E---3.5.1.THM-CRf.s

View TPTP
Problem Process solution in
SystemOnTSTP Download .tgz
%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SEU580^1 : 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 : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:24:35 AM UTC 2026

% Result   : Theorem 1.65s 0.39s
% Output   : CNFRefutation 1.65s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01  % Problem  : SEU580^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.09  % Computer : n012.cluster.edu
% 0.00/0.09  % Model    : x86_64 x86_64
% 0.00/0.09  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.09  % Memory   : 8046.5625MB
% 0.00/0.09  % OS       : Linux 6.8.0-71-generic
% 0.00/0.10  % CPULimit : 300
% 0.00/0.10  % WCLimit  : 300
% 0.00/0.10  % DateTime : Tue Sep 29 13:51:33 UTC 2026
% 0.00/0.10  % CPUTime  : 
% 0.00/0.10  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12  Running higher-order theorem proving
% 0.08/0.13  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.arBos1G6G3/E---3.1_139219.p
% 1.65/0.39  % Version: 3.5.1-ho
% 1.65/0.39  % Preprocessing class: HSMMSLSSLLLCHSA.
% 1.65/0.39  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.65/0.39  % Starting new_ho_10 with 1500s (5) cores
% 1.65/0.39  % Starting sh5l with 300s (1) cores
% 1.65/0.39  % Starting new_bool_1 with 300s (1) cores
% 1.65/0.39  % Starting new_bool_2 with 300s (1) cores
% 1.65/0.39  % new_bool_2 with pid 139235 completed with status 0
% 1.65/0.39  % Result found by new_bool_2
% 1.65/0.39  % Preprocessing class: HSMMSLSSLLLCHSA.
% 1.65/0.39  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.65/0.39  % Starting new_ho_10 with 1500s (5) cores
% 1.65/0.39  % Starting sh5l with 300s (1) cores
% 1.65/0.39  % Starting new_bool_1 with 300s (1) cores
% 1.65/0.39  % Starting new_bool_2 with 300s (1) cores
% 1.65/0.39  % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.65/0.39  % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.65/0.39  % Search class: HGHSM-FSLS31-SHSMMSBN
% 1.65/0.39  % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.65/0.39  % Starting SubtermCWHack with 31s (1) cores
% 1.65/0.39  % SubtermCWHack with pid 139236 completed with status 0
% 1.65/0.39  % Result found by SubtermCWHack
% 1.65/0.39  % Preprocessing class: HSMMSLSSLLLCHSA.
% 1.65/0.39  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.65/0.39  % Starting new_ho_10 with 1500s (5) cores
% 1.65/0.39  % Starting sh5l with 300s (1) cores
% 1.65/0.39  % Starting new_bool_1 with 300s (1) cores
% 1.65/0.39  % Starting new_bool_2 with 300s (1) cores
% 1.65/0.39  % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.65/0.39  % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.65/0.39  % Search class: HGHSM-FSLS31-SHSMMSBN
% 1.65/0.39  % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.65/0.39  % Starting SubtermCWHack with 31s (1) cores
% 1.65/0.39  % Preprocessing time       : 0.002 s
% 1.65/0.39  
% 1.65/0.39  % Proof found!
% 1.65/0.39  % SZS status Theorem
% 1.65/0.39  % SZS output start CNFRefutation
% 1.65/0.39  thf(decl_23, type, in: $i > $i > $o).
% 1.65/0.39  thf(decl_24, type, exu: ($i > $o) > $o).
% 1.65/0.39  thf(decl_25, type, setextAx: $o).
% 1.65/0.39  thf(decl_26, type, emptyset: $i).
% 1.65/0.39  thf(decl_27, type, emptysetAx: $o).
% 1.65/0.39  thf(decl_28, type, setadjoin: $i > $i > $i).
% 1.65/0.39  thf(decl_29, type, setadjoinAx: $o).
% 1.65/0.39  thf(decl_30, type, powerset: $i > $i).
% 1.65/0.39  thf(decl_31, type, powersetAx: $o).
% 1.65/0.39  thf(decl_32, type, setunion: $i > $i).
% 1.65/0.39  thf(decl_33, type, setunionAx: $o).
% 1.65/0.39  thf(decl_34, type, omega: $i).
% 1.65/0.39  thf(decl_35, type, omega0Ax: $o).
% 1.65/0.39  thf(decl_36, type, omegaSAx: $o).
% 1.65/0.39  thf(decl_37, type, omegaIndAx: $o).
% 1.65/0.39  thf(decl_38, type, replAx: $o).
% 1.65/0.39  thf(decl_39, type, foundationAx: $o).
% 1.65/0.39  thf(decl_40, type, wellorderingAx: $o).
% 1.65/0.39  thf(decl_41, type, descr: ($i > $o) > $i).
% 1.65/0.39  thf(decl_42, type, descrp: $o).
% 1.65/0.39  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 1.65/0.39  thf(decl_44, type, dsetconstrI: $o).
% 1.65/0.39  thf(decl_45, type, dsetconstrEL: $o).
% 1.65/0.39  thf(decl_46, type, dsetconstrER: $o).
% 1.65/0.39  thf(decl_47, type, exuE1: $o).
% 1.65/0.39  thf(decl_48, type, prop2set: $o > $i).
% 1.65/0.39  thf(decl_49, type, prop2setE: $o).
% 1.65/0.39  thf(decl_50, type, emptysetE: $o).
% 1.65/0.39  thf(decl_51, type, emptysetimpfalse: $o).
% 1.65/0.39  thf(decl_52, type, notinemptyset: $o).
% 1.65/0.39  thf(decl_53, type, exuE3e: $o).
% 1.65/0.39  thf(decl_54, type, setext: $o).
% 1.65/0.39  thf(decl_55, type, emptyI: $o).
% 1.65/0.39  thf(decl_56, type, noeltsimpempty: $o).
% 1.65/0.39  thf(decl_57, type, setbeta: $o).
% 1.65/0.39  thf(decl_58, type, nonempty: $i > $o).
% 1.65/0.39  thf(decl_59, type, nonemptyE1: $o).
% 1.65/0.39  thf(decl_60, type, nonemptyI: $o).
% 1.65/0.39  thf(decl_61, type, nonemptyI1: $o).
% 1.65/0.39  thf(decl_62, type, setadjoinIL: $o).
% 1.65/0.39  thf(decl_63, type, emptyinunitempty: $o).
% 1.65/0.39  thf(decl_64, type, setadjoinIR: $o).
% 1.65/0.39  thf(decl_65, type, setadjoinE: $o).
% 1.65/0.39  thf(decl_66, type, setadjoinOr: $o).
% 1.65/0.39  thf(decl_67, type, setoftrueEq: $o).
% 1.65/0.39  thf(decl_68, type, powersetI: $o).
% 1.65/0.39  thf(decl_69, type, emptyinPowerset: $o).
% 1.65/0.39  thf(decl_70, type, emptyInPowerset: $o).
% 1.65/0.39  thf(decl_71, type, powersetE: $o).
% 1.65/0.39  thf(decl_72, type, setunionI: $o).
% 1.65/0.39  thf(decl_73, type, setunionE: $o).
% 1.65/0.39  thf(decl_74, type, subPowSU: $o).
% 1.65/0.39  thf(decl_75, type, exuE2: $o).
% 1.65/0.39  thf(decl_76, type, nonemptyImpWitness: $o).
% 1.65/0.39  thf(decl_77, type, uniqinunit: $o).
% 1.65/0.39  thf(decl_78, type, notinsingleton: $o).
% 1.65/0.39  thf(decl_79, type, eqinunit: $o).
% 1.65/0.39  thf(decl_80, type, singletonsswitch: $o).
% 1.65/0.39  thf(decl_81, type, upairsetE: $o).
% 1.65/0.39  thf(decl_82, type, upairsetIL: $o).
% 1.65/0.39  thf(decl_83, type, upairsetIR: $o).
% 1.65/0.39  thf(decl_84, type, emptyE1: $o).
% 1.65/0.39  thf(decl_85, type, vacuousDall: $o).
% 1.65/0.39  thf(decl_86, type, quantDeMorgan1: $o).
% 1.65/0.39  thf(decl_87, type, quantDeMorgan2: $o).
% 1.65/0.39  thf(decl_88, type, quantDeMorgan3: $o).
% 1.65/0.39  thf(decl_89, type, quantDeMorgan4: $o).
% 1.65/0.39  thf(decl_90, type, prop2setI: $o).
% 1.65/0.39  thf(decl_92, type, prop2set2propI: $o).
% 1.65/0.39  thf(decl_93, type, notdexE: $o).
% 1.65/0.39  thf(decl_94, type, notdallE: $o).
% 1.65/0.39  thf(decl_95, type, exuI1: $o).
% 1.65/0.39  thf(decl_96, type, exuI3: $o).
% 1.65/0.39  thf(decl_97, type, exuI2: $o).
% 1.65/0.39  thf(decl_98, type, inCongP: $o).
% 1.65/0.39  thf(decl_99, type, in__Cong: $o).
% 1.65/0.39  thf(decl_100, type, exuE3u: $o).
% 1.65/0.39  thf(decl_101, type, exu__Cong: $o).
% 1.65/0.39  thf(decl_102, type, emptyset__Cong: $o).
% 1.65/0.39  thf(decl_103, type, setadjoin__Cong: $o).
% 1.65/0.39  thf(decl_104, type, powerset__Cong: $o).
% 1.65/0.39  thf(decl_105, type, setunion__Cong: $o).
% 1.65/0.39  thf(decl_106, type, omega__Cong: $o).
% 1.65/0.39  thf(decl_107, type, exuEu: $o).
% 1.65/0.39  thf(decl_108, type, descr__Cong: $o).
% 1.65/0.39  thf(decl_109, type, dsetconstr__Cong: $o).
% 1.65/0.39  thf(decl_110, type, subset: $i > $i > $o).
% 1.65/0.39  thf(decl_113, type, subsetI1: $o).
% 1.65/0.39  thf(decl_114, type, eqimpsubset2: $o).
% 1.65/0.39  thf(decl_115, type, eqimpsubset1: $o).
% 1.65/0.39  thf(decl_116, type, subsetI2: $o).
% 1.65/0.39  thf(decl_117, type, emptysetsubset: $o).
% 1.65/0.39  thf(decl_118, type, subsetE: $o).
% 1.65/0.39  thf(decl_119, type, subsetE2: $o).
% 1.65/0.39  thf(decl_120, type, notsubsetI: $o).
% 1.65/0.39  thf(decl_121, type, notequalI1: $o).
% 1.65/0.39  thf(decl_122, type, notequalI2: $o).
% 1.65/0.39  thf(decl_123, type, subsetRefl: $o).
% 1.65/0.39  thf(decl_124, type, subsetTrans: $o).
% 1.65/0.39  thf(decl_125, type, setadjoinSub: $o).
% 1.65/0.39  thf(decl_126, type, setadjoinSub2: $o).
% 1.65/0.39  thf(decl_127, type, subset2powerset: $o).
% 1.65/0.39  thf(decl_128, type, setextsub: $o).
% 1.65/0.39  thf(decl_129, type, subsetemptysetimpeq: $o).
% 1.65/0.39  thf(decl_130, type, powersetI1: $o).
% 1.65/0.39  thf(decl_131, type, powersetE1: $o).
% 1.65/0.39  thf(decl_132, type, inPowerset: $o).
% 1.65/0.39  thf(decl_133, type, powersetsubset: $o).
% 1.65/0.39  thf(decl_134, type, epred1_0: $o).
% 1.65/0.39  thf(decl_135, type, esk1_2: $i > $i > $i).
% 1.65/0.39  thf(decl_136, type, esk2_2: $i > $i > $i).
% 1.65/0.39  thf(decl_137, type, esk3_2: $i > $i > $i).
% 1.65/0.39  thf(decl_138, type, esk4_1: $i > $i).
% 1.65/0.39  thf(decl_139, type, esk5_2: ($i > $i > $o) > $i > $i).
% 1.65/0.39  thf(decl_140, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 1.65/0.39  thf(decl_141, type, esk7_2: ($i > $i > $o) > $i > $i).
% 1.65/0.39  thf(decl_142, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 1.65/0.39  thf(decl_143, type, esk9_1: $i > $i).
% 1.65/0.39  thf(decl_144, type, esk10_2: ($i > $o) > $i > $i).
% 1.65/0.39  thf(decl_145, type, esk11_2: ($i > $o) > $i > $i).
% 1.65/0.39  thf(decl_146, type, esk12_1: ($i > $o) > $i).
% 1.65/0.39  thf(decl_147, type, esk13_2: ($i > $o) > $i > $i).
% 1.65/0.39  thf(decl_148, type, esk14_1: ($i > $o) > $i).
% 1.65/0.39  thf(decl_149, type, esk15_2: $i > $i > $i).
% 1.65/0.39  thf(decl_150, type, esk16_2: $i > $i > $i).
% 1.65/0.39  thf(decl_151, type, esk17_1: $i > $i).
% 1.65/0.39  thf(decl_152, type, esk18_1: $i > $i).
% 1.65/0.39  thf(decl_153, type, esk19_1: $i > $i).
% 1.65/0.39  thf(decl_154, type, esk20_2: $i > $i > $i).
% 1.65/0.39  thf(decl_155, type, esk21_3: $i > $i > $o > $i).
% 1.65/0.39  thf(decl_156, type, esk22_2: ($i > $o) > $i > $i).
% 1.65/0.39  thf(decl_157, type, esk23_1: ($i > $o) > $i).
% 1.65/0.39  thf(decl_158, type, esk24_1: $i > $i).
% 1.65/0.39  thf(decl_159, type, esk25_2: $i > ($i > $o) > $i).
% 1.65/0.39  thf(decl_160, type, esk26_2: $i > ($i > $o) > $i).
% 1.65/0.39  thf(decl_161, type, esk27_2: $i > ($i > $o) > $i).
% 1.65/0.39  thf(decl_162, type, esk28_2: $i > ($i > $o) > $i).
% 1.65/0.39  thf(decl_163, type, esk29_2: $i > ($i > $o) > $i).
% 1.65/0.39  thf(decl_164, type, esk30_2: $i > ($i > $o) > $i).
% 1.65/0.39  thf(decl_165, type, esk31_2: ($i > $o) > $i > $i).
% 1.65/0.39  thf(decl_166, type, esk32_1: ($i > $o) > $i).
% 1.65/0.39  thf(decl_167, type, esk33_1: ($i > $o) > $i).
% 1.65/0.39  thf(decl_168, type, esk34_1: ($i > $o) > $i).
% 1.65/0.39  thf(decl_169, type, esk35_1: ($i > $o) > $i).
% 1.65/0.39  thf(decl_170, type, esk36_2: ($i > $o) > $i > $i).
% 1.65/0.39  thf(decl_171, type, esk37_1: ($i > $o) > $i).
% 1.65/0.39  thf(decl_172, type, esk38_2: ($i > $o) > $i > $i).
% 1.65/0.39  thf(decl_173, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 1.65/0.39  thf(decl_174, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 1.65/0.39  thf(decl_175, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.65/0.39  thf(decl_176, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 1.65/0.39  thf(decl_177, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.65/0.39  thf(decl_178, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 1.65/0.39  thf(decl_179, type, esk45_2: ($i > $o) > $i > $i).
% 1.65/0.39  thf(decl_180, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 1.65/0.39  thf(decl_181, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 1.65/0.39  thf(decl_182, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.65/0.39  thf(decl_183, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.65/0.39  thf(decl_184, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.65/0.39  thf(decl_185, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.65/0.39  thf(decl_186, type, esk52_2: $i > $i > $i).
% 1.65/0.39  thf(decl_187, type, esk53_2: $i > $i > $i).
% 1.65/0.39  thf(decl_188, type, esk54_0: $i).
% 1.65/0.39  thf(decl_189, type, epred2_0: $i > $o).
% 1.65/0.39  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', exuE3e)).
% 1.65/0.39  thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', exu)).
% 1.65/0.39  thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', nonempty)).
% 1.65/0.39  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', nonemptyI)).
% 1.65/0.39  thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', exuE2)).
% 1.65/0.39  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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', exu__Cong)).
% 1.65/0.39  thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', exuE3u)).
% 1.65/0.39  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.arBos1G6G3/E---3.1_139219.p', exuI2)).
% 1.65/0.39  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', exuI3)).
% 1.65/0.39  thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', exuI1)).
% 1.65/0.39  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', descr__Cong)).
% 1.65/0.39  thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', exuEu)).
% 1.65/0.39  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.arBos1G6G3/E---3.1_139219.p', exuE1)).
% 1.65/0.39  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', descrp)).
% 1.65/0.39  thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', replAx)).
% 1.65/0.39  thf(sepInPowerset, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', sepInPowerset)).
% 1.65/0.39  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', nonemptyE1)).
% 1.65/0.39  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setbeta)).
% 1.65/0.39  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setoftrueEq)).
% 1.65/0.39  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', nonemptyI1)).
% 1.65/0.39  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', nonemptyImpWitness)).
% 1.65/0.39  thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.arBos1G6G3/E---3.1_139219.p', emptyE1)).
% 1.65/0.39  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', dsetconstr__Cong)).
% 1.65/0.39  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', dsetconstrER)).
% 1.65/0.39  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', dsetconstrEL)).
% 1.65/0.39  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', dsetconstrI)).
% 1.65/0.39  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', subsetE2)).
% 1.65/0.39  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', subsetE)).
% 1.65/0.39  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', notsubsetI)).
% 1.65/0.39  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', notequalI1)).
% 1.65/0.39  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', notequalI2)).
% 1.65/0.39  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', subsetRefl)).
% 1.65/0.39  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', subsetTrans)).
% 1.65/0.39  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setadjoinSub)).
% 1.65/0.39  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setadjoinSub2)).
% 1.65/0.39  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', subset2powerset)).
% 1.65/0.39  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setextsub)).
% 1.65/0.39  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', subsetemptysetimpeq)).
% 1.65/0.39  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', powersetI1)).
% 1.65/0.39  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', powersetE1)).
% 1.65/0.39  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', inPowerset)).
% 1.65/0.39  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', emptysetE)).
% 1.65/0.39  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', powersetsubset)).
% 1.65/0.39  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', noeltsimpempty)).
% 1.65/0.39  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', emptyI)).
% 1.65/0.39  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.arBos1G6G3/E---3.1_139219.p', setext)).
% 1.65/0.39  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', powersetE)).
% 1.65/0.39  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', emptyInPowerset)).
% 1.65/0.39  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', notinemptyset)).
% 1.65/0.39  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setadjoinOr)).
% 1.65/0.39  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.arBos1G6G3/E---3.1_139219.p', setadjoinE)).
% 1.65/0.39  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setadjoinIR)).
% 1.65/0.39  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', emptyinunitempty)).
% 1.65/0.39  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setadjoinIL)).
% 1.65/0.39  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', powersetI)).
% 1.65/0.39  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', subPowSU)).
% 1.65/0.39  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.arBos1G6G3/E---3.1_139219.p', setunionE)).
% 1.65/0.39  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setunionI)).
% 1.65/0.39  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', emptyinPowerset)).
% 1.65/0.39  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', upairsetIR)).
% 1.65/0.39  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', upairsetIL)).
% 1.65/0.39  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', upairsetE)).
% 1.65/0.39  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', singletonsswitch)).
% 1.65/0.39  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', eqinunit)).
% 1.65/0.39  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', notinsingleton)).
% 1.65/0.39  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', uniqinunit)).
% 1.65/0.39  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', emptysetimpfalse)).
% 1.65/0.39  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', notdexE)).
% 1.65/0.39  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', prop2setI)).
% 1.65/0.39  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', quantDeMorgan4)).
% 1.65/0.39  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', quantDeMorgan3)).
% 1.65/0.39  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', quantDeMorgan2)).
% 1.65/0.39  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', quantDeMorgan1)).
% 1.65/0.39  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', vacuousDall)).
% 1.65/0.39  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', notdallE)).
% 1.65/0.39  thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', in__Cong)).
% 1.65/0.39  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', inCongP)).
% 1.65/0.39  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', emptyset__Cong)).
% 1.65/0.39  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', omega__Cong)).
% 1.65/0.39  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setunion__Cong)).
% 1.65/0.39  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', powerset__Cong)).
% 1.65/0.39  thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setadjoin__Cong)).
% 1.65/0.39  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', eqimpsubset2)).
% 1.65/0.39  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', eqimpsubset1)).
% 1.65/0.39  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', subsetI2)).
% 1.65/0.39  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', emptysetsubset)).
% 1.65/0.39  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', subsetI1)).
% 1.65/0.39  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', prop2setE)).
% 1.65/0.39  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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', wellorderingAx)).
% 1.65/0.39  thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', foundationAx)).
% 1.65/0.39  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.arBos1G6G3/E---3.1_139219.p', omegaIndAx)).
% 1.65/0.39  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', omegaSAx)).
% 1.65/0.39  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', omega0Ax)).
% 1.65/0.39  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setunionAx)).
% 1.65/0.39  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', powersetAx)).
% 1.65/0.39  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setadjoinAx)).
% 1.65/0.39  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', emptysetAx)).
% 1.65/0.39  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.arBos1G6G3/E---3.1_139219.p', setextAx)).
% 1.65/0.39  thf(c_0_98, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 1.65/0.39  thf(c_0_99, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 1.65/0.39  thf(c_0_100, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 1.65/0.39  thf(c_0_101, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.65/0.39  thf(c_0_102, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 1.65/0.39  thf(c_0_103, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 1.65/0.39  thf(c_0_104, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 1.65/0.39  thf(c_0_105, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 1.65/0.39  thf(c_0_106, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 1.65/0.39  thf(c_0_107, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 1.65/0.39  thf(c_0_108, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 1.65/0.39  thf(c_0_109, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 1.65/0.39  thf(c_0_110, 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])).
% 1.65/0.39  thf(c_0_111, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 1.65/0.39  thf(c_0_112, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 1.65/0.39  thf(c_0_113, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[sepInPowerset])).
% 1.65/0.39  thf(c_0_114, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X284:$i]:(((((X1 @ X284)))&(![X285:$i]:(((((X1 @ X285)))=>(((X284)=(X285))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_98, c_0_99])).
% 1.65/0.39  thf(c_0_115, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_100])).
% 1.65/0.39  thf(c_0_116, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 1.65/0.39  thf(c_0_117, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_101, c_0_100])).
% 1.65/0.39  thf(c_0_118, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 1.65/0.39  thf(c_0_119, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_100])).
% 1.65/0.39  thf(c_0_120, plain, ((exuE2)=(![X1:$i > $o]:((((?[X286:$i]:(((((X1 @ X286)))&(![X287:$i]:(((((X1 @ X287)))=>(((X286)=(X287))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_102, c_0_99])).
% 1.65/0.39  thf(c_0_121, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_100])).
% 1.65/0.39  thf(c_0_122, 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])).
% 1.65/0.39  thf(c_0_123, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X296:$i]:(((((X1 @ X296)))&(![X297:$i]:(((((X1 @ X297)))=>(((X296)=(X297))))))))))<=>((?[X298:$i]:(((((X17 @ X298)))&(![X299:$i]:(((((X17 @ X299)))=>(((X298)=(X299)))))))))))))))), inference(apply_def,[status(thm)],[c_0_103, c_0_99])).
% 1.65/0.39  thf(c_0_124, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X294:$i]:(((((X1 @ X294)))&(![X295:$i]:(((((X1 @ X295)))=>(((X294)=(X295))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_104, c_0_99])).
% 1.65/0.39  thf(c_0_125, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X292:$i]:(((((X1 @ X292)))&(![X293:$i]:(((((X1 @ X293)))=>(((X292)=(X293)))))))))))))), inference(apply_def,[status(thm)],[c_0_105, c_0_99])).
% 1.65/0.39  thf(c_0_126, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X290:$i]:(((((X1 @ X290)))&(![X291:$i]:(((((X1 @ X291)))=>(((X290)=(X291)))))))))))))))), inference(apply_def,[status(thm)],[c_0_106, c_0_99])).
% 1.65/0.39  thf(c_0_127, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X288:$i]:(((((X1 @ X288)))&(![X289:$i]:(((((X1 @ X289)))=>(((X288)=(X289)))))))))))))), inference(apply_def,[status(thm)],[c_0_107, c_0_99])).
% 1.65/0.39  thf(c_0_128, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 1.65/0.39  thf(c_0_129, plain, ((descr__Cong)=(![X1:$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:$i]:(((((X17 @ X305)))=>(((X304)=(X305))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_108, c_0_99])).
% 1.65/0.39  thf(c_0_130, plain, ((exuEu)=(![X1:$i > $o]:((((?[X300:$i]:(((((X1 @ X300)))&(![X301:$i]:(((((X1 @ X301)))=>(((X300)=(X301))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_109, c_0_99])).
% 1.65/0.39  thf(c_0_131, plain, ((exuE1)=(![X1:$i > $o]:((((?[X282:$i]:(((((X1 @ X282)))&(![X283:$i]:(((((X1 @ X283)))=>(((X282)=(X283))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_110, c_0_99])).
% 1.65/0.39  thf(c_0_132, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 1.65/0.39  thf(c_0_133, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 1.65/0.39  thf(c_0_134, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 1.65/0.39  thf(c_0_135, plain, ((descrp)=(![X1:$i > $o]:((((?[X280:$i]:(((((X1 @ X280)))&(![X281:$i]:(((((X1 @ X281)))=>(((X280)=(X281))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_111, c_0_99])).
% 1.65/0.39  thf(c_0_136, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X278:$i]:(((((X6 @ X2 @ X278)))&(![X279:$i]:(((((X6 @ X2 @ X279)))=>(((X278)=(X279)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_112, c_0_99])).
% 1.65/0.39  thf(c_0_137, plain, ((epred1_0)<=>![X335:$i]:(?[X336:$i]:((((![X337:$i]:(((in @ X337 @ X336)=>![X338:$i]:(((in @ X338 @ X337)=>(in @ X338 @ X335)))))&![X339:$i, X340:$i]:((((in @ X339 @ X335)&(in @ X340 @ X335))=>(![X341:$i]:(((in @ X341 @ X336)=>((in @ X339 @ X341)<=>(in @ X340 @ X341))))=>((X339)=(X340))))))&![X342:$i, X343:$i]:((((in @ X342 @ X336)&(in @ X343 @ X336))=>(![X344:$i]:(((in @ X344 @ X342)=>(in @ X344 @ X343)))|![X345:$i]:(((in @ X345 @ X343)=>(in @ X345 @ X342)))))))&![X346:$i]:(((![X347:$i]:(((in @ X347 @ X346)=>(in @ X347 @ X335)))&?[X348:$i]:((in @ X348 @ X346)))=>?[X349:$i, X350:$i]:(((((in @ X349 @ X336)&(in @ X350 @ X346))&~(?[X351:$i]:(((in @ X351 @ X349)&(in @ X351 @ X346)))))&![X352:$i]:(((in @ X352 @ X336)=>(![X353:$i]:(((in @ X353 @ X352)=>(in @ X353 @ X349)))|(in @ X350 @ X352)))))))))))), introduced(definition)).
% 1.65/0.39  thf(c_0_138, negated_conjecture, ~((![X306:$i, X307:$i]:((![X308:$i]:(((in @ X308 @ X306)<=>(in @ X308 @ X307)))=>((X306)=(X307))))=>(![X309:$i]:(~(in @ X309 @ emptyset))=>(![X310:$i, X311:$i, X312:$i]:(((in @ X312 @ (setadjoin @ X310 @ X311))<=>(((X312)=(X310))|(in @ X312 @ X311))))=>(![X313:$i, X314:$i]:(((in @ X314 @ (powerset @ X313))<=>![X315:$i]:(((in @ X315 @ X314)=>(in @ X315 @ X313)))))=>(![X316:$i, X317:$i]:(((in @ X317 @ (setunion @ X316))<=>?[X318:$i]:(((in @ X317 @ X318)&(in @ X318 @ X316)))))=>((in @ emptyset @ omega)=>(![X319:$i]:(((in @ X319 @ omega)=>(in @ (setadjoin @ X319 @ X319) @ omega)))=>(![X320:$i]:((((in @ emptyset @ X320)&![X321:$i]:((((in @ X321 @ omega)&(in @ X321 @ X320))=>(in @ (setadjoin @ X321 @ X321) @ X320))))=>![X322:$i]:(((in @ X322 @ omega)=>(in @ X322 @ X320)))))=>(![X323:$i > $i > $o, X324:$i]:((![X325:$i]:(((in @ X325 @ X324)=>?[X326:$i]:(((X323 @ X325 @ X326)&![X327:$i]:(((X323 @ X325 @ X327)=>((X326)=(X327))))))))=>?[X328:$i]:(![X329:$i]:(((in @ X329 @ X328)<=>?[X330:$i]:(((in @ X330 @ X324)&(X323 @ X330 @ X329))))))))=>(![X331:$i]:((?[X332:$i]:((in @ X332 @ X331))=>?[X333:$i]:(((in @ X333 @ X331)&~(?[X334:$i]:(((in @ X334 @ X333)&(in @ X334 @ X331))))))))=>((epred1_0)=>(![X354:$i > $o]:((?[X355:$i]:(((X354 @ X355)&![X356:$i]:(((X354 @ X356)=>((X355)=(X356))))))=>(X354 @ (descr @ (^[Z0:$i]:((X354 @ Z0)))))))=>(![X357:$i, X358:$i > $o, X359:$i]:(((in @ X359 @ X357)=>((X358 @ X359)=>(in @ X359 @ (dsetconstr @ X357 @ (^[Z0:$i]:((X358 @ Z0))))))))=>(![X360:$i, X361:$i > $o, X362:$i]:(((in @ X362 @ (dsetconstr @ X360 @ (^[Z0:$i]:((X361 @ Z0)))))=>(in @ X362 @ X360)))=>(![X363:$i, X364:$i > $o, X365:$i]:(((in @ X365 @ (dsetconstr @ X363 @ (^[Z0:$i]:((X364 @ Z0)))))=>(X364 @ X365)))=>(![X366:$i > $o]:((?[X367:$i]:(((X366 @ X367)&![X368:$i]:(((X366 @ X368)=>((X367)=(X368))))))=>?[X369:$i]:(((X366 @ X369)&![X370:$i]:(((X366 @ X370)=>((X369)=(X370))))))))=>(![X371:$o, X372:$i]:(((in @ X372 @ (prop2set @ ((X371))))=>(X371)))=>(![X373:$i]:(((in @ X373 @ emptyset)=>![X374:$o]:((X374))))=>(![X375:$i]:(~(in @ X375 @ emptyset))=>(![X376:$i]:(~(in @ X376 @ emptyset))=>(![X377:$i > $o]:((?[X378:$i]:(((X377 @ X378)&![X379:$i]:(((X377 @ X379)=>((X378)=(X379))))))=>?[X380:$i]:((X377 @ X380))))=>(![X381:$i, X382:$i]:((![X383:$i]:(((in @ X383 @ X381)=>(in @ X383 @ X382)))=>(![X384:$i]:(((in @ X384 @ X382)=>(in @ X384 @ X381)))=>((X381)=(X382)))))=>(![X385:$i]:((![X386:$i]:(~(in @ X386 @ X385))=>((X385)=(emptyset))))=>(![X387:$i]:((![X388:$i]:(~(in @ X388 @ X387))=>((X387)=(emptyset))))=>(![X389:$i, X390:$i > $o, X391:$i]:(((in @ X391 @ X389)=>((in @ X391 @ (dsetconstr @ X389 @ (^[Z0:$i]:((X390 @ Z0)))))<=>(X390 @ X391))))=>(![X392:$i]:((((X392)!=(emptyset))=>?[X393:$i]:((in @ X393 @ X392))))=>(![X394:$i, X395:$i > $o, X396:$i]:(((in @ X396 @ X394)=>((X395 @ X396)=>((dsetconstr @ X394 @ (^[Z0:$i]:((X395 @ Z0))))!=(emptyset)))))=>(![X397:$i]:((?[X398:$i]:((in @ X398 @ X397))=>((X397)!=(emptyset))))=>(![X399:$i, X400:$i]:((in @ X399 @ (setadjoin @ X399 @ X400)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X401:$i, X402:$i, X403:$i]:(((in @ X403 @ X402)=>(in @ X403 @ (setadjoin @ X401 @ X402))))=>(![X404:$i, X405:$i, X406:$i]:(((in @ X406 @ (setadjoin @ X404 @ X405))=>![X407:$o]:(((((X406)=(X404))=>(X407))=>(((in @ X406 @ X405)=>(X407))=>(X407))))))=>(![X408:$i, X409:$i, X410:$i]:(((in @ X410 @ (setadjoin @ X408 @ X409))=>(((X410)=(X408))|(in @ X410 @ X409))))=>(![X411:$i]:(((dsetconstr @ X411 @ (^[Z0:$i]:(($true))))=(X411)))=>(![X412:$i, X413:$i]:((![X414:$i]:(((in @ X414 @ X413)=>(in @ X414 @ X412)))=>(in @ X413 @ (powerset @ X412))))=>(![X415:$i]:((in @ emptyset @ (powerset @ X415)))=>(![X416:$i]:((in @ emptyset @ (powerset @ X416)))=>(![X417:$i, X418:$i, X419:$i]:(((in @ X418 @ (powerset @ X417))=>((in @ X419 @ X418)=>(in @ X419 @ X417))))=>(![X420:$i, X421:$i, X422:$i]:(((in @ X421 @ X422)=>((in @ X422 @ X420)=>(in @ X421 @ (setunion @ X420)))))=>(![X423:$i, X424:$i]:(((in @ X424 @ (setunion @ X423))=>![X425:$o]:((![X426:$i]:(((in @ X424 @ X426)=>((in @ X426 @ X423)=>(X425))))=>(X425)))))=>(![X427:$i, X428:$i]:(((in @ X428 @ X427)=>(in @ X428 @ (powerset @ (setunion @ X427)))))=>(![X429:$i > $o]:((?[X430:$i]:(((X429 @ X430)&![X431:$i]:(((X429 @ X431)=>((X430)=(X431))))))=>?[X432:$i]:(![X433:$i]:(((X429 @ X433)<=>((X433)=(X432)))))))=>(![X434:$i]:((((X434)!=(emptyset))=>?[X435:$i]:((in @ X435 @ X434))))=>(![X436:$i, X437:$i]:(((in @ X436 @ (setadjoin @ X437 @ emptyset))=>((X436)=(X437))))=>(![X438:$i, X439:$i]:((((X438)!=(X439))=>~(in @ X439 @ (setadjoin @ X438 @ emptyset))))=>(![X440:$i, X441:$i]:((((X440)=(X441))=>(in @ X440 @ (setadjoin @ X441 @ emptyset))))=>(![X442:$i, X443:$i]:(((in @ X442 @ (setadjoin @ X443 @ emptyset))=>(in @ X443 @ (setadjoin @ X442 @ emptyset))))=>(![X444:$i, X445:$i, X446:$i]:(((in @ X446 @ (setadjoin @ X444 @ (setadjoin @ X445 @ emptyset)))=>(((X446)=(X444))|((X446)=(X445)))))=>(![X447:$i, X448:$i]:((in @ X447 @ (setadjoin @ X447 @ (setadjoin @ X448 @ emptyset))))=>(![X449:$i, X450:$i]:((in @ X450 @ (setadjoin @ X449 @ (setadjoin @ X450 @ emptyset))))=>(![X451:$i, X452:$i > $o]:((?[X453:$i]:(((in @ X453 @ X451)&(X452 @ X453)))=>((dsetconstr @ X451 @ (^[Z0:$i]:((X452 @ Z0))))!=(emptyset))))=>(![X454:$i > $o, X455:$i]:(((in @ X455 @ emptyset)=>(X454 @ X455)))=>(![X456:$i, X457:$i > $o]:((~(![X458:$i]:(((in @ X458 @ X456)=>(X457 @ X458))))=>?[X459:$i]:(((in @ X459 @ X456)&~(X457 @ X459)))))=>(![X460:$i, X461:$i > $o]:((![X462:$i]:(((in @ X462 @ X460)=>~(X461 @ X462)))=>~(?[X463:$i]:(((in @ X463 @ X460)&(X461 @ X463))))))=>(![X464:$i, X465:$i > $o]:((~(?[X466:$i]:(((in @ X466 @ X464)&(X465 @ X466))))=>![X467:$i]:(((in @ X467 @ X464)=>~(X465 @ X467)))))=>(![X468:$i, X469:$i > $o]:((?[X470:$i]:(((in @ X470 @ X468)&~(X469 @ X470)))=>~(![X471:$i]:(((in @ X471 @ X468)=>(X469 @ X471))))))=>(![X472:$o]:(((X472)=>(in @ emptyset @ (prop2set @ ((X472))))))=>((prop2set2propI)=>(![X473:$i, X474:$i > $o]:((~(?[X475:$i]:(((in @ X475 @ X473)&(X474 @ X475))))=>![X476:$i]:(((in @ X476 @ X473)=>~(X474 @ X476)))))=>(![X477:$i, X478:$i > $o]:((~(![X479:$i]:(((in @ X479 @ X477)=>(X478 @ X479))))=>?[X480:$i]:(((in @ X480 @ X477)&~(X478 @ X480)))))=>(![X481:$i > $o]:((?[X482:$i]:(((X481 @ X482)&![X483:$i]:(((X481 @ X483)=>((X482)=(X483))))))=>?[X484:$i]:(((X481 @ X484)&![X485:$i]:(((X481 @ X485)=>((X484)=(X485))))))))=>(![X486:$i > $o]:((?[X487:$i]:((X486 @ X487))=>(![X488:$i, X489:$i]:(((X486 @ X488)=>((X486 @ X489)=>((X488)=(X489)))))=>?[X490:$i]:(((X486 @ X490)&![X491:$i]:(((X486 @ X491)=>((X490)=(X491)))))))))=>(![X492:$i > $o]:((?[X493:$i]:(![X494:$i]:(((X492 @ X494)<=>((X494)=(X493)))))=>?[X495:$i]:(((X492 @ X495)&![X496:$i]:(((X492 @ X496)=>((X495)=(X496))))))))=>(![X497:$i, X498:$i]:((((X497)=(X498))=>![X499:$i, X500:$i]:((((X499)=(X500))=>((in @ X499 @ X497)=>(in @ X500 @ X498))))))=>(![X501:$i, X502:$i]:((((X501)=(X502))=>![X503:$i, X504:$i]:((((X503)=(X504))=>((in @ X503 @ X501)<=>(in @ X504 @ X502))))))=>(![X505:$i > $o]:((?[X506:$i]:(((X505 @ X506)&![X507:$i]:(((X505 @ X507)=>((X506)=(X507))))))=>![X508:$i, X509:$i]:(((X505 @ X508)=>((X505 @ X509)=>((X508)=(X509)))))))=>(![X510:$i > $o, X511:$i > $o]:((![X512:$i, X513:$i]:((((X512)=(X513))=>((X510 @ X512)<=>(X511 @ X513))))=>(?[X514:$i]:(((X510 @ X514)&![X515:$i]:(((X510 @ X515)=>((X514)=(X515))))))<=>?[X516:$i]:(((X511 @ X516)&![X517:$i]:(((X511 @ X517)=>((X516)=(X517)))))))))=>(((emptyset)=(emptyset))=>(![X518:$i, X519:$i]:((((X518)=(X519))=>![X520:$i, X521:$i]:((((X520)=(X521))=>((setadjoin @ X518 @ X520)=(setadjoin @ X519 @ X521))))))=>(![X522:$i, X523:$i]:((((X522)=(X523))=>((powerset @ X522)=(powerset @ X523))))=>(![X524:$i, X525:$i]:((((X524)=(X525))=>((setunion @ X524)=(setunion @ X525))))=>(((omega)=(omega))=>(![X526:$i > $o]:((?[X527:$i]:(((X526 @ X527)&![X528:$i]:(((X526 @ X528)=>((X527)=(X528))))))=>![X529:$i, X530:$i]:(((X526 @ X529)=>((X526 @ X530)=>((X529)=(X530)))))))=>(![X531:$i > $o, X532:$i > $o]:((![X533:$i, X534:$i]:((((X533)=(X534))=>((X531 @ X533)<=>(X532 @ X534))))=>(?[X535:$i]:(((X531 @ X535)&![X536:$i]:(((X531 @ X536)=>((X535)=(X536))))))=>(?[X537:$i]:(((X532 @ X537)&![X538:$i]:(((X532 @ X538)=>((X537)=(X538))))))=>((descr @ (^[Z0:$i]:((X531 @ Z0))))=(descr @ (^[Z0:$i]:((X532 @ Z0)))))))))=>(![X539:$i, X540:$i]:((((X539)=(X540))=>![X541:$i > $o, X542:$i > $o]:((![X543:$i]:(((in @ X543 @ X539)=>![X544:$i]:(((in @ X544 @ X540)=>(((X543)=(X544))=>((X541 @ X543)<=>(X542 @ X544)))))))=>((dsetconstr @ X539 @ (^[Z0:$i]:((X541 @ Z0))))=(dsetconstr @ X540 @ (^[Z0:$i]:((X542 @ Z0)))))))))=>(![X545:$i, X546:$i]:((![X547:$i]:(((in @ X547 @ X545)=>(in @ X547 @ X546)))=>(subset @ X545 @ X546)))=>(![X548:$i, X549:$i]:((((X548)=(X549))=>(subset @ X549 @ X548)))=>(![X550:$i, X551:$i]:((((X550)=(X551))=>(subset @ X550 @ X551)))=>(![X552:$i, X553:$i]:((![X554:$i]:(((in @ X554 @ X552)=>(in @ X554 @ X553)))=>(subset @ X552 @ X553)))=>(![X555:$i]:((subset @ emptyset @ X555))=>(![X556:$i, X557:$i, X558:$i]:(((subset @ X556 @ X557)=>((in @ X558 @ X556)=>(in @ X558 @ X557))))=>(![X559:$i, X560:$i, X561:$i]:(((subset @ X559 @ X560)=>(~(in @ X561 @ X560)=>~(in @ X561 @ X559))))=>(![X562:$i, X563:$i, X564:$i]:(((in @ X564 @ X562)=>(~(in @ X564 @ X563)=>~(subset @ X562 @ X563))))=>(![X565:$i, X566:$i]:((~(subset @ X565 @ X566)=>((X565)!=(X566))))=>(![X567:$i, X568:$i, X569:$i]:(((in @ X569 @ X567)=>(~(in @ X569 @ X568)=>((X567)!=(X568)))))=>(![X570:$i]:((subset @ X570 @ X570))=>(![X571:$i, X572:$i, X573:$i]:(((subset @ X571 @ X572)=>((subset @ X572 @ X573)=>(subset @ X571 @ X573))))=>(![X574:$i, X575:$i]:((subset @ X575 @ (setadjoin @ X574 @ X575)))=>(![X576:$i, X577:$i, X578:$i]:(((subset @ X576 @ X578)=>(subset @ X576 @ (setadjoin @ X577 @ X578))))=>(![X579:$i, X580:$i]:(((subset @ X579 @ X580)=>(in @ X579 @ (powerset @ X580))))=>(![X581:$i, X582:$i]:(((subset @ X581 @ X582)=>((subset @ X582 @ X581)=>((X581)=(X582)))))=>(![X583:$i]:(((subset @ X583 @ emptyset)=>((X583)=(emptyset))))=>(![X584:$i, X585:$i]:(((subset @ X585 @ X584)=>(in @ X585 @ (powerset @ X584))))=>(![X586:$i, X587:$i]:(((in @ X587 @ (powerset @ X586))=>(subset @ X587 @ X586)))=>(![X588:$i]:((in @ X588 @ (powerset @ X588)))=>(![X589:$i, X590:$i]:(((subset @ X589 @ X590)=>(subset @ (powerset @ X589) @ (powerset @ X590))))=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_113]), c_0_114]), subsetE2]), subsetE]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), c_0_115]), inPowerset]), emptysetE]), powersetsubset]), c_0_116]), noeltsimpempty]), emptyI]), setext]), powersetE]), emptyInPowerset]), notinemptyset]), c_0_117]), c_0_118]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_119]), powersetI]), c_0_120]), subPowSU]), setunionE]), setunionI]), emptyinPowerset]), c_0_121]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), emptysetimpfalse]), c_0_122]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), notdallE]), c_0_123]), c_0_124]), in__Cong]), inCongP]), c_0_125]), c_0_126]), c_0_127]), emptyset__Cong]), c_0_128]), c_0_129]), c_0_130]), omega__Cong]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetI1]), prop2setE]), c_0_131]), c_0_132]), c_0_133]), c_0_134]), c_0_135]), wellorderingAx]), foundationAx]), c_0_136]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_137])).
% 1.65/0.39  thf(c_0_139, negated_conjecture, ![X591:$i, X592:$i, X594:$i, X595:$i, X596:$i, X597:$i, X598:$i, X599:$i, X600:$i, X601:$i, X602:$i, X604:$i, X605:$i, X607:$i, X608:$i, X609:$i, X610:$i, X611:$i, X613:$i, X614:$i > $i > $o, X615:$i, X617:$i, X620:$i, X622:$i, X623:$i, X624:$i, X625:$i, X627:$i, X628:$i > $o, X629:$i, X631:$i, X632:$i > $o, X633:$i, X634:$i, X635:$i > $o, X636:$i, X637:$i, X638:$i > $o, X639:$i, X640:$i > $o, X641:$i, X644:$i, X645:$o, X646:$i, X647:$i, X648:$o, X649:$i, X650:$i, X651:$i > $o, X652:$i, X655:$i, X656:$i, X659:$i, X661:$i, X663:$i, X664:$i > $o, X665:$i, X666:$i, X668:$i, X669:$i > $o, X670:$i, X671:$i, X672:$i, X673:$i, X674:$i, X675:$i, X676:$i, X677:$i, X678:$i, X679:$i, X680:$i, X681:$o, X682:$i, X683:$i, X684:$i, X685:$i, X686:$i, X687:$i, X689:$i, X690:$i, X691:$i, X692:$i, X693:$i, X694:$i, X695:$i, X696:$i, X697:$i, X698:$i, X699:$o, X701:$i, X702:$i, X703:$i > $o, X704:$i, X707:$i, X708:$i, X709:$i, X711:$i, X712:$i, X713:$i, X714:$i, X715:$i, X716:$i, X717:$i, X718:$i, X719:$i, X720:$i, X721:$i, X722:$i, X723:$i, X724:$i, X725:$i, X726:$i, X727:$i > $o, X728:$i, X729:$i > $o, X730:$i, X731:$i, X732:$i > $o, X733:$i, X735:$i, X736:$i > $o, X738:$i, X739:$i, X740:$i > $o, X742:$i, X743:$i, X744:$i > $o, X745:$i, X747:$o, X748:$i, X749:$i > $o, X751:$i, X752:$i, X753:$i > $o, X754:$i, X756:$i > $o, X757:$i, X760:$i, X761:$i > $o, X762:$i, X766:$i, X767:$i > $o, X768:$i, X771:$i, X772:$i, X773:$i, X774:$i, X775:$i, X776:$i, X777:$i, X778:$i, X779:$i, X780:$i > $o, X781:$i, X783:$i, X784:$i, X785:$i > $o, X786:$i > $o, X789:$i, X792:$i, X793:$i, X796:$i, X797:$i, X798:$i, X799:$i, X800:$i, X801:$i, X802:$i, X803:$i, X804:$i, X805:$i > $o, X806:$i, X808:$i, X809:$i, X810:$i > $o, X811:$i > $o, X814:$i, X816:$i, X818:$i, X819:$i, X820:$i > $o, X821:$i > $o, X824:$i, X825:$i, X827:$i, X828:$i, X829:$i, X830:$i, X831:$i, X832:$i, X834:$i, X835:$i, X836:$i, X837:$i, X838:$i, X839:$i, X840:$i, X841:$i, X842:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i, X848:$i, X849:$i, X850:$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]:((((~(in @ (esk1_2 @ X591 @ X592) @ X591)|~(in @ (esk1_2 @ X591 @ X592) @ X592)|((X591)=(X592)))&((in @ (esk1_2 @ X591 @ X592) @ X591)|(in @ (esk1_2 @ X591 @ X592) @ X592)|((X591)=(X592))))&(~(in @ X594 @ emptyset)&(((~(in @ X597 @ (setadjoin @ X595 @ X596))|(((X597)=(X595))|(in @ X597 @ X596)))&((((X597)!=(X595))|(in @ X597 @ (setadjoin @ X595 @ X596)))&(~(in @ X597 @ X596)|(in @ X597 @ (setadjoin @ X595 @ X596)))))&(((~(in @ X599 @ (powerset @ X598))|(~(in @ X600 @ X599)|(in @ X600 @ X598)))&(((in @ (esk2_2 @ X601 @ X602) @ X602)|(in @ X602 @ (powerset @ X601)))&(~(in @ (esk2_2 @ X601 @ X602) @ X601)|(in @ X602 @ (powerset @ X601)))))&(((((in @ X605 @ (esk3_2 @ X604 @ X605))|~(in @ X605 @ (setunion @ X604)))&((in @ (esk3_2 @ X604 @ X605) @ X604)|~(in @ X605 @ (setunion @ X604))))&(~(in @ X608 @ X609)|~(in @ X609 @ X607)|(in @ X608 @ (setunion @ X607))))&((in @ emptyset @ omega)&((~(in @ X610 @ omega)|(in @ (setadjoin @ X610 @ X610) @ omega))&(((((in @ (esk4_1 @ X611) @ omega)|~(in @ emptyset @ X611)|(~(in @ X613 @ omega)|(in @ X613 @ X611)))&((in @ (esk4_1 @ X611) @ X611)|~(in @ emptyset @ X611)|(~(in @ X613 @ omega)|(in @ X613 @ X611))))&(~(in @ (setadjoin @ (esk4_1 @ X611) @ (esk4_1 @ X611)) @ X611)|~(in @ emptyset @ X611)|(~(in @ X613 @ omega)|(in @ X613 @ X611))))&((((((in @ (esk8_3 @ X614 @ X615 @ X620) @ X615)|~(in @ X620 @ (esk7_2 @ X614 @ X615))|(in @ (esk5_2 @ X614 @ X615) @ X615))&((X614 @ (esk8_3 @ X614 @ X615 @ X620) @ X620)|~(in @ X620 @ (esk7_2 @ X614 @ X615))|(in @ (esk5_2 @ X614 @ X615) @ X615)))&(~(in @ X623 @ X615)|~(X614 @ X623 @ X622)|(in @ X622 @ (esk7_2 @ X614 @ X615))|(in @ (esk5_2 @ X614 @ X615) @ X615)))&(((((in @ (esk8_3 @ X614 @ X615 @ X620) @ X615)|~(in @ X620 @ (esk7_2 @ X614 @ X615))|((X614 @ (esk5_2 @ X614 @ X615) @ (esk6_3 @ X614 @ X615 @ X617))|~(X614 @ (esk5_2 @ X614 @ X615) @ X617)))&((X614 @ (esk8_3 @ X614 @ X615 @ X620) @ X620)|~(in @ X620 @ (esk7_2 @ X614 @ X615))|((X614 @ (esk5_2 @ X614 @ X615) @ (esk6_3 @ X614 @ X615 @ X617))|~(X614 @ (esk5_2 @ X614 @ X615) @ X617))))&(~(in @ X623 @ X615)|~(X614 @ X623 @ X622)|(in @ X622 @ (esk7_2 @ X614 @ X615))|((X614 @ (esk5_2 @ X614 @ X615) @ (esk6_3 @ X614 @ X615 @ X617))|~(X614 @ (esk5_2 @ X614 @ X615) @ X617))))&((((in @ (esk8_3 @ X614 @ X615 @ X620) @ X615)|~(in @ X620 @ (esk7_2 @ X614 @ X615))|(((X617)!=(esk6_3 @ X614 @ X615 @ X617))|~(X614 @ (esk5_2 @ X614 @ X615) @ X617)))&((X614 @ (esk8_3 @ X614 @ X615 @ X620) @ X620)|~(in @ X620 @ (esk7_2 @ X614 @ X615))|(((X617)!=(esk6_3 @ X614 @ X615 @ X617))|~(X614 @ (esk5_2 @ X614 @ X615) @ X617))))&(~(in @ X623 @ X615)|~(X614 @ X623 @ X622)|(in @ X622 @ (esk7_2 @ X614 @ X615))|(((X617)!=(esk6_3 @ X614 @ X615 @ X617))|~(X614 @ (esk5_2 @ X614 @ X615) @ X617))))))&((((in @ (esk9_1 @ X624) @ X624)|~(in @ X625 @ X624))&(~(in @ X627 @ (esk9_1 @ X624))|~(in @ X627 @ X624)|~(in @ X625 @ X624)))&((epred1_0)&((((X628 @ (esk10_2 @ X628 @ X629))|~(X628 @ X629)|(X628 @ (descr @ (^[Z0:$i]:((X628 @ Z0))))))&(((X629)!=(esk10_2 @ X628 @ X629))|~(X628 @ X629)|(X628 @ (descr @ (^[Z0:$i]:((X628 @ Z0)))))))&((~(in @ X633 @ X631)|(~(X632 @ X633)|(in @ X633 @ (dsetconstr @ X631 @ (^[Z0:$i]:((X632 @ Z0)))))))&((~(in @ X636 @ (dsetconstr @ X634 @ (^[Z0:$i]:((X635 @ Z0)))))|(in @ X636 @ X634))&((~(in @ X639 @ (dsetconstr @ X637 @ (^[Z0:$i]:((X638 @ Z0)))))|(X638 @ X639))&(((((X640 @ (esk12_1 @ X640))|((X640 @ (esk11_2 @ X640 @ X641))|~(X640 @ X641)))&(~(X640 @ X644)|((esk12_1 @ X640)=(X644))|((X640 @ (esk11_2 @ X640 @ X641))|~(X640 @ X641))))&(((X640 @ (esk12_1 @ X640))|(((X641)!=(esk11_2 @ X640 @ X641))|~(X640 @ X641)))&(~(X640 @ X644)|((esk12_1 @ X640)=(X644))|(((X641)!=(esk11_2 @ X640 @ X641))|~(X640 @ X641)))))&((~(in @ X646 @ (prop2set @ ((X645))))|(X645))&((~(in @ X647 @ emptyset)|(X648))&(~(in @ X649 @ emptyset)&(~(in @ X650 @ emptyset)&((((X651 @ (esk13_2 @ X651 @ X652))|~(X651 @ X652)|(X651 @ (esk14_1 @ X651)))&(((X652)!=(esk13_2 @ X651 @ X652))|~(X651 @ X652)|(X651 @ (esk14_1 @ X651))))&(((((in @ (esk16_2 @ X655 @ X656) @ X656)|((X655)=(X656))|(in @ (esk15_2 @ X655 @ X656) @ X655))&(~(in @ (esk16_2 @ X655 @ X656) @ X655)|((X655)=(X656))|(in @ (esk15_2 @ X655 @ X656) @ X655)))&(((in @ (esk16_2 @ X655 @ X656) @ X656)|((X655)=(X656))|~(in @ (esk15_2 @ X655 @ X656) @ X656))&(~(in @ (esk16_2 @ X655 @ X656) @ X655)|((X655)=(X656))|~(in @ (esk15_2 @ X655 @ X656) @ X656))))&(((in @ (esk17_1 @ X659) @ X659)|((X659)=(emptyset)))&(((in @ (esk18_1 @ X661) @ X661)|((X661)=(emptyset)))&(((~(in @ X665 @ (dsetconstr @ X663 @ (^[Z0:$i]:((X664 @ Z0)))))|(X664 @ X665)|~(in @ X665 @ X663))&(~(X664 @ X665)|(in @ X665 @ (dsetconstr @ X663 @ (^[Z0:$i]:((X664 @ Z0)))))|~(in @ X665 @ X663)))&((((X666)=(emptyset))|(in @ (esk19_1 @ X666) @ X666))&((~(in @ X670 @ X668)|(~(X669 @ X670)|((dsetconstr @ X668 @ (^[Z0:$i]:((X669 @ Z0))))!=(emptyset))))&((~(in @ X672 @ X671)|((X671)!=(emptyset)))&((in @ X673 @ (setadjoin @ X673 @ X674))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X677 @ X676)|(in @ X677 @ (setadjoin @ X675 @ X676)))&(((((in @ X680 @ X679)|(X681)|((X680)=(X678))|~(in @ X680 @ (setadjoin @ X678 @ X679)))&(~(X681)|(X681)|((X680)=(X678))|~(in @ X680 @ (setadjoin @ X678 @ X679))))&(((in @ X680 @ X679)|(X681)|~(X681)|~(in @ X680 @ (setadjoin @ X678 @ X679)))&(~(X681)|(X681)|~(X681)|~(in @ X680 @ (setadjoin @ X678 @ X679)))))&((~(in @ X684 @ (setadjoin @ X682 @ X683))|(((X684)=(X682))|(in @ X684 @ X683)))&(((dsetconstr @ X685 @ (^[Z0:$i]:(($true))))=(X685))&((((in @ (esk20_2 @ X686 @ X687) @ X687)|(in @ X687 @ (powerset @ X686)))&(~(in @ (esk20_2 @ X686 @ X687) @ X686)|(in @ X687 @ (powerset @ X686))))&((in @ emptyset @ (powerset @ X689))&((in @ emptyset @ (powerset @ X690))&((~(in @ X692 @ (powerset @ X691))|(~(in @ X693 @ X692)|(in @ X693 @ X691)))&((~(in @ X695 @ X696)|(~(in @ X696 @ X694)|(in @ X695 @ (setunion @ X694))))&((((in @ X698 @ (esk21_3 @ X697 @ X698 @ X699))|(X699)|~(in @ X698 @ (setunion @ X697)))&(((in @ (esk21_3 @ X697 @ X698 @ X699) @ X697)|(X699)|~(in @ X698 @ (setunion @ X697)))&(~(X699)|(X699)|~(in @ X698 @ (setunion @ X697)))))&((~(in @ X702 @ X701)|(in @ X702 @ (powerset @ (setunion @ X701))))&((((~(X703 @ X707)|((X707)=(esk23_1 @ X703))|((X703 @ (esk22_2 @ X703 @ X704))|~(X703 @ X704)))&(((X708)!=(esk23_1 @ X703))|(X703 @ X708)|((X703 @ (esk22_2 @ X703 @ X704))|~(X703 @ X704))))&((~(X703 @ X707)|((X707)=(esk23_1 @ X703))|(((X704)!=(esk22_2 @ X703 @ X704))|~(X703 @ X704)))&(((X708)!=(esk23_1 @ X703))|(X703 @ X708)|(((X704)!=(esk22_2 @ X703 @ X704))|~(X703 @ X704)))))&((((X709)=(emptyset))|(in @ (esk24_1 @ X709) @ X709))&((~(in @ X711 @ (setadjoin @ X712 @ emptyset))|((X711)=(X712)))&((((X713)=(X714))|~(in @ X714 @ (setadjoin @ X713 @ emptyset)))&((((X715)!=(X716))|(in @ X715 @ (setadjoin @ X716 @ emptyset)))&((~(in @ X717 @ (setadjoin @ X718 @ emptyset))|(in @ X718 @ (setadjoin @ X717 @ emptyset)))&((~(in @ X721 @ (setadjoin @ X719 @ (setadjoin @ X720 @ emptyset)))|(((X721)=(X719))|((X721)=(X720))))&((in @ X722 @ (setadjoin @ X722 @ (setadjoin @ X723 @ emptyset)))&((in @ X725 @ (setadjoin @ X724 @ (setadjoin @ X725 @ emptyset)))&((~(in @ X728 @ X726)|~(X727 @ X728)|((dsetconstr @ X726 @ (^[Z0:$i]:((X727 @ Z0))))!=(emptyset)))&((~(in @ X730 @ emptyset)|(X729 @ X730))&((((in @ (esk25_2 @ X731 @ X732) @ X731)|(~(in @ X733 @ X731)|(X732 @ X733)))&(~(X732 @ (esk25_2 @ X731 @ X732))|(~(in @ X733 @ X731)|(X732 @ X733))))&((((in @ (esk26_2 @ X735 @ X736) @ X735)|(~(in @ X738 @ X735)|~(X736 @ X738)))&((X736 @ (esk26_2 @ X735 @ X736))|(~(in @ X738 @ X735)|~(X736 @ X738))))&((((in @ (esk27_2 @ X739 @ X740) @ X739)|(~(in @ X742 @ X739)|~(X740 @ X742)))&((X740 @ (esk27_2 @ X739 @ X740))|(~(in @ X742 @ X739)|~(X740 @ X742))))&((((in @ (esk28_2 @ X743 @ X744) @ X743)|(~(in @ X745 @ X743)|(X744 @ X745)))&(~(X744 @ (esk28_2 @ X743 @ X744))|(~(in @ X745 @ X743)|(X744 @ X745))))&((~(X747)|(in @ emptyset @ (prop2set @ ((X747)))))&((prop2set2propI)&((((in @ (esk29_2 @ X748 @ X749) @ X748)|(~(in @ X751 @ X748)|~(X749 @ X751)))&((X749 @ (esk29_2 @ X748 @ X749))|(~(in @ X751 @ X748)|~(X749 @ X751))))&((((in @ (esk30_2 @ X752 @ X753) @ X752)|(~(in @ X754 @ X752)|(X753 @ X754)))&(~(X753 @ (esk30_2 @ X752 @ X753))|(~(in @ X754 @ X752)|(X753 @ X754))))&(((((X756 @ (esk32_1 @ X756))|((X756 @ (esk31_2 @ X756 @ X757))|~(X756 @ X757)))&(~(X756 @ X760)|((esk32_1 @ X756)=(X760))|((X756 @ (esk31_2 @ X756 @ X757))|~(X756 @ X757))))&(((X756 @ (esk32_1 @ X756))|(((X757)!=(esk31_2 @ X756 @ X757))|~(X756 @ X757)))&(~(X756 @ X760)|((esk32_1 @ X756)=(X760))|(((X757)!=(esk31_2 @ X756 @ X757))|~(X756 @ X757)))))&(((((X761 @ (esk35_1 @ X761))|(X761 @ (esk33_1 @ X761))|~(X761 @ X762))&(~(X761 @ X766)|((esk35_1 @ X761)=(X766))|(X761 @ (esk33_1 @ X761))|~(X761 @ X762)))&((((X761 @ (esk35_1 @ X761))|(X761 @ (esk34_1 @ X761))|~(X761 @ X762))&(~(X761 @ X766)|((esk35_1 @ X761)=(X766))|(X761 @ (esk34_1 @ X761))|~(X761 @ X762)))&(((X761 @ (esk35_1 @ X761))|((esk33_1 @ X761)!=(esk34_1 @ X761))|~(X761 @ X762))&(~(X761 @ X766)|((esk35_1 @ X761)=(X766))|((esk33_1 @ X761)!=(esk34_1 @ X761))|~(X761 @ X762)))))&(((((X767 @ (esk37_1 @ X767))|(~(X767 @ (esk36_2 @ X767 @ X768))|((esk36_2 @ X767 @ X768)!=(X768))))&(~(X767 @ X771)|((esk37_1 @ X767)=(X771))|(~(X767 @ (esk36_2 @ X767 @ X768))|((esk36_2 @ X767 @ X768)!=(X768)))))&(((X767 @ (esk37_1 @ X767))|((X767 @ (esk36_2 @ X767 @ X768))|((esk36_2 @ X767 @ X768)=(X768))))&(~(X767 @ X771)|((esk37_1 @ X767)=(X771))|((X767 @ (esk36_2 @ X767 @ X768))|((esk36_2 @ X767 @ X768)=(X768))))))&((((X772)!=(X773))|(((X774)!=(X775))|(~(in @ X774 @ X772)|(in @ X775 @ X773))))&(((~(in @ X778 @ X776)|(in @ X779 @ X777)|((X778)!=(X779))|((X776)!=(X777)))&(~(in @ X779 @ X777)|(in @ X778 @ X776)|((X778)!=(X779))|((X776)!=(X777))))&((((X780 @ (esk38_2 @ X780 @ X781))|~(X780 @ X781)|(~(X780 @ X783)|(~(X780 @ X784)|((X783)=(X784)))))&(((X781)!=(esk38_2 @ X780 @ X781))|~(X780 @ X781)|(~(X780 @ X783)|(~(X780 @ X784)|((X783)=(X784))))))&(((((((X786 @ (esk42_2 @ X785 @ X786))|((X785 @ (esk41_3 @ X785 @ X786 @ X789))|~(X785 @ X789))|((esk39_2 @ X785 @ X786)=(esk40_2 @ X785 @ X786)))&(~(X786 @ X792)|((esk42_2 @ X785 @ X786)=(X792))|((X785 @ (esk41_3 @ X785 @ X786 @ X789))|~(X785 @ X789))|((esk39_2 @ X785 @ X786)=(esk40_2 @ X785 @ X786))))&(((X786 @ (esk42_2 @ X785 @ X786))|(((X789)!=(esk41_3 @ X785 @ X786 @ X789))|~(X785 @ X789))|((esk39_2 @ X785 @ X786)=(esk40_2 @ X785 @ X786)))&(~(X786 @ X792)|((esk42_2 @ X785 @ X786)=(X792))|(((X789)!=(esk41_3 @ X785 @ X786 @ X789))|~(X785 @ X789))|((esk39_2 @ X785 @ X786)=(esk40_2 @ X785 @ X786)))))&((((X785 @ (esk44_2 @ X785 @ X786))|((X786 @ (esk43_3 @ X785 @ X786 @ X793))|~(X786 @ X793))|((esk39_2 @ X785 @ X786)=(esk40_2 @ X785 @ X786)))&(~(X785 @ X796)|((esk44_2 @ X785 @ X786)=(X796))|((X786 @ (esk43_3 @ X785 @ X786 @ X793))|~(X786 @ X793))|((esk39_2 @ X785 @ X786)=(esk40_2 @ X785 @ X786))))&(((X785 @ (esk44_2 @ X785 @ X786))|(((X793)!=(esk43_3 @ X785 @ X786 @ X793))|~(X786 @ X793))|((esk39_2 @ X785 @ X786)=(esk40_2 @ X785 @ X786)))&(~(X785 @ X796)|((esk44_2 @ X785 @ X786)=(X796))|(((X793)!=(esk43_3 @ X785 @ X786 @ X793))|~(X786 @ X793))|((esk39_2 @ X785 @ X786)=(esk40_2 @ X785 @ X786))))))&((((((X786 @ (esk42_2 @ X785 @ X786))|((X785 @ (esk41_3 @ X785 @ X786 @ X789))|~(X785 @ X789))|(~(X785 @ (esk39_2 @ X785 @ X786))|~(X786 @ (esk40_2 @ X785 @ X786))))&(~(X786 @ X792)|((esk42_2 @ X785 @ X786)=(X792))|((X785 @ (esk41_3 @ X785 @ X786 @ X789))|~(X785 @ X789))|(~(X785 @ (esk39_2 @ X785 @ X786))|~(X786 @ (esk40_2 @ X785 @ X786)))))&(((X786 @ (esk42_2 @ X785 @ X786))|(((X789)!=(esk41_3 @ X785 @ X786 @ X789))|~(X785 @ X789))|(~(X785 @ (esk39_2 @ X785 @ X786))|~(X786 @ (esk40_2 @ X785 @ X786))))&(~(X786 @ X792)|((esk42_2 @ X785 @ X786)=(X792))|(((X789)!=(esk41_3 @ X785 @ X786 @ X789))|~(X785 @ X789))|(~(X785 @ (esk39_2 @ X785 @ X786))|~(X786 @ (esk40_2 @ X785 @ X786))))))&((((X785 @ (esk44_2 @ X785 @ X786))|((X786 @ (esk43_3 @ X785 @ X786 @ X793))|~(X786 @ X793))|(~(X785 @ (esk39_2 @ X785 @ X786))|~(X786 @ (esk40_2 @ X785 @ X786))))&(~(X785 @ X796)|((esk44_2 @ X785 @ X786)=(X796))|((X786 @ (esk43_3 @ X785 @ X786 @ X793))|~(X786 @ X793))|(~(X785 @ (esk39_2 @ X785 @ X786))|~(X786 @ (esk40_2 @ X785 @ X786)))))&(((X785 @ (esk44_2 @ X785 @ X786))|(((X793)!=(esk43_3 @ X785 @ X786 @ X793))|~(X786 @ X793))|(~(X785 @ (esk39_2 @ X785 @ X786))|~(X786 @ (esk40_2 @ X785 @ X786))))&(~(X785 @ X796)|((esk44_2 @ X785 @ X786)=(X796))|(((X793)!=(esk43_3 @ X785 @ X786 @ X793))|~(X786 @ X793))|(~(X785 @ (esk39_2 @ X785 @ X786))|~(X786 @ (esk40_2 @ X785 @ X786)))))))&(((((X786 @ (esk42_2 @ X785 @ X786))|((X785 @ (esk41_3 @ X785 @ X786 @ X789))|~(X785 @ X789))|((X785 @ (esk39_2 @ X785 @ X786))|(X786 @ (esk40_2 @ X785 @ X786))))&(~(X786 @ X792)|((esk42_2 @ X785 @ X786)=(X792))|((X785 @ (esk41_3 @ X785 @ X786 @ X789))|~(X785 @ X789))|((X785 @ (esk39_2 @ X785 @ X786))|(X786 @ (esk40_2 @ X785 @ X786)))))&(((X786 @ (esk42_2 @ X785 @ X786))|(((X789)!=(esk41_3 @ X785 @ X786 @ X789))|~(X785 @ X789))|((X785 @ (esk39_2 @ X785 @ X786))|(X786 @ (esk40_2 @ X785 @ X786))))&(~(X786 @ X792)|((esk42_2 @ X785 @ X786)=(X792))|(((X789)!=(esk41_3 @ X785 @ X786 @ X789))|~(X785 @ X789))|((X785 @ (esk39_2 @ X785 @ X786))|(X786 @ (esk40_2 @ X785 @ X786))))))&((((X785 @ (esk44_2 @ X785 @ X786))|((X786 @ (esk43_3 @ X785 @ X786 @ X793))|~(X786 @ X793))|((X785 @ (esk39_2 @ X785 @ X786))|(X786 @ (esk40_2 @ X785 @ X786))))&(~(X785 @ X796)|((esk44_2 @ X785 @ X786)=(X796))|((X786 @ (esk43_3 @ X785 @ X786 @ X793))|~(X786 @ X793))|((X785 @ (esk39_2 @ X785 @ X786))|(X786 @ (esk40_2 @ X785 @ X786)))))&(((X785 @ (esk44_2 @ X785 @ X786))|(((X793)!=(esk43_3 @ X785 @ X786 @ X793))|~(X786 @ X793))|((X785 @ (esk39_2 @ X785 @ X786))|(X786 @ (esk40_2 @ X785 @ X786))))&(~(X785 @ X796)|((esk44_2 @ X785 @ X786)=(X796))|(((X793)!=(esk43_3 @ X785 @ X786 @ X793))|~(X786 @ X793))|((X785 @ (esk39_2 @ X785 @ X786))|(X786 @ (esk40_2 @ X785 @ X786)))))))))&(((emptyset)=(emptyset))&((((X797)!=(X798))|(((X799)!=(X800))|((setadjoin @ X797 @ X799)=(setadjoin @ X798 @ X800))))&((((X801)!=(X802))|((powerset @ X801)=(powerset @ X802)))&((((X803)!=(X804))|((setunion @ X803)=(setunion @ X804)))&(((omega)=(omega))&((((X805 @ (esk45_2 @ X805 @ X806))|~(X805 @ X806)|(~(X805 @ X808)|(~(X805 @ X809)|((X808)=(X809)))))&(((X806)!=(esk45_2 @ X805 @ X806))|~(X805 @ X806)|(~(X805 @ X808)|(~(X805 @ X809)|((X808)=(X809))))))&((((((X811 @ (esk49_3 @ X810 @ X811 @ X816))|~(X811 @ X816)|((descr @ (^[Z0:$i]:((X810 @ Z0))))=(descr @ (^[Z0:$i]:((X811 @ Z0)))))|((X810 @ (esk48_3 @ X810 @ X811 @ X814))|~(X810 @ X814))|((esk46_2 @ X810 @ X811)=(esk47_2 @ X810 @ X811)))&(((X816)!=(esk49_3 @ X810 @ X811 @ X816))|~(X811 @ X816)|((descr @ (^[Z0:$i]:((X810 @ Z0))))=(descr @ (^[Z0:$i]:((X811 @ Z0)))))|((X810 @ (esk48_3 @ X810 @ X811 @ X814))|~(X810 @ X814))|((esk46_2 @ X810 @ X811)=(esk47_2 @ X810 @ X811))))&(((X811 @ (esk49_3 @ X810 @ X811 @ X816))|~(X811 @ X816)|((descr @ (^[Z0:$i]:((X810 @ Z0))))=(descr @ (^[Z0:$i]:((X811 @ Z0)))))|(((X814)!=(esk48_3 @ X810 @ X811 @ X814))|~(X810 @ X814))|((esk46_2 @ X810 @ X811)=(esk47_2 @ X810 @ X811)))&(((X816)!=(esk49_3 @ X810 @ X811 @ X816))|~(X811 @ X816)|((descr @ (^[Z0:$i]:((X810 @ Z0))))=(descr @ (^[Z0:$i]:((X811 @ Z0)))))|(((X814)!=(esk48_3 @ X810 @ X811 @ X814))|~(X810 @ X814))|((esk46_2 @ X810 @ X811)=(esk47_2 @ X810 @ X811)))))&(((((X811 @ (esk49_3 @ X810 @ X811 @ X816))|~(X811 @ X816)|((descr @ (^[Z0:$i]:((X810 @ Z0))))=(descr @ (^[Z0:$i]:((X811 @ Z0)))))|((X810 @ (esk48_3 @ X810 @ X811 @ X814))|~(X810 @ X814))|(~(X810 @ (esk46_2 @ X810 @ X811))|~(X811 @ (esk47_2 @ X810 @ X811))))&(((X816)!=(esk49_3 @ X810 @ X811 @ X816))|~(X811 @ X816)|((descr @ (^[Z0:$i]:((X810 @ Z0))))=(descr @ (^[Z0:$i]:((X811 @ Z0)))))|((X810 @ (esk48_3 @ X810 @ X811 @ X814))|~(X810 @ X814))|(~(X810 @ (esk46_2 @ X810 @ X811))|~(X811 @ (esk47_2 @ X810 @ X811)))))&(((X811 @ (esk49_3 @ X810 @ X811 @ X816))|~(X811 @ X816)|((descr @ (^[Z0:$i]:((X810 @ Z0))))=(descr @ (^[Z0:$i]:((X811 @ Z0)))))|(((X814)!=(esk48_3 @ X810 @ X811 @ X814))|~(X810 @ X814))|(~(X810 @ (esk46_2 @ X810 @ X811))|~(X811 @ (esk47_2 @ X810 @ X811))))&(((X816)!=(esk49_3 @ X810 @ X811 @ X816))|~(X811 @ X816)|((descr @ (^[Z0:$i]:((X810 @ Z0))))=(descr @ (^[Z0:$i]:((X811 @ Z0)))))|(((X814)!=(esk48_3 @ X810 @ X811 @ X814))|~(X810 @ X814))|(~(X810 @ (esk46_2 @ X810 @ X811))|~(X811 @ (esk47_2 @ X810 @ X811))))))&((((X811 @ (esk49_3 @ X810 @ X811 @ X816))|~(X811 @ X816)|((descr @ (^[Z0:$i]:((X810 @ Z0))))=(descr @ (^[Z0:$i]:((X811 @ Z0)))))|((X810 @ (esk48_3 @ X810 @ X811 @ X814))|~(X810 @ X814))|((X810 @ (esk46_2 @ X810 @ X811))|(X811 @ (esk47_2 @ X810 @ X811))))&(((X816)!=(esk49_3 @ X810 @ X811 @ X816))|~(X811 @ X816)|((descr @ (^[Z0:$i]:((X810 @ Z0))))=(descr @ (^[Z0:$i]:((X811 @ Z0)))))|((X810 @ (esk48_3 @ X810 @ X811 @ X814))|~(X810 @ X814))|((X810 @ (esk46_2 @ X810 @ X811))|(X811 @ (esk47_2 @ X810 @ X811)))))&(((X811 @ (esk49_3 @ X810 @ X811 @ X816))|~(X811 @ X816)|((descr @ (^[Z0:$i]:((X810 @ Z0))))=(descr @ (^[Z0:$i]:((X811 @ Z0)))))|(((X814)!=(esk48_3 @ X810 @ X811 @ X814))|~(X810 @ X814))|((X810 @ (esk46_2 @ X810 @ X811))|(X811 @ (esk47_2 @ X810 @ X811))))&(((X816)!=(esk49_3 @ X810 @ X811 @ X816))|~(X811 @ X816)|((descr @ (^[Z0:$i]:((X810 @ Z0))))=(descr @ (^[Z0:$i]:((X811 @ Z0)))))|(((X814)!=(esk48_3 @ X810 @ X811 @ X814))|~(X810 @ X814))|((X810 @ (esk46_2 @ X810 @ X811))|(X811 @ (esk47_2 @ X810 @ X811))))))))&((((in @ (esk50_4 @ X818 @ X819 @ X820 @ X821) @ X818)|((dsetconstr @ X818 @ (^[Z0:$i]:((X820 @ Z0))))=(dsetconstr @ X819 @ (^[Z0:$i]:((X821 @ Z0)))))|((X818)!=(X819)))&(((in @ (esk51_4 @ X818 @ X819 @ X820 @ X821) @ X819)|((dsetconstr @ X818 @ (^[Z0:$i]:((X820 @ Z0))))=(dsetconstr @ X819 @ (^[Z0:$i]:((X821 @ Z0)))))|((X818)!=(X819)))&((((esk50_4 @ X818 @ X819 @ X820 @ X821)=(esk51_4 @ X818 @ X819 @ X820 @ X821))|((dsetconstr @ X818 @ (^[Z0:$i]:((X820 @ Z0))))=(dsetconstr @ X819 @ (^[Z0:$i]:((X821 @ Z0)))))|((X818)!=(X819)))&((~(X820 @ (esk50_4 @ X818 @ X819 @ X820 @ X821))|~(X821 @ (esk51_4 @ X818 @ X819 @ X820 @ X821))|((dsetconstr @ X818 @ (^[Z0:$i]:((X820 @ Z0))))=(dsetconstr @ X819 @ (^[Z0:$i]:((X821 @ Z0)))))|((X818)!=(X819)))&((X820 @ (esk50_4 @ X818 @ X819 @ X820 @ X821))|(X821 @ (esk51_4 @ X818 @ X819 @ X820 @ X821))|((dsetconstr @ X818 @ (^[Z0:$i]:((X820 @ Z0))))=(dsetconstr @ X819 @ (^[Z0:$i]:((X821 @ Z0)))))|((X818)!=(X819)))))))&((((in @ (esk52_2 @ X824 @ X825) @ X824)|(subset @ X824 @ X825))&(~(in @ (esk52_2 @ X824 @ X825) @ X825)|(subset @ X824 @ X825)))&((((X827)!=(X828))|(subset @ X828 @ X827))&((((X829)!=(X830))|(subset @ X829 @ X830))&((((in @ (esk53_2 @ X831 @ X832) @ X831)|(subset @ X831 @ X832))&(~(in @ (esk53_2 @ X831 @ X832) @ X832)|(subset @ X831 @ X832)))&((subset @ emptyset @ X834)&((~(subset @ X835 @ X836)|(~(in @ X837 @ X835)|(in @ X837 @ X836)))&((~(subset @ X838 @ X839)|((in @ X840 @ X839)|~(in @ X840 @ X838)))&((~(in @ X843 @ X841)|((in @ X843 @ X842)|~(subset @ X841 @ X842)))&(((subset @ X844 @ X845)|((X844)!=(X845)))&((~(in @ X848 @ X846)|((in @ X848 @ X847)|((X846)!=(X847))))&((subset @ X849 @ X849)&((~(subset @ X850 @ X851)|(~(subset @ X851 @ X852)|(subset @ X850 @ X852)))&((subset @ X854 @ (setadjoin @ X853 @ X854))&((~(subset @ X855 @ X857)|(subset @ X855 @ (setadjoin @ X856 @ X857)))&((~(subset @ X858 @ X859)|(in @ X858 @ (powerset @ X859)))&((~(subset @ X860 @ X861)|(~(subset @ X861 @ X860)|((X860)=(X861))))&((~(subset @ X862 @ emptyset)|((X862)=(emptyset)))&((~(subset @ X864 @ X863)|(in @ X864 @ (powerset @ X863)))&((~(in @ X866 @ (powerset @ X865))|(subset @ X866 @ X865))&((in @ X867 @ (powerset @ X867))&((~(subset @ X868 @ X869)|(subset @ (powerset @ X868) @ (powerset @ X869)))&~(in @ (dsetconstr @ esk54_0 @ (^[Z0:$i]:((epred2_0 @ Z0)))) @ (powerset @ esk54_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_138])])])])])])).
% 1.65/0.40  thf(c_0_140, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((in @ X2 @ X3)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_139])).
% 1.65/0.40  thf(c_0_141, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_139])).
% 1.65/0.40  thf(c_0_142, negated_conjecture, ~((in @ (dsetconstr @ esk54_0 @ epred2_0) @ (powerset @ esk54_0))), inference(split_conjunct,[status(thm)],[c_0_139])).
% 1.65/0.40  thf(c_0_143, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_139])).
% 1.65/0.40  thf(c_0_144, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_139])).
% 1.65/0.40  thf(c_0_145, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ (esk53_2 @ (dsetconstr @ X2 @ X1) @ X3) @ X2)|(subset @ (dsetconstr @ X2 @ X1) @ X3))), inference(spm,[status(thm)],[c_0_140, c_0_141])).
% 1.65/0.40  thf(c_0_146, negated_conjecture, ~((subset @ (dsetconstr @ esk54_0 @ epred2_0) @ esk54_0)), inference(spm,[status(thm)],[c_0_142, c_0_143])).
% 1.65/0.40  thf(c_0_147, negated_conjecture, ![X1:$i > $o, X2:$i]:((subset @ (dsetconstr @ X2 @ X1) @ X2)), inference(spm,[status(thm)],[c_0_144, c_0_145])).
% 1.65/0.40  thf(c_0_148, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146, c_0_147])]), ['proof']).
% 1.65/0.40  % SZS output end CNFRefutation
% 1.65/0.40  % Parsed axioms                        : 210
% 1.65/0.40  % Removed by relevancy pruning/SinE    : 112
% 1.65/0.40  % Initial clauses                      : 206
% 1.65/0.40  % Removed in clause preprocessing      : 13
% 1.65/0.40  % Initial clauses in saturation        : 193
% 1.65/0.40  % Processed clauses                    : 1861
% 1.65/0.40  % ...of these trivial                  : 10
% 1.65/0.40  % ...subsumed                          : 1243
% 1.65/0.40  % ...remaining for further processing  : 608
% 1.65/0.40  % Other redundant clauses eliminated   : 14
% 1.65/0.40  % Clauses deleted for lack of memory   : 0
% 1.65/0.40  % Backward-subsumed                    : 5
% 1.65/0.40  % Backward-rewritten                   : 7
% 1.65/0.40  % Generated clauses                    : 23241
% 1.65/0.40  % ...of the previous two non-redundant : 21763
% 1.65/0.40  % ...aggressively subsumed             : 0
% 1.65/0.40  % Contextual simplify-reflections      : 0
% 1.65/0.40  % Paramodulations                      : 23225
% 1.65/0.40  % Factorizations                       : 2
% 1.65/0.40  % NegExts                              : 0
% 1.65/0.40  % Equation resolutions                 : 14
% 1.65/0.40  % Disequality decompositions           : 0
% 1.65/0.40  % Total rewrite steps                  : 2480
% 1.65/0.40  % ...of those cached                   : 2316
% 1.65/0.40  % Propositional unsat checks           : 0
% 1.65/0.40  %    Propositional check models        : 0
% 1.65/0.40  %    Propositional check unsatisfiable : 0
% 1.65/0.40  %    Propositional clauses             : 0
% 1.65/0.40  %    Propositional clauses after purity: 0
% 1.65/0.40  %    Propositional unsat core size     : 0
% 1.65/0.40  %    Propositional preprocessing time  : 0.000
% 1.65/0.40  %    Propositional encoding time       : 0.000
% 1.65/0.40  %    Propositional solver time         : 0.000
% 1.65/0.40  %    Success case prop preproc time    : 0.000
% 1.65/0.40  %    Success case prop encoding time   : 0.000
% 1.65/0.40  %    Success case prop solver time     : 0.000
% 1.65/0.40  % Current number of processed clauses  : 583
% 1.65/0.40  %    Positive orientable unit clauses  : 36
% 1.65/0.40  %    Positive unorientable unit clauses: 0
% 1.65/0.40  %    Negative unit clauses             : 3
% 1.65/0.40  %    Non-unit-clauses                  : 544
% 1.65/0.40  % Current number of unprocessed clauses: 20028
% 1.65/0.40  % ...number of literals in the above   : 71479
% 1.65/0.40  % Current number of archived formulas  : 0
% 1.65/0.40  % Current number of archived clauses   : 12
% 1.65/0.40  % Clause-clause subsumption calls (NU) : 29561
% 1.65/0.40  % Rec. Clause-clause subsumption calls : 21484
% 1.65/0.40  % Non-unit clause-clause subsumptions  : 1091
% 1.65/0.40  % Unit Clause-clause subsumption calls : 478
% 1.65/0.40  % Rewrite failures with RHS unbound    : 0
% 1.65/0.40  % BW rewrite match attempts            : 16
% 1.65/0.40  % BW rewrite match successes           : 5
% 1.65/0.40  % Condensation attempts                : 0
% 1.65/0.40  % Condensation successes               : 0
% 1.65/0.40  % Termbank termtop insertions          : 448163
% 1.65/0.40  % Search garbage collected termcells   : 8772
% 1.65/0.40  
% 1.65/0.40  % -------------------------------------------------
% 1.65/0.40  % User time                : 0.223 s
% 1.65/0.40  % System time              : 0.020 s
% 1.65/0.40  % Total time               : 0.243 s
% 1.65/0.40  % Maximum resident set size: 6400 pages
% 1.65/0.40  
% 1.65/0.40  % -------------------------------------------------
% 1.65/0.40  % User time                : 0.228 s
% 1.65/0.40  % System time              : 0.021 s
% 1.65/0.40  % Total time               : 0.248 s
% 1.65/0.40  % Maximum resident set size: 5120 pages
% 1.65/0.40  % E exiting
%------------------------------------------------------------------------------