%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU602^1 : 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 : n019.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 08:26:52 AM UTC 2026
% Result : Theorem 0.19s 0.31s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU602^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n019.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:57:02 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.19/0.26 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.WY8GZZNdxw/E---3.1_807434.p
% 0.19/0.31 % Version: 3.5.1-ho
% 0.19/0.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.19/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.31 % Starting ehoh_best5 with 300s (1) cores
% 0.19/0.31 % Starting almost_fo_3_lam with 300s (1) cores
% 0.19/0.31 % Starting new_bool_5 with 300s (1) cores
% 0.19/0.31 % Starting pre_casc_3 with 300s (1) cores
% 0.19/0.31 % Starting ho_unfolding_8 with 300s (1) cores
% 0.19/0.31 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.19/0.31 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.31 % Starting new_ho_5 with 300s (1) cores
% 0.19/0.31 % ho_unfolding_8 with pid 807452 completed with status 0
% 0.19/0.31 % Result found by ho_unfolding_8
% 0.19/0.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.19/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.31 % Starting ehoh_best5 with 300s (1) cores
% 0.19/0.31 % Starting almost_fo_3_lam with 300s (1) cores
% 0.19/0.31 % Starting new_bool_5 with 300s (1) cores
% 0.19/0.31 % Starting pre_casc_3 with 300s (1) cores
% 0.19/0.31 % Starting ho_unfolding_8 with 300s (1) cores
% 0.19/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.31 % No SInE strategy applied
% 0.19/0.31 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.19/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.19/0.31 % SubtermCWHack with pid 807468 completed with status 0
% 0.19/0.31 % Result found by SubtermCWHack
% 0.19/0.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.19/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.31 % Starting ehoh_best5 with 300s (1) cores
% 0.19/0.31 % Starting almost_fo_3_lam with 300s (1) cores
% 0.19/0.31 % Starting new_bool_5 with 300s (1) cores
% 0.19/0.31 % Starting pre_casc_3 with 300s (1) cores
% 0.19/0.31 % Starting ho_unfolding_8 with 300s (1) cores
% 0.19/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.31 % No SInE strategy applied
% 0.19/0.31 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.19/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.19/0.31 % Preprocessing time : 0.002 s
% 0.19/0.31
% 0.19/0.31 % Proof found!
% 0.19/0.31 % SZS status Theorem
% 0.19/0.31 % SZS output start CNFRefutation
% 0.19/0.31 thf(decl_23, type, in: $i > $i > $o).
% 0.19/0.31 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.19/0.31 thf(decl_25, type, setextAx: $o).
% 0.19/0.31 thf(decl_26, type, emptyset: $i).
% 0.19/0.31 thf(decl_27, type, emptysetAx: $o).
% 0.19/0.31 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.19/0.31 thf(decl_29, type, setadjoinAx: $o).
% 0.19/0.31 thf(decl_30, type, powerset: $i > $i).
% 0.19/0.31 thf(decl_31, type, powersetAx: $o).
% 0.19/0.31 thf(decl_32, type, setunion: $i > $i).
% 0.19/0.31 thf(decl_33, type, setunionAx: $o).
% 0.19/0.31 thf(decl_34, type, omega: $i).
% 0.19/0.31 thf(decl_35, type, omega0Ax: $o).
% 0.19/0.31 thf(decl_36, type, omegaSAx: $o).
% 0.19/0.31 thf(decl_37, type, omegaIndAx: $o).
% 0.19/0.31 thf(decl_38, type, replAx: $o).
% 0.19/0.31 thf(decl_39, type, foundationAx: $o).
% 0.19/0.31 thf(decl_40, type, wellorderingAx: $o).
% 0.19/0.31 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.19/0.31 thf(decl_42, type, descrp: $o).
% 0.19/0.31 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.19/0.31 thf(decl_44, type, dsetconstrI: $o).
% 0.19/0.31 thf(decl_45, type, dsetconstrEL: $o).
% 0.19/0.31 thf(decl_46, type, dsetconstrER: $o).
% 0.19/0.31 thf(decl_47, type, exuE1: $o).
% 0.19/0.31 thf(decl_48, type, prop2set: $o > $i).
% 0.19/0.31 thf(decl_49, type, prop2setE: $o).
% 0.19/0.31 thf(decl_50, type, emptysetE: $o).
% 0.19/0.31 thf(decl_51, type, emptysetimpfalse: $o).
% 0.19/0.31 thf(decl_52, type, notinemptyset: $o).
% 0.19/0.31 thf(decl_53, type, exuE3e: $o).
% 0.19/0.31 thf(decl_54, type, setext: $o).
% 0.19/0.31 thf(decl_55, type, emptyI: $o).
% 0.19/0.31 thf(decl_56, type, noeltsimpempty: $o).
% 0.19/0.31 thf(decl_57, type, setbeta: $o).
% 0.19/0.31 thf(decl_58, type, nonempty: $i > $o).
% 0.19/0.31 thf(decl_59, type, nonemptyE1: $o).
% 0.19/0.31 thf(decl_60, type, nonemptyI: $o).
% 0.19/0.31 thf(decl_61, type, nonemptyI1: $o).
% 0.19/0.31 thf(decl_62, type, setadjoinIL: $o).
% 0.19/0.31 thf(decl_63, type, emptyinunitempty: $o).
% 0.19/0.31 thf(decl_64, type, setadjoinIR: $o).
% 0.19/0.31 thf(decl_65, type, setadjoinE: $o).
% 0.19/0.31 thf(decl_66, type, setadjoinOr: $o).
% 0.19/0.31 thf(decl_67, type, setoftrueEq: $o).
% 0.19/0.31 thf(decl_68, type, powersetI: $o).
% 0.19/0.31 thf(decl_69, type, emptyinPowerset: $o).
% 0.19/0.31 thf(decl_70, type, emptyInPowerset: $o).
% 0.19/0.31 thf(decl_71, type, powersetE: $o).
% 0.19/0.31 thf(decl_72, type, setunionI: $o).
% 0.19/0.31 thf(decl_73, type, setunionE: $o).
% 0.19/0.31 thf(decl_74, type, subPowSU: $o).
% 0.19/0.31 thf(decl_75, type, exuE2: $o).
% 0.19/0.31 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.19/0.31 thf(decl_77, type, uniqinunit: $o).
% 0.19/0.31 thf(decl_78, type, notinsingleton: $o).
% 0.19/0.31 thf(decl_79, type, eqinunit: $o).
% 0.19/0.31 thf(decl_80, type, singletonsswitch: $o).
% 0.19/0.31 thf(decl_81, type, upairsetE: $o).
% 0.19/0.31 thf(decl_82, type, upairsetIL: $o).
% 0.19/0.31 thf(decl_83, type, upairsetIR: $o).
% 0.19/0.31 thf(decl_84, type, emptyE1: $o).
% 0.19/0.31 thf(decl_85, type, vacuousDall: $o).
% 0.19/0.31 thf(decl_86, type, quantDeMorgan1: $o).
% 0.19/0.31 thf(decl_87, type, quantDeMorgan2: $o).
% 0.19/0.31 thf(decl_88, type, quantDeMorgan3: $o).
% 0.19/0.31 thf(decl_89, type, quantDeMorgan4: $o).
% 0.19/0.31 thf(decl_90, type, prop2setI: $o).
% 0.19/0.31 thf(decl_91, type, set2prop: $i > $o).
% 0.19/0.31 thf(decl_92, type, prop2set2propI: $o).
% 0.19/0.31 thf(decl_93, type, notdexE: $o).
% 0.19/0.31 thf(decl_94, type, notdallE: $o).
% 0.19/0.31 thf(decl_95, type, exuI1: $o).
% 0.19/0.31 thf(decl_96, type, exuI3: $o).
% 0.19/0.31 thf(decl_97, type, exuI2: $o).
% 0.19/0.31 thf(decl_98, type, inCongP: $o).
% 0.19/0.31 thf(decl_99, type, in__Cong: $o).
% 0.19/0.31 thf(decl_100, type, exuE3u: $o).
% 0.19/0.31 thf(decl_101, type, exu__Cong: $o).
% 0.19/0.31 thf(decl_102, type, emptyset__Cong: $o).
% 0.19/0.31 thf(decl_103, type, setadjoin__Cong: $o).
% 0.19/0.31 thf(decl_104, type, powerset__Cong: $o).
% 0.19/0.31 thf(decl_105, type, setunion__Cong: $o).
% 0.19/0.31 thf(decl_106, type, omega__Cong: $o).
% 0.19/0.31 thf(decl_107, type, exuEu: $o).
% 0.19/0.31 thf(decl_108, type, descr__Cong: $o).
% 0.19/0.31 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.19/0.31 thf(decl_110, type, subset: $i > $i > $o).
% 0.19/0.32 thf(decl_113, type, subsetI1: $o).
% 0.19/0.32 thf(decl_114, type, eqimpsubset2: $o).
% 0.19/0.32 thf(decl_115, type, eqimpsubset1: $o).
% 0.19/0.32 thf(decl_116, type, subsetI2: $o).
% 0.19/0.32 thf(decl_117, type, emptysetsubset: $o).
% 0.19/0.32 thf(decl_118, type, subsetE: $o).
% 0.19/0.32 thf(decl_119, type, subsetE2: $o).
% 0.19/0.32 thf(decl_120, type, notsubsetI: $o).
% 0.19/0.32 thf(decl_121, type, notequalI1: $o).
% 0.19/0.32 thf(decl_122, type, notequalI2: $o).
% 0.19/0.32 thf(decl_123, type, subsetRefl: $o).
% 0.19/0.32 thf(decl_124, type, subsetTrans: $o).
% 0.19/0.32 thf(decl_125, type, setadjoinSub: $o).
% 0.19/0.32 thf(decl_126, type, setadjoinSub2: $o).
% 0.19/0.32 thf(decl_127, type, subset2powerset: $o).
% 0.19/0.32 thf(decl_128, type, setextsub: $o).
% 0.19/0.32 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.19/0.32 thf(decl_130, type, powersetI1: $o).
% 0.19/0.32 thf(decl_131, type, powersetE1: $o).
% 0.19/0.32 thf(decl_132, type, inPowerset: $o).
% 0.19/0.32 thf(decl_133, type, powersetsubset: $o).
% 0.19/0.32 thf(decl_134, type, sepInPowerset: $o).
% 0.19/0.32 thf(decl_135, type, sepSubset: $o).
% 0.19/0.32 thf(decl_136, type, binunion: $i > $i > $i).
% 0.19/0.32 thf(decl_137, type, binunionIL: $o).
% 0.19/0.32 thf(decl_138, type, upairset2IR: $o).
% 0.19/0.32 thf(decl_139, type, binunionIR: $o).
% 0.19/0.32 thf(decl_140, type, binunionEcases: $o).
% 0.19/0.32 thf(decl_141, type, binunionE: $o).
% 0.19/0.32 thf(decl_142, type, binunionLsub: $o).
% 0.19/0.32 thf(decl_143, type, binunionRsub: $o).
% 0.19/0.32 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.19/0.32 thf(decl_145, type, binintersectI: $o).
% 0.19/0.32 thf(decl_146, type, binintersectSubset5: $o).
% 0.19/0.32 thf(decl_147, type, binintersectEL: $o).
% 0.19/0.32 thf(decl_148, type, binintersectLsub: $o).
% 0.19/0.32 thf(decl_149, type, binintersectSubset2: $o).
% 0.19/0.32 thf(decl_150, type, binintersectSubset3: $o).
% 0.19/0.32 thf(decl_151, type, binintersectER: $o).
% 0.19/0.32 thf(decl_152, type, disjointsetsI1: $o).
% 0.19/0.32 thf(decl_153, type, binintersectRsub: $o).
% 0.19/0.32 thf(decl_154, type, binintersectSubset4: $o).
% 0.19/0.32 thf(decl_155, type, binintersectSubset1: $o).
% 0.19/0.32 thf(decl_156, type, bs114d: $o).
% 0.19/0.32 thf(decl_158, type, setminus: $i > $i > $i).
% 0.19/0.32 thf(decl_159, type, setminusI: $o).
% 0.19/0.32 thf(decl_160, type, epred1_0: $o).
% 0.19/0.32 thf(decl_161, type, esk1_2: $i > $i > $i).
% 0.19/0.32 thf(decl_162, type, esk2_2: $i > $i > $i).
% 0.19/0.32 thf(decl_163, type, esk3_2: $i > $i > $i).
% 0.19/0.32 thf(decl_164, type, esk4_1: $i > $i).
% 0.19/0.32 thf(decl_165, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.19/0.32 thf(decl_166, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.19/0.32 thf(decl_167, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.19/0.32 thf(decl_168, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.19/0.32 thf(decl_169, type, esk9_1: $i > $i).
% 0.19/0.32 thf(decl_170, type, esk10_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_171, type, esk11_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_172, type, esk12_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_173, type, esk13_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_174, type, esk14_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_175, type, esk15_2: $i > $i > $i).
% 0.19/0.32 thf(decl_176, type, esk16_2: $i > $i > $i).
% 0.19/0.32 thf(decl_177, type, esk17_1: $i > $i).
% 0.19/0.32 thf(decl_178, type, esk18_1: $i > $i).
% 0.19/0.32 thf(decl_179, type, esk19_1: $i > $i).
% 0.19/0.32 thf(decl_180, type, esk20_2: $i > $i > $i).
% 0.19/0.32 thf(decl_181, type, esk21_3: $i > $i > $o > $i).
% 0.19/0.32 thf(decl_182, type, esk22_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_183, type, esk23_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_184, type, esk24_1: $i > $i).
% 0.19/0.32 thf(decl_185, type, esk25_2: $i > ($i > $o) > $i).
% 0.19/0.32 thf(decl_186, type, esk26_2: $i > ($i > $o) > $i).
% 0.19/0.32 thf(decl_187, type, esk27_2: $i > ($i > $o) > $i).
% 0.19/0.32 thf(decl_188, type, esk28_2: $i > ($i > $o) > $i).
% 0.19/0.32 thf(decl_189, type, esk29_2: $i > ($i > $o) > $i).
% 0.19/0.32 thf(decl_190, type, esk30_2: $i > ($i > $o) > $i).
% 0.19/0.32 thf(decl_191, type, esk31_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_192, type, esk32_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_193, type, esk33_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_194, type, esk34_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_195, type, esk35_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_196, type, esk36_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_197, type, esk37_1: ($i > $o) > $i).
% 0.19/0.32 thf(decl_198, type, esk38_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_199, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_200, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_201, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_202, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_203, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_204, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_205, type, esk45_2: ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_206, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_207, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_208, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_209, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.19/0.32 thf(decl_210, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_211, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.19/0.32 thf(decl_212, type, esk52_2: $i > $i > $i).
% 0.19/0.32 thf(decl_213, type, esk53_2: $i > $i > $i).
% 0.19/0.32 thf(decl_214, type, esk54_2: $i > $i > $i).
% 0.19/0.32 thf(decl_215, type, esk55_0: $i).
% 0.19/0.32 thf(decl_216, type, esk56_0: $i).
% 0.19/0.32 thf(decl_217, type, esk57_0: $i).
% 0.19/0.32 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', replAx)).
% 0.19/0.32 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', exu)).
% 0.19/0.32 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', descrp)).
% 0.19/0.32 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', exuE1)).
% 0.19/0.32 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', exuE3e)).
% 0.19/0.32 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', nonempty)).
% 0.19/0.32 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', nonemptyI)).
% 0.19/0.32 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', exuE2)).
% 0.19/0.32 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.WY8GZZNdxw/E---3.1_807434.p', exuI1)).
% 0.19/0.32 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', exuI3)).
% 0.19/0.32 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', exuI2)).
% 0.19/0.32 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.WY8GZZNdxw/E---3.1_807434.p', exuE3u)).
% 0.19/0.32 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', exu__Cong)).
% 0.19/0.32 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', exuEu)).
% 0.19/0.32 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.WY8GZZNdxw/E---3.1_807434.p', descr__Cong)).
% 0.19/0.32 thf(setminusEL, 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)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setminusEL)).
% 0.19/0.32 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', dsetconstrI)).
% 0.19/0.32 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', dsetconstrEL)).
% 0.19/0.32 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', dsetconstrER)).
% 0.19/0.32 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setbeta)).
% 0.19/0.32 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', nonemptyE1)).
% 0.19/0.32 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', nonemptyI1)).
% 0.19/0.32 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setoftrueEq)).
% 0.19/0.32 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', nonemptyImpWitness)).
% 0.19/0.32 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.WY8GZZNdxw/E---3.1_807434.p', emptyE1)).
% 0.19/0.32 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', dsetconstr__Cong)).
% 0.19/0.32 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', sepInPowerset)).
% 0.19/0.32 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', sepSubset)).
% 0.19/0.32 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setextAx)).
% 0.19/0.32 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', emptysetAx)).
% 0.19/0.32 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setadjoinAx)).
% 0.19/0.32 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', powersetAx)).
% 0.19/0.32 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setunionAx)).
% 0.19/0.32 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', omega0Ax)).
% 0.19/0.32 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', omegaSAx)).
% 0.19/0.32 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', omegaIndAx)).
% 0.19/0.32 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', foundationAx)).
% 0.19/0.32 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.WY8GZZNdxw/E---3.1_807434.p', wellorderingAx)).
% 0.19/0.32 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', prop2setE)).
% 0.19/0.32 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', emptysetE)).
% 0.19/0.32 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', emptysetimpfalse)).
% 0.19/0.32 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', notinemptyset)).
% 0.19/0.32 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setext)).
% 0.19/0.32 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', emptyI)).
% 0.19/0.32 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', noeltsimpempty)).
% 0.19/0.32 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setadjoinIL)).
% 0.19/0.32 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', emptyinunitempty)).
% 0.19/0.32 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setadjoinIR)).
% 0.19/0.32 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.WY8GZZNdxw/E---3.1_807434.p', setadjoinE)).
% 0.19/0.32 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setadjoinOr)).
% 0.19/0.32 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', powersetI)).
% 0.19/0.32 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', emptyinPowerset)).
% 0.19/0.32 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', emptyInPowerset)).
% 0.19/0.32 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', powersetE)).
% 0.19/0.32 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setunionI)).
% 0.19/0.32 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.WY8GZZNdxw/E---3.1_807434.p', setunionE)).
% 0.19/0.32 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', subPowSU)).
% 0.19/0.32 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', uniqinunit)).
% 0.19/0.32 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', notinsingleton)).
% 0.19/0.32 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', eqinunit)).
% 0.19/0.32 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', singletonsswitch)).
% 0.19/0.32 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', upairsetE)).
% 0.19/0.32 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', upairsetIL)).
% 0.19/0.32 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', upairsetIR)).
% 0.19/0.32 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', vacuousDall)).
% 0.19/0.32 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', quantDeMorgan1)).
% 0.19/0.32 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', quantDeMorgan2)).
% 0.19/0.32 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', quantDeMorgan3)).
% 0.19/0.32 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', quantDeMorgan4)).
% 0.19/0.32 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', prop2setI)).
% 0.19/0.32 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', prop2set2propI)).
% 0.19/0.32 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', notdexE)).
% 0.19/0.32 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', notdallE)).
% 0.19/0.32 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', inCongP)).
% 0.19/0.32 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', in__Cong)).
% 0.19/0.32 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', emptyset__Cong)).
% 0.19/0.32 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setadjoin__Cong)).
% 0.19/0.32 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', powerset__Cong)).
% 0.19/0.32 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setunion__Cong)).
% 0.19/0.32 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', omega__Cong)).
% 0.19/0.32 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', subsetI1)).
% 0.19/0.32 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', eqimpsubset2)).
% 0.19/0.32 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', eqimpsubset1)).
% 0.19/0.32 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', subsetI2)).
% 0.19/0.32 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', emptysetsubset)).
% 0.19/0.32 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', subsetE)).
% 0.19/0.32 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', subsetE2)).
% 0.19/0.32 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', notsubsetI)).
% 0.19/0.32 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', notequalI1)).
% 0.19/0.32 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', notequalI2)).
% 0.19/0.32 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', subsetRefl)).
% 0.19/0.32 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', subsetTrans)).
% 0.19/0.32 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setadjoinSub)).
% 0.19/0.32 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setadjoinSub2)).
% 0.19/0.32 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', subset2powerset)).
% 0.19/0.32 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setextsub)).
% 0.19/0.32 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', subsetemptysetimpeq)).
% 0.19/0.32 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', powersetI1)).
% 0.19/0.32 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', powersetE1)).
% 0.19/0.32 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', inPowerset)).
% 0.19/0.32 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', powersetsubset)).
% 0.19/0.32 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binunionIL)).
% 0.19/0.32 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', upairset2IR)).
% 0.19/0.32 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binunionIR)).
% 0.19/0.32 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binunionEcases)).
% 0.19/0.32 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binunionE)).
% 0.19/0.32 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binunionLsub)).
% 0.19/0.32 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binunionRsub)).
% 0.19/0.32 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binintersectI)).
% 0.19/0.32 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binintersectSubset5)).
% 0.19/0.32 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binintersectEL)).
% 0.19/0.32 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binintersectLsub)).
% 0.19/0.32 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binintersectSubset2)).
% 0.19/0.32 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binintersectSubset3)).
% 0.19/0.32 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binintersectER)).
% 0.19/0.32 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', disjointsetsI1)).
% 0.19/0.32 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binintersectRsub)).
% 0.19/0.32 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binintersectSubset4)).
% 0.19/0.32 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', binintersectSubset1)).
% 0.19/0.32 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', bs114d)).
% 0.19/0.32 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setminusI)).
% 0.19/0.32 thf(setminus, axiom, ((setminus)=(^[X4:$i, X5:$i]:(dsetconstr @ X4 @ (^[X2:$i]:(~((in @ X2 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.WY8GZZNdxw/E---3.1_807434.p', setminus)).
% 0.19/0.32 thf(c_0_122, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.19/0.32 thf(c_0_123, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.19/0.32 thf(c_0_124, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.19/0.32 thf(c_0_125, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.19/0.32 thf(c_0_126, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.19/0.32 thf(c_0_127, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.19/0.32 thf(c_0_128, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.19/0.32 thf(c_0_129, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.19/0.32 thf(c_0_130, 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])).
% 0.19/0.32 thf(c_0_131, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.19/0.32 thf(c_0_132, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.19/0.32 thf(c_0_133, 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])).
% 0.19/0.32 thf(c_0_134, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.19/0.32 thf(c_0_135, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.19/0.32 thf(c_0_136, 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])).
% 0.19/0.32 thf(c_0_137, 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)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setminusEL])).
% 0.19/0.32 thf(c_0_138, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X337:$i]:(((((X6 @ X2 @ X337)))&(![X338:$i]:(((((X6 @ X2 @ X338)))=>(((X337)=(X338)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_122, c_0_123])).
% 0.19/0.32 thf(c_0_139, plain, ((descrp)=(![X1:$i > $o]:((((?[X339:$i]:(((((X1 @ X339)))&(![X340:$i]:(((((X1 @ X340)))=>(((X339)=(X340))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_124, c_0_123])).
% 0.19/0.32 thf(c_0_140, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.19/0.32 thf(c_0_141, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.19/0.32 thf(c_0_142, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.19/0.32 thf(c_0_143, plain, ((exuE1)=(![X1:$i > $o]:((((?[X341:$i]:(((((X1 @ X341)))&(![X342:$i]:(((((X1 @ X342)))=>(((X341)=(X342))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_125, c_0_123])).
% 0.19/0.32 thf(c_0_144, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X343:$i]:(((((X1 @ X343)))&(![X344:$i]:(((((X1 @ X344)))=>(((X343)=(X344))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_126, c_0_123])).
% 0.19/0.32 thf(c_0_145, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.19/0.32 thf(c_0_146, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_127])).
% 0.19/0.32 thf(c_0_147, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_128, c_0_127])).
% 0.19/0.32 thf(c_0_148, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_127])).
% 0.19/0.32 thf(c_0_149, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.19/0.32 thf(c_0_150, plain, ((exuE2)=(![X1:$i > $o]:((((?[X345:$i]:(((((X1 @ X345)))&(![X346:$i]:(((((X1 @ X346)))=>(((X345)=(X346))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_129, c_0_123])).
% 0.19/0.32 thf(c_0_151, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_127])).
% 0.19/0.32 thf(c_0_152, 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])).
% 0.19/0.32 thf(c_0_153, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X347:$i]:(((((X1 @ X347)))&(![X348:$i]:(((((X1 @ X348)))=>(((X347)=(X348)))))))))))))), inference(apply_def,[status(thm)],[c_0_130, c_0_123])).
% 0.19/0.32 thf(c_0_154, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X349:$i]:(((((X1 @ X349)))&(![X350:$i]:(((((X1 @ X350)))=>(((X349)=(X350)))))))))))))))), inference(apply_def,[status(thm)],[c_0_131, c_0_123])).
% 0.19/0.32 thf(c_0_155, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X351:$i]:(((((X1 @ X351)))&(![X352:$i]:(((((X1 @ X352)))=>(((X351)=(X352)))))))))))))), inference(apply_def,[status(thm)],[c_0_132, c_0_123])).
% 0.19/0.32 thf(c_0_156, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X353:$i]:(((((X1 @ X353)))&(![X354:$i]:(((((X1 @ X354)))=>(((X353)=(X354))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_133, c_0_123])).
% 0.19/0.32 thf(c_0_157, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X355:$i]:(((((X1 @ X355)))&(![X356:$i]:(((((X1 @ X356)))=>(((X355)=(X356))))))))))<=>((?[X357:$i]:(((((X17 @ X357)))&(![X358:$i]:(((((X17 @ X358)))=>(((X357)=(X358)))))))))))))))), inference(apply_def,[status(thm)],[c_0_134, c_0_123])).
% 0.19/0.32 thf(c_0_158, plain, ((exuEu)=(![X1:$i > $o]:((((?[X359:$i]:(((((X1 @ X359)))&(![X360:$i]:(((((X1 @ X360)))=>(((X359)=(X360))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_135, c_0_123])).
% 0.19/0.32 thf(c_0_159, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X361:$i]:(((((X1 @ X361)))&(![X362:$i]:(((((X1 @ X362)))=>(((X361)=(X362))))))))))=>((((?[X363:$i]:(((((X17 @ X363)))&(![X364:$i]:(((((X17 @ X364)))=>(((X363)=(X364))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_136, c_0_123])).
% 0.19/0.32 thf(c_0_160, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.19/0.32 thf(c_0_161, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.19/0.32 thf(c_0_162, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.19/0.32 thf(c_0_163, plain, ((epred1_0)<=>![X394:$i]:(?[X395:$i]:((((![X396:$i]:(((in @ X396 @ X395)=>![X397:$i]:(((in @ X397 @ X396)=>(in @ X397 @ X394)))))&![X398:$i, X399:$i]:((((in @ X398 @ X394)&(in @ X399 @ X394))=>(![X400:$i]:(((in @ X400 @ X395)=>((in @ X398 @ X400)<=>(in @ X399 @ X400))))=>((X398)=(X399))))))&![X401:$i, X402:$i]:((((in @ X401 @ X395)&(in @ X402 @ X395))=>(![X403:$i]:(((in @ X403 @ X401)=>(in @ X403 @ X402)))|![X404:$i]:(((in @ X404 @ X402)=>(in @ X404 @ X401)))))))&![X405:$i]:(((![X406:$i]:(((in @ X406 @ X405)=>(in @ X406 @ X394)))&?[X407:$i]:((in @ X407 @ X405)))=>?[X408:$i, X409:$i]:(((((in @ X408 @ X395)&(in @ X409 @ X405))&~(?[X410:$i]:(((in @ X410 @ X408)&(in @ X410 @ X405)))))&![X411:$i]:(((in @ X411 @ X395)=>(![X412:$i]:(((in @ X412 @ X411)=>(in @ X412 @ X408)))|(in @ X409 @ X411)))))))))))), introduced(definition)).
% 0.19/0.32 thf(c_0_164, negated_conjecture, ~((![X365:$i, X366:$i]:((![X367:$i]:(((in @ X367 @ X365)<=>(in @ X367 @ X366)))=>((X365)=(X366))))=>(![X368:$i]:(~(in @ X368 @ emptyset))=>(![X369:$i, X370:$i, X371:$i]:(((in @ X371 @ (setadjoin @ X369 @ X370))<=>(((X371)=(X369))|(in @ X371 @ X370))))=>(![X372:$i, X373:$i]:(((in @ X373 @ (powerset @ X372))<=>![X374:$i]:(((in @ X374 @ X373)=>(in @ X374 @ X372)))))=>(![X375:$i, X376:$i]:(((in @ X376 @ (setunion @ X375))<=>?[X377:$i]:(((in @ X376 @ X377)&(in @ X377 @ X375)))))=>((in @ emptyset @ omega)=>(![X378:$i]:(((in @ X378 @ omega)=>(in @ (setadjoin @ X378 @ X378) @ omega)))=>(![X379:$i]:((((in @ emptyset @ X379)&![X380:$i]:((((in @ X380 @ omega)&(in @ X380 @ X379))=>(in @ (setadjoin @ X380 @ X380) @ X379))))=>![X381:$i]:(((in @ X381 @ omega)=>(in @ X381 @ X379)))))=>(![X382:$i > $i > $o, X383:$i]:((![X384:$i]:(((in @ X384 @ X383)=>?[X385:$i]:(((X382 @ X384 @ X385)&![X386:$i]:(((X382 @ X384 @ X386)=>((X385)=(X386))))))))=>?[X387:$i]:(![X388:$i]:(((in @ X388 @ X387)<=>?[X389:$i]:(((in @ X389 @ X383)&(X382 @ X389 @ X388))))))))=>(![X390:$i]:((?[X391:$i]:((in @ X391 @ X390))=>?[X392:$i]:(((in @ X392 @ X390)&~(?[X393:$i]:(((in @ X393 @ X392)&(in @ X393 @ X390))))))))=>((epred1_0)=>(![X413:$i > $o]:((?[X414:$i]:(((X413 @ X414)&![X415:$i]:(((X413 @ X415)=>((X414)=(X415))))))=>(X413 @ (descr @ (^[Z0:$i]:(X413 @ Z0))))))=>(![X416:$i, X417:$i > $o, X418:$i]:(((in @ X418 @ X416)=>((X417 @ X418)=>(in @ X418 @ (dsetconstr @ X416 @ X417)))))=>(![X419:$i, X420:$i > $o, X421:$i]:(((in @ X421 @ (dsetconstr @ X419 @ X420))=>(in @ X421 @ X419)))=>(![X422:$i, X423:$i > $o, X424:$i]:(((in @ X424 @ (dsetconstr @ X422 @ X423))=>(X423 @ X424)))=>(![X425:$i > $o]:((?[X426:$i]:(((X425 @ X426)&![X427:$i]:(((X425 @ X427)=>((X426)=(X427))))))=>?[X428:$i]:(((X425 @ X428)&![X429:$i]:(((X425 @ X429)=>((X428)=(X429))))))))=>(![X430:$o, X431:$i]:(((in @ X431 @ (prop2set @ ((X430))))=>(X430)))=>(![X432:$i]:(((in @ X432 @ emptyset)=>![X433:$o]:((X433))))=>(![X434:$i]:(((in @ X434 @ emptyset)=>~($true)))=>(![X435:$i]:(~(in @ X435 @ emptyset))=>(![X436:$i > $o]:((?[X437:$i]:(((X436 @ X437)&![X438:$i]:(((X436 @ X438)=>((X437)=(X438))))))=>?[X439:$i]:((X436 @ X439))))=>(![X440:$i, X441:$i]:((![X442:$i]:(((in @ X442 @ X440)=>(in @ X442 @ X441)))=>(![X443:$i]:(((in @ X443 @ X441)=>(in @ X443 @ X440)))=>((X440)=(X441)))))=>(![X444:$i]:((![X445:$i]:(~(in @ X445 @ X444))=>((X444)=(emptyset))))=>(![X446:$i]:((![X447:$i]:(~(in @ X447 @ X446))=>((X446)=(emptyset))))=>(![X448:$i, X449:$i > $o, X450:$i]:(((in @ X450 @ X448)=>((in @ X450 @ (dsetconstr @ X448 @ X449))<=>(X449 @ X450))))=>(![X451:$i]:((((X451)!=(emptyset))=>?[X452:$i]:((in @ X452 @ X451))))=>(![X453:$i, X454:$i > $o, X455:$i]:(((in @ X455 @ X453)=>((X454 @ X455)=>((dsetconstr @ X453 @ X454)!=(emptyset)))))=>(![X456:$i]:((?[X457:$i]:((in @ X457 @ X456))=>((X456)!=(emptyset))))=>(![X458:$i, X459:$i]:((in @ X458 @ (setadjoin @ X458 @ X459)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X460:$i, X461:$i, X462:$i]:(((in @ X462 @ X461)=>(in @ X462 @ (setadjoin @ X460 @ X461))))=>(![X463:$i, X464:$i, X465:$i]:(((in @ X465 @ (setadjoin @ X463 @ X464))=>![X466:$o]:(((((X465)=(X463))=>(X466))=>(((in @ X465 @ X464)=>(X466))=>(X466))))))=>(![X467:$i, X468:$i, X469:$i]:(((in @ X469 @ (setadjoin @ X467 @ X468))=>(((X469)=(X467))|(in @ X469 @ X468))))=>(![X470:$i]:(((dsetconstr @ X470 @ (^[Z0:$i]:($true)))=(X470)))=>(![X471:$i, X472:$i]:((![X473:$i]:(((in @ X473 @ X472)=>(in @ X473 @ X471)))=>(in @ X472 @ (powerset @ X471))))=>(![X474:$i]:((in @ emptyset @ (powerset @ X474)))=>(![X475:$i]:((in @ emptyset @ (powerset @ X475)))=>(![X476:$i, X477:$i, X478:$i]:(((in @ X477 @ (powerset @ X476))=>((in @ X478 @ X477)=>(in @ X478 @ X476))))=>(![X479:$i, X480:$i, X481:$i]:(((in @ X480 @ X481)=>((in @ X481 @ X479)=>(in @ X480 @ (setunion @ X479)))))=>(![X482:$i, X483:$i]:(((in @ X483 @ (setunion @ X482))=>![X484:$o]:((![X485:$i]:(((in @ X483 @ X485)=>((in @ X485 @ X482)=>(X484))))=>(X484)))))=>(![X486:$i, X487:$i]:(((in @ X487 @ X486)=>(in @ X487 @ (powerset @ (setunion @ X486)))))=>(![X488:$i > $o]:((?[X489:$i]:(((X488 @ X489)&![X490:$i]:(((X488 @ X490)=>((X489)=(X490))))))=>?[X491:$i]:(![X492:$i]:(((X488 @ X492)<=>((X492)=(X491)))))))=>(![X493:$i]:((((X493)!=(emptyset))=>?[X494:$i]:(((in @ X494 @ X493)&$true))))=>(![X495:$i, X496:$i]:(((in @ X495 @ (setadjoin @ X496 @ emptyset))=>((X495)=(X496))))=>(![X497:$i, X498:$i]:((((X497)!=(X498))=>~(in @ X498 @ (setadjoin @ X497 @ emptyset))))=>(![X499:$i, X500:$i]:((((X499)=(X500))=>(in @ X499 @ (setadjoin @ X500 @ emptyset))))=>(![X501:$i, X502:$i]:(((in @ X501 @ (setadjoin @ X502 @ emptyset))=>(in @ X502 @ (setadjoin @ X501 @ emptyset))))=>(![X503:$i, X504:$i, X505:$i]:(((in @ X505 @ (setadjoin @ X503 @ (setadjoin @ X504 @ emptyset)))=>(((X505)=(X503))|((X505)=(X504)))))=>(![X506:$i, X507:$i]:((in @ X506 @ (setadjoin @ X506 @ (setadjoin @ X507 @ emptyset))))=>(![X508:$i, X509:$i]:((in @ X509 @ (setadjoin @ X508 @ (setadjoin @ X509 @ emptyset))))=>(![X510:$i, X511:$i > $o]:((?[X512:$i]:(((in @ X512 @ X510)&(X511 @ X512)))=>(((dsetconstr @ X510 @ X511)=(emptyset))=>~($true))))=>(![X513:$i > $o, X514:$i]:(((in @ X514 @ emptyset)=>(X513 @ X514)))=>(![X515:$i, X516:$i > $o]:((~(![X517:$i]:(((in @ X517 @ X515)=>(X516 @ X517))))=>?[X518:$i]:(((in @ X518 @ X515)&~((X516 @ X518))))))=>(![X519:$i, X520:$i > $o]:((![X521:$i]:(((in @ X521 @ X519)=>~((X520 @ X521))))=>~(?[X522:$i]:(((in @ X522 @ X519)&(X520 @ X522))))))=>(![X523:$i, X524:$i > $o]:((~(?[X525:$i]:(((in @ X525 @ X523)&(X524 @ X525))))=>![X526:$i]:(((in @ X526 @ X523)=>~((X524 @ X526))))))=>(![X527:$i, X528:$i > $o]:((?[X529:$i]:(((in @ X529 @ X527)&~((X528 @ X529))))=>~(![X530:$i]:(((in @ X530 @ X527)=>(X528 @ X530))))))=>(![X531:$o]:(((X531)=>(in @ emptyset @ (prop2set @ ((X531))))))=>(![X532:$o]:(((X532)=>(set2prop @ (prop2set @ ((X532))))))=>(![X533:$i, X534:$i > $o]:((~(?[X535:$i]:(((in @ X535 @ X533)&(X534 @ X535))))=>![X536:$i]:(((in @ X536 @ X533)=>~((X534 @ X536))))))=>(![X537:$i, X538:$i > $o]:((~(![X539:$i]:(((in @ X539 @ X537)=>(X538 @ X539))))=>?[X540:$i]:(((in @ X540 @ X537)&~((X538 @ X540))))))=>(![X541:$i > $o]:((?[X542:$i]:(((X541 @ X542)&![X543:$i]:(((X541 @ X543)=>((X542)=(X543))))))=>?[X544:$i]:(((X541 @ X544)&![X545:$i]:(((X541 @ X545)=>((X544)=(X545))))))))=>(![X546:$i > $o]:((?[X547:$i]:((X546 @ X547))=>(![X548:$i, X549:$i]:(((X546 @ X548)=>((X546 @ X549)=>((X548)=(X549)))))=>?[X550:$i]:(((X546 @ X550)&![X551:$i]:(((X546 @ X551)=>((X550)=(X551)))))))))=>(![X552:$i > $o]:((?[X553:$i]:(![X554:$i]:(((X552 @ X554)<=>((X554)=(X553)))))=>?[X555:$i]:(((X552 @ X555)&![X556:$i]:(((X552 @ X556)=>((X555)=(X556))))))))=>(![X557:$i, X558:$i]:((((X557)=(X558))=>![X559:$i, X560:$i]:((((X559)=(X560))=>((in @ X559 @ X557)=>(in @ X560 @ X558))))))=>(![X561:$i, X562:$i]:((((X561)=(X562))=>![X563:$i, X564:$i]:((((X563)=(X564))=>((in @ X563 @ X561)<=>(in @ X564 @ X562))))))=>(![X565:$i > $o]:((?[X566:$i]:(((X565 @ X566)&![X567:$i]:(((X565 @ X567)=>((X566)=(X567))))))=>![X568:$i, X569:$i]:(((X565 @ X568)=>((X565 @ X569)=>((X568)=(X569)))))))=>(![X570:$i > $o, X571:$i > $o]:((![X572:$i, X573:$i]:((((X572)=(X573))=>((X570 @ X572)<=>(X571 @ X573))))=>(?[X574:$i]:(((X570 @ X574)&![X575:$i]:(((X570 @ X575)=>((X574)=(X575))))))<=>?[X576:$i]:(((X571 @ X576)&![X577:$i]:(((X571 @ X577)=>((X576)=(X577)))))))))=>(((emptyset)=(emptyset))=>(![X578:$i, X579:$i]:((((X578)=(X579))=>![X580:$i, X581:$i]:((((X580)=(X581))=>((setadjoin @ X578 @ X580)=(setadjoin @ X579 @ X581))))))=>(![X582:$i, X583:$i]:((((X582)=(X583))=>((powerset @ X582)=(powerset @ X583))))=>(![X584:$i, X585:$i]:((((X584)=(X585))=>((setunion @ X584)=(setunion @ X585))))=>(((omega)=(omega))=>(![X586:$i > $o]:((?[X587:$i]:(((X586 @ X587)&![X588:$i]:(((X586 @ X588)=>((X587)=(X588))))))=>![X589:$i, X590:$i]:(((X586 @ X589)=>((X586 @ X590)=>((X589)=(X590)))))))=>(![X591:$i > $o, X592:$i > $o]:((![X593:$i, X594:$i]:((((X593)=(X594))=>((X591 @ X593)<=>(X592 @ X594))))=>(?[X595:$i]:(((X591 @ X595)&![X596:$i]:(((X591 @ X596)=>((X595)=(X596))))))=>(?[X597:$i]:(((X592 @ X597)&![X598:$i]:(((X592 @ X598)=>((X597)=(X598))))))=>((descr @ X591)=(descr @ X592))))))=>(![X599:$i, X600:$i]:((((X599)=(X600))=>![X601:$i > $o, X602:$i > $o]:((![X603:$i]:(((in @ X603 @ X599)=>![X604:$i]:(((in @ X604 @ X600)=>(((X603)=(X604))=>((X601 @ X603)<=>(X602 @ X604)))))))=>((dsetconstr @ X599 @ X601)=(dsetconstr @ X600 @ X602))))))=>(![X605:$i, X606:$i]:((![X607:$i]:(((in @ X607 @ X605)=>(in @ X607 @ X606)))=>(subset @ X605 @ X606)))=>(![X608:$i, X609:$i]:((((X608)=(X609))=>(subset @ X609 @ X608)))=>(![X610:$i, X611:$i]:((((X610)=(X611))=>(subset @ X610 @ X611)))=>(![X612:$i, X613:$i]:((![X614:$i]:(((in @ X614 @ X612)=>(in @ X614 @ X613)))=>(subset @ X612 @ X613)))=>(![X615:$i]:((subset @ emptyset @ X615))=>(![X616:$i, X617:$i, X618:$i]:(((subset @ X616 @ X617)=>((in @ X618 @ X616)=>(in @ X618 @ X617))))=>(![X619:$i, X620:$i, X621:$i]:(((subset @ X619 @ X620)=>(~(in @ X621 @ X620)=>~(in @ X621 @ X619))))=>(![X622:$i, X623:$i, X624:$i]:(((in @ X624 @ X622)=>(~(in @ X624 @ X623)=>~(subset @ X622 @ X623))))=>(![X625:$i, X626:$i]:((~(subset @ X625 @ X626)=>((X625)!=(X626))))=>(![X627:$i, X628:$i, X629:$i]:(((in @ X629 @ X627)=>(~(in @ X629 @ X628)=>((X627)!=(X628)))))=>(![X630:$i]:((subset @ X630 @ X630))=>(![X631:$i, X632:$i, X633:$i]:(((subset @ X631 @ X632)=>((subset @ X632 @ X633)=>(subset @ X631 @ X633))))=>(![X634:$i, X635:$i]:((subset @ X635 @ (setadjoin @ X634 @ X635)))=>(![X636:$i, X637:$i, X638:$i]:(((subset @ X636 @ X638)=>(subset @ X636 @ (setadjoin @ X637 @ X638))))=>(![X639:$i, X640:$i]:(((subset @ X639 @ X640)=>(in @ X639 @ (powerset @ X640))))=>(![X641:$i, X642:$i]:(((subset @ X641 @ X642)=>((subset @ X642 @ X641)=>((X641)=(X642)))))=>(![X643:$i]:(((subset @ X643 @ emptyset)=>((X643)=(emptyset))))=>(![X644:$i, X645:$i]:(((subset @ X645 @ X644)=>(in @ X645 @ (powerset @ X644))))=>(![X646:$i, X647:$i]:(((in @ X647 @ (powerset @ X646))=>(subset @ X647 @ X646)))=>(![X648:$i]:((in @ X648 @ (powerset @ X648)))=>(![X649:$i, X650:$i]:(((subset @ X649 @ X650)=>(subset @ (powerset @ X649) @ (powerset @ X650))))=>(![X651:$i, X652:$i > $o]:((in @ (dsetconstr @ X651 @ X652) @ (powerset @ X651)))=>(![X653:$i, X654:$i > $o]:((subset @ (dsetconstr @ X653 @ X654) @ X653))=>(![X655:$i, X656:$i, X657:$i]:(((in @ X657 @ X655)=>(in @ X657 @ (binunion @ X655 @ X656))))=>(![X658:$i, X659:$i]:((in @ X659 @ (setadjoin @ X658 @ (setadjoin @ X659 @ emptyset))))=>(![X660:$i, X661:$i, X662:$i]:(((in @ X662 @ X661)=>(in @ X662 @ (binunion @ X660 @ X661))))=>(![X663:$i, X664:$i, X665:$i, X666:$o]:(((in @ X665 @ (binunion @ X663 @ X664))=>(((in @ X665 @ X663)=>(X666))=>(((in @ X665 @ X664)=>(X666))=>(X666)))))=>(![X667:$i, X668:$i, X669:$i]:(((in @ X669 @ (binunion @ X667 @ X668))=>((in @ X669 @ X667)|(in @ X669 @ X668))))=>(![X670:$i, X671:$i]:((subset @ X670 @ (binunion @ X670 @ X671)))=>(![X672:$i, X673:$i]:((subset @ X673 @ (binunion @ X672 @ X673)))=>(![X674:$i, X675:$i, X676:$i]:(((in @ X676 @ X674)=>((in @ X676 @ X675)=>(in @ X676 @ (binintersect @ X674 @ X675)))))=>(![X677:$i, X678:$i, X679:$i]:(((subset @ X679 @ X677)=>((subset @ X679 @ X678)=>(subset @ X679 @ (binintersect @ X677 @ X678)))))=>(![X680:$i, X681:$i, X682:$i]:(((in @ X682 @ (binintersect @ X680 @ X681))=>(in @ X682 @ X680)))=>(![X683:$i, X684:$i]:((subset @ (binintersect @ X683 @ X684) @ X683))=>(![X685:$i, X686:$i]:(((subset @ X685 @ X686)=>((binintersect @ X685 @ X686)=(X685))))=>(![X687:$i, X688:$i]:((((binintersect @ X687 @ X688)=(X688))=>(subset @ X688 @ X687)))=>(![X689:$i, X690:$i, X691:$i]:(((in @ X691 @ (binintersect @ X689 @ X690))=>(in @ X691 @ X690)))=>(![X692:$i, X693:$i]:((~(?[X694:$i]:(((in @ X694 @ X692)&(in @ X694 @ X693))))=>((binintersect @ X692 @ X693)=(emptyset))))=>(![X695:$i, X696:$i]:((subset @ (binintersect @ X695 @ X696) @ X696))=>(![X697:$i, X698:$i]:(((subset @ X698 @ X697)=>((binintersect @ X697 @ X698)=(X698))))=>(![X699:$i, X700:$i]:((((binintersect @ X699 @ X700)=(X699))=>(subset @ X699 @ X700)))=>(![X701:$i, X702:$i, X703:$i]:(((binintersect @ X701 @ (binunion @ X702 @ X703))=(binunion @ (binintersect @ X701 @ X702) @ (binintersect @ X701 @ X703))))=>(![X704:$i, X705:$i, X706:$i]:(((in @ X706 @ X704)=>(~(in @ X706 @ X705)=>(in @ X706 @ (setminus @ X704 @ X705)))))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_137, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_138]), foundationAx]), wellorderingAx]), c_0_139]), c_0_140]), c_0_141]), c_0_142]), c_0_143]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_144]), setext]), emptyI]), noeltsimpempty]), c_0_145]), c_0_146]), c_0_147]), c_0_148]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_149]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_150]), c_0_151]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_152]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_153]), c_0_154]), c_0_155]), inCongP]), in__Cong]), c_0_156]), c_0_157]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_158]), c_0_159]), c_0_160]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_161]), c_0_162]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI])])]), c_0_163])).
% 0.19/0.32 thf(c_0_165, plain, ![X707:$i, X708:$i]:(((setminus @ X707 @ X708)=(dsetconstr @ X707 @ (^[Z0:$i]:(~((in @ Z0 @ X708))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[setminus])])).
% 0.19/0.32 thf(c_0_166, negated_conjecture, ![X711:$i, X712:$i, X714:$i, X715:$i, X716:$i, X717:$i, X718:$i, X719:$i, X720:$i, X721:$i, X722:$i, X724:$i, X725:$i, X727:$i, X728:$i, X729:$i, X730:$i, X731:$i, X733:$i, X734:$i > $i > $o, X735:$i, X737:$i, X740:$i, X742:$i, X743:$i, X744:$i, X745:$i, X747:$i, X748:$i > $o, X749:$i, X751:$i, X752:$i > $o, X753:$i, X754:$i, X755:$i > $o, X756:$i, X757:$i, X758:$i > $o, X759:$i, X760:$i > $o, X761:$i, X764:$i, X765:$o, X766:$i, X767:$i, X768:$o, X769:$i, X770:$i, X771:$i > $o, X772:$i, X775:$i, X776:$i, X779:$i, X781:$i, X783:$i, X784:$i > $o, X785:$i, X786:$i, X788:$i, X789:$i > $o, X790:$i, X791:$i, X792:$i, X793:$i, X794:$i, X795:$i, X796:$i, X797:$i, X798:$i, X799:$i, X800:$i, X801:$o, X802:$i, X803:$i, X804:$i, X805:$i, X806:$i, X807:$i, X809:$i, X810:$i, X811:$i, X812:$i, X813:$i, X814:$i, X815:$i, X816:$i, X817:$i, X818:$i, X819:$o, X821:$i, X822:$i, X823:$i > $o, X824:$i, X827:$i, X828:$i, X829:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i, X836:$i, X837:$i, X838:$i, X839:$i, X840:$i, X841:$i, X842:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i > $o, X848:$i, X849:$i > $o, X850:$i, X851:$i, X852:$i > $o, X853:$i, X855:$i, X856:$i > $o, X858:$i, X859:$i, X860:$i > $o, X862:$i, X863:$i, X864:$i > $o, X865:$i, X867:$o, X868:$o, X869:$i, X870:$i > $o, X872:$i, X873:$i, X874:$i > $o, X875:$i, X877:$i > $o, X878:$i, X881:$i, X882:$i > $o, X883:$i, X887:$i, X888:$i > $o, X889:$i, X892:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$i, X898:$i, X899:$i, X900:$i, X901:$i > $o, X902:$i, X904:$i, X905:$i, X906:$i > $o, X907:$i > $o, X910:$i, X913:$i, X914:$i, X917:$i, X918:$i, X919:$i, X920:$i, X921:$i, X922:$i, X923:$i, X924:$i, X925:$i, X926:$i > $o, X927:$i, X929:$i, X930:$i, X931:$i > $o, X932:$i > $o, X935:$i, X937:$i, X939:$i, X940:$i, X941:$i > $o, X942:$i > $o, X945:$i, X946:$i, X948:$i, X949:$i, X950:$i, X951:$i, X952:$i, X953:$i, X955:$i, X956:$i, X957:$i, X958:$i, X959:$i, X960:$i, X961:$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 > $o, X993:$i, X994:$i > $o, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i, X1004:$i, X1005:$i, X1006:$o, X1007:$i, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$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, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i]:((((~(in @ (esk1_2 @ X711 @ X712) @ X711)|~(in @ (esk1_2 @ X711 @ X712) @ X712)|((X711)=(X712)))&((in @ (esk1_2 @ X711 @ X712) @ X711)|(in @ (esk1_2 @ X711 @ X712) @ X712)|((X711)=(X712))))&(~(in @ 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X927))|~(X926 @ X927)|(~(X926 @ X929)|(~(X926 @ X930)|((X929)=(X930))))))&((((((X932 @ (esk49_3 @ X931 @ X932 @ X937))|~(X932 @ X937)|((descr @ X931)=(descr @ X932))|((X931 @ (esk48_3 @ X931 @ X932 @ X935))|~(X931 @ X935))|((esk46_2 @ X931 @ X932)=(esk47_2 @ X931 @ X932)))&(((X937)!=(esk49_3 @ X931 @ X932 @ X937))|~(X932 @ X937)|((descr @ X931)=(descr @ X932))|((X931 @ (esk48_3 @ X931 @ X932 @ X935))|~(X931 @ X935))|((esk46_2 @ X931 @ X932)=(esk47_2 @ X931 @ X932))))&(((X932 @ (esk49_3 @ X931 @ X932 @ X937))|~(X932 @ X937)|((descr @ X931)=(descr @ X932))|(((X935)!=(esk48_3 @ X931 @ X932 @ X935))|~(X931 @ X935))|((esk46_2 @ X931 @ X932)=(esk47_2 @ X931 @ X932)))&(((X937)!=(esk49_3 @ X931 @ X932 @ X937))|~(X932 @ X937)|((descr @ X931)=(descr @ X932))|(((X935)!=(esk48_3 @ X931 @ X932 @ X935))|~(X931 @ X935))|((esk46_2 @ X931 @ X932)=(esk47_2 @ X931 @ X932)))))&(((((X932 @ (esk49_3 @ X931 @ X932 @ X937))|~(X932 @ X937)|((descr @ X931)=(descr @ X932))|((X931 @ (esk48_3 @ X931 @ X932 @ X935))|~(X931 @ X935))|(~(X931 @ (esk46_2 @ X931 @ X932))|~(X932 @ (esk47_2 @ X931 @ X932))))&(((X937)!=(esk49_3 @ X931 @ X932 @ X937))|~(X932 @ X937)|((descr @ X931)=(descr @ X932))|((X931 @ (esk48_3 @ X931 @ X932 @ X935))|~(X931 @ X935))|(~(X931 @ (esk46_2 @ X931 @ X932))|~(X932 @ (esk47_2 @ X931 @ X932)))))&(((X932 @ (esk49_3 @ X931 @ X932 @ X937))|~(X932 @ X937)|((descr @ X931)=(descr @ X932))|(((X935)!=(esk48_3 @ X931 @ X932 @ X935))|~(X931 @ X935))|(~(X931 @ (esk46_2 @ X931 @ X932))|~(X932 @ (esk47_2 @ X931 @ X932))))&(((X937)!=(esk49_3 @ X931 @ X932 @ X937))|~(X932 @ X937)|((descr @ X931)=(descr @ X932))|(((X935)!=(esk48_3 @ X931 @ X932 @ X935))|~(X931 @ X935))|(~(X931 @ (esk46_2 @ X931 @ X932))|~(X932 @ (esk47_2 @ X931 @ X932))))))&((((X932 @ (esk49_3 @ X931 @ X932 @ X937))|~(X932 @ X937)|((descr @ X931)=(descr @ X932))|((X931 @ (esk48_3 @ X931 @ X932 @ X935))|~(X931 @ X935))|((X931 @ (esk46_2 @ X931 @ X932))|(X932 @ (esk47_2 @ X931 @ X932))))&(((X937)!=(esk49_3 @ X931 @ X932 @ X937))|~(X932 @ X937)|((descr @ X931)=(descr @ X932))|((X931 @ (esk48_3 @ X931 @ X932 @ X935))|~(X931 @ X935))|((X931 @ (esk46_2 @ X931 @ X932))|(X932 @ (esk47_2 @ X931 @ X932)))))&(((X932 @ (esk49_3 @ X931 @ X932 @ X937))|~(X932 @ X937)|((descr @ X931)=(descr @ X932))|(((X935)!=(esk48_3 @ X931 @ X932 @ X935))|~(X931 @ X935))|((X931 @ (esk46_2 @ X931 @ X932))|(X932 @ (esk47_2 @ X931 @ X932))))&(((X937)!=(esk49_3 @ X931 @ X932 @ X937))|~(X932 @ X937)|((descr @ X931)=(descr @ X932))|(((X935)!=(esk48_3 @ X931 @ X932 @ X935))|~(X931 @ X935))|((X931 @ (esk46_2 @ X931 @ X932))|(X932 @ (esk47_2 @ X931 @ X932))))))))&((((in @ (esk50_4 @ X939 @ X940 @ X941 @ X942) @ X939)|((dsetconstr @ X939 @ X941)=(dsetconstr @ X940 @ X942))|((X939)!=(X940)))&(((in @ (esk51_4 @ X939 @ X940 @ X941 @ X942) @ X940)|((dsetconstr @ X939 @ X941)=(dsetconstr @ X940 @ X942))|((X939)!=(X940)))&((((esk50_4 @ X939 @ X940 @ X941 @ X942)=(esk51_4 @ X939 @ X940 @ X941 @ X942))|((dsetconstr @ X939 @ X941)=(dsetconstr @ X940 @ X942))|((X939)!=(X940)))&((~(X941 @ (esk50_4 @ X939 @ X940 @ X941 @ X942))|~(X942 @ (esk51_4 @ X939 @ X940 @ X941 @ X942))|((dsetconstr @ X939 @ X941)=(dsetconstr @ X940 @ X942))|((X939)!=(X940)))&((X941 @ (esk50_4 @ X939 @ X940 @ X941 @ X942))|(X942 @ (esk51_4 @ X939 @ X940 @ X941 @ X942))|((dsetconstr @ X939 @ X941)=(dsetconstr @ X940 @ X942))|((X939)!=(X940)))))))&((((in @ (esk52_2 @ X945 @ X946) @ X945)|(subset @ X945 @ X946))&(~(in @ (esk52_2 @ X945 @ X946) @ X946)|(subset @ X945 @ X946)))&((((X948)!=(X949))|(subset @ X949 @ X948))&((((X950)!=(X951))|(subset @ X950 @ X951))&((((in @ (esk53_2 @ X952 @ X953) @ X952)|(subset @ X952 @ X953))&(~(in @ (esk53_2 @ X952 @ X953) @ X953)|(subset @ X952 @ X953)))&((subset @ emptyset @ X955)&((~(subset @ X956 @ X957)|(~(in @ X958 @ X956)|(in @ X958 @ X957)))&((~(subset @ X959 @ X960)|((in @ X961 @ X960)|~(in @ X961 @ X959)))&((~(in @ X964 @ X962)|((in @ X964 @ X963)|~(subset @ X962 @ X963)))&(((subset @ X965 @ X966)|((X965)!=(X966)))&((~(in @ X969 @ X967)|((in @ X969 @ X968)|((X967)!=(X968))))&((subset @ X970 @ X970)&((~(subset @ X971 @ X972)|(~(subset @ X972 @ X973)|(subset @ X971 @ X973)))&((subset @ X975 @ (setadjoin @ X974 @ X975))&((~(subset @ X976 @ X978)|(subset @ X976 @ (setadjoin @ X977 @ X978)))&((~(subset @ X979 @ X980)|(in @ X979 @ (powerset @ X980)))&((~(subset @ X981 @ X982)|(~(subset @ X982 @ X981)|((X981)=(X982))))&((~(subset @ X983 @ emptyset)|((X983)=(emptyset)))&((~(subset @ X985 @ X984)|(in @ X985 @ (powerset @ X984)))&((~(in @ X987 @ (powerset @ X986))|(subset @ X987 @ X986))&((in @ X988 @ (powerset @ X988))&((~(subset @ X989 @ X990)|(subset @ (powerset @ X989) @ (powerset @ X990)))&((in @ (dsetconstr @ X991 @ X992) @ (powerset @ X991))&((subset @ (dsetconstr @ X993 @ X994) @ X993)&((~(in @ X997 @ X995)|(in @ X997 @ (binunion @ X995 @ X996)))&((in @ X999 @ (setadjoin @ X998 @ (setadjoin @ X999 @ emptyset)))&((~(in @ X1002 @ X1001)|(in @ X1002 @ (binunion @ X1000 @ X1001)))&(((((in @ X1005 @ X1004)|(X1006)|(in @ X1005 @ X1003)|~(in @ X1005 @ (binunion @ X1003 @ X1004)))&(~(X1006)|(X1006)|(in @ X1005 @ X1003)|~(in @ X1005 @ (binunion @ X1003 @ X1004))))&(((in @ X1005 @ X1004)|(X1006)|~(X1006)|~(in @ X1005 @ (binunion @ X1003 @ X1004)))&(~(X1006)|(X1006)|~(X1006)|~(in @ X1005 @ (binunion @ X1003 @ X1004)))))&((~(in @ X1009 @ (binunion @ X1007 @ X1008))|((in @ X1009 @ X1007)|(in @ X1009 @ X1008)))&((subset @ X1010 @ (binunion @ X1010 @ X1011))&((subset @ X1013 @ (binunion @ X1012 @ X1013))&((~(in @ X1016 @ X1014)|(~(in @ X1016 @ X1015)|(in @ X1016 @ (binintersect @ X1014 @ X1015))))&((~(subset @ X1019 @ X1017)|(~(subset @ X1019 @ X1018)|(subset @ X1019 @ (binintersect @ X1017 @ X1018))))&((~(in @ X1022 @ (binintersect @ X1020 @ X1021))|(in @ X1022 @ X1020))&((subset @ (binintersect @ X1023 @ X1024) @ X1023)&((~(subset @ X1025 @ X1026)|((binintersect @ X1025 @ X1026)=(X1025)))&((((binintersect @ X1027 @ X1028)!=(X1028))|(subset @ X1028 @ X1027))&((~(in @ X1031 @ (binintersect @ X1029 @ X1030))|(in @ X1031 @ X1030))&((((in @ (esk54_2 @ X1032 @ X1033) @ X1032)|((binintersect @ X1032 @ X1033)=(emptyset)))&((in @ (esk54_2 @ X1032 @ X1033) @ X1033)|((binintersect @ X1032 @ X1033)=(emptyset))))&((subset @ (binintersect @ X1035 @ X1036) @ X1036)&((~(subset @ X1038 @ X1037)|((binintersect @ X1037 @ X1038)=(X1038)))&((((binintersect @ X1039 @ X1040)!=(X1039))|(subset @ X1039 @ X1040))&(((binintersect @ X1041 @ (binunion @ X1042 @ X1043))=(binunion @ (binintersect @ X1041 @ X1042) @ (binintersect @ X1041 @ X1043)))&((~(in @ X1046 @ X1044)|((in @ X1046 @ X1045)|(in @ X1046 @ (setminus @ X1044 @ X1045))))&((in @ esk57_0 @ (setminus @ esk55_0 @ esk56_0))&~(in @ esk57_0 @ esk55_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_164])])])])])])])).
% 0.19/0.32 thf(c_0_167, plain, ![X709:$i, X710:$i]:(((setminus @ X709 @ X710)=(dsetconstr @ X709 @ (^[Z0:$i]:(~((in @ Z0 @ X710))))))), inference(variable_rename,[status(thm)],[c_0_165])).
% 0.19/0.32 thf(c_0_168, negated_conjecture, (in @ esk57_0 @ (setminus @ esk55_0 @ esk56_0)), inference(split_conjunct,[status(thm)],[c_0_166])).
% 0.19/0.32 thf(c_0_169, plain, ![X2:$i, X3:$i]:(((setminus @ X2 @ X3)=(dsetconstr @ X2 @ (^[Z0:$i]:(~((in @ Z0 @ X3))))))), inference(split_conjunct,[status(thm)],[c_0_167])).
% 0.19/0.32 thf(c_0_170, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((in @ X2 @ X3)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_166])).
% 0.19/0.32 thf(c_0_171, negated_conjecture, (in @ esk57_0 @ (dsetconstr @ esk55_0 @ (^[Z0:$i]:(~((in @ Z0 @ esk56_0)))))), inference(rw,[status(thm)],[c_0_168, c_0_169])).
% 0.19/0.32 thf(c_0_172, negated_conjecture, ~((in @ esk57_0 @ esk55_0)), inference(split_conjunct,[status(thm)],[c_0_166])).
% 0.19/0.32 thf(c_0_173, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_170, c_0_171]), c_0_172]), ['proof']).
% 0.19/0.32 % SZS output end CNFRefutation
% 0.19/0.32 % Parsed axioms : 259
% 0.19/0.32 % Removed by relevancy pruning/SinE : 0
% 0.19/0.32 % Initial clauses : 372
% 0.19/0.32 % Removed in clause preprocessing : 155
% 0.19/0.32 % Initial clauses in saturation : 217
% 0.19/0.32 % Processed clauses : 107
% 0.19/0.32 % ...of these trivial : 5
% 0.19/0.32 % ...subsumed : 26
% 0.19/0.32 % ...remaining for further processing : 76
% 0.19/0.32 % Other redundant clauses eliminated : 10
% 0.19/0.32 % Clauses deleted for lack of memory : 0
% 0.19/0.32 % Backward-subsumed : 0
% 0.19/0.32 % Backward-rewritten : 2
% 0.19/0.32 % Generated clauses : 264
% 0.19/0.32 % ...of the previous two non-redundant : 204
% 0.19/0.32 % ...aggressively subsumed : 0
% 0.19/0.32 % Contextual simplify-reflections : 0
% 0.19/0.32 % Paramodulations : 254
% 0.19/0.32 % Factorizations : 0
% 0.19/0.32 % NegExts : 0
% 0.19/0.32 % Equation resolutions : 10
% 0.19/0.32 % Disequality decompositions : 0
% 0.19/0.32 % Total rewrite steps : 55
% 0.19/0.32 % ...of those cached : 31
% 0.19/0.32 % Propositional unsat checks : 0
% 0.19/0.32 % Propositional check models : 0
% 0.19/0.32 % Propositional check unsatisfiable : 0
% 0.19/0.32 % Propositional clauses : 0
% 0.19/0.32 % Propositional clauses after purity: 0
% 0.19/0.32 % Propositional unsat core size : 0
% 0.19/0.32 % Propositional preprocessing time : 0.000
% 0.19/0.32 % Propositional encoding time : 0.000
% 0.19/0.32 % Propositional solver time : 0.000
% 0.19/0.32 % Success case prop preproc time : 0.000
% 0.19/0.32 % Success case prop encoding time : 0.000
% 0.19/0.32 % Success case prop solver time : 0.000
% 0.19/0.32 % Current number of processed clauses : 68
% 0.19/0.32 % Positive orientable unit clauses : 28
% 0.19/0.32 % Positive unorientable unit clauses: 0
% 0.19/0.32 % Negative unit clauses : 2
% 0.19/0.32 % Non-unit-clauses : 38
% 0.19/0.32 % Current number of unprocessed clauses: 311
% 0.19/0.32 % ...number of literals in the above : 961
% 0.19/0.32 % Current number of archived formulas : 0
% 0.19/0.32 % Current number of archived clauses : 3
% 0.19/0.32 % Clause-clause subsumption calls (NU) : 132
% 0.19/0.32 % Rec. Clause-clause subsumption calls : 129
% 0.19/0.32 % Non-unit clause-clause subsumptions : 16
% 0.19/0.32 % Unit Clause-clause subsumption calls : 2
% 0.19/0.32 % Rewrite failures with RHS unbound : 0
% 0.19/0.32 % BW rewrite match attempts : 6
% 0.19/0.32 % BW rewrite match successes : 2
% 0.19/0.32 % Condensation attempts : 0
% 0.19/0.32 % Condensation successes : 0
% 0.19/0.32 % Termbank termtop insertions : 33687
% 0.19/0.32 % Search garbage collected termcells : 11905
% 0.19/0.32
% 0.19/0.32 % -------------------------------------------------
% 0.19/0.32 % User time : 0.022 s
% 0.19/0.32 % System time : 0.008 s
% 0.19/0.32 % Total time : 0.030 s
% 0.19/0.32 % Maximum resident set size: 6444 pages
% 0.19/0.32
% 0.19/0.32 % -------------------------------------------------
% 0.19/0.32 % User time : 0.029 s
% 0.19/0.32 % System time : 0.013 s
% 0.19/0.32 % Total time : 0.042 s
% 0.19/0.32 % Maximum resident set size: 5120 pages
% 0.19/0.32 % E exiting
%------------------------------------------------------------------------------