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

%------------------------------------------------------------------------------
% File     : E-SAT---3.5.1
% Problem  : SEU582^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n009.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 0.23s 0.34s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEU582^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18  % Computer : n009.cluster.edu
% 0.07/0.18  % Model    : x86_64 x86_64
% 0.07/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18  % Memory   : 8046.5625MB
% 0.07/0.18  % OS       : Linux 6.8.0-71-generic
% 0.07/0.18  % CPULimit : 300
% 0.07/0.18  % WCLimit  : 300
% 0.07/0.18  % DateTime : Tue Sep 29 13:52:30 UTC 2026
% 0.07/0.18  % CPUTime  : 
% 0.07/0.18  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22  Running higher-order theorem proving
% 0.07/0.25  Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p
% 0.23/0.34  % Version: 3.5.1-ho
% 0.23/0.34  % Preprocessing class: HSMMSLSSLLLCHFA.
% 0.23/0.34  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.34  % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.23/0.34  % Starting ehoh_best3_rw with 300s (1) cores
% 0.23/0.34  % Starting almost_fo_3 with 300s (1) cores
% 0.23/0.34  % Starting new_ho_13 with 300s (1) cores
% 0.23/0.34  % ehoh_best3_avoidappvar with pid 4033496 completed with status 0
% 0.23/0.34  % Result found by ehoh_best3_avoidappvar
% 0.23/0.34  % Preprocessing class: HSMMSLSSLLLCHFA.
% 0.23/0.34  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.34  % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.23/0.34  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.34  % No SInE strategy applied
% 0.23/0.34  % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.23/0.34  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.34  % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.34  % Starting ehoh_best3_avoidappvar with 151s (1) cores
% 0.23/0.34  % Starting additional_ho_1 with 136s (1) cores
% 0.23/0.34  % Starting ho_unfolding_7 with 136s (1) cores
% 0.23/0.34  % Starting lpo8_s with 136s (1) cores
% 0.23/0.34  % ehoh_best3_avoidappvar with pid 4033502 completed with status 0
% 0.23/0.34  % Result found by ehoh_best3_avoidappvar
% 0.23/0.34  % Preprocessing class: HSMMSLSSLLLCHFA.
% 0.23/0.34  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.34  % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.23/0.34  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.34  % No SInE strategy applied
% 0.23/0.34  % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.23/0.34  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.34  % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.34  % Starting ehoh_best3_avoidappvar with 151s (1) cores
% 0.23/0.34  % Preprocessing time       : 0.004 s
% 0.23/0.34  % Presaturation interreduction done
% 0.23/0.34  
% 0.23/0.34  % Proof found!
% 0.23/0.34  % SZS status Theorem
% 0.23/0.34  % SZS output start CNFRefutation
% 0.23/0.34  thf(decl_23, type, in: $i > $i > $o).
% 0.23/0.34  thf(decl_24, type, exu: ($i > $o) > $o).
% 0.23/0.34  thf(decl_25, type, setextAx: $o).
% 0.23/0.34  thf(decl_26, type, emptyset: $i).
% 0.23/0.34  thf(decl_27, type, emptysetAx: $o).
% 0.23/0.34  thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.23/0.34  thf(decl_29, type, setadjoinAx: $o).
% 0.23/0.34  thf(decl_30, type, powerset: $i > $i).
% 0.23/0.34  thf(decl_31, type, powersetAx: $o).
% 0.23/0.34  thf(decl_32, type, setunion: $i > $i).
% 0.23/0.34  thf(decl_33, type, setunionAx: $o).
% 0.23/0.34  thf(decl_34, type, omega: $i).
% 0.23/0.34  thf(decl_35, type, omega0Ax: $o).
% 0.23/0.34  thf(decl_36, type, omegaSAx: $o).
% 0.23/0.34  thf(decl_37, type, omegaIndAx: $o).
% 0.23/0.34  thf(decl_38, type, replAx: $o).
% 0.23/0.34  thf(decl_39, type, foundationAx: $o).
% 0.23/0.34  thf(decl_40, type, wellorderingAx: $o).
% 0.23/0.34  thf(decl_41, type, descr: ($i > $o) > $i).
% 0.23/0.34  thf(decl_42, type, descrp: $o).
% 0.23/0.34  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.23/0.34  thf(decl_44, type, dsetconstrI: $o).
% 0.23/0.34  thf(decl_45, type, dsetconstrEL: $o).
% 0.23/0.34  thf(decl_46, type, dsetconstrER: $o).
% 0.23/0.34  thf(decl_47, type, exuE1: $o).
% 0.23/0.34  thf(decl_48, type, prop2set: $o > $i).
% 0.23/0.34  thf(decl_49, type, prop2setE: $o).
% 0.23/0.34  thf(decl_50, type, emptysetE: $o).
% 0.23/0.34  thf(decl_51, type, emptysetimpfalse: $o).
% 0.23/0.34  thf(decl_52, type, notinemptyset: $o).
% 0.23/0.34  thf(decl_53, type, exuE3e: $o).
% 0.23/0.34  thf(decl_54, type, setext: $o).
% 0.23/0.34  thf(decl_55, type, emptyI: $o).
% 0.23/0.34  thf(decl_56, type, noeltsimpempty: $o).
% 0.23/0.34  thf(decl_57, type, setbeta: $o).
% 0.23/0.34  thf(decl_58, type, nonempty: $i > $o).
% 0.23/0.34  thf(decl_59, type, nonemptyE1: $o).
% 0.23/0.34  thf(decl_60, type, nonemptyI: $o).
% 0.23/0.34  thf(decl_61, type, nonemptyI1: $o).
% 0.23/0.34  thf(decl_62, type, setadjoinIL: $o).
% 0.23/0.34  thf(decl_63, type, emptyinunitempty: $o).
% 0.23/0.34  thf(decl_64, type, setadjoinIR: $o).
% 0.23/0.34  thf(decl_65, type, setadjoinE: $o).
% 0.23/0.34  thf(decl_66, type, setadjoinOr: $o).
% 0.23/0.34  thf(decl_67, type, setoftrueEq: $o).
% 0.23/0.34  thf(decl_68, type, powersetI: $o).
% 0.23/0.34  thf(decl_69, type, emptyinPowerset: $o).
% 0.23/0.34  thf(decl_70, type, emptyInPowerset: $o).
% 0.23/0.34  thf(decl_71, type, powersetE: $o).
% 0.23/0.34  thf(decl_72, type, setunionI: $o).
% 0.23/0.34  thf(decl_73, type, setunionE: $o).
% 0.23/0.34  thf(decl_74, type, subPowSU: $o).
% 0.23/0.34  thf(decl_75, type, exuE2: $o).
% 0.23/0.34  thf(decl_76, type, nonemptyImpWitness: $o).
% 0.23/0.34  thf(decl_77, type, uniqinunit: $o).
% 0.23/0.34  thf(decl_78, type, notinsingleton: $o).
% 0.23/0.34  thf(decl_79, type, eqinunit: $o).
% 0.23/0.34  thf(decl_80, type, singletonsswitch: $o).
% 0.23/0.34  thf(decl_81, type, upairsetE: $o).
% 0.23/0.34  thf(decl_82, type, upairsetIL: $o).
% 0.23/0.34  thf(decl_83, type, upairsetIR: $o).
% 0.23/0.34  thf(decl_84, type, emptyE1: $o).
% 0.23/0.34  thf(decl_85, type, vacuousDall: $o).
% 0.23/0.34  thf(decl_86, type, quantDeMorgan1: $o).
% 0.23/0.34  thf(decl_87, type, quantDeMorgan2: $o).
% 0.23/0.34  thf(decl_88, type, quantDeMorgan3: $o).
% 0.23/0.34  thf(decl_89, type, quantDeMorgan4: $o).
% 0.23/0.34  thf(decl_90, type, prop2setI: $o).
% 0.23/0.34  thf(decl_91, type, set2prop: $i > $o).
% 0.23/0.34  thf(decl_92, type, prop2set2propI: $o).
% 0.23/0.34  thf(decl_93, type, notdexE: $o).
% 0.23/0.34  thf(decl_94, type, notdallE: $o).
% 0.23/0.34  thf(decl_95, type, exuI1: $o).
% 0.23/0.34  thf(decl_96, type, exuI3: $o).
% 0.23/0.34  thf(decl_97, type, exuI2: $o).
% 0.23/0.34  thf(decl_98, type, inCongP: $o).
% 0.23/0.34  thf(decl_99, type, in__Cong: $o).
% 0.23/0.34  thf(decl_100, type, exuE3u: $o).
% 0.23/0.34  thf(decl_101, type, exu__Cong: $o).
% 0.23/0.34  thf(decl_102, type, emptyset__Cong: $o).
% 0.23/0.34  thf(decl_103, type, setadjoin__Cong: $o).
% 0.23/0.34  thf(decl_104, type, powerset__Cong: $o).
% 0.23/0.34  thf(decl_105, type, setunion__Cong: $o).
% 0.23/0.34  thf(decl_106, type, omega__Cong: $o).
% 0.23/0.34  thf(decl_107, type, exuEu: $o).
% 0.23/0.34  thf(decl_108, type, descr__Cong: $o).
% 0.23/0.34  thf(decl_109, type, dsetconstr__Cong: $o).
% 0.23/0.34  thf(decl_110, type, subset: $i > $i > $o).
% 0.23/0.34  thf(decl_113, type, subsetI1: $o).
% 0.23/0.34  thf(decl_114, type, eqimpsubset2: $o).
% 0.23/0.34  thf(decl_115, type, eqimpsubset1: $o).
% 0.23/0.34  thf(decl_116, type, subsetI2: $o).
% 0.23/0.34  thf(decl_117, type, emptysetsubset: $o).
% 0.23/0.34  thf(decl_118, type, subsetE: $o).
% 0.23/0.34  thf(decl_119, type, subsetE2: $o).
% 0.23/0.34  thf(decl_120, type, notsubsetI: $o).
% 0.23/0.34  thf(decl_121, type, notequalI1: $o).
% 0.23/0.34  thf(decl_122, type, notequalI2: $o).
% 0.23/0.34  thf(decl_123, type, subsetRefl: $o).
% 0.23/0.34  thf(decl_124, type, subsetTrans: $o).
% 0.23/0.34  thf(decl_125, type, setadjoinSub: $o).
% 0.23/0.34  thf(decl_126, type, setadjoinSub2: $o).
% 0.23/0.34  thf(decl_127, type, subset2powerset: $o).
% 0.23/0.34  thf(decl_128, type, setextsub: $o).
% 0.23/0.34  thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.23/0.34  thf(decl_130, type, powersetI1: $o).
% 0.23/0.34  thf(decl_131, type, powersetE1: $o).
% 0.23/0.34  thf(decl_132, type, inPowerset: $o).
% 0.23/0.34  thf(decl_133, type, powersetsubset: $o).
% 0.23/0.34  thf(decl_134, type, sepInPowerset: $o).
% 0.23/0.34  thf(decl_135, type, sepSubset: $o).
% 0.23/0.34  thf(decl_136, type, binunion: $i > $i > $i).
% 0.23/0.34  thf(decl_137, type, epred1_0: $o).
% 0.23/0.34  thf(decl_138, type, esk1_2: $i > $i > $i).
% 0.23/0.34  thf(decl_139, type, esk2_2: $i > $i > $i).
% 0.23/0.34  thf(decl_140, type, esk3_2: $i > $i > $i).
% 0.23/0.34  thf(decl_141, type, esk4_1: $i > $i).
% 0.23/0.34  thf(decl_142, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.23/0.34  thf(decl_143, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.34  thf(decl_144, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.23/0.34  thf(decl_145, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.34  thf(decl_146, type, esk9_1: $i > $i).
% 0.23/0.34  thf(decl_147, type, esk10_2: ($i > $o) > $i > $i).
% 0.23/0.34  thf(decl_148, type, esk11_2: ($i > $o) > $i > $i).
% 0.23/0.34  thf(decl_149, type, esk12_1: ($i > $o) > $i).
% 0.23/0.34  thf(decl_150, type, esk13_2: ($i > $o) > $i > $i).
% 0.23/0.34  thf(decl_151, type, esk14_1: ($i > $o) > $i).
% 0.23/0.34  thf(decl_152, type, esk15_2: $i > $i > $i).
% 0.23/0.34  thf(decl_153, type, esk16_2: $i > $i > $i).
% 0.23/0.34  thf(decl_154, type, esk17_1: $i > $i).
% 0.23/0.34  thf(decl_155, type, esk18_1: $i > $i).
% 0.23/0.34  thf(decl_156, type, esk19_1: $i > $i).
% 0.23/0.34  thf(decl_157, type, esk20_2: $i > $i > $i).
% 0.23/0.34  thf(decl_158, type, esk21_3: $i > $i > $o > $i).
% 0.23/0.34  thf(decl_159, type, esk22_2: ($i > $o) > $i > $i).
% 0.23/0.34  thf(decl_160, type, esk23_1: ($i > $o) > $i).
% 0.23/0.34  thf(decl_161, type, esk24_1: $i > $i).
% 0.23/0.34  thf(decl_162, type, esk25_2: $i > ($i > $o) > $i).
% 0.23/0.34  thf(decl_163, type, esk26_2: $i > ($i > $o) > $i).
% 0.23/0.34  thf(decl_164, type, esk27_2: $i > ($i > $o) > $i).
% 0.23/0.34  thf(decl_165, type, esk28_2: $i > ($i > $o) > $i).
% 0.23/0.34  thf(decl_166, type, esk29_2: $i > ($i > $o) > $i).
% 0.23/0.34  thf(decl_167, type, esk30_2: $i > ($i > $o) > $i).
% 0.23/0.34  thf(decl_168, type, esk31_2: ($i > $o) > $i > $i).
% 0.23/0.34  thf(decl_169, type, esk32_1: ($i > $o) > $i).
% 0.23/0.34  thf(decl_170, type, esk33_1: ($i > $o) > $i).
% 0.23/0.34  thf(decl_171, type, esk34_1: ($i > $o) > $i).
% 0.23/0.34  thf(decl_172, type, esk35_1: ($i > $o) > $i).
% 0.23/0.34  thf(decl_173, type, esk36_2: ($i > $o) > $i > $i).
% 0.23/0.34  thf(decl_174, type, esk37_1: ($i > $o) > $i).
% 0.23/0.34  thf(decl_175, type, esk38_2: ($i > $o) > $i > $i).
% 0.23/0.34  thf(decl_176, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.34  thf(decl_177, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.34  thf(decl_178, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.34  thf(decl_179, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.34  thf(decl_180, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.34  thf(decl_181, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.34  thf(decl_182, type, esk45_2: ($i > $o) > $i > $i).
% 0.23/0.34  thf(decl_183, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.34  thf(decl_184, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.34  thf(decl_185, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.34  thf(decl_186, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.34  thf(decl_187, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.23/0.34  thf(decl_188, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.23/0.34  thf(decl_189, type, esk52_2: $i > $i > $i).
% 0.23/0.34  thf(decl_190, type, esk53_2: $i > $i > $i).
% 0.23/0.34  thf(decl_191, type, esk54_0: $i).
% 0.23/0.34  thf(decl_192, type, esk55_0: $i).
% 0.23/0.34  thf(decl_193, type, esk56_0: $i).
% 0.23/0.34  thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', replAx)).
% 0.23/0.34  thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', exu)).
% 0.23/0.34  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', descrp)).
% 0.23/0.34  thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', exuE1)).
% 0.23/0.34  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', exuE3e)).
% 0.23/0.34  thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', nonempty)).
% 0.23/0.34  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', nonemptyI)).
% 0.23/0.34  thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', exuE2)).
% 0.23/0.34  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/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', exuI1)).
% 0.23/0.34  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', exuI3)).
% 0.23/0.34  thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', exuI2)).
% 0.23/0.34  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/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', exuE3u)).
% 0.23/0.34  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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', exu__Cong)).
% 0.23/0.34  thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', exuEu)).
% 0.23/0.34  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', descr__Cong)).
% 0.23/0.34  thf(binunionIL, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', binunionIL)).
% 0.23/0.34  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', dsetconstrI)).
% 0.23/0.34  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', dsetconstrEL)).
% 0.23/0.34  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', dsetconstrER)).
% 0.23/0.34  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setbeta)).
% 0.23/0.34  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', nonemptyE1)).
% 0.23/0.34  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', nonemptyI1)).
% 0.23/0.34  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setoftrueEq)).
% 0.23/0.34  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', nonemptyImpWitness)).
% 0.23/0.34  thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', emptyE1)).
% 0.23/0.34  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', dsetconstr__Cong)).
% 0.23/0.34  thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', sepInPowerset)).
% 0.23/0.34  thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', sepSubset)).
% 0.23/0.34  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setextAx)).
% 0.23/0.34  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', emptysetAx)).
% 0.23/0.34  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setadjoinAx)).
% 0.23/0.34  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', powersetAx)).
% 0.23/0.34  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setunionAx)).
% 0.23/0.34  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', omega0Ax)).
% 0.23/0.34  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', omegaSAx)).
% 0.23/0.34  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', omegaIndAx)).
% 0.23/0.34  thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', foundationAx)).
% 0.23/0.34  thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', wellorderingAx)).
% 0.23/0.34  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', prop2setE)).
% 0.23/0.34  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', emptysetE)).
% 0.23/0.34  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', emptysetimpfalse)).
% 0.23/0.34  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', notinemptyset)).
% 0.23/0.34  thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setext)).
% 0.23/0.34  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', emptyI)).
% 0.23/0.34  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', noeltsimpempty)).
% 0.23/0.34  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setadjoinIL)).
% 0.23/0.34  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', emptyinunitempty)).
% 0.23/0.34  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setadjoinIR)).
% 0.23/0.34  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/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setadjoinE)).
% 0.23/0.34  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setadjoinOr)).
% 0.23/0.34  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', powersetI)).
% 0.23/0.34  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', emptyinPowerset)).
% 0.23/0.34  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', emptyInPowerset)).
% 0.23/0.34  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', powersetE)).
% 0.23/0.34  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setunionI)).
% 0.23/0.34  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/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setunionE)).
% 0.23/0.34  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', subPowSU)).
% 0.23/0.34  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', uniqinunit)).
% 0.23/0.34  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', notinsingleton)).
% 0.23/0.34  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', eqinunit)).
% 0.23/0.34  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', singletonsswitch)).
% 0.23/0.34  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', upairsetE)).
% 0.23/0.34  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', upairsetIL)).
% 0.23/0.34  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', upairsetIR)).
% 0.23/0.34  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', vacuousDall)).
% 0.23/0.34  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', quantDeMorgan1)).
% 0.23/0.34  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', quantDeMorgan2)).
% 0.23/0.34  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', quantDeMorgan3)).
% 0.23/0.34  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', quantDeMorgan4)).
% 0.23/0.34  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', prop2setI)).
% 0.23/0.34  thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', prop2set2propI)).
% 0.23/0.34  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', notdexE)).
% 0.23/0.34  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', notdallE)).
% 0.23/0.34  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', inCongP)).
% 0.23/0.34  thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', in__Cong)).
% 0.23/0.34  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', emptyset__Cong)).
% 0.23/0.34  thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setadjoin__Cong)).
% 0.23/0.34  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', powerset__Cong)).
% 0.23/0.34  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setunion__Cong)).
% 0.23/0.34  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', omega__Cong)).
% 0.23/0.34  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', subsetI1)).
% 0.23/0.34  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', eqimpsubset2)).
% 0.23/0.34  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', eqimpsubset1)).
% 0.23/0.34  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', subsetI2)).
% 0.23/0.34  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', emptysetsubset)).
% 0.23/0.34  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', subsetE)).
% 0.23/0.34  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', subsetE2)).
% 0.23/0.34  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', notsubsetI)).
% 0.23/0.34  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', notequalI1)).
% 0.23/0.34  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', notequalI2)).
% 0.23/0.34  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', subsetRefl)).
% 0.23/0.34  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', subsetTrans)).
% 0.23/0.34  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setadjoinSub)).
% 0.23/0.34  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setadjoinSub2)).
% 0.23/0.34  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', subset2powerset)).
% 0.23/0.34  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', setextsub)).
% 0.23/0.34  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', subsetemptysetimpeq)).
% 0.23/0.34  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', powersetI1)).
% 0.23/0.34  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', powersetE1)).
% 0.23/0.34  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', inPowerset)).
% 0.23/0.34  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', powersetsubset)).
% 0.23/0.34  thf(binunion, axiom, ((binunion)=(^[X2:$i, X3:$i]:(setunion @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.SaV8W7AEP1/E---3.1_4033467.p', binunion)).
% 0.23/0.34  thf(c_0_102, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.23/0.34  thf(c_0_103, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.23/0.34  thf(c_0_104, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.23/0.34  thf(c_0_105, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.23/0.34  thf(c_0_106, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.23/0.34  thf(c_0_107, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.23/0.34  thf(c_0_108, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.23/0.34  thf(c_0_109, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.23/0.34  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])).
% 0.23/0.34  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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.23/0.34  thf(c_0_112, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.23/0.34  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])).
% 0.23/0.34  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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.23/0.34  thf(c_0_115, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.23/0.34  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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.23/0.34  thf(c_0_117, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[binunionIL])).
% 0.23/0.34  thf(c_0_118, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X284:$i]:(((((X6 @ X2 @ X284)))&(![X285:$i]:(((((X6 @ X2 @ X285)))=>(((X284)=(X285)))))))))))))=>(?[X5:$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])).
% 0.23/0.34  thf(c_0_119, plain, ((descrp)=(![X1:$i > $o]:((((?[X286:$i]:(((((X1 @ X286)))&(![X287:$i]:(((((X1 @ X287)))=>(((X286)=(X287))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_104, c_0_103])).
% 0.23/0.34  thf(c_0_120, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.23/0.34  thf(c_0_121, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.23/0.34  thf(c_0_122, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.23/0.34  thf(c_0_123, plain, ((exuE1)=(![X1:$i > $o]:((((?[X288:$i]:(((((X1 @ X288)))&(![X289:$i]:(((((X1 @ X289)))=>(((X288)=(X289))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_105, c_0_103])).
% 0.23/0.34  thf(c_0_124, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X290:$i]:(((((X1 @ X290)))&(![X291:$i]:(((((X1 @ X291)))=>(((X290)=(X291))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_106, c_0_103])).
% 0.23/0.34  thf(c_0_125, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.23/0.34  thf(c_0_126, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_107])).
% 0.23/0.34  thf(c_0_127, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_108, c_0_107])).
% 0.23/0.34  thf(c_0_128, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_107])).
% 0.23/0.34  thf(c_0_129, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.23/0.34  thf(c_0_130, plain, ((exuE2)=(![X1:$i > $o]:((((?[X292:$i]:(((((X1 @ X292)))&(![X293:$i]:(((((X1 @ X293)))=>(((X292)=(X293))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_109, c_0_103])).
% 0.23/0.34  thf(c_0_131, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_107])).
% 0.23/0.34  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])).
% 0.23/0.34  thf(c_0_133, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X294:$i]:(((((X1 @ X294)))&(![X295:$i]:(((((X1 @ X295)))=>(((X294)=(X295)))))))))))))), inference(apply_def,[status(thm)],[c_0_110, c_0_103])).
% 0.23/0.34  thf(c_0_134, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X296:$i]:(((((X1 @ X296)))&(![X297:$i]:(((((X1 @ X297)))=>(((X296)=(X297)))))))))))))))), inference(apply_def,[status(thm)],[c_0_111, c_0_103])).
% 0.23/0.34  thf(c_0_135, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X298:$i]:(((((X1 @ X298)))&(![X299:$i]:(((((X1 @ X299)))=>(((X298)=(X299)))))))))))))), inference(apply_def,[status(thm)],[c_0_112, c_0_103])).
% 0.23/0.34  thf(c_0_136, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X300:$i]:(((((X1 @ X300)))&(![X301:$i]:(((((X1 @ X301)))=>(((X300)=(X301))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_113, c_0_103])).
% 0.23/0.34  thf(c_0_137, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X302:$i]:(((((X1 @ X302)))&(![X303:$i]:(((((X1 @ X303)))=>(((X302)=(X303))))))))))<=>((?[X304:$i]:(((((X17 @ X304)))&(![X305:$i]:(((((X17 @ X305)))=>(((X304)=(X305)))))))))))))))), inference(apply_def,[status(thm)],[c_0_114, c_0_103])).
% 0.23/0.34  thf(c_0_138, plain, ((exuEu)=(![X1:$i > $o]:((((?[X306:$i]:(((((X1 @ X306)))&(![X307:$i]:(((((X1 @ X307)))=>(((X306)=(X307))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_115, c_0_103])).
% 0.23/0.34  thf(c_0_139, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X308:$i]:(((((X1 @ X308)))&(![X309:$i]:(((((X1 @ X309)))=>(((X308)=(X309))))))))))=>((((?[X310:$i]:(((((X17 @ X310)))&(![X311:$i]:(((((X17 @ X311)))=>(((X310)=(X311))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_116, c_0_103])).
% 0.23/0.34  thf(c_0_140, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.23/0.34  thf(c_0_141, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.23/0.34  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])).
% 0.23/0.34  thf(c_0_143, plain, ((epred1_0)<=>![X341:$i]:(?[X342:$i]:((((![X343:$i]:(((in @ X343 @ X342)=>![X344:$i]:(((in @ X344 @ X343)=>(in @ X344 @ X341)))))&![X345:$i, X346:$i]:((((in @ X345 @ X341)&(in @ X346 @ X341))=>(![X347:$i]:(((in @ X347 @ X342)=>((in @ X345 @ X347)<=>(in @ X346 @ X347))))=>((X345)=(X346))))))&![X348:$i, X349:$i]:((((in @ X348 @ X342)&(in @ X349 @ X342))=>(![X350:$i]:(((in @ X350 @ X348)=>(in @ X350 @ X349)))|![X351:$i]:(((in @ X351 @ X349)=>(in @ X351 @ X348)))))))&![X352:$i]:(((![X353:$i]:(((in @ X353 @ X352)=>(in @ X353 @ X341)))&?[X354:$i]:((in @ X354 @ X352)))=>?[X355:$i, X356:$i]:(((((in @ X355 @ X342)&(in @ X356 @ X352))&~(?[X357:$i]:(((in @ X357 @ X355)&(in @ X357 @ X352)))))&![X358:$i]:(((in @ X358 @ X342)=>(![X359:$i]:(((in @ X359 @ X358)=>(in @ X359 @ X355)))|(in @ X356 @ X358)))))))))))), introduced(definition)).
% 0.23/0.34  thf(c_0_144, negated_conjecture, ~((![X312:$i, X313:$i]:((![X314:$i]:(((in @ X314 @ X312)<=>(in @ X314 @ X313)))=>((X312)=(X313))))=>(![X315:$i]:(~(in @ X315 @ emptyset))=>(![X316:$i, X317:$i, X318:$i]:(((in @ X318 @ (setadjoin @ X316 @ X317))<=>(((X318)=(X316))|(in @ X318 @ X317))))=>(![X319:$i, X320:$i]:(((in @ X320 @ (powerset @ X319))<=>![X321:$i]:(((in @ X321 @ X320)=>(in @ X321 @ X319)))))=>(![X322:$i, X323:$i]:(((in @ X323 @ (setunion @ X322))<=>?[X324:$i]:(((in @ X323 @ X324)&(in @ X324 @ X322)))))=>((in @ emptyset @ omega)=>(![X325:$i]:(((in @ X325 @ omega)=>(in @ (setadjoin @ X325 @ X325) @ omega)))=>(![X326:$i]:((((in @ emptyset @ X326)&![X327:$i]:((((in @ X327 @ omega)&(in @ X327 @ X326))=>(in @ (setadjoin @ X327 @ X327) @ X326))))=>![X328:$i]:(((in @ X328 @ omega)=>(in @ X328 @ X326)))))=>(![X329:$i > $i > $o, X330:$i]:((![X331:$i]:(((in @ X331 @ X330)=>?[X332:$i]:(((X329 @ X331 @ X332)&![X333:$i]:(((X329 @ X331 @ X333)=>((X332)=(X333))))))))=>?[X334:$i]:(![X335:$i]:(((in @ X335 @ X334)<=>?[X336:$i]:(((in @ X336 @ X330)&(X329 @ X336 @ X335))))))))=>(![X337:$i]:((?[X338:$i]:((in @ X338 @ X337))=>?[X339:$i]:(((in @ X339 @ X337)&~(?[X340:$i]:(((in @ X340 @ X339)&(in @ X340 @ X337))))))))=>((epred1_0)=>(![X360:$i > $o]:((?[X361:$i]:(((X360 @ X361)&![X362:$i]:(((X360 @ X362)=>((X361)=(X362))))))=>(X360 @ (descr @ (^[Z0:$i]:(X360 @ Z0))))))=>(![X363:$i, X364:$i > $o, X365:$i]:(((in @ X365 @ X363)=>((X364 @ X365)=>(in @ X365 @ (dsetconstr @ X363 @ X364)))))=>(![X366:$i, X367:$i > $o, X368:$i]:(((in @ X368 @ (dsetconstr @ X366 @ X367))=>(in @ X368 @ X366)))=>(![X369:$i, X370:$i > $o, X371:$i]:(((in @ X371 @ (dsetconstr @ X369 @ X370))=>(X370 @ X371)))=>(![X372:$i > $o]:((?[X373:$i]:(((X372 @ X373)&![X374:$i]:(((X372 @ X374)=>((X373)=(X374))))))=>?[X375:$i]:(((X372 @ X375)&![X376:$i]:(((X372 @ X376)=>((X375)=(X376))))))))=>(![X377:$o, X378:$i]:(((in @ X378 @ (prop2set @ ((X377))))=>(X377)))=>(![X379:$i]:(((in @ X379 @ emptyset)=>![X380:$o]:((X380))))=>(![X381:$i]:(((in @ X381 @ emptyset)=>~($true)))=>(![X382:$i]:(~(in @ X382 @ emptyset))=>(![X383:$i > $o]:((?[X384:$i]:(((X383 @ X384)&![X385:$i]:(((X383 @ X385)=>((X384)=(X385))))))=>?[X386:$i]:((X383 @ X386))))=>(![X387:$i, X388:$i]:((![X389:$i]:(((in @ X389 @ X387)=>(in @ X389 @ X388)))=>(![X390:$i]:(((in @ X390 @ X388)=>(in @ X390 @ X387)))=>((X387)=(X388)))))=>(![X391:$i]:((![X392:$i]:(~(in @ X392 @ X391))=>((X391)=(emptyset))))=>(![X393:$i]:((![X394:$i]:(~(in @ X394 @ X393))=>((X393)=(emptyset))))=>(![X395:$i, X396:$i > $o, X397:$i]:(((in @ X397 @ X395)=>((in @ X397 @ (dsetconstr @ X395 @ X396))<=>(X396 @ X397))))=>(![X398:$i]:((((X398)!=(emptyset))=>?[X399:$i]:((in @ X399 @ X398))))=>(![X400:$i, X401:$i > $o, X402:$i]:(((in @ X402 @ X400)=>((X401 @ X402)=>((dsetconstr @ X400 @ X401)!=(emptyset)))))=>(![X403:$i]:((?[X404:$i]:((in @ X404 @ X403))=>((X403)!=(emptyset))))=>(![X405:$i, X406:$i]:((in @ X405 @ (setadjoin @ X405 @ X406)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X407:$i, X408:$i, X409:$i]:(((in @ X409 @ X408)=>(in @ X409 @ (setadjoin @ X407 @ X408))))=>(![X410:$i, X411:$i, X412:$i]:(((in @ X412 @ (setadjoin @ X410 @ X411))=>![X413:$o]:(((((X412)=(X410))=>(X413))=>(((in @ X412 @ X411)=>(X413))=>(X413))))))=>(![X414:$i, X415:$i, X416:$i]:(((in @ X416 @ (setadjoin @ X414 @ X415))=>(((X416)=(X414))|(in @ X416 @ X415))))=>(![X417:$i]:(((dsetconstr @ X417 @ (^[Z0:$i]:($true)))=(X417)))=>(![X418:$i, X419:$i]:((![X420:$i]:(((in @ X420 @ X419)=>(in @ X420 @ X418)))=>(in @ X419 @ (powerset @ X418))))=>(![X421:$i]:((in @ emptyset @ (powerset @ X421)))=>(![X422:$i]:((in @ emptyset @ (powerset @ X422)))=>(![X423:$i, X424:$i, X425:$i]:(((in @ X424 @ (powerset @ X423))=>((in @ X425 @ X424)=>(in @ X425 @ X423))))=>(![X426:$i, X427:$i, X428:$i]:(((in @ X427 @ X428)=>((in @ X428 @ X426)=>(in @ X427 @ (setunion @ X426)))))=>(![X429:$i, X430:$i]:(((in @ X430 @ (setunion @ X429))=>![X431:$o]:((![X432:$i]:(((in @ X430 @ X432)=>((in @ X432 @ X429)=>(X431))))=>(X431)))))=>(![X433:$i, X434:$i]:(((in @ X434 @ X433)=>(in @ X434 @ (powerset @ (setunion @ X433)))))=>(![X435:$i > $o]:((?[X436:$i]:(((X435 @ X436)&![X437:$i]:(((X435 @ X437)=>((X436)=(X437))))))=>?[X438:$i]:(![X439:$i]:(((X435 @ X439)<=>((X439)=(X438)))))))=>(![X440:$i]:((((X440)!=(emptyset))=>?[X441:$i]:(((in @ X441 @ X440)&$true))))=>(![X442:$i, X443:$i]:(((in @ X442 @ (setadjoin @ X443 @ emptyset))=>((X442)=(X443))))=>(![X444:$i, X445:$i]:((((X444)!=(X445))=>~(in @ X445 @ (setadjoin @ X444 @ emptyset))))=>(![X446:$i, X447:$i]:((((X446)=(X447))=>(in @ X446 @ (setadjoin @ X447 @ emptyset))))=>(![X448:$i, X449:$i]:(((in @ X448 @ (setadjoin @ X449 @ emptyset))=>(in @ X449 @ (setadjoin @ X448 @ emptyset))))=>(![X450:$i, X451:$i, X452:$i]:(((in @ X452 @ (setadjoin @ X450 @ (setadjoin @ X451 @ emptyset)))=>(((X452)=(X450))|((X452)=(X451)))))=>(![X453:$i, X454:$i]:((in @ X453 @ (setadjoin @ X453 @ (setadjoin @ X454 @ emptyset))))=>(![X455:$i, X456:$i]:((in @ X456 @ (setadjoin @ X455 @ (setadjoin @ X456 @ emptyset))))=>(![X457:$i, X458:$i > $o]:((?[X459:$i]:(((in @ X459 @ X457)&(X458 @ X459)))=>(((dsetconstr @ X457 @ X458)=(emptyset))=>~($true))))=>(![X460:$i > $o, X461:$i]:(((in @ X461 @ emptyset)=>(X460 @ X461)))=>(![X462:$i, X463:$i > $o]:((~(![X464:$i]:(((in @ X464 @ X462)=>(X463 @ X464))))=>?[X465:$i]:(((in @ X465 @ X462)&~((X463 @ X465))))))=>(![X466:$i, X467:$i > $o]:((![X468:$i]:(((in @ X468 @ X466)=>~((X467 @ X468))))=>~(?[X469:$i]:(((in @ X469 @ X466)&(X467 @ X469))))))=>(![X470:$i, X471:$i > $o]:((~(?[X472:$i]:(((in @ X472 @ X470)&(X471 @ X472))))=>![X473:$i]:(((in @ X473 @ X470)=>~((X471 @ X473))))))=>(![X474:$i, X475:$i > $o]:((?[X476:$i]:(((in @ X476 @ X474)&~((X475 @ X476))))=>~(![X477:$i]:(((in @ X477 @ X474)=>(X475 @ X477))))))=>(![X478:$o]:(((X478)=>(in @ emptyset @ (prop2set @ ((X478))))))=>(![X479:$o]:(((X479)=>(set2prop @ (prop2set @ ((X479))))))=>(![X480:$i, X481:$i > $o]:((~(?[X482:$i]:(((in @ X482 @ X480)&(X481 @ X482))))=>![X483:$i]:(((in @ X483 @ X480)=>~((X481 @ X483))))))=>(![X484:$i, X485:$i > $o]:((~(![X486:$i]:(((in @ X486 @ X484)=>(X485 @ X486))))=>?[X487:$i]:(((in @ X487 @ X484)&~((X485 @ X487))))))=>(![X488:$i > $o]:((?[X489:$i]:(((X488 @ X489)&![X490:$i]:(((X488 @ X490)=>((X489)=(X490))))))=>?[X491:$i]:(((X488 @ X491)&![X492:$i]:(((X488 @ X492)=>((X491)=(X492))))))))=>(![X493:$i > $o]:((?[X494:$i]:((X493 @ X494))=>(![X495:$i, X496:$i]:(((X493 @ X495)=>((X493 @ X496)=>((X495)=(X496)))))=>?[X497:$i]:(((X493 @ X497)&![X498:$i]:(((X493 @ X498)=>((X497)=(X498)))))))))=>(![X499:$i > $o]:((?[X500:$i]:(![X501:$i]:(((X499 @ X501)<=>((X501)=(X500)))))=>?[X502:$i]:(((X499 @ X502)&![X503:$i]:(((X499 @ X503)=>((X502)=(X503))))))))=>(![X504:$i, X505:$i]:((((X504)=(X505))=>![X506:$i, X507:$i]:((((X506)=(X507))=>((in @ X506 @ X504)=>(in @ X507 @ X505))))))=>(![X508:$i, X509:$i]:((((X508)=(X509))=>![X510:$i, X511:$i]:((((X510)=(X511))=>((in @ X510 @ X508)<=>(in @ X511 @ X509))))))=>(![X512:$i > $o]:((?[X513:$i]:(((X512 @ X513)&![X514:$i]:(((X512 @ X514)=>((X513)=(X514))))))=>![X515:$i, X516:$i]:(((X512 @ X515)=>((X512 @ X516)=>((X515)=(X516)))))))=>(![X517:$i > $o, X518:$i > $o]:((![X519:$i, X520:$i]:((((X519)=(X520))=>((X517 @ X519)<=>(X518 @ X520))))=>(?[X521:$i]:(((X517 @ X521)&![X522:$i]:(((X517 @ X522)=>((X521)=(X522))))))<=>?[X523:$i]:(((X518 @ X523)&![X524:$i]:(((X518 @ X524)=>((X523)=(X524)))))))))=>(((emptyset)=(emptyset))=>(![X525:$i, X526:$i]:((((X525)=(X526))=>![X527:$i, X528:$i]:((((X527)=(X528))=>((setadjoin @ X525 @ X527)=(setadjoin @ X526 @ X528))))))=>(![X529:$i, X530:$i]:((((X529)=(X530))=>((powerset @ X529)=(powerset @ X530))))=>(![X531:$i, X532:$i]:((((X531)=(X532))=>((setunion @ X531)=(setunion @ X532))))=>(((omega)=(omega))=>(![X533:$i > $o]:((?[X534:$i]:(((X533 @ X534)&![X535:$i]:(((X533 @ X535)=>((X534)=(X535))))))=>![X536:$i, X537:$i]:(((X533 @ X536)=>((X533 @ X537)=>((X536)=(X537)))))))=>(![X538:$i > $o, X539:$i > $o]:((![X540:$i, X541:$i]:((((X540)=(X541))=>((X538 @ X540)<=>(X539 @ X541))))=>(?[X542:$i]:(((X538 @ X542)&![X543:$i]:(((X538 @ X543)=>((X542)=(X543))))))=>(?[X544:$i]:(((X539 @ X544)&![X545:$i]:(((X539 @ X545)=>((X544)=(X545))))))=>((descr @ X538)=(descr @ X539))))))=>(![X546:$i, X547:$i]:((((X546)=(X547))=>![X548:$i > $o, X549:$i > $o]:((![X550:$i]:(((in @ X550 @ X546)=>![X551:$i]:(((in @ X551 @ X547)=>(((X550)=(X551))=>((X548 @ X550)<=>(X549 @ X551)))))))=>((dsetconstr @ X546 @ X548)=(dsetconstr @ X547 @ X549))))))=>(![X552:$i, X553:$i]:((![X554:$i]:(((in @ X554 @ X552)=>(in @ X554 @ X553)))=>(subset @ X552 @ X553)))=>(![X555:$i, X556:$i]:((((X555)=(X556))=>(subset @ X556 @ X555)))=>(![X557:$i, X558:$i]:((((X557)=(X558))=>(subset @ X557 @ X558)))=>(![X559:$i, X560:$i]:((![X561:$i]:(((in @ X561 @ X559)=>(in @ X561 @ X560)))=>(subset @ X559 @ X560)))=>(![X562:$i]:((subset @ emptyset @ X562))=>(![X563:$i, X564:$i, X565:$i]:(((subset @ X563 @ X564)=>((in @ X565 @ X563)=>(in @ X565 @ X564))))=>(![X566:$i, X567:$i, X568:$i]:(((subset @ X566 @ X567)=>(~(in @ X568 @ X567)=>~(in @ X568 @ X566))))=>(![X569:$i, X570:$i, X571:$i]:(((in @ X571 @ X569)=>(~(in @ X571 @ X570)=>~(subset @ X569 @ X570))))=>(![X572:$i, X573:$i]:((~(subset @ X572 @ X573)=>((X572)!=(X573))))=>(![X574:$i, X575:$i, X576:$i]:(((in @ X576 @ X574)=>(~(in @ X576 @ X575)=>((X574)!=(X575)))))=>(![X577:$i]:((subset @ X577 @ X577))=>(![X578:$i, X579:$i, X580:$i]:(((subset @ X578 @ X579)=>((subset @ X579 @ X580)=>(subset @ X578 @ X580))))=>(![X581:$i, X582:$i]:((subset @ X582 @ (setadjoin @ X581 @ X582)))=>(![X583:$i, X584:$i, X585:$i]:(((subset @ X583 @ X585)=>(subset @ X583 @ (setadjoin @ X584 @ X585))))=>(![X586:$i, X587:$i]:(((subset @ X586 @ X587)=>(in @ X586 @ (powerset @ X587))))=>(![X588:$i, X589:$i]:(((subset @ X588 @ X589)=>((subset @ X589 @ X588)=>((X588)=(X589)))))=>(![X590:$i]:(((subset @ X590 @ emptyset)=>((X590)=(emptyset))))=>(![X591:$i, X592:$i]:(((subset @ X592 @ X591)=>(in @ X592 @ (powerset @ X591))))=>(![X593:$i, X594:$i]:(((in @ X594 @ (powerset @ X593))=>(subset @ X594 @ X593)))=>(![X595:$i]:((in @ X595 @ (powerset @ X595)))=>(![X596:$i, X597:$i]:(((subset @ X596 @ X597)=>(subset @ (powerset @ X596) @ (powerset @ X597))))=>(![X598:$i, X599:$i > $o]:((in @ (dsetconstr @ X598 @ X599) @ (powerset @ X598)))=>(![X600:$i, X601:$i > $o]:((subset @ (dsetconstr @ X600 @ X601) @ X600))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[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])])]), c_0_143])).
% 0.23/0.34  thf(c_0_145, negated_conjecture, ![X606:$i, X607:$i, X609:$i, X610:$i, X611:$i, X612:$i, X613:$i, X614:$i, X615:$i, X616:$i, X617:$i, X619:$i, X620:$i, X622:$i, X623:$i, X624:$i, X625:$i, X626:$i, X628:$i, X629:$i > $i > $o, X630:$i, X632:$i, X635:$i, X637:$i, X638:$i, X639:$i, X640:$i, X642:$i, X643:$i > $o, X644:$i, X646:$i, X647:$i > $o, X648:$i, X649:$i, X650:$i > $o, X651:$i, X652:$i, X653:$i > $o, X654:$i, X655:$i > $o, X656:$i, X659:$i, X660:$o, X661:$i, X662:$i, X663:$o, X664:$i, X665:$i, X666:$i > $o, X667:$i, X670:$i, X671:$i, X674:$i, X676:$i, X678:$i, X679:$i > $o, X680:$i, X681:$i, X683:$i, X684:$i > $o, X685:$i, X686:$i, X687:$i, X688:$i, X689:$i, X690:$i, X691:$i, X692:$i, X693:$i, X694:$i, X695:$i, X696:$o, X697:$i, X698:$i, X699:$i, X700:$i, X701:$i, X702:$i, X704:$i, X705:$i, X706:$i, X707:$i, X708:$i, X709:$i, X710:$i, X711:$i, X712:$i, X713:$i, X714:$o, X716:$i, X717:$i, X718:$i > $o, X719:$i, X722:$i, X723:$i, X724:$i, X726:$i, X727:$i, X728:$i, X729:$i, X730:$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 > $o, X743:$i, X744:$i > $o, X745:$i, X746:$i, X747:$i > $o, X748:$i, X750:$i, X751:$i > $o, X753:$i, X754:$i, X755:$i > $o, X757:$i, X758:$i, X759:$i > $o, X760:$i, X762:$o, X763:$o, X764:$i, X765:$i > $o, X767:$i, X768:$i, X769:$i > $o, X770:$i, X772:$i > $o, X773:$i, X776:$i, X777:$i > $o, X778:$i, X782:$i, X783:$i > $o, X784:$i, X787:$i, X788:$i, X789:$i, X790:$i, X791:$i, X792:$i, X793:$i, X794:$i, X795:$i, X796:$i > $o, X797:$i, X799:$i, X800:$i, X801:$i > $o, X802:$i > $o, X805:$i, X808:$i, X809:$i, X812:$i, X813:$i, X814:$i, X815:$i, X816:$i, X817:$i, X818:$i, X819:$i, X820:$i, X821:$i > $o, X822:$i, X824:$i, X825:$i, X826:$i > $o, X827:$i > $o, X830:$i, X832:$i, X834:$i, X835:$i, X836:$i > $o, X837:$i > $o, X840:$i, X841:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i, X848:$i, X850:$i, X851:$i, X852:$i, X853:$i, X854:$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 > $o, X888:$i, X889:$i > $o]:((((~(in @ (esk1_2 @ X606 @ X607) @ X606)|~(in @ (esk1_2 @ X606 @ X607) @ X607)|((X606)=(X607)))&((in @ (esk1_2 @ X606 @ X607) @ X606)|(in @ (esk1_2 @ X606 @ X607) @ X607)|((X606)=(X607))))&(~(in @ X609 @ emptyset)&(((~(in @ X612 @ (setadjoin @ X610 @ X611))|(((X612)=(X610))|(in @ X612 @ X611)))&((((X612)!=(X610))|(in @ X612 @ (setadjoin @ X610 @ X611)))&(~(in @ X612 @ X611)|(in @ X612 @ (setadjoin @ X610 @ X611)))))&(((~(in @ X614 @ (powerset @ X613))|(~(in @ X615 @ X614)|(in @ X615 @ X613)))&(((in @ (esk2_2 @ X616 @ X617) @ X617)|(in @ X617 @ (powerset @ X616)))&(~(in @ (esk2_2 @ X616 @ X617) @ X616)|(in @ X617 @ (powerset @ X616)))))&(((((in @ X620 @ (esk3_2 @ X619 @ X620))|~(in @ X620 @ (setunion @ X619)))&((in @ (esk3_2 @ X619 @ X620) @ X619)|~(in @ X620 @ (setunion @ X619))))&(~(in @ X623 @ X624)|~(in @ X624 @ X622)|(in @ X623 @ (setunion @ X622))))&((in @ emptyset @ omega)&((~(in @ X625 @ omega)|(in @ (setadjoin @ X625 @ X625) @ omega))&(((((in @ (esk4_1 @ X626) @ omega)|~(in @ emptyset @ X626)|(~(in @ X628 @ omega)|(in @ X628 @ X626)))&((in @ (esk4_1 @ X626) @ X626)|~(in @ emptyset @ X626)|(~(in @ X628 @ omega)|(in @ X628 @ X626))))&(~(in @ (setadjoin @ (esk4_1 @ X626) @ (esk4_1 @ X626)) @ X626)|~(in @ emptyset @ X626)|(~(in @ X628 @ omega)|(in @ X628 @ X626))))&((((((in @ (esk8_3 @ X629 @ X630 @ X635) @ X630)|~(in @ X635 @ (esk7_2 @ X629 @ X630))|(in @ (esk5_2 @ X629 @ X630) @ X630))&((X629 @ (esk8_3 @ X629 @ X630 @ X635) @ X635)|~(in @ X635 @ (esk7_2 @ X629 @ X630))|(in @ (esk5_2 @ X629 @ X630) @ X630)))&(~(in @ X638 @ X630)|~(X629 @ X638 @ X637)|(in @ X637 @ (esk7_2 @ X629 @ X630))|(in @ (esk5_2 @ X629 @ X630) @ X630)))&(((((in @ (esk8_3 @ X629 @ X630 @ X635) @ X630)|~(in @ X635 @ (esk7_2 @ X629 @ X630))|((X629 @ (esk5_2 @ X629 @ X630) @ (esk6_3 @ X629 @ X630 @ X632))|~(X629 @ (esk5_2 @ X629 @ X630) @ X632)))&((X629 @ (esk8_3 @ X629 @ X630 @ X635) @ X635)|~(in @ X635 @ (esk7_2 @ X629 @ X630))|((X629 @ (esk5_2 @ X629 @ X630) @ (esk6_3 @ X629 @ X630 @ X632))|~(X629 @ (esk5_2 @ X629 @ X630) @ X632))))&(~(in @ X638 @ X630)|~(X629 @ X638 @ X637)|(in @ X637 @ (esk7_2 @ X629 @ X630))|((X629 @ (esk5_2 @ X629 @ X630) @ (esk6_3 @ X629 @ X630 @ X632))|~(X629 @ (esk5_2 @ X629 @ X630) @ X632))))&((((in @ (esk8_3 @ X629 @ X630 @ X635) @ X630)|~(in @ X635 @ (esk7_2 @ X629 @ X630))|(((X632)!=(esk6_3 @ X629 @ X630 @ X632))|~(X629 @ (esk5_2 @ X629 @ X630) @ X632)))&((X629 @ (esk8_3 @ X629 @ X630 @ X635) @ X635)|~(in @ X635 @ (esk7_2 @ X629 @ X630))|(((X632)!=(esk6_3 @ X629 @ X630 @ X632))|~(X629 @ (esk5_2 @ X629 @ X630) @ X632))))&(~(in @ X638 @ X630)|~(X629 @ X638 @ X637)|(in @ X637 @ (esk7_2 @ X629 @ X630))|(((X632)!=(esk6_3 @ X629 @ X630 @ X632))|~(X629 @ (esk5_2 @ X629 @ X630) @ X632))))))&((((in @ (esk9_1 @ X639) @ X639)|~(in @ X640 @ X639))&(~(in @ X642 @ (esk9_1 @ X639))|~(in @ X642 @ X639)|~(in @ X640 @ X639)))&((epred1_0)&((((X643 @ (esk10_2 @ X643 @ X644))|~(X643 @ X644)|(X643 @ (descr @ X643)))&(((X644)!=(esk10_2 @ X643 @ X644))|~(X643 @ X644)|(X643 @ (descr @ X643))))&((~(in @ X648 @ X646)|(~(X647 @ X648)|(in @ X648 @ (dsetconstr @ X646 @ X647))))&((~(in @ X651 @ (dsetconstr @ X649 @ X650))|(in @ X651 @ X649))&((~(in @ X654 @ (dsetconstr @ X652 @ X653))|(X653 @ X654))&(((((X655 @ (esk12_1 @ X655))|((X655 @ (esk11_2 @ X655 @ X656))|~(X655 @ X656)))&(~(X655 @ X659)|((esk12_1 @ X655)=(X659))|((X655 @ (esk11_2 @ X655 @ X656))|~(X655 @ X656))))&(((X655 @ (esk12_1 @ X655))|(((X656)!=(esk11_2 @ X655 @ X656))|~(X655 @ X656)))&(~(X655 @ X659)|((esk12_1 @ X655)=(X659))|(((X656)!=(esk11_2 @ X655 @ X656))|~(X655 @ X656)))))&((~(in @ X661 @ (prop2set @ ((X660))))|(X660))&((~(in @ X662 @ emptyset)|(X663))&((~(in @ X664 @ emptyset)|~($true))&(~(in @ X665 @ emptyset)&((((X666 @ (esk13_2 @ X666 @ X667))|~(X666 @ X667)|(X666 @ (esk14_1 @ X666)))&(((X667)!=(esk13_2 @ X666 @ X667))|~(X666 @ X667)|(X666 @ (esk14_1 @ X666))))&(((((in @ (esk16_2 @ X670 @ X671) @ X671)|((X670)=(X671))|(in @ (esk15_2 @ X670 @ X671) @ X670))&(~(in @ (esk16_2 @ X670 @ X671) @ X670)|((X670)=(X671))|(in @ (esk15_2 @ X670 @ X671) @ X670)))&(((in @ (esk16_2 @ X670 @ X671) @ X671)|((X670)=(X671))|~(in @ (esk15_2 @ X670 @ X671) @ X671))&(~(in @ (esk16_2 @ X670 @ X671) @ X670)|((X670)=(X671))|~(in @ (esk15_2 @ X670 @ X671) @ X671))))&(((in @ (esk17_1 @ X674) @ X674)|((X674)=(emptyset)))&(((in @ (esk18_1 @ X676) @ X676)|((X676)=(emptyset)))&(((~(in @ X680 @ (dsetconstr @ X678 @ X679))|(X679 @ X680)|~(in @ X680 @ X678))&(~(X679 @ X680)|(in @ X680 @ (dsetconstr @ X678 @ X679))|~(in @ X680 @ X678)))&((((X681)=(emptyset))|(in @ (esk19_1 @ X681) @ X681))&((~(in @ X685 @ X683)|(~(X684 @ X685)|((dsetconstr @ X683 @ X684)!=(emptyset))))&((~(in @ X687 @ X686)|((X686)!=(emptyset)))&((in @ X688 @ (setadjoin @ X688 @ X689))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X692 @ X691)|(in @ X692 @ (setadjoin @ X690 @ X691)))&(((((in @ X695 @ X694)|(X696)|((X695)=(X693))|~(in @ X695 @ (setadjoin @ X693 @ X694)))&(~(X696)|(X696)|((X695)=(X693))|~(in @ X695 @ (setadjoin @ X693 @ X694))))&(((in @ X695 @ X694)|(X696)|~(X696)|~(in @ X695 @ (setadjoin @ X693 @ X694)))&(~(X696)|(X696)|~(X696)|~(in @ X695 @ (setadjoin @ X693 @ X694)))))&((~(in @ X699 @ (setadjoin @ X697 @ X698))|(((X699)=(X697))|(in @ X699 @ X698)))&(((dsetconstr @ X700 @ (^[Z0:$i]:($true)))=(X700))&((((in @ (esk20_2 @ X701 @ X702) @ X702)|(in @ X702 @ (powerset @ X701)))&(~(in @ (esk20_2 @ X701 @ X702) @ X701)|(in @ X702 @ (powerset @ X701))))&((in @ emptyset @ (powerset @ X704))&((in @ emptyset @ (powerset @ X705))&((~(in @ X707 @ (powerset @ X706))|(~(in @ X708 @ X707)|(in @ X708 @ X706)))&((~(in @ X710 @ X711)|(~(in @ X711 @ X709)|(in @ X710 @ (setunion @ X709))))&((((in @ X713 @ (esk21_3 @ X712 @ X713 @ X714))|(X714)|~(in @ X713 @ (setunion @ X712)))&(((in @ (esk21_3 @ X712 @ X713 @ X714) @ X712)|(X714)|~(in @ X713 @ (setunion @ X712)))&(~(X714)|(X714)|~(in @ X713 @ (setunion @ X712)))))&((~(in @ X717 @ X716)|(in @ X717 @ (powerset @ (setunion @ X716))))&((((~(X718 @ X722)|((X722)=(esk23_1 @ X718))|((X718 @ (esk22_2 @ X718 @ X719))|~(X718 @ X719)))&(((X723)!=(esk23_1 @ X718))|(X718 @ X723)|((X718 @ (esk22_2 @ X718 @ X719))|~(X718 @ X719))))&((~(X718 @ X722)|((X722)=(esk23_1 @ X718))|(((X719)!=(esk22_2 @ X718 @ X719))|~(X718 @ X719)))&(((X723)!=(esk23_1 @ X718))|(X718 @ X723)|(((X719)!=(esk22_2 @ X718 @ X719))|~(X718 @ X719)))))&((((in @ (esk24_1 @ X724) @ X724)|((X724)=(emptyset)))&(($true)|((X724)=(emptyset))))&((~(in @ X726 @ (setadjoin @ X727 @ emptyset))|((X726)=(X727)))&((((X728)=(X729))|~(in @ X729 @ (setadjoin @ X728 @ emptyset)))&((((X730)!=(X731))|(in @ X730 @ (setadjoin @ X731 @ emptyset)))&((~(in @ X732 @ (setadjoin @ X733 @ emptyset))|(in @ X733 @ (setadjoin @ X732 @ emptyset)))&((~(in @ X736 @ (setadjoin @ X734 @ (setadjoin @ X735 @ emptyset)))|(((X736)=(X734))|((X736)=(X735))))&((in @ X737 @ (setadjoin @ X737 @ (setadjoin @ X738 @ emptyset)))&((in @ X740 @ (setadjoin @ X739 @ (setadjoin @ X740 @ emptyset)))&((~(in @ X743 @ X741)|~(X742 @ X743)|(((dsetconstr @ X741 @ X742)!=(emptyset))|~($true)))&((~(in @ X745 @ emptyset)|(X744 @ X745))&((((in @ (esk25_2 @ X746 @ X747) @ X746)|(~(in @ X748 @ X746)|(X747 @ X748)))&(~(X747 @ (esk25_2 @ X746 @ X747))|(~(in @ X748 @ X746)|(X747 @ X748))))&((((in @ (esk26_2 @ X750 @ X751) @ X750)|(~(in @ X753 @ X750)|~(X751 @ X753)))&((X751 @ (esk26_2 @ X750 @ X751))|(~(in @ X753 @ X750)|~(X751 @ X753))))&((((in @ (esk27_2 @ X754 @ X755) @ X754)|(~(in @ X757 @ X754)|~(X755 @ X757)))&((X755 @ (esk27_2 @ X754 @ X755))|(~(in @ X757 @ X754)|~(X755 @ X757))))&((((in @ (esk28_2 @ X758 @ X759) @ X758)|(~(in @ X760 @ X758)|(X759 @ X760)))&(~(X759 @ (esk28_2 @ X758 @ X759))|(~(in @ X760 @ X758)|(X759 @ X760))))&((~(X762)|(in @ emptyset @ (prop2set @ ((X762)))))&((~(X763)|(set2prop @ (prop2set @ ((X763)))))&((((in @ (esk29_2 @ X764 @ X765) @ X764)|(~(in @ X767 @ X764)|~(X765 @ X767)))&((X765 @ (esk29_2 @ X764 @ X765))|(~(in @ X767 @ X764)|~(X765 @ X767))))&((((in @ (esk30_2 @ X768 @ X769) @ X768)|(~(in @ X770 @ X768)|(X769 @ X770)))&(~(X769 @ (esk30_2 @ X768 @ X769))|(~(in @ X770 @ X768)|(X769 @ X770))))&(((((X772 @ (esk32_1 @ X772))|((X772 @ (esk31_2 @ X772 @ X773))|~(X772 @ X773)))&(~(X772 @ X776)|((esk32_1 @ X772)=(X776))|((X772 @ (esk31_2 @ X772 @ X773))|~(X772 @ X773))))&(((X772 @ (esk32_1 @ X772))|(((X773)!=(esk31_2 @ X772 @ X773))|~(X772 @ X773)))&(~(X772 @ X776)|((esk32_1 @ X772)=(X776))|(((X773)!=(esk31_2 @ X772 @ X773))|~(X772 @ X773)))))&(((((X777 @ (esk35_1 @ X777))|(X777 @ (esk33_1 @ X777))|~(X777 @ X778))&(~(X777 @ X782)|((esk35_1 @ X777)=(X782))|(X777 @ (esk33_1 @ X777))|~(X777 @ X778)))&((((X777 @ (esk35_1 @ X777))|(X777 @ (esk34_1 @ X777))|~(X777 @ X778))&(~(X777 @ X782)|((esk35_1 @ X777)=(X782))|(X777 @ (esk34_1 @ X777))|~(X777 @ X778)))&(((X777 @ (esk35_1 @ X777))|((esk33_1 @ X777)!=(esk34_1 @ X777))|~(X777 @ X778))&(~(X777 @ X782)|((esk35_1 @ X777)=(X782))|((esk33_1 @ X777)!=(esk34_1 @ X777))|~(X777 @ X778)))))&(((((X783 @ (esk37_1 @ X783))|(~(X783 @ (esk36_2 @ X783 @ X784))|((esk36_2 @ X783 @ X784)!=(X784))))&(~(X783 @ X787)|((esk37_1 @ X783)=(X787))|(~(X783 @ (esk36_2 @ X783 @ X784))|((esk36_2 @ X783 @ X784)!=(X784)))))&(((X783 @ (esk37_1 @ X783))|((X783 @ (esk36_2 @ X783 @ X784))|((esk36_2 @ X783 @ X784)=(X784))))&(~(X783 @ X787)|((esk37_1 @ X783)=(X787))|((X783 @ (esk36_2 @ X783 @ X784))|((esk36_2 @ X783 @ X784)=(X784))))))&((((X788)!=(X789))|(((X790)!=(X791))|(~(in @ X790 @ X788)|(in @ X791 @ X789))))&(((~(in @ X794 @ X792)|(in @ X795 @ X793)|((X794)!=(X795))|((X792)!=(X793)))&(~(in @ X795 @ X793)|(in @ X794 @ X792)|((X794)!=(X795))|((X792)!=(X793))))&((((X796 @ (esk38_2 @ X796 @ X797))|~(X796 @ X797)|(~(X796 @ X799)|(~(X796 @ X800)|((X799)=(X800)))))&(((X797)!=(esk38_2 @ X796 @ X797))|~(X796 @ X797)|(~(X796 @ X799)|(~(X796 @ X800)|((X799)=(X800))))))&(((((((X802 @ (esk42_2 @ X801 @ X802))|((X801 @ (esk41_3 @ X801 @ X802 @ X805))|~(X801 @ X805))|((esk39_2 @ X801 @ X802)=(esk40_2 @ X801 @ X802)))&(~(X802 @ X808)|((esk42_2 @ X801 @ X802)=(X808))|((X801 @ (esk41_3 @ X801 @ X802 @ X805))|~(X801 @ X805))|((esk39_2 @ X801 @ X802)=(esk40_2 @ X801 @ X802))))&(((X802 @ (esk42_2 @ X801 @ X802))|(((X805)!=(esk41_3 @ X801 @ X802 @ X805))|~(X801 @ X805))|((esk39_2 @ X801 @ X802)=(esk40_2 @ X801 @ X802)))&(~(X802 @ X808)|((esk42_2 @ X801 @ X802)=(X808))|(((X805)!=(esk41_3 @ X801 @ X802 @ X805))|~(X801 @ X805))|((esk39_2 @ X801 @ X802)=(esk40_2 @ X801 @ X802)))))&((((X801 @ (esk44_2 @ X801 @ X802))|((X802 @ (esk43_3 @ X801 @ X802 @ X809))|~(X802 @ X809))|((esk39_2 @ X801 @ X802)=(esk40_2 @ X801 @ X802)))&(~(X801 @ X812)|((esk44_2 @ X801 @ X802)=(X812))|((X802 @ (esk43_3 @ X801 @ X802 @ X809))|~(X802 @ X809))|((esk39_2 @ X801 @ X802)=(esk40_2 @ X801 @ X802))))&(((X801 @ (esk44_2 @ X801 @ X802))|(((X809)!=(esk43_3 @ X801 @ X802 @ X809))|~(X802 @ X809))|((esk39_2 @ X801 @ X802)=(esk40_2 @ X801 @ X802)))&(~(X801 @ X812)|((esk44_2 @ X801 @ X802)=(X812))|(((X809)!=(esk43_3 @ X801 @ X802 @ X809))|~(X802 @ X809))|((esk39_2 @ X801 @ X802)=(esk40_2 @ X801 @ X802))))))&((((((X802 @ (esk42_2 @ X801 @ X802))|((X801 @ (esk41_3 @ X801 @ X802 @ X805))|~(X801 @ X805))|(~(X801 @ (esk39_2 @ X801 @ X802))|~(X802 @ (esk40_2 @ X801 @ X802))))&(~(X802 @ X808)|((esk42_2 @ X801 @ X802)=(X808))|((X801 @ (esk41_3 @ X801 @ X802 @ X805))|~(X801 @ X805))|(~(X801 @ (esk39_2 @ X801 @ X802))|~(X802 @ (esk40_2 @ X801 @ X802)))))&(((X802 @ (esk42_2 @ X801 @ X802))|(((X805)!=(esk41_3 @ X801 @ X802 @ X805))|~(X801 @ X805))|(~(X801 @ (esk39_2 @ X801 @ X802))|~(X802 @ (esk40_2 @ X801 @ X802))))&(~(X802 @ X808)|((esk42_2 @ X801 @ X802)=(X808))|(((X805)!=(esk41_3 @ X801 @ X802 @ X805))|~(X801 @ X805))|(~(X801 @ (esk39_2 @ X801 @ X802))|~(X802 @ (esk40_2 @ X801 @ X802))))))&((((X801 @ (esk44_2 @ X801 @ X802))|((X802 @ (esk43_3 @ X801 @ X802 @ X809))|~(X802 @ X809))|(~(X801 @ (esk39_2 @ X801 @ X802))|~(X802 @ (esk40_2 @ X801 @ X802))))&(~(X801 @ X812)|((esk44_2 @ X801 @ X802)=(X812))|((X802 @ (esk43_3 @ X801 @ X802 @ X809))|~(X802 @ X809))|(~(X801 @ (esk39_2 @ X801 @ X802))|~(X802 @ (esk40_2 @ X801 @ X802)))))&(((X801 @ (esk44_2 @ X801 @ X802))|(((X809)!=(esk43_3 @ X801 @ X802 @ X809))|~(X802 @ X809))|(~(X801 @ (esk39_2 @ X801 @ X802))|~(X802 @ (esk40_2 @ X801 @ X802))))&(~(X801 @ X812)|((esk44_2 @ X801 @ X802)=(X812))|(((X809)!=(esk43_3 @ X801 @ X802 @ X809))|~(X802 @ X809))|(~(X801 @ (esk39_2 @ X801 @ X802))|~(X802 @ (esk40_2 @ X801 @ X802)))))))&(((((X802 @ (esk42_2 @ X801 @ X802))|((X801 @ (esk41_3 @ X801 @ X802 @ X805))|~(X801 @ X805))|((X801 @ (esk39_2 @ X801 @ X802))|(X802 @ (esk40_2 @ X801 @ X802))))&(~(X802 @ X808)|((esk42_2 @ X801 @ X802)=(X808))|((X801 @ (esk41_3 @ X801 @ X802 @ X805))|~(X801 @ X805))|((X801 @ (esk39_2 @ X801 @ X802))|(X802 @ (esk40_2 @ X801 @ X802)))))&(((X802 @ (esk42_2 @ X801 @ X802))|(((X805)!=(esk41_3 @ X801 @ X802 @ X805))|~(X801 @ X805))|((X801 @ (esk39_2 @ X801 @ X802))|(X802 @ (esk40_2 @ X801 @ X802))))&(~(X802 @ X808)|((esk42_2 @ X801 @ X802)=(X808))|(((X805)!=(esk41_3 @ X801 @ X802 @ X805))|~(X801 @ X805))|((X801 @ (esk39_2 @ X801 @ X802))|(X802 @ (esk40_2 @ X801 @ X802))))))&((((X801 @ (esk44_2 @ X801 @ X802))|((X802 @ (esk43_3 @ X801 @ X802 @ X809))|~(X802 @ X809))|((X801 @ (esk39_2 @ X801 @ X802))|(X802 @ (esk40_2 @ X801 @ X802))))&(~(X801 @ X812)|((esk44_2 @ X801 @ X802)=(X812))|((X802 @ (esk43_3 @ X801 @ X802 @ X809))|~(X802 @ X809))|((X801 @ (esk39_2 @ X801 @ X802))|(X802 @ (esk40_2 @ X801 @ X802)))))&(((X801 @ (esk44_2 @ X801 @ X802))|(((X809)!=(esk43_3 @ X801 @ X802 @ X809))|~(X802 @ X809))|((X801 @ (esk39_2 @ X801 @ X802))|(X802 @ (esk40_2 @ X801 @ X802))))&(~(X801 @ X812)|((esk44_2 @ X801 @ X802)=(X812))|(((X809)!=(esk43_3 @ X801 @ X802 @ X809))|~(X802 @ X809))|((X801 @ (esk39_2 @ X801 @ X802))|(X802 @ (esk40_2 @ X801 @ X802)))))))))&(((emptyset)=(emptyset))&((((X813)!=(X814))|(((X815)!=(X816))|((setadjoin @ X813 @ X815)=(setadjoin @ X814 @ X816))))&((((X817)!=(X818))|((powerset @ X817)=(powerset @ X818)))&((((X819)!=(X820))|((setunion @ X819)=(setunion @ X820)))&(((omega)=(omega))&((((X821 @ (esk45_2 @ X821 @ X822))|~(X821 @ X822)|(~(X821 @ X824)|(~(X821 @ X825)|((X824)=(X825)))))&(((X822)!=(esk45_2 @ X821 @ X822))|~(X821 @ X822)|(~(X821 @ X824)|(~(X821 @ X825)|((X824)=(X825))))))&((((((X827 @ (esk49_3 @ X826 @ X827 @ X832))|~(X827 @ X832)|((descr @ X826)=(descr @ X827))|((X826 @ (esk48_3 @ X826 @ X827 @ X830))|~(X826 @ X830))|((esk46_2 @ X826 @ X827)=(esk47_2 @ X826 @ X827)))&(((X832)!=(esk49_3 @ X826 @ X827 @ X832))|~(X827 @ X832)|((descr @ X826)=(descr @ X827))|((X826 @ (esk48_3 @ X826 @ X827 @ X830))|~(X826 @ X830))|((esk46_2 @ X826 @ X827)=(esk47_2 @ X826 @ X827))))&(((X827 @ (esk49_3 @ X826 @ X827 @ X832))|~(X827 @ X832)|((descr @ X826)=(descr @ X827))|(((X830)!=(esk48_3 @ X826 @ X827 @ X830))|~(X826 @ X830))|((esk46_2 @ X826 @ X827)=(esk47_2 @ X826 @ X827)))&(((X832)!=(esk49_3 @ X826 @ X827 @ X832))|~(X827 @ X832)|((descr @ X826)=(descr @ X827))|(((X830)!=(esk48_3 @ X826 @ X827 @ X830))|~(X826 @ X830))|((esk46_2 @ X826 @ X827)=(esk47_2 @ X826 @ X827)))))&(((((X827 @ (esk49_3 @ X826 @ X827 @ X832))|~(X827 @ X832)|((descr @ X826)=(descr @ X827))|((X826 @ (esk48_3 @ X826 @ X827 @ X830))|~(X826 @ X830))|(~(X826 @ (esk46_2 @ X826 @ X827))|~(X827 @ (esk47_2 @ X826 @ X827))))&(((X832)!=(esk49_3 @ X826 @ X827 @ X832))|~(X827 @ X832)|((descr @ X826)=(descr @ X827))|((X826 @ (esk48_3 @ X826 @ X827 @ X830))|~(X826 @ X830))|(~(X826 @ (esk46_2 @ X826 @ X827))|~(X827 @ (esk47_2 @ X826 @ X827)))))&(((X827 @ (esk49_3 @ X826 @ X827 @ X832))|~(X827 @ X832)|((descr @ X826)=(descr @ X827))|(((X830)!=(esk48_3 @ X826 @ X827 @ X830))|~(X826 @ X830))|(~(X826 @ (esk46_2 @ X826 @ X827))|~(X827 @ (esk47_2 @ X826 @ X827))))&(((X832)!=(esk49_3 @ X826 @ X827 @ X832))|~(X827 @ X832)|((descr @ X826)=(descr @ X827))|(((X830)!=(esk48_3 @ X826 @ X827 @ X830))|~(X826 @ X830))|(~(X826 @ (esk46_2 @ X826 @ X827))|~(X827 @ (esk47_2 @ X826 @ X827))))))&((((X827 @ (esk49_3 @ X826 @ X827 @ X832))|~(X827 @ X832)|((descr @ X826)=(descr @ X827))|((X826 @ (esk48_3 @ X826 @ X827 @ X830))|~(X826 @ X830))|((X826 @ (esk46_2 @ X826 @ X827))|(X827 @ (esk47_2 @ X826 @ X827))))&(((X832)!=(esk49_3 @ X826 @ X827 @ X832))|~(X827 @ X832)|((descr @ X826)=(descr @ X827))|((X826 @ (esk48_3 @ X826 @ X827 @ X830))|~(X826 @ X830))|((X826 @ (esk46_2 @ X826 @ X827))|(X827 @ (esk47_2 @ X826 @ X827)))))&(((X827 @ (esk49_3 @ X826 @ X827 @ X832))|~(X827 @ X832)|((descr @ X826)=(descr @ X827))|(((X830)!=(esk48_3 @ X826 @ X827 @ X830))|~(X826 @ X830))|((X826 @ (esk46_2 @ X826 @ X827))|(X827 @ (esk47_2 @ X826 @ X827))))&(((X832)!=(esk49_3 @ X826 @ X827 @ X832))|~(X827 @ X832)|((descr @ X826)=(descr @ X827))|(((X830)!=(esk48_3 @ X826 @ X827 @ X830))|~(X826 @ X830))|((X826 @ (esk46_2 @ X826 @ X827))|(X827 @ (esk47_2 @ X826 @ X827))))))))&((((in @ (esk50_4 @ X834 @ X835 @ X836 @ X837) @ X834)|((dsetconstr @ X834 @ X836)=(dsetconstr @ X835 @ X837))|((X834)!=(X835)))&(((in @ (esk51_4 @ X834 @ X835 @ X836 @ X837) @ X835)|((dsetconstr @ X834 @ X836)=(dsetconstr @ X835 @ X837))|((X834)!=(X835)))&((((esk50_4 @ X834 @ X835 @ X836 @ X837)=(esk51_4 @ X834 @ X835 @ X836 @ X837))|((dsetconstr @ X834 @ X836)=(dsetconstr @ X835 @ X837))|((X834)!=(X835)))&((~(X836 @ (esk50_4 @ X834 @ X835 @ X836 @ X837))|~(X837 @ (esk51_4 @ X834 @ X835 @ X836 @ X837))|((dsetconstr @ X834 @ X836)=(dsetconstr @ X835 @ X837))|((X834)!=(X835)))&((X836 @ (esk50_4 @ X834 @ X835 @ X836 @ X837))|(X837 @ (esk51_4 @ X834 @ X835 @ X836 @ X837))|((dsetconstr @ X834 @ X836)=(dsetconstr @ X835 @ X837))|((X834)!=(X835)))))))&((((in @ (esk52_2 @ X840 @ X841) @ X840)|(subset @ X840 @ X841))&(~(in @ (esk52_2 @ X840 @ X841) @ X841)|(subset @ X840 @ X841)))&((((X843)!=(X844))|(subset @ X844 @ X843))&((((X845)!=(X846))|(subset @ X845 @ X846))&((((in @ (esk53_2 @ X847 @ X848) @ X847)|(subset @ X847 @ X848))&(~(in @ (esk53_2 @ X847 @ X848) @ X848)|(subset @ X847 @ X848)))&((subset @ emptyset @ X850)&((~(subset @ X851 @ X852)|(~(in @ X853 @ X851)|(in @ X853 @ X852)))&((~(subset @ X854 @ X855)|((in @ X856 @ X855)|~(in @ X856 @ X854)))&((~(in @ X859 @ X857)|((in @ X859 @ X858)|~(subset @ X857 @ X858)))&(((subset @ X860 @ X861)|((X860)!=(X861)))&((~(in @ X864 @ X862)|((in @ X864 @ X863)|((X862)!=(X863))))&((subset @ X865 @ X865)&((~(subset @ X866 @ X867)|(~(subset @ X867 @ X868)|(subset @ X866 @ X868)))&((subset @ X870 @ (setadjoin @ X869 @ X870))&((~(subset @ X871 @ X873)|(subset @ X871 @ (setadjoin @ X872 @ X873)))&((~(subset @ X874 @ X875)|(in @ X874 @ (powerset @ X875)))&((~(subset @ X876 @ X877)|(~(subset @ X877 @ X876)|((X876)=(X877))))&((~(subset @ X878 @ emptyset)|((X878)=(emptyset)))&((~(subset @ X880 @ X879)|(in @ X880 @ (powerset @ X879)))&((~(in @ X882 @ (powerset @ X881))|(subset @ X882 @ X881))&((in @ X883 @ (powerset @ X883))&((~(subset @ X884 @ X885)|(subset @ (powerset @ X884) @ (powerset @ X885)))&((in @ (dsetconstr @ X886 @ X887) @ (powerset @ X886))&((subset @ (dsetconstr @ X888 @ X889) @ X888)&((in @ esk56_0 @ esk54_0)&~(in @ esk56_0 @ (binunion @ esk54_0 @ esk55_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_144])])])])])])])).
% 0.23/0.34  thf(c_0_146, plain, ![X602:$i, X603:$i]:(((binunion @ X602 @ X603)=(setunion @ (setadjoin @ X602 @ (setadjoin @ X603 @ emptyset))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[binunion])])).
% 0.23/0.34  thf(c_0_147, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ (setunion @ X4))|~((in @ X2 @ X3))|~((in @ X3 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 0.23/0.34  thf(c_0_148, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 0.23/0.34  thf(c_0_149, plain, ![X604:$i, X605:$i]:(((binunion @ X604 @ X605)=(setunion @ (setadjoin @ X604 @ (setadjoin @ X605 @ emptyset))))), inference(variable_rename,[status(thm)],[c_0_146])).
% 0.23/0.34  thf(c_0_150, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setunion @ (setadjoin @ X3 @ X4)))|~((in @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_147, c_0_148])).
% 0.23/0.34  thf(c_0_151, plain, ![X2:$i, X3:$i]:(((binunion @ X2 @ X3)=(setunion @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_149])).
% 0.23/0.34  thf(c_0_152, negated_conjecture, ~((in @ esk56_0 @ (binunion @ esk54_0 @ esk55_0))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 0.23/0.34  thf(c_0_153, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_150, c_0_151])).
% 0.23/0.34  thf(c_0_154, negated_conjecture, (in @ esk56_0 @ esk54_0), inference(split_conjunct,[status(thm)],[c_0_145])).
% 0.23/0.34  thf(c_0_155, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_153]), c_0_154])]), ['proof']).
% 0.23/0.34  % SZS output end CNFRefutation
% 0.23/0.34  % Parsed axioms                        : 216
% 0.23/0.34  % Removed by relevancy pruning/SinE    : 0
% 0.23/0.34  % Initial clauses                      : 325
% 0.23/0.34  % Removed in clause preprocessing      : 128
% 0.23/0.34  % Initial clauses in saturation        : 197
% 0.23/0.34  % Processed clauses                    : 338
% 0.23/0.34  % ...of these trivial                  : 7
% 0.23/0.34  % ...subsumed                          : 49
% 0.23/0.34  % ...remaining for further processing  : 282
% 0.23/0.34  % Other redundant clauses eliminated   : 13
% 0.23/0.34  % Clauses deleted for lack of memory   : 0
% 0.23/0.34  % Backward-subsumed                    : 0
% 0.23/0.34  % Backward-rewritten                   : 5
% 0.23/0.34  % Generated clauses                    : 398
% 0.23/0.34  % ...of the previous two non-redundant : 313
% 0.23/0.34  % ...aggressively subsumed             : 0
% 0.23/0.34  % Contextual simplify-reflections      : 0
% 0.23/0.34  % Paramodulations                      : 377
% 0.23/0.34  % Factorizations                       : 2
% 0.23/0.34  % NegExts                              : 0
% 0.23/0.34  % Equation resolutions                 : 13
% 0.23/0.34  % Disequality decompositions           : 0
% 0.23/0.34  % Total rewrite steps                  : 108
% 0.23/0.34  % ...of those cached                   : 79
% 0.23/0.34  % Propositional unsat checks           : 0
% 0.23/0.34  %    Propositional check models        : 0
% 0.23/0.34  %    Propositional check unsatisfiable : 0
% 0.23/0.34  %    Propositional clauses             : 0
% 0.23/0.34  %    Propositional clauses after purity: 0
% 0.23/0.34  %    Propositional unsat core size     : 0
% 0.23/0.34  %    Propositional preprocessing time  : 0.000
% 0.23/0.34  %    Propositional encoding time       : 0.000
% 0.23/0.34  %    Propositional solver time         : 0.000
% 0.23/0.34  %    Success case prop preproc time    : 0.000
% 0.23/0.34  %    Success case prop encoding time   : 0.000
% 0.23/0.34  %    Success case prop solver time     : 0.000
% 0.23/0.34  % Current number of processed clauses  : 92
% 0.23/0.34  %    Positive orientable unit clauses  : 30
% 0.23/0.34  %    Positive unorientable unit clauses: 0
% 0.23/0.34  %    Negative unit clauses             : 3
% 0.23/0.34  %    Non-unit-clauses                  : 59
% 0.23/0.34  % Current number of unprocessed clauses: 331
% 0.23/0.34  % ...number of literals in the above   : 989
% 0.23/0.34  % Current number of archived formulas  : 0
% 0.23/0.34  % Current number of archived clauses   : 177
% 0.23/0.34  % Clause-clause subsumption calls (NU) : 5611
% 0.23/0.34  % Rec. Clause-clause subsumption calls : 1477
% 0.23/0.34  % Non-unit clause-clause subsumptions  : 35
% 0.23/0.34  % Unit Clause-clause subsumption calls : 60
% 0.23/0.34  % Rewrite failures with RHS unbound    : 0
% 0.23/0.34  % BW rewrite match attempts            : 10
% 0.23/0.34  % BW rewrite match successes           : 4
% 0.23/0.34  % Condensation attempts                : 0
% 0.23/0.34  % Condensation successes               : 0
% 0.23/0.34  % Termbank termtop insertions          : 47690
% 0.23/0.34  % Search garbage collected termcells   : 10581
% 0.23/0.34  
% 0.23/0.34  % -------------------------------------------------
% 0.23/0.34  % User time                : 0.043 s
% 0.23/0.34  % System time              : 0.014 s
% 0.23/0.34  % Total time               : 0.057 s
% 0.23/0.34  % Maximum resident set size: 6148 pages
% 0.23/0.34  
% 0.23/0.34  % -------------------------------------------------
% 0.23/0.34  % User time                : 0.140 s
% 0.23/0.34  % System time              : 0.040 s
% 0.23/0.34  % Total time               : 0.180 s
% 0.23/0.34  % Maximum resident set size: 5120 pages
% 0.23/0.34  % E exiting
%------------------------------------------------------------------------------