E-SAT---3.5.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : E-SAT---3.5.1
% Problem  : SEU583^1 : 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 : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:26:48 AM UTC 2026

% Result   : Theorem 0.22s 0.30s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEU583^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18  % Computer : n005.cluster.edu
% 0.09/0.18  % Model    : x86_64 x86_64
% 0.09/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18  % Memory   : 8046.5625MB
% 0.09/0.18  % OS       : Linux 6.8.0-71-generic
% 0.09/0.18  % CPULimit : 300
% 0.09/0.18  % WCLimit  : 300
% 0.09/0.18  % DateTime : Tue Sep 29 13:52:15 UTC 2026
% 0.09/0.18  % CPUTime  : 
% 0.09/0.18  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22  Running higher-order theorem proving
% 0.09/0.25  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.AuzUWX4ikf/E---3.1_1702585.p
% 0.22/0.30  % Version: 3.5.1-ho
% 0.22/0.30  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.22/0.30  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30  % Starting ehoh_best5 with 300s (1) cores
% 0.22/0.30  % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.30  % Starting new_bool_5 with 300s (1) cores
% 0.22/0.30  % Starting pre_casc_3 with 300s (1) cores
% 0.22/0.30  % Starting ho_unfolding_8 with 300s (1) cores
% 0.22/0.30  % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.22/0.30  % Starting new_bool_3 with 300s (1) cores
% 0.22/0.30  % Starting new_ho_5 with 300s (1) cores
% 0.22/0.30  % ho_unfolding_8 with pid 1702602 completed with status 0
% 0.22/0.30  % Result found by ho_unfolding_8
% 0.22/0.30  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.22/0.30  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30  % Starting ehoh_best5 with 300s (1) cores
% 0.22/0.30  % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.30  % Starting new_bool_5 with 300s (1) cores
% 0.22/0.30  % Starting pre_casc_3 with 300s (1) cores
% 0.22/0.30  % Starting ho_unfolding_8 with 300s (1) cores
% 0.22/0.30  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.30  % No SInE strategy applied
% 0.22/0.30  % Search class: HGHSM-FSLS31-MHFMMSBN
% 0.22/0.30  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.30  % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.30  % SubtermCWHack with pid 1702609 completed with status 0
% 0.22/0.30  % Result found by SubtermCWHack
% 0.22/0.30  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.22/0.30  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30  % Starting ehoh_best5 with 300s (1) cores
% 0.22/0.30  % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.30  % Starting new_bool_5 with 300s (1) cores
% 0.22/0.30  % Starting pre_casc_3 with 300s (1) cores
% 0.22/0.30  % Starting ho_unfolding_8 with 300s (1) cores
% 0.22/0.30  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.30  % No SInE strategy applied
% 0.22/0.30  % Search class: HGHSM-FSLS31-MHFMMSBN
% 0.22/0.30  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.30  % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.30  % Preprocessing time       : 0.002 s
% 0.22/0.30  
% 0.22/0.30  % Proof found!
% 0.22/0.30  % SZS status Theorem
% 0.22/0.30  % SZS output start CNFRefutation
% 0.22/0.30  thf(decl_23, type, in: $i > $i > $o).
% 0.22/0.30  thf(decl_24, type, exu: ($i > $o) > $o).
% 0.22/0.30  thf(decl_25, type, setextAx: $o).
% 0.22/0.30  thf(decl_26, type, emptyset: $i).
% 0.22/0.30  thf(decl_27, type, emptysetAx: $o).
% 0.22/0.30  thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.22/0.30  thf(decl_29, type, setadjoinAx: $o).
% 0.22/0.30  thf(decl_30, type, powerset: $i > $i).
% 0.22/0.30  thf(decl_31, type, powersetAx: $o).
% 0.22/0.30  thf(decl_32, type, setunion: $i > $i).
% 0.22/0.30  thf(decl_33, type, setunionAx: $o).
% 0.22/0.30  thf(decl_34, type, omega: $i).
% 0.22/0.30  thf(decl_35, type, omega0Ax: $o).
% 0.22/0.30  thf(decl_36, type, omegaSAx: $o).
% 0.22/0.30  thf(decl_37, type, omegaIndAx: $o).
% 0.22/0.30  thf(decl_38, type, replAx: $o).
% 0.22/0.30  thf(decl_39, type, foundationAx: $o).
% 0.22/0.30  thf(decl_40, type, wellorderingAx: $o).
% 0.22/0.30  thf(decl_41, type, descr: ($i > $o) > $i).
% 0.22/0.30  thf(decl_42, type, descrp: $o).
% 0.22/0.30  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.30  thf(decl_44, type, dsetconstrI: $o).
% 0.22/0.30  thf(decl_45, type, dsetconstrEL: $o).
% 0.22/0.30  thf(decl_46, type, dsetconstrER: $o).
% 0.22/0.30  thf(decl_47, type, exuE1: $o).
% 0.22/0.30  thf(decl_48, type, prop2set: $o > $i).
% 0.22/0.30  thf(decl_49, type, prop2setE: $o).
% 0.22/0.30  thf(decl_50, type, emptysetE: $o).
% 0.22/0.30  thf(decl_51, type, emptysetimpfalse: $o).
% 0.22/0.30  thf(decl_52, type, notinemptyset: $o).
% 0.22/0.30  thf(decl_53, type, exuE3e: $o).
% 0.22/0.30  thf(decl_54, type, setext: $o).
% 0.22/0.30  thf(decl_55, type, emptyI: $o).
% 0.22/0.30  thf(decl_56, type, noeltsimpempty: $o).
% 0.22/0.30  thf(decl_57, type, setbeta: $o).
% 0.22/0.30  thf(decl_58, type, nonempty: $i > $o).
% 0.22/0.30  thf(decl_59, type, nonemptyE1: $o).
% 0.22/0.30  thf(decl_60, type, nonemptyI: $o).
% 0.22/0.30  thf(decl_61, type, nonemptyI1: $o).
% 0.22/0.30  thf(decl_62, type, setadjoinIL: $o).
% 0.22/0.30  thf(decl_63, type, emptyinunitempty: $o).
% 0.22/0.30  thf(decl_64, type, setadjoinIR: $o).
% 0.22/0.30  thf(decl_65, type, setadjoinE: $o).
% 0.22/0.30  thf(decl_66, type, setadjoinOr: $o).
% 0.22/0.30  thf(decl_67, type, setoftrueEq: $o).
% 0.22/0.30  thf(decl_68, type, powersetI: $o).
% 0.22/0.30  thf(decl_69, type, emptyinPowerset: $o).
% 0.22/0.30  thf(decl_70, type, emptyInPowerset: $o).
% 0.22/0.30  thf(decl_71, type, powersetE: $o).
% 0.22/0.30  thf(decl_72, type, setunionI: $o).
% 0.22/0.30  thf(decl_73, type, setunionE: $o).
% 0.22/0.30  thf(decl_74, type, subPowSU: $o).
% 0.22/0.30  thf(decl_75, type, exuE2: $o).
% 0.22/0.30  thf(decl_76, type, nonemptyImpWitness: $o).
% 0.22/0.30  thf(decl_77, type, uniqinunit: $o).
% 0.22/0.30  thf(decl_78, type, notinsingleton: $o).
% 0.22/0.30  thf(decl_79, type, eqinunit: $o).
% 0.22/0.30  thf(decl_80, type, singletonsswitch: $o).
% 0.22/0.30  thf(decl_81, type, upairsetE: $o).
% 0.22/0.30  thf(decl_82, type, upairsetIL: $o).
% 0.22/0.30  thf(decl_83, type, upairsetIR: $o).
% 0.22/0.30  thf(decl_84, type, emptyE1: $o).
% 0.22/0.30  thf(decl_85, type, vacuousDall: $o).
% 0.22/0.30  thf(decl_86, type, quantDeMorgan1: $o).
% 0.22/0.30  thf(decl_87, type, quantDeMorgan2: $o).
% 0.22/0.30  thf(decl_88, type, quantDeMorgan3: $o).
% 0.22/0.30  thf(decl_89, type, quantDeMorgan4: $o).
% 0.22/0.30  thf(decl_90, type, prop2setI: $o).
% 0.22/0.30  thf(decl_91, type, set2prop: $i > $o).
% 0.22/0.30  thf(decl_92, type, prop2set2propI: $o).
% 0.22/0.30  thf(decl_93, type, notdexE: $o).
% 0.22/0.30  thf(decl_94, type, notdallE: $o).
% 0.22/0.30  thf(decl_95, type, exuI1: $o).
% 0.22/0.30  thf(decl_96, type, exuI3: $o).
% 0.22/0.30  thf(decl_97, type, exuI2: $o).
% 0.22/0.30  thf(decl_98, type, inCongP: $o).
% 0.22/0.30  thf(decl_99, type, in__Cong: $o).
% 0.22/0.30  thf(decl_100, type, exuE3u: $o).
% 0.22/0.30  thf(decl_101, type, exu__Cong: $o).
% 0.22/0.30  thf(decl_102, type, emptyset__Cong: $o).
% 0.22/0.30  thf(decl_103, type, setadjoin__Cong: $o).
% 0.22/0.30  thf(decl_104, type, powerset__Cong: $o).
% 0.22/0.30  thf(decl_105, type, setunion__Cong: $o).
% 0.22/0.30  thf(decl_106, type, omega__Cong: $o).
% 0.22/0.30  thf(decl_107, type, exuEu: $o).
% 0.22/0.30  thf(decl_108, type, descr__Cong: $o).
% 0.22/0.30  thf(decl_109, type, dsetconstr__Cong: $o).
% 0.22/0.30  thf(decl_110, type, subset: $i > $i > $o).
% 0.22/0.30  thf(decl_113, type, subsetI1: $o).
% 0.22/0.30  thf(decl_114, type, eqimpsubset2: $o).
% 0.22/0.30  thf(decl_115, type, eqimpsubset1: $o).
% 0.22/0.30  thf(decl_116, type, subsetI2: $o).
% 0.22/0.30  thf(decl_117, type, emptysetsubset: $o).
% 0.22/0.30  thf(decl_118, type, subsetE: $o).
% 0.22/0.30  thf(decl_119, type, subsetE2: $o).
% 0.22/0.30  thf(decl_120, type, notsubsetI: $o).
% 0.22/0.30  thf(decl_121, type, notequalI1: $o).
% 0.22/0.30  thf(decl_122, type, notequalI2: $o).
% 0.22/0.30  thf(decl_123, type, subsetRefl: $o).
% 0.22/0.30  thf(decl_124, type, subsetTrans: $o).
% 0.22/0.30  thf(decl_125, type, setadjoinSub: $o).
% 0.22/0.30  thf(decl_126, type, setadjoinSub2: $o).
% 0.22/0.30  thf(decl_127, type, subset2powerset: $o).
% 0.22/0.30  thf(decl_128, type, setextsub: $o).
% 0.22/0.30  thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.22/0.30  thf(decl_130, type, powersetI1: $o).
% 0.22/0.30  thf(decl_131, type, powersetE1: $o).
% 0.22/0.30  thf(decl_132, type, inPowerset: $o).
% 0.22/0.30  thf(decl_133, type, powersetsubset: $o).
% 0.22/0.30  thf(decl_134, type, sepInPowerset: $o).
% 0.22/0.30  thf(decl_135, type, sepSubset: $o).
% 0.22/0.30  thf(decl_136, type, binunion: $i > $i > $i).
% 0.22/0.30  thf(decl_137, type, binunionIL: $o).
% 0.22/0.30  thf(decl_138, type, epred1_0: $o).
% 0.22/0.30  thf(decl_139, type, esk1_2: $i > $i > $i).
% 0.22/0.30  thf(decl_140, type, esk2_2: $i > $i > $i).
% 0.22/0.30  thf(decl_141, type, esk3_2: $i > $i > $i).
% 0.22/0.30  thf(decl_142, type, esk4_1: $i > $i).
% 0.22/0.30  thf(decl_143, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.22/0.30  thf(decl_144, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.30  thf(decl_145, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.22/0.30  thf(decl_146, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.30  thf(decl_147, type, esk9_1: $i > $i).
% 0.22/0.30  thf(decl_148, type, esk10_2: ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_149, type, esk11_2: ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_150, type, esk12_1: ($i > $o) > $i).
% 0.22/0.30  thf(decl_151, type, esk13_2: ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_152, type, esk14_1: ($i > $o) > $i).
% 0.22/0.30  thf(decl_153, type, esk15_2: $i > $i > $i).
% 0.22/0.30  thf(decl_154, type, esk16_2: $i > $i > $i).
% 0.22/0.30  thf(decl_155, type, esk17_1: $i > $i).
% 0.22/0.30  thf(decl_156, type, esk18_1: $i > $i).
% 0.22/0.30  thf(decl_157, type, esk19_1: $i > $i).
% 0.22/0.30  thf(decl_158, type, esk20_2: $i > $i > $i).
% 0.22/0.30  thf(decl_159, type, esk21_3: $i > $i > $o > $i).
% 0.22/0.30  thf(decl_160, type, esk22_2: ($i > $o) > $i > $i).
% 0.22/0.31  thf(decl_161, type, esk23_1: ($i > $o) > $i).
% 0.22/0.31  thf(decl_162, type, esk24_1: $i > $i).
% 0.22/0.31  thf(decl_163, type, esk25_2: $i > ($i > $o) > $i).
% 0.22/0.31  thf(decl_164, type, esk26_2: $i > ($i > $o) > $i).
% 0.22/0.31  thf(decl_165, type, esk27_2: $i > ($i > $o) > $i).
% 0.22/0.31  thf(decl_166, type, esk28_2: $i > ($i > $o) > $i).
% 0.22/0.31  thf(decl_167, type, esk29_2: $i > ($i > $o) > $i).
% 0.22/0.31  thf(decl_168, type, esk30_2: $i > ($i > $o) > $i).
% 0.22/0.31  thf(decl_169, type, esk31_2: ($i > $o) > $i > $i).
% 0.22/0.31  thf(decl_170, type, esk32_1: ($i > $o) > $i).
% 0.22/0.31  thf(decl_171, type, esk33_1: ($i > $o) > $i).
% 0.22/0.31  thf(decl_172, type, esk34_1: ($i > $o) > $i).
% 0.22/0.31  thf(decl_173, type, esk35_1: ($i > $o) > $i).
% 0.22/0.31  thf(decl_174, type, esk36_2: ($i > $o) > $i > $i).
% 0.22/0.31  thf(decl_175, type, esk37_1: ($i > $o) > $i).
% 0.22/0.31  thf(decl_176, type, esk38_2: ($i > $o) > $i > $i).
% 0.22/0.31  thf(decl_177, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.31  thf(decl_178, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.31  thf(decl_179, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.31  thf(decl_180, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.31  thf(decl_181, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.31  thf(decl_182, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.31  thf(decl_183, type, esk45_2: ($i > $o) > $i > $i).
% 0.22/0.31  thf(decl_184, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.31  thf(decl_185, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.31  thf(decl_186, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.31  thf(decl_187, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.31  thf(decl_188, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.31  thf(decl_189, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.31  thf(decl_190, type, esk52_2: $i > $i > $i).
% 0.22/0.31  thf(decl_191, type, esk53_2: $i > $i > $i).
% 0.22/0.31  thf(decl_192, type, esk54_0: $i).
% 0.22/0.31  thf(decl_193, type, esk55_0: $i).
% 0.22/0.31  thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', replAx)).
% 0.22/0.31  thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', exu)).
% 0.22/0.31  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', descrp)).
% 0.22/0.31  thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', exuE1)).
% 0.22/0.31  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', exuE3e)).
% 0.22/0.31  thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', nonempty)).
% 0.22/0.31  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', nonemptyI)).
% 0.22/0.31  thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', exuE2)).
% 0.22/0.31  thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', exuI1)).
% 0.22/0.31  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', exuI3)).
% 0.22/0.31  thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', exuI2)).
% 0.22/0.31  thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', exuE3u)).
% 0.22/0.31  thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', exu__Cong)).
% 0.22/0.31  thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', exuEu)).
% 0.22/0.31  thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', descr__Cong)).
% 0.22/0.31  thf(upairset2IR, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', upairset2IR)).
% 0.22/0.31  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', dsetconstrI)).
% 0.22/0.31  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', dsetconstrEL)).
% 0.22/0.31  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', dsetconstrER)).
% 0.22/0.31  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setbeta)).
% 0.22/0.31  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', nonemptyE1)).
% 0.22/0.31  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', nonemptyI1)).
% 0.22/0.31  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setoftrueEq)).
% 0.22/0.31  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', nonemptyImpWitness)).
% 0.22/0.31  thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', emptyE1)).
% 0.22/0.31  thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', dsetconstr__Cong)).
% 0.22/0.31  thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', sepInPowerset)).
% 0.22/0.31  thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', sepSubset)).
% 0.22/0.31  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setextAx)).
% 0.22/0.31  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', emptysetAx)).
% 0.22/0.31  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setadjoinAx)).
% 0.22/0.31  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', powersetAx)).
% 0.22/0.31  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setunionAx)).
% 0.22/0.31  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', omega0Ax)).
% 0.22/0.31  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', omegaSAx)).
% 0.22/0.31  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', omegaIndAx)).
% 0.22/0.31  thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', foundationAx)).
% 0.22/0.31  thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', wellorderingAx)).
% 0.22/0.31  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', prop2setE)).
% 0.22/0.31  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', emptysetE)).
% 0.22/0.31  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', emptysetimpfalse)).
% 0.22/0.31  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', notinemptyset)).
% 0.22/0.31  thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setext)).
% 0.22/0.31  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', emptyI)).
% 0.22/0.31  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', noeltsimpempty)).
% 0.22/0.31  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setadjoinIL)).
% 0.22/0.31  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', emptyinunitempty)).
% 0.22/0.31  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setadjoinIR)).
% 0.22/0.31  thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setadjoinE)).
% 0.22/0.31  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setadjoinOr)).
% 0.22/0.31  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', powersetI)).
% 0.22/0.31  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', emptyinPowerset)).
% 0.22/0.31  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', emptyInPowerset)).
% 0.22/0.31  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', powersetE)).
% 0.22/0.31  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setunionI)).
% 0.22/0.31  thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setunionE)).
% 0.22/0.31  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', subPowSU)).
% 0.22/0.31  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', uniqinunit)).
% 0.22/0.31  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', notinsingleton)).
% 0.22/0.31  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', eqinunit)).
% 0.22/0.31  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', singletonsswitch)).
% 0.22/0.31  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', upairsetE)).
% 0.22/0.31  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', upairsetIL)).
% 0.22/0.31  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', upairsetIR)).
% 0.22/0.31  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', vacuousDall)).
% 0.22/0.31  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', quantDeMorgan1)).
% 0.22/0.31  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', quantDeMorgan2)).
% 0.22/0.31  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', quantDeMorgan3)).
% 0.22/0.31  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', quantDeMorgan4)).
% 0.22/0.31  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', prop2setI)).
% 0.22/0.31  thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', prop2set2propI)).
% 0.22/0.31  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', notdexE)).
% 0.22/0.31  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', notdallE)).
% 0.22/0.31  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', inCongP)).
% 0.22/0.31  thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', in__Cong)).
% 0.22/0.31  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', emptyset__Cong)).
% 0.22/0.31  thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setadjoin__Cong)).
% 0.22/0.31  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', powerset__Cong)).
% 0.22/0.31  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setunion__Cong)).
% 0.22/0.31  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', omega__Cong)).
% 0.22/0.31  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', subsetI1)).
% 0.22/0.31  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', eqimpsubset2)).
% 0.22/0.31  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', eqimpsubset1)).
% 0.22/0.31  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', subsetI2)).
% 0.22/0.31  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', emptysetsubset)).
% 0.22/0.31  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', subsetE)).
% 0.22/0.31  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', subsetE2)).
% 0.22/0.31  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', notsubsetI)).
% 0.22/0.31  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', notequalI1)).
% 0.22/0.31  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', notequalI2)).
% 0.22/0.31  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', subsetRefl)).
% 0.22/0.31  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', subsetTrans)).
% 0.22/0.31  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setadjoinSub)).
% 0.22/0.31  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setadjoinSub2)).
% 0.22/0.31  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', subset2powerset)).
% 0.22/0.31  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', setextsub)).
% 0.22/0.31  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', subsetemptysetimpeq)).
% 0.22/0.31  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', powersetI1)).
% 0.22/0.31  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', powersetE1)).
% 0.22/0.31  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', inPowerset)).
% 0.22/0.31  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', powersetsubset)).
% 0.22/0.31  thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.AuzUWX4ikf/E---3.1_1702585.p', binunionIL)).
% 0.22/0.31  thf(c_0_102, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.22/0.31  thf(c_0_103, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.22/0.31  thf(c_0_104, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.22/0.31  thf(c_0_105, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.22/0.31  thf(c_0_106, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.22/0.31  thf(c_0_107, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.22/0.31  thf(c_0_108, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.22/0.31  thf(c_0_109, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.22/0.31  thf(c_0_110, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.22/0.31  thf(c_0_111, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.22/0.31  thf(c_0_112, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.22/0.31  thf(c_0_113, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.22/0.31  thf(c_0_114, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.22/0.31  thf(c_0_115, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.22/0.31  thf(c_0_116, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.22/0.31  thf(c_0_117, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[upairset2IR])).
% 0.22/0.31  thf(c_0_118, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X286:$i]:(((((X6 @ X2 @ X286)))&(![X287:$i]:(((((X6 @ X2 @ X287)))=>(((X286)=(X287)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_102, c_0_103])).
% 0.22/0.31  thf(c_0_119, plain, ((descrp)=(![X1:$i > $o]:((((?[X288:$i]:(((((X1 @ X288)))&(![X289:$i]:(((((X1 @ X289)))=>(((X288)=(X289))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_104, c_0_103])).
% 0.22/0.31  thf(c_0_120, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.22/0.31  thf(c_0_121, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.22/0.31  thf(c_0_122, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.22/0.31  thf(c_0_123, plain, ((exuE1)=(![X1:$i > $o]:((((?[X290:$i]:(((((X1 @ X290)))&(![X291:$i]:(((((X1 @ X291)))=>(((X290)=(X291))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_105, c_0_103])).
% 0.22/0.31  thf(c_0_124, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X292:$i]:(((((X1 @ X292)))&(![X293:$i]:(((((X1 @ X293)))=>(((X292)=(X293))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_106, c_0_103])).
% 0.22/0.31  thf(c_0_125, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.22/0.31  thf(c_0_126, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_107])).
% 0.22/0.31  thf(c_0_127, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_108, c_0_107])).
% 0.22/0.31  thf(c_0_128, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_107])).
% 0.22/0.31  thf(c_0_129, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.22/0.31  thf(c_0_130, plain, ((exuE2)=(![X1:$i > $o]:((((?[X294:$i]:(((((X1 @ X294)))&(![X295:$i]:(((((X1 @ X295)))=>(((X294)=(X295))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_109, c_0_103])).
% 0.22/0.31  thf(c_0_131, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_107])).
% 0.22/0.31  thf(c_0_132, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.22/0.31  thf(c_0_133, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X296:$i]:(((((X1 @ X296)))&(![X297:$i]:(((((X1 @ X297)))=>(((X296)=(X297)))))))))))))), inference(apply_def,[status(thm)],[c_0_110, c_0_103])).
% 0.22/0.31  thf(c_0_134, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X298:$i]:(((((X1 @ X298)))&(![X299:$i]:(((((X1 @ X299)))=>(((X298)=(X299)))))))))))))))), inference(apply_def,[status(thm)],[c_0_111, c_0_103])).
% 0.22/0.31  thf(c_0_135, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X300:$i]:(((((X1 @ X300)))&(![X301:$i]:(((((X1 @ X301)))=>(((X300)=(X301)))))))))))))), inference(apply_def,[status(thm)],[c_0_112, c_0_103])).
% 0.22/0.31  thf(c_0_136, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X302:$i]:(((((X1 @ X302)))&(![X303:$i]:(((((X1 @ X303)))=>(((X302)=(X303))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_113, c_0_103])).
% 0.22/0.31  thf(c_0_137, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X304:$i]:(((((X1 @ X304)))&(![X305:$i]:(((((X1 @ X305)))=>(((X304)=(X305))))))))))<=>((?[X306:$i]:(((((X17 @ X306)))&(![X307:$i]:(((((X17 @ X307)))=>(((X306)=(X307)))))))))))))))), inference(apply_def,[status(thm)],[c_0_114, c_0_103])).
% 0.22/0.31  thf(c_0_138, plain, ((exuEu)=(![X1:$i > $o]:((((?[X308:$i]:(((((X1 @ X308)))&(![X309:$i]:(((((X1 @ X309)))=>(((X308)=(X309))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_115, c_0_103])).
% 0.22/0.31  thf(c_0_139, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X310:$i]:(((((X1 @ X310)))&(![X311:$i]:(((((X1 @ X311)))=>(((X310)=(X311))))))))))=>((((?[X312:$i]:(((((X17 @ X312)))&(![X313:$i]:(((((X17 @ X313)))=>(((X312)=(X313))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_116, c_0_103])).
% 0.22/0.31  thf(c_0_140, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.22/0.31  thf(c_0_141, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.22/0.31  thf(c_0_142, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.22/0.31  thf(c_0_143, plain, ((epred1_0)<=>![X343:$i]:(?[X344:$i]:((((![X345:$i]:(((in @ X345 @ X344)=>![X346:$i]:(((in @ X346 @ X345)=>(in @ X346 @ X343)))))&![X347:$i, X348:$i]:((((in @ X347 @ X343)&(in @ X348 @ X343))=>(![X349:$i]:(((in @ X349 @ X344)=>((in @ X347 @ X349)<=>(in @ X348 @ X349))))=>((X347)=(X348))))))&![X350:$i, X351:$i]:((((in @ X350 @ X344)&(in @ X351 @ X344))=>(![X352:$i]:(((in @ X352 @ X350)=>(in @ X352 @ X351)))|![X353:$i]:(((in @ X353 @ X351)=>(in @ X353 @ X350)))))))&![X354:$i]:(((![X355:$i]:(((in @ X355 @ X354)=>(in @ X355 @ X343)))&?[X356:$i]:((in @ X356 @ X354)))=>?[X357:$i, X358:$i]:(((((in @ X357 @ X344)&(in @ X358 @ X354))&~(?[X359:$i]:(((in @ X359 @ X357)&(in @ X359 @ X354)))))&![X360:$i]:(((in @ X360 @ X344)=>(![X361:$i]:(((in @ X361 @ X360)=>(in @ X361 @ X357)))|(in @ X358 @ X360)))))))))))), introduced(definition)).
% 0.22/0.31  thf(c_0_144, negated_conjecture, ~((![X314:$i, X315:$i]:((![X316:$i]:(((in @ X316 @ X314)<=>(in @ X316 @ X315)))=>((X314)=(X315))))=>(![X317:$i]:(~(in @ X317 @ emptyset))=>(![X318:$i, X319:$i, X320:$i]:(((in @ X320 @ (setadjoin @ X318 @ X319))<=>(((X320)=(X318))|(in @ X320 @ X319))))=>(![X321:$i, X322:$i]:(((in @ X322 @ (powerset @ X321))<=>![X323:$i]:(((in @ X323 @ X322)=>(in @ X323 @ X321)))))=>(![X324:$i, X325:$i]:(((in @ X325 @ (setunion @ X324))<=>?[X326:$i]:(((in @ X325 @ X326)&(in @ X326 @ X324)))))=>((in @ emptyset @ omega)=>(![X327:$i]:(((in @ X327 @ omega)=>(in @ (setadjoin @ X327 @ X327) @ omega)))=>(![X328:$i]:((((in @ emptyset @ X328)&![X329:$i]:((((in @ X329 @ omega)&(in @ X329 @ X328))=>(in @ (setadjoin @ X329 @ X329) @ X328))))=>![X330:$i]:(((in @ X330 @ omega)=>(in @ X330 @ X328)))))=>(![X331:$i > $i > $o, X332:$i]:((![X333:$i]:(((in @ X333 @ X332)=>?[X334:$i]:(((X331 @ X333 @ X334)&![X335:$i]:(((X331 @ X333 @ X335)=>((X334)=(X335))))))))=>?[X336:$i]:(![X337:$i]:(((in @ X337 @ X336)<=>?[X338:$i]:(((in @ X338 @ X332)&(X331 @ X338 @ X337))))))))=>(![X339:$i]:((?[X340:$i]:((in @ X340 @ X339))=>?[X341:$i]:(((in @ X341 @ X339)&~(?[X342:$i]:(((in @ X342 @ X341)&(in @ X342 @ X339))))))))=>((epred1_0)=>(![X362:$i > $o]:((?[X363:$i]:(((X362 @ X363)&![X364:$i]:(((X362 @ X364)=>((X363)=(X364))))))=>(X362 @ (descr @ (^[Z0:$i]:(X362 @ Z0))))))=>(![X365:$i, X366:$i > $o, X367:$i]:(((in @ X367 @ X365)=>((X366 @ X367)=>(in @ X367 @ (dsetconstr @ X365 @ X366)))))=>(![X368:$i, X369:$i > $o, X370:$i]:(((in @ X370 @ (dsetconstr @ X368 @ X369))=>(in @ X370 @ X368)))=>(![X371:$i, X372:$i > $o, X373:$i]:(((in @ X373 @ (dsetconstr @ X371 @ X372))=>(X372 @ X373)))=>(![X374:$i > $o]:((?[X375:$i]:(((X374 @ X375)&![X376:$i]:(((X374 @ X376)=>((X375)=(X376))))))=>?[X377:$i]:(((X374 @ X377)&![X378:$i]:(((X374 @ X378)=>((X377)=(X378))))))))=>(![X379:$o, X380:$i]:(((in @ X380 @ (prop2set @ ((X379))))=>(X379)))=>(![X381:$i]:(((in @ X381 @ emptyset)=>![X382:$o]:((X382))))=>(![X383:$i]:(((in @ X383 @ emptyset)=>~($true)))=>(![X384:$i]:(~(in @ X384 @ emptyset))=>(![X385:$i > $o]:((?[X386:$i]:(((X385 @ X386)&![X387:$i]:(((X385 @ X387)=>((X386)=(X387))))))=>?[X388:$i]:((X385 @ X388))))=>(![X389:$i, X390:$i]:((![X391:$i]:(((in @ X391 @ X389)=>(in @ X391 @ X390)))=>(![X392:$i]:(((in @ X392 @ X390)=>(in @ X392 @ X389)))=>((X389)=(X390)))))=>(![X393:$i]:((![X394:$i]:(~(in @ X394 @ X393))=>((X393)=(emptyset))))=>(![X395:$i]:((![X396:$i]:(~(in @ X396 @ X395))=>((X395)=(emptyset))))=>(![X397:$i, X398:$i > $o, X399:$i]:(((in @ X399 @ X397)=>((in @ X399 @ (dsetconstr @ X397 @ X398))<=>(X398 @ X399))))=>(![X400:$i]:((((X400)!=(emptyset))=>?[X401:$i]:((in @ X401 @ X400))))=>(![X402:$i, X403:$i > $o, X404:$i]:(((in @ X404 @ X402)=>((X403 @ X404)=>((dsetconstr @ X402 @ X403)!=(emptyset)))))=>(![X405:$i]:((?[X406:$i]:((in @ X406 @ X405))=>((X405)!=(emptyset))))=>(![X407:$i, X408:$i]:((in @ X407 @ (setadjoin @ X407 @ X408)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X409:$i, X410:$i, X411:$i]:(((in @ X411 @ X410)=>(in @ X411 @ (setadjoin @ X409 @ X410))))=>(![X412:$i, X413:$i, X414:$i]:(((in @ X414 @ (setadjoin @ X412 @ X413))=>![X415:$o]:(((((X414)=(X412))=>(X415))=>(((in @ X414 @ X413)=>(X415))=>(X415))))))=>(![X416:$i, X417:$i, X418:$i]:(((in @ X418 @ (setadjoin @ X416 @ X417))=>(((X418)=(X416))|(in @ X418 @ X417))))=>(![X419:$i]:(((dsetconstr @ X419 @ (^[Z0:$i]:($true)))=(X419)))=>(![X420:$i, X421:$i]:((![X422:$i]:(((in @ X422 @ X421)=>(in @ X422 @ X420)))=>(in @ X421 @ (powerset @ X420))))=>(![X423:$i]:((in @ emptyset @ (powerset @ X423)))=>(![X424:$i]:((in @ emptyset @ (powerset @ X424)))=>(![X425:$i, X426:$i, X427:$i]:(((in @ X426 @ (powerset @ X425))=>((in @ X427 @ X426)=>(in @ X427 @ X425))))=>(![X428:$i, X429:$i, X430:$i]:(((in @ X429 @ X430)=>((in @ X430 @ X428)=>(in @ X429 @ (setunion @ X428)))))=>(![X431:$i, X432:$i]:(((in @ X432 @ (setunion @ X431))=>![X433:$o]:((![X434:$i]:(((in @ X432 @ X434)=>((in @ X434 @ X431)=>(X433))))=>(X433)))))=>(![X435:$i, X436:$i]:(((in @ X436 @ X435)=>(in @ X436 @ (powerset @ (setunion @ X435)))))=>(![X437:$i > $o]:((?[X438:$i]:(((X437 @ X438)&![X439:$i]:(((X437 @ X439)=>((X438)=(X439))))))=>?[X440:$i]:(![X441:$i]:(((X437 @ X441)<=>((X441)=(X440)))))))=>(![X442:$i]:((((X442)!=(emptyset))=>?[X443:$i]:(((in @ X443 @ X442)&$true))))=>(![X444:$i, X445:$i]:(((in @ X444 @ (setadjoin @ X445 @ emptyset))=>((X444)=(X445))))=>(![X446:$i, X447:$i]:((((X446)!=(X447))=>~(in @ X447 @ (setadjoin @ X446 @ emptyset))))=>(![X448:$i, X449:$i]:((((X448)=(X449))=>(in @ X448 @ (setadjoin @ X449 @ emptyset))))=>(![X450:$i, X451:$i]:(((in @ X450 @ (setadjoin @ X451 @ emptyset))=>(in @ X451 @ (setadjoin @ X450 @ emptyset))))=>(![X452:$i, X453:$i, X454:$i]:(((in @ X454 @ (setadjoin @ X452 @ (setadjoin @ X453 @ emptyset)))=>(((X454)=(X452))|((X454)=(X453)))))=>(![X455:$i, X456:$i]:((in @ X455 @ (setadjoin @ X455 @ (setadjoin @ X456 @ emptyset))))=>(![X457:$i, X458:$i]:((in @ X458 @ (setadjoin @ X457 @ (setadjoin @ X458 @ emptyset))))=>(![X459:$i, X460:$i > $o]:((?[X461:$i]:(((in @ X461 @ X459)&(X460 @ X461)))=>(((dsetconstr @ X459 @ X460)=(emptyset))=>~($true))))=>(![X462:$i > $o, X463:$i]:(((in @ X463 @ emptyset)=>(X462 @ X463)))=>(![X464:$i, X465:$i > $o]:((~(![X466:$i]:(((in @ X466 @ X464)=>(X465 @ X466))))=>?[X467:$i]:(((in @ X467 @ X464)&~((X465 @ X467))))))=>(![X468:$i, X469:$i > $o]:((![X470:$i]:(((in @ X470 @ X468)=>~((X469 @ X470))))=>~(?[X471:$i]:(((in @ X471 @ X468)&(X469 @ X471))))))=>(![X472:$i, X473:$i > $o]:((~(?[X474:$i]:(((in @ X474 @ X472)&(X473 @ X474))))=>![X475:$i]:(((in @ X475 @ X472)=>~((X473 @ X475))))))=>(![X476:$i, X477:$i > $o]:((?[X478:$i]:(((in @ X478 @ X476)&~((X477 @ X478))))=>~(![X479:$i]:(((in @ X479 @ X476)=>(X477 @ X479))))))=>(![X480:$o]:(((X480)=>(in @ emptyset @ (prop2set @ ((X480))))))=>(![X481:$o]:(((X481)=>(set2prop @ (prop2set @ ((X481))))))=>(![X482:$i, X483:$i > $o]:((~(?[X484:$i]:(((in @ X484 @ X482)&(X483 @ X484))))=>![X485:$i]:(((in @ X485 @ X482)=>~((X483 @ X485))))))=>(![X486:$i, X487:$i > $o]:((~(![X488:$i]:(((in @ X488 @ X486)=>(X487 @ X488))))=>?[X489:$i]:(((in @ X489 @ X486)&~((X487 @ X489))))))=>(![X490:$i > $o]:((?[X491:$i]:(((X490 @ X491)&![X492:$i]:(((X490 @ X492)=>((X491)=(X492))))))=>?[X493:$i]:(((X490 @ X493)&![X494:$i]:(((X490 @ X494)=>((X493)=(X494))))))))=>(![X495:$i > $o]:((?[X496:$i]:((X495 @ X496))=>(![X497:$i, X498:$i]:(((X495 @ X497)=>((X495 @ X498)=>((X497)=(X498)))))=>?[X499:$i]:(((X495 @ X499)&![X500:$i]:(((X495 @ X500)=>((X499)=(X500)))))))))=>(![X501:$i > $o]:((?[X502:$i]:(![X503:$i]:(((X501 @ X503)<=>((X503)=(X502)))))=>?[X504:$i]:(((X501 @ X504)&![X505:$i]:(((X501 @ X505)=>((X504)=(X505))))))))=>(![X506:$i, X507:$i]:((((X506)=(X507))=>![X508:$i, X509:$i]:((((X508)=(X509))=>((in @ X508 @ X506)=>(in @ X509 @ X507))))))=>(![X510:$i, X511:$i]:((((X510)=(X511))=>![X512:$i, X513:$i]:((((X512)=(X513))=>((in @ X512 @ X510)<=>(in @ X513 @ X511))))))=>(![X514:$i > $o]:((?[X515:$i]:(((X514 @ X515)&![X516:$i]:(((X514 @ X516)=>((X515)=(X516))))))=>![X517:$i, X518:$i]:(((X514 @ X517)=>((X514 @ X518)=>((X517)=(X518)))))))=>(![X519:$i > $o, X520:$i > $o]:((![X521:$i, X522:$i]:((((X521)=(X522))=>((X519 @ X521)<=>(X520 @ X522))))=>(?[X523:$i]:(((X519 @ X523)&![X524:$i]:(((X519 @ X524)=>((X523)=(X524))))))<=>?[X525:$i]:(((X520 @ X525)&![X526:$i]:(((X520 @ X526)=>((X525)=(X526)))))))))=>(((emptyset)=(emptyset))=>(![X527:$i, X528:$i]:((((X527)=(X528))=>![X529:$i, X530:$i]:((((X529)=(X530))=>((setadjoin @ X527 @ X529)=(setadjoin @ X528 @ X530))))))=>(![X531:$i, X532:$i]:((((X531)=(X532))=>((powerset @ X531)=(powerset @ X532))))=>(![X533:$i, X534:$i]:((((X533)=(X534))=>((setunion @ X533)=(setunion @ X534))))=>(((omega)=(omega))=>(![X535:$i > $o]:((?[X536:$i]:(((X535 @ X536)&![X537:$i]:(((X535 @ X537)=>((X536)=(X537))))))=>![X538:$i, X539:$i]:(((X535 @ X538)=>((X535 @ X539)=>((X538)=(X539)))))))=>(![X540:$i > $o, X541:$i > $o]:((![X542:$i, X543:$i]:((((X542)=(X543))=>((X540 @ X542)<=>(X541 @ X543))))=>(?[X544:$i]:(((X540 @ X544)&![X545:$i]:(((X540 @ X545)=>((X544)=(X545))))))=>(?[X546:$i]:(((X541 @ X546)&![X547:$i]:(((X541 @ X547)=>((X546)=(X547))))))=>((descr @ X540)=(descr @ X541))))))=>(![X548:$i, X549:$i]:((((X548)=(X549))=>![X550:$i > $o, X551:$i > $o]:((![X552:$i]:(((in @ X552 @ X548)=>![X553:$i]:(((in @ X553 @ X549)=>(((X552)=(X553))=>((X550 @ X552)<=>(X551 @ X553)))))))=>((dsetconstr @ X548 @ X550)=(dsetconstr @ X549 @ X551))))))=>(![X554:$i, X555:$i]:((![X556:$i]:(((in @ X556 @ X554)=>(in @ X556 @ X555)))=>(subset @ X554 @ X555)))=>(![X557:$i, X558:$i]:((((X557)=(X558))=>(subset @ X558 @ X557)))=>(![X559:$i, X560:$i]:((((X559)=(X560))=>(subset @ X559 @ X560)))=>(![X561:$i, X562:$i]:((![X563:$i]:(((in @ X563 @ X561)=>(in @ X563 @ X562)))=>(subset @ X561 @ X562)))=>(![X564:$i]:((subset @ emptyset @ X564))=>(![X565:$i, X566:$i, X567:$i]:(((subset @ X565 @ X566)=>((in @ X567 @ X565)=>(in @ X567 @ X566))))=>(![X568:$i, X569:$i, X570:$i]:(((subset @ X568 @ X569)=>(~(in @ X570 @ X569)=>~(in @ X570 @ X568))))=>(![X571:$i, X572:$i, X573:$i]:(((in @ X573 @ X571)=>(~(in @ X573 @ X572)=>~(subset @ X571 @ X572))))=>(![X574:$i, X575:$i]:((~(subset @ X574 @ X575)=>((X574)!=(X575))))=>(![X576:$i, X577:$i, X578:$i]:(((in @ X578 @ X576)=>(~(in @ X578 @ X577)=>((X576)!=(X577)))))=>(![X579:$i]:((subset @ X579 @ X579))=>(![X580:$i, X581:$i, X582:$i]:(((subset @ X580 @ X581)=>((subset @ X581 @ X582)=>(subset @ X580 @ X582))))=>(![X583:$i, X584:$i]:((subset @ X584 @ (setadjoin @ X583 @ X584)))=>(![X585:$i, X586:$i, X587:$i]:(((subset @ X585 @ X587)=>(subset @ X585 @ (setadjoin @ X586 @ X587))))=>(![X588:$i, X589:$i]:(((subset @ X588 @ X589)=>(in @ X588 @ (powerset @ X589))))=>(![X590:$i, X591:$i]:(((subset @ X590 @ X591)=>((subset @ X591 @ X590)=>((X590)=(X591)))))=>(![X592:$i]:(((subset @ X592 @ emptyset)=>((X592)=(emptyset))))=>(![X593:$i, X594:$i]:(((subset @ X594 @ X593)=>(in @ X594 @ (powerset @ X593))))=>(![X595:$i, X596:$i]:(((in @ X596 @ (powerset @ X595))=>(subset @ X596 @ X595)))=>(![X597:$i]:((in @ X597 @ (powerset @ X597)))=>(![X598:$i, X599:$i]:(((subset @ X598 @ X599)=>(subset @ (powerset @ X598) @ (powerset @ X599))))=>(![X600:$i, X601:$i > $o]:((in @ (dsetconstr @ X600 @ X601) @ (powerset @ X600)))=>(![X602:$i, X603:$i > $o]:((subset @ (dsetconstr @ X602 @ X603) @ X602))=>(![X604:$i, X605:$i, X606:$i]:(((in @ X606 @ X604)=>(in @ X606 @ (binunion @ X604 @ X605))))=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_117, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_118]), foundationAx]), wellorderingAx]), c_0_119]), c_0_120]), c_0_121]), c_0_122]), c_0_123]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_124]), setext]), emptyI]), noeltsimpempty]), c_0_125]), c_0_126]), c_0_127]), c_0_128]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_129]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_130]), c_0_131]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_132]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_133]), c_0_134]), c_0_135]), inCongP]), in__Cong]), c_0_136]), c_0_137]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_138]), c_0_139]), c_0_140]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_141]), c_0_142]), binunionIL])])]), c_0_143])).
% 0.22/0.31  thf(c_0_145, negated_conjecture, ![X611:$i, X612:$i, X614:$i, X615:$i, X616:$i, X617:$i, X618:$i, X619:$i, X620:$i, X621:$i, X622:$i, X624:$i, X625:$i, X627:$i, X628:$i, X629:$i, X630:$i, X631:$i, X633:$i, X634:$i > $i > $o, X635:$i, X637:$i, X640:$i, X642:$i, X643:$i, X644:$i, X645:$i, X647:$i, X648:$i > $o, X649:$i, X651:$i, X652:$i > $o, X653:$i, X654:$i, X655:$i > $o, X656:$i, X657:$i, X658:$i > $o, X659:$i, X660:$i > $o, X661:$i, X664:$i, X665:$o, X666:$i, X667:$i, X668:$o, X669:$i, X670:$i, X671:$i > $o, X672:$i, X675:$i, X676:$i, X679:$i, X681:$i, X683:$i, X684:$i > $o, X685:$i, X686:$i, X688:$i, X689:$i > $o, X690:$i, X691:$i, X692:$i, X693:$i, X694:$i, X695:$i, X696:$i, X697:$i, X698:$i, X699:$i, X700:$i, X701:$o, X702:$i, X703:$i, X704:$i, X705:$i, X706:$i, X707:$i, X709:$i, X710:$i, X711:$i, X712:$i, X713:$i, X714:$i, X715:$i, X716:$i, X717:$i, X718:$i, X719:$o, X721:$i, X722:$i, X723:$i > $o, X724:$i, X727:$i, X728:$i, X729:$i, X731:$i, X732:$i, X733:$i, X734:$i, X735:$i, X736:$i, X737:$i, X738:$i, X739:$i, X740:$i, X741:$i, X742:$i, X743:$i, X744:$i, X745:$i, X746:$i, X747:$i > $o, X748:$i, X749:$i > $o, X750:$i, X751:$i, X752:$i > $o, X753:$i, X755:$i, X756:$i > $o, X758:$i, X759:$i, X760:$i > $o, X762:$i, X763:$i, X764:$i > $o, X765:$i, X767:$o, X768:$o, X769:$i, X770:$i > $o, X772:$i, X773:$i, X774:$i > $o, X775:$i, X777:$i > $o, X778:$i, X781:$i, X782:$i > $o, X783:$i, X787:$i, X788:$i > $o, X789:$i, X792:$i, X793:$i, X794:$i, X795:$i, X796:$i, X797:$i, X798:$i, X799:$i, X800:$i, X801:$i > $o, X802:$i, X804:$i, X805:$i, X806:$i > $o, X807:$i > $o, X810:$i, X813:$i, X814:$i, X817:$i, X818:$i, X819:$i, X820:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$i, X826:$i > $o, X827:$i, X829:$i, X830:$i, X831:$i > $o, X832:$i > $o, X835:$i, X837:$i, X839:$i, X840:$i, X841:$i > $o, X842:$i > $o, X845:$i, X846:$i, X848:$i, X849:$i, X850:$i, X851:$i, X852:$i, X853:$i, X855:$i, X856:$i, X857:$i, X858:$i, X859:$i, X860:$i, X861:$i, X862:$i, X863:$i, X864:$i, X865:$i, X866:$i, X867:$i, X868:$i, X869:$i, X870:$i, X871:$i, X872:$i, X873:$i, X874:$i, X875:$i, X876:$i, X877:$i, X878:$i, X879:$i, X880:$i, X881:$i, X882:$i, X883:$i, X884:$i, X885:$i, X886:$i, X887:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i > $o, X893:$i, X894:$i > $o, X895:$i, X896:$i, X897:$i]:((((~(in @ (esk1_2 @ X611 @ X612) @ X611)|~(in @ (esk1_2 @ X611 @ X612) @ X612)|((X611)=(X612)))&((in @ (esk1_2 @ X611 @ X612) @ X611)|(in @ (esk1_2 @ X611 @ X612) @ X612)|((X611)=(X612))))&(~(in @ X614 @ emptyset)&(((~(in @ X617 @ (setadjoin @ X615 @ X616))|(((X617)=(X615))|(in @ X617 @ X616)))&((((X617)!=(X615))|(in @ X617 @ (setadjoin @ X615 @ X616)))&(~(in @ X617 @ X616)|(in @ X617 @ (setadjoin @ X615 @ X616)))))&(((~(in @ X619 @ (powerset @ X618))|(~(in @ X620 @ X619)|(in @ X620 @ X618)))&(((in @ (esk2_2 @ X621 @ X622) @ X622)|(in @ X622 @ (powerset @ X621)))&(~(in @ (esk2_2 @ X621 @ X622) @ X621)|(in @ X622 @ (powerset @ X621)))))&(((((in @ X625 @ (esk3_2 @ X624 @ X625))|~(in @ X625 @ (setunion @ X624)))&((in @ (esk3_2 @ X624 @ X625) @ X624)|~(in @ X625 @ (setunion @ X624))))&(~(in @ X628 @ X629)|~(in @ X629 @ X627)|(in @ X628 @ (setunion @ X627))))&((in @ emptyset @ omega)&((~(in @ X630 @ omega)|(in @ (setadjoin @ X630 @ X630) @ omega))&(((((in @ (esk4_1 @ X631) @ omega)|~(in @ emptyset @ X631)|(~(in @ X633 @ omega)|(in @ X633 @ X631)))&((in @ (esk4_1 @ X631) @ X631)|~(in @ emptyset @ X631)|(~(in @ X633 @ omega)|(in @ X633 @ X631))))&(~(in @ (setadjoin @ (esk4_1 @ X631) @ (esk4_1 @ X631)) @ X631)|~(in @ emptyset @ X631)|(~(in @ X633 @ omega)|(in @ X633 @ X631))))&((((((in @ (esk8_3 @ X634 @ X635 @ X640) @ X635)|~(in @ X640 @ (esk7_2 @ X634 @ X635))|(in @ (esk5_2 @ X634 @ X635) @ X635))&((X634 @ (esk8_3 @ X634 @ X635 @ X640) @ X640)|~(in @ X640 @ (esk7_2 @ X634 @ X635))|(in @ (esk5_2 @ X634 @ X635) @ X635)))&(~(in @ X643 @ X635)|~(X634 @ X643 @ X642)|(in @ X642 @ (esk7_2 @ X634 @ X635))|(in @ (esk5_2 @ X634 @ X635) @ X635)))&(((((in @ (esk8_3 @ X634 @ X635 @ X640) @ X635)|~(in @ X640 @ (esk7_2 @ X634 @ X635))|((X634 @ (esk5_2 @ X634 @ X635) @ (esk6_3 @ X634 @ X635 @ X637))|~(X634 @ (esk5_2 @ X634 @ X635) @ X637)))&((X634 @ (esk8_3 @ X634 @ X635 @ X640) @ X640)|~(in @ X640 @ (esk7_2 @ X634 @ X635))|((X634 @ (esk5_2 @ X634 @ X635) @ (esk6_3 @ X634 @ X635 @ X637))|~(X634 @ (esk5_2 @ X634 @ X635) @ X637))))&(~(in @ X643 @ X635)|~(X634 @ X643 @ X642)|(in @ X642 @ (esk7_2 @ X634 @ X635))|((X634 @ (esk5_2 @ X634 @ X635) @ (esk6_3 @ X634 @ X635 @ X637))|~(X634 @ (esk5_2 @ X634 @ X635) @ X637))))&((((in @ (esk8_3 @ X634 @ X635 @ X640) @ X635)|~(in @ X640 @ (esk7_2 @ X634 @ X635))|(((X637)!=(esk6_3 @ X634 @ X635 @ X637))|~(X634 @ (esk5_2 @ X634 @ X635) @ X637)))&((X634 @ (esk8_3 @ X634 @ X635 @ X640) @ X640)|~(in @ X640 @ (esk7_2 @ X634 @ X635))|(((X637)!=(esk6_3 @ X634 @ X635 @ X637))|~(X634 @ (esk5_2 @ X634 @ X635) @ X637))))&(~(in @ X643 @ X635)|~(X634 @ X643 @ X642)|(in @ X642 @ (esk7_2 @ X634 @ X635))|(((X637)!=(esk6_3 @ X634 @ X635 @ X637))|~(X634 @ (esk5_2 @ X634 @ X635) @ X637))))))&((((in @ (esk9_1 @ X644) @ X644)|~(in @ X645 @ X644))&(~(in @ X647 @ (esk9_1 @ X644))|~(in @ X647 @ X644)|~(in @ X645 @ X644)))&((epred1_0)&((((X648 @ (esk10_2 @ X648 @ X649))|~(X648 @ X649)|(X648 @ (descr @ X648)))&(((X649)!=(esk10_2 @ X648 @ X649))|~(X648 @ X649)|(X648 @ (descr @ X648))))&((~(in @ X653 @ X651)|(~(X652 @ X653)|(in @ X653 @ (dsetconstr @ X651 @ X652))))&((~(in @ X656 @ (dsetconstr @ X654 @ X655))|(in @ X656 @ X654))&((~(in @ X659 @ (dsetconstr @ X657 @ X658))|(X658 @ X659))&(((((X660 @ (esk12_1 @ X660))|((X660 @ (esk11_2 @ X660 @ X661))|~(X660 @ X661)))&(~(X660 @ X664)|((esk12_1 @ X660)=(X664))|((X660 @ (esk11_2 @ X660 @ X661))|~(X660 @ X661))))&(((X660 @ (esk12_1 @ X660))|(((X661)!=(esk11_2 @ X660 @ X661))|~(X660 @ X661)))&(~(X660 @ X664)|((esk12_1 @ X660)=(X664))|(((X661)!=(esk11_2 @ X660 @ X661))|~(X660 @ X661)))))&((~(in @ X666 @ (prop2set @ ((X665))))|(X665))&((~(in @ X667 @ emptyset)|(X668))&((~(in @ X669 @ emptyset)|~($true))&(~(in @ X670 @ emptyset)&((((X671 @ (esk13_2 @ X671 @ X672))|~(X671 @ X672)|(X671 @ (esk14_1 @ X671)))&(((X672)!=(esk13_2 @ X671 @ X672))|~(X671 @ X672)|(X671 @ (esk14_1 @ X671))))&(((((in @ (esk16_2 @ X675 @ X676) @ X676)|((X675)=(X676))|(in @ (esk15_2 @ X675 @ X676) @ X675))&(~(in @ (esk16_2 @ X675 @ X676) @ X675)|((X675)=(X676))|(in @ (esk15_2 @ X675 @ X676) @ X675)))&(((in @ (esk16_2 @ X675 @ X676) @ X676)|((X675)=(X676))|~(in @ (esk15_2 @ X675 @ X676) @ X676))&(~(in @ (esk16_2 @ X675 @ X676) @ X675)|((X675)=(X676))|~(in @ (esk15_2 @ X675 @ X676) @ X676))))&(((in @ (esk17_1 @ X679) @ X679)|((X679)=(emptyset)))&(((in @ (esk18_1 @ X681) @ X681)|((X681)=(emptyset)))&(((~(in @ X685 @ (dsetconstr @ X683 @ X684))|(X684 @ X685)|~(in @ X685 @ X683))&(~(X684 @ X685)|(in @ X685 @ (dsetconstr @ X683 @ X684))|~(in @ X685 @ X683)))&((((X686)=(emptyset))|(in @ (esk19_1 @ X686) @ X686))&((~(in @ X690 @ X688)|(~(X689 @ X690)|((dsetconstr @ X688 @ X689)!=(emptyset))))&((~(in @ X692 @ X691)|((X691)!=(emptyset)))&((in @ X693 @ (setadjoin @ X693 @ X694))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X697 @ X696)|(in @ X697 @ (setadjoin @ X695 @ X696)))&(((((in @ X700 @ X699)|(X701)|((X700)=(X698))|~(in @ X700 @ (setadjoin @ X698 @ X699)))&(~(X701)|(X701)|((X700)=(X698))|~(in @ X700 @ (setadjoin @ X698 @ X699))))&(((in @ X700 @ X699)|(X701)|~(X701)|~(in @ X700 @ (setadjoin @ X698 @ X699)))&(~(X701)|(X701)|~(X701)|~(in @ X700 @ (setadjoin @ X698 @ X699)))))&((~(in @ X704 @ (setadjoin @ X702 @ X703))|(((X704)=(X702))|(in @ X704 @ X703)))&(((dsetconstr @ X705 @ (^[Z0:$i]:($true)))=(X705))&((((in @ (esk20_2 @ X706 @ X707) @ X707)|(in @ X707 @ (powerset @ X706)))&(~(in @ (esk20_2 @ X706 @ X707) @ X706)|(in @ X707 @ (powerset @ X706))))&((in @ emptyset @ (powerset @ X709))&((in @ emptyset @ (powerset @ X710))&((~(in @ X712 @ (powerset @ X711))|(~(in @ X713 @ X712)|(in @ X713 @ X711)))&((~(in @ X715 @ X716)|(~(in @ X716 @ X714)|(in @ X715 @ (setunion @ X714))))&((((in @ X718 @ (esk21_3 @ X717 @ X718 @ X719))|(X719)|~(in @ X718 @ (setunion @ X717)))&(((in @ (esk21_3 @ X717 @ X718 @ X719) @ X717)|(X719)|~(in @ X718 @ (setunion @ X717)))&(~(X719)|(X719)|~(in @ X718 @ (setunion @ X717)))))&((~(in @ X722 @ X721)|(in @ X722 @ (powerset @ (setunion @ X721))))&((((~(X723 @ X727)|((X727)=(esk23_1 @ X723))|((X723 @ (esk22_2 @ X723 @ X724))|~(X723 @ X724)))&(((X728)!=(esk23_1 @ X723))|(X723 @ X728)|((X723 @ (esk22_2 @ X723 @ X724))|~(X723 @ X724))))&((~(X723 @ X727)|((X727)=(esk23_1 @ X723))|(((X724)!=(esk22_2 @ X723 @ X724))|~(X723 @ X724)))&(((X728)!=(esk23_1 @ X723))|(X723 @ X728)|(((X724)!=(esk22_2 @ X723 @ X724))|~(X723 @ X724)))))&((((in @ (esk24_1 @ X729) @ X729)|((X729)=(emptyset)))&(($true)|((X729)=(emptyset))))&((~(in @ X731 @ (setadjoin @ X732 @ emptyset))|((X731)=(X732)))&((((X733)=(X734))|~(in @ X734 @ (setadjoin @ X733 @ emptyset)))&((((X735)!=(X736))|(in @ X735 @ (setadjoin @ X736 @ emptyset)))&((~(in @ X737 @ (setadjoin @ X738 @ emptyset))|(in @ X738 @ (setadjoin @ X737 @ emptyset)))&((~(in @ X741 @ (setadjoin @ X739 @ (setadjoin @ X740 @ emptyset)))|(((X741)=(X739))|((X741)=(X740))))&((in @ X742 @ (setadjoin @ X742 @ (setadjoin @ X743 @ emptyset)))&((in @ X745 @ (setadjoin @ X744 @ (setadjoin @ X745 @ emptyset)))&((~(in @ X748 @ X746)|~(X747 @ X748)|(((dsetconstr @ X746 @ X747)!=(emptyset))|~($true)))&((~(in @ X750 @ emptyset)|(X749 @ X750))&((((in @ (esk25_2 @ X751 @ X752) @ X751)|(~(in @ X753 @ X751)|(X752 @ X753)))&(~(X752 @ (esk25_2 @ X751 @ X752))|(~(in @ X753 @ X751)|(X752 @ X753))))&((((in @ (esk26_2 @ X755 @ X756) @ X755)|(~(in @ X758 @ X755)|~(X756 @ X758)))&((X756 @ (esk26_2 @ X755 @ X756))|(~(in @ X758 @ X755)|~(X756 @ X758))))&((((in @ (esk27_2 @ X759 @ X760) @ X759)|(~(in @ X762 @ X759)|~(X760 @ X762)))&((X760 @ (esk27_2 @ X759 @ X760))|(~(in @ X762 @ X759)|~(X760 @ X762))))&((((in @ (esk28_2 @ X763 @ X764) @ X763)|(~(in @ X765 @ X763)|(X764 @ X765)))&(~(X764 @ (esk28_2 @ X763 @ X764))|(~(in @ X765 @ X763)|(X764 @ X765))))&((~(X767)|(in @ emptyset @ (prop2set @ ((X767)))))&((~(X768)|(set2prop @ (prop2set @ ((X768)))))&((((in @ (esk29_2 @ X769 @ X770) @ X769)|(~(in @ X772 @ X769)|~(X770 @ X772)))&((X770 @ (esk29_2 @ X769 @ X770))|(~(in @ X772 @ X769)|~(X770 @ X772))))&((((in @ (esk30_2 @ X773 @ X774) @ X773)|(~(in @ X775 @ X773)|(X774 @ X775)))&(~(X774 @ (esk30_2 @ X773 @ X774))|(~(in @ X775 @ X773)|(X774 @ X775))))&(((((X777 @ (esk32_1 @ X777))|((X777 @ (esk31_2 @ X777 @ X778))|~(X777 @ X778)))&(~(X777 @ X781)|((esk32_1 @ X777)=(X781))|((X777 @ (esk31_2 @ X777 @ X778))|~(X777 @ X778))))&(((X777 @ (esk32_1 @ X777))|(((X778)!=(esk31_2 @ X777 @ X778))|~(X777 @ X778)))&(~(X777 @ X781)|((esk32_1 @ X777)=(X781))|(((X778)!=(esk31_2 @ X777 @ X778))|~(X777 @ X778)))))&(((((X782 @ (esk35_1 @ X782))|(X782 @ (esk33_1 @ X782))|~(X782 @ X783))&(~(X782 @ X787)|((esk35_1 @ X782)=(X787))|(X782 @ (esk33_1 @ X782))|~(X782 @ X783)))&((((X782 @ (esk35_1 @ X782))|(X782 @ (esk34_1 @ X782))|~(X782 @ X783))&(~(X782 @ X787)|((esk35_1 @ X782)=(X787))|(X782 @ (esk34_1 @ X782))|~(X782 @ X783)))&(((X782 @ (esk35_1 @ X782))|((esk33_1 @ X782)!=(esk34_1 @ X782))|~(X782 @ X783))&(~(X782 @ X787)|((esk35_1 @ X782)=(X787))|((esk33_1 @ X782)!=(esk34_1 @ X782))|~(X782 @ X783)))))&(((((X788 @ (esk37_1 @ X788))|(~(X788 @ (esk36_2 @ X788 @ X789))|((esk36_2 @ X788 @ X789)!=(X789))))&(~(X788 @ X792)|((esk37_1 @ X788)=(X792))|(~(X788 @ (esk36_2 @ X788 @ X789))|((esk36_2 @ X788 @ X789)!=(X789)))))&(((X788 @ (esk37_1 @ X788))|((X788 @ (esk36_2 @ X788 @ X789))|((esk36_2 @ X788 @ X789)=(X789))))&(~(X788 @ X792)|((esk37_1 @ X788)=(X792))|((X788 @ (esk36_2 @ X788 @ X789))|((esk36_2 @ X788 @ X789)=(X789))))))&((((X793)!=(X794))|(((X795)!=(X796))|(~(in @ X795 @ X793)|(in @ X796 @ X794))))&(((~(in @ X799 @ X797)|(in @ X800 @ X798)|((X799)!=(X800))|((X797)!=(X798)))&(~(in @ X800 @ X798)|(in @ X799 @ X797)|((X799)!=(X800))|((X797)!=(X798))))&((((X801 @ (esk38_2 @ X801 @ X802))|~(X801 @ X802)|(~(X801 @ X804)|(~(X801 @ X805)|((X804)=(X805)))))&(((X802)!=(esk38_2 @ X801 @ X802))|~(X801 @ X802)|(~(X801 @ X804)|(~(X801 @ X805)|((X804)=(X805))))))&(((((((X807 @ (esk42_2 @ X806 @ X807))|((X806 @ (esk41_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((esk39_2 @ X806 @ X807)=(esk40_2 @ X806 @ X807)))&(~(X807 @ X813)|((esk42_2 @ X806 @ X807)=(X813))|((X806 @ (esk41_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((esk39_2 @ X806 @ X807)=(esk40_2 @ X806 @ X807))))&(((X807 @ (esk42_2 @ X806 @ X807))|(((X810)!=(esk41_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((esk39_2 @ X806 @ X807)=(esk40_2 @ X806 @ X807)))&(~(X807 @ X813)|((esk42_2 @ X806 @ X807)=(X813))|(((X810)!=(esk41_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((esk39_2 @ X806 @ X807)=(esk40_2 @ X806 @ X807)))))&((((X806 @ (esk44_2 @ X806 @ X807))|((X807 @ (esk43_3 @ X806 @ X807 @ X814))|~(X807 @ X814))|((esk39_2 @ X806 @ X807)=(esk40_2 @ X806 @ X807)))&(~(X806 @ X817)|((esk44_2 @ X806 @ X807)=(X817))|((X807 @ (esk43_3 @ X806 @ X807 @ X814))|~(X807 @ X814))|((esk39_2 @ X806 @ X807)=(esk40_2 @ X806 @ X807))))&(((X806 @ (esk44_2 @ X806 @ X807))|(((X814)!=(esk43_3 @ X806 @ X807 @ X814))|~(X807 @ X814))|((esk39_2 @ X806 @ X807)=(esk40_2 @ X806 @ X807)))&(~(X806 @ X817)|((esk44_2 @ X806 @ X807)=(X817))|(((X814)!=(esk43_3 @ X806 @ X807 @ X814))|~(X807 @ X814))|((esk39_2 @ X806 @ X807)=(esk40_2 @ X806 @ X807))))))&((((((X807 @ (esk42_2 @ X806 @ X807))|((X806 @ (esk41_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|(~(X806 @ (esk39_2 @ X806 @ X807))|~(X807 @ (esk40_2 @ X806 @ X807))))&(~(X807 @ X813)|((esk42_2 @ X806 @ X807)=(X813))|((X806 @ (esk41_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|(~(X806 @ (esk39_2 @ X806 @ X807))|~(X807 @ (esk40_2 @ X806 @ X807)))))&(((X807 @ (esk42_2 @ X806 @ X807))|(((X810)!=(esk41_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|(~(X806 @ (esk39_2 @ X806 @ X807))|~(X807 @ (esk40_2 @ X806 @ X807))))&(~(X807 @ X813)|((esk42_2 @ X806 @ X807)=(X813))|(((X810)!=(esk41_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|(~(X806 @ (esk39_2 @ X806 @ X807))|~(X807 @ (esk40_2 @ X806 @ X807))))))&((((X806 @ (esk44_2 @ X806 @ X807))|((X807 @ (esk43_3 @ X806 @ X807 @ X814))|~(X807 @ X814))|(~(X806 @ (esk39_2 @ X806 @ X807))|~(X807 @ (esk40_2 @ X806 @ X807))))&(~(X806 @ X817)|((esk44_2 @ X806 @ X807)=(X817))|((X807 @ (esk43_3 @ X806 @ X807 @ X814))|~(X807 @ X814))|(~(X806 @ (esk39_2 @ X806 @ X807))|~(X807 @ (esk40_2 @ X806 @ X807)))))&(((X806 @ (esk44_2 @ X806 @ X807))|(((X814)!=(esk43_3 @ X806 @ X807 @ X814))|~(X807 @ X814))|(~(X806 @ (esk39_2 @ X806 @ X807))|~(X807 @ (esk40_2 @ X806 @ X807))))&(~(X806 @ X817)|((esk44_2 @ X806 @ X807)=(X817))|(((X814)!=(esk43_3 @ X806 @ X807 @ X814))|~(X807 @ X814))|(~(X806 @ (esk39_2 @ X806 @ X807))|~(X807 @ (esk40_2 @ X806 @ X807)))))))&(((((X807 @ (esk42_2 @ X806 @ X807))|((X806 @ (esk41_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((X806 @ (esk39_2 @ X806 @ X807))|(X807 @ (esk40_2 @ X806 @ X807))))&(~(X807 @ X813)|((esk42_2 @ X806 @ X807)=(X813))|((X806 @ (esk41_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((X806 @ (esk39_2 @ X806 @ X807))|(X807 @ (esk40_2 @ X806 @ X807)))))&(((X807 @ (esk42_2 @ X806 @ X807))|(((X810)!=(esk41_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((X806 @ (esk39_2 @ X806 @ X807))|(X807 @ (esk40_2 @ X806 @ X807))))&(~(X807 @ X813)|((esk42_2 @ X806 @ X807)=(X813))|(((X810)!=(esk41_3 @ X806 @ X807 @ X810))|~(X806 @ X810))|((X806 @ (esk39_2 @ X806 @ X807))|(X807 @ (esk40_2 @ X806 @ X807))))))&((((X806 @ (esk44_2 @ X806 @ X807))|((X807 @ (esk43_3 @ X806 @ X807 @ X814))|~(X807 @ X814))|((X806 @ (esk39_2 @ X806 @ X807))|(X807 @ (esk40_2 @ X806 @ X807))))&(~(X806 @ X817)|((esk44_2 @ X806 @ X807)=(X817))|((X807 @ (esk43_3 @ X806 @ X807 @ X814))|~(X807 @ X814))|((X806 @ (esk39_2 @ X806 @ X807))|(X807 @ (esk40_2 @ X806 @ X807)))))&(((X806 @ (esk44_2 @ X806 @ X807))|(((X814)!=(esk43_3 @ X806 @ X807 @ X814))|~(X807 @ X814))|((X806 @ (esk39_2 @ X806 @ X807))|(X807 @ (esk40_2 @ X806 @ X807))))&(~(X806 @ X817)|((esk44_2 @ X806 @ X807)=(X817))|(((X814)!=(esk43_3 @ X806 @ X807 @ X814))|~(X807 @ X814))|((X806 @ (esk39_2 @ X806 @ X807))|(X807 @ (esk40_2 @ X806 @ X807)))))))))&(((emptyset)=(emptyset))&((((X818)!=(X819))|(((X820)!=(X821))|((setadjoin @ X818 @ X820)=(setadjoin @ X819 @ X821))))&((((X822)!=(X823))|((powerset @ X822)=(powerset @ X823)))&((((X824)!=(X825))|((setunion @ X824)=(setunion @ X825)))&(((omega)=(omega))&((((X826 @ (esk45_2 @ X826 @ X827))|~(X826 @ X827)|(~(X826 @ X829)|(~(X826 @ X830)|((X829)=(X830)))))&(((X827)!=(esk45_2 @ X826 @ X827))|~(X826 @ X827)|(~(X826 @ X829)|(~(X826 @ X830)|((X829)=(X830))))))&((((((X832 @ (esk49_3 @ X831 @ X832 @ X837))|~(X832 @ X837)|((descr @ X831)=(descr @ X832))|((X831 @ (esk48_3 @ X831 @ X832 @ X835))|~(X831 @ X835))|((esk46_2 @ X831 @ X832)=(esk47_2 @ X831 @ X832)))&(((X837)!=(esk49_3 @ X831 @ X832 @ X837))|~(X832 @ X837)|((descr @ X831)=(descr @ X832))|((X831 @ (esk48_3 @ X831 @ X832 @ X835))|~(X831 @ X835))|((esk46_2 @ X831 @ X832)=(esk47_2 @ X831 @ X832))))&(((X832 @ (esk49_3 @ X831 @ X832 @ X837))|~(X832 @ X837)|((descr @ X831)=(descr @ X832))|(((X835)!=(esk48_3 @ X831 @ X832 @ X835))|~(X831 @ X835))|((esk46_2 @ X831 @ X832)=(esk47_2 @ X831 @ X832)))&(((X837)!=(esk49_3 @ X831 @ X832 @ X837))|~(X832 @ X837)|((descr @ X831)=(descr @ X832))|(((X835)!=(esk48_3 @ X831 @ X832 @ X835))|~(X831 @ X835))|((esk46_2 @ X831 @ X832)=(esk47_2 @ X831 @ X832)))))&(((((X832 @ (esk49_3 @ X831 @ X832 @ X837))|~(X832 @ X837)|((descr @ X831)=(descr @ X832))|((X831 @ (esk48_3 @ X831 @ X832 @ X835))|~(X831 @ X835))|(~(X831 @ (esk46_2 @ X831 @ X832))|~(X832 @ (esk47_2 @ X831 @ X832))))&(((X837)!=(esk49_3 @ X831 @ X832 @ X837))|~(X832 @ X837)|((descr @ X831)=(descr @ X832))|((X831 @ (esk48_3 @ X831 @ X832 @ X835))|~(X831 @ X835))|(~(X831 @ (esk46_2 @ X831 @ X832))|~(X832 @ (esk47_2 @ X831 @ X832)))))&(((X832 @ (esk49_3 @ X831 @ X832 @ X837))|~(X832 @ X837)|((descr @ X831)=(descr @ X832))|(((X835)!=(esk48_3 @ X831 @ X832 @ X835))|~(X831 @ X835))|(~(X831 @ (esk46_2 @ X831 @ X832))|~(X832 @ (esk47_2 @ X831 @ X832))))&(((X837)!=(esk49_3 @ X831 @ X832 @ X837))|~(X832 @ X837)|((descr @ X831)=(descr @ X832))|(((X835)!=(esk48_3 @ X831 @ X832 @ X835))|~(X831 @ X835))|(~(X831 @ (esk46_2 @ X831 @ X832))|~(X832 @ (esk47_2 @ X831 @ X832))))))&((((X832 @ (esk49_3 @ X831 @ X832 @ X837))|~(X832 @ X837)|((descr @ X831)=(descr @ X832))|((X831 @ (esk48_3 @ X831 @ X832 @ X835))|~(X831 @ X835))|((X831 @ (esk46_2 @ X831 @ X832))|(X832 @ (esk47_2 @ X831 @ X832))))&(((X837)!=(esk49_3 @ X831 @ X832 @ X837))|~(X832 @ X837)|((descr @ X831)=(descr @ X832))|((X831 @ (esk48_3 @ X831 @ X832 @ X835))|~(X831 @ X835))|((X831 @ (esk46_2 @ X831 @ X832))|(X832 @ (esk47_2 @ X831 @ X832)))))&(((X832 @ (esk49_3 @ X831 @ X832 @ X837))|~(X832 @ X837)|((descr @ X831)=(descr @ X832))|(((X835)!=(esk48_3 @ X831 @ X832 @ X835))|~(X831 @ X835))|((X831 @ (esk46_2 @ X831 @ X832))|(X832 @ (esk47_2 @ X831 @ X832))))&(((X837)!=(esk49_3 @ X831 @ X832 @ X837))|~(X832 @ X837)|((descr @ X831)=(descr @ X832))|(((X835)!=(esk48_3 @ X831 @ X832 @ X835))|~(X831 @ X835))|((X831 @ (esk46_2 @ X831 @ X832))|(X832 @ (esk47_2 @ X831 @ X832))))))))&((((in @ (esk50_4 @ X839 @ X840 @ X841 @ X842) @ X839)|((dsetconstr @ X839 @ X841)=(dsetconstr @ X840 @ X842))|((X839)!=(X840)))&(((in @ (esk51_4 @ X839 @ X840 @ X841 @ X842) @ X840)|((dsetconstr @ X839 @ X841)=(dsetconstr @ X840 @ X842))|((X839)!=(X840)))&((((esk50_4 @ X839 @ X840 @ X841 @ X842)=(esk51_4 @ X839 @ X840 @ X841 @ X842))|((dsetconstr @ X839 @ X841)=(dsetconstr @ X840 @ X842))|((X839)!=(X840)))&((~(X841 @ (esk50_4 @ X839 @ X840 @ X841 @ X842))|~(X842 @ (esk51_4 @ X839 @ X840 @ X841 @ X842))|((dsetconstr @ X839 @ X841)=(dsetconstr @ X840 @ X842))|((X839)!=(X840)))&((X841 @ (esk50_4 @ X839 @ X840 @ X841 @ X842))|(X842 @ (esk51_4 @ X839 @ X840 @ X841 @ X842))|((dsetconstr @ X839 @ X841)=(dsetconstr @ X840 @ X842))|((X839)!=(X840)))))))&((((in @ (esk52_2 @ X845 @ X846) @ X845)|(subset @ X845 @ X846))&(~(in @ (esk52_2 @ X845 @ X846) @ X846)|(subset @ X845 @ X846)))&((((X848)!=(X849))|(subset @ X849 @ X848))&((((X850)!=(X851))|(subset @ X850 @ X851))&((((in @ (esk53_2 @ X852 @ X853) @ X852)|(subset @ X852 @ X853))&(~(in @ (esk53_2 @ X852 @ X853) @ X853)|(subset @ X852 @ X853)))&((subset @ emptyset @ X855)&((~(subset @ X856 @ X857)|(~(in @ X858 @ X856)|(in @ X858 @ X857)))&((~(subset @ X859 @ X860)|((in @ X861 @ X860)|~(in @ X861 @ X859)))&((~(in @ X864 @ X862)|((in @ X864 @ X863)|~(subset @ X862 @ X863)))&(((subset @ X865 @ X866)|((X865)!=(X866)))&((~(in @ X869 @ X867)|((in @ X869 @ X868)|((X867)!=(X868))))&((subset @ X870 @ X870)&((~(subset @ X871 @ X872)|(~(subset @ X872 @ X873)|(subset @ X871 @ X873)))&((subset @ X875 @ (setadjoin @ X874 @ X875))&((~(subset @ X876 @ X878)|(subset @ X876 @ (setadjoin @ X877 @ X878)))&((~(subset @ X879 @ X880)|(in @ X879 @ (powerset @ X880)))&((~(subset @ X881 @ X882)|(~(subset @ X882 @ X881)|((X881)=(X882))))&((~(subset @ X883 @ emptyset)|((X883)=(emptyset)))&((~(subset @ X885 @ X884)|(in @ X885 @ (powerset @ X884)))&((~(in @ X887 @ (powerset @ X886))|(subset @ X887 @ X886))&((in @ X888 @ (powerset @ X888))&((~(subset @ X889 @ X890)|(subset @ (powerset @ X889) @ (powerset @ X890)))&((in @ (dsetconstr @ X891 @ X892) @ (powerset @ X891))&((subset @ (dsetconstr @ X893 @ X894) @ X893)&((~(in @ X897 @ X895)|(in @ X897 @ (binunion @ X895 @ X896)))&~(in @ esk55_0 @ (setadjoin @ esk54_0 @ (setadjoin @ esk55_0 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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_144])])])])])])])).
% 0.22/0.31  thf(c_0_146, negated_conjecture, ~((in @ esk55_0 @ (setadjoin @ esk54_0 @ (setadjoin @ esk55_0 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 0.22/0.31  thf(c_0_147, negated_conjecture, ![X3:$i, X2:$i]:((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 0.22/0.31  thf(c_0_148, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146, c_0_147])]), ['proof']).
% 0.22/0.31  % SZS output end CNFRefutation
% 0.22/0.31  % Parsed axioms                        : 218
% 0.22/0.31  % Removed by relevancy pruning/SinE    : 0
% 0.22/0.31  % Initial clauses                      : 326
% 0.22/0.31  % Removed in clause preprocessing      : 130
% 0.22/0.31  % Initial clauses in saturation        : 196
% 0.22/0.31  % Processed clauses                    : 51
% 0.22/0.31  % ...of these trivial                  : 4
% 0.22/0.31  % ...subsumed                          : 8
% 0.22/0.31  % ...remaining for further processing  : 38
% 0.22/0.31  % Other redundant clauses eliminated   : 5
% 0.22/0.31  % Clauses deleted for lack of memory   : 0
% 0.22/0.31  % Backward-subsumed                    : 0
% 0.22/0.31  % Backward-rewritten                   : 2
% 0.22/0.31  % Generated clauses                    : 43
% 0.22/0.31  % ...of the previous two non-redundant : 27
% 0.22/0.31  % ...aggressively subsumed             : 0
% 0.22/0.31  % Contextual simplify-reflections      : 0
% 0.22/0.31  % Paramodulations                      : 38
% 0.22/0.31  % Factorizations                       : 0
% 0.22/0.31  % NegExts                              : 0
% 0.22/0.31  % Equation resolutions                 : 5
% 0.22/0.31  % Disequality decompositions           : 0
% 0.22/0.31  % Total rewrite steps                  : 23
% 0.22/0.31  % ...of those cached                   : 8
% 0.22/0.31  % Propositional unsat checks           : 0
% 0.22/0.31  %    Propositional check models        : 0
% 0.22/0.31  %    Propositional check unsatisfiable : 0
% 0.22/0.31  %    Propositional clauses             : 0
% 0.22/0.31  %    Propositional clauses after purity: 0
% 0.22/0.31  %    Propositional unsat core size     : 0
% 0.22/0.31  %    Propositional preprocessing time  : 0.000
% 0.22/0.31  %    Propositional encoding time       : 0.000
% 0.22/0.31  %    Propositional solver time         : 0.000
% 0.22/0.31  %    Success case prop preproc time    : 0.000
% 0.22/0.31  %    Success case prop encoding time   : 0.000
% 0.22/0.31  %    Success case prop solver time     : 0.000
% 0.22/0.31  % Current number of processed clauses  : 31
% 0.22/0.31  %    Positive orientable unit clauses  : 21
% 0.22/0.31  %    Positive unorientable unit clauses: 0
% 0.22/0.31  %    Negative unit clauses             : 1
% 0.22/0.31  %    Non-unit-clauses                  : 9
% 0.22/0.31  % Current number of unprocessed clauses: 172
% 0.22/0.31  % ...number of literals in the above   : 635
% 0.22/0.31  % Current number of archived formulas  : 0
% 0.22/0.31  % Current number of archived clauses   : 3
% 0.22/0.31  % Clause-clause subsumption calls (NU) : 6
% 0.22/0.31  % Rec. Clause-clause subsumption calls : 6
% 0.22/0.31  % Non-unit clause-clause subsumptions  : 1
% 0.22/0.31  % Unit Clause-clause subsumption calls : 4
% 0.22/0.31  % Rewrite failures with RHS unbound    : 0
% 0.22/0.31  % BW rewrite match attempts            : 4
% 0.22/0.31  % BW rewrite match successes           : 2
% 0.22/0.31  % Condensation attempts                : 0
% 0.22/0.31  % Condensation successes               : 0
% 0.22/0.31  % Termbank termtop insertions          : 27806
% 0.22/0.31  % Search garbage collected termcells   : 10626
% 0.22/0.31  
% 0.22/0.31  % -------------------------------------------------
% 0.22/0.31  % User time                : 0.019 s
% 0.22/0.31  % System time              : 0.005 s
% 0.22/0.31  % Total time               : 0.023 s
% 0.22/0.31  % Maximum resident set size: 6404 pages
% 0.22/0.31  
% 0.22/0.31  % -------------------------------------------------
% 0.22/0.31  % User time                : 0.024 s
% 0.22/0.31  % System time              : 0.010 s
% 0.22/0.31  % Total time               : 0.034 s
% 0.22/0.31  % Maximum resident set size: 5120 pages
% 0.22/0.31  % E exiting
%------------------------------------------------------------------------------