E---3.5.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SEU611^1 : 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 : n020.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 08:24:43 AM UTC 2026

% Result   : Theorem 3.25s 0.74s
% Output   : CNFRefutation 3.25s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEU611^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16  % Computer : n020.cluster.edu
% 0.10/0.16  % Model    : x86_64 x86_64
% 0.10/0.16  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16  % Memory   : 8046.5625MB
% 0.10/0.16  % OS       : Linux 6.8.0-71-generic
% 0.10/0.17  % CPULimit : 300
% 0.10/0.17  % WCLimit  : 300
% 0.10/0.17  % DateTime : Tue Sep 29 13:58:34 UTC 2026
% 0.10/0.17  % CPUTime  : 
% 0.10/0.17  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21  Running higher-order theorem proving
% 0.10/0.25  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p
% 3.25/0.74  % Version: 3.5.1-ho
% 3.25/0.74  % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.25/0.74  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.25/0.74  % Starting ehoh_best5 with 300s (1) cores
% 3.25/0.74  % Starting almost_fo_3_lam with 300s (1) cores
% 3.25/0.74  % Starting new_bool_5 with 300s (1) cores
% 3.25/0.74  % Starting pre_casc_3 with 300s (1) cores
% 3.25/0.74  % Starting ho_unfolding_8 with 300s (1) cores
% 3.25/0.74  % Starting new_ho_10_cnf2 with 300s (1) cores
% 3.25/0.74  % Starting new_bool_3 with 300s (1) cores
% 3.25/0.74  % Starting new_ho_5 with 300s (1) cores
% 3.25/0.74  % new_ho_5 with pid 1095683 completed with status 9
% 3.25/0.74  % ho_unfolding_8 with pid 1095680 completed with status 0
% 3.25/0.74  % Result found by ho_unfolding_8
% 3.25/0.74  % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.25/0.74  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.25/0.74  % Starting ehoh_best5 with 300s (1) cores
% 3.25/0.74  % Starting almost_fo_3_lam with 300s (1) cores
% 3.25/0.74  % Starting new_bool_5 with 300s (1) cores
% 3.25/0.74  % Starting pre_casc_3 with 300s (1) cores
% 3.25/0.74  % Starting ho_unfolding_8 with 300s (1) cores
% 3.25/0.74  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.25/0.74  % No SInE strategy applied
% 3.25/0.74  % Search class: HGHSM-FSLM31-MHFMMSBN
% 3.25/0.74  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.25/0.74  % Starting SubtermCWHack with 28s (1) cores
% 3.25/0.74  % SubtermCWHack with pid 1095692 completed with status 0
% 3.25/0.74  % Result found by SubtermCWHack
% 3.25/0.74  % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.25/0.74  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.25/0.74  % Starting ehoh_best5 with 300s (1) cores
% 3.25/0.74  % Starting almost_fo_3_lam with 300s (1) cores
% 3.25/0.74  % Starting new_bool_5 with 300s (1) cores
% 3.25/0.74  % Starting pre_casc_3 with 300s (1) cores
% 3.25/0.74  % Starting ho_unfolding_8 with 300s (1) cores
% 3.25/0.74  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.25/0.74  % No SInE strategy applied
% 3.25/0.74  % Search class: HGHSM-FSLM31-MHFMMSBN
% 3.25/0.74  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.25/0.74  % Starting SubtermCWHack with 28s (1) cores
% 3.25/0.74  % Preprocessing time       : 0.004 s
% 3.25/0.74  
% 3.25/0.74  % Proof found!
% 3.25/0.74  % SZS status Theorem
% 3.25/0.74  % SZS output start CNFRefutation
% 3.25/0.74  thf(decl_23, type, in: $i > $i > $o).
% 3.25/0.74  thf(decl_24, type, exu: ($i > $o) > $o).
% 3.25/0.74  thf(decl_25, type, setextAx: $o).
% 3.25/0.74  thf(decl_26, type, emptyset: $i).
% 3.25/0.74  thf(decl_27, type, emptysetAx: $o).
% 3.25/0.74  thf(decl_28, type, setadjoin: $i > $i > $i).
% 3.25/0.74  thf(decl_29, type, setadjoinAx: $o).
% 3.25/0.74  thf(decl_30, type, powerset: $i > $i).
% 3.25/0.74  thf(decl_31, type, powersetAx: $o).
% 3.25/0.74  thf(decl_32, type, setunion: $i > $i).
% 3.25/0.74  thf(decl_33, type, setunionAx: $o).
% 3.25/0.74  thf(decl_34, type, omega: $i).
% 3.25/0.74  thf(decl_35, type, omega0Ax: $o).
% 3.25/0.74  thf(decl_36, type, omegaSAx: $o).
% 3.25/0.74  thf(decl_37, type, omegaIndAx: $o).
% 3.25/0.74  thf(decl_38, type, replAx: $o).
% 3.25/0.74  thf(decl_39, type, foundationAx: $o).
% 3.25/0.74  thf(decl_40, type, wellorderingAx: $o).
% 3.25/0.74  thf(decl_41, type, descr: ($i > $o) > $i).
% 3.25/0.74  thf(decl_42, type, descrp: $o).
% 3.25/0.74  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 3.25/0.74  thf(decl_44, type, dsetconstrI: $o).
% 3.25/0.74  thf(decl_45, type, dsetconstrEL: $o).
% 3.25/0.74  thf(decl_46, type, dsetconstrER: $o).
% 3.25/0.74  thf(decl_47, type, exuE1: $o).
% 3.25/0.74  thf(decl_48, type, prop2set: $o > $i).
% 3.25/0.74  thf(decl_49, type, prop2setE: $o).
% 3.25/0.74  thf(decl_50, type, emptysetE: $o).
% 3.25/0.74  thf(decl_51, type, emptysetimpfalse: $o).
% 3.25/0.74  thf(decl_52, type, notinemptyset: $o).
% 3.25/0.74  thf(decl_53, type, exuE3e: $o).
% 3.25/0.74  thf(decl_54, type, setext: $o).
% 3.25/0.74  thf(decl_55, type, emptyI: $o).
% 3.25/0.74  thf(decl_56, type, noeltsimpempty: $o).
% 3.25/0.74  thf(decl_57, type, setbeta: $o).
% 3.25/0.74  thf(decl_58, type, nonempty: $i > $o).
% 3.25/0.74  thf(decl_59, type, nonemptyE1: $o).
% 3.25/0.74  thf(decl_60, type, nonemptyI: $o).
% 3.25/0.74  thf(decl_61, type, nonemptyI1: $o).
% 3.25/0.74  thf(decl_62, type, setadjoinIL: $o).
% 3.25/0.74  thf(decl_63, type, emptyinunitempty: $o).
% 3.25/0.74  thf(decl_64, type, setadjoinIR: $o).
% 3.25/0.74  thf(decl_65, type, setadjoinE: $o).
% 3.25/0.74  thf(decl_66, type, setadjoinOr: $o).
% 3.25/0.74  thf(decl_67, type, setoftrueEq: $o).
% 3.25/0.74  thf(decl_68, type, powersetI: $o).
% 3.25/0.74  thf(decl_69, type, emptyinPowerset: $o).
% 3.25/0.74  thf(decl_70, type, emptyInPowerset: $o).
% 3.25/0.74  thf(decl_71, type, powersetE: $o).
% 3.25/0.74  thf(decl_72, type, setunionI: $o).
% 3.25/0.74  thf(decl_73, type, setunionE: $o).
% 3.25/0.74  thf(decl_74, type, subPowSU: $o).
% 3.25/0.74  thf(decl_75, type, exuE2: $o).
% 3.25/0.74  thf(decl_76, type, nonemptyImpWitness: $o).
% 3.25/0.74  thf(decl_77, type, uniqinunit: $o).
% 3.25/0.74  thf(decl_78, type, notinsingleton: $o).
% 3.25/0.74  thf(decl_79, type, eqinunit: $o).
% 3.25/0.74  thf(decl_80, type, singletonsswitch: $o).
% 3.25/0.74  thf(decl_81, type, upairsetE: $o).
% 3.25/0.74  thf(decl_82, type, upairsetIL: $o).
% 3.25/0.74  thf(decl_83, type, upairsetIR: $o).
% 3.25/0.74  thf(decl_84, type, emptyE1: $o).
% 3.25/0.74  thf(decl_85, type, vacuousDall: $o).
% 3.25/0.74  thf(decl_86, type, quantDeMorgan1: $o).
% 3.25/0.74  thf(decl_87, type, quantDeMorgan2: $o).
% 3.25/0.74  thf(decl_88, type, quantDeMorgan3: $o).
% 3.25/0.74  thf(decl_89, type, quantDeMorgan4: $o).
% 3.25/0.74  thf(decl_90, type, prop2setI: $o).
% 3.25/0.74  thf(decl_91, type, set2prop: $i > $o).
% 3.25/0.74  thf(decl_92, type, prop2set2propI: $o).
% 3.25/0.74  thf(decl_93, type, notdexE: $o).
% 3.25/0.74  thf(decl_94, type, notdallE: $o).
% 3.25/0.74  thf(decl_95, type, exuI1: $o).
% 3.25/0.74  thf(decl_96, type, exuI3: $o).
% 3.25/0.74  thf(decl_97, type, exuI2: $o).
% 3.25/0.74  thf(decl_98, type, inCongP: $o).
% 3.25/0.74  thf(decl_99, type, in__Cong: $o).
% 3.25/0.74  thf(decl_100, type, exuE3u: $o).
% 3.25/0.74  thf(decl_101, type, exu__Cong: $o).
% 3.25/0.74  thf(decl_102, type, emptyset__Cong: $o).
% 3.25/0.74  thf(decl_103, type, setadjoin__Cong: $o).
% 3.25/0.74  thf(decl_104, type, powerset__Cong: $o).
% 3.25/0.74  thf(decl_105, type, setunion__Cong: $o).
% 3.25/0.74  thf(decl_106, type, omega__Cong: $o).
% 3.25/0.74  thf(decl_107, type, exuEu: $o).
% 3.25/0.74  thf(decl_108, type, descr__Cong: $o).
% 3.25/0.74  thf(decl_109, type, dsetconstr__Cong: $o).
% 3.25/0.74  thf(decl_110, type, subset: $i > $i > $o).
% 3.25/0.74  thf(decl_113, type, subsetI1: $o).
% 3.25/0.74  thf(decl_114, type, eqimpsubset2: $o).
% 3.25/0.74  thf(decl_115, type, eqimpsubset1: $o).
% 3.25/0.74  thf(decl_116, type, subsetI2: $o).
% 3.25/0.74  thf(decl_117, type, emptysetsubset: $o).
% 3.25/0.74  thf(decl_118, type, subsetE: $o).
% 3.25/0.74  thf(decl_119, type, subsetE2: $o).
% 3.25/0.74  thf(decl_120, type, notsubsetI: $o).
% 3.25/0.74  thf(decl_121, type, notequalI1: $o).
% 3.25/0.74  thf(decl_122, type, notequalI2: $o).
% 3.25/0.74  thf(decl_123, type, subsetRefl: $o).
% 3.25/0.74  thf(decl_124, type, subsetTrans: $o).
% 3.25/0.74  thf(decl_125, type, setadjoinSub: $o).
% 3.25/0.74  thf(decl_126, type, setadjoinSub2: $o).
% 3.25/0.74  thf(decl_127, type, subset2powerset: $o).
% 3.25/0.74  thf(decl_128, type, setextsub: $o).
% 3.25/0.74  thf(decl_129, type, subsetemptysetimpeq: $o).
% 3.25/0.74  thf(decl_130, type, powersetI1: $o).
% 3.25/0.74  thf(decl_131, type, powersetE1: $o).
% 3.25/0.74  thf(decl_132, type, inPowerset: $o).
% 3.25/0.74  thf(decl_133, type, powersetsubset: $o).
% 3.25/0.74  thf(decl_134, type, sepInPowerset: $o).
% 3.25/0.74  thf(decl_135, type, sepSubset: $o).
% 3.25/0.74  thf(decl_136, type, binunion: $i > $i > $i).
% 3.25/0.74  thf(decl_137, type, binunionIL: $o).
% 3.25/0.74  thf(decl_138, type, upairset2IR: $o).
% 3.25/0.74  thf(decl_139, type, binunionIR: $o).
% 3.25/0.74  thf(decl_140, type, binunionEcases: $o).
% 3.25/0.74  thf(decl_141, type, binunionE: $o).
% 3.25/0.74  thf(decl_142, type, binunionLsub: $o).
% 3.25/0.74  thf(decl_143, type, binunionRsub: $o).
% 3.25/0.74  thf(decl_144, type, binintersect: $i > $i > $i).
% 3.25/0.74  thf(decl_145, type, binintersectI: $o).
% 3.25/0.74  thf(decl_146, type, binintersectSubset5: $o).
% 3.25/0.74  thf(decl_147, type, binintersectEL: $o).
% 3.25/0.74  thf(decl_148, type, binintersectLsub: $o).
% 3.25/0.74  thf(decl_149, type, binintersectSubset2: $o).
% 3.25/0.74  thf(decl_150, type, binintersectSubset3: $o).
% 3.25/0.74  thf(decl_151, type, binintersectER: $o).
% 3.25/0.74  thf(decl_152, type, disjointsetsI1: $o).
% 3.25/0.74  thf(decl_153, type, binintersectRsub: $o).
% 3.25/0.74  thf(decl_154, type, binintersectSubset4: $o).
% 3.25/0.74  thf(decl_155, type, binintersectSubset1: $o).
% 3.25/0.74  thf(decl_156, type, bs114d: $o).
% 3.25/0.74  thf(decl_158, type, setminus: $i > $i > $i).
% 3.25/0.74  thf(decl_159, type, setminusI: $o).
% 3.25/0.74  thf(decl_160, type, setminusEL: $o).
% 3.25/0.74  thf(decl_161, type, setminusER: $o).
% 3.25/0.74  thf(decl_162, type, setminusSubset2: $o).
% 3.25/0.74  thf(decl_163, type, setminusERneg: $o).
% 3.25/0.74  thf(decl_164, type, setminusELneg: $o).
% 3.25/0.74  thf(decl_165, type, setminusILneg: $o).
% 3.25/0.74  thf(decl_166, type, setminusIRneg: $o).
% 3.25/0.74  thf(decl_167, type, setminusLsub: $o).
% 3.25/0.74  thf(decl_168, type, setminusSubset1: $o).
% 3.25/0.74  thf(decl_169, type, symdiff: $i > $i > $i).
% 3.25/0.74  thf(decl_170, type, epred1_0: $o).
% 3.25/0.74  thf(decl_171, type, esk1_2: $i > $i > $i).
% 3.25/0.74  thf(decl_172, type, esk2_2: $i > $i > $i).
% 3.25/0.74  thf(decl_173, type, esk3_2: $i > $i > $i).
% 3.25/0.74  thf(decl_174, type, esk4_1: $i > $i).
% 3.25/0.74  thf(decl_175, type, esk5_2: ($i > $i > $o) > $i > $i).
% 3.25/0.74  thf(decl_176, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 3.25/0.74  thf(decl_177, type, esk7_2: ($i > $i > $o) > $i > $i).
% 3.25/0.74  thf(decl_178, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 3.25/0.74  thf(decl_179, type, esk9_1: $i > $i).
% 3.25/0.74  thf(decl_180, type, esk10_2: ($i > $o) > $i > $i).
% 3.25/0.74  thf(decl_181, type, esk11_2: ($i > $o) > $i > $i).
% 3.25/0.74  thf(decl_182, type, esk12_1: ($i > $o) > $i).
% 3.25/0.74  thf(decl_183, type, esk13_2: ($i > $o) > $i > $i).
% 3.25/0.74  thf(decl_184, type, esk14_1: ($i > $o) > $i).
% 3.25/0.74  thf(decl_185, type, esk15_2: $i > $i > $i).
% 3.25/0.74  thf(decl_186, type, esk16_2: $i > $i > $i).
% 3.25/0.74  thf(decl_187, type, esk17_1: $i > $i).
% 3.25/0.74  thf(decl_188, type, esk18_1: $i > $i).
% 3.25/0.74  thf(decl_189, type, esk19_1: $i > $i).
% 3.25/0.74  thf(decl_190, type, esk20_2: $i > $i > $i).
% 3.25/0.74  thf(decl_191, type, esk21_3: $i > $i > $o > $i).
% 3.25/0.74  thf(decl_192, type, esk22_2: ($i > $o) > $i > $i).
% 3.25/0.74  thf(decl_193, type, esk23_1: ($i > $o) > $i).
% 3.25/0.74  thf(decl_194, type, esk24_1: $i > $i).
% 3.25/0.74  thf(decl_195, type, esk25_2: $i > ($i > $o) > $i).
% 3.25/0.74  thf(decl_196, type, esk26_2: $i > ($i > $o) > $i).
% 3.25/0.74  thf(decl_197, type, esk27_2: $i > ($i > $o) > $i).
% 3.25/0.74  thf(decl_198, type, esk28_2: $i > ($i > $o) > $i).
% 3.25/0.74  thf(decl_199, type, esk29_2: $i > ($i > $o) > $i).
% 3.25/0.74  thf(decl_200, type, esk30_2: $i > ($i > $o) > $i).
% 3.25/0.74  thf(decl_201, type, esk31_2: ($i > $o) > $i > $i).
% 3.25/0.74  thf(decl_202, type, esk32_1: ($i > $o) > $i).
% 3.25/0.74  thf(decl_203, type, esk33_1: ($i > $o) > $i).
% 3.25/0.74  thf(decl_204, type, esk34_1: ($i > $o) > $i).
% 3.25/0.74  thf(decl_205, type, esk35_1: ($i > $o) > $i).
% 3.25/0.74  thf(decl_206, type, esk36_2: ($i > $o) > $i > $i).
% 3.25/0.74  thf(decl_207, type, esk37_1: ($i > $o) > $i).
% 3.25/0.74  thf(decl_208, type, esk38_2: ($i > $o) > $i > $i).
% 3.25/0.74  thf(decl_209, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 3.25/0.74  thf(decl_210, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 3.25/0.74  thf(decl_211, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 3.25/0.74  thf(decl_212, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 3.25/0.74  thf(decl_213, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 3.25/0.74  thf(decl_214, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 3.25/0.74  thf(decl_215, type, esk45_2: ($i > $o) > $i > $i).
% 3.25/0.74  thf(decl_216, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 3.25/0.74  thf(decl_217, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 3.25/0.74  thf(decl_218, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 3.25/0.74  thf(decl_219, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 3.25/0.74  thf(decl_220, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 3.25/0.74  thf(decl_221, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 3.25/0.74  thf(decl_222, type, esk52_2: $i > $i > $i).
% 3.25/0.74  thf(decl_223, type, esk53_2: $i > $i > $i).
% 3.25/0.74  thf(decl_224, type, esk54_2: $i > $i > $i).
% 3.25/0.74  thf(decl_225, type, esk55_0: $i).
% 3.25/0.74  thf(decl_226, type, esk56_0: $i).
% 3.25/0.74  thf(decl_227, type, esk57_0: $i).
% 3.25/0.74  thf(decl_228, type, epred2_0: $o).
% 3.25/0.74  thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', replAx)).
% 3.25/0.74  thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', exu)).
% 3.25/0.74  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', descrp)).
% 3.25/0.74  thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', exuE1)).
% 3.25/0.74  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', exuE3e)).
% 3.25/0.74  thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', nonempty)).
% 3.25/0.74  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', nonemptyI)).
% 3.25/0.74  thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', exuE2)).
% 3.25/0.74  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.DQ5N4zzQ6j/E---3.1_1095663.p', exuI1)).
% 3.25/0.74  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', exuI3)).
% 3.25/0.74  thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', exuI2)).
% 3.25/0.74  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.DQ5N4zzQ6j/E---3.1_1095663.p', exuE3u)).
% 3.25/0.74  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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', exu__Cong)).
% 3.25/0.74  thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', exuEu)).
% 3.25/0.74  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.DQ5N4zzQ6j/E---3.1_1095663.p', descr__Cong)).
% 3.25/0.74  thf(symdiffE, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', symdiffE)).
% 3.25/0.74  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', dsetconstrI)).
% 3.25/0.74  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', dsetconstrEL)).
% 3.25/0.74  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', dsetconstrER)).
% 3.25/0.74  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setbeta)).
% 3.25/0.74  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', nonemptyE1)).
% 3.25/0.74  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', nonemptyI1)).
% 3.25/0.74  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setoftrueEq)).
% 3.25/0.74  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', nonemptyImpWitness)).
% 3.25/0.74  thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.DQ5N4zzQ6j/E---3.1_1095663.p', emptyE1)).
% 3.25/0.74  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', dsetconstr__Cong)).
% 3.25/0.74  thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', sepInPowerset)).
% 3.25/0.74  thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', sepSubset)).
% 3.25/0.74  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setextAx)).
% 3.25/0.74  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', emptysetAx)).
% 3.25/0.74  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setadjoinAx)).
% 3.25/0.74  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', powersetAx)).
% 3.25/0.74  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setunionAx)).
% 3.25/0.74  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', omega0Ax)).
% 3.25/0.74  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', omegaSAx)).
% 3.25/0.74  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', omegaIndAx)).
% 3.25/0.74  thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', foundationAx)).
% 3.25/0.74  thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.DQ5N4zzQ6j/E---3.1_1095663.p', wellorderingAx)).
% 3.25/0.74  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', prop2setE)).
% 3.25/0.74  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', emptysetE)).
% 3.25/0.74  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', emptysetimpfalse)).
% 3.25/0.74  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', notinemptyset)).
% 3.25/0.74  thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setext)).
% 3.25/0.74  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', emptyI)).
% 3.25/0.74  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', noeltsimpempty)).
% 3.25/0.74  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setadjoinIL)).
% 3.25/0.74  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', emptyinunitempty)).
% 3.25/0.74  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setadjoinIR)).
% 3.25/0.74  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.DQ5N4zzQ6j/E---3.1_1095663.p', setadjoinE)).
% 3.25/0.74  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setadjoinOr)).
% 3.25/0.74  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', powersetI)).
% 3.25/0.74  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', emptyinPowerset)).
% 3.25/0.74  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', emptyInPowerset)).
% 3.25/0.74  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', powersetE)).
% 3.25/0.74  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setunionI)).
% 3.25/0.74  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.DQ5N4zzQ6j/E---3.1_1095663.p', setunionE)).
% 3.25/0.74  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', subPowSU)).
% 3.25/0.74  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', uniqinunit)).
% 3.25/0.74  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', notinsingleton)).
% 3.25/0.74  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', eqinunit)).
% 3.25/0.74  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', singletonsswitch)).
% 3.25/0.74  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', upairsetE)).
% 3.25/0.74  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', upairsetIL)).
% 3.25/0.74  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', upairsetIR)).
% 3.25/0.74  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', vacuousDall)).
% 3.25/0.74  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', quantDeMorgan1)).
% 3.25/0.74  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', quantDeMorgan2)).
% 3.25/0.74  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', quantDeMorgan3)).
% 3.25/0.74  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', quantDeMorgan4)).
% 3.25/0.74  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', prop2setI)).
% 3.25/0.74  thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', prop2set2propI)).
% 3.25/0.74  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', notdexE)).
% 3.25/0.74  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', notdallE)).
% 3.25/0.74  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', inCongP)).
% 3.25/0.74  thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', in__Cong)).
% 3.25/0.74  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', emptyset__Cong)).
% 3.25/0.74  thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setadjoin__Cong)).
% 3.25/0.74  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', powerset__Cong)).
% 3.25/0.74  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setunion__Cong)).
% 3.25/0.74  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', omega__Cong)).
% 3.25/0.74  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', subsetI1)).
% 3.25/0.74  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', eqimpsubset2)).
% 3.25/0.74  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', eqimpsubset1)).
% 3.25/0.74  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', subsetI2)).
% 3.25/0.74  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', emptysetsubset)).
% 3.25/0.74  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', subsetE)).
% 3.25/0.74  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', subsetE2)).
% 3.25/0.74  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', notsubsetI)).
% 3.25/0.74  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', notequalI1)).
% 3.25/0.74  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', notequalI2)).
% 3.25/0.74  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', subsetRefl)).
% 3.25/0.74  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', subsetTrans)).
% 3.25/0.74  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setadjoinSub)).
% 3.25/0.74  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setadjoinSub2)).
% 3.25/0.74  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', subset2powerset)).
% 3.25/0.74  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setextsub)).
% 3.25/0.74  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', subsetemptysetimpeq)).
% 3.25/0.74  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', powersetI1)).
% 3.25/0.74  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', powersetE1)).
% 3.25/0.74  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', inPowerset)).
% 3.25/0.74  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', powersetsubset)).
% 3.25/0.74  thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binunionIL)).
% 3.25/0.74  thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', upairset2IR)).
% 3.25/0.74  thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binunionIR)).
% 3.25/0.74  thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binunionEcases)).
% 3.25/0.74  thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binunionE)).
% 3.25/0.74  thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binunionLsub)).
% 3.25/0.74  thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binunionRsub)).
% 3.25/0.74  thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binintersectI)).
% 3.25/0.74  thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binintersectSubset5)).
% 3.25/0.74  thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binintersectEL)).
% 3.25/0.74  thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binintersectLsub)).
% 3.25/0.74  thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binintersectSubset2)).
% 3.25/0.74  thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binintersectSubset3)).
% 3.25/0.74  thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binintersectER)).
% 3.25/0.74  thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', disjointsetsI1)).
% 3.25/0.74  thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binintersectRsub)).
% 3.25/0.74  thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binintersectSubset4)).
% 3.25/0.74  thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', binintersectSubset1)).
% 3.25/0.74  thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', bs114d)).
% 3.25/0.74  thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setminusI)).
% 3.25/0.74  thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setminusEL)).
% 3.25/0.74  thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setminusER)).
% 3.25/0.74  thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setminusSubset2)).
% 3.25/0.74  thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setminusERneg)).
% 3.25/0.74  thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setminusELneg)).
% 3.25/0.74  thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setminusILneg)).
% 3.25/0.74  thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setminusIRneg)).
% 3.25/0.74  thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setminusLsub)).
% 3.25/0.74  thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', setminusSubset1)).
% 3.25/0.74  thf(symdiff, axiom, ((symdiff)=(^[X4:$i, X5:$i]:(dsetconstr @ (binunion @ X4 @ X5) @ (^[X2:$i]:(((~((in @ X2 @ X4)))|(~((in @ X2 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.DQ5N4zzQ6j/E---3.1_1095663.p', symdiff)).
% 3.25/0.74  thf(c_0_131, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 3.25/0.74  thf(c_0_132, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 3.25/0.74  thf(c_0_133, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 3.25/0.74  thf(c_0_134, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 3.25/0.74  thf(c_0_135, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 3.25/0.74  thf(c_0_136, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 3.25/0.74  thf(c_0_137, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 3.25/0.74  thf(c_0_138, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 3.25/0.74  thf(c_0_139, 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])).
% 3.25/0.74  thf(c_0_140, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 3.25/0.74  thf(c_0_141, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 3.25/0.74  thf(c_0_142, 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])).
% 3.25/0.74  thf(c_0_143, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 3.25/0.74  thf(c_0_144, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 3.25/0.74  thf(c_0_145, 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])).
% 3.25/0.74  thf(c_0_146, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[symdiffE])).
% 3.25/0.74  thf(c_0_147, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X363:$i]:(((((X6 @ X2 @ X363)))&(![X364:$i]:(((((X6 @ X2 @ X364)))=>(((X363)=(X364)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_131, c_0_132])).
% 3.25/0.74  thf(c_0_148, plain, ((descrp)=(![X1:$i > $o]:((((?[X365:$i]:(((((X1 @ X365)))&(![X366:$i]:(((((X1 @ X366)))=>(((X365)=(X366))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_133, c_0_132])).
% 3.25/0.74  thf(c_0_149, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 3.25/0.74  thf(c_0_150, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 3.25/0.74  thf(c_0_151, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 3.25/0.74  thf(c_0_152, plain, ((exuE1)=(![X1:$i > $o]:((((?[X367:$i]:(((((X1 @ X367)))&(![X368:$i]:(((((X1 @ X368)))=>(((X367)=(X368))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_134, c_0_132])).
% 3.25/0.74  thf(c_0_153, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X369:$i]:(((((X1 @ X369)))&(![X370:$i]:(((((X1 @ X370)))=>(((X369)=(X370))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_135, c_0_132])).
% 3.25/0.74  thf(c_0_154, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 3.25/0.74  thf(c_0_155, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_136])).
% 3.25/0.74  thf(c_0_156, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_137, c_0_136])).
% 3.25/0.74  thf(c_0_157, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_136])).
% 3.25/0.74  thf(c_0_158, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 3.25/0.74  thf(c_0_159, plain, ((exuE2)=(![X1:$i > $o]:((((?[X371:$i]:(((((X1 @ X371)))&(![X372:$i]:(((((X1 @ X372)))=>(((X371)=(X372))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_138, c_0_132])).
% 3.25/0.74  thf(c_0_160, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_136])).
% 3.25/0.74  thf(c_0_161, 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])).
% 3.25/0.74  thf(c_0_162, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X373:$i]:(((((X1 @ X373)))&(![X374:$i]:(((((X1 @ X374)))=>(((X373)=(X374)))))))))))))), inference(apply_def,[status(thm)],[c_0_139, c_0_132])).
% 3.25/0.74  thf(c_0_163, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X375:$i]:(((((X1 @ X375)))&(![X376:$i]:(((((X1 @ X376)))=>(((X375)=(X376)))))))))))))))), inference(apply_def,[status(thm)],[c_0_140, c_0_132])).
% 3.25/0.74  thf(c_0_164, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X377:$i]:(((((X1 @ X377)))&(![X378:$i]:(((((X1 @ X378)))=>(((X377)=(X378)))))))))))))), inference(apply_def,[status(thm)],[c_0_141, c_0_132])).
% 3.25/0.74  thf(c_0_165, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X379:$i]:(((((X1 @ X379)))&(![X380:$i]:(((((X1 @ X380)))=>(((X379)=(X380))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_142, c_0_132])).
% 3.25/0.74  thf(c_0_166, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X381:$i]:(((((X1 @ X381)))&(![X382:$i]:(((((X1 @ X382)))=>(((X381)=(X382))))))))))<=>((?[X383:$i]:(((((X17 @ X383)))&(![X384:$i]:(((((X17 @ X384)))=>(((X383)=(X384)))))))))))))))), inference(apply_def,[status(thm)],[c_0_143, c_0_132])).
% 3.25/0.74  thf(c_0_167, plain, ((exuEu)=(![X1:$i > $o]:((((?[X385:$i]:(((((X1 @ X385)))&(![X386:$i]:(((((X1 @ X386)))=>(((X385)=(X386))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_144, c_0_132])).
% 3.25/0.74  thf(c_0_168, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X387:$i]:(((((X1 @ X387)))&(![X388:$i]:(((((X1 @ X388)))=>(((X387)=(X388))))))))))=>((((?[X389:$i]:(((((X17 @ X389)))&(![X390:$i]:(((((X17 @ X390)))=>(((X389)=(X390))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_145, c_0_132])).
% 3.25/0.74  thf(c_0_169, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 3.25/0.74  thf(c_0_170, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 3.25/0.74  thf(c_0_171, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 3.25/0.74  thf(c_0_172, plain, ((epred1_0)<=>![X420:$i]:(?[X421:$i]:((((![X422:$i]:(((in @ X422 @ X421)=>![X423:$i]:(((in @ X423 @ X422)=>(in @ X423 @ X420)))))&![X424:$i, X425:$i]:((((in @ X424 @ X420)&(in @ X425 @ X420))=>(![X426:$i]:(((in @ X426 @ X421)=>((in @ X424 @ X426)<=>(in @ X425 @ X426))))=>((X424)=(X425))))))&![X427:$i, X428:$i]:((((in @ X427 @ X421)&(in @ X428 @ X421))=>(![X429:$i]:(((in @ X429 @ X427)=>(in @ X429 @ X428)))|![X430:$i]:(((in @ X430 @ X428)=>(in @ X430 @ X427)))))))&![X431:$i]:(((![X432:$i]:(((in @ X432 @ X431)=>(in @ X432 @ X420)))&?[X433:$i]:((in @ X433 @ X431)))=>?[X434:$i, X435:$i]:(((((in @ X434 @ X421)&(in @ X435 @ X431))&~(?[X436:$i]:(((in @ X436 @ X434)&(in @ X436 @ X431)))))&![X437:$i]:(((in @ X437 @ X421)=>(![X438:$i]:(((in @ X438 @ X437)=>(in @ X438 @ X434)))|(in @ X435 @ X437)))))))))))), introduced(definition)).
% 3.25/0.74  thf(c_0_173, negated_conjecture, ~((![X391:$i, X392:$i]:((![X393:$i]:(((in @ X393 @ X391)<=>(in @ X393 @ X392)))=>((X391)=(X392))))=>(![X394:$i]:(~(in @ X394 @ emptyset))=>(![X395:$i, X396:$i, X397:$i]:(((in @ X397 @ (setadjoin @ X395 @ X396))<=>(((X397)=(X395))|(in @ X397 @ X396))))=>(![X398:$i, X399:$i]:(((in @ X399 @ (powerset @ X398))<=>![X400:$i]:(((in @ X400 @ X399)=>(in @ X400 @ X398)))))=>(![X401:$i, X402:$i]:(((in @ X402 @ (setunion @ X401))<=>?[X403:$i]:(((in @ X402 @ X403)&(in @ X403 @ X401)))))=>((in @ emptyset @ omega)=>(![X404:$i]:(((in @ X404 @ omega)=>(in @ (setadjoin @ X404 @ X404) @ omega)))=>(![X405:$i]:((((in @ emptyset @ X405)&![X406:$i]:((((in @ X406 @ omega)&(in @ X406 @ X405))=>(in @ (setadjoin @ X406 @ X406) @ X405))))=>![X407:$i]:(((in @ X407 @ omega)=>(in @ X407 @ X405)))))=>(![X408:$i > $i > $o, X409:$i]:((![X410:$i]:(((in @ X410 @ X409)=>?[X411:$i]:(((X408 @ X410 @ X411)&![X412:$i]:(((X408 @ X410 @ X412)=>((X411)=(X412))))))))=>?[X413:$i]:(![X414:$i]:(((in @ X414 @ X413)<=>?[X415:$i]:(((in @ X415 @ X409)&(X408 @ X415 @ X414))))))))=>(![X416:$i]:((?[X417:$i]:((in @ X417 @ X416))=>?[X418:$i]:(((in @ X418 @ X416)&~(?[X419:$i]:(((in @ X419 @ X418)&(in @ X419 @ X416))))))))=>((epred1_0)=>(![X439:$i > $o]:((?[X440:$i]:(((X439 @ X440)&![X441:$i]:(((X439 @ X441)=>((X440)=(X441))))))=>(X439 @ (descr @ (^[Z0:$i]:(X439 @ Z0))))))=>(![X442:$i, X443:$i > $o, X444:$i]:(((in @ X444 @ X442)=>((X443 @ X444)=>(in @ X444 @ (dsetconstr @ X442 @ X443)))))=>(![X445:$i, X446:$i > $o, X447:$i]:(((in @ X447 @ (dsetconstr @ X445 @ X446))=>(in @ X447 @ X445)))=>(![X448:$i, X449:$i > $o, X450:$i]:(((in @ X450 @ (dsetconstr @ X448 @ X449))=>(X449 @ X450)))=>(![X451:$i > $o]:((?[X452:$i]:(((X451 @ X452)&![X453:$i]:(((X451 @ X453)=>((X452)=(X453))))))=>?[X454:$i]:(((X451 @ X454)&![X455:$i]:(((X451 @ X455)=>((X454)=(X455))))))))=>(![X456:$o, X457:$i]:(((in @ X457 @ (prop2set @ ((X456))))=>(X456)))=>(![X458:$i]:(((in @ X458 @ emptyset)=>![X459:$o]:((X459))))=>(![X460:$i]:(((in @ X460 @ emptyset)=>~($true)))=>(![X461:$i]:(~(in @ X461 @ emptyset))=>(![X462:$i > $o]:((?[X463:$i]:(((X462 @ X463)&![X464:$i]:(((X462 @ X464)=>((X463)=(X464))))))=>?[X465:$i]:((X462 @ X465))))=>(![X466:$i, X467:$i]:((![X468:$i]:(((in @ X468 @ X466)=>(in @ X468 @ X467)))=>(![X469:$i]:(((in @ X469 @ X467)=>(in @ X469 @ X466)))=>((X466)=(X467)))))=>(![X470:$i]:((![X471:$i]:(~(in @ X471 @ X470))=>((X470)=(emptyset))))=>(![X472:$i]:((![X473:$i]:(~(in @ X473 @ X472))=>((X472)=(emptyset))))=>(![X474:$i, X475:$i > $o, X476:$i]:(((in @ X476 @ X474)=>((in @ X476 @ (dsetconstr @ X474 @ X475))<=>(X475 @ X476))))=>(![X477:$i]:((((X477)!=(emptyset))=>?[X478:$i]:((in @ X478 @ X477))))=>(![X479:$i, X480:$i > $o, X481:$i]:(((in @ X481 @ X479)=>((X480 @ X481)=>((dsetconstr @ X479 @ X480)!=(emptyset)))))=>(![X482:$i]:((?[X483:$i]:((in @ X483 @ X482))=>((X482)!=(emptyset))))=>(![X484:$i, X485:$i]:((in @ X484 @ (setadjoin @ X484 @ X485)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X486:$i, X487:$i, X488:$i]:(((in @ X488 @ X487)=>(in @ X488 @ (setadjoin @ X486 @ X487))))=>(![X489:$i, X490:$i, X491:$i]:(((in @ X491 @ (setadjoin @ X489 @ X490))=>![X492:$o]:(((((X491)=(X489))=>(X492))=>(((in @ X491 @ X490)=>(X492))=>(X492))))))=>(![X493:$i, X494:$i, X495:$i]:(((in @ X495 @ (setadjoin @ X493 @ X494))=>(((X495)=(X493))|(in @ X495 @ X494))))=>(![X496:$i]:(((dsetconstr @ X496 @ (^[Z0:$i]:($true)))=(X496)))=>(![X497:$i, X498:$i]:((![X499:$i]:(((in @ X499 @ X498)=>(in @ X499 @ X497)))=>(in @ X498 @ (powerset @ X497))))=>(![X500:$i]:((in @ emptyset @ (powerset @ X500)))=>(![X501:$i]:((in @ emptyset @ (powerset @ X501)))=>(![X502:$i, X503:$i, X504:$i]:(((in @ X503 @ (powerset @ X502))=>((in @ X504 @ X503)=>(in @ X504 @ X502))))=>(![X505:$i, X506:$i, X507:$i]:(((in @ X506 @ X507)=>((in @ X507 @ X505)=>(in @ X506 @ (setunion @ X505)))))=>(![X508:$i, X509:$i]:(((in @ X509 @ (setunion @ X508))=>![X510:$o]:((![X511:$i]:(((in @ X509 @ X511)=>((in @ X511 @ X508)=>(X510))))=>(X510)))))=>(![X512:$i, X513:$i]:(((in @ X513 @ X512)=>(in @ X513 @ (powerset @ (setunion @ X512)))))=>(![X514:$i > $o]:((?[X515:$i]:(((X514 @ X515)&![X516:$i]:(((X514 @ X516)=>((X515)=(X516))))))=>?[X517:$i]:(![X518:$i]:(((X514 @ X518)<=>((X518)=(X517)))))))=>(![X519:$i]:((((X519)!=(emptyset))=>?[X520:$i]:(((in @ X520 @ X519)&$true))))=>(![X521:$i, X522:$i]:(((in @ X521 @ (setadjoin @ X522 @ emptyset))=>((X521)=(X522))))=>(![X523:$i, X524:$i]:((((X523)!=(X524))=>~(in @ X524 @ (setadjoin @ X523 @ emptyset))))=>(![X525:$i, X526:$i]:((((X525)=(X526))=>(in @ X525 @ (setadjoin @ X526 @ emptyset))))=>(![X527:$i, X528:$i]:(((in @ X527 @ (setadjoin @ X528 @ emptyset))=>(in @ X528 @ (setadjoin @ X527 @ emptyset))))=>(![X529:$i, X530:$i, X531:$i]:(((in @ X531 @ (setadjoin @ X529 @ (setadjoin @ X530 @ emptyset)))=>(((X531)=(X529))|((X531)=(X530)))))=>(![X532:$i, X533:$i]:((in @ X532 @ (setadjoin @ X532 @ (setadjoin @ X533 @ emptyset))))=>(![X534:$i, X535:$i]:((in @ X535 @ (setadjoin @ X534 @ (setadjoin @ X535 @ emptyset))))=>(![X536:$i, X537:$i > $o]:((?[X538:$i]:(((in @ X538 @ X536)&(X537 @ X538)))=>(((dsetconstr @ X536 @ X537)=(emptyset))=>~($true))))=>(![X539:$i > $o, X540:$i]:(((in @ X540 @ emptyset)=>(X539 @ X540)))=>(![X541:$i, X542:$i > $o]:((~(![X543:$i]:(((in @ X543 @ X541)=>(X542 @ X543))))=>?[X544:$i]:(((in @ X544 @ X541)&~((X542 @ X544))))))=>(![X545:$i, X546:$i > $o]:((![X547:$i]:(((in @ X547 @ X545)=>~((X546 @ X547))))=>~(?[X548:$i]:(((in @ X548 @ X545)&(X546 @ X548))))))=>(![X549:$i, X550:$i > $o]:((~(?[X551:$i]:(((in @ X551 @ X549)&(X550 @ X551))))=>![X552:$i]:(((in @ X552 @ X549)=>~((X550 @ X552))))))=>(![X553:$i, X554:$i > $o]:((?[X555:$i]:(((in @ X555 @ X553)&~((X554 @ X555))))=>~(![X556:$i]:(((in @ X556 @ X553)=>(X554 @ X556))))))=>(![X557:$o]:(((X557)=>(in @ emptyset @ (prop2set @ ((X557))))))=>(![X558:$o]:(((X558)=>(set2prop @ (prop2set @ ((X558))))))=>(![X559:$i, X560:$i > $o]:((~(?[X561:$i]:(((in @ X561 @ X559)&(X560 @ X561))))=>![X562:$i]:(((in @ X562 @ X559)=>~((X560 @ X562))))))=>(![X563:$i, X564:$i > $o]:((~(![X565:$i]:(((in @ X565 @ X563)=>(X564 @ X565))))=>?[X566:$i]:(((in @ X566 @ X563)&~((X564 @ X566))))))=>(![X567:$i > $o]:((?[X568:$i]:(((X567 @ X568)&![X569:$i]:(((X567 @ X569)=>((X568)=(X569))))))=>?[X570:$i]:(((X567 @ X570)&![X571:$i]:(((X567 @ X571)=>((X570)=(X571))))))))=>(![X572:$i > $o]:((?[X573:$i]:((X572 @ X573))=>(![X574:$i, X575:$i]:(((X572 @ X574)=>((X572 @ X575)=>((X574)=(X575)))))=>?[X576:$i]:(((X572 @ X576)&![X577:$i]:(((X572 @ X577)=>((X576)=(X577)))))))))=>(![X578:$i > $o]:((?[X579:$i]:(![X580:$i]:(((X578 @ X580)<=>((X580)=(X579)))))=>?[X581:$i]:(((X578 @ X581)&![X582:$i]:(((X578 @ X582)=>((X581)=(X582))))))))=>(![X583:$i, X584:$i]:((((X583)=(X584))=>![X585:$i, X586:$i]:((((X585)=(X586))=>((in @ X585 @ X583)=>(in @ X586 @ X584))))))=>(![X587:$i, X588:$i]:((((X587)=(X588))=>![X589:$i, X590:$i]:((((X589)=(X590))=>((in @ X589 @ X587)<=>(in @ X590 @ X588))))))=>(![X591:$i > $o]:((?[X592:$i]:(((X591 @ X592)&![X593:$i]:(((X591 @ X593)=>((X592)=(X593))))))=>![X594:$i, X595:$i]:(((X591 @ X594)=>((X591 @ X595)=>((X594)=(X595)))))))=>(![X596:$i > $o, X597:$i > $o]:((![X598:$i, X599:$i]:((((X598)=(X599))=>((X596 @ X598)<=>(X597 @ X599))))=>(?[X600:$i]:(((X596 @ X600)&![X601:$i]:(((X596 @ X601)=>((X600)=(X601))))))<=>?[X602:$i]:(((X597 @ X602)&![X603:$i]:(((X597 @ X603)=>((X602)=(X603)))))))))=>(((emptyset)=(emptyset))=>(![X604:$i, X605:$i]:((((X604)=(X605))=>![X606:$i, X607:$i]:((((X606)=(X607))=>((setadjoin @ X604 @ X606)=(setadjoin @ X605 @ X607))))))=>(![X608:$i, X609:$i]:((((X608)=(X609))=>((powerset @ X608)=(powerset @ X609))))=>(![X610:$i, X611:$i]:((((X610)=(X611))=>((setunion @ X610)=(setunion @ X611))))=>(((omega)=(omega))=>(![X612:$i > $o]:((?[X613:$i]:(((X612 @ X613)&![X614:$i]:(((X612 @ X614)=>((X613)=(X614))))))=>![X615:$i, X616:$i]:(((X612 @ X615)=>((X612 @ X616)=>((X615)=(X616)))))))=>(![X617:$i > $o, X618:$i > $o]:((![X619:$i, X620:$i]:((((X619)=(X620))=>((X617 @ X619)<=>(X618 @ X620))))=>(?[X621:$i]:(((X617 @ X621)&![X622:$i]:(((X617 @ X622)=>((X621)=(X622))))))=>(?[X623:$i]:(((X618 @ X623)&![X624:$i]:(((X618 @ X624)=>((X623)=(X624))))))=>((descr @ X617)=(descr @ X618))))))=>(![X625:$i, X626:$i]:((((X625)=(X626))=>![X627:$i > $o, X628:$i > $o]:((![X629:$i]:(((in @ X629 @ X625)=>![X630:$i]:(((in @ X630 @ X626)=>(((X629)=(X630))=>((X627 @ X629)<=>(X628 @ X630)))))))=>((dsetconstr @ X625 @ X627)=(dsetconstr @ X626 @ X628))))))=>(![X631:$i, X632:$i]:((![X633:$i]:(((in @ X633 @ X631)=>(in @ X633 @ X632)))=>(subset @ X631 @ X632)))=>(![X634:$i, X635:$i]:((((X634)=(X635))=>(subset @ X635 @ X634)))=>(![X636:$i, X637:$i]:((((X636)=(X637))=>(subset @ X636 @ X637)))=>(![X638:$i, X639:$i]:((![X640:$i]:(((in @ X640 @ X638)=>(in @ X640 @ X639)))=>(subset @ X638 @ X639)))=>(![X641:$i]:((subset @ emptyset @ X641))=>(![X642:$i, X643:$i, X644:$i]:(((subset @ X642 @ X643)=>((in @ X644 @ X642)=>(in @ X644 @ X643))))=>(![X645:$i, X646:$i, X647:$i]:(((subset @ X645 @ X646)=>(~(in @ X647 @ X646)=>~(in @ X647 @ X645))))=>(![X648:$i, X649:$i, X650:$i]:(((in @ X650 @ X648)=>(~(in @ X650 @ X649)=>~(subset @ X648 @ X649))))=>(![X651:$i, X652:$i]:((~(subset @ X651 @ X652)=>((X651)!=(X652))))=>(![X653:$i, X654:$i, X655:$i]:(((in @ X655 @ X653)=>(~(in @ X655 @ X654)=>((X653)!=(X654)))))=>(![X656:$i]:((subset @ X656 @ X656))=>(![X657:$i, X658:$i, X659:$i]:(((subset @ X657 @ X658)=>((subset @ X658 @ X659)=>(subset @ X657 @ X659))))=>(![X660:$i, X661:$i]:((subset @ X661 @ (setadjoin @ X660 @ X661)))=>(![X662:$i, X663:$i, X664:$i]:(((subset @ X662 @ X664)=>(subset @ X662 @ (setadjoin @ X663 @ X664))))=>(![X665:$i, X666:$i]:(((subset @ X665 @ X666)=>(in @ X665 @ (powerset @ X666))))=>(![X667:$i, X668:$i]:(((subset @ X667 @ X668)=>((subset @ X668 @ X667)=>((X667)=(X668)))))=>(![X669:$i]:(((subset @ X669 @ emptyset)=>((X669)=(emptyset))))=>(![X670:$i, X671:$i]:(((subset @ X671 @ X670)=>(in @ X671 @ (powerset @ X670))))=>(![X672:$i, X673:$i]:(((in @ X673 @ (powerset @ X672))=>(subset @ X673 @ X672)))=>(![X674:$i]:((in @ X674 @ (powerset @ X674)))=>(![X675:$i, X676:$i]:(((subset @ X675 @ X676)=>(subset @ (powerset @ X675) @ (powerset @ X676))))=>(![X677:$i, X678:$i > $o]:((in @ (dsetconstr @ X677 @ X678) @ (powerset @ X677)))=>(![X679:$i, X680:$i > $o]:((subset @ (dsetconstr @ X679 @ X680) @ X679))=>(![X681:$i, X682:$i, X683:$i]:(((in @ X683 @ X681)=>(in @ X683 @ (binunion @ X681 @ X682))))=>(![X684:$i, X685:$i]:((in @ X685 @ (setadjoin @ X684 @ (setadjoin @ X685 @ emptyset))))=>(![X686:$i, X687:$i, X688:$i]:(((in @ X688 @ X687)=>(in @ X688 @ (binunion @ X686 @ X687))))=>(![X689:$i, X690:$i, X691:$i, X692:$o]:(((in @ X691 @ (binunion @ X689 @ X690))=>(((in @ X691 @ X689)=>(X692))=>(((in @ X691 @ X690)=>(X692))=>(X692)))))=>(![X693:$i, X694:$i, X695:$i]:(((in @ X695 @ (binunion @ X693 @ X694))=>((in @ X695 @ X693)|(in @ X695 @ X694))))=>(![X696:$i, X697:$i]:((subset @ X696 @ (binunion @ X696 @ X697)))=>(![X698:$i, X699:$i]:((subset @ X699 @ (binunion @ X698 @ X699)))=>(![X700:$i, X701:$i, X702:$i]:(((in @ X702 @ X700)=>((in @ X702 @ X701)=>(in @ X702 @ (binintersect @ X700 @ X701)))))=>(![X703:$i, X704:$i, X705:$i]:(((subset @ X705 @ X703)=>((subset @ X705 @ X704)=>(subset @ X705 @ (binintersect @ X703 @ X704)))))=>(![X706:$i, X707:$i, X708:$i]:(((in @ X708 @ (binintersect @ X706 @ X707))=>(in @ X708 @ X706)))=>(![X709:$i, X710:$i]:((subset @ (binintersect @ X709 @ X710) @ X709))=>(![X711:$i, X712:$i]:(((subset @ X711 @ X712)=>((binintersect @ X711 @ X712)=(X711))))=>(![X713:$i, X714:$i]:((((binintersect @ X713 @ X714)=(X714))=>(subset @ X714 @ X713)))=>(![X715:$i, X716:$i, X717:$i]:(((in @ X717 @ (binintersect @ X715 @ X716))=>(in @ X717 @ X716)))=>(![X718:$i, X719:$i]:((~(?[X720:$i]:(((in @ X720 @ X718)&(in @ X720 @ X719))))=>((binintersect @ X718 @ X719)=(emptyset))))=>(![X721:$i, X722:$i]:((subset @ (binintersect @ X721 @ X722) @ X722))=>(![X723:$i, X724:$i]:(((subset @ X724 @ X723)=>((binintersect @ X723 @ X724)=(X724))))=>(![X725:$i, X726:$i]:((((binintersect @ X725 @ X726)=(X725))=>(subset @ X725 @ X726)))=>(![X727:$i, X728:$i, X729:$i]:(((binintersect @ X727 @ (binunion @ X728 @ X729))=(binunion @ (binintersect @ X727 @ X728) @ (binintersect @ X727 @ X729))))=>(![X730:$i, X731:$i, X732:$i]:(((in @ X732 @ X730)=>(~(in @ X732 @ X731)=>(in @ X732 @ (setminus @ X730 @ X731)))))=>(![X733:$i, X734:$i, X735:$i]:(((in @ X735 @ (setminus @ X733 @ X734))=>(in @ X735 @ X733)))=>(![X736:$i, X737:$i, X738:$i]:(((in @ X738 @ (setminus @ X736 @ X737))=>~(in @ X738 @ X737)))=>(![X739:$i, X740:$i]:(((subset @ X739 @ X740)=>((setminus @ X739 @ X740)=(emptyset))))=>(![X741:$i, X742:$i, X743:$i]:((~(in @ X743 @ (setminus @ X741 @ X742))=>((in @ X743 @ X741)=>(in @ X743 @ X742))))=>(![X744:$i, X745:$i, X746:$i]:((~(in @ X746 @ (setminus @ X744 @ X745))=>(~(in @ X746 @ X745)=>~(in @ X746 @ X744))))=>(![X747:$i, X748:$i, X749:$i]:((~(in @ X749 @ X747)=>~(in @ X749 @ (setminus @ X747 @ X748))))=>(![X750:$i, X751:$i, X752:$i]:(((in @ X752 @ X751)=>~(in @ X752 @ (setminus @ X750 @ X751))))=>(![X753:$i, X754:$i]:((subset @ (setminus @ X753 @ X754) @ X753))=>(![X755:$i, X756:$i]:((((setminus @ X755 @ X756)=(emptyset))=>(subset @ X755 @ X756)))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~(in @ X2 @ X5)=>(X20)))=>((~(in @ X2 @ X4)=>((in @ X2 @ X5)=>(X20)))=>(X20)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_146, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_147]), foundationAx]), wellorderingAx]), c_0_148]), c_0_149]), c_0_150]), c_0_151]), c_0_152]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_153]), setext]), emptyI]), noeltsimpempty]), c_0_154]), c_0_155]), c_0_156]), c_0_157]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_158]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_159]), c_0_160]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_161]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_162]), c_0_163]), c_0_164]), inCongP]), in__Cong]), c_0_165]), c_0_166]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_167]), c_0_168]), c_0_169]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_170]), c_0_171]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1])])]), c_0_172])).
% 3.25/0.74  thf(c_0_174, plain, ![X757:$i, X758:$i]:(((symdiff @ X757 @ X758)=(dsetconstr @ (binunion @ X757 @ X758) @ (^[Z0:$i]:(((~((in @ Z0 @ X757)))|(~((in @ Z0 @ X758))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[symdiff])])).
% 3.25/0.74  thf(c_0_175, negated_conjecture, ![X761:$i, X762:$i, X764:$i, X765:$i, X766:$i, X767:$i, X768:$i, X769:$i, X770:$i, X771:$i, X772:$i, X774:$i, X775:$i, X777:$i, X778:$i, X779:$i, X780:$i, X781:$i, X783:$i, X784:$i > $i > $o, X785:$i, X787:$i, X790:$i, X792:$i, X793:$i, X794:$i, X795:$i, X797:$i, X798:$i > $o, X799:$i, X801:$i, X802:$i > $o, X803:$i, X804:$i, X805:$i > $o, X806:$i, X807:$i, X808:$i > $o, X809:$i, X810:$i > $o, X811:$i, X814:$i, X815:$o, X816:$i, X817:$i, X818:$o, X819:$i, X820:$i, X821:$i > $o, X822:$i, X825:$i, X826:$i, X829:$i, X831:$i, X833:$i, X834:$i > $o, X835:$i, X836:$i, X838:$i, X839:$i > $o, X840:$i, X841:$i, X842:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i, X848:$i, X849:$i, X850:$i, X851:$o, X852:$i, X853:$i, X854:$i, X855:$i, X856:$i, X857:$i, X859:$i, X860:$i, X861:$i, X862:$i, X863:$i, X864:$i, X865:$i, X866:$i, X867:$i, X868:$i, X869:$o, X871:$i, X872:$i, X873:$i > $o, X874:$i, X877:$i, X878:$i, X879:$i, X881:$i, X882:$i, X883:$i, X884:$i, X885:$i, X886:$i, X887:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$i > $o, X898:$i, X899:$i > $o, X900:$i, X901:$i, X902:$i > $o, X903:$i, X905:$i, X906:$i > $o, X908:$i, X909:$i, X910:$i > $o, X912:$i, X913:$i, X914:$i > $o, X915:$i, X917:$o, X918:$o, X919:$i, X920:$i > $o, X922:$i, X923:$i, X924:$i > $o, X925:$i, X927:$i > $o, X928:$i, X931:$i, X932:$i > $o, X933:$i, X937:$i, X938:$i > $o, X939:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X949:$i, X950:$i, X951:$i > $o, X952:$i, X954:$i, X955:$i, X956:$i > $o, X957:$i > $o, X960:$i, X963:$i, X964:$i, X967:$i, X968:$i, X969:$i, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i > $o, X977:$i, X979:$i, X980:$i, X981:$i > $o, X982:$i > $o, X985:$i, X987:$i, X989:$i, X990:$i, X991:$i > $o, X992:$i > $o, X995:$i, X996:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i, X1005:$i, X1006:$i, X1007:$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, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i > $o, X1043:$i, X1044:$i > $o, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1055:$i, X1056:$o, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1075:$i, X1076:$i, X1077:$i, X1078:$i, X1079:$i, X1080:$i, X1081:$i, X1082:$i, X1083:$i, X1085:$i, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i]:((((~(in @ (esk1_2 @ X761 @ X762) @ X761)|~(in @ (esk1_2 @ X761 @ X762) @ X762)|((X761)=(X762)))&((in @ (esk1_2 @ X761 @ X762) @ X761)|(in @ (esk1_2 @ X761 @ X762) @ X762)|((X761)=(X762))))&(~(in @ X764 @ emptyset)&(((~(in @ X767 @ (setadjoin @ X765 @ X766))|(((X767)=(X765))|(in @ X767 @ X766)))&((((X767)!=(X765))|(in @ X767 @ (setadjoin @ X765 @ X766)))&(~(in @ X767 @ X766)|(in @ X767 @ (setadjoin @ X765 @ X766)))))&(((~(in @ X769 @ (powerset @ X768))|(~(in @ X770 @ X769)|(in @ X770 @ X768)))&(((in @ (esk2_2 @ X771 @ X772) @ X772)|(in @ X772 @ (powerset @ X771)))&(~(in @ (esk2_2 @ X771 @ X772) @ X771)|(in @ X772 @ (powerset @ X771)))))&(((((in @ X775 @ (esk3_2 @ X774 @ X775))|~(in @ X775 @ (setunion @ X774)))&((in @ (esk3_2 @ X774 @ X775) @ X774)|~(in @ X775 @ (setunion @ X774))))&(~(in @ X778 @ X779)|~(in @ X779 @ X777)|(in @ X778 @ (setunion @ X777))))&((in @ emptyset @ omega)&((~(in @ X780 @ omega)|(in @ (setadjoin @ X780 @ X780) @ omega))&(((((in @ (esk4_1 @ X781) @ omega)|~(in @ emptyset @ X781)|(~(in @ X783 @ omega)|(in @ X783 @ X781)))&((in @ (esk4_1 @ X781) @ X781)|~(in @ emptyset @ X781)|(~(in @ X783 @ omega)|(in @ X783 @ X781))))&(~(in @ (setadjoin @ (esk4_1 @ X781) @ (esk4_1 @ X781)) @ X781)|~(in @ emptyset @ X781)|(~(in @ X783 @ omega)|(in @ X783 @ X781))))&((((((in @ (esk8_3 @ X784 @ X785 @ X790) @ X785)|~(in @ X790 @ (esk7_2 @ X784 @ X785))|(in @ (esk5_2 @ X784 @ X785) @ X785))&((X784 @ (esk8_3 @ X784 @ X785 @ X790) @ X790)|~(in @ X790 @ (esk7_2 @ X784 @ X785))|(in @ (esk5_2 @ X784 @ X785) @ X785)))&(~(in @ X793 @ X785)|~(X784 @ X793 @ X792)|(in @ X792 @ (esk7_2 @ X784 @ X785))|(in @ (esk5_2 @ X784 @ X785) @ X785)))&(((((in @ (esk8_3 @ X784 @ X785 @ X790) @ X785)|~(in @ X790 @ (esk7_2 @ X784 @ X785))|((X784 @ (esk5_2 @ X784 @ X785) @ (esk6_3 @ X784 @ X785 @ X787))|~(X784 @ (esk5_2 @ X784 @ X785) @ X787)))&((X784 @ (esk8_3 @ X784 @ X785 @ X790) @ X790)|~(in @ X790 @ (esk7_2 @ X784 @ X785))|((X784 @ (esk5_2 @ X784 @ X785) @ (esk6_3 @ X784 @ X785 @ X787))|~(X784 @ (esk5_2 @ X784 @ X785) @ X787))))&(~(in @ X793 @ X785)|~(X784 @ X793 @ X792)|(in @ X792 @ (esk7_2 @ X784 @ X785))|((X784 @ (esk5_2 @ X784 @ X785) @ (esk6_3 @ X784 @ X785 @ X787))|~(X784 @ (esk5_2 @ X784 @ X785) @ X787))))&((((in @ (esk8_3 @ X784 @ X785 @ X790) @ X785)|~(in @ X790 @ (esk7_2 @ X784 @ X785))|(((X787)!=(esk6_3 @ X784 @ X785 @ X787))|~(X784 @ (esk5_2 @ X784 @ X785) @ X787)))&((X784 @ (esk8_3 @ X784 @ X785 @ X790) @ X790)|~(in @ X790 @ (esk7_2 @ X784 @ X785))|(((X787)!=(esk6_3 @ X784 @ X785 @ X787))|~(X784 @ (esk5_2 @ X784 @ X785) @ X787))))&(~(in @ X793 @ X785)|~(X784 @ X793 @ X792)|(in @ X792 @ (esk7_2 @ X784 @ X785))|(((X787)!=(esk6_3 @ X784 @ X785 @ X787))|~(X784 @ (esk5_2 @ X784 @ X785) @ X787))))))&((((in @ (esk9_1 @ X794) @ X794)|~(in @ X795 @ X794))&(~(in @ X797 @ (esk9_1 @ X794))|~(in @ X797 @ X794)|~(in @ X795 @ X794)))&((epred1_0)&((((X798 @ (esk10_2 @ X798 @ X799))|~(X798 @ X799)|(X798 @ (descr @ X798)))&(((X799)!=(esk10_2 @ X798 @ X799))|~(X798 @ X799)|(X798 @ (descr @ X798))))&((~(in @ X803 @ X801)|(~(X802 @ X803)|(in @ X803 @ (dsetconstr @ X801 @ X802))))&((~(in @ X806 @ (dsetconstr @ X804 @ X805))|(in @ X806 @ X804))&((~(in @ X809 @ (dsetconstr @ X807 @ X808))|(X808 @ X809))&(((((X810 @ (esk12_1 @ X810))|((X810 @ (esk11_2 @ X810 @ X811))|~(X810 @ X811)))&(~(X810 @ X814)|((esk12_1 @ X810)=(X814))|((X810 @ (esk11_2 @ X810 @ X811))|~(X810 @ X811))))&(((X810 @ (esk12_1 @ X810))|(((X811)!=(esk11_2 @ X810 @ X811))|~(X810 @ X811)))&(~(X810 @ X814)|((esk12_1 @ X810)=(X814))|(((X811)!=(esk11_2 @ X810 @ X811))|~(X810 @ X811)))))&((~(in @ X816 @ (prop2set @ ((X815))))|(X815))&((~(in @ X817 @ emptyset)|(X818))&((~(in @ X819 @ emptyset)|~($true))&(~(in @ X820 @ emptyset)&((((X821 @ (esk13_2 @ X821 @ X822))|~(X821 @ X822)|(X821 @ (esk14_1 @ X821)))&(((X822)!=(esk13_2 @ X821 @ X822))|~(X821 @ X822)|(X821 @ (esk14_1 @ X821))))&(((((in @ (esk16_2 @ 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X849)|(X851)|((X850)=(X848))|~(in @ X850 @ (setadjoin @ X848 @ X849)))&(~(X851)|(X851)|((X850)=(X848))|~(in @ X850 @ (setadjoin @ X848 @ X849))))&(((in @ X850 @ X849)|(X851)|~(X851)|~(in @ X850 @ (setadjoin @ X848 @ X849)))&(~(X851)|(X851)|~(X851)|~(in @ X850 @ (setadjoin @ X848 @ X849)))))&((~(in @ X854 @ (setadjoin @ X852 @ X853))|(((X854)=(X852))|(in @ X854 @ X853)))&(((dsetconstr @ X855 @ (^[Z0:$i]:($true)))=(X855))&((((in @ (esk20_2 @ X856 @ X857) @ X857)|(in @ X857 @ (powerset @ X856)))&(~(in @ (esk20_2 @ X856 @ X857) @ X856)|(in @ X857 @ (powerset @ X856))))&((in @ emptyset @ (powerset @ X859))&((in @ emptyset @ (powerset @ X860))&((~(in @ X862 @ (powerset @ X861))|(~(in @ X863 @ X862)|(in @ X863 @ X861)))&((~(in @ X865 @ X866)|(~(in @ X866 @ X864)|(in @ X865 @ (setunion @ X864))))&((((in @ X868 @ (esk21_3 @ X867 @ X868 @ X869))|(X869)|~(in @ X868 @ (setunion @ X867)))&(((in @ (esk21_3 @ X867 @ X868 @ X869) @ X867)|(X869)|~(in @ X868 @ (setunion @ X867)))&(~(X869)|(X869)|~(in @ 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X1003) @ X1003)|(subset @ X1002 @ X1003)))&((subset @ emptyset @ X1005)&((~(subset @ X1006 @ X1007)|(~(in @ X1008 @ X1006)|(in @ X1008 @ X1007)))&((~(subset @ X1009 @ X1010)|((in @ X1011 @ X1010)|~(in @ X1011 @ X1009)))&((~(in @ X1014 @ X1012)|((in @ X1014 @ X1013)|~(subset @ X1012 @ X1013)))&(((subset @ X1015 @ X1016)|((X1015)!=(X1016)))&((~(in @ X1019 @ X1017)|((in @ X1019 @ X1018)|((X1017)!=(X1018))))&((subset @ X1020 @ X1020)&((~(subset @ X1021 @ X1022)|(~(subset @ X1022 @ X1023)|(subset @ X1021 @ X1023)))&((subset @ X1025 @ (setadjoin @ X1024 @ X1025))&((~(subset @ X1026 @ X1028)|(subset @ X1026 @ (setadjoin @ X1027 @ X1028)))&((~(subset @ X1029 @ X1030)|(in @ X1029 @ (powerset @ X1030)))&((~(subset @ X1031 @ X1032)|(~(subset @ X1032 @ X1031)|((X1031)=(X1032))))&((~(subset @ X1033 @ emptyset)|((X1033)=(emptyset)))&((~(subset @ X1035 @ X1034)|(in @ X1035 @ (powerset @ X1034)))&((~(in @ X1037 @ (powerset @ X1036))|(subset @ X1037 @ X1036))&((in @ X1038 @ (powerset @ X1038))&((~(subset @ X1039 @ X1040)|(subset @ (powerset @ X1039) @ (powerset @ X1040)))&((in @ (dsetconstr @ X1041 @ X1042) @ (powerset @ X1041))&((subset @ (dsetconstr @ X1043 @ X1044) @ X1043)&((~(in @ X1047 @ X1045)|(in @ X1047 @ (binunion @ X1045 @ X1046)))&((in @ X1049 @ (setadjoin @ X1048 @ (setadjoin @ X1049 @ emptyset)))&((~(in @ X1052 @ X1051)|(in @ X1052 @ (binunion @ X1050 @ X1051)))&(((((in @ X1055 @ X1054)|(X1056)|(in @ X1055 @ X1053)|~(in @ X1055 @ (binunion @ X1053 @ X1054)))&(~(X1056)|(X1056)|(in @ X1055 @ X1053)|~(in @ X1055 @ (binunion @ X1053 @ X1054))))&(((in @ X1055 @ X1054)|(X1056)|~(X1056)|~(in @ X1055 @ (binunion @ X1053 @ X1054)))&(~(X1056)|(X1056)|~(X1056)|~(in @ X1055 @ (binunion @ X1053 @ X1054)))))&((~(in @ X1059 @ (binunion @ X1057 @ X1058))|((in @ X1059 @ X1057)|(in @ X1059 @ X1058)))&((subset @ X1060 @ (binunion @ X1060 @ X1061))&((subset @ X1063 @ (binunion @ X1062 @ X1063))&((~(in @ X1066 @ X1064)|(~(in @ X1066 @ X1065)|(in @ X1066 @ (binintersect @ X1064 @ X1065))))&((~(subset @ X1069 @ X1067)|(~(subset @ X1069 @ X1068)|(subset @ X1069 @ (binintersect @ X1067 @ X1068))))&((~(in @ X1072 @ (binintersect @ X1070 @ X1071))|(in @ X1072 @ X1070))&((subset @ (binintersect @ X1073 @ X1074) @ X1073)&((~(subset @ X1075 @ X1076)|((binintersect @ X1075 @ X1076)=(X1075)))&((((binintersect @ X1077 @ X1078)!=(X1078))|(subset @ X1078 @ X1077))&((~(in @ X1081 @ (binintersect @ X1079 @ X1080))|(in @ X1081 @ X1080))&((((in @ (esk54_2 @ X1082 @ X1083) @ X1082)|((binintersect @ X1082 @ X1083)=(emptyset)))&((in @ (esk54_2 @ X1082 @ X1083) @ X1083)|((binintersect @ X1082 @ X1083)=(emptyset))))&((subset @ (binintersect @ X1085 @ X1086) @ X1086)&((~(subset @ X1088 @ X1087)|((binintersect @ X1087 @ X1088)=(X1088)))&((((binintersect @ X1089 @ X1090)!=(X1089))|(subset @ X1089 @ X1090))&(((binintersect @ X1091 @ (binunion @ X1092 @ X1093))=(binunion @ (binintersect @ X1091 @ X1092) @ (binintersect @ X1091 @ X1093)))&((~(in @ X1096 @ X1094)|((in @ X1096 @ X1095)|(in @ X1096 @ (setminus @ X1094 @ X1095))))&((~(in @ X1099 @ (setminus @ X1097 @ X1098))|(in @ X1099 @ X1097))&((~(in @ X1102 @ (setminus @ X1100 @ X1101))|~(in @ X1102 @ X1101))&((~(subset @ X1103 @ X1104)|((setminus @ X1103 @ X1104)=(emptyset)))&(((in @ X1107 @ (setminus @ X1105 @ X1106))|(~(in @ X1107 @ X1105)|(in @ X1107 @ X1106)))&(((in @ X1110 @ (setminus @ X1108 @ X1109))|((in @ X1110 @ X1109)|~(in @ X1110 @ X1108)))&(((in @ X1113 @ X1111)|~(in @ X1113 @ (setminus @ X1111 @ X1112)))&((~(in @ X1116 @ X1115)|~(in @ X1116 @ (setminus @ X1114 @ X1115)))&((subset @ (setminus @ X1117 @ X1118) @ X1117)&((((setminus @ X1119 @ X1120)!=(emptyset))|(subset @ X1119 @ X1120))&((in @ esk57_0 @ (symdiff @ esk55_0 @ esk56_0))&((~(in @ esk57_0 @ esk55_0)|((in @ esk57_0 @ esk56_0)|(epred2_0)))&(((in @ esk57_0 @ esk55_0)|(~(in @ esk57_0 @ esk56_0)|(epred2_0)))&~(epred2_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_173])])])])])])])).
% 3.25/0.74  thf(c_0_176, plain, ![X759:$i, X760:$i]:(((symdiff @ X759 @ X760)=(dsetconstr @ (binunion @ X759 @ X760) @ (^[Z0:$i]:(((~((in @ Z0 @ X759)))|(~((in @ Z0 @ X760))))))))), inference(variable_rename,[status(thm)],[c_0_174])).
% 3.25/0.74  thf(c_0_177, negated_conjecture, (in @ esk57_0 @ (symdiff @ esk55_0 @ esk56_0)), inference(split_conjunct,[status(thm)],[c_0_175])).
% 3.25/0.74  thf(c_0_178, plain, ![X2:$i, X3:$i]:(((symdiff @ X2 @ X3)=(dsetconstr @ (binunion @ X2 @ X3) @ (^[Z0:$i]:(((~((in @ Z0 @ X2)))|(~((in @ Z0 @ X3))))))))), inference(split_conjunct,[status(thm)],[c_0_176])).
% 3.25/0.74  thf(c_0_179, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((in @ X2 @ X3)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_175])).
% 3.25/0.74  thf(c_0_180, negated_conjecture, (in @ esk57_0 @ (dsetconstr @ (binunion @ esk55_0 @ esk56_0) @ (^[Z0:$i]:(((~((in @ Z0 @ esk55_0)))|(~((in @ Z0 @ esk56_0)))))))), inference(rw,[status(thm)],[c_0_177, c_0_178])).
% 3.25/0.74  thf(c_0_181, negated_conjecture, ((in @ esk57_0 @ esk56_0)|(epred2_0)|~((in @ esk57_0 @ esk55_0))), inference(split_conjunct,[status(thm)],[c_0_175])).
% 3.25/0.74  thf(c_0_182, negated_conjecture, ~((epred2_0)), inference(split_conjunct,[status(thm)],[c_0_175])).
% 3.25/0.74  thf(c_0_183, negated_conjecture, ((in @ esk57_0 @ esk55_0)|(epred2_0)|~((in @ esk57_0 @ esk56_0))), inference(split_conjunct,[status(thm)],[c_0_175])).
% 3.25/0.74  thf(c_0_184, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|(in @ X2 @ X4)|~((in @ X2 @ (binunion @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_175])])])).
% 3.25/0.74  thf(c_0_185, negated_conjecture, (in @ esk57_0 @ (binunion @ esk55_0 @ esk56_0)), inference(spm,[status(thm)],[c_0_179, c_0_180])).
% 3.25/0.74  thf(c_0_186, negated_conjecture, ((in @ esk57_0 @ esk56_0)|~((in @ esk57_0 @ esk55_0))), inference(sr,[status(thm)],[c_0_181, c_0_182])).
% 3.25/0.74  thf(c_0_187, negated_conjecture, ((in @ esk57_0 @ esk55_0)|~((in @ esk57_0 @ esk56_0))), inference(sr,[status(thm)],[c_0_183, c_0_182])).
% 3.25/0.74  thf(c_0_188, negated_conjecture, (in @ esk57_0 @ esk56_0), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_184, c_0_185]), c_0_186])).
% 3.25/0.74  thf(c_0_189, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_175])).
% 3.25/0.74  thf(c_0_190, negated_conjecture, (in @ esk57_0 @ esk55_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_187, c_0_188])])).
% 3.25/0.74  thf(c_0_191, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189, c_0_180]), c_0_190]), c_0_188])])]), ['proof']).
% 3.25/0.74  % SZS output end CNFRefutation
% 3.25/0.74  % Parsed axioms                        : 278
% 3.25/0.74  % Removed by relevancy pruning/SinE    : 0
% 3.25/0.74  % Initial clauses                      : 393
% 3.25/0.74  % Removed in clause preprocessing      : 165
% 3.25/0.74  % Initial clauses in saturation        : 228
% 3.25/0.74  % Processed clauses                    : 2006
% 3.25/0.74  % ...of these trivial                  : 20
% 3.25/0.74  % ...subsumed                          : 1345
% 3.25/0.74  % ...remaining for further processing  : 640
% 3.25/0.74  % Other redundant clauses eliminated   : 26
% 3.25/0.74  % Clauses deleted for lack of memory   : 0
% 3.25/0.74  % Backward-subsumed                    : 8
% 3.25/0.74  % Backward-rewritten                   : 12
% 3.25/0.74  % Generated clauses                    : 21369
% 3.25/0.74  % ...of the previous two non-redundant : 18939
% 3.25/0.74  % ...aggressively subsumed             : 0
% 3.25/0.74  % Contextual simplify-reflections      : 2
% 3.25/0.74  % Paramodulations                      : 21341
% 3.25/0.74  % Factorizations                       : 2
% 3.25/0.74  % NegExts                              : 0
% 3.25/0.74  % Equation resolutions                 : 26
% 3.25/0.74  % Disequality decompositions           : 0
% 3.25/0.74  % Total rewrite steps                  : 6772
% 3.25/0.74  % ...of those cached                   : 6562
% 3.25/0.74  % Propositional unsat checks           : 0
% 3.25/0.74  %    Propositional check models        : 0
% 3.25/0.74  %    Propositional check unsatisfiable : 0
% 3.25/0.74  %    Propositional clauses             : 0
% 3.25/0.74  %    Propositional clauses after purity: 0
% 3.25/0.74  %    Propositional unsat core size     : 0
% 3.25/0.74  %    Propositional preprocessing time  : 0.000
% 3.25/0.74  %    Propositional encoding time       : 0.000
% 3.25/0.74  %    Propositional solver time         : 0.000
% 3.25/0.74  %    Success case prop preproc time    : 0.000
% 3.25/0.74  %    Success case prop encoding time   : 0.000
% 3.25/0.74  %    Success case prop solver time     : 0.000
% 3.25/0.74  % Current number of processed clauses  : 607
% 3.25/0.74  %    Positive orientable unit clauses  : 204
% 3.25/0.74  %    Positive unorientable unit clauses: 0
% 3.25/0.74  %    Negative unit clauses             : 3
% 3.25/0.74  %    Non-unit-clauses                  : 400
% 3.25/0.74  % Current number of unprocessed clauses: 17119
% 3.25/0.74  % ...number of literals in the above   : 59668
% 3.25/0.74  % Current number of archived formulas  : 0
% 3.25/0.74  % Current number of archived clauses   : 21
% 3.25/0.74  % Clause-clause subsumption calls (NU) : 14028
% 3.25/0.74  % Rec. Clause-clause subsumption calls : 8361
% 3.25/0.74  % Non-unit clause-clause subsumptions  : 805
% 3.25/0.74  % Unit Clause-clause subsumption calls : 150
% 3.25/0.74  % Rewrite failures with RHS unbound    : 0
% 3.25/0.74  % BW rewrite match attempts            : 947
% 3.25/0.74  % BW rewrite match successes           : 7
% 3.25/0.74  % Condensation attempts                : 0
% 3.25/0.74  % Condensation successes               : 0
% 3.25/0.74  % Termbank termtop insertions          : 421210
% 3.25/0.74  % Search garbage collected termcells   : 12613
% 3.25/0.74  
% 3.25/0.74  % -------------------------------------------------
% 3.25/0.74  % User time                : 0.423 s
% 3.25/0.74  % System time              : 0.031 s
% 3.25/0.74  % Total time               : 0.454 s
% 3.25/0.74  % Maximum resident set size: 6472 pages
% 3.25/0.74  
% 3.25/0.74  % -------------------------------------------------
% 3.25/0.74  % User time                : 0.502 s
% 3.25/0.74  % System time              : 0.078 s
% 3.25/0.74  % Total time               : 0.581 s
% 3.25/0.74  % Maximum resident set size: 5120 pages
% 3.25/0.74  % E exiting
%------------------------------------------------------------------------------