%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU603^1 : 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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:41 AM UTC 2026
% Result : Theorem 0.08s 0.19s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU603^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:56:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.14 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.mMW5BltzOS/E---3.1_144687.p
% 0.08/0.19 % Version: 3.5.1-ho
% 0.08/0.19 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.08/0.19 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.19 % Starting ehoh_best5 with 300s (1) cores
% 0.08/0.19 % Starting almost_fo_3_lam with 300s (1) cores
% 0.08/0.19 % Starting new_bool_5 with 300s (1) cores
% 0.08/0.19 % Starting pre_casc_3 with 300s (1) cores
% 0.08/0.19 % Starting ho_unfolding_8 with 300s (1) cores
% 0.08/0.19 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.19 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.19 % Starting new_ho_5 with 300s (1) cores
% 0.08/0.19 % new_ho_10_cnf2 with pid 144725 completed with status 0
% 0.08/0.19 % Result found by new_ho_10_cnf2
% 0.08/0.19 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.08/0.19 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.19 % Starting ehoh_best5 with 300s (1) cores
% 0.08/0.19 % Starting almost_fo_3_lam with 300s (1) cores
% 0.08/0.19 % Starting new_bool_5 with 300s (1) cores
% 0.08/0.19 % Starting pre_casc_3 with 300s (1) cores
% 0.08/0.19 % Starting ho_unfolding_8 with 300s (1) cores
% 0.08/0.19 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.19 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.19 % No SInE strategy applied
% 0.08/0.19 % Search class: HGHSM-FSLM31-SHFMMSBN
% 0.08/0.19 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.19 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.19 % SubtermCWHack with pid 144740 completed with status 0
% 0.08/0.19 % Result found by SubtermCWHack
% 0.08/0.19 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.08/0.19 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.19 % Starting ehoh_best5 with 300s (1) cores
% 0.08/0.19 % Starting almost_fo_3_lam with 300s (1) cores
% 0.08/0.19 % Starting new_bool_5 with 300s (1) cores
% 0.08/0.19 % Starting pre_casc_3 with 300s (1) cores
% 0.08/0.19 % Starting ho_unfolding_8 with 300s (1) cores
% 0.08/0.19 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.19 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.19 % No SInE strategy applied
% 0.08/0.19 % Search class: HGHSM-FSLM31-SHFMMSBN
% 0.08/0.19 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.19 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.19 % Preprocessing time : 0.003 s
% 0.08/0.19
% 0.08/0.19 % Proof found!
% 0.08/0.19 % SZS status Theorem
% 0.08/0.19 % SZS output start CNFRefutation
% 0.08/0.19 thf(decl_23, type, in: $i > $i > $o).
% 0.08/0.19 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.08/0.19 thf(decl_25, type, setextAx: $o).
% 0.08/0.19 thf(decl_26, type, emptyset: $i).
% 0.08/0.19 thf(decl_27, type, emptysetAx: $o).
% 0.08/0.19 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.08/0.19 thf(decl_29, type, setadjoinAx: $o).
% 0.08/0.19 thf(decl_30, type, powerset: $i > $i).
% 0.08/0.19 thf(decl_31, type, powersetAx: $o).
% 0.08/0.19 thf(decl_32, type, setunion: $i > $i).
% 0.08/0.19 thf(decl_33, type, setunionAx: $o).
% 0.08/0.19 thf(decl_34, type, omega: $i).
% 0.08/0.19 thf(decl_35, type, omega0Ax: $o).
% 0.08/0.19 thf(decl_36, type, omegaSAx: $o).
% 0.08/0.19 thf(decl_37, type, omegaIndAx: $o).
% 0.08/0.19 thf(decl_38, type, replAx: $o).
% 0.08/0.19 thf(decl_39, type, foundationAx: $o).
% 0.08/0.19 thf(decl_40, type, wellorderingAx: $o).
% 0.08/0.19 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.08/0.19 thf(decl_42, type, descrp: $o).
% 0.08/0.19 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.08/0.19 thf(decl_44, type, dsetconstrI: $o).
% 0.08/0.19 thf(decl_45, type, dsetconstrEL: $o).
% 0.08/0.19 thf(decl_46, type, dsetconstrER: $o).
% 0.08/0.19 thf(decl_47, type, exuE1: $o).
% 0.08/0.19 thf(decl_48, type, prop2set: $o > $i).
% 0.08/0.19 thf(decl_49, type, prop2setE: $o).
% 0.08/0.19 thf(decl_50, type, emptysetE: $o).
% 0.08/0.19 thf(decl_51, type, emptysetimpfalse: $o).
% 0.08/0.19 thf(decl_52, type, notinemptyset: $o).
% 0.08/0.19 thf(decl_53, type, exuE3e: $o).
% 0.08/0.19 thf(decl_54, type, setext: $o).
% 0.08/0.19 thf(decl_55, type, emptyI: $o).
% 0.08/0.19 thf(decl_56, type, noeltsimpempty: $o).
% 0.08/0.19 thf(decl_57, type, setbeta: $o).
% 0.08/0.19 thf(decl_58, type, nonempty: $i > $o).
% 0.08/0.19 thf(decl_59, type, nonemptyE1: $o).
% 0.08/0.19 thf(decl_60, type, nonemptyI: $o).
% 0.08/0.19 thf(decl_61, type, nonemptyI1: $o).
% 0.08/0.19 thf(decl_62, type, setadjoinIL: $o).
% 0.08/0.19 thf(decl_63, type, emptyinunitempty: $o).
% 0.08/0.19 thf(decl_64, type, setadjoinIR: $o).
% 0.08/0.19 thf(decl_65, type, setadjoinE: $o).
% 0.08/0.19 thf(decl_66, type, setadjoinOr: $o).
% 0.08/0.19 thf(decl_67, type, setoftrueEq: $o).
% 0.08/0.19 thf(decl_68, type, powersetI: $o).
% 0.08/0.19 thf(decl_69, type, emptyinPowerset: $o).
% 0.08/0.19 thf(decl_70, type, emptyInPowerset: $o).
% 0.08/0.19 thf(decl_71, type, powersetE: $o).
% 0.08/0.19 thf(decl_72, type, setunionI: $o).
% 0.08/0.19 thf(decl_73, type, setunionE: $o).
% 0.08/0.19 thf(decl_74, type, subPowSU: $o).
% 0.08/0.19 thf(decl_75, type, exuE2: $o).
% 0.08/0.19 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.08/0.19 thf(decl_77, type, uniqinunit: $o).
% 0.08/0.19 thf(decl_78, type, notinsingleton: $o).
% 0.08/0.19 thf(decl_79, type, eqinunit: $o).
% 0.08/0.19 thf(decl_80, type, singletonsswitch: $o).
% 0.08/0.19 thf(decl_81, type, upairsetE: $o).
% 0.08/0.19 thf(decl_82, type, upairsetIL: $o).
% 0.08/0.19 thf(decl_83, type, upairsetIR: $o).
% 0.08/0.19 thf(decl_84, type, emptyE1: $o).
% 0.08/0.19 thf(decl_85, type, vacuousDall: $o).
% 0.08/0.19 thf(decl_86, type, quantDeMorgan1: $o).
% 0.08/0.19 thf(decl_87, type, quantDeMorgan2: $o).
% 0.08/0.19 thf(decl_88, type, quantDeMorgan3: $o).
% 0.08/0.19 thf(decl_89, type, quantDeMorgan4: $o).
% 0.08/0.19 thf(decl_90, type, prop2setI: $o).
% 0.08/0.19 thf(decl_91, type, set2prop: $i > $o).
% 0.08/0.19 thf(decl_92, type, prop2set2propI: $o).
% 0.08/0.19 thf(decl_93, type, notdexE: $o).
% 0.08/0.19 thf(decl_94, type, notdallE: $o).
% 0.08/0.19 thf(decl_95, type, exuI1: $o).
% 0.08/0.19 thf(decl_96, type, exuI3: $o).
% 0.08/0.19 thf(decl_97, type, exuI2: $o).
% 0.08/0.19 thf(decl_98, type, inCongP: $o).
% 0.08/0.19 thf(decl_99, type, in__Cong: $o).
% 0.08/0.19 thf(decl_100, type, exuE3u: $o).
% 0.08/0.19 thf(decl_101, type, exu__Cong: $o).
% 0.08/0.19 thf(decl_102, type, emptyset__Cong: $o).
% 0.08/0.19 thf(decl_103, type, setadjoin__Cong: $o).
% 0.08/0.19 thf(decl_104, type, powerset__Cong: $o).
% 0.08/0.19 thf(decl_105, type, setunion__Cong: $o).
% 0.08/0.19 thf(decl_106, type, omega__Cong: $o).
% 0.08/0.19 thf(decl_107, type, exuEu: $o).
% 0.08/0.19 thf(decl_108, type, descr__Cong: $o).
% 0.08/0.19 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.08/0.19 thf(decl_110, type, subset: $i > $i > $o).
% 0.08/0.19 thf(decl_113, type, subsetI1: $o).
% 0.08/0.19 thf(decl_114, type, eqimpsubset2: $o).
% 0.08/0.19 thf(decl_115, type, eqimpsubset1: $o).
% 0.08/0.19 thf(decl_116, type, subsetI2: $o).
% 0.08/0.19 thf(decl_117, type, emptysetsubset: $o).
% 0.08/0.19 thf(decl_118, type, subsetE: $o).
% 0.08/0.19 thf(decl_119, type, subsetE2: $o).
% 0.08/0.19 thf(decl_120, type, notsubsetI: $o).
% 0.08/0.19 thf(decl_121, type, notequalI1: $o).
% 0.08/0.19 thf(decl_122, type, notequalI2: $o).
% 0.08/0.19 thf(decl_123, type, subsetRefl: $o).
% 0.08/0.19 thf(decl_124, type, subsetTrans: $o).
% 0.08/0.19 thf(decl_125, type, setadjoinSub: $o).
% 0.08/0.19 thf(decl_126, type, setadjoinSub2: $o).
% 0.08/0.19 thf(decl_127, type, subset2powerset: $o).
% 0.08/0.19 thf(decl_128, type, setextsub: $o).
% 0.08/0.19 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.08/0.19 thf(decl_130, type, powersetI1: $o).
% 0.08/0.19 thf(decl_131, type, powersetE1: $o).
% 0.08/0.19 thf(decl_132, type, inPowerset: $o).
% 0.08/0.19 thf(decl_133, type, powersetsubset: $o).
% 0.08/0.19 thf(decl_134, type, sepInPowerset: $o).
% 0.08/0.19 thf(decl_135, type, sepSubset: $o).
% 0.08/0.19 thf(decl_136, type, binunion: $i > $i > $i).
% 0.08/0.19 thf(decl_137, type, binunionIL: $o).
% 0.08/0.19 thf(decl_138, type, upairset2IR: $o).
% 0.08/0.19 thf(decl_139, type, binunionIR: $o).
% 0.08/0.19 thf(decl_140, type, binunionEcases: $o).
% 0.08/0.19 thf(decl_141, type, binunionE: $o).
% 0.08/0.19 thf(decl_142, type, binunionLsub: $o).
% 0.08/0.19 thf(decl_143, type, binunionRsub: $o).
% 0.08/0.19 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.08/0.19 thf(decl_145, type, binintersectI: $o).
% 0.08/0.19 thf(decl_146, type, binintersectSubset5: $o).
% 0.08/0.19 thf(decl_147, type, binintersectEL: $o).
% 0.08/0.19 thf(decl_148, type, binintersectLsub: $o).
% 0.08/0.19 thf(decl_149, type, binintersectSubset2: $o).
% 0.08/0.19 thf(decl_150, type, binintersectSubset3: $o).
% 0.08/0.19 thf(decl_151, type, binintersectER: $o).
% 0.08/0.19 thf(decl_152, type, disjointsetsI1: $o).
% 0.08/0.19 thf(decl_153, type, binintersectRsub: $o).
% 0.08/0.19 thf(decl_154, type, binintersectSubset4: $o).
% 0.08/0.19 thf(decl_155, type, binintersectSubset1: $o).
% 0.08/0.19 thf(decl_156, type, bs114d: $o).
% 0.08/0.19 thf(decl_158, type, setminus: $i > $i > $i).
% 0.08/0.19 thf(decl_159, type, setminusI: $o).
% 0.08/0.19 thf(decl_160, type, setminusEL: $o).
% 0.08/0.19 thf(decl_161, type, epred1_0: $o).
% 0.08/0.19 thf(decl_162, type, esk1_2: $i > $i > $i).
% 0.08/0.19 thf(decl_163, type, esk2_2: $i > $i > $i).
% 0.08/0.19 thf(decl_164, type, esk3_2: $i > $i > $i).
% 0.08/0.19 thf(decl_165, type, esk4_1: $i > $i).
% 0.08/0.19 thf(decl_166, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.08/0.19 thf(decl_167, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.19 thf(decl_168, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.08/0.19 thf(decl_169, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.19 thf(decl_170, type, esk9_1: $i > $i).
% 0.08/0.19 thf(decl_171, type, esk10_2: ($i > $o) > $i > $i).
% 0.08/0.19 thf(decl_172, type, esk11_2: ($i > $o) > $i > $i).
% 0.08/0.19 thf(decl_173, type, esk12_1: ($i > $o) > $i).
% 0.08/0.19 thf(decl_174, type, esk13_2: ($i > $o) > $i > $i).
% 0.08/0.19 thf(decl_175, type, esk14_1: ($i > $o) > $i).
% 0.08/0.19 thf(decl_176, type, esk15_2: $i > $i > $i).
% 0.08/0.19 thf(decl_177, type, esk16_2: $i > $i > $i).
% 0.08/0.19 thf(decl_178, type, esk17_1: $i > $i).
% 0.08/0.19 thf(decl_179, type, esk18_1: $i > $i).
% 0.08/0.19 thf(decl_180, type, esk19_1: $i > $i).
% 0.08/0.19 thf(decl_181, type, esk20_2: $i > $i > $i).
% 0.08/0.19 thf(decl_182, type, esk21_3: $i > $i > $o > $i).
% 0.08/0.19 thf(decl_183, type, esk22_2: ($i > $o) > $i > $i).
% 0.08/0.19 thf(decl_184, type, esk23_1: ($i > $o) > $i).
% 0.08/0.19 thf(decl_185, type, esk24_1: $i > $i).
% 0.08/0.19 thf(decl_186, type, esk25_2: $i > ($i > $o) > $i).
% 0.08/0.19 thf(decl_187, type, esk26_2: $i > ($i > $o) > $i).
% 0.08/0.19 thf(decl_188, type, esk27_2: $i > ($i > $o) > $i).
% 0.08/0.19 thf(decl_189, type, esk28_2: $i > ($i > $o) > $i).
% 0.08/0.19 thf(decl_190, type, esk29_2: $i > ($i > $o) > $i).
% 0.08/0.19 thf(decl_191, type, esk30_2: $i > ($i > $o) > $i).
% 0.08/0.19 thf(decl_192, type, esk31_2: ($i > $o) > $i > $i).
% 0.08/0.19 thf(decl_193, type, esk32_1: ($i > $o) > $i).
% 0.08/0.19 thf(decl_194, type, esk33_1: ($i > $o) > $i).
% 0.08/0.19 thf(decl_195, type, esk34_1: ($i > $o) > $i).
% 0.08/0.19 thf(decl_196, type, esk35_1: ($i > $o) > $i).
% 0.08/0.19 thf(decl_197, type, esk36_2: ($i > $o) > $i > $i).
% 0.08/0.19 thf(decl_198, type, esk37_1: ($i > $o) > $i).
% 0.08/0.19 thf(decl_199, type, esk38_2: ($i > $o) > $i > $i).
% 0.08/0.19 thf(decl_200, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.08/0.19 thf(decl_201, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.08/0.19 thf(decl_202, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.08/0.19 thf(decl_203, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.08/0.19 thf(decl_204, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.08/0.19 thf(decl_205, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.08/0.19 thf(decl_206, type, esk45_2: ($i > $o) > $i > $i).
% 0.08/0.19 thf(decl_207, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.08/0.19 thf(decl_208, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.08/0.19 thf(decl_209, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.08/0.19 thf(decl_210, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.08/0.19 thf(decl_211, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.08/0.19 thf(decl_212, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.08/0.19 thf(decl_213, type, esk52_2: $i > $i > $i).
% 0.08/0.19 thf(decl_214, type, esk53_2: $i > $i > $i).
% 0.08/0.19 thf(decl_215, type, esk54_2: $i > $i > $i).
% 0.08/0.19 thf(decl_216, type, esk55_0: $i).
% 0.08/0.19 thf(decl_217, type, esk56_0: $i).
% 0.08/0.19 thf(decl_218, type, esk57_0: $i).
% 0.08/0.19 thf(decl_224, type, epred2_1: $i > $i > $o).
% 0.08/0.19 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', replAx)).
% 0.08/0.19 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', exu)).
% 0.08/0.19 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', descrp)).
% 0.08/0.19 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', exuE1)).
% 0.08/0.19 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', exuE3e)).
% 0.08/0.19 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', nonempty)).
% 0.08/0.19 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', nonemptyI)).
% 0.08/0.19 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', exuE2)).
% 0.08/0.19 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.mMW5BltzOS/E---3.1_144687.p', exuI1)).
% 0.08/0.19 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', exuI3)).
% 0.08/0.19 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', exuI2)).
% 0.08/0.19 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.mMW5BltzOS/E---3.1_144687.p', exuE3u)).
% 0.08/0.19 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', exu__Cong)).
% 0.08/0.19 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', exuEu)).
% 0.08/0.19 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.mMW5BltzOS/E---3.1_144687.p', descr__Cong)).
% 0.08/0.19 thf(setminusER, 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)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setminusER)).
% 0.08/0.19 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', dsetconstrI)).
% 0.08/0.19 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', dsetconstrEL)).
% 0.08/0.19 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', dsetconstrER)).
% 0.08/0.19 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setbeta)).
% 0.08/0.19 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', nonemptyE1)).
% 0.08/0.19 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', nonemptyI1)).
% 0.08/0.19 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setoftrueEq)).
% 0.08/0.19 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', nonemptyImpWitness)).
% 0.08/0.19 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.mMW5BltzOS/E---3.1_144687.p', emptyE1)).
% 0.08/0.19 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', dsetconstr__Cong)).
% 0.08/0.19 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', sepInPowerset)).
% 0.08/0.19 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', sepSubset)).
% 0.08/0.19 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setextAx)).
% 0.08/0.19 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', emptysetAx)).
% 0.08/0.19 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setadjoinAx)).
% 0.08/0.19 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', powersetAx)).
% 0.08/0.19 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setunionAx)).
% 0.08/0.19 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', omega0Ax)).
% 0.08/0.19 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', omegaSAx)).
% 0.08/0.19 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', omegaIndAx)).
% 0.08/0.19 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', foundationAx)).
% 0.08/0.19 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.mMW5BltzOS/E---3.1_144687.p', wellorderingAx)).
% 0.08/0.19 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', prop2setE)).
% 0.08/0.19 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', emptysetE)).
% 0.08/0.19 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', emptysetimpfalse)).
% 0.08/0.19 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', notinemptyset)).
% 0.08/0.19 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setext)).
% 0.08/0.19 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', emptyI)).
% 0.08/0.19 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', noeltsimpempty)).
% 0.08/0.19 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setadjoinIL)).
% 0.08/0.19 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', emptyinunitempty)).
% 0.08/0.19 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setadjoinIR)).
% 0.08/0.19 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.mMW5BltzOS/E---3.1_144687.p', setadjoinE)).
% 0.08/0.19 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setadjoinOr)).
% 0.08/0.19 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', powersetI)).
% 0.08/0.19 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', emptyinPowerset)).
% 0.08/0.19 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', emptyInPowerset)).
% 0.08/0.19 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', powersetE)).
% 0.08/0.19 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setunionI)).
% 0.08/0.19 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.mMW5BltzOS/E---3.1_144687.p', setunionE)).
% 0.08/0.19 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', subPowSU)).
% 0.08/0.19 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', uniqinunit)).
% 0.08/0.19 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', notinsingleton)).
% 0.08/0.19 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', eqinunit)).
% 0.08/0.19 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', singletonsswitch)).
% 0.08/0.19 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', upairsetE)).
% 0.08/0.19 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', upairsetIL)).
% 0.08/0.19 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', upairsetIR)).
% 0.08/0.19 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', vacuousDall)).
% 0.08/0.19 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', quantDeMorgan1)).
% 0.08/0.19 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', quantDeMorgan2)).
% 0.08/0.19 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', quantDeMorgan3)).
% 0.08/0.19 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', quantDeMorgan4)).
% 0.08/0.19 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', prop2setI)).
% 0.08/0.19 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', prop2set2propI)).
% 0.08/0.19 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', notdexE)).
% 0.08/0.19 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', notdallE)).
% 0.08/0.19 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', inCongP)).
% 0.08/0.19 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', in__Cong)).
% 0.08/0.19 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', emptyset__Cong)).
% 0.08/0.19 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setadjoin__Cong)).
% 0.08/0.19 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', powerset__Cong)).
% 0.08/0.19 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setunion__Cong)).
% 0.08/0.19 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', omega__Cong)).
% 0.08/0.19 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', subsetI1)).
% 0.08/0.19 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', eqimpsubset2)).
% 0.08/0.19 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', eqimpsubset1)).
% 0.08/0.19 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', subsetI2)).
% 0.08/0.19 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', emptysetsubset)).
% 0.08/0.19 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', subsetE)).
% 0.08/0.19 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', subsetE2)).
% 0.08/0.19 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', notsubsetI)).
% 0.08/0.19 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', notequalI1)).
% 0.08/0.19 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', notequalI2)).
% 0.08/0.19 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', subsetRefl)).
% 0.08/0.19 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', subsetTrans)).
% 0.08/0.19 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setadjoinSub)).
% 0.08/0.19 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setadjoinSub2)).
% 0.08/0.19 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', subset2powerset)).
% 0.08/0.19 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setextsub)).
% 0.08/0.19 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', subsetemptysetimpeq)).
% 0.08/0.19 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', powersetI1)).
% 0.08/0.19 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', powersetE1)).
% 0.08/0.19 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', inPowerset)).
% 0.08/0.19 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', powersetsubset)).
% 0.08/0.19 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binunionIL)).
% 0.08/0.19 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', upairset2IR)).
% 0.08/0.19 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binunionIR)).
% 0.08/0.19 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binunionEcases)).
% 0.08/0.19 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binunionE)).
% 0.08/0.19 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binunionLsub)).
% 0.08/0.19 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binunionRsub)).
% 0.08/0.19 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binintersectI)).
% 0.08/0.19 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binintersectSubset5)).
% 0.08/0.19 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binintersectEL)).
% 0.08/0.19 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binintersectLsub)).
% 0.08/0.19 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binintersectSubset2)).
% 0.08/0.19 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binintersectSubset3)).
% 0.08/0.19 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binintersectER)).
% 0.08/0.19 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', disjointsetsI1)).
% 0.08/0.19 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binintersectRsub)).
% 0.08/0.19 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binintersectSubset4)).
% 0.08/0.19 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', binintersectSubset1)).
% 0.08/0.19 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', bs114d)).
% 0.08/0.19 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setminusI)).
% 0.08/0.19 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setminusEL)).
% 0.08/0.19 thf(setminus, axiom, ((setminus)=(^[X4:$i, X5:$i]:(dsetconstr @ X4 @ (^[X2:$i]:(~((in @ X2 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.mMW5BltzOS/E---3.1_144687.p', setminus)).
% 0.08/0.19 thf(c_0_123, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.08/0.19 thf(c_0_124, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.08/0.19 thf(c_0_125, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.08/0.19 thf(c_0_126, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.08/0.19 thf(c_0_127, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.08/0.19 thf(c_0_128, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.08/0.19 thf(c_0_129, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.08/0.19 thf(c_0_130, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.08/0.19 thf(c_0_131, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.08/0.19 thf(c_0_132, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.08/0.19 thf(c_0_133, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.08/0.19 thf(c_0_134, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.08/0.19 thf(c_0_135, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.08/0.19 thf(c_0_136, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.08/0.19 thf(c_0_137, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.08/0.19 thf(c_0_138, 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)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setminusER])).
% 0.08/0.19 thf(c_0_139, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X340:$i]:(((((X6 @ X2 @ X340)))&(![X341:$i]:(((((X6 @ X2 @ X341)))=>(((X340)=(X341)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_123, c_0_124])).
% 0.08/0.19 thf(c_0_140, plain, ((descrp)=(![X1:$i > $o]:((((?[X342:$i]:(((((X1 @ X342)))&(![X343:$i]:(((((X1 @ X343)))=>(((X342)=(X343))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_125, c_0_124])).
% 0.08/0.19 thf(c_0_141, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.08/0.19 thf(c_0_142, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.08/0.19 thf(c_0_143, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.08/0.19 thf(c_0_144, plain, ((exuE1)=(![X1:$i > $o]:((((?[X344:$i]:(((((X1 @ X344)))&(![X345:$i]:(((((X1 @ X345)))=>(((X344)=(X345))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_126, c_0_124])).
% 0.08/0.19 thf(c_0_145, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X346:$i]:(((((X1 @ X346)))&(![X347:$i]:(((((X1 @ X347)))=>(((X346)=(X347))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_127, c_0_124])).
% 0.08/0.19 thf(c_0_146, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.08/0.19 thf(c_0_147, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_128])).
% 0.08/0.19 thf(c_0_148, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_129, c_0_128])).
% 0.08/0.19 thf(c_0_149, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_128])).
% 0.08/0.19 thf(c_0_150, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.08/0.19 thf(c_0_151, plain, ((exuE2)=(![X1:$i > $o]:((((?[X348:$i]:(((((X1 @ X348)))&(![X349:$i]:(((((X1 @ X349)))=>(((X348)=(X349))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_130, c_0_124])).
% 0.08/0.19 thf(c_0_152, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_128])).
% 0.08/0.19 thf(c_0_153, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.08/0.19 thf(c_0_154, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X350:$i]:(((((X1 @ X350)))&(![X351:$i]:(((((X1 @ X351)))=>(((X350)=(X351)))))))))))))), inference(apply_def,[status(thm)],[c_0_131, c_0_124])).
% 0.08/0.19 thf(c_0_155, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X352:$i]:(((((X1 @ X352)))&(![X353:$i]:(((((X1 @ X353)))=>(((X352)=(X353)))))))))))))))), inference(apply_def,[status(thm)],[c_0_132, c_0_124])).
% 0.08/0.19 thf(c_0_156, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X354:$i]:(((((X1 @ X354)))&(![X355:$i]:(((((X1 @ X355)))=>(((X354)=(X355)))))))))))))), inference(apply_def,[status(thm)],[c_0_133, c_0_124])).
% 0.08/0.19 thf(c_0_157, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X356:$i]:(((((X1 @ X356)))&(![X357:$i]:(((((X1 @ X357)))=>(((X356)=(X357))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_134, c_0_124])).
% 0.08/0.19 thf(c_0_158, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X358:$i]:(((((X1 @ X358)))&(![X359:$i]:(((((X1 @ X359)))=>(((X358)=(X359))))))))))<=>((?[X360:$i]:(((((X17 @ X360)))&(![X361:$i]:(((((X17 @ X361)))=>(((X360)=(X361)))))))))))))))), inference(apply_def,[status(thm)],[c_0_135, c_0_124])).
% 0.08/0.19 thf(c_0_159, plain, ((exuEu)=(![X1:$i > $o]:((((?[X362:$i]:(((((X1 @ X362)))&(![X363:$i]:(((((X1 @ X363)))=>(((X362)=(X363))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_136, c_0_124])).
% 0.08/0.19 thf(c_0_160, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X364:$i]:(((((X1 @ X364)))&(![X365:$i]:(((((X1 @ X365)))=>(((X364)=(X365))))))))))=>((((?[X366:$i]:(((((X17 @ X366)))&(![X367:$i]:(((((X17 @ X367)))=>(((X366)=(X367))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_137, c_0_124])).
% 0.08/0.19 thf(c_0_161, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.08/0.19 thf(c_0_162, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.08/0.19 thf(c_0_163, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.08/0.19 thf(c_0_164, plain, ((epred1_0)<=>![X397:$i]:(?[X398:$i]:((((![X399:$i]:(((in @ X399 @ X398)=>![X400:$i]:(((in @ X400 @ X399)=>(in @ X400 @ X397)))))&![X401:$i, X402:$i]:((((in @ X401 @ X397)&(in @ X402 @ X397))=>(![X403:$i]:(((in @ X403 @ X398)=>((in @ X401 @ X403)<=>(in @ X402 @ X403))))=>((X401)=(X402))))))&![X404:$i, X405:$i]:((((in @ X404 @ X398)&(in @ X405 @ X398))=>(![X406:$i]:(((in @ X406 @ X404)=>(in @ X406 @ X405)))|![X407:$i]:(((in @ X407 @ X405)=>(in @ X407 @ X404)))))))&![X408:$i]:(((![X409:$i]:(((in @ X409 @ X408)=>(in @ X409 @ X397)))&?[X410:$i]:((in @ X410 @ X408)))=>?[X411:$i, X412:$i]:(((((in @ X411 @ X398)&(in @ X412 @ X408))&~(?[X413:$i]:(((in @ X413 @ X411)&(in @ X413 @ X408)))))&![X414:$i]:(((in @ X414 @ X398)=>(![X415:$i]:(((in @ X415 @ X414)=>(in @ X415 @ X411)))|(in @ X412 @ X414)))))))))))), introduced(definition)).
% 0.08/0.19 thf(c_0_165, negated_conjecture, ~((![X368:$i, X369:$i]:((![X370:$i]:(((in @ X370 @ X368)<=>(in @ X370 @ X369)))=>((X368)=(X369))))=>(![X371:$i]:(~(in @ X371 @ emptyset))=>(![X372:$i, X373:$i, X374:$i]:(((in @ X374 @ (setadjoin @ X372 @ X373))<=>(((X374)=(X372))|(in @ X374 @ X373))))=>(![X375:$i, X376:$i]:(((in @ X376 @ (powerset @ X375))<=>![X377:$i]:(((in @ X377 @ X376)=>(in @ X377 @ X375)))))=>(![X378:$i, X379:$i]:(((in @ X379 @ (setunion @ X378))<=>?[X380:$i]:(((in @ X379 @ X380)&(in @ X380 @ X378)))))=>((in @ emptyset @ omega)=>(![X381:$i]:(((in @ X381 @ omega)=>(in @ (setadjoin @ X381 @ X381) @ omega)))=>(![X382:$i]:((((in @ emptyset @ X382)&![X383:$i]:((((in @ X383 @ omega)&(in @ X383 @ X382))=>(in @ (setadjoin @ X383 @ X383) @ X382))))=>![X384:$i]:(((in @ X384 @ omega)=>(in @ X384 @ X382)))))=>(![X385:$i > $i > $o, X386:$i]:((![X387:$i]:(((in @ X387 @ X386)=>?[X388:$i]:(((X385 @ X387 @ X388)&![X389:$i]:(((X385 @ X387 @ X389)=>((X388)=(X389))))))))=>?[X390:$i]:(![X391:$i]:(((in @ X391 @ X390)<=>?[X392:$i]:(((in @ X392 @ X386)&(X385 @ X392 @ X391))))))))=>(![X393:$i]:((?[X394:$i]:((in @ X394 @ X393))=>?[X395:$i]:(((in @ X395 @ X393)&~(?[X396:$i]:(((in @ X396 @ X395)&(in @ X396 @ X393))))))))=>((epred1_0)=>(![X416:$i > $o]:((?[X417:$i]:(((X416 @ X417)&![X418:$i]:(((X416 @ X418)=>((X417)=(X418))))))=>(X416 @ (descr @ (^[Z0:$i]:(X416 @ Z0))))))=>(![X419:$i, X420:$i > $o, X421:$i]:(((in @ X421 @ X419)=>((X420 @ X421)=>(in @ X421 @ (dsetconstr @ X419 @ X420)))))=>(![X422:$i, X423:$i > $o, X424:$i]:(((in @ X424 @ (dsetconstr @ X422 @ X423))=>(in @ X424 @ X422)))=>(![X425:$i, X426:$i > $o, X427:$i]:(((in @ X427 @ (dsetconstr @ X425 @ X426))=>(X426 @ X427)))=>(![X428:$i > $o]:((?[X429:$i]:(((X428 @ X429)&![X430:$i]:(((X428 @ X430)=>((X429)=(X430))))))=>?[X431:$i]:(((X428 @ X431)&![X432:$i]:(((X428 @ X432)=>((X431)=(X432))))))))=>(![X433:$o, X434:$i]:(((in @ X434 @ (prop2set @ ((X433))))=>(X433)))=>(![X435:$i]:(((in @ X435 @ emptyset)=>![X436:$o]:((X436))))=>(![X437:$i]:(((in @ X437 @ emptyset)=>~($true)))=>(![X438:$i]:(~(in @ X438 @ emptyset))=>(![X439:$i > $o]:((?[X440:$i]:(((X439 @ X440)&![X441:$i]:(((X439 @ X441)=>((X440)=(X441))))))=>?[X442:$i]:((X439 @ X442))))=>(![X443:$i, X444:$i]:((![X445:$i]:(((in @ X445 @ X443)=>(in @ X445 @ X444)))=>(![X446:$i]:(((in @ X446 @ X444)=>(in @ X446 @ X443)))=>((X443)=(X444)))))=>(![X447:$i]:((![X448:$i]:(~(in @ X448 @ X447))=>((X447)=(emptyset))))=>(![X449:$i]:((![X450:$i]:(~(in @ X450 @ X449))=>((X449)=(emptyset))))=>(![X451:$i, X452:$i > $o, X453:$i]:(((in @ X453 @ X451)=>((in @ X453 @ (dsetconstr @ X451 @ X452))<=>(X452 @ X453))))=>(![X454:$i]:((((X454)!=(emptyset))=>?[X455:$i]:((in @ X455 @ X454))))=>(![X456:$i, X457:$i > $o, X458:$i]:(((in @ X458 @ X456)=>((X457 @ X458)=>((dsetconstr @ X456 @ X457)!=(emptyset)))))=>(![X459:$i]:((?[X460:$i]:((in @ X460 @ X459))=>((X459)!=(emptyset))))=>(![X461:$i, X462:$i]:((in @ X461 @ (setadjoin @ X461 @ X462)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X463:$i, X464:$i, X465:$i]:(((in @ X465 @ X464)=>(in @ X465 @ (setadjoin @ X463 @ X464))))=>(![X466:$i, X467:$i, X468:$i]:(((in @ X468 @ (setadjoin @ X466 @ X467))=>![X469:$o]:(((((X468)=(X466))=>(X469))=>(((in @ X468 @ X467)=>(X469))=>(X469))))))=>(![X470:$i, X471:$i, X472:$i]:(((in @ X472 @ (setadjoin @ X470 @ X471))=>(((X472)=(X470))|(in @ X472 @ X471))))=>(![X473:$i]:(((dsetconstr @ X473 @ (^[Z0:$i]:($true)))=(X473)))=>(![X474:$i, X475:$i]:((![X476:$i]:(((in @ X476 @ X475)=>(in @ X476 @ X474)))=>(in @ X475 @ (powerset @ X474))))=>(![X477:$i]:((in @ emptyset @ (powerset @ X477)))=>(![X478:$i]:((in @ emptyset @ (powerset @ X478)))=>(![X479:$i, X480:$i, X481:$i]:(((in @ X480 @ (powerset @ X479))=>((in @ X481 @ X480)=>(in @ X481 @ X479))))=>(![X482:$i, X483:$i, X484:$i]:(((in @ X483 @ X484)=>((in @ X484 @ X482)=>(in @ X483 @ (setunion @ X482)))))=>(![X485:$i, X486:$i]:(((in @ X486 @ (setunion @ X485))=>![X487:$o]:((![X488:$i]:(((in @ X486 @ X488)=>((in @ X488 @ X485)=>(X487))))=>(X487)))))=>(![X489:$i, X490:$i]:(((in @ X490 @ X489)=>(in @ X490 @ (powerset @ (setunion @ X489)))))=>(![X491:$i > $o]:((?[X492:$i]:(((X491 @ X492)&![X493:$i]:(((X491 @ X493)=>((X492)=(X493))))))=>?[X494:$i]:(![X495:$i]:(((X491 @ X495)<=>((X495)=(X494)))))))=>(![X496:$i]:((((X496)!=(emptyset))=>?[X497:$i]:(((in @ X497 @ X496)&$true))))=>(![X498:$i, X499:$i]:(((in @ X498 @ (setadjoin @ X499 @ emptyset))=>((X498)=(X499))))=>(![X500:$i, X501:$i]:((((X500)!=(X501))=>~(in @ X501 @ (setadjoin @ X500 @ emptyset))))=>(![X502:$i, X503:$i]:((((X502)=(X503))=>(in @ X502 @ (setadjoin @ X503 @ emptyset))))=>(![X504:$i, X505:$i]:(((in @ X504 @ (setadjoin @ X505 @ emptyset))=>(in @ X505 @ (setadjoin @ X504 @ emptyset))))=>(![X506:$i, X507:$i, X508:$i]:(((in @ X508 @ (setadjoin @ X506 @ (setadjoin @ X507 @ emptyset)))=>(((X508)=(X506))|((X508)=(X507)))))=>(![X509:$i, X510:$i]:((in @ X509 @ (setadjoin @ X509 @ (setadjoin @ X510 @ emptyset))))=>(![X511:$i, X512:$i]:((in @ X512 @ (setadjoin @ X511 @ (setadjoin @ X512 @ emptyset))))=>(![X513:$i, X514:$i > $o]:((?[X515:$i]:(((in @ X515 @ X513)&(X514 @ X515)))=>(((dsetconstr @ X513 @ X514)=(emptyset))=>~($true))))=>(![X516:$i > $o, X517:$i]:(((in @ X517 @ emptyset)=>(X516 @ X517)))=>(![X518:$i, X519:$i > $o]:((~(![X520:$i]:(((in @ X520 @ X518)=>(X519 @ X520))))=>?[X521:$i]:(((in @ X521 @ X518)&~((X519 @ X521))))))=>(![X522:$i, X523:$i > $o]:((![X524:$i]:(((in @ X524 @ X522)=>~((X523 @ X524))))=>~(?[X525:$i]:(((in @ X525 @ X522)&(X523 @ X525))))))=>(![X526:$i, X527:$i > $o]:((~(?[X528:$i]:(((in @ X528 @ X526)&(X527 @ X528))))=>![X529:$i]:(((in @ X529 @ X526)=>~((X527 @ X529))))))=>(![X530:$i, X531:$i > $o]:((?[X532:$i]:(((in @ X532 @ X530)&~((X531 @ X532))))=>~(![X533:$i]:(((in @ X533 @ X530)=>(X531 @ X533))))))=>(![X534:$o]:(((X534)=>(in @ emptyset @ (prop2set @ ((X534))))))=>(![X535:$o]:(((X535)=>(set2prop @ (prop2set @ ((X535))))))=>(![X536:$i, X537:$i > $o]:((~(?[X538:$i]:(((in @ X538 @ X536)&(X537 @ X538))))=>![X539:$i]:(((in @ X539 @ X536)=>~((X537 @ X539))))))=>(![X540:$i, X541:$i > $o]:((~(![X542:$i]:(((in @ X542 @ X540)=>(X541 @ X542))))=>?[X543:$i]:(((in @ X543 @ X540)&~((X541 @ X543))))))=>(![X544:$i > $o]:((?[X545:$i]:(((X544 @ X545)&![X546:$i]:(((X544 @ X546)=>((X545)=(X546))))))=>?[X547:$i]:(((X544 @ X547)&![X548:$i]:(((X544 @ X548)=>((X547)=(X548))))))))=>(![X549:$i > $o]:((?[X550:$i]:((X549 @ X550))=>(![X551:$i, X552:$i]:(((X549 @ X551)=>((X549 @ X552)=>((X551)=(X552)))))=>?[X553:$i]:(((X549 @ X553)&![X554:$i]:(((X549 @ X554)=>((X553)=(X554)))))))))=>(![X555:$i > $o]:((?[X556:$i]:(![X557:$i]:(((X555 @ X557)<=>((X557)=(X556)))))=>?[X558:$i]:(((X555 @ X558)&![X559:$i]:(((X555 @ X559)=>((X558)=(X559))))))))=>(![X560:$i, X561:$i]:((((X560)=(X561))=>![X562:$i, X563:$i]:((((X562)=(X563))=>((in @ X562 @ X560)=>(in @ X563 @ X561))))))=>(![X564:$i, X565:$i]:((((X564)=(X565))=>![X566:$i, X567:$i]:((((X566)=(X567))=>((in @ X566 @ X564)<=>(in @ X567 @ X565))))))=>(![X568:$i > $o]:((?[X569:$i]:(((X568 @ X569)&![X570:$i]:(((X568 @ X570)=>((X569)=(X570))))))=>![X571:$i, X572:$i]:(((X568 @ X571)=>((X568 @ X572)=>((X571)=(X572)))))))=>(![X573:$i > $o, X574:$i > $o]:((![X575:$i, X576:$i]:((((X575)=(X576))=>((X573 @ X575)<=>(X574 @ X576))))=>(?[X577:$i]:(((X573 @ X577)&![X578:$i]:(((X573 @ X578)=>((X577)=(X578))))))<=>?[X579:$i]:(((X574 @ X579)&![X580:$i]:(((X574 @ X580)=>((X579)=(X580)))))))))=>(((emptyset)=(emptyset))=>(![X581:$i, X582:$i]:((((X581)=(X582))=>![X583:$i, X584:$i]:((((X583)=(X584))=>((setadjoin @ X581 @ X583)=(setadjoin @ X582 @ X584))))))=>(![X585:$i, X586:$i]:((((X585)=(X586))=>((powerset @ X585)=(powerset @ X586))))=>(![X587:$i, X588:$i]:((((X587)=(X588))=>((setunion @ X587)=(setunion @ X588))))=>(((omega)=(omega))=>(![X589:$i > $o]:((?[X590:$i]:(((X589 @ X590)&![X591:$i]:(((X589 @ X591)=>((X590)=(X591))))))=>![X592:$i, X593:$i]:(((X589 @ X592)=>((X589 @ X593)=>((X592)=(X593)))))))=>(![X594:$i > $o, X595:$i > $o]:((![X596:$i, X597:$i]:((((X596)=(X597))=>((X594 @ X596)<=>(X595 @ X597))))=>(?[X598:$i]:(((X594 @ X598)&![X599:$i]:(((X594 @ X599)=>((X598)=(X599))))))=>(?[X600:$i]:(((X595 @ X600)&![X601:$i]:(((X595 @ X601)=>((X600)=(X601))))))=>((descr @ X594)=(descr @ X595))))))=>(![X602:$i, X603:$i]:((((X602)=(X603))=>![X604:$i > $o, X605:$i > $o]:((![X606:$i]:(((in @ X606 @ X602)=>![X607:$i]:(((in @ X607 @ X603)=>(((X606)=(X607))=>((X604 @ X606)<=>(X605 @ X607)))))))=>((dsetconstr @ X602 @ X604)=(dsetconstr @ X603 @ X605))))))=>(![X608:$i, X609:$i]:((![X610:$i]:(((in @ X610 @ X608)=>(in @ X610 @ X609)))=>(subset @ X608 @ X609)))=>(![X611:$i, X612:$i]:((((X611)=(X612))=>(subset @ X612 @ X611)))=>(![X613:$i, X614:$i]:((((X613)=(X614))=>(subset @ X613 @ X614)))=>(![X615:$i, X616:$i]:((![X617:$i]:(((in @ X617 @ X615)=>(in @ X617 @ X616)))=>(subset @ X615 @ X616)))=>(![X618:$i]:((subset @ emptyset @ X618))=>(![X619:$i, X620:$i, X621:$i]:(((subset @ X619 @ X620)=>((in @ X621 @ X619)=>(in @ X621 @ X620))))=>(![X622:$i, X623:$i, X624:$i]:(((subset @ X622 @ X623)=>(~(in @ X624 @ X623)=>~(in @ X624 @ X622))))=>(![X625:$i, X626:$i, X627:$i]:(((in @ X627 @ X625)=>(~(in @ X627 @ X626)=>~(subset @ X625 @ X626))))=>(![X628:$i, X629:$i]:((~(subset @ X628 @ X629)=>((X628)!=(X629))))=>(![X630:$i, X631:$i, X632:$i]:(((in @ X632 @ X630)=>(~(in @ X632 @ X631)=>((X630)!=(X631)))))=>(![X633:$i]:((subset @ X633 @ X633))=>(![X634:$i, X635:$i, X636:$i]:(((subset @ X634 @ X635)=>((subset @ X635 @ X636)=>(subset @ X634 @ X636))))=>(![X637:$i, X638:$i]:((subset @ X638 @ (setadjoin @ X637 @ X638)))=>(![X639:$i, X640:$i, X641:$i]:(((subset @ X639 @ X641)=>(subset @ X639 @ (setadjoin @ X640 @ X641))))=>(![X642:$i, X643:$i]:(((subset @ X642 @ X643)=>(in @ X642 @ (powerset @ X643))))=>(![X644:$i, X645:$i]:(((subset @ X644 @ X645)=>((subset @ X645 @ X644)=>((X644)=(X645)))))=>(![X646:$i]:(((subset @ X646 @ emptyset)=>((X646)=(emptyset))))=>(![X647:$i, X648:$i]:(((subset @ X648 @ X647)=>(in @ X648 @ (powerset @ X647))))=>(![X649:$i, X650:$i]:(((in @ X650 @ (powerset @ X649))=>(subset @ X650 @ X649)))=>(![X651:$i]:((in @ X651 @ (powerset @ X651)))=>(![X652:$i, X653:$i]:(((subset @ X652 @ X653)=>(subset @ (powerset @ X652) @ (powerset @ X653))))=>(![X654:$i, X655:$i > $o]:((in @ (dsetconstr @ X654 @ X655) @ (powerset @ X654)))=>(![X656:$i, X657:$i > $o]:((subset @ (dsetconstr @ X656 @ X657) @ X656))=>(![X658:$i, X659:$i, X660:$i]:(((in @ X660 @ X658)=>(in @ X660 @ (binunion @ X658 @ X659))))=>(![X661:$i, X662:$i]:((in @ X662 @ (setadjoin @ X661 @ (setadjoin @ X662 @ emptyset))))=>(![X663:$i, X664:$i, X665:$i]:(((in @ X665 @ X664)=>(in @ X665 @ (binunion @ X663 @ X664))))=>(![X666:$i, X667:$i, X668:$i, X669:$o]:(((in @ X668 @ (binunion @ X666 @ X667))=>(((in @ X668 @ X666)=>(X669))=>(((in @ X668 @ X667)=>(X669))=>(X669)))))=>(![X670:$i, X671:$i, X672:$i]:(((in @ X672 @ (binunion @ X670 @ X671))=>((in @ X672 @ X670)|(in @ X672 @ X671))))=>(![X673:$i, X674:$i]:((subset @ X673 @ (binunion @ X673 @ X674)))=>(![X675:$i, X676:$i]:((subset @ X676 @ (binunion @ X675 @ X676)))=>(![X677:$i, X678:$i, X679:$i]:(((in @ X679 @ X677)=>((in @ X679 @ X678)=>(in @ X679 @ (binintersect @ X677 @ X678)))))=>(![X680:$i, X681:$i, X682:$i]:(((subset @ X682 @ X680)=>((subset @ X682 @ X681)=>(subset @ X682 @ (binintersect @ X680 @ X681)))))=>(![X683:$i, X684:$i, X685:$i]:(((in @ X685 @ (binintersect @ X683 @ X684))=>(in @ X685 @ X683)))=>(![X686:$i, X687:$i]:((subset @ (binintersect @ X686 @ X687) @ X686))=>(![X688:$i, X689:$i]:(((subset @ X688 @ X689)=>((binintersect @ X688 @ X689)=(X688))))=>(![X690:$i, X691:$i]:((((binintersect @ X690 @ X691)=(X691))=>(subset @ X691 @ X690)))=>(![X692:$i, X693:$i, X694:$i]:(((in @ X694 @ (binintersect @ X692 @ X693))=>(in @ X694 @ X693)))=>(![X695:$i, X696:$i]:((~(?[X697:$i]:(((in @ X697 @ X695)&(in @ X697 @ X696))))=>((binintersect @ X695 @ X696)=(emptyset))))=>(![X698:$i, X699:$i]:((subset @ (binintersect @ X698 @ X699) @ X699))=>(![X700:$i, X701:$i]:(((subset @ X701 @ X700)=>((binintersect @ X700 @ X701)=(X701))))=>(![X702:$i, X703:$i]:((((binintersect @ X702 @ X703)=(X702))=>(subset @ X702 @ X703)))=>(![X704:$i, X705:$i, X706:$i]:(((binintersect @ X704 @ (binunion @ X705 @ X706))=(binunion @ (binintersect @ X704 @ X705) @ (binintersect @ X704 @ X706))))=>(![X707:$i, X708:$i, X709:$i]:(((in @ X709 @ X707)=>(~(in @ X709 @ X708)=>(in @ X709 @ (setminus @ X707 @ X708)))))=>(![X710:$i, X711:$i, X712:$i]:(((in @ X712 @ (setminus @ X710 @ X711))=>(in @ X712 @ X710)))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~(in @ X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_138, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_139]), foundationAx]), wellorderingAx]), c_0_140]), c_0_141]), c_0_142]), c_0_143]), c_0_144]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_145]), setext]), emptyI]), noeltsimpempty]), c_0_146]), c_0_147]), c_0_148]), c_0_149]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_150]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_151]), c_0_152]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_153]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_154]), c_0_155]), c_0_156]), inCongP]), in__Cong]), c_0_157]), c_0_158]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_159]), c_0_160]), c_0_161]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_162]), c_0_163]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL])])]), c_0_164])).
% 0.08/0.19 thf(c_0_166, plain, ![X713:$i, X714:$i]:(((setminus @ X713 @ X714)=(dsetconstr @ X713 @ (^[Z0:$i]:(~((in @ Z0 @ X714))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[setminus])])).
% 0.08/0.19 thf(c_0_167, negated_conjecture, ![X717:$i, X718:$i, X720:$i, X721:$i, X722:$i, X723:$i, X724:$i, X725:$i, X726:$i, X727:$i, X728:$i, X730:$i, X731:$i, X733:$i, X734:$i, X735:$i, X736:$i, X737:$i, X739:$i, X740:$i > $i > $o, X741:$i, X743:$i, X746:$i, X748:$i, X749:$i, X750:$i, X751:$i, X753:$i, X754:$i > $o, X755:$i, X757:$i, X758:$i > $o, X759:$i, X760:$i, X761:$i > $o, X762:$i, X763:$i, X764:$i > $o, X765:$i, X766:$i > $o, X767:$i, X770:$i, X771:$o, X772:$i, X773:$i, X774:$o, X775:$i, X776:$i, X777:$i > $o, X778:$i, X781:$i, X782:$i, X785:$i, X787:$i, X789:$i, X790:$i > $o, X791:$i, X792:$i, X794:$i, X795:$i > $o, X796:$i, X797:$i, X798:$i, X799:$i, X800:$i, X801:$i, X802:$i, X803:$i, X804:$i, X805:$i, X806:$i, X807:$o, X808:$i, X809:$i, X810:$i, X811:$i, X812:$i, X813:$i, X815:$i, X816:$i, X817:$i, X818:$i, X819:$i, X820:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$o, X827:$i, X828:$i, X829:$i > $o, X830:$i, X833:$i, X834:$i, X835:$i, X837:$i, X838:$i, X839:$i, X840:$i, X841:$i, X842:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i, X848:$i, X849:$i, X850:$i, X851:$i, X852:$i, X853:$i > $o, X854:$i, X855:$i > $o, X856:$i, X857:$i, X858:$i > $o, X859:$i, X861:$i, X862:$i > $o, X864:$i, X865:$i, X866:$i > $o, X868:$i, X869:$i, X870:$i > $o, X871:$i, X873:$o, X874:$o, X875:$i, X876:$i > $o, X878:$i, X879:$i, X880:$i > $o, X881:$i, X883:$i > $o, X884:$i, X887:$i, X888:$i > $o, X889:$i, X893:$i, X894:$i > $o, X895:$i, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X904:$i, X905:$i, X906:$i, X907:$i > $o, X908:$i, X910:$i, X911:$i, X912:$i > $o, X913:$i > $o, X916:$i, X919:$i, X920:$i, X923:$i, X924:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i, X932:$i > $o, X933:$i, X935:$i, X936:$i, X937:$i > $o, X938:$i > $o, X941:$i, X943:$i, X945:$i, X946:$i, X947:$i > $o, X948:$i > $o, X951:$i, X952:$i, X954:$i, X955:$i, X956:$i, X957:$i, X958:$i, X959:$i, X961:$i, X962:$i, X963:$i, X964:$i, X965:$i, X966:$i, X967:$i, X968:$i, X969:$i, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i, X977:$i, X978:$i, X979:$i, X980:$i, X981:$i, X982:$i, X983:$i, X984:$i, X985:$i, X986:$i, X987:$i, X988:$i, X989:$i, X990:$i, X991:$i, X992:$i, X993:$i, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i > $o, X999:$i, X1000:$i > $o, X1001:$i, X1002:$i, X1003:$i, X1004:$i, X1005:$i, X1006:$i, X1007:$i, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$o, X1013:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1055:$i]:((((~(in @ (esk1_2 @ X717 @ X718) @ X717)|~(in @ (esk1_2 @ X717 @ X718) @ X718)|((X717)=(X718)))&((in @ (esk1_2 @ X717 @ X718) @ X717)|(in @ (esk1_2 @ X717 @ 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X913))))))&((((X912 @ (esk44_2 @ X912 @ X913))|((X913 @ (esk43_3 @ X912 @ X913 @ X920))|~(X913 @ X920))|((X912 @ (esk39_2 @ X912 @ X913))|(X913 @ (esk40_2 @ X912 @ X913))))&(~(X912 @ X923)|((esk44_2 @ X912 @ X913)=(X923))|((X913 @ (esk43_3 @ X912 @ X913 @ X920))|~(X913 @ X920))|((X912 @ (esk39_2 @ X912 @ X913))|(X913 @ (esk40_2 @ X912 @ X913)))))&(((X912 @ (esk44_2 @ X912 @ X913))|(((X920)!=(esk43_3 @ X912 @ X913 @ X920))|~(X913 @ X920))|((X912 @ (esk39_2 @ X912 @ X913))|(X913 @ (esk40_2 @ X912 @ X913))))&(~(X912 @ X923)|((esk44_2 @ X912 @ X913)=(X923))|(((X920)!=(esk43_3 @ X912 @ X913 @ X920))|~(X913 @ X920))|((X912 @ (esk39_2 @ X912 @ X913))|(X913 @ (esk40_2 @ X912 @ X913)))))))))&(((emptyset)=(emptyset))&((((X924)!=(X925))|(((X926)!=(X927))|((setadjoin @ X924 @ X926)=(setadjoin @ X925 @ X927))))&((((X928)!=(X929))|((powerset @ X928)=(powerset @ X929)))&((((X930)!=(X931))|((setunion @ X930)=(setunion @ X931)))&(((omega)=(omega))&((((X932 @ (esk45_2 @ X932 @ X933))|~(X932 @ X933)|(~(X932 @ X935)|(~(X932 @ X936)|((X935)=(X936)))))&(((X933)!=(esk45_2 @ X932 @ X933))|~(X932 @ X933)|(~(X932 @ X935)|(~(X932 @ X936)|((X935)=(X936))))))&((((((X938 @ (esk49_3 @ X937 @ X938 @ X943))|~(X938 @ X943)|((descr @ X937)=(descr @ X938))|((X937 @ (esk48_3 @ X937 @ X938 @ X941))|~(X937 @ X941))|((esk46_2 @ X937 @ X938)=(esk47_2 @ X937 @ X938)))&(((X943)!=(esk49_3 @ X937 @ X938 @ X943))|~(X938 @ X943)|((descr @ X937)=(descr @ X938))|((X937 @ (esk48_3 @ X937 @ X938 @ X941))|~(X937 @ X941))|((esk46_2 @ X937 @ X938)=(esk47_2 @ X937 @ X938))))&(((X938 @ (esk49_3 @ X937 @ X938 @ X943))|~(X938 @ X943)|((descr @ X937)=(descr @ X938))|(((X941)!=(esk48_3 @ X937 @ X938 @ X941))|~(X937 @ X941))|((esk46_2 @ X937 @ X938)=(esk47_2 @ X937 @ X938)))&(((X943)!=(esk49_3 @ X937 @ X938 @ X943))|~(X938 @ X943)|((descr @ X937)=(descr @ X938))|(((X941)!=(esk48_3 @ X937 @ X938 @ X941))|~(X937 @ X941))|((esk46_2 @ X937 @ X938)=(esk47_2 @ X937 @ X938)))))&(((((X938 @ (esk49_3 @ X937 @ X938 @ X943))|~(X938 @ X943)|((descr @ X937)=(descr @ X938))|((X937 @ (esk48_3 @ X937 @ X938 @ X941))|~(X937 @ X941))|(~(X937 @ (esk46_2 @ X937 @ X938))|~(X938 @ (esk47_2 @ X937 @ X938))))&(((X943)!=(esk49_3 @ X937 @ X938 @ X943))|~(X938 @ X943)|((descr @ X937)=(descr @ X938))|((X937 @ (esk48_3 @ X937 @ X938 @ X941))|~(X937 @ X941))|(~(X937 @ (esk46_2 @ X937 @ X938))|~(X938 @ (esk47_2 @ X937 @ X938)))))&(((X938 @ (esk49_3 @ X937 @ X938 @ X943))|~(X938 @ X943)|((descr @ X937)=(descr @ X938))|(((X941)!=(esk48_3 @ X937 @ X938 @ X941))|~(X937 @ X941))|(~(X937 @ (esk46_2 @ X937 @ X938))|~(X938 @ (esk47_2 @ X937 @ X938))))&(((X943)!=(esk49_3 @ X937 @ X938 @ X943))|~(X938 @ X943)|((descr @ X937)=(descr @ X938))|(((X941)!=(esk48_3 @ X937 @ X938 @ X941))|~(X937 @ X941))|(~(X937 @ (esk46_2 @ X937 @ X938))|~(X938 @ (esk47_2 @ X937 @ X938))))))&((((X938 @ (esk49_3 @ X937 @ X938 @ X943))|~(X938 @ X943)|((descr @ X937)=(descr @ X938))|((X937 @ (esk48_3 @ X937 @ X938 @ X941))|~(X937 @ X941))|((X937 @ (esk46_2 @ X937 @ X938))|(X938 @ (esk47_2 @ X937 @ X938))))&(((X943)!=(esk49_3 @ X937 @ X938 @ X943))|~(X938 @ X943)|((descr @ X937)=(descr @ X938))|((X937 @ (esk48_3 @ X937 @ X938 @ X941))|~(X937 @ X941))|((X937 @ (esk46_2 @ X937 @ X938))|(X938 @ (esk47_2 @ X937 @ X938)))))&(((X938 @ (esk49_3 @ X937 @ X938 @ X943))|~(X938 @ X943)|((descr @ X937)=(descr @ X938))|(((X941)!=(esk48_3 @ X937 @ X938 @ X941))|~(X937 @ X941))|((X937 @ (esk46_2 @ X937 @ X938))|(X938 @ (esk47_2 @ X937 @ X938))))&(((X943)!=(esk49_3 @ X937 @ X938 @ X943))|~(X938 @ X943)|((descr @ X937)=(descr @ X938))|(((X941)!=(esk48_3 @ X937 @ X938 @ X941))|~(X937 @ X941))|((X937 @ (esk46_2 @ X937 @ X938))|(X938 @ (esk47_2 @ X937 @ X938))))))))&((((in @ (esk50_4 @ X945 @ X946 @ X947 @ X948) @ X945)|((dsetconstr @ X945 @ X947)=(dsetconstr @ X946 @ X948))|((X945)!=(X946)))&(((in @ (esk51_4 @ X945 @ X946 @ X947 @ X948) @ X946)|((dsetconstr @ X945 @ X947)=(dsetconstr @ X946 @ X948))|((X945)!=(X946)))&((((esk50_4 @ X945 @ X946 @ X947 @ X948)=(esk51_4 @ X945 @ X946 @ X947 @ X948))|((dsetconstr @ X945 @ X947)=(dsetconstr @ X946 @ X948))|((X945)!=(X946)))&((~(X947 @ (esk50_4 @ X945 @ X946 @ X947 @ X948))|~(X948 @ (esk51_4 @ X945 @ X946 @ X947 @ X948))|((dsetconstr @ X945 @ X947)=(dsetconstr @ X946 @ X948))|((X945)!=(X946)))&((X947 @ (esk50_4 @ X945 @ X946 @ X947 @ X948))|(X948 @ (esk51_4 @ X945 @ X946 @ X947 @ X948))|((dsetconstr @ X945 @ X947)=(dsetconstr @ X946 @ X948))|((X945)!=(X946)))))))&((((in @ (esk52_2 @ X951 @ X952) @ X951)|(subset @ X951 @ X952))&(~(in @ (esk52_2 @ X951 @ X952) @ X952)|(subset @ X951 @ X952)))&((((X954)!=(X955))|(subset @ X955 @ X954))&((((X956)!=(X957))|(subset @ X956 @ X957))&((((in @ (esk53_2 @ X958 @ X959) @ X958)|(subset @ X958 @ X959))&(~(in @ (esk53_2 @ X958 @ X959) @ X959)|(subset @ X958 @ X959)))&((subset @ emptyset @ X961)&((~(subset @ X962 @ X963)|(~(in @ X964 @ X962)|(in @ X964 @ X963)))&((~(subset @ X965 @ X966)|((in @ X967 @ X966)|~(in @ X967 @ X965)))&((~(in @ X970 @ X968)|((in @ X970 @ X969)|~(subset @ X968 @ X969)))&(((subset @ X971 @ X972)|((X971)!=(X972)))&((~(in @ X975 @ X973)|((in @ X975 @ X974)|((X973)!=(X974))))&((subset @ X976 @ X976)&((~(subset @ X977 @ X978)|(~(subset @ X978 @ X979)|(subset @ X977 @ X979)))&((subset @ X981 @ (setadjoin @ X980 @ X981))&((~(subset @ X982 @ X984)|(subset @ X982 @ (setadjoin @ X983 @ X984)))&((~(subset @ X985 @ X986)|(in @ X985 @ (powerset @ X986)))&((~(subset @ X987 @ X988)|(~(subset @ X988 @ X987)|((X987)=(X988))))&((~(subset @ X989 @ emptyset)|((X989)=(emptyset)))&((~(subset @ X991 @ X990)|(in @ X991 @ (powerset @ X990)))&((~(in @ X993 @ (powerset @ X992))|(subset @ X993 @ X992))&((in @ X994 @ (powerset @ X994))&((~(subset @ X995 @ X996)|(subset @ (powerset @ X995) @ (powerset @ X996)))&((in @ (dsetconstr @ X997 @ X998) @ (powerset @ X997))&((subset @ (dsetconstr @ X999 @ X1000) @ X999)&((~(in @ X1003 @ X1001)|(in @ X1003 @ (binunion @ X1001 @ X1002)))&((in @ X1005 @ (setadjoin @ X1004 @ (setadjoin @ X1005 @ emptyset)))&((~(in @ X1008 @ X1007)|(in @ X1008 @ (binunion @ X1006 @ X1007)))&(((((in @ X1011 @ X1010)|(X1012)|(in @ X1011 @ X1009)|~(in @ X1011 @ (binunion @ X1009 @ X1010)))&(~(X1012)|(X1012)|(in @ X1011 @ X1009)|~(in @ X1011 @ (binunion @ X1009 @ X1010))))&(((in @ X1011 @ X1010)|(X1012)|~(X1012)|~(in @ X1011 @ (binunion @ X1009 @ X1010)))&(~(X1012)|(X1012)|~(X1012)|~(in @ X1011 @ (binunion @ X1009 @ X1010)))))&((~(in @ X1015 @ (binunion @ X1013 @ X1014))|((in @ X1015 @ X1013)|(in @ X1015 @ X1014)))&((subset @ X1016 @ (binunion @ X1016 @ X1017))&((subset @ X1019 @ (binunion @ X1018 @ X1019))&((~(in @ X1022 @ X1020)|(~(in @ X1022 @ X1021)|(in @ X1022 @ (binintersect @ X1020 @ X1021))))&((~(subset @ X1025 @ X1023)|(~(subset @ X1025 @ X1024)|(subset @ X1025 @ (binintersect @ X1023 @ X1024))))&((~(in @ X1028 @ (binintersect @ X1026 @ X1027))|(in @ X1028 @ X1026))&((subset @ (binintersect @ X1029 @ X1030) @ X1029)&((~(subset @ X1031 @ X1032)|((binintersect @ X1031 @ X1032)=(X1031)))&((((binintersect @ X1033 @ X1034)!=(X1034))|(subset @ X1034 @ X1033))&((~(in @ X1037 @ (binintersect @ X1035 @ X1036))|(in @ X1037 @ X1036))&((((in @ (esk54_2 @ X1038 @ X1039) @ X1038)|((binintersect @ X1038 @ X1039)=(emptyset)))&((in @ (esk54_2 @ X1038 @ X1039) @ X1039)|((binintersect @ X1038 @ X1039)=(emptyset))))&((subset @ (binintersect @ X1041 @ X1042) @ X1042)&((~(subset @ X1044 @ X1043)|((binintersect @ X1043 @ X1044)=(X1044)))&((((binintersect @ X1045 @ X1046)!=(X1045))|(subset @ X1045 @ X1046))&(((binintersect @ X1047 @ (binunion @ X1048 @ X1049))=(binunion @ (binintersect @ X1047 @ X1048) @ (binintersect @ X1047 @ X1049)))&((~(in @ X1052 @ X1050)|((in @ X1052 @ X1051)|(in @ X1052 @ (setminus @ X1050 @ X1051))))&((~(in @ X1055 @ (setminus @ X1053 @ X1054))|(in @ X1055 @ X1053))&((in @ esk57_0 @ (setminus @ esk55_0 @ esk56_0))&(in @ esk57_0 @ esk56_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_165])])])])])])])).
% 0.08/0.19 thf(c_0_168, plain, ![X715:$i, X716:$i]:(((setminus @ X715 @ X716)=(dsetconstr @ X715 @ (^[Z0:$i]:(~((in @ Z0 @ X716))))))), inference(variable_rename,[status(thm)],[c_0_166])).
% 0.08/0.19 thf(c_0_169, plain, ![X1078:$i, X3:$i]:(((epred2_1 @ X3 @ X1078)<=>~((in @ X1078 @ X3)))), introduced(definition)).
% 0.08/0.19 thf(c_0_170, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_167])).
% 0.08/0.19 thf(c_0_171, plain, ![X2:$i, X3:$i]:(((setminus @ X2 @ X3)=(dsetconstr @ X2 @ (epred2_1 @ X3)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_168]), c_0_169])).
% 0.08/0.19 thf(c_0_172, plain, ![X1080:$i, X1081:$i]:(((~(epred2_1 @ X1081 @ X1080)|~(in @ X1080 @ X1081))&((in @ X1080 @ X1081)|(epred2_1 @ X1081 @ X1080)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[])])])])).
% 0.08/0.19 thf(c_0_173, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((epred2_1 @ X2 @ X3)|~((in @ X3 @ (setminus @ X4 @ X2))))), inference(spm,[status(thm)],[c_0_170, c_0_171])).
% 0.08/0.19 thf(c_0_174, negated_conjecture, (in @ esk57_0 @ (setminus @ esk55_0 @ esk56_0)), inference(split_conjunct,[status(thm)],[c_0_167])).
% 0.08/0.19 thf(c_0_175, plain, ![X3:$i, X2:$i]:((~((epred2_1 @ X2 @ X3))|~((in @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_172])).
% 0.08/0.19 thf(c_0_176, negated_conjecture, (epred2_1 @ esk56_0 @ esk57_0), inference(spm,[status(thm)],[c_0_173, c_0_174])).
% 0.08/0.19 thf(c_0_177, negated_conjecture, (in @ esk57_0 @ esk56_0), inference(split_conjunct,[status(thm)],[c_0_167])).
% 0.08/0.19 thf(c_0_178, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175, c_0_176]), c_0_177])]), ['proof']).
% 0.08/0.19 % SZS output end CNFRefutation
% 0.08/0.19 % Parsed axioms : 261
% 0.08/0.19 % Removed by relevancy pruning/SinE : 0
% 0.08/0.19 % Initial clauses : 378
% 0.08/0.19 % Removed in clause preprocessing : 156
% 0.08/0.19 % Initial clauses in saturation : 222
% 0.08/0.19 % Processed clauses : 125
% 0.08/0.19 % ...of these trivial : 5
% 0.08/0.19 % ...subsumed : 26
% 0.08/0.19 % ...remaining for further processing : 94
% 0.08/0.19 % Other redundant clauses eliminated : 10
% 0.08/0.19 % Clauses deleted for lack of memory : 0
% 0.08/0.19 % Backward-subsumed : 0
% 0.08/0.19 % Backward-rewritten : 2
% 0.08/0.19 % Generated clauses : 337
% 0.08/0.19 % ...of the previous two non-redundant : 260
% 0.08/0.19 % ...aggressively subsumed : 0
% 0.08/0.19 % Contextual simplify-reflections : 0
% 0.08/0.19 % Paramodulations : 327
% 0.08/0.19 % Factorizations : 0
% 0.08/0.19 % NegExts : 0
% 0.08/0.19 % Equation resolutions : 10
% 0.08/0.19 % Disequality decompositions : 0
% 0.08/0.19 % Total rewrite steps : 74
% 0.08/0.19 % ...of those cached : 39
% 0.08/0.19 % Propositional unsat checks : 0
% 0.08/0.19 % Propositional check models : 0
% 0.08/0.19 % Propositional check unsatisfiable : 0
% 0.08/0.19 % Propositional clauses : 0
% 0.08/0.19 % Propositional clauses after purity: 0
% 0.08/0.19 % Propositional unsat core size : 0
% 0.08/0.19 % Propositional preprocessing time : 0.000
% 0.08/0.19 % Propositional encoding time : 0.000
% 0.08/0.19 % Propositional solver time : 0.000
% 0.08/0.19 % Success case prop preproc time : 0.000
% 0.08/0.19 % Success case prop encoding time : 0.000
% 0.08/0.19 % Success case prop solver time : 0.000
% 0.08/0.19 % Current number of processed clauses : 86
% 0.08/0.19 % Positive orientable unit clauses : 42
% 0.08/0.19 % Positive unorientable unit clauses: 0
% 0.08/0.19 % Negative unit clauses : 1
% 0.08/0.19 % Non-unit-clauses : 43
% 0.08/0.19 % Current number of unprocessed clauses: 355
% 0.08/0.19 % ...number of literals in the above : 1050
% 0.08/0.19 % Current number of archived formulas : 0
% 0.08/0.19 % Current number of archived clauses : 2
% 0.08/0.19 % Clause-clause subsumption calls (NU) : 204
% 0.08/0.19 % Rec. Clause-clause subsumption calls : 192
% 0.08/0.19 % Non-unit clause-clause subsumptions : 16
% 0.08/0.19 % Unit Clause-clause subsumption calls : 44
% 0.08/0.19 % Rewrite failures with RHS unbound : 0
% 0.08/0.19 % BW rewrite match attempts : 6
% 0.08/0.19 % BW rewrite match successes : 2
% 0.08/0.19 % Condensation attempts : 0
% 0.08/0.19 % Condensation successes : 0
% 0.08/0.19 % Termbank termtop insertions : 34876
% 0.08/0.19 % Search garbage collected termcells : 12023
% 0.08/0.19
% 0.08/0.19 % -------------------------------------------------
% 0.08/0.19 % User time : 0.027 s
% 0.08/0.19 % System time : 0.004 s
% 0.08/0.19 % Total time : 0.031 s
% 0.08/0.19 % Maximum resident set size: 6448 pages
% 0.08/0.19
% 0.08/0.19 % -------------------------------------------------
% 0.08/0.19 % User time : 0.030 s
% 0.08/0.19 % System time : 0.008 s
% 0.08/0.19 % Total time : 0.038 s
% 0.08/0.19 % Maximum resident set size: 4864 pages
% 0.08/0.19 % E exiting
%------------------------------------------------------------------------------