>(((X480)=(X481))))))))))=>((((?[X482:$i]:(((((X17 @ X482)))&(![X483:$i]:(((((X17 @ X483)))=>(((X482)=(X483))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_180, c_0_167])).
% 172.84/29.76 thf(c_0_210, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 172.84/29.76 thf(c_0_211, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 172.84/29.76 thf(c_0_212, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 172.84/29.76 thf(c_0_213, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X484:$i]:((((in @ X484 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(?[X485:$i]:((((in @ X485 @ (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 @ X484 @ emptyset) @ (setadjoin @ (setadjoin @ X484 @ (setadjoin @ X485 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_181])).
% 172.84/29.76 thf(c_0_214, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X486:$i]:((((in @ X486 @ (setunion @ (kpair @ X2 @ X3))))&(?[X487:$i]:((((in @ X487 @ (setunion @ (kpair @ X2 @ X3))))&(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X486 @ emptyset) @ (setadjoin @ (setadjoin @ X486 @ (setadjoin @ X487 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_181])).
% 172.84/29.76 thf(c_0_215, axiom, ((cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:((((in @ X18 @ (cartprod @ X4 @ X5)))=>((?[X488:$i]:((((in @ X488 @ (setunion @ X18)))&(?[X489:$i]:((((in @ X489 @ (setunion @ X18)))&(((X18)=(setadjoin @ (setadjoin @ X488 @ emptyset) @ (setadjoin @ (setadjoin @ X488 @ (setadjoin @ X489 @ emptyset)) @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[cartprodmempair, c_0_181])).
% 172.84/29.76 thf(c_0_216, plain, ((singletonprop)=(![X4:$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)))))=>((?[X490:$i]:((((in @ X490 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X490 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_182, c_0_165])).
% 172.84/29.76 thf(c_0_217, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X492:$i]:((((in @ X492 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X492 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_183, c_0_184])).
% 172.84/29.76 thf(c_0_218, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X493:$i]:((((in @ X493 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X493 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_185, c_0_184])).
% 172.84/29.76 thf(c_0_219, 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)))))=>((?[X494:$i]:((((in @ X494 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X494 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_186, c_0_184])).
% 172.84/29.76 thf(c_0_220, plain, ((epred1_0)<=>![X524:$i]:(?[X525:$i]:((((![X526:$i]:(((in @ X526 @ X525)=>![X527:$i]:(((in @ X527 @ X526)=>(in @ X527 @ X524)))))&![X528:$i, X529:$i]:((((in @ X528 @ X524)&(in @ X529 @ X524))=>(![X530:$i]:(((in @ X530 @ X525)=>((in @ X528 @ X530)<=>(in @ X529 @ X530))))=>((X528)=(X529))))))&![X531:$i, X532:$i]:((((in @ X531 @ X525)&(in @ X532 @ X525))=>(![X533:$i]:(((in @ X533 @ X531)=>(in @ X533 @ X532)))|![X534:$i]:(((in @ X534 @ X532)=>(in @ X534 @ X531)))))))&![X535:$i]:(((![X536:$i]:(((in @ X536 @ X535)=>(in @ X536 @ X524)))&?[X537:$i]:((in @ X537 @ X535)))=>?[X538:$i, X539:$i]:(((((in @ X538 @ X525)&(in @ X539 @ X535))&~(?[X540:$i]:(((in @ X540 @ X538)&(in @ X540 @ X535)))))&![X541:$i]:(((in @ X541 @ X525)=>(![X542:$i]:(((in @ X542 @ X541)=>(in @ X542 @ X538)))|(in @ X539 @ X541)))))))))))), introduced(definition)).
% 172.84/29.76 thf(c_0_221, negated_conjecture, ~((![X495:$i, X496:$i]:((![X497:$i]:(((in @ X497 @ X495)<=>(in @ X497 @ X496)))=>((X495)=(X496))))=>(![X498:$i]:(~(in @ X498 @ emptyset))=>(![X499:$i, X500:$i, X501:$i]:(((in @ X501 @ (setadjoin @ X499 @ X500))<=>(((X501)=(X499))|(in @ X501 @ X500))))=>(![X502:$i, X503:$i]:(((in @ X503 @ (powerset @ X502))<=>![X504:$i]:(((in @ X504 @ X503)=>(in @ X504 @ X502)))))=>(![X505:$i, X506:$i]:(((in @ X506 @ (setunion @ X505))<=>?[X507:$i]:(((in @ X506 @ X507)&(in @ X507 @ X505)))))=>((in @ emptyset @ omega)=>(![X508:$i]:(((in @ X508 @ omega)=>(in @ (setadjoin @ X508 @ X508) @ omega)))=>(![X509:$i]:((((in @ emptyset @ X509)&![X510:$i]:((((in @ X510 @ omega)&(in @ X510 @ X509))=>(in @ (setadjoin @ X510 @ X510) @ X509))))=>![X511:$i]:(((in @ X511 @ omega)=>(in @ X511 @ X509)))))=>(![X512:$i > $i > $o, X513:$i]:((![X514:$i]:(((in @ X514 @ X513)=>?[X515:$i]:(((X512 @ X514 @ X515)&![X516:$i]:(((X512 @ X514 @ X516)=>((X515)=(X516))))))))=>?[X517:$i]:(![X518:$i]:(((in @ X518 @ X517)<=>?[X519:$i]:(((in @ X519 @ X513)&(X512 @ X519 @ X518))))))))=>(![X520:$i]:((?[X521:$i]:((in @ X521 @ X520))=>?[X522:$i]:(((in @ X522 @ X520)&~(?[X523:$i]:(((in @ X523 @ X522)&(in @ X523 @ X520))))))))=>((epred1_0)=>(![X543:$i > $o]:((?[X544:$i]:(((X543 @ X544)&![X545:$i]:(((X543 @ X545)=>((X544)=(X545))))))=>(X543 @ (descr @ (^[Z0:$i]:(X543 @ Z0))))))=>(![X546:$i, X547:$i > $o, X548:$i]:(((in @ X548 @ X546)=>((X547 @ X548)=>(in @ X548 @ (dsetconstr @ X546 @ X547)))))=>(![X549:$i, X550:$i > $o, X551:$i]:(((in @ X551 @ (dsetconstr @ X549 @ X550))=>(in @ X551 @ X549)))=>(![X552:$i, X553:$i > $o, X554:$i]:(((in @ X554 @ (dsetconstr @ X552 @ X553))=>(X553 @ X554)))=>(![X555:$i > $o]:((?[X556:$i]:(((X555 @ X556)&![X557:$i]:(((X555 @ X557)=>((X556)=(X557))))))=>?[X558:$i]:(((X555 @ X558)&![X559:$i]:(((X555 @ X559)=>((X558)=(X559))))))))=>(![X560:$o, X561:$i]:(((in @ X561 @ (prop2set @ ((X560))))=>(X560)))=>(![X562:$i]:(((in @ X562 @ emptyset)=>![X563:$o]:((X563))))=>(![X564:$i]:(((in @ X564 @ emptyset)=>~($true)))=>(![X565:$i]:(~(in @ X565 @ emptyset))=>(![X566:$i > $o]:((?[X567:$i]:(((X566 @ X567)&![X568:$i]:(((X566 @ X568)=>((X567)=(X568))))))=>?[X569:$i]:((X566 @ X569))))=>(![X570:$i, X571:$i]:((![X572:$i]:(((in @ X572 @ X570)=>(in @ X572 @ X571)))=>(![X573:$i]:(((in @ X573 @ X571)=>(in @ X573 @ X570)))=>((X570)=(X571)))))=>(![X574:$i]:((![X575:$i]:(~(in @ X575 @ X574))=>((X574)=(emptyset))))=>(![X576:$i]:((![X577:$i]:(~(in @ X577 @ X576))=>((X576)=(emptyset))))=>(![X578:$i, X579:$i > $o, X580:$i]:(((in @ X580 @ X578)=>((in @ X580 @ (dsetconstr @ X578 @ X579))<=>(X579 @ X580))))=>(![X581:$i]:((((X581)!=(emptyset))=>?[X582:$i]:((in @ X582 @ X581))))=>(![X583:$i, X584:$i > $o, X585:$i]:(((in @ X585 @ X583)=>((X584 @ X585)=>((dsetconstr @ X583 @ X584)!=(emptyset)))))=>(![X586:$i]:((?[X587:$i]:((in @ X587 @ X586))=>((X586)!=(emptyset))))=>(![X588:$i, X589:$i]:((in @ X588 @ (setadjoin @ X588 @ X589)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X590:$i, X591:$i, X592:$i]:(((in @ X592 @ X591)=>(in @ X592 @ (setadjoin @ X590 @ X591))))=>(![X593:$i, X594:$i, X595:$i]:(((in @ X595 @ (setadjoin @ X593 @ X594))=>![X596:$o]:(((((X595)=(X593))=>(X596))=>(((in @ X595 @ X594)=>(X596))=>(X596))))))=>(![X597:$i, X598:$i, X599:$i]:(((in @ X599 @ (setadjoin @ X597 @ X598))=>(((X599)=(X597))|(in @ X599 @ X598))))=>(![X600:$i]:(((dsetconstr @ X600 @ (^[Z0:$i]:($true)))=(X600)))=>(![X601:$i, X602:$i]:((![X603:$i]:(((in @ X603 @ X602)=>(in @ X603 @ X601)))=>(in @ X602 @ (powerset @ X601))))=>(![X604:$i]:((in @ emptyset @ (powerset @ X604)))=>(![X605:$i]:((in @ emptyset @ (powerset @ X605)))=>(![X606:$i, X607:$i, X608:$i]:(((in @ X607 @ (powerset @ X606))=>((in @ X608 @ X607)=>(in @ X608 @ X606))))=>(![X609:$i, X610:$i, X611:$i]:(((in @ X610 @ X611)=>((in @ X611 @ X609)=>(in @ X610 @ (setunion @ X609)))))=>(![X612:$i, X613:$i]:(((in @ X613 @ (setunion @ X612))=>![X614:$o]:((![X615:$i]:(((in @ X613 @ X615)=>((in @ X615 @ X612)=>(X614))))=>(X614)))))=>(![X616:$i, X617:$i]:(((in @ X617 @ X616)=>(in @ X617 @ (powerset @ (setunion @ X616)))))=>(![X618:$i > $o]:((?[X619:$i]:(((X618 @ X619)&![X620:$i]:(((X618 @ X620)=>((X619)=(X620))))))=>?[X621:$i]:(![X622:$i]:(((X618 @ X622)<=>((X622)=(X621)))))))=>(![X623:$i]:((((X623)!=(emptyset))=>?[X624:$i]:(((in @ X624 @ X623)&$true))))=>(![X625:$i, X626:$i]:(((in @ X625 @ (setadjoin @ X626 @ emptyset))=>((X625)=(X626))))=>(![X627:$i, X628:$i]:((((X627)!=(X628))=>~(in @ X628 @ (setadjoin @ X627 @ emptyset))))=>(![X629:$i, X630:$i]:((((X629)=(X630))=>(in @ X629 @ (setadjoin @ X630 @ emptyset))))=>(![X631:$i, X632:$i]:(((in @ X631 @ (setadjoin @ X632 @ emptyset))=>(in @ X632 @ (setadjoin @ X631 @ emptyset))))=>(![X633:$i, X634:$i, X635:$i]:(((in @ X635 @ (setadjoin @ X633 @ (setadjoin @ X634 @ emptyset)))=>(((X635)=(X633))|((X635)=(X634)))))=>(![X636:$i, X637:$i]:((in @ X636 @ (setadjoin @ X636 @ (setadjoin @ X637 @ emptyset))))=>(![X638:$i, X639:$i]:((in @ X639 @ (setadjoin @ X638 @ (setadjoin @ X639 @ emptyset))))=>(![X640:$i, X641:$i > $o]:((?[X642:$i]:(((in @ X642 @ X640)&(X641 @ X642)))=>(((dsetconstr @ X640 @ X641)=(emptyset))=>~($true))))=>(![X643:$i > $o, X644:$i]:(((in @ X644 @ emptyset)=>(X643 @ X644)))=>(![X645:$i, X646:$i > $o]:((~(![X647:$i]:(((in @ X647 @ X645)=>(X646 @ X647))))=>?[X648:$i]:(((in @ X648 @ X645)&~((X646 @ X648))))))=>(![X649:$i, X650:$i > $o]:((![X651:$i]:(((in @ X651 @ X649)=>~((X650 @ X651))))=>~(?[X652:$i]:(((in @ X652 @ X649)&(X650 @ X652))))))=>(![X653:$i, X654:$i > $o]:((~(?[X655:$i]:(((in @ X655 @ X653)&(X654 @ X655))))=>![X656:$i]:(((in @ X656 @ X653)=>~((X654 @ X656))))))=>(![X657:$i, X658:$i > $o]:((?[X659:$i]:(((in @ X659 @ X657)&~((X658 @ X659))))=>~(![X660:$i]:(((in @ X660 @ X657)=>(X658 @ X660))))))=>(![X661:$o]:(((X661)=>(in @ emptyset @ (prop2set @ ((X661))))))=>(![X662:$o]:(((X662)=>(set2prop @ (prop2set @ ((X662))))))=>(![X663:$i, X664:$i > $o]:((~(?[X665:$i]:(((in @ X665 @ X663)&(X664 @ X665))))=>![X666:$i]:(((in @ X666 @ X663)=>~((X664 @ X666))))))=>(![X667:$i, X668:$i > $o]:((~(![X669:$i]:(((in @ X669 @ X667)=>(X668 @ X669))))=>?[X670:$i]:(((in @ X670 @ X667)&~((X668 @ X670))))))=>(![X671:$i > $o]:((?[X672:$i]:(((X671 @ X672)&![X673:$i]:(((X671 @ X673)=>((X672)=(X673))))))=>?[X674:$i]:(((X671 @ X674)&![X675:$i]:(((X671 @ X675)=>((X674)=(X675))))))))=>(![X676:$i > $o]:((?[X677:$i]:((X676 @ X677))=>(![X678:$i, X679:$i]:(((X676 @ X678)=>((X676 @ X679)=>((X678)=(X679)))))=>?[X680:$i]:(((X676 @ X680)&![X681:$i]:(((X676 @ X681)=>((X680)=(X681)))))))))=>(![X682:$i > $o]:((?[X683:$i]:(![X684:$i]:(((X682 @ X684)<=>((X684)=(X683)))))=>?[X685:$i]:(((X682 @ X685)&![X686:$i]:(((X682 @ X686)=>((X685)=(X686))))))))=>(![X687:$i, X688:$i]:((((X687)=(X688))=>![X689:$i, X690:$i]:((((X689)=(X690))=>((in @ X689 @ X687)=>(in @ X690 @ X688))))))=>(![X691:$i, X692:$i]:((((X691)=(X692))=>![X693:$i, X694:$i]:((((X693)=(X694))=>((in @ X693 @ X691)<=>(in @ X694 @ X692))))))=>(![X695:$i > $o]:((?[X696:$i]:(((X695 @ X696)&![X697:$i]:(((X695 @ X697)=>((X696)=(X697))))))=>![X698:$i, X699:$i]:(((X695 @ X698)=>((X695 @ X699)=>((X698)=(X699)))))))=>(![X700:$i > $o, X701:$i > $o]:((![X702:$i, X703:$i]:((((X702)=(X703))=>((X700 @ X702)<=>(X701 @ X703))))=>(?[X704:$i]:(((X700 @ X704)&![X705:$i]:(((X700 @ X705)=>((X704)=(X705))))))<=>?[X706:$i]:(((X701 @ X706)&![X707:$i]:(((X701 @ X707)=>((X706)=(X707)))))))))=>(((emptyset)=(emptyset))=>(![X708:$i, X709:$i]:((((X708)=(X709))=>![X710:$i, X711:$i]:((((X710)=(X711))=>((setadjoin @ X708 @ X710)=(setadjoin @ X709 @ X711))))))=>(![X712:$i, X713:$i]:((((X712)=(X713))=>((powerset @ X712)=(powerset @ X713))))=>(![X714:$i, X715:$i]:((((X714)=(X715))=>((setunion @ X714)=(setunion @ X715))))=>(((omega)=(omega))=>(![X716:$i > $o]:((?[X717:$i]:(((X716 @ X717)&![X718:$i]:(((X716 @ X718)=>((X717)=(X718))))))=>![X719:$i, X720:$i]:(((X716 @ X719)=>((X716 @ X720)=>((X719)=(X720)))))))=>(![X721:$i > $o, X722:$i > $o]:((![X723:$i, X724:$i]:((((X723)=(X724))=>((X721 @ X723)<=>(X722 @ X724))))=>(?[X725:$i]:(((X721 @ X725)&![X726:$i]:(((X721 @ X726)=>((X725)=(X726))))))=>(?[X727:$i]:(((X722 @ X727)&![X728:$i]:(((X722 @ X728)=>((X727)=(X728))))))=>((descr @ X721)=(descr @ X722))))))=>(![X729:$i, X730:$i]:((((X729)=(X730))=>![X731:$i > $o, X732:$i > $o]:((![X733:$i]:(((in @ X733 @ X729)=>![X734:$i]:(((in @ X734 @ X730)=>(((X733)=(X734))=>((X731 @ X733)<=>(X732 @ X734)))))))=>((dsetconstr @ X729 @ X731)=(dsetconstr @ X730 @ X732))))))=>(![X735:$i, X736:$i]:((![X737:$i]:(((in @ X737 @ X735)=>(in @ X737 @ X736)))=>(subset @ X735 @ X736)))=>(![X738:$i, X739:$i]:((((X738)=(X739))=>(subset @ X739 @ X738)))=>(![X740:$i, X741:$i]:((((X740)=(X741))=>(subset @ X740 @ X741)))=>(![X742:$i, X743:$i]:((![X744:$i]:(((in @ X744 @ X742)=>(in @ X744 @ X743)))=>(subset @ X742 @ X743)))=>(![X745:$i]:((subset @ emptyset @ X745))=>(![X746:$i, X747:$i, X748:$i]:(((subset @ X746 @ X747)=>((in @ X748 @ X746)=>(in @ X748 @ X747))))=>(![X749:$i, X750:$i, X751:$i]:(((subset @ X749 @ X750)=>(~(in @ X751 @ X750)=>~(in @ X751 @ X749))))=>(![X752:$i, X753:$i, X754:$i]:(((in @ X754 @ X752)=>(~(in @ X754 @ X753)=>~(subset @ X752 @ X753))))=>(![X755:$i, X756:$i]:((~(subset @ X755 @ X756)=>((X755)!=(X756))))=>(![X757:$i, X758:$i, X759:$i]:(((in @ X759 @ X757)=>(~(in @ X759 @ X758)=>((X757)!=(X758)))))=>(![X760:$i]:((subset @ X760 @ X760))=>(![X761:$i, X762:$i, X763:$i]:(((subset @ X761 @ X762)=>((subset @ X762 @ X763)=>(subset @ X761 @ X763))))=>(![X764:$i, X765:$i]:((subset @ X765 @ (setadjoin @ X764 @ X765)))=>(![X766:$i, X767:$i, X768:$i]:(((subset @ X766 @ X768)=>(subset @ X766 @ (setadjoin @ X767 @ X768))))=>(![X769:$i, X770:$i]:(((subset @ X769 @ X770)=>(in @ X769 @ (powerset @ X770))))=>(![X771:$i, X772:$i]:(((subset @ X771 @ X772)=>((subset @ X772 @ X771)=>((X771)=(X772)))))=>(![X773:$i]:(((subset @ X773 @ emptyset)=>((X773)=(emptyset))))=>(![X774:$i, X775:$i]:(((subset @ X775 @ X774)=>(in @ X775 @ (powerset @ X774))))=>(![X776:$i, X777:$i]:(((in @ X777 @ (powerset @ X776))=>(subset @ X777 @ X776)))=>(![X778:$i]:((in @ X778 @ (powerset @ X778)))=>(![X779:$i, X780:$i]:(((subset @ X779 @ X780)=>(subset @ (powerset @ X779) @ (powerset @ X780))))=>(![X781:$i, X782:$i > $o]:((in @ (dsetconstr @ X781 @ X782) @ (powerset @ X781)))=>(![X783:$i, X784:$i > $o]:((subset @ (dsetconstr @ X783 @ X784) @ X783))=>(![X785:$i, X786:$i, X787:$i]:(((in @ X787 @ X785)=>(in @ X787 @ (binunion @ X785 @ X786))))=>(![X788:$i, X789:$i]:((in @ X789 @ (setadjoin @ X788 @ (setadjoin @ X789 @ emptyset))))=>(![X790:$i, X791:$i, X792:$i]:(((in @ X792 @ X791)=>(in @ X792 @ (binunion @ X790 @ X791))))=>(![X793:$i, X794:$i, X795:$i, X796:$o]:(((in @ X795 @ (binunion @ X793 @ X794))=>(((in @ X795 @ X793)=>(X796))=>(((in @ X795 @ X794)=>(X796))=>(X796)))))=>(![X797:$i, X798:$i, X799:$i]:(((in @ X799 @ (binunion @ X797 @ X798))=>((in @ X799 @ X797)|(in @ X799 @ X798))))=>(![X800:$i, X801:$i]:((subset @ X800 @ (binunion @ X800 @ X801)))=>(![X802:$i, X803:$i]:((subset @ X803 @ (binunion @ X802 @ X803)))=>(![X804:$i, X805:$i, X806:$i]:(((in @ X806 @ X804)=>((in @ X806 @ X805)=>(in @ X806 @ (binintersect @ X804 @ X805)))))=>(![X807:$i, X808:$i, X809:$i]:(((subset @ X809 @ X807)=>((subset @ X809 @ X808)=>(subset @ X809 @ (binintersect @ X807 @ X808)))))=>(![X810:$i, X811:$i, X812:$i]:(((in @ X812 @ (binintersect @ X810 @ X811))=>(in @ X812 @ X810)))=>(![X813:$i, X814:$i]:((subset @ (binintersect @ X813 @ X814) @ X813))=>(![X815:$i, X816:$i]:(((subset @ X815 @ X816)=>((binintersect @ X815 @ X816)=(X815))))=>(![X817:$i, X818:$i]:((((binintersect @ X817 @ X818)=(X818))=>(subset @ X818 @ X817)))=>(![X819:$i, X820:$i, X821:$i]:(((in @ X821 @ (binintersect @ X819 @ X820))=>(in @ X821 @ X820)))=>(![X822:$i, X823:$i]:((~(?[X824:$i]:(((in @ X824 @ X822)&(in @ X824 @ X823))))=>((binintersect @ X822 @ X823)=(emptyset))))=>(![X825:$i, X826:$i]:((subset @ (binintersect @ X825 @ X826) @ X826))=>(![X827:$i, X828:$i]:(((subset @ X828 @ X827)=>((binintersect @ X827 @ X828)=(X828))))=>(![X829:$i, X830:$i]:((((binintersect @ X829 @ X830)=(X829))=>(subset @ X829 @ X830)))=>(![X831:$i, X832:$i, X833:$i]:(((binintersect @ X831 @ (binunion @ X832 @ X833))=(binunion @ (binintersect @ X831 @ X832) @ (binintersect @ X831 @ X833))))=>(![X834:$i, X835:$i, X836:$i]:(((in @ X836 @ X834)=>(~(in @ X836 @ X835)=>(in @ X836 @ (setminus @ X834 @ X835)))))=>(![X837:$i, X838:$i, X839:$i]:(((in @ X839 @ (setminus @ X837 @ X838))=>(in @ X839 @ X837)))=>(![X840:$i, X841:$i, X842:$i]:(((in @ X842 @ (setminus @ X840 @ X841))=>~(in @ X842 @ X841)))=>(![X843:$i, X844:$i]:(((subset @ X843 @ X844)=>((setminus @ X843 @ X844)=(emptyset))))=>(![X845:$i, X846:$i, X847:$i]:((~(in @ X847 @ (setminus @ X845 @ X846))=>((in @ X847 @ X845)=>(in @ X847 @ X846))))=>(![X848:$i, X849:$i, X850:$i]:((~(in @ X850 @ (setminus @ X848 @ X849))=>(~(in @ X850 @ X849)=>~(in @ X850 @ X848))))=>(![X851:$i, X852:$i, X853:$i]:((~(in @ X853 @ X851)=>~(in @ X853 @ (setminus @ X851 @ X852))))=>(![X854:$i, X855:$i, X856:$i]:(((in @ X856 @ X855)=>~(in @ X856 @ (setminus @ X854 @ X855))))=>(![X857:$i, X858:$i]:((subset @ (setminus @ X857 @ X858) @ X857))=>(![X859:$i, X860:$i]:((((setminus @ X859 @ X860)=(emptyset))=>(subset @ X859 @ X860)))=>(![X861:$i, X862:$i, X863:$i]:(((in @ X863 @ (symdiff @ X861 @ X862))=>![X864:$o]:((((in @ X863 @ X861)=>(~(in @ X863 @ X862)=>(X864)))=>((~(in @ X863 @ X861)=>((in @ X863 @ X862)=>(X864)))=>(X864))))))=>(![X865:$i, X866:$i, X867:$i]:(((in @ X867 @ X865)=>(~(in @ X867 @ X866)=>(in @ X867 @ (symdiff @ X865 @ X866)))))=>(![X868:$i, X869:$i, X870:$i]:((~(in @ X870 @ X868)=>((in @ X870 @ X869)=>(in @ X870 @ (symdiff @ X868 @ X869)))))=>(![X871:$i, X872:$i, X873:$i]:(((in @ X873 @ X871)=>((in @ X873 @ X872)=>~(in @ X873 @ (symdiff @ X871 @ X872)))))=>(![X874:$i, X875:$i, X876:$i]:((~(in @ X876 @ X874)=>(~(in @ X876 @ X875)=>~(in @ X876 @ (symdiff @ X874 @ X875)))))=>(![X877:$i, X878:$i]:((in @ X878 @ (setadjoin @ X877 @ (setadjoin @ X878 @ emptyset))))=>(![X879:$i, X880:$i]:((in @ X879 @ (setunion @ (setadjoin @ (setadjoin @ X879 @ emptyset) @ (setadjoin @ (setadjoin @ X879 @ (setadjoin @ X880 @ emptyset)) @ emptyset)))))=>(![X881:$i, X882:$i]:((in @ X882 @ (setunion @ (setadjoin @ (setadjoin @ X881 @ emptyset) @ (setadjoin @ (setadjoin @ X881 @ (setadjoin @ X882 @ emptyset)) @ emptyset)))))=>(![X883:$i, X884:$i]:(?[X885:$i]:(((in @ X885 @ (setunion @ (setadjoin @ (setadjoin @ X883 @ emptyset) @ (setadjoin @ (setadjoin @ X883 @ (setadjoin @ X884 @ emptyset)) @ emptyset))))&?[X886:$i]:(((in @ X886 @ (setunion @ (setadjoin @ (setadjoin @ X883 @ emptyset) @ (setadjoin @ (setadjoin @ X883 @ (setadjoin @ X884 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X883 @ emptyset) @ (setadjoin @ (setadjoin @ X883 @ (setadjoin @ X884 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X885 @ emptyset) @ (setadjoin @ (setadjoin @ X885 @ (setadjoin @ X886 @ emptyset)) @ emptyset))))))))=>(![X887:$i, X888:$i]:(?[X889:$i]:(((in @ X889 @ (setunion @ (kpair @ X887 @ X888)))&?[X890:$i]:(((in @ X890 @ (setunion @ (kpair @ X887 @ X888)))&((kpair @ X887 @ X888)=(setadjoin @ (setadjoin @ X889 @ emptyset) @ (setadjoin @ (setadjoin @ X889 @ (setadjoin @ X890 @ emptyset)) @ emptyset))))))))=>(![X891:$i, X892:$i]:(((in @ X892 @ X891)=>(subset @ (setadjoin @ X892 @ emptyset) @ X891)))=>(![X893:$i, X894:$i]:(((in @ X894 @ X893)=>(in @ (setadjoin @ X894 @ emptyset) @ (powerset @ X893))))=>(![X895:$i, X896:$i, X897:$i]:(((in @ X897 @ X895)=>(in @ (setadjoin @ X897 @ emptyset) @ (powerset @ (binunion @ X895 @ X896)))))=>(![X898:$i, X899:$i, X900:$i]:(((in @ X900 @ (setadjoin @ X898 @ (setadjoin @ X899 @ emptyset)))=>(((X900)=(X898))|((X900)=(X899)))))=>(![X901:$i, X902:$i, X903:$i]:(((in @ X903 @ X901)=>![X904:$i]:(((in @ X904 @ X902)=>(subset @ (setadjoin @ X903 @ (setadjoin @ X904 @ emptyset)) @ (binunion @ X901 @ X902))))))=>(![X905:$i, X906:$i, X907:$i]:(((in @ X907 @ X905)=>![X908:$i]:(((in @ X908 @ X906)=>(in @ (setadjoin @ X907 @ (setadjoin @ X908 @ emptyset)) @ (powerset @ (binunion @ X905 @ X906)))))))=>(![X909:$i, X910:$i, X911:$i]:(((in @ X911 @ X909)=>![X912:$i]:(((in @ X912 @ X910)=>(subset @ (setadjoin @ (setadjoin @ X911 @ emptyset) @ (setadjoin @ (setadjoin @ X911 @ (setadjoin @ X912 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X909 @ X910)))))))=>(![X913:$i, X914:$i, X915:$i]:(((in @ X915 @ X913)=>![X916:$i]:(((in @ X916 @ X914)=>(in @ (setadjoin @ (setadjoin @ X915 @ emptyset) @ (setadjoin @ (setadjoin @ X915 @ (setadjoin @ X916 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X913 @ X914))))))))=>(![X917:$i, X918:$i, X919:$i]:(((in @ X919 @ X917)=>![X920:$i]:(((in @ X920 @ X918)=>(in @ (kpair @ X919 @ X920) @ (powerset @ (powerset @ (binunion @ X917 @ X918))))))))=>(![X921:$i, X922:$i, X923:$i]:(((in @ X923 @ X921)=>![X924:$i]:(((in @ X924 @ X922)=>(in @ (kpair @ X923 @ X924) @ (cartprod @ X921 @ X922))))))=>(![X925:$i, X926:$i, X927:$i]:(((in @ X927 @ (cartprod @ X925 @ X926))=>?[X928:$i]:(((in @ X928 @ X925)&?[X929:$i]:(((in @ X929 @ X926)&((X927)=(kpair @ X928 @ X929))))))))=>(![X930:$i, X931:$i, X932:$i]:(((in @ X932 @ (cartprod @ X930 @ X931))=>?[X933:$i]:(((in @ X933 @ (setunion @ X932))&?[X934:$i]:(((in @ X934 @ (setunion @ X932))&((X932)=(setadjoin @ (setadjoin @ X933 @ emptyset) @ (setadjoin @ (setadjoin @ X933 @ (setadjoin @ X934 @ emptyset)) @ emptyset)))))))))=>(![X935:$i, X936:$i]:(((in @ X936 @ (setunion @ X935))=>?[X937:$i]:(((in @ X937 @ X935)&(in @ X936 @ X937)))))=>(![X938:$i]:((subset @ (setunion @ (setadjoin @ X938 @ emptyset)) @ X938))=>(![X939:$i]:((subset @ X939 @ (setunion @ (setadjoin @ X939 @ emptyset))))=>(![X940:$i]:(((setunion @ (setadjoin @ X940 @ emptyset))=(X940)))=>(![X941:$i, X942:$i > $o]:((![X943:$i]:(((in @ X943 @ X941)=>![X944:$i]:(((in @ X944 @ X941)=>((X942 @ X943)=>((X942 @ X944)=>((X943)=(X944))))))))=>(?[X945:$i]:(((in @ X945 @ X941)&(X942 @ X945)))=>?[X946:$i]:(((in @ X946 @ (dsetconstr @ X941 @ X942))&((dsetconstr @ X941 @ X942)=(setadjoin @ X946 @ emptyset)))))))=>(![X947:$i, X948:$i > $o]:((?[X949:$i]:(((in @ X949 @ (dsetconstr @ X947 @ X948))&((dsetconstr @ X947 @ X948)=(setadjoin @ X949 @ emptyset))))=>?[X950:$i]:(((in @ X950 @ X947)&(X948 @ X950)))))=>(![X951:$i, X952:$i > $o, X953:$i]:(((in @ X953 @ X951)=>((X952 @ X953)=>(![X954:$i]:(((in @ X954 @ X951)=>((X952 @ X954)=>((X954)=(X953)))))=>?[X955:$i]:(((in @ X955 @ (dsetconstr @ X951 @ X952))&((dsetconstr @ X951 @ X952)=(setadjoin @ X955 @ emptyset))))))))=>(![X956:$i, X957:$i > $o]:((![X958:$i]:(((in @ X958 @ X956)=>![X959:$i]:(((in @ X959 @ X956)=>((X957 @ X958)=>((X957 @ X959)=>((X958)=(X959))))))))=>(?[X960:$i]:(((in @ X960 @ X956)&(X957 @ X960)))=>?[X961:$i]:(((in @ X961 @ (dsetconstr @ X956 @ X957))&((dsetconstr @ X956 @ X957)=(setadjoin @ X961 @ emptyset)))))))=>(![X962:$i, X963:$i]:((((setadjoin @ X962 @ emptyset)=(setadjoin @ X963 @ emptyset))=>((X962)=(X963))))=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_187, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_188]), foundationAx]), wellorderingAx]), c_0_189]), c_0_190]), c_0_191]), c_0_192]), c_0_193]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_194]), setext]), emptyI]), noeltsimpempty]), c_0_195]), c_0_196]), c_0_197]), c_0_198]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_199]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_200]), c_0_201]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_202]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_203]), c_0_204]), c_0_205]), inCongP]), in__Cong]), c_0_206]), c_0_207]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_208]), c_0_209]), c_0_210]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_211]), c_0_212]), 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_213]), c_0_214]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), c_0_215]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_216]), c_0_217]), c_0_218]), c_0_219]), singletonsuniq])])]), c_0_220])).
% 172.84/29.77 thf(c_0_222, negated_conjecture, ![X968:$i, X969:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i, X977:$i, X978:$i, X979:$i, X981:$i, X982:$i, X984:$i, X985:$i, X986:$i, X987:$i, X988:$i, X990:$i, X991:$i > $i > $o, X992:$i, X994:$i, X997:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1004:$i, X1005:$i > $o, X1006:$i, X1008:$i, X1009:$i > $o, X1010:$i, X1011:$i, X1012:$i > $o, X1013:$i, X1014:$i, X1015:$i > $o, X1016:$i, X1017:$i > $o, X1018:$i, X1021:$i, X1022:$o, X1023:$i, X1024:$i, X1025:$o, X1026:$i, X1027:$i, X1028:$i > $o, X1029:$i, X1032:$i, X1033:$i, X1036:$i, X1038:$i, X1040:$i, X1041:$i > $o, X1042:$i, X1043:$i, X1045:$i, X1046:$i > $o, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1055:$i, X1056:$i, X1057:$i, X1058:$o, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i, X1064:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1075:$i, X1076:$o, X1078:$i, X1079:$i, X1080:$i > $o, X1081:$i, X1084:$i, X1085:$i, X1086:$i, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i > $o, X1105:$i, X1106:$i > $o, X1107:$i, X1108:$i, X1109:$i > $o, X1110:$i, X1112:$i, X1113:$i > $o, X1115:$i, X1116:$i, X1117:$i > $o, X1119:$i, X1120:$i, X1121:$i > $o, X1122:$i, X1124:$o, X1125:$o, X1126:$i, X1127:$i > $o, X1129:$i, X1130:$i, X1131:$i > $o, X1132:$i, X1134:$i > $o, X1135:$i, X1138:$i, X1139:$i > $o, X1140:$i, X1144:$i, X1145:$i > $o, X1146:$i, X1149:$i, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i > $o, X1159:$i, X1161:$i, X1162:$i, X1163:$i > $o, X1164:$i > $o, X1167:$i, X1170:$i, X1171:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i > $o, X1184:$i, X1186:$i, X1187:$i, X1188:$i > $o, X1189:$i > $o, X1192:$i, X1194:$i, X1196:$i, X1197:$i, X1198:$i > $o, X1199:$i > $o, X1202:$i, X1203:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1228:$i, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i > $o, X1250:$i, X1251:$i > $o, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$o, X1264:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$o, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$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, X1354:$i, X1355:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$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:$i, X1397:$i, X1398:$i, X1399:$i, X1402:$i, X1403:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i > $o, X1412:$i, X1414:$i, X1415:$i > $o, X1416:$i, X1418:$i, X1419:$i > $o, X1420:$i, X1423:$i, X1424:$i > $o, X1427:$i, X1429:$i, X1430:$i]:((((~(in @ (esk1_2 @ X968 @ X969) @ X968)|~(in @ (esk1_2 @ X968 @ X969) @ X969)|((X968)=(X969)))&((in @ (esk1_2 @ X968 @ X969) @ X968)|(in @ (esk1_2 @ X968 @ X969) @ X969)|((X968)=(X969))))&(~(in @ X971 @ emptyset)&(((~(in @ X974 @ (setadjoin @ X972 @ X973))|(((X974)=(X972))|(in @ X974 @ X973)))&((((X974)!=(X972))|(in @ X974 @ (setadjoin @ X972 @ X973)))&(~(in @ X974 @ X973)|(in @ X974 @ (setadjoin @ X972 @ X973)))))&(((~(in @ X976 @ (powerset @ X975))|(~(in @ X977 @ X976)|(in @ X977 @ X975)))&(((in @ (esk2_2 @ X978 @ X979) @ X979)|(in @ X979 @ (powerset @ X978)))&(~(in @ (esk2_2 @ X978 @ X979) @ X978)|(in @ X979 @ (powerset @ X978)))))&(((((in @ X982 @ (esk3_2 @ X981 @ X982))|~(in @ X982 @ (setunion @ X981)))&((in @ (esk3_2 @ X981 @ X982) @ X981)|~(in @ X982 @ (setunion @ X981))))&(~(in @ X985 @ X986)|~(in @ X986 @ X984)|(in @ X985 @ (setunion @ X984))))&((in @ 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X1368)|(~(in @ X1371 @ X1369)|(subset @ (setadjoin @ X1370 @ (setadjoin @ X1371 @ emptyset)) @ (binunion @ X1368 @ X1369))))&((~(in @ X1374 @ X1372)|(~(in @ X1375 @ X1373)|(in @ (setadjoin @ X1374 @ (setadjoin @ X1375 @ emptyset)) @ (powerset @ (binunion @ X1372 @ X1373)))))&((~(in @ X1378 @ X1376)|(~(in @ X1379 @ X1377)|(subset @ (setadjoin @ (setadjoin @ X1378 @ emptyset) @ (setadjoin @ (setadjoin @ X1378 @ (setadjoin @ X1379 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1376 @ X1377)))))&((~(in @ X1382 @ X1380)|(~(in @ X1383 @ X1381)|(in @ (setadjoin @ (setadjoin @ X1382 @ emptyset) @ (setadjoin @ (setadjoin @ X1382 @ (setadjoin @ X1383 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1380 @ X1381))))))&((~(in @ X1386 @ X1384)|(~(in @ X1387 @ X1385)|(in @ (kpair @ X1386 @ X1387) @ (powerset @ (powerset @ (binunion @ X1384 @ X1385))))))&((~(in @ X1390 @ X1388)|(~(in @ X1391 @ X1389)|(in @ (kpair @ X1390 @ X1391) @ (cartprod @ X1388 @ X1389))))&((((in @ (esk59_3 @ X1392 @ X1393 @ X1394) @ X1392)|~(in @ X1394 @ (cartprod @ X1392 @ X1393)))&(((in @ (esk60_3 @ X1392 @ X1393 @ X1394) @ X1393)|~(in @ X1394 @ (cartprod @ X1392 @ X1393)))&(((X1394)=(kpair @ (esk59_3 @ X1392 @ X1393 @ X1394) @ (esk60_3 @ X1392 @ X1393 @ X1394)))|~(in @ X1394 @ (cartprod @ X1392 @ X1393)))))&((((in @ (esk61_3 @ X1397 @ X1398 @ X1399) @ (setunion @ X1399))|~(in @ X1399 @ (cartprod @ X1397 @ X1398)))&(((in @ (esk62_3 @ X1397 @ X1398 @ X1399) @ (setunion @ X1399))|~(in @ X1399 @ (cartprod @ X1397 @ X1398)))&(((X1399)=(setadjoin @ (setadjoin @ (esk61_3 @ X1397 @ X1398 @ X1399) @ emptyset) @ (setadjoin @ (setadjoin @ (esk61_3 @ X1397 @ X1398 @ X1399) @ (setadjoin @ (esk62_3 @ X1397 @ X1398 @ X1399) @ emptyset)) @ emptyset)))|~(in @ X1399 @ (cartprod @ X1397 @ X1398)))))&((((in @ (esk63_2 @ X1402 @ X1403) @ X1402)|~(in @ X1403 @ (setunion @ X1402)))&((in @ X1403 @ (esk63_2 @ X1402 @ X1403))|~(in @ X1403 @ (setunion @ X1402))))&((subset @ (setunion @ (setadjoin @ X1405 @ emptyset)) @ X1405)&((subset @ X1406 @ (setunion @ (setadjoin @ X1406 @ emptyset)))&(((setunion @ (setadjoin @ X1407 @ emptyset))=(X1407))&(((((in @ (esk66_2 @ X1408 @ X1409) @ (dsetconstr @ X1408 @ X1409))|(~(in @ X1412 @ X1408)|~(X1409 @ X1412))|(in @ (esk64_2 @ X1408 @ X1409) @ X1408))&(((dsetconstr @ X1408 @ X1409)=(setadjoin @ (esk66_2 @ X1408 @ X1409) @ emptyset))|(~(in @ X1412 @ X1408)|~(X1409 @ X1412))|(in @ (esk64_2 @ X1408 @ X1409) @ X1408)))&((((in @ (esk66_2 @ X1408 @ X1409) @ (dsetconstr @ X1408 @ X1409))|(~(in @ X1412 @ X1408)|~(X1409 @ X1412))|(in @ (esk65_2 @ X1408 @ X1409) @ X1408))&(((dsetconstr @ X1408 @ X1409)=(setadjoin @ (esk66_2 @ X1408 @ X1409) @ emptyset))|(~(in @ X1412 @ X1408)|~(X1409 @ X1412))|(in @ (esk65_2 @ X1408 @ X1409) @ X1408)))&((((in @ (esk66_2 @ X1408 @ X1409) @ (dsetconstr @ X1408 @ X1409))|(~(in @ X1412 @ X1408)|~(X1409 @ X1412))|(X1409 @ (esk64_2 @ X1408 @ X1409)))&(((dsetconstr @ X1408 @ X1409)=(setadjoin @ (esk66_2 @ X1408 @ X1409) @ emptyset))|(~(in @ X1412 @ X1408)|~(X1409 @ X1412))|(X1409 @ (esk64_2 @ X1408 @ X1409))))&((((in @ (esk66_2 @ X1408 @ X1409) @ (dsetconstr @ X1408 @ X1409))|(~(in @ X1412 @ X1408)|~(X1409 @ X1412))|(X1409 @ (esk65_2 @ X1408 @ X1409)))&(((dsetconstr @ X1408 @ X1409)=(setadjoin @ (esk66_2 @ X1408 @ X1409) @ emptyset))|(~(in @ X1412 @ X1408)|~(X1409 @ X1412))|(X1409 @ (esk65_2 @ X1408 @ X1409))))&(((in @ (esk66_2 @ X1408 @ X1409) @ (dsetconstr @ X1408 @ X1409))|(~(in @ X1412 @ X1408)|~(X1409 @ X1412))|((esk64_2 @ X1408 @ X1409)!=(esk65_2 @ X1408 @ X1409)))&(((dsetconstr @ X1408 @ X1409)=(setadjoin @ (esk66_2 @ X1408 @ X1409) @ emptyset))|(~(in @ X1412 @ X1408)|~(X1409 @ X1412))|((esk64_2 @ X1408 @ X1409)!=(esk65_2 @ X1408 @ X1409))))))))&((((in @ (esk67_2 @ X1414 @ X1415) @ X1414)|(~(in @ X1416 @ (dsetconstr @ X1414 @ X1415))|((dsetconstr @ X1414 @ X1415)!=(setadjoin @ X1416 @ emptyset))))&((X1415 @ (esk67_2 @ X1414 @ X1415))|(~(in @ X1416 @ (dsetconstr @ X1414 @ X1415))|((dsetconstr @ X1414 @ X1415)!=(setadjoin @ X1416 @ emptyset)))))&(((((in @ (esk69_3 @ X1418 @ X1419 @ X1420) @ (dsetconstr @ X1418 @ X1419))|(in @ (esk68_3 @ X1418 @ X1419 @ X1420) @ X1418)|~(X1419 @ X1420)|~(in @ X1420 @ X1418))&(((dsetconstr @ X1418 @ X1419)=(setadjoin @ (esk69_3 @ X1418 @ X1419 @ X1420) @ emptyset))|(in @ (esk68_3 @ X1418 @ X1419 @ X1420) @ X1418)|~(X1419 @ X1420)|~(in @ X1420 @ X1418)))&((((in @ (esk69_3 @ X1418 @ X1419 @ X1420) @ (dsetconstr @ X1418 @ X1419))|(X1419 @ (esk68_3 @ X1418 @ X1419 @ X1420))|~(X1419 @ X1420)|~(in @ X1420 @ X1418))&(((dsetconstr @ X1418 @ X1419)=(setadjoin @ (esk69_3 @ X1418 @ X1419 @ X1420) @ emptyset))|(X1419 @ (esk68_3 @ X1418 @ X1419 @ X1420))|~(X1419 @ X1420)|~(in @ X1420 @ X1418)))&(((in @ (esk69_3 @ X1418 @ X1419 @ X1420) @ (dsetconstr @ X1418 @ X1419))|((esk68_3 @ X1418 @ X1419 @ X1420)!=(X1420))|~(X1419 @ X1420)|~(in @ X1420 @ X1418))&(((dsetconstr @ X1418 @ X1419)=(setadjoin @ (esk69_3 @ X1418 @ X1419 @ X1420) @ emptyset))|((esk68_3 @ X1418 @ X1419 @ X1420)!=(X1420))|~(X1419 @ X1420)|~(in @ X1420 @ X1418)))))&(((((in @ (esk72_2 @ X1423 @ X1424) @ (dsetconstr @ X1423 @ X1424))|(~(in @ X1427 @ X1423)|~(X1424 @ X1427))|(in @ (esk70_2 @ X1423 @ X1424) @ X1423))&(((dsetconstr @ X1423 @ X1424)=(setadjoin @ (esk72_2 @ X1423 @ X1424) @ emptyset))|(~(in @ X1427 @ X1423)|~(X1424 @ X1427))|(in @ (esk70_2 @ X1423 @ X1424) @ X1423)))&((((in @ (esk72_2 @ X1423 @ X1424) @ (dsetconstr @ X1423 @ X1424))|(~(in @ X1427 @ X1423)|~(X1424 @ X1427))|(in @ (esk71_2 @ X1423 @ X1424) @ X1423))&(((dsetconstr @ X1423 @ X1424)=(setadjoin @ (esk72_2 @ X1423 @ X1424) @ emptyset))|(~(in @ X1427 @ X1423)|~(X1424 @ X1427))|(in @ (esk71_2 @ X1423 @ X1424) @ X1423)))&((((in @ (esk72_2 @ X1423 @ X1424) @ (dsetconstr @ X1423 @ X1424))|(~(in @ X1427 @ X1423)|~(X1424 @ X1427))|(X1424 @ (esk70_2 @ X1423 @ X1424)))&(((dsetconstr @ X1423 @ X1424)=(setadjoin @ (esk72_2 @ X1423 @ X1424) @ emptyset))|(~(in @ X1427 @ X1423)|~(X1424 @ X1427))|(X1424 @ (esk70_2 @ X1423 @ X1424))))&((((in @ (esk72_2 @ X1423 @ X1424) @ (dsetconstr @ X1423 @ X1424))|(~(in @ X1427 @ X1423)|~(X1424 @ X1427))|(X1424 @ (esk71_2 @ X1423 @ X1424)))&(((dsetconstr @ X1423 @ X1424)=(setadjoin @ (esk72_2 @ X1423 @ X1424) @ emptyset))|(~(in @ X1427 @ X1423)|~(X1424 @ X1427))|(X1424 @ (esk71_2 @ X1423 @ X1424))))&(((in @ (esk72_2 @ X1423 @ X1424) @ (dsetconstr @ X1423 @ X1424))|(~(in @ X1427 @ X1423)|~(X1424 @ X1427))|((esk70_2 @ X1423 @ X1424)!=(esk71_2 @ X1423 @ X1424)))&(((dsetconstr @ X1423 @ X1424)=(setadjoin @ (esk72_2 @ X1423 @ X1424) @ emptyset))|(~(in @ X1427 @ X1423)|~(X1424 @ X1427))|((esk70_2 @ X1423 @ X1424)!=(esk71_2 @ X1423 @ X1424))))))))&((((setadjoin @ X1429 @ emptyset)!=(setadjoin @ X1430 @ emptyset))|((X1429)=(X1430)))&((in @ (setadjoin @ esk75_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk73_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk73_0 @ (setadjoin @ esk74_0 @ emptyset)) @ emptyset)))&((esk73_0)!=(esk75_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_221])])])])])])])).
% 172.84/29.77 thf(c_0_223, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((X2)=(X3))|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)))))), inference(split_conjunct,[status(thm)],[c_0_222])).
% 172.84/29.77 thf(c_0_224, negated_conjecture, (in @ (setadjoin @ esk75_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk73_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk73_0 @ (setadjoin @ esk74_0 @ emptyset)) @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_222])).
% 172.84/29.77 thf(c_0_225, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_222])).
% 172.84/29.77 thf(c_0_226, negated_conjecture, (((setadjoin @ esk73_0 @ (setadjoin @ esk74_0 @ emptyset))=(setadjoin @ esk75_0 @ emptyset))|((setadjoin @ esk75_0 @ emptyset)=(setadjoin @ esk73_0 @ emptyset))), inference(spm,[status(thm)],[c_0_223, c_0_224])).
% 172.84/29.77 thf(c_0_227, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_222])])])).
% 172.84/29.77 thf(c_0_228, negated_conjecture, (((setadjoin @ esk75_0 @ emptyset)=(setadjoin @ esk73_0 @ emptyset))|(in @ esk73_0 @ (setadjoin @ esk75_0 @ emptyset))), inference(spm,[status(thm)],[c_0_225, c_0_226])).
% 172.84/29.77 thf(c_0_229, negated_conjecture, ((esk73_0)!=(esk75_0)), inference(split_conjunct,[status(thm)],[c_0_222])).
% 172.84/29.77 thf(c_0_230, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_222])).
% 172.84/29.77 thf(c_0_231, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(split_conjunct,[status(thm)],[c_0_222])).
% 172.84/29.77 thf(c_0_232, negated_conjecture, ((setadjoin @ esk75_0 @ emptyset)=(setadjoin @ esk73_0 @ emptyset)), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_227, c_0_228]), c_0_229]), c_0_230])).
% 172.84/29.77 thf(c_0_233, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231, c_0_232]), c_0_231]), c_0_229]), ['proof']).
% 172.84/29.77 % SZS output end CNFRefutation
% 172.84/29.77 % Parsed axioms : 352
% 172.84/29.77 % Removed by relevancy pruning/SinE : 0
% 172.84/29.77 % Initial clauses : 503
% 172.84/29.77 % Removed in clause preprocessing : 212
% 172.84/29.77 % Initial clauses in saturation : 291
% 172.84/29.77 % Processed clauses : 619
% 172.84/29.77 % ...of these trivial : 6
% 172.84/29.77 % ...subsumed : 51
% 172.84/29.77 % ...remaining for further processing : 562
% 172.84/29.77 % Other redundant clauses eliminated : 17
% 172.84/29.77 % Clauses deleted for lack of memory : 0
% 172.84/29.77 % Backward-subsumed : 0
% 172.84/29.77 % Backward-rewritten : 11
% 172.84/29.77 % Generated clauses : 6976
% 172.84/29.77 % ...of the previous two non-redundant : 6854
% 172.84/29.77 % ...aggressively subsumed : 0
% 172.84/29.77 % Contextual simplify-reflections : 0
% 172.84/29.77 % Paramodulations : 6955
% 172.84/29.77 % Factorizations : 2
% 172.84/29.77 % NegExts : 0
% 172.84/29.77 % Equation resolutions : 18
% 172.84/29.77 % Disequality decompositions : 0
% 172.84/29.77 % Total rewrite steps : 147
% 172.84/29.77 % ...of those cached : 94
% 172.84/29.77 % Propositional unsat checks : 0
% 172.84/29.77 % Propositional check models : 0
% 172.84/29.77 % Propositional check unsatisfiable : 0
% 172.84/29.77 % Propositional clauses : 0
% 172.84/29.77 % Propositional clauses after purity: 0
% 172.84/29.77 % Propositional unsat core size : 0
% 172.84/29.77 % Propositional preprocessing time : 0.000
% 172.84/29.77 % Propositional encoding time : 0.000
% 172.84/29.77 % Propositional solver time : 0.000
% 172.84/29.77 % Success case prop preproc time : 0.000
% 172.84/29.77 % Success case prop encoding time : 0.000
% 172.84/29.77 % Success case prop solver time : 0.000
% 172.84/29.77 % Current number of processed clauses : 285
% 172.84/29.77 % Positive orientable unit clauses : 34
% 172.84/29.77 % Positive unorientable unit clauses: 0
% 172.84/29.77 % Negative unit clauses : 7
% 172.84/29.77 % Non-unit-clauses : 244
% 172.84/29.77 % Current number of unprocessed clauses: 6734
% 172.84/29.77 % ...number of literals in the above : 26930
% 172.84/29.77 % Current number of archived formulas : 0
% 172.84/29.77 % Current number of archived clauses : 265
% 172.84/29.77 % Clause-clause subsumption calls (NU) : 17915
% 172.84/29.77 % Rec. Clause-clause subsumption calls : 6721
% 172.84/29.77 % Non-unit clause-clause subsumptions : 37
% 172.84/29.77 % Unit Clause-clause subsumption calls : 150
% 172.84/29.77 % Rewrite failures with RHS unbound : 0
% 172.84/29.77 % BW rewrite match attempts : 21
% 172.84/29.77 % BW rewrite match successes : 4
% 172.84/29.77 % Condensation attempts : 0
% 172.84/29.77 % Condensation successes : 0
% 172.84/29.77 % Termbank termtop insertions : 183902
% 172.84/29.77 % Search garbage collected termcells : 15910
% 172.84/29.77
% 172.84/29.77 % -------------------------------------------------
% 172.84/29.77 % User time : 27.673 s
% 172.84/29.77 % System time : 0.977 s
% 172.84/29.77 % Total time : 28.650 s
% 172.84/29.77 % Maximum resident set size: 7312 pages
% 172.84/29.77
% 172.84/29.77 % -------------------------------------------------
% 172.84/29.77 % User time : 27.788 s
% 172.84/29.77 % System time : 1.022 s
% 172.84/29.77 % Total time : 28.811 s
% 172.84/29.77 % Maximum resident set size: 5120 pages
% 172.84/29.77 % E exiting
%------------------------------------------------------------------------------