%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU566^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:18 AM UTC 2026
% Result : Theorem 2.62s 1.85s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 1811 ( 503 equ; 0 cnn)
% Maximal formula atoms : 85 ( 56 avg)
% Number of connectives : 972 ( 65 ~; 28 |; 269 &; 176 @)
% ( 4 <=>; 430 =>; 0 <=; 0 <~>)
% Maximal formula depth : 92 ( 26 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 198 ( 195 usr; 90 con; 0-4 aty)
% Number of variables : 67 ( 0 ^; 49 !; 18 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_111,type,
sP1: $i > $i > $o ).
thf(func_def_112,type,
sP2: $i > $o ).
thf(func_def_113,type,
sP3: $i > $i > $o ).
thf(func_def_114,type,
sP4: $i > $i > $o ).
thf(func_def_116,type,
sK6: $i > $o ).
thf(func_def_118,type,
sK8: $i > $o ).
thf(func_def_124,type,
sK14: $i > $o ).
thf(func_def_129,type,
sK19: $i > $i ).
thf(func_def_139,type,
sK29: $i > $o ).
thf(func_def_143,type,
sK33: $i > $o ).
thf(func_def_149,type,
sK39: $i > $i > $i ).
thf(func_def_157,type,
sK47: ( $i > $o ) > $i > $i ).
thf(func_def_159,type,
sK49: $i > $o ).
thf(func_def_163,type,
sK53: $i > $i ).
thf(func_def_166,type,
sK56: $i > $i > $i ).
thf(func_def_167,type,
sK57: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_168,type,
sK58: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_171,type,
sK61: $i > $o ).
thf(func_def_172,type,
sK62: $i > $o ).
thf(func_def_173,type,
sK63: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_174,type,
sK64: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_175,type,
sK65: $i > $o ).
thf(func_def_176,type,
sK66: $i > $o ).
thf(func_def_177,type,
sK67: $i > $o ).
thf(func_def_184,type,
sK74: $i > $o ).
thf(func_def_186,type,
sK76: $i > $i > $i ).
thf(func_def_187,type,
sK77: $i > $i > $i ).
thf(func_def_190,type,
sK80: $i > ( $i > $o ) > $i ).
thf(func_def_191,type,
sK81: $i > $o ).
thf(func_def_194,type,
sK84: $i > $i > $i ).
thf(func_def_199,type,
sK89: ( $i > $o ) > $i ).
thf(func_def_200,type,
sK90: $i > $o ).
thf(func_def_201,type,
sK91: $i > $i ).
thf(func_def_204,type,
sK94: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_205,type,
sK95: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_206,type,
sK96: $i > $o ).
thf(func_def_207,type,
sK97: $i > $o ).
thf(func_def_215,type,
sK105: ( $i > $o ) > $i ).
thf(func_def_216,type,
sK106: ( $i > $o ) > $i ).
thf(func_def_217,type,
sK107: $i > $o ).
thf(func_def_219,type,
sK109: $i > $o ).
thf(func_def_221,type,
sK111: $i > ( $i > $o ) > $i ).
thf(func_def_223,type,
sK113: $i > $o ).
thf(func_def_229,type,
sK119: $i > $o ).
thf(func_def_232,type,
sK122: $i > ( $i > $o ) > $i ).
thf(func_def_238,type,
sK128: $i > $i ).
thf(func_def_240,type,
sK130: $i > $i > $i ).
thf(func_def_248,type,
sK138: $i > $o ).
thf(func_def_250,type,
sK140: $i > $i > $o ).
thf(func_def_252,type,
sK142: $i > $i ).
thf(func_def_253,type,
sK143: $i > $i ).
thf(func_def_254,type,
sK144: $i > ( $i > $i > $o ) > $i ).
thf(func_def_255,type,
sK145: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_256,type,
sK146: $i > ( $i > $i > $o ) > $i ).
thf(func_def_258,type,
sK148: $i > $o ).
thf(func_def_260,type,
sK150: ( $i > $o ) > $i > $i ).
thf(func_def_263,type,
sK153: $i > $i ).
thf(func_def_264,type,
sK154: $i > $i > $i ).
thf(func_def_268,type,
sK158: $i > $o ).
thf(func_def_269,type,
sK159: ( $i > $o ) > $i ).
thf(func_def_273,type,
sK163: $i > ( $i > $o ) > $i ).
thf(func_def_274,type,
sK164: $i > $o ).
thf(func_def_279,type,
sK169: $i > $i > $i ).
thf(func_def_285,type,
sK175: $i > $o ).
thf(func_def_287,type,
sK177: $i > ( $i > $o ) > $i ).
thf(func_def_288,type,
sK178: $i > $i ).
thf(func_def_293,type,
sK183: $i > $i ).
thf(func_def_295,type,
sK185: $i > $i ).
thf(func_def_306,type,
sK196: $i > ( $i > $o ) > $i ).
thf(func_def_307,type,
sK197: $i > $o ).
thf(func_def_312,type,
sK202: $i > $o ).
thf(func_def_314,type,
sK204: $i > $o ).
thf(func_def_315,type,
sK205: $i > $i ).
thf(func_def_316,type,
sK206: ( $i > $o ) > $i ).
thf(func_def_323,type,
sK213: $i > $i > $i ).
thf(func_def_324,type,
sK214: $i > $i > $i ).
thf(func_def_325,type,
sK215: $i > $i > $i ).
thf(func_def_326,type,
sK216: $i > $i > $i ).
thf(func_def_327,type,
sK217: $i > $i > $i ).
thf(func_def_328,type,
sK218: $i > $i > $i > $i ).
thf(func_def_329,type,
sK219: $i > $i ).
thf(func_def_330,type,
sK220: $i > $i ).
thf(func_def_331,type,
sK221: $i > $i ).
thf(func_def_332,type,
sK222: $i > $i ).
thf(func_def_333,type,
sK223: $i > $i > $i ).
thf(func_def_334,type,
sK224: $i > $i > $i > $i ).
thf(func_def_335,type,
sK225: $i > $i > $i > $i ).
thf(func_def_336,type,
sK226: $i > $i > $i ).
thf(func_def_337,type,
sK227: $i > $i > $i ).
thf(func_def_338,type,
sK228: $i > $i ).
thf(func_def_340,type,
sK230: $i > $i ).
thf(func_def_341,type,
sK231: $i > $i ).
thf(func_def_345,type,
sK235: $o > $i > $i > $i ).
thf(func_def_351,type,
ph241:
!>[X0: $tType] : X0 ).
thf(f2040,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f2031]) ).
thf(f2031,plain,
$true != $true,
inference(superposition,[status(thm)],[f1319,f1108]) ).
thf(f1108,plain,
( ( in @ sK207 @ sK209 )
= $true ),
inference(cnf_transformation,[status(thm)],[f731]) ).
thf(f731,plain,
( ( replAx = $true )
& ( eqimpsubset2 = $true )
& ( omegaSAx = $true )
& ( setunionI = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( noeltsimpempty = $true )
& ( uniqinunit = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyI = $true )
& ( setadjoinAx = $true )
& ( exuE1 = $true )
& ( vacuousDall = $true )
& ( setunionAx = $true )
& ( exuI1 = $true )
& ( exuE2 = $true )
& ( eqinunit = $true )
& ( emptysetsubset = $true )
& ( quantDeMorgan2 = $true )
& ( nonemptyI1 = $true )
& ( emptyinPowerset = $true )
& ( inCongP = $true )
& ( notinemptyset = $true )
& ( setadjoinIR = $true )
& ( exuE3e = $true )
& ( subPowSU = $true )
& ( setunion__Cong = $true )
& ( exuE3u = $true )
& ( omegaIndAx = $true )
& ( setadjoin__Cong = $true )
& ( notdexE = $true )
& ( upairsetIL = $true )
& ( emptysetAx = $true )
& ( wellorderingAx = $true )
& ( notdallE = $true )
& ( dsetconstrER = $true )
& ( subsetI2 = $true )
& ( subsetE2 = $true )
& ( emptyE1 = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( powerset__Cong = $true )
& ( exuI3 = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( nonemptyImpWitness = $true )
& ( quantDeMorgan1 = $true )
& ( in__Cong = $true )
& ( prop2setI = $true )
& ( emptyinunitempty = $true )
& ( omega0Ax = $true )
& ( dsetconstrEL = $true )
& ( ( subset @ sK209 @ sK208 )
= $true )
& ( ( in @ sK207 @ sK208 )
!= $true )
& ( ( in @ sK207 @ sK209 )
= $true )
& ( prop2set2propI = $true )
& ( powersetE = $true )
& ( descrp = $true )
& ( exuI2 = $true )
& ( exu__Cong = $true )
& ( setextAx = $true )
& ( emptyInPowerset = $true )
& ( subsetI1 = $true )
& ( setadjoinE = $true )
& ( emptyI = $true )
& ( setbeta = $true )
& ( setoftrueEq = $true )
& ( subsetE = $true )
& ( setadjoinOr = $true )
& ( emptyset__Cong = $true )
& ( nonemptyE1 = $true )
& ( exuEu = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrI = $true )
& ( setext = $true )
& ( notinsingleton = $true )
& ( powersetAx = $true )
& ( dsetconstr__Cong = $true )
& ( setunionE = $true )
& ( upairsetIR = $true )
& ( omega__Cong = $true )
& ( foundationAx = $true )
& ( eqimpsubset1 = $true )
& ( setadjoinIL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK207,sK208,sK209])],[f345,f730]) ).
thf(f730,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ X2 )
= $true ) )
=> ( ( ( subset @ sK209 @ sK208 )
= $true )
& ( ( in @ sK207 @ sK208 )
!= $true )
& ( ( in @ sK207 @ sK209 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f345,plain,
( ( replAx = $true )
& ( eqimpsubset2 = $true )
& ( omegaSAx = $true )
& ( setunionI = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( noeltsimpempty = $true )
& ( uniqinunit = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyI = $true )
& ( setadjoinAx = $true )
& ( exuE1 = $true )
& ( vacuousDall = $true )
& ( setunionAx = $true )
& ( exuI1 = $true )
& ( exuE2 = $true )
& ( eqinunit = $true )
& ( emptysetsubset = $true )
& ( quantDeMorgan2 = $true )
& ( nonemptyI1 = $true )
& ( emptyinPowerset = $true )
& ( inCongP = $true )
& ( notinemptyset = $true )
& ( setadjoinIR = $true )
& ( exuE3e = $true )
& ( subPowSU = $true )
& ( setunion__Cong = $true )
& ( exuE3u = $true )
& ( omegaIndAx = $true )
& ( setadjoin__Cong = $true )
& ( notdexE = $true )
& ( upairsetIL = $true )
& ( emptysetAx = $true )
& ( wellorderingAx = $true )
& ( notdallE = $true )
& ( dsetconstrER = $true )
& ( subsetI2 = $true )
& ( subsetE2 = $true )
& ( emptyE1 = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( powerset__Cong = $true )
& ( exuI3 = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( nonemptyImpWitness = $true )
& ( quantDeMorgan1 = $true )
& ( in__Cong = $true )
& ( prop2setI = $true )
& ( emptyinunitempty = $true )
& ( omega0Ax = $true )
& ( dsetconstrEL = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ X2 )
= $true ) )
& ( prop2set2propI = $true )
& ( powersetE = $true )
& ( descrp = $true )
& ( exuI2 = $true )
& ( exu__Cong = $true )
& ( setextAx = $true )
& ( emptyInPowerset = $true )
& ( subsetI1 = $true )
& ( setadjoinE = $true )
& ( emptyI = $true )
& ( setbeta = $true )
& ( setoftrueEq = $true )
& ( subsetE = $true )
& ( setadjoinOr = $true )
& ( emptyset__Cong = $true )
& ( nonemptyE1 = $true )
& ( exuEu = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrI = $true )
& ( setext = $true )
& ( notinsingleton = $true )
& ( powersetAx = $true )
& ( dsetconstr__Cong = $true )
& ( setunionE = $true )
& ( upairsetIR = $true )
& ( omega__Cong = $true )
& ( foundationAx = $true )
& ( eqimpsubset1 = $true )
& ( setadjoinIL = $true ) ),
inference(flattening,[status(thm)],[f344]) ).
thf(f344,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ X2 )
= $true ) )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f256]) ).
thf(f256,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( subset @ X2 @ X1 )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f128]) ).
thf(f128,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( subset @ X2 @ X1 )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f127]) ).
thf(f127,plain,
~ ( 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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ( ~ ( in @ X0 @ X1 )
=> ~ ( subset @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f86]) ).
thf(f86,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
=> ! [X1: $i,X4: $i,X3: $i] :
( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( subset @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f85]) ).
thf(f85,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
=> ! [X1: $i,X4: $i,X3: $i] :
( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( subset @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nkEZQ3bEXD/DTF2THF_30771.p',notsubsetI) ).
thf(f1319,plain,
( ( in @ sK207 @ sK209 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1313]) ).
thf(f1313,plain,
( ( ( in @ sK207 @ sK209 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1310,f1110]) ).
thf(f1110,plain,
( ( subset @ sK209 @ sK208 )
= $true ),
inference(cnf_transformation,[status(thm)],[f731]) ).
thf(f1310,plain,
! [X0: $i] :
( ( ( subset @ X0 @ sK208 )
!= $true )
| ( ( in @ sK207 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1309]) ).
thf(f1309,plain,
! [X0: $i] :
( ( ( in @ sK207 @ X0 )
!= $true )
| ( $true != $true )
| ( ( subset @ X0 @ sK208 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f1307,f1125]) ).
thf(f1125,plain,
subsetE2 = $true,
inference(cnf_transformation,[status(thm)],[f731]) ).
thf(f1307,plain,
! [X0: $i] :
( ( subsetE2 != $true )
| ( ( in @ sK207 @ X0 )
!= $true )
| ( ( subset @ X0 @ sK208 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1304]) ).
thf(f1304,plain,
! [X0: $i] :
( ( $true != $true )
| ( subsetE2 != $true )
| ( ( in @ sK207 @ X0 )
!= $true )
| ( ( subset @ X0 @ sK208 )
!= $true ) ),
inference(superposition,[status(thm)],[f1109,f829]) ).
thf(f829,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( subsetE2 != $true )
| ( ( subset @ X3 @ X4 )
!= $true )
| ( ( in @ X5 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
thf(f442,plain,
( ( ( subsetE2 = $true )
| ( ( ( in @ sK44 @ sK42 )
= $true )
& ( $true
!= ( in @ sK44 @ sK43 ) )
& ( ( subset @ sK42 @ sK43 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
= $true )
| ( ( subset @ X3 @ X4 )
!= $true ) )
| ( subsetE2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43,sK44])],[f440,f441]) ).
thf(f441,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( subset @ X0 @ X1 )
= $true ) )
=> ( ( ( in @ sK44 @ sK42 )
= $true )
& ( $true
!= ( in @ sK44 @ sK43 ) )
& ( ( subset @ sK42 @ sK43 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f440,plain,
( ( ( subsetE2 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( subset @ X0 @ X1 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
| ( ( in @ X5 @ X4 )
= $true )
| ( ( subset @ X3 @ X4 )
!= $true ) )
| ( subsetE2 != $true ) ) ),
inference(rectify,[status(thm)],[f439]) ).
thf(f439,plain,
( ( ( subsetE2 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( subset @ X0 @ X1 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( subsetE2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f324]) ).
thf(f324,plain,
( ( subsetE2 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f323]) ).
thf(f323,plain,
( ( subsetE2 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f254]) ).
thf(f254,plain,
( ( subsetE2 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ X0 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f110]) ).
thf(f110,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ X0 )
!= $true ) ) )
<=> ( subsetE2 = $true ) ),
inference(fool_elimination,[status(thm)],[f109]) ).
thf(f109,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X0 ) ) )
= subsetE2 ),
inference(rectify,[status(thm)],[f84]) ).
thf(f84,axiom,
! [X3: $i,X4: $i,X1: $i] :
( ( ( subset @ X3 @ X4 )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( in @ X1 @ X3 ) ) )
= subsetE2 ),
file('/export/starexec/sandbox/tmp/tmp.nkEZQ3bEXD/DTF2THF_30771.p',subsetE2) ).
thf(f1109,plain,
( ( in @ sK207 @ sK208 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f731]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU566^1 : TPTP v9.2.1. Released v3.7.0.
% 0.14/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n004.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:26:56 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.34/0.50 ---- Original DTF file ---
% 0.34/0.50 thf(spec,logic,$$dhol).
% 0.34/0.50 %------------------------------------------------------------------------------
% 0.34/0.50 % File : SEU566^1 : TPTP v9.2.1. Released v3.7.0.
% 0.34/0.50 % Domain : Set Theory
% 0.34/0.50 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.34/0.50 % Version : Especial.
% 0.34/0.50 % English : (! A:i.! B:i.! x:i.in x A -> ~(in x B) -> ~(subset A B))
% 0.34/0.50
% 0.34/0.50 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.34/0.50 % Source : [Bro08]
% 0.34/0.50 % Names : ZFC068g [Bro08]
% 0.34/0.50
% 0.34/0.50 % Status : Theorem
% 0.34/0.50 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v4.0.1, 1.00 v3.7.0
% 0.34/0.50 % Syntax : Number of formulae : 182 ( 84 unt; 97 typ; 84 def)
% 0.34/0.50 % Number of atoms : 462 ( 129 equ; 0 cnn)
% 0.34/0.50 % Maximal formula atoms : 85 ( 5 avg)
% 0.34/0.50 % Number of connectives : 740 ( 25 ~; 5 |; 27 &; 456 @)
% 0.34/0.50 % ( 14 <=>; 213 =>; 0 <=; 0 <~>)
% 0.34/0.50 % Maximal formula depth : 91 ( 2 avg)
% 0.34/0.50 % Number of types : 2 ( 0 usr)
% 0.34/0.50 % Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% 0.34/0.50 % Number of symbols : 100 ( 97 usr; 86 con; 0-2 aty)
% 0.34/0.50 % Number of variables : 262 ( 28 ^; 206 !; 28 ?; 262 :)
% 0.34/0.50 % SPC : TH0_THM_EQU_NAR
% 0.34/0.50
% 0.34/0.50 % Comments : http://mathgate.info/detsetitem.php?id=438
% 0.34/0.50 %------------------------------------------------------------------------------
% 0.34/0.50 thf(in_type,type,
% 0.34/0.50 in: $i > $i > $o ).
% 0.34/0.50
% 0.34/0.50 thf(exu_type,type,
% 0.34/0.50 exu: ( $i > $o ) > $o ).
% 0.34/0.50
% 0.34/0.50 thf(exu,definition,
% 0.34/0.50 ( exu
% 0.34/0.50 = ( ^ [Xphi: $i > $o] :
% 0.34/0.50 ? [Xx: $i] :
% 0.34/0.50 ( ( Xphi @ Xx )
% 0.34/0.50 & ! [Xy: $i] :
% 0.34/0.50 ( ( Xphi @ Xy )
% 0.34/0.50 => ( Xx = Xy ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setextAx_type,type,
% 0.34/0.50 setextAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setextAx,definition,
% 0.34/0.50 ( setextAx
% 0.34/0.50 = ( ! [A: $i,B: $i] :
% 0.34/0.50 ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ A )
% 0.34/0.50 <=> ( in @ Xx @ B ) )
% 0.34/0.50 => ( A = B ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptyset_type,type,
% 0.34/0.50 emptyset: $i ).
% 0.34/0.50
% 0.34/0.50 thf(emptysetAx_type,type,
% 0.34/0.50 emptysetAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptysetAx,definition,
% 0.34/0.50 ( emptysetAx
% 0.34/0.50 = ( ! [Xx: $i] :
% 0.34/0.50 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoin_type,type,
% 0.34/0.50 setadjoin: $i > $i > $i ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinAx_type,type,
% 0.34/0.50 setadjoinAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinAx,definition,
% 0.34/0.50 ( setadjoinAx
% 0.34/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.34/0.50 <=> ( ( Xy = Xx )
% 0.34/0.50 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(powerset_type,type,
% 0.34/0.50 powerset: $i > $i ).
% 0.34/0.50
% 0.34/0.50 thf(powersetAx_type,type,
% 0.34/0.50 powersetAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(powersetAx,definition,
% 0.34/0.50 ( powersetAx
% 0.34/0.50 = ( ! [A: $i,B: $i] :
% 0.34/0.50 ( ( in @ B @ ( powerset @ A ) )
% 0.34/0.50 <=> ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setunion_type,type,
% 0.34/0.50 setunion: $i > $i ).
% 0.34/0.50
% 0.34/0.50 thf(setunionAx_type,type,
% 0.34/0.50 setunionAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setunionAx,definition,
% 0.34/0.50 ( setunionAx
% 0.34/0.50 = ( ! [A: $i,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ ( setunion @ A ) )
% 0.34/0.50 <=> ? [B: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 & ( in @ B @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(omega_type,type,
% 0.34/0.50 omega: $i ).
% 0.34/0.50
% 0.34/0.50 thf(omega0Ax_type,type,
% 0.34/0.50 omega0Ax: $o ).
% 0.34/0.50
% 0.34/0.50 thf(omega0Ax,definition,
% 0.34/0.50 ( omega0Ax
% 0.34/0.50 = ( in @ emptyset @ omega ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(omegaSAx_type,type,
% 0.34/0.50 omegaSAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(omegaSAx,definition,
% 0.34/0.50 ( omegaSAx
% 0.34/0.50 = ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ omega )
% 0.34/0.50 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(omegaIndAx_type,type,
% 0.34/0.50 omegaIndAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(omegaIndAx,definition,
% 0.34/0.50 ( omegaIndAx
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ( ( in @ emptyset @ A )
% 0.34/0.50 & ! [Xx: $i] :
% 0.34/0.50 ( ( ( in @ Xx @ omega )
% 0.34/0.50 & ( in @ Xx @ A ) )
% 0.34/0.50 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.34/0.50 => ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ omega )
% 0.34/0.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(replAx_type,type,
% 0.34/0.50 replAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(replAx,definition,
% 0.34/0.50 ( replAx
% 0.34/0.50 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.34/0.50 ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ A )
% 0.34/0.50 => ( exu
% 0.34/0.50 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.34/0.50 => ? [B: $i] :
% 0.34/0.50 ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 <=> ? [Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ A )
% 0.34/0.50 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(foundationAx_type,type,
% 0.34/0.50 foundationAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(foundationAx,definition,
% 0.34/0.50 ( foundationAx
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.34/0.50 => ? [B: $i] :
% 0.34/0.50 ( ( in @ B @ A )
% 0.34/0.50 & ~ ? [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(wellorderingAx_type,type,
% 0.34/0.50 wellorderingAx: $o ).
% 0.34/0.50
% 0.34/0.50 thf(wellorderingAx,definition,
% 0.34/0.50 ( wellorderingAx
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ? [B: $i] :
% 0.34/0.50 ( ! [C: $i] :
% 0.34/0.50 ( ( in @ C @ B )
% 0.34/0.50 => ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ C )
% 0.34/0.50 => ( in @ Xx @ A ) ) )
% 0.34/0.50 & ! [Xx: $i,Xy: $i] :
% 0.34/0.50 ( ( ( in @ Xx @ A )
% 0.34/0.50 & ( in @ Xy @ A ) )
% 0.34/0.50 => ( ! [C: $i] :
% 0.34/0.50 ( ( in @ C @ B )
% 0.34/0.50 => ( ( in @ Xx @ C )
% 0.34/0.50 <=> ( in @ Xy @ C ) ) )
% 0.34/0.50 => ( Xx = Xy ) ) )
% 0.34/0.50 & ! [C: $i,D: $i] :
% 0.34/0.50 ( ( ( in @ C @ B )
% 0.34/0.50 & ( in @ D @ B ) )
% 0.34/0.50 => ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ C )
% 0.34/0.50 => ( in @ Xx @ D ) )
% 0.34/0.50 | ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ D )
% 0.34/0.50 => ( in @ Xx @ C ) ) ) )
% 0.34/0.50 & ! [C: $i] :
% 0.34/0.50 ( ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ C )
% 0.34/0.50 => ( in @ Xx @ A ) )
% 0.34/0.50 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.34/0.50 => ? [D: $i,Xx: $i] :
% 0.34/0.50 ( ( in @ D @ B )
% 0.34/0.50 & ( in @ Xx @ C )
% 0.34/0.50 & ~ ? [Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ D )
% 0.34/0.50 & ( in @ Xy @ C ) )
% 0.34/0.50 & ! [E: $i] :
% 0.34/0.50 ( ( in @ E @ B )
% 0.34/0.50 => ( ! [Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ E )
% 0.34/0.50 => ( in @ Xy @ D ) )
% 0.34/0.50 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(descr_type,type,
% 0.34/0.50 descr: ( $i > $o ) > $i ).
% 0.34/0.50
% 0.34/0.50 thf(descrp_type,type,
% 0.34/0.50 descrp: $o ).
% 0.34/0.50
% 0.34/0.50 thf(descrp,definition,
% 0.34/0.50 ( descrp
% 0.34/0.50 = ( ! [Xphi: $i > $o] :
% 0.34/0.50 ( ( exu
% 0.34/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.50 => ( Xphi
% 0.34/0.50 @ ( descr
% 0.34/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstr_type,type,
% 0.34/0.50 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstrI_type,type,
% 0.34/0.50 dsetconstrI: $o ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstrI,definition,
% 0.34/0.50 ( dsetconstrI
% 0.34/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ A )
% 0.34/0.50 => ( ( Xphi @ Xx )
% 0.34/0.50 => ( in @ Xx
% 0.34/0.50 @ ( dsetconstr @ A
% 0.34/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstrEL_type,type,
% 0.34/0.50 dsetconstrEL: $o ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstrEL,definition,
% 0.34/0.50 ( dsetconstrEL
% 0.34/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx
% 0.34/0.50 @ ( dsetconstr @ A
% 0.34/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.34/0.50 => ( in @ Xx @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstrER_type,type,
% 0.34/0.50 dsetconstrER: $o ).
% 0.34/0.50
% 0.34/0.50 thf(dsetconstrER,definition,
% 0.34/0.50 ( dsetconstrER
% 0.34/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx
% 0.34/0.50 @ ( dsetconstr @ A
% 0.34/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.34/0.50 => ( Xphi @ Xx ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(exuE1_type,type,
% 0.34/0.50 exuE1: $o ).
% 0.34/0.50
% 0.34/0.50 thf(exuE1,definition,
% 0.34/0.50 ( exuE1
% 0.34/0.50 = ( ! [Xphi: $i > $o] :
% 0.34/0.50 ( ( exu
% 0.34/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.50 => ? [Xx: $i] :
% 0.34/0.50 ( ( Xphi @ Xx )
% 0.34/0.50 & ! [Xy: $i] :
% 0.34/0.50 ( ( Xphi @ Xy )
% 0.34/0.50 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(prop2set_type,type,
% 0.34/0.50 prop2set: $o > $i ).
% 0.34/0.50
% 0.34/0.50 thf(prop2setE_type,type,
% 0.34/0.50 prop2setE: $o ).
% 0.34/0.50
% 0.34/0.50 thf(prop2setE,definition,
% 0.34/0.50 ( prop2setE
% 0.34/0.50 = ( ! [Xphi: $o,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.34/0.50 => Xphi ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptysetE_type,type,
% 0.34/0.50 emptysetE: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptysetE,definition,
% 0.34/0.50 ( emptysetE
% 0.34/0.50 = ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ emptyset )
% 0.34/0.50 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptysetimpfalse_type,type,
% 0.34/0.50 emptysetimpfalse: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptysetimpfalse,definition,
% 0.34/0.50 ( emptysetimpfalse
% 0.34/0.50 = ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ emptyset )
% 0.34/0.50 => $false ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(notinemptyset_type,type,
% 0.34/0.50 notinemptyset: $o ).
% 0.34/0.50
% 0.34/0.50 thf(notinemptyset,definition,
% 0.34/0.50 ( notinemptyset
% 0.34/0.50 = ( ! [Xx: $i] :
% 0.34/0.50 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(exuE3e_type,type,
% 0.34/0.50 exuE3e: $o ).
% 0.34/0.50
% 0.34/0.50 thf(exuE3e,definition,
% 0.34/0.50 ( exuE3e
% 0.34/0.50 = ( ! [Xphi: $i > $o] :
% 0.34/0.50 ( ( exu
% 0.34/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.50 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setext_type,type,
% 0.34/0.50 setext: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setext,definition,
% 0.34/0.50 ( setext
% 0.34/0.50 = ( ! [A: $i,B: $i] :
% 0.34/0.50 ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ A )
% 0.34/0.50 => ( in @ Xx @ B ) )
% 0.34/0.50 => ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 => ( in @ Xx @ A ) )
% 0.34/0.50 => ( A = B ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptyI_type,type,
% 0.34/0.50 emptyI: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptyI,definition,
% 0.34/0.50 ( emptyI
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ! [Xx: $i] :
% 0.34/0.50 ~ ( in @ Xx @ A )
% 0.34/0.50 => ( A = emptyset ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(noeltsimpempty_type,type,
% 0.34/0.50 noeltsimpempty: $o ).
% 0.34/0.50
% 0.34/0.50 thf(noeltsimpempty,definition,
% 0.34/0.50 ( noeltsimpempty
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ! [Xx: $i] :
% 0.34/0.50 ~ ( in @ Xx @ A )
% 0.34/0.50 => ( A = emptyset ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setbeta_type,type,
% 0.34/0.50 setbeta: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setbeta,definition,
% 0.34/0.50 ( setbeta
% 0.34/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ A )
% 0.34/0.50 => ( ( in @ Xx
% 0.34/0.50 @ ( dsetconstr @ A
% 0.34/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.34/0.50 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(nonempty_type,type,
% 0.34/0.50 nonempty: $i > $o ).
% 0.34/0.50
% 0.34/0.50 thf(nonempty,definition,
% 0.34/0.50 ( nonempty
% 0.34/0.50 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(nonemptyE1_type,type,
% 0.34/0.50 nonemptyE1: $o ).
% 0.34/0.50
% 0.34/0.50 thf(nonemptyE1,definition,
% 0.34/0.50 ( nonemptyE1
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ( nonempty @ A )
% 0.34/0.50 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(nonemptyI_type,type,
% 0.34/0.50 nonemptyI: $o ).
% 0.34/0.50
% 0.34/0.50 thf(nonemptyI,definition,
% 0.34/0.50 ( nonemptyI
% 0.34/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ A )
% 0.34/0.50 => ( ( Xphi @ Xx )
% 0.34/0.50 => ( nonempty
% 0.34/0.50 @ ( dsetconstr @ A
% 0.34/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(nonemptyI1_type,type,
% 0.34/0.50 nonemptyI1: $o ).
% 0.34/0.50
% 0.34/0.50 thf(nonemptyI1,definition,
% 0.34/0.50 ( nonemptyI1
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.34/0.50 => ( nonempty @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinIL_type,type,
% 0.34/0.50 setadjoinIL: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinIL,definition,
% 0.34/0.50 ( setadjoinIL
% 0.34/0.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptyinunitempty_type,type,
% 0.34/0.50 emptyinunitempty: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptyinunitempty,definition,
% 0.34/0.50 ( emptyinunitempty
% 0.34/0.50 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinIR_type,type,
% 0.34/0.50 setadjoinIR: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinIR,definition,
% 0.34/0.50 ( setadjoinIR
% 0.34/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ A )
% 0.34/0.50 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinE_type,type,
% 0.34/0.50 setadjoinE: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinE,definition,
% 0.34/0.50 ( setadjoinE
% 0.34/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.34/0.50 => ! [Xphi: $o] :
% 0.34/0.50 ( ( ( Xy = Xx )
% 0.34/0.50 => Xphi )
% 0.34/0.50 => ( ( ( in @ Xy @ A )
% 0.34/0.50 => Xphi )
% 0.34/0.50 => Xphi ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinOr_type,type,
% 0.34/0.50 setadjoinOr: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setadjoinOr,definition,
% 0.34/0.50 ( setadjoinOr
% 0.34/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.34/0.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.34/0.50 => ( ( Xy = Xx )
% 0.34/0.50 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setoftrueEq_type,type,
% 0.34/0.50 setoftrueEq: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setoftrueEq,definition,
% 0.34/0.50 ( setoftrueEq
% 0.34/0.50 = ( ! [A: $i] :
% 0.34/0.50 ( ( dsetconstr @ A
% 0.34/0.50 @ ^ [Xx: $i] : $true )
% 0.34/0.50 = A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(powersetI_type,type,
% 0.34/0.50 powersetI: $o ).
% 0.34/0.50
% 0.34/0.50 thf(powersetI,definition,
% 0.34/0.50 ( powersetI
% 0.34/0.50 = ( ! [A: $i,B: $i] :
% 0.34/0.50 ( ! [Xx: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 => ( in @ Xx @ A ) )
% 0.34/0.50 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptyinPowerset_type,type,
% 0.34/0.50 emptyinPowerset: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptyinPowerset,definition,
% 0.34/0.50 ( emptyinPowerset
% 0.34/0.50 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(emptyInPowerset_type,type,
% 0.34/0.50 emptyInPowerset: $o ).
% 0.34/0.50
% 0.34/0.50 thf(emptyInPowerset,definition,
% 0.34/0.50 ( emptyInPowerset
% 0.34/0.50 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(powersetE_type,type,
% 0.34/0.50 powersetE: $o ).
% 0.34/0.50
% 0.34/0.50 thf(powersetE,definition,
% 0.34/0.50 ( powersetE
% 0.34/0.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.50 ( ( in @ B @ ( powerset @ A ) )
% 0.34/0.50 => ( ( in @ Xx @ B )
% 0.34/0.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(setunionI_type,type,
% 0.34/0.50 setunionI: $o ).
% 0.34/0.50
% 0.34/0.50 thf(setunionI,definition,
% 0.34/0.50 ( setunionI
% 0.34/0.50 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.34/0.50 ( ( in @ Xx @ B )
% 0.34/0.50 => ( ( in @ B @ A )
% 0.34/0.50 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(setunionE_type,type,
% 0.34/0.51 setunionE: $o ).
% 0.34/0.51
% 0.34/0.51 thf(setunionE,definition,
% 0.34/0.51 ( setunionE
% 0.34/0.51 = ( ! [A: $i,Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ ( setunion @ A ) )
% 0.34/0.51 => ! [Xphi: $o] :
% 0.34/0.51 ( ! [B: $i] :
% 0.34/0.51 ( ( in @ Xx @ B )
% 0.34/0.51 => ( ( in @ B @ A )
% 0.34/0.51 => Xphi ) )
% 0.34/0.51 => Xphi ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(subPowSU_type,type,
% 0.34/0.51 subPowSU: $o ).
% 0.34/0.51
% 0.34/0.51 thf(subPowSU,definition,
% 0.34/0.51 ( subPowSU
% 0.34/0.51 = ( ! [A: $i,Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(exuE2_type,type,
% 0.34/0.51 exuE2: $o ).
% 0.34/0.51
% 0.34/0.51 thf(exuE2,definition,
% 0.34/0.51 ( exuE2
% 0.34/0.51 = ( ! [Xphi: $i > $o] :
% 0.34/0.51 ( ( exu
% 0.34/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.51 => ? [Xx: $i] :
% 0.34/0.51 ! [Xy: $i] :
% 0.34/0.51 ( ( Xphi @ Xy )
% 0.34/0.51 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(nonemptyImpWitness_type,type,
% 0.34/0.51 nonemptyImpWitness: $o ).
% 0.34/0.51
% 0.34/0.51 thf(nonemptyImpWitness,definition,
% 0.34/0.51 ( nonemptyImpWitness
% 0.34/0.51 = ( ! [A: $i] :
% 0.34/0.51 ( ( nonempty @ A )
% 0.34/0.51 => ? [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 & $true ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(uniqinunit_type,type,
% 0.34/0.51 uniqinunit: $o ).
% 0.34/0.51
% 0.34/0.51 thf(uniqinunit,definition,
% 0.34/0.51 ( uniqinunit
% 0.34/0.51 = ( ! [Xx: $i,Xy: $i] :
% 0.34/0.51 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.34/0.51 => ( Xx = Xy ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(notinsingleton_type,type,
% 0.34/0.51 notinsingleton: $o ).
% 0.34/0.51
% 0.34/0.51 thf(notinsingleton,definition,
% 0.34/0.51 ( notinsingleton
% 0.34/0.51 = ( ! [Xx: $i,Xy: $i] :
% 0.34/0.51 ( ( Xx != Xy )
% 0.34/0.51 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(eqinunit_type,type,
% 0.34/0.51 eqinunit: $o ).
% 0.34/0.51
% 0.34/0.51 thf(eqinunit,definition,
% 0.34/0.51 ( eqinunit
% 0.34/0.51 = ( ! [Xx: $i,Xy: $i] :
% 0.34/0.51 ( ( Xx = Xy )
% 0.34/0.51 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(singletonsswitch_type,type,
% 0.34/0.51 singletonsswitch: $o ).
% 0.34/0.51
% 0.34/0.51 thf(singletonsswitch,definition,
% 0.34/0.51 ( singletonsswitch
% 0.34/0.51 = ( ! [Xx: $i,Xy: $i] :
% 0.34/0.51 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.34/0.51 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(upairsetE_type,type,
% 0.34/0.51 upairsetE: $o ).
% 0.34/0.51
% 0.34/0.51 thf(upairsetE,definition,
% 0.34/0.51 ( upairsetE
% 0.34/0.51 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.34/0.51 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.34/0.51 => ( ( Xz = Xx )
% 0.34/0.51 | ( Xz = Xy ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(upairsetIL_type,type,
% 0.34/0.51 upairsetIL: $o ).
% 0.34/0.51
% 0.34/0.51 thf(upairsetIL,definition,
% 0.34/0.51 ( upairsetIL
% 0.34/0.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(upairsetIR_type,type,
% 0.34/0.51 upairsetIR: $o ).
% 0.34/0.51
% 0.34/0.51 thf(upairsetIR,definition,
% 0.34/0.51 ( upairsetIR
% 0.34/0.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(emptyE1_type,type,
% 0.34/0.51 emptyE1: $o ).
% 0.34/0.51
% 0.34/0.51 thf(emptyE1,definition,
% 0.34/0.51 ( emptyE1
% 0.34/0.51 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.51 ( ? [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 & ( Xphi @ Xx ) )
% 0.34/0.51 => ( ( ( dsetconstr @ A
% 0.34/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.51 = emptyset )
% 0.34/0.51 => $false ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(vacuousDall_type,type,
% 0.34/0.51 vacuousDall: $o ).
% 0.34/0.51
% 0.34/0.51 thf(vacuousDall,definition,
% 0.34/0.51 ( vacuousDall
% 0.34/0.51 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ emptyset )
% 0.34/0.51 => ( Xphi @ Xx ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(quantDeMorgan1_type,type,
% 0.34/0.51 quantDeMorgan1: $o ).
% 0.34/0.51
% 0.34/0.51 thf(quantDeMorgan1,definition,
% 0.34/0.51 ( quantDeMorgan1
% 0.34/0.51 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.51 ( ~ ! [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 => ( Xphi @ Xx ) )
% 0.34/0.51 => ? [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(quantDeMorgan2_type,type,
% 0.34/0.51 quantDeMorgan2: $o ).
% 0.34/0.51
% 0.34/0.51 thf(quantDeMorgan2,definition,
% 0.34/0.51 ( quantDeMorgan2
% 0.34/0.51 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.51 ( ! [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 => ~ ( Xphi @ Xx ) )
% 0.34/0.51 => ~ ? [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(quantDeMorgan3_type,type,
% 0.34/0.51 quantDeMorgan3: $o ).
% 0.34/0.51
% 0.34/0.51 thf(quantDeMorgan3,definition,
% 0.34/0.51 ( quantDeMorgan3
% 0.34/0.51 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.51 ( ~ ? [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 & ( Xphi @ Xx ) )
% 0.34/0.51 => ! [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(quantDeMorgan4_type,type,
% 0.34/0.51 quantDeMorgan4: $o ).
% 0.34/0.51
% 0.34/0.51 thf(quantDeMorgan4,definition,
% 0.34/0.51 ( quantDeMorgan4
% 0.34/0.51 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.51 ( ? [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 & ~ ( Xphi @ Xx ) )
% 0.34/0.51 => ~ ! [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(prop2setI_type,type,
% 0.34/0.51 prop2setI: $o ).
% 0.34/0.51
% 0.34/0.51 thf(prop2setI,definition,
% 0.34/0.51 ( prop2setI
% 0.34/0.51 = ( ! [Xphi: $o] :
% 0.34/0.51 ( Xphi
% 0.34/0.51 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(set2prop_type,type,
% 0.34/0.51 set2prop: $i > $o ).
% 0.34/0.51
% 0.34/0.51 thf(prop2set2propI_type,type,
% 0.34/0.51 prop2set2propI: $o ).
% 0.34/0.51
% 0.34/0.51 thf(prop2set2propI,definition,
% 0.34/0.51 ( prop2set2propI
% 0.34/0.51 = ( ! [Xphi: $o] :
% 0.34/0.51 ( Xphi
% 0.34/0.51 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(notdexE_type,type,
% 0.34/0.51 notdexE: $o ).
% 0.34/0.51
% 0.34/0.51 thf(notdexE,definition,
% 0.34/0.51 ( notdexE
% 0.34/0.51 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.51 ( ~ ? [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 & ( Xphi @ Xx ) )
% 0.34/0.51 => ! [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(notdallE_type,type,
% 0.34/0.51 notdallE: $o ).
% 0.34/0.51
% 0.34/0.51 thf(notdallE,definition,
% 0.34/0.51 ( notdallE
% 0.34/0.51 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.51 ( ~ ! [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 => ( Xphi @ Xx ) )
% 0.34/0.51 => ? [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(exuI1_type,type,
% 0.34/0.51 exuI1: $o ).
% 0.34/0.51
% 0.34/0.51 thf(exuI1,definition,
% 0.34/0.51 ( exuI1
% 0.34/0.51 = ( ! [Xphi: $i > $o] :
% 0.34/0.51 ( ? [Xx: $i] :
% 0.34/0.51 ( ( Xphi @ Xx )
% 0.34/0.51 & ! [Xy: $i] :
% 0.34/0.51 ( ( Xphi @ Xy )
% 0.34/0.51 => ( Xx = Xy ) ) )
% 0.34/0.51 => ( exu
% 0.34/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(exuI3_type,type,
% 0.34/0.51 exuI3: $o ).
% 0.34/0.51
% 0.34/0.51 thf(exuI3,definition,
% 0.34/0.51 ( exuI3
% 0.34/0.51 = ( ! [Xphi: $i > $o] :
% 0.34/0.51 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.34/0.51 => ( ! [Xx: $i,Xy: $i] :
% 0.34/0.51 ( ( Xphi @ Xx )
% 0.34/0.51 => ( ( Xphi @ Xy )
% 0.34/0.51 => ( Xx = Xy ) ) )
% 0.34/0.51 => ( exu
% 0.34/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(exuI2_type,type,
% 0.34/0.51 exuI2: $o ).
% 0.34/0.51
% 0.34/0.51 thf(exuI2,definition,
% 0.34/0.51 ( exuI2
% 0.34/0.51 = ( ! [Xphi: $i > $o] :
% 0.34/0.51 ( ? [Xx: $i] :
% 0.34/0.51 ! [Xy: $i] :
% 0.34/0.51 ( ( Xphi @ Xy )
% 0.34/0.51 <=> ( Xy = Xx ) )
% 0.34/0.51 => ( exu
% 0.34/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(inCongP_type,type,
% 0.34/0.51 inCongP: $o ).
% 0.34/0.51
% 0.34/0.51 thf(inCongP,definition,
% 0.34/0.51 ( inCongP
% 0.34/0.51 = ( ! [A: $i,B: $i] :
% 0.34/0.51 ( ( A = B )
% 0.34/0.51 => ! [Xx: $i,Xy: $i] :
% 0.34/0.51 ( ( Xx = Xy )
% 0.34/0.51 => ( ( in @ Xx @ A )
% 0.34/0.51 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(in__Cong_type,type,
% 0.34/0.51 in__Cong: $o ).
% 0.34/0.51
% 0.34/0.51 thf(in__Cong,definition,
% 0.34/0.51 ( in__Cong
% 0.34/0.51 = ( ! [A: $i,B: $i] :
% 0.34/0.51 ( ( A = B )
% 0.34/0.51 => ! [Xx: $i,Xy: $i] :
% 0.34/0.51 ( ( Xx = Xy )
% 0.34/0.51 => ( ( in @ Xx @ A )
% 0.34/0.51 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(exuE3u_type,type,
% 0.34/0.51 exuE3u: $o ).
% 0.34/0.51
% 0.34/0.51 thf(exuE3u,definition,
% 0.34/0.51 ( exuE3u
% 0.34/0.51 = ( ! [Xphi: $i > $o] :
% 0.34/0.51 ( ( exu
% 0.34/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.51 => ! [Xx: $i,Xy: $i] :
% 0.34/0.51 ( ( Xphi @ Xx )
% 0.34/0.51 => ( ( Xphi @ Xy )
% 0.34/0.51 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(exu__Cong_type,type,
% 0.34/0.51 exu__Cong: $o ).
% 0.34/0.51
% 0.34/0.51 thf(exu__Cong,definition,
% 0.34/0.51 ( exu__Cong
% 0.34/0.51 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.34/0.51 ( ! [Xx: $i,Xy: $i] :
% 0.34/0.51 ( ( Xx = Xy )
% 0.34/0.51 => ( ( Xphi @ Xx )
% 0.34/0.51 <=> ( Xpsi @ Xy ) ) )
% 0.34/0.51 => ( ( exu
% 0.34/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.51 <=> ( exu
% 0.34/0.51 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(emptyset__Cong_type,type,
% 0.34/0.51 emptyset__Cong: $o ).
% 0.34/0.51
% 0.34/0.51 thf(emptyset__Cong,definition,
% 0.34/0.51 ( emptyset__Cong
% 0.34/0.51 = ( emptyset = emptyset ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(setadjoin__Cong_type,type,
% 0.34/0.51 setadjoin__Cong: $o ).
% 0.34/0.51
% 0.34/0.51 thf(setadjoin__Cong,definition,
% 0.34/0.51 ( setadjoin__Cong
% 0.34/0.51 = ( ! [Xx: $i,Xy: $i] :
% 0.34/0.51 ( ( Xx = Xy )
% 0.34/0.51 => ! [Xz: $i,Xu: $i] :
% 0.34/0.51 ( ( Xz = Xu )
% 0.34/0.51 => ( ( setadjoin @ Xx @ Xz )
% 0.34/0.51 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(powerset__Cong_type,type,
% 0.34/0.51 powerset__Cong: $o ).
% 0.34/0.51
% 0.34/0.51 thf(powerset__Cong,definition,
% 0.34/0.51 ( powerset__Cong
% 0.34/0.51 = ( ! [A: $i,B: $i] :
% 0.34/0.51 ( ( A = B )
% 0.34/0.51 => ( ( powerset @ A )
% 0.34/0.51 = ( powerset @ B ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(setunion__Cong_type,type,
% 0.34/0.51 setunion__Cong: $o ).
% 0.34/0.51
% 0.34/0.51 thf(setunion__Cong,definition,
% 0.34/0.51 ( setunion__Cong
% 0.34/0.51 = ( ! [A: $i,B: $i] :
% 0.34/0.51 ( ( A = B )
% 0.34/0.51 => ( ( setunion @ A )
% 0.34/0.51 = ( setunion @ B ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(omega__Cong_type,type,
% 0.34/0.51 omega__Cong: $o ).
% 0.34/0.51
% 0.34/0.51 thf(omega__Cong,definition,
% 0.34/0.51 ( omega__Cong
% 0.34/0.51 = ( omega = omega ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(exuEu_type,type,
% 0.34/0.51 exuEu: $o ).
% 0.34/0.51
% 0.34/0.51 thf(exuEu,definition,
% 0.34/0.51 ( exuEu
% 0.34/0.51 = ( ! [Xphi: $i > $o] :
% 0.34/0.51 ( ( exu
% 0.34/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.51 => ! [Xx: $i,Xy: $i] :
% 0.34/0.51 ( ( Xphi @ Xx )
% 0.34/0.51 => ( ( Xphi @ Xy )
% 0.34/0.51 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(descr__Cong_type,type,
% 0.34/0.51 descr__Cong: $o ).
% 0.34/0.51
% 0.34/0.51 thf(descr__Cong,definition,
% 0.34/0.51 ( descr__Cong
% 0.34/0.51 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.34/0.51 ( ! [Xx: $i,Xy: $i] :
% 0.34/0.51 ( ( Xx = Xy )
% 0.34/0.51 => ( ( Xphi @ Xx )
% 0.34/0.51 <=> ( Xpsi @ Xy ) ) )
% 0.34/0.51 => ( ( exu
% 0.34/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.51 => ( ( exu
% 0.34/0.51 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.34/0.51 => ( ( descr
% 0.34/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.51 = ( descr
% 0.34/0.51 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(dsetconstr__Cong_type,type,
% 0.34/0.51 dsetconstr__Cong: $o ).
% 0.34/0.51
% 0.34/0.51 thf(dsetconstr__Cong,definition,
% 0.34/0.51 ( dsetconstr__Cong
% 0.34/0.51 = ( ! [A: $i,B: $i] :
% 0.34/0.51 ( ( A = B )
% 0.34/0.51 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.34/0.51 ( ! [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 => ! [Xy: $i] :
% 0.34/0.51 ( ( in @ Xy @ B )
% 0.34/0.51 => ( ( Xx = Xy )
% 0.34/0.51 => ( ( Xphi @ Xx )
% 0.34/0.51 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.34/0.51 => ( ( dsetconstr @ A
% 0.34/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.51 = ( dsetconstr @ B
% 0.34/0.51 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(subset_type,type,
% 0.34/0.51 subset: $i > $i > $o ).
% 0.34/0.51
% 0.34/0.51 thf(disjoint_type,type,
% 0.34/0.51 disjoint: $i > $i > $o ).
% 0.34/0.51
% 0.34/0.51 thf(setsmeet_type,type,
% 0.34/0.51 setsmeet: $i > $i > $o ).
% 0.34/0.51
% 0.34/0.51 thf(subsetI1_type,type,
% 0.34/0.51 subsetI1: $o ).
% 0.34/0.51
% 0.34/0.51 thf(subsetI1,definition,
% 0.34/0.51 ( subsetI1
% 0.34/0.51 = ( ! [A: $i,B: $i] :
% 0.34/0.51 ( ! [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 => ( in @ Xx @ B ) )
% 0.34/0.51 => ( subset @ A @ B ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(eqimpsubset2_type,type,
% 0.34/0.51 eqimpsubset2: $o ).
% 0.34/0.51
% 0.34/0.51 thf(eqimpsubset2,definition,
% 0.34/0.51 ( eqimpsubset2
% 0.34/0.51 = ( ! [A: $i,B: $i] :
% 0.34/0.51 ( ( A = B )
% 0.34/0.51 => ( subset @ B @ A ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(eqimpsubset1_type,type,
% 0.34/0.51 eqimpsubset1: $o ).
% 0.34/0.51
% 0.34/0.51 thf(eqimpsubset1,definition,
% 0.34/0.51 ( eqimpsubset1
% 0.34/0.51 = ( ! [A: $i,B: $i] :
% 0.34/0.51 ( ( A = B )
% 0.34/0.51 => ( subset @ A @ B ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(subsetI2_type,type,
% 0.34/0.51 subsetI2: $o ).
% 0.34/0.51
% 0.34/0.51 thf(subsetI2,definition,
% 0.34/0.51 ( subsetI2
% 0.34/0.51 = ( ! [A: $i,B: $i] :
% 0.34/0.51 ( ! [Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 => ( in @ Xx @ B ) )
% 0.34/0.51 => ( subset @ A @ B ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(emptysetsubset_type,type,
% 0.34/0.51 emptysetsubset: $o ).
% 0.34/0.51
% 0.34/0.51 thf(emptysetsubset,definition,
% 0.34/0.51 ( emptysetsubset
% 0.34/0.51 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(subsetE_type,type,
% 0.34/0.51 subsetE: $o ).
% 0.34/0.51
% 0.34/0.51 thf(subsetE,definition,
% 0.34/0.51 ( subsetE
% 0.34/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.51 ( ( subset @ A @ B )
% 0.34/0.51 => ( ( in @ Xx @ A )
% 0.34/0.51 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(subsetE2_type,type,
% 0.34/0.51 subsetE2: $o ).
% 0.34/0.51
% 0.34/0.51 thf(subsetE2,definition,
% 0.34/0.51 ( subsetE2
% 0.34/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.51 ( ( subset @ A @ B )
% 0.34/0.51 => ( ~ ( in @ Xx @ B )
% 0.34/0.51 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 thf(notsubsetI,conjecture,
% 0.34/0.51 ( setextAx
% 0.34/0.51 => ( emptysetAx
% 0.34/0.51 => ( setadjoinAx
% 0.34/0.51 => ( powersetAx
% 0.34/0.51 => ( setunionAx
% 0.34/0.51 => ( omega0Ax
% 0.34/0.51 => ( omegaSAx
% 0.34/0.51 => ( omegaIndAx
% 0.34/0.51 => ( replAx
% 0.34/0.51 => ( foundationAx
% 0.34/0.51 => ( wellorderingAx
% 0.34/0.51 => ( descrp
% 0.34/0.51 => ( dsetconstrI
% 0.34/0.51 => ( dsetconstrEL
% 0.34/0.51 => ( dsetconstrER
% 0.34/0.51 => ( exuE1
% 0.34/0.51 => ( prop2setE
% 0.34/0.51 => ( emptysetE
% 0.34/0.51 => ( emptysetimpfalse
% 0.34/0.51 => ( notinemptyset
% 0.34/0.51 => ( exuE3e
% 0.34/0.51 => ( setext
% 0.34/0.51 => ( emptyI
% 0.34/0.51 => ( noeltsimpempty
% 0.34/0.51 => ( setbeta
% 0.34/0.51 => ( nonemptyE1
% 0.34/0.51 => ( nonemptyI
% 0.34/0.51 => ( nonemptyI1
% 0.34/0.51 => ( setadjoinIL
% 0.34/0.51 => ( emptyinunitempty
% 0.34/0.51 => ( setadjoinIR
% 0.34/0.51 => ( setadjoinE
% 0.34/0.51 => ( setadjoinOr
% 0.34/0.51 => ( setoftrueEq
% 0.34/0.51 => ( powersetI
% 0.34/0.51 => ( emptyinPowerset
% 0.34/0.51 => ( emptyInPowerset
% 0.34/0.51 => ( powersetE
% 0.34/0.51 => ( setunionI
% 0.34/0.51 => ( setunionE
% 0.34/0.51 => ( subPowSU
% 0.34/0.51 => ( exuE2
% 0.34/0.51 => ( nonemptyImpWitness
% 0.34/0.51 => ( uniqinunit
% 0.34/0.51 => ( notinsingleton
% 0.34/0.51 => ( eqinunit
% 0.34/0.51 => ( singletonsswitch
% 0.34/0.51 => ( upairsetE
% 0.34/0.51 => ( upairsetIL
% 0.34/0.51 => ( upairsetIR
% 0.34/0.51 => ( emptyE1
% 0.34/0.51 => ( vacuousDall
% 0.34/0.51 => ( quantDeMorgan1
% 0.34/0.51 => ( quantDeMorgan2
% 0.34/0.51 => ( quantDeMorgan3
% 0.34/0.51 => ( quantDeMorgan4
% 0.34/0.51 => ( prop2setI
% 0.34/0.51 => ( prop2set2propI
% 0.34/0.51 => ( notdexE
% 0.34/0.51 => ( notdallE
% 0.34/0.51 => ( exuI1
% 0.34/0.51 => ( exuI3
% 0.34/0.51 => ( exuI2
% 0.34/0.51 => ( inCongP
% 0.34/0.51 => ( in__Cong
% 0.34/0.51 => ( exuE3u
% 0.34/0.51 => ( exu__Cong
% 0.34/0.51 => ( emptyset__Cong
% 0.34/0.51 => ( setadjoin__Cong
% 0.34/0.51 => ( powerset__Cong
% 0.34/0.51 => ( setunion__Cong
% 0.34/0.51 => ( omega__Cong
% 0.34/0.51 => ( exuEu
% 0.34/0.51 => ( descr__Cong
% 0.34/0.51 => ( dsetconstr__Cong
% 0.34/0.51 => ( subsetI1
% 0.34/0.51 => ( eqimpsubset2
% 0.34/0.51 => ( eqimpsubset1
% 0.34/0.51 => ( subsetI2
% 0.34/0.51 => ( emptysetsubset
% 0.34/0.51 => ( subsetE
% 0.34/0.51 => ( subsetE2
% 0.34/0.51 => ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.51 ( ( in @ Xx @ A )
% 0.34/0.51 => ( ~ ( in @ Xx @ B )
% 0.34/0.51 => ~ ( subset @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.34/0.51
% 0.34/0.51 %------------------------------------------------------------------------------
% 0.34/0.51 ------------------------
% 2.52/1.63 ---- Embedded in THF ---
% 2.52/1.63 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.52/1.63 %%% Generated on Tue Feb 24 12:26:57 EST 2026
% 2.52/1.63 %%% using '$$dhol' embedding, version 1.3.0.
% 2.52/1.63 %%% Logic specification used:
% 2.52/1.63 %%% thf(spec, logic, $$dhol).
% 2.52/1.63
% 2.52/1.63 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.nkEZQ3bEXD/DTF2DTF30771.p
% See solution above
% 2.52/1.64 ------------------------
% 2.52/1.65 ---- Cleaned THF ---
% 2.52/1.66 thf(in_type,type,
% 2.52/1.66 in: $i > $i > $o ).
% 2.52/1.66
% 2.52/1.66 thf(exu_type,type,
% 2.52/1.66 exu: ( $i > $o ) > $o ).
% 2.52/1.66
% 2.52/1.66 thf(exu,definition,
% 2.52/1.66 ( exu
% 2.52/1.66 = ( ^ [Xphi: $i > $o] :
% 2.52/1.66 ? [Xx: $i] :
% 2.52/1.66 ( ( Xphi @ Xx )
% 2.52/1.66 & ! [Xy: $i] :
% 2.52/1.66 ( ( Xphi @ Xy )
% 2.52/1.66 => ( Xx = Xy ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setextAx_type,type,
% 2.52/1.66 setextAx: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setextAx,definition,
% 2.52/1.66 ( setextAx
% 2.52/1.66 = ( ! [A: $i,B: $i] :
% 2.52/1.66 ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 <=> ( in @ Xx @ B ) )
% 2.52/1.66 => ( A = B ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(emptyset_type,type,
% 2.52/1.66 emptyset: $i ).
% 2.52/1.66
% 2.52/1.66 thf(emptysetAx_type,type,
% 2.52/1.66 emptysetAx: $o ).
% 2.52/1.66
% 2.52/1.66 thf(emptysetAx,definition,
% 2.52/1.66 ( emptysetAx
% 2.52/1.66 = ( ! [Xx: $i] :
% 2.52/1.66 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setadjoin_type,type,
% 2.52/1.66 setadjoin: $i > $i > $i ).
% 2.52/1.66
% 2.52/1.66 thf(setadjoinAx_type,type,
% 2.52/1.66 setadjoinAx: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setadjoinAx,definition,
% 2.52/1.66 ( setadjoinAx
% 2.52/1.66 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.52/1.66 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.52/1.66 <=> ( ( Xy = Xx )
% 2.52/1.66 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(powerset_type,type,
% 2.52/1.66 powerset: $i > $i ).
% 2.52/1.66
% 2.52/1.66 thf(powersetAx_type,type,
% 2.52/1.66 powersetAx: $o ).
% 2.52/1.66
% 2.52/1.66 thf(powersetAx,definition,
% 2.52/1.66 ( powersetAx
% 2.52/1.66 = ( ! [A: $i,B: $i] :
% 2.52/1.66 ( ( in @ B @ ( powerset @ A ) )
% 2.52/1.66 <=> ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ B )
% 2.52/1.66 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setunion_type,type,
% 2.52/1.66 setunion: $i > $i ).
% 2.52/1.66
% 2.52/1.66 thf(setunionAx_type,type,
% 2.52/1.66 setunionAx: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setunionAx,definition,
% 2.52/1.66 ( setunionAx
% 2.52/1.66 = ( ! [A: $i,Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ ( setunion @ A ) )
% 2.52/1.66 <=> ? [B: $i] :
% 2.52/1.66 ( ( in @ Xx @ B )
% 2.52/1.66 & ( in @ B @ A ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(omega_type,type,
% 2.52/1.66 omega: $i ).
% 2.52/1.66
% 2.52/1.66 thf(omega0Ax_type,type,
% 2.52/1.66 omega0Ax: $o ).
% 2.52/1.66
% 2.52/1.66 thf(omega0Ax,definition,
% 2.52/1.66 ( omega0Ax
% 2.52/1.66 = ( in @ emptyset @ omega ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(omegaSAx_type,type,
% 2.52/1.66 omegaSAx: $o ).
% 2.52/1.66
% 2.52/1.66 thf(omegaSAx,definition,
% 2.52/1.66 ( omegaSAx
% 2.52/1.66 = ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ omega )
% 2.52/1.66 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(omegaIndAx_type,type,
% 2.52/1.66 omegaIndAx: $o ).
% 2.52/1.66
% 2.52/1.66 thf(omegaIndAx,definition,
% 2.52/1.66 ( omegaIndAx
% 2.52/1.66 = ( ! [A: $i] :
% 2.52/1.66 ( ( ( in @ emptyset @ A )
% 2.52/1.66 & ! [Xx: $i] :
% 2.52/1.66 ( ( ( in @ Xx @ omega )
% 2.52/1.66 & ( in @ Xx @ A ) )
% 2.52/1.66 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.52/1.66 => ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ omega )
% 2.52/1.66 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(replAx_type,type,
% 2.52/1.66 replAx: $o ).
% 2.52/1.66
% 2.52/1.66 thf(replAx,definition,
% 2.52/1.66 ( replAx
% 2.52/1.66 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.52/1.66 ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ( exu
% 2.52/1.66 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.52/1.66 => ? [B: $i] :
% 2.52/1.66 ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ B )
% 2.52/1.66 <=> ? [Xy: $i] :
% 2.52/1.66 ( ( in @ Xy @ A )
% 2.52/1.66 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(foundationAx_type,type,
% 2.52/1.66 foundationAx: $o ).
% 2.52/1.66
% 2.52/1.66 thf(foundationAx,definition,
% 2.52/1.66 ( foundationAx
% 2.52/1.66 = ( ! [A: $i] :
% 2.52/1.66 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.52/1.66 => ? [B: $i] :
% 2.52/1.66 ( ( in @ B @ A )
% 2.52/1.66 & ~ ? [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ B )
% 2.52/1.66 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(wellorderingAx_type,type,
% 2.52/1.66 wellorderingAx: $o ).
% 2.52/1.66
% 2.52/1.66 thf(wellorderingAx,definition,
% 2.52/1.66 ( wellorderingAx
% 2.52/1.66 = ( ! [A: $i] :
% 2.52/1.66 ? [B: $i] :
% 2.52/1.66 ( ! [C: $i] :
% 2.52/1.66 ( ( in @ C @ B )
% 2.52/1.66 => ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ C )
% 2.52/1.66 => ( in @ Xx @ A ) ) )
% 2.52/1.66 & ! [Xx: $i,Xy: $i] :
% 2.52/1.66 ( ( ( in @ Xx @ A )
% 2.52/1.66 & ( in @ Xy @ A ) )
% 2.52/1.66 => ( ! [C: $i] :
% 2.52/1.66 ( ( in @ C @ B )
% 2.52/1.66 => ( ( in @ Xx @ C )
% 2.52/1.66 <=> ( in @ Xy @ C ) ) )
% 2.52/1.66 => ( Xx = Xy ) ) )
% 2.52/1.66 & ! [C: $i,D: $i] :
% 2.52/1.66 ( ( ( in @ C @ B )
% 2.52/1.66 & ( in @ D @ B ) )
% 2.52/1.66 => ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ C )
% 2.52/1.66 => ( in @ Xx @ D ) )
% 2.52/1.66 | ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ D )
% 2.52/1.66 => ( in @ Xx @ C ) ) ) )
% 2.52/1.66 & ! [C: $i] :
% 2.52/1.66 ( ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ C )
% 2.52/1.66 => ( in @ Xx @ A ) )
% 2.52/1.66 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.52/1.66 => ? [D: $i,Xx: $i] :
% 2.52/1.66 ( ( in @ D @ B )
% 2.52/1.66 & ( in @ Xx @ C )
% 2.52/1.66 & ~ ? [Xy: $i] :
% 2.52/1.66 ( ( in @ Xy @ D )
% 2.52/1.66 & ( in @ Xy @ C ) )
% 2.52/1.66 & ! [E: $i] :
% 2.52/1.66 ( ( in @ E @ B )
% 2.52/1.66 => ( ! [Xy: $i] :
% 2.52/1.66 ( ( in @ Xy @ E )
% 2.52/1.66 => ( in @ Xy @ D ) )
% 2.52/1.66 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(descr_type,type,
% 2.52/1.66 descr: ( $i > $o ) > $i ).
% 2.52/1.66
% 2.52/1.66 thf(descrp_type,type,
% 2.52/1.66 descrp: $o ).
% 2.52/1.66
% 2.52/1.66 thf(descrp,definition,
% 2.52/1.66 ( descrp
% 2.52/1.66 = ( ! [Xphi: $i > $o] :
% 2.52/1.66 ( ( exu
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.66 => ( Xphi
% 2.52/1.66 @ ( descr
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(dsetconstr_type,type,
% 2.52/1.66 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.52/1.66
% 2.52/1.66 thf(dsetconstrI_type,type,
% 2.52/1.66 dsetconstrI: $o ).
% 2.52/1.66
% 2.52/1.66 thf(dsetconstrI,definition,
% 2.52/1.66 ( dsetconstrI
% 2.52/1.66 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ( ( Xphi @ Xx )
% 2.52/1.66 => ( in @ Xx
% 2.52/1.66 @ ( dsetconstr @ A
% 2.52/1.66 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(dsetconstrEL_type,type,
% 2.52/1.66 dsetconstrEL: $o ).
% 2.52/1.66
% 2.52/1.66 thf(dsetconstrEL,definition,
% 2.52/1.66 ( dsetconstrEL
% 2.52/1.66 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.52/1.66 ( ( in @ Xx
% 2.52/1.66 @ ( dsetconstr @ A
% 2.52/1.66 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.52/1.66 => ( in @ Xx @ A ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(dsetconstrER_type,type,
% 2.52/1.66 dsetconstrER: $o ).
% 2.52/1.66
% 2.52/1.66 thf(dsetconstrER,definition,
% 2.52/1.66 ( dsetconstrER
% 2.52/1.66 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.52/1.66 ( ( in @ Xx
% 2.52/1.66 @ ( dsetconstr @ A
% 2.52/1.66 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.52/1.66 => ( Xphi @ Xx ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(exuE1_type,type,
% 2.52/1.66 exuE1: $o ).
% 2.52/1.66
% 2.52/1.66 thf(exuE1,definition,
% 2.52/1.66 ( exuE1
% 2.52/1.66 = ( ! [Xphi: $i > $o] :
% 2.52/1.66 ( ( exu
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.66 => ? [Xx: $i] :
% 2.52/1.66 ( ( Xphi @ Xx )
% 2.52/1.66 & ! [Xy: $i] :
% 2.52/1.66 ( ( Xphi @ Xy )
% 2.52/1.66 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(prop2set_type,type,
% 2.52/1.66 prop2set: $o > $i ).
% 2.52/1.66
% 2.52/1.66 thf(prop2setE_type,type,
% 2.52/1.66 prop2setE: $o ).
% 2.52/1.66
% 2.52/1.66 thf(prop2setE,definition,
% 2.52/1.66 ( prop2setE
% 2.52/1.66 = ( ! [Xphi: $o,Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.52/1.66 => Xphi ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(emptysetE_type,type,
% 2.52/1.66 emptysetE: $o ).
% 2.52/1.66
% 2.52/1.66 thf(emptysetE,definition,
% 2.52/1.66 ( emptysetE
% 2.52/1.66 = ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ emptyset )
% 2.52/1.66 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(emptysetimpfalse_type,type,
% 2.52/1.66 emptysetimpfalse: $o ).
% 2.52/1.66
% 2.52/1.66 thf(emptysetimpfalse,definition,
% 2.52/1.66 ( emptysetimpfalse
% 2.52/1.66 = ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ emptyset )
% 2.52/1.66 => $false ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(notinemptyset_type,type,
% 2.52/1.66 notinemptyset: $o ).
% 2.52/1.66
% 2.52/1.66 thf(notinemptyset,definition,
% 2.52/1.66 ( notinemptyset
% 2.52/1.66 = ( ! [Xx: $i] :
% 2.52/1.66 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(exuE3e_type,type,
% 2.52/1.66 exuE3e: $o ).
% 2.52/1.66
% 2.52/1.66 thf(exuE3e,definition,
% 2.52/1.66 ( exuE3e
% 2.52/1.66 = ( ! [Xphi: $i > $o] :
% 2.52/1.66 ( ( exu
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.66 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setext_type,type,
% 2.52/1.66 setext: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setext,definition,
% 2.52/1.66 ( setext
% 2.52/1.66 = ( ! [A: $i,B: $i] :
% 2.52/1.66 ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ( in @ Xx @ B ) )
% 2.52/1.66 => ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ B )
% 2.52/1.66 => ( in @ Xx @ A ) )
% 2.52/1.66 => ( A = B ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(emptyI_type,type,
% 2.52/1.66 emptyI: $o ).
% 2.52/1.66
% 2.52/1.66 thf(emptyI,definition,
% 2.52/1.66 ( emptyI
% 2.52/1.66 = ( ! [A: $i] :
% 2.52/1.66 ( ! [Xx: $i] :
% 2.52/1.66 ~ ( in @ Xx @ A )
% 2.52/1.66 => ( A = emptyset ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(noeltsimpempty_type,type,
% 2.52/1.66 noeltsimpempty: $o ).
% 2.52/1.66
% 2.52/1.66 thf(noeltsimpempty,definition,
% 2.52/1.66 ( noeltsimpempty
% 2.52/1.66 = ( ! [A: $i] :
% 2.52/1.66 ( ! [Xx: $i] :
% 2.52/1.66 ~ ( in @ Xx @ A )
% 2.52/1.66 => ( A = emptyset ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setbeta_type,type,
% 2.52/1.66 setbeta: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setbeta,definition,
% 2.52/1.66 ( setbeta
% 2.52/1.66 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ( ( in @ Xx
% 2.52/1.66 @ ( dsetconstr @ A
% 2.52/1.66 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.52/1.66 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(nonempty_type,type,
% 2.52/1.66 nonempty: $i > $o ).
% 2.52/1.66
% 2.52/1.66 thf(nonempty,definition,
% 2.52/1.66 ( nonempty
% 2.52/1.66 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(nonemptyE1_type,type,
% 2.52/1.66 nonemptyE1: $o ).
% 2.52/1.66
% 2.52/1.66 thf(nonemptyE1,definition,
% 2.52/1.66 ( nonemptyE1
% 2.52/1.66 = ( ! [A: $i] :
% 2.52/1.66 ( ( nonempty @ A )
% 2.52/1.66 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(nonemptyI_type,type,
% 2.52/1.66 nonemptyI: $o ).
% 2.52/1.66
% 2.52/1.66 thf(nonemptyI,definition,
% 2.52/1.66 ( nonemptyI
% 2.52/1.66 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ( ( Xphi @ Xx )
% 2.52/1.66 => ( nonempty
% 2.52/1.66 @ ( dsetconstr @ A
% 2.52/1.66 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(nonemptyI1_type,type,
% 2.52/1.66 nonemptyI1: $o ).
% 2.52/1.66
% 2.52/1.66 thf(nonemptyI1,definition,
% 2.52/1.66 ( nonemptyI1
% 2.52/1.66 = ( ! [A: $i] :
% 2.52/1.66 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.52/1.66 => ( nonempty @ A ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setadjoinIL_type,type,
% 2.52/1.66 setadjoinIL: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setadjoinIL,definition,
% 2.52/1.66 ( setadjoinIL
% 2.52/1.66 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(emptyinunitempty_type,type,
% 2.52/1.66 emptyinunitempty: $o ).
% 2.52/1.66
% 2.52/1.66 thf(emptyinunitempty,definition,
% 2.52/1.66 ( emptyinunitempty
% 2.52/1.66 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setadjoinIR_type,type,
% 2.52/1.66 setadjoinIR: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setadjoinIR,definition,
% 2.52/1.66 ( setadjoinIR
% 2.52/1.66 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.52/1.66 ( ( in @ Xy @ A )
% 2.52/1.66 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setadjoinE_type,type,
% 2.52/1.66 setadjoinE: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setadjoinE,definition,
% 2.52/1.66 ( setadjoinE
% 2.52/1.66 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.52/1.66 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.52/1.66 => ! [Xphi: $o] :
% 2.52/1.66 ( ( ( Xy = Xx )
% 2.52/1.66 => Xphi )
% 2.52/1.66 => ( ( ( in @ Xy @ A )
% 2.52/1.66 => Xphi )
% 2.52/1.66 => Xphi ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setadjoinOr_type,type,
% 2.52/1.66 setadjoinOr: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setadjoinOr,definition,
% 2.52/1.66 ( setadjoinOr
% 2.52/1.66 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.52/1.66 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.52/1.66 => ( ( Xy = Xx )
% 2.52/1.66 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setoftrueEq_type,type,
% 2.52/1.66 setoftrueEq: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setoftrueEq,definition,
% 2.52/1.66 ( setoftrueEq
% 2.52/1.66 = ( ! [A: $i] :
% 2.52/1.66 ( ( dsetconstr @ A
% 2.52/1.66 @ ^ [Xx: $i] : $true )
% 2.52/1.66 = A ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(powersetI_type,type,
% 2.52/1.66 powersetI: $o ).
% 2.52/1.66
% 2.52/1.66 thf(powersetI,definition,
% 2.52/1.66 ( powersetI
% 2.52/1.66 = ( ! [A: $i,B: $i] :
% 2.52/1.66 ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ B )
% 2.52/1.66 => ( in @ Xx @ A ) )
% 2.52/1.66 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(emptyinPowerset_type,type,
% 2.52/1.66 emptyinPowerset: $o ).
% 2.52/1.66
% 2.52/1.66 thf(emptyinPowerset,definition,
% 2.52/1.66 ( emptyinPowerset
% 2.52/1.66 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(emptyInPowerset_type,type,
% 2.52/1.66 emptyInPowerset: $o ).
% 2.52/1.66
% 2.52/1.66 thf(emptyInPowerset,definition,
% 2.52/1.66 ( emptyInPowerset
% 2.52/1.66 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(powersetE_type,type,
% 2.52/1.66 powersetE: $o ).
% 2.52/1.66
% 2.52/1.66 thf(powersetE,definition,
% 2.52/1.66 ( powersetE
% 2.52/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.66 ( ( in @ B @ ( powerset @ A ) )
% 2.52/1.66 => ( ( in @ Xx @ B )
% 2.52/1.66 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setunionI_type,type,
% 2.52/1.66 setunionI: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setunionI,definition,
% 2.52/1.66 ( setunionI
% 2.52/1.66 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.52/1.66 ( ( in @ Xx @ B )
% 2.52/1.66 => ( ( in @ B @ A )
% 2.52/1.66 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setunionE_type,type,
% 2.52/1.66 setunionE: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setunionE,definition,
% 2.52/1.66 ( setunionE
% 2.52/1.66 = ( ! [A: $i,Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ ( setunion @ A ) )
% 2.52/1.66 => ! [Xphi: $o] :
% 2.52/1.66 ( ! [B: $i] :
% 2.52/1.66 ( ( in @ Xx @ B )
% 2.52/1.66 => ( ( in @ B @ A )
% 2.52/1.66 => Xphi ) )
% 2.52/1.66 => Xphi ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(subPowSU_type,type,
% 2.52/1.66 subPowSU: $o ).
% 2.52/1.66
% 2.52/1.66 thf(subPowSU,definition,
% 2.52/1.66 ( subPowSU
% 2.52/1.66 = ( ! [A: $i,Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(exuE2_type,type,
% 2.52/1.66 exuE2: $o ).
% 2.52/1.66
% 2.52/1.66 thf(exuE2,definition,
% 2.52/1.66 ( exuE2
% 2.52/1.66 = ( ! [Xphi: $i > $o] :
% 2.52/1.66 ( ( exu
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.66 => ? [Xx: $i] :
% 2.52/1.66 ! [Xy: $i] :
% 2.52/1.66 ( ( Xphi @ Xy )
% 2.52/1.66 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(nonemptyImpWitness_type,type,
% 2.52/1.66 nonemptyImpWitness: $o ).
% 2.52/1.66
% 2.52/1.66 thf(nonemptyImpWitness,definition,
% 2.52/1.66 ( nonemptyImpWitness
% 2.52/1.66 = ( ! [A: $i] :
% 2.52/1.66 ( ( nonempty @ A )
% 2.52/1.66 => ? [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 & $true ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(uniqinunit_type,type,
% 2.52/1.66 uniqinunit: $o ).
% 2.52/1.66
% 2.52/1.66 thf(uniqinunit,definition,
% 2.52/1.66 ( uniqinunit
% 2.52/1.66 = ( ! [Xx: $i,Xy: $i] :
% 2.52/1.66 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.52/1.66 => ( Xx = Xy ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(notinsingleton_type,type,
% 2.52/1.66 notinsingleton: $o ).
% 2.52/1.66
% 2.52/1.66 thf(notinsingleton,definition,
% 2.52/1.66 ( notinsingleton
% 2.52/1.66 = ( ! [Xx: $i,Xy: $i] :
% 2.52/1.66 ( ( Xx != Xy )
% 2.52/1.66 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(eqinunit_type,type,
% 2.52/1.66 eqinunit: $o ).
% 2.52/1.66
% 2.52/1.66 thf(eqinunit,definition,
% 2.52/1.66 ( eqinunit
% 2.52/1.66 = ( ! [Xx: $i,Xy: $i] :
% 2.52/1.66 ( ( Xx = Xy )
% 2.52/1.66 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(singletonsswitch_type,type,
% 2.52/1.66 singletonsswitch: $o ).
% 2.52/1.66
% 2.52/1.66 thf(singletonsswitch,definition,
% 2.52/1.66 ( singletonsswitch
% 2.52/1.66 = ( ! [Xx: $i,Xy: $i] :
% 2.52/1.66 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.52/1.66 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(upairsetE_type,type,
% 2.52/1.66 upairsetE: $o ).
% 2.52/1.66
% 2.52/1.66 thf(upairsetE,definition,
% 2.52/1.66 ( upairsetE
% 2.52/1.66 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.52/1.66 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.52/1.66 => ( ( Xz = Xx )
% 2.52/1.66 | ( Xz = Xy ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(upairsetIL_type,type,
% 2.52/1.66 upairsetIL: $o ).
% 2.52/1.66
% 2.52/1.66 thf(upairsetIL,definition,
% 2.52/1.66 ( upairsetIL
% 2.52/1.66 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(upairsetIR_type,type,
% 2.52/1.66 upairsetIR: $o ).
% 2.52/1.66
% 2.52/1.66 thf(upairsetIR,definition,
% 2.52/1.66 ( upairsetIR
% 2.52/1.66 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(emptyE1_type,type,
% 2.52/1.66 emptyE1: $o ).
% 2.52/1.66
% 2.52/1.66 thf(emptyE1,definition,
% 2.52/1.66 ( emptyE1
% 2.52/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.66 ( ? [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 & ( Xphi @ Xx ) )
% 2.52/1.66 => ( ( ( dsetconstr @ A
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.66 = emptyset )
% 2.52/1.66 => $false ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(vacuousDall_type,type,
% 2.52/1.66 vacuousDall: $o ).
% 2.52/1.66
% 2.52/1.66 thf(vacuousDall,definition,
% 2.52/1.66 ( vacuousDall
% 2.52/1.66 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ emptyset )
% 2.52/1.66 => ( Xphi @ Xx ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(quantDeMorgan1_type,type,
% 2.52/1.66 quantDeMorgan1: $o ).
% 2.52/1.66
% 2.52/1.66 thf(quantDeMorgan1,definition,
% 2.52/1.66 ( quantDeMorgan1
% 2.52/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.66 ( ~ ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ( Xphi @ Xx ) )
% 2.52/1.66 => ? [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(quantDeMorgan2_type,type,
% 2.52/1.66 quantDeMorgan2: $o ).
% 2.52/1.66
% 2.52/1.66 thf(quantDeMorgan2,definition,
% 2.52/1.66 ( quantDeMorgan2
% 2.52/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.66 ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ~ ( Xphi @ Xx ) )
% 2.52/1.66 => ~ ? [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(quantDeMorgan3_type,type,
% 2.52/1.66 quantDeMorgan3: $o ).
% 2.52/1.66
% 2.52/1.66 thf(quantDeMorgan3,definition,
% 2.52/1.66 ( quantDeMorgan3
% 2.52/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.66 ( ~ ? [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 & ( Xphi @ Xx ) )
% 2.52/1.66 => ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(quantDeMorgan4_type,type,
% 2.52/1.66 quantDeMorgan4: $o ).
% 2.52/1.66
% 2.52/1.66 thf(quantDeMorgan4,definition,
% 2.52/1.66 ( quantDeMorgan4
% 2.52/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.66 ( ? [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 & ~ ( Xphi @ Xx ) )
% 2.52/1.66 => ~ ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(prop2setI_type,type,
% 2.52/1.66 prop2setI: $o ).
% 2.52/1.66
% 2.52/1.66 thf(prop2setI,definition,
% 2.52/1.66 ( prop2setI
% 2.52/1.66 = ( ! [Xphi: $o] :
% 2.52/1.66 ( Xphi
% 2.52/1.66 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(set2prop_type,type,
% 2.52/1.66 set2prop: $i > $o ).
% 2.52/1.66
% 2.52/1.66 thf(prop2set2propI_type,type,
% 2.52/1.66 prop2set2propI: $o ).
% 2.52/1.66
% 2.52/1.66 thf(prop2set2propI,definition,
% 2.52/1.66 ( prop2set2propI
% 2.52/1.66 = ( ! [Xphi: $o] :
% 2.52/1.66 ( Xphi
% 2.52/1.66 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(notdexE_type,type,
% 2.52/1.66 notdexE: $o ).
% 2.52/1.66
% 2.52/1.66 thf(notdexE,definition,
% 2.52/1.66 ( notdexE
% 2.52/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.66 ( ~ ? [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 & ( Xphi @ Xx ) )
% 2.52/1.66 => ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(notdallE_type,type,
% 2.52/1.66 notdallE: $o ).
% 2.52/1.66
% 2.52/1.66 thf(notdallE,definition,
% 2.52/1.66 ( notdallE
% 2.52/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.66 ( ~ ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ( Xphi @ Xx ) )
% 2.52/1.66 => ? [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(exuI1_type,type,
% 2.52/1.66 exuI1: $o ).
% 2.52/1.66
% 2.52/1.66 thf(exuI1,definition,
% 2.52/1.66 ( exuI1
% 2.52/1.66 = ( ! [Xphi: $i > $o] :
% 2.52/1.66 ( ? [Xx: $i] :
% 2.52/1.66 ( ( Xphi @ Xx )
% 2.52/1.66 & ! [Xy: $i] :
% 2.52/1.66 ( ( Xphi @ Xy )
% 2.52/1.66 => ( Xx = Xy ) ) )
% 2.52/1.66 => ( exu
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(exuI3_type,type,
% 2.52/1.66 exuI3: $o ).
% 2.52/1.66
% 2.52/1.66 thf(exuI3,definition,
% 2.52/1.66 ( exuI3
% 2.52/1.66 = ( ! [Xphi: $i > $o] :
% 2.52/1.66 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.52/1.66 => ( ! [Xx: $i,Xy: $i] :
% 2.52/1.66 ( ( Xphi @ Xx )
% 2.52/1.66 => ( ( Xphi @ Xy )
% 2.52/1.66 => ( Xx = Xy ) ) )
% 2.52/1.66 => ( exu
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(exuI2_type,type,
% 2.52/1.66 exuI2: $o ).
% 2.52/1.66
% 2.52/1.66 thf(exuI2,definition,
% 2.52/1.66 ( exuI2
% 2.52/1.66 = ( ! [Xphi: $i > $o] :
% 2.52/1.66 ( ? [Xx: $i] :
% 2.52/1.66 ! [Xy: $i] :
% 2.52/1.66 ( ( Xphi @ Xy )
% 2.52/1.66 <=> ( Xy = Xx ) )
% 2.52/1.66 => ( exu
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(inCongP_type,type,
% 2.52/1.66 inCongP: $o ).
% 2.52/1.66
% 2.52/1.66 thf(inCongP,definition,
% 2.52/1.66 ( inCongP
% 2.52/1.66 = ( ! [A: $i,B: $i] :
% 2.52/1.66 ( ( A = B )
% 2.52/1.66 => ! [Xx: $i,Xy: $i] :
% 2.52/1.66 ( ( Xx = Xy )
% 2.52/1.66 => ( ( in @ Xx @ A )
% 2.52/1.66 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(in__Cong_type,type,
% 2.52/1.66 in__Cong: $o ).
% 2.52/1.66
% 2.52/1.66 thf(in__Cong,definition,
% 2.52/1.66 ( in__Cong
% 2.52/1.66 = ( ! [A: $i,B: $i] :
% 2.52/1.66 ( ( A = B )
% 2.52/1.66 => ! [Xx: $i,Xy: $i] :
% 2.52/1.66 ( ( Xx = Xy )
% 2.52/1.66 => ( ( in @ Xx @ A )
% 2.52/1.66 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(exuE3u_type,type,
% 2.52/1.66 exuE3u: $o ).
% 2.52/1.66
% 2.52/1.66 thf(exuE3u,definition,
% 2.52/1.66 ( exuE3u
% 2.52/1.66 = ( ! [Xphi: $i > $o] :
% 2.52/1.66 ( ( exu
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.66 => ! [Xx: $i,Xy: $i] :
% 2.52/1.66 ( ( Xphi @ Xx )
% 2.52/1.66 => ( ( Xphi @ Xy )
% 2.52/1.66 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(exu__Cong_type,type,
% 2.52/1.66 exu__Cong: $o ).
% 2.52/1.66
% 2.52/1.66 thf(exu__Cong,definition,
% 2.52/1.66 ( exu__Cong
% 2.52/1.66 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.52/1.66 ( ! [Xx: $i,Xy: $i] :
% 2.52/1.66 ( ( Xx = Xy )
% 2.52/1.66 => ( ( Xphi @ Xx )
% 2.52/1.66 <=> ( Xpsi @ Xy ) ) )
% 2.52/1.66 => ( ( exu
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.66 <=> ( exu
% 2.52/1.66 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(emptyset__Cong_type,type,
% 2.52/1.66 emptyset__Cong: $o ).
% 2.52/1.66
% 2.52/1.66 thf(emptyset__Cong,definition,
% 2.52/1.66 ( emptyset__Cong
% 2.52/1.66 = ( emptyset = emptyset ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setadjoin__Cong_type,type,
% 2.52/1.66 setadjoin__Cong: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setadjoin__Cong,definition,
% 2.52/1.66 ( setadjoin__Cong
% 2.52/1.66 = ( ! [Xx: $i,Xy: $i] :
% 2.52/1.66 ( ( Xx = Xy )
% 2.52/1.66 => ! [Xz: $i,Xu: $i] :
% 2.52/1.66 ( ( Xz = Xu )
% 2.52/1.66 => ( ( setadjoin @ Xx @ Xz )
% 2.52/1.66 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(powerset__Cong_type,type,
% 2.52/1.66 powerset__Cong: $o ).
% 2.52/1.66
% 2.52/1.66 thf(powerset__Cong,definition,
% 2.52/1.66 ( powerset__Cong
% 2.52/1.66 = ( ! [A: $i,B: $i] :
% 2.52/1.66 ( ( A = B )
% 2.52/1.66 => ( ( powerset @ A )
% 2.52/1.66 = ( powerset @ B ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(setunion__Cong_type,type,
% 2.52/1.66 setunion__Cong: $o ).
% 2.52/1.66
% 2.52/1.66 thf(setunion__Cong,definition,
% 2.52/1.66 ( setunion__Cong
% 2.52/1.66 = ( ! [A: $i,B: $i] :
% 2.52/1.66 ( ( A = B )
% 2.52/1.66 => ( ( setunion @ A )
% 2.52/1.66 = ( setunion @ B ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(omega__Cong_type,type,
% 2.52/1.66 omega__Cong: $o ).
% 2.52/1.66
% 2.52/1.66 thf(omega__Cong,definition,
% 2.52/1.66 ( omega__Cong
% 2.52/1.66 = ( omega = omega ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(exuEu_type,type,
% 2.52/1.66 exuEu: $o ).
% 2.52/1.66
% 2.52/1.66 thf(exuEu,definition,
% 2.52/1.66 ( exuEu
% 2.52/1.66 = ( ! [Xphi: $i > $o] :
% 2.52/1.66 ( ( exu
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.66 => ! [Xx: $i,Xy: $i] :
% 2.52/1.66 ( ( Xphi @ Xx )
% 2.52/1.66 => ( ( Xphi @ Xy )
% 2.52/1.66 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(descr__Cong_type,type,
% 2.52/1.66 descr__Cong: $o ).
% 2.52/1.66
% 2.52/1.66 thf(descr__Cong,definition,
% 2.52/1.66 ( descr__Cong
% 2.52/1.66 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.52/1.66 ( ! [Xx: $i,Xy: $i] :
% 2.52/1.66 ( ( Xx = Xy )
% 2.52/1.66 => ( ( Xphi @ Xx )
% 2.52/1.66 <=> ( Xpsi @ Xy ) ) )
% 2.52/1.66 => ( ( exu
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.66 => ( ( exu
% 2.52/1.66 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.52/1.66 => ( ( descr
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.66 = ( descr
% 2.52/1.66 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(dsetconstr__Cong_type,type,
% 2.52/1.66 dsetconstr__Cong: $o ).
% 2.52/1.66
% 2.52/1.66 thf(dsetconstr__Cong,definition,
% 2.52/1.66 ( dsetconstr__Cong
% 2.52/1.66 = ( ! [A: $i,B: $i] :
% 2.52/1.66 ( ( A = B )
% 2.52/1.66 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.52/1.66 ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ! [Xy: $i] :
% 2.52/1.66 ( ( in @ Xy @ B )
% 2.52/1.66 => ( ( Xx = Xy )
% 2.52/1.66 => ( ( Xphi @ Xx )
% 2.52/1.66 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.52/1.66 => ( ( dsetconstr @ A
% 2.52/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.66 = ( dsetconstr @ B
% 2.52/1.66 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(subset_type,type,
% 2.52/1.66 subset: $i > $i > $o ).
% 2.52/1.66
% 2.52/1.66 thf(disjoint_type,type,
% 2.52/1.66 disjoint: $i > $i > $o ).
% 2.52/1.66
% 2.52/1.66 thf(setsmeet_type,type,
% 2.52/1.66 setsmeet: $i > $i > $o ).
% 2.52/1.66
% 2.52/1.66 thf(subsetI1_type,type,
% 2.52/1.66 subsetI1: $o ).
% 2.52/1.66
% 2.52/1.66 thf(subsetI1,definition,
% 2.52/1.66 ( subsetI1
% 2.52/1.66 = ( ! [A: $i,B: $i] :
% 2.52/1.66 ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ( in @ Xx @ B ) )
% 2.52/1.66 => ( subset @ A @ B ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(eqimpsubset2_type,type,
% 2.52/1.66 eqimpsubset2: $o ).
% 2.52/1.66
% 2.52/1.66 thf(eqimpsubset2,definition,
% 2.52/1.66 ( eqimpsubset2
% 2.52/1.66 = ( ! [A: $i,B: $i] :
% 2.52/1.66 ( ( A = B )
% 2.52/1.66 => ( subset @ B @ A ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(eqimpsubset1_type,type,
% 2.52/1.66 eqimpsubset1: $o ).
% 2.52/1.66
% 2.52/1.66 thf(eqimpsubset1,definition,
% 2.52/1.66 ( eqimpsubset1
% 2.52/1.66 = ( ! [A: $i,B: $i] :
% 2.52/1.66 ( ( A = B )
% 2.52/1.66 => ( subset @ A @ B ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(subsetI2_type,type,
% 2.52/1.66 subsetI2: $o ).
% 2.52/1.66
% 2.52/1.66 thf(subsetI2,definition,
% 2.52/1.66 ( subsetI2
% 2.52/1.66 = ( ! [A: $i,B: $i] :
% 2.52/1.66 ( ! [Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ( in @ Xx @ B ) )
% 2.52/1.66 => ( subset @ A @ B ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(emptysetsubset_type,type,
% 2.52/1.66 emptysetsubset: $o ).
% 2.52/1.66
% 2.52/1.66 thf(emptysetsubset,definition,
% 2.52/1.66 ( emptysetsubset
% 2.52/1.66 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(subsetE_type,type,
% 2.52/1.66 subsetE: $o ).
% 2.52/1.66
% 2.52/1.66 thf(subsetE,definition,
% 2.52/1.66 ( subsetE
% 2.52/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.66 ( ( subset @ A @ B )
% 2.52/1.66 => ( ( in @ Xx @ A )
% 2.52/1.66 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(subsetE2_type,type,
% 2.52/1.66 subsetE2: $o ).
% 2.52/1.66
% 2.52/1.66 thf(subsetE2,definition,
% 2.52/1.66 ( subsetE2
% 2.52/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.66 ( ( subset @ A @ B )
% 2.52/1.66 => ( ~ ( in @ Xx @ B )
% 2.52/1.66 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.52/1.66
% 2.52/1.66 thf(notsubsetI,conjecture,
% 2.52/1.66 ( setextAx
% 2.52/1.66 => ( emptysetAx
% 2.52/1.66 => ( setadjoinAx
% 2.52/1.66 => ( powersetAx
% 2.52/1.66 => ( setunionAx
% 2.52/1.66 => ( omega0Ax
% 2.52/1.66 => ( omegaSAx
% 2.52/1.66 => ( omegaIndAx
% 2.52/1.66 => ( replAx
% 2.52/1.66 => ( foundationAx
% 2.52/1.66 => ( wellorderingAx
% 2.52/1.66 => ( descrp
% 2.52/1.66 => ( dsetconstrI
% 2.52/1.66 => ( dsetconstrEL
% 2.52/1.66 => ( dsetconstrER
% 2.52/1.66 => ( exuE1
% 2.52/1.66 => ( prop2setE
% 2.52/1.66 => ( emptysetE
% 2.52/1.66 => ( emptysetimpfalse
% 2.52/1.66 => ( notinemptyset
% 2.52/1.66 => ( exuE3e
% 2.52/1.66 => ( setext
% 2.52/1.66 => ( emptyI
% 2.52/1.66 => ( noeltsimpempty
% 2.52/1.66 => ( setbeta
% 2.52/1.66 => ( nonemptyE1
% 2.52/1.66 => ( nonemptyI
% 2.52/1.66 => ( nonemptyI1
% 2.52/1.66 => ( setadjoinIL
% 2.52/1.66 => ( emptyinunitempty
% 2.52/1.66 => ( setadjoinIR
% 2.52/1.66 => ( setadjoinE
% 2.52/1.66 => ( setadjoinOr
% 2.52/1.66 => ( setoftrueEq
% 2.52/1.66 => ( powersetI
% 2.52/1.66 => ( emptyinPowerset
% 2.52/1.66 => ( emptyInPowerset
% 2.52/1.66 => ( powersetE
% 2.52/1.66 => ( setunionI
% 2.52/1.66 => ( setunionE
% 2.52/1.66 => ( subPowSU
% 2.52/1.66 => ( exuE2
% 2.52/1.66 => ( nonemptyImpWitness
% 2.52/1.66 => ( uniqinunit
% 2.52/1.66 => ( notinsingleton
% 2.52/1.66 => ( eqinunit
% 2.52/1.66 => ( singletonsswitch
% 2.52/1.66 => ( upairsetE
% 2.52/1.66 => ( upairsetIL
% 2.52/1.66 => ( upairsetIR
% 2.52/1.66 => ( emptyE1
% 2.52/1.66 => ( vacuousDall
% 2.52/1.66 => ( quantDeMorgan1
% 2.52/1.66 => ( quantDeMorgan2
% 2.52/1.66 => ( quantDeMorgan3
% 2.52/1.66 => ( quantDeMorgan4
% 2.52/1.66 => ( prop2setI
% 2.52/1.66 => ( prop2set2propI
% 2.52/1.66 => ( notdexE
% 2.52/1.66 => ( notdallE
% 2.52/1.66 => ( exuI1
% 2.52/1.66 => ( exuI3
% 2.52/1.66 => ( exuI2
% 2.52/1.66 => ( inCongP
% 2.52/1.66 => ( in__Cong
% 2.52/1.66 => ( exuE3u
% 2.52/1.66 => ( exu__Cong
% 2.52/1.66 => ( emptyset__Cong
% 2.52/1.66 => ( setadjoin__Cong
% 2.52/1.66 => ( powerset__Cong
% 2.52/1.66 => ( setunion__Cong
% 2.52/1.66 => ( omega__Cong
% 2.52/1.66 => ( exuEu
% 2.52/1.66 => ( descr__Cong
% 2.52/1.66 => ( dsetconstr__Cong
% 2.52/1.66 => ( subsetI1
% 2.52/1.66 => ( eqimpsubset2
% 2.52/1.66 => ( eqimpsubset1
% 2.52/1.66 => ( subsetI2
% 2.52/1.66 => ( emptysetsubset
% 2.52/1.66 => ( subsetE
% 2.52/1.66 => ( subsetE2
% 2.52/1.66 => ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.66 ( ( in @ Xx @ A )
% 2.52/1.66 => ( ~ ( in @ Xx @ B )
% 2.52/1.66 => ~ ( subset @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.52/1.66 ------------------------
% 2.52/1.68 % (30880)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/27Mi)
% 2.52/1.68 % (30878)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/183Mi)
% 2.52/1.68 % (30879)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/4Mi)
% 2.52/1.68 % (30881)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/2Mi)
% 2.52/1.68 % (30882)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/2Mi)
% 2.52/1.68 % (30883)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/275Mi)
% 2.52/1.68 % (30884)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/18Mi)
% 2.52/1.68 % (30881)Instruction limit reached!
% 2.52/1.68 % (30881)------------------------------
% 2.52/1.68 % (30881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.68 % (30881)Termination reason: Unknown
% 2.52/1.68 % (30882)Instruction limit reached!
% 2.52/1.68 % (30882)------------------------------
% 2.52/1.68 % (30882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.68 % (30881)Termination phase: shuffling
% 2.52/1.68
% 2.52/1.68 % (30881)Memory used [KB]: 1151
% 2.52/1.68 % (30881)Time elapsed: 0.003 s
% 2.52/1.68 % (30881)Instructions burned: 3 (million)
% 2.52/1.68 % (30881)------------------------------
% 2.52/1.68 % (30881)------------------------------
% 2.52/1.68 % (30882)Termination reason: Unknown
% 2.52/1.68 % (30882)Termination phase: shuffling
% 2.52/1.68
% 2.52/1.68 % (30882)Memory used [KB]: 1151
% 2.52/1.68 % (30882)Time elapsed: 0.003 s
% 2.52/1.68 % (30882)Instructions burned: 3 (million)
% 2.52/1.68 % (30882)------------------------------
% 2.52/1.68 % (30882)------------------------------
% 2.52/1.68 % (30879)Instruction limit reached!
% 2.52/1.68 % (30879)------------------------------
% 2.52/1.68 % (30879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.68 % (30879)Termination reason: Unknown
% 2.52/1.68 % (30879)Termination phase: shuffling
% 2.52/1.68
% 2.52/1.68 % (30879)Memory used [KB]: 1151
% 2.52/1.68 % (30879)Time elapsed: 0.004 s
% 2.52/1.68 % (30879)Instructions burned: 5 (million)
% 2.52/1.68 % (30879)------------------------------
% 2.52/1.68 % (30879)------------------------------
% 2.52/1.69 % (30884)Instruction limit reached!
% 2.52/1.69 % (30884)------------------------------
% 2.52/1.69 % (30884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.69 % (30884)Termination reason: Unknown
% 2.52/1.69 % (30884)Termination phase: Preprocessing 3
% 2.52/1.69
% 2.52/1.69 % (30884)Memory used [KB]: 1663
% 2.52/1.69 % (30884)Time elapsed: 0.011 s
% 2.52/1.69 % (30884)Instructions burned: 19 (million)
% 2.52/1.69 % (30884)------------------------------
% 2.52/1.69 % (30884)------------------------------
% 2.52/1.69 % (30880)Instruction limit reached!
% 2.52/1.69 % (30880)------------------------------
% 2.52/1.69 % (30880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.69 % (30880)Termination reason: Unknown
% 2.52/1.69 % (30880)Termination phase: Property scanning
% 2.52/1.69
% 2.52/1.69 % (30880)Memory used [KB]: 1407
% 2.52/1.69 % (30880)Time elapsed: 0.014 s
% 2.52/1.69 % (30880)Instructions burned: 27 (million)
% 2.52/1.69 % (30880)------------------------------
% 2.52/1.69 % (30880)------------------------------
% 2.62/1.70 % (30885)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/3Mi)
% 2.62/1.70 % (30886)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/37Mi)
% 2.62/1.70 % (30887)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/15Mi)
% 2.62/1.70 % (30885)Instruction limit reached!
% 2.62/1.70 % (30885)------------------------------
% 2.62/1.70 % (30885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.70 % (30885)Termination reason: Unknown
% 2.62/1.70 % (30885)Termination phase: shuffling
% 2.62/1.70
% 2.62/1.70 % (30885)Memory used [KB]: 1151
% 2.62/1.70 % (30885)Time elapsed: 0.003 s
% 2.62/1.70 % (30885)Instructions burned: 3 (million)
% 2.62/1.70 % (30885)------------------------------
% 2.62/1.70 % (30885)------------------------------
% 2.62/1.71 % (30887)Instruction limit reached!
% 2.62/1.71 % (30887)------------------------------
% 2.62/1.71 % (30887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.71 % (30887)Termination reason: Unknown
% 2.62/1.71 % (30887)Termination phase: Preprocessing 3
% 2.62/1.71
% 2.62/1.71 % (30887)Memory used [KB]: 1535
% 2.62/1.71 % (30887)Time elapsed: 0.009 s
% 2.62/1.71 % (30887)Instructions burned: 16 (million)
% 2.62/1.71 % (30887)------------------------------
% 2.62/1.71 % (30887)------------------------------
% 2.62/1.71 % (30888)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/3Mi)
% 2.62/1.71 % (30888)Instruction limit reached!
% 2.62/1.71 % (30888)------------------------------
% 2.62/1.71 % (30888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.71 % (30888)Termination reason: Unknown
% 2.62/1.71 % (30888)Termination phase: shuffling
% 2.62/1.71
% 2.62/1.71 % (30888)Memory used [KB]: 1151
% 2.62/1.71 % (30888)Time elapsed: 0.003 s
% 2.62/1.71 % (30888)Instructions burned: 3 (million)
% 2.62/1.71 % (30888)------------------------------
% 2.62/1.71 % (30888)------------------------------
% 2.62/1.71 % (30889)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/1041Mi)
% 2.62/1.71 % (30886)Instruction limit reached!
% 2.62/1.71 % (30886)------------------------------
% 2.62/1.71 % (30886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.71 % (30886)Termination reason: Unknown
% 2.62/1.71 % (30886)Termination phase: Property scanning
% 2.62/1.71
% 2.62/1.71 % (30886)Memory used [KB]: 1407
% 2.62/1.71 % (30886)Time elapsed: 0.018 s
% 2.62/1.71 % (30886)Instructions burned: 39 (million)
% 2.62/1.71 % (30886)------------------------------
% 2.62/1.71 % (30886)------------------------------
% 2.62/1.72 % (30890)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/7Mi)
% 2.62/1.72 % (30890)Instruction limit reached!
% 2.62/1.72 % (30890)------------------------------
% 2.62/1.72 % (30890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.72 % (30890)Termination reason: Unknown
% 2.62/1.72 % (30890)Termination phase: shuffling
% 2.62/1.72
% 2.62/1.72 % (30890)Memory used [KB]: 1279
% 2.62/1.72 % (30890)Time elapsed: 0.005 s
% 2.62/1.72 % (30890)Instructions burned: 8 (million)
% 2.62/1.72 % (30890)------------------------------
% 2.62/1.72 % (30890)------------------------------
% 2.62/1.72 % (30891)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/16Mi)
% 2.62/1.72 % (30892)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/3Mi)
% 2.62/1.72 % (30892)Instruction limit reached!
% 2.62/1.72 % (30892)------------------------------
% 2.62/1.72 % (30892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.72 % (30892)Termination reason: Unknown
% 2.62/1.72 % (30892)Termination phase: shuffling
% 2.62/1.72
% 2.62/1.72 % (30892)Memory used [KB]: 1151
% 2.62/1.72 % (30892)Time elapsed: 0.003 s
% 2.62/1.72 % (30892)Instructions burned: 4 (million)
% 2.62/1.73 % (30892)------------------------------
% 2.62/1.73 % (30892)------------------------------
% 2.62/1.73 % (30891)Instruction limit reached!
% 2.62/1.73 % (30891)------------------------------
% 2.62/1.73 % (30891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.73 % (30891)Termination reason: Unknown
% 2.62/1.73 % (30891)Termination phase: Property scanning
% 2.62/1.73
% 2.62/1.73 % (30891)Memory used [KB]: 1407
% 2.62/1.73 % (30891)Time elapsed: 0.009 s
% 2.62/1.73 % (30891)Instructions burned: 17 (million)
% 2.62/1.73 % (30891)------------------------------
% 2.62/1.73 % (30891)------------------------------
% 2.62/1.73 % (30893)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/3Mi)
% 2.62/1.73 % (30893)Instruction limit reached!
% 2.62/1.73 % (30893)------------------------------
% 2.62/1.73 % (30893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.73 % (30893)Termination reason: Unknown
% 2.62/1.73 % (30893)Termination phase: shuffling
% 2.62/1.73
% 2.62/1.73 % (30893)Memory used [KB]: 1151
% 2.62/1.73 % (30893)Time elapsed: 0.003 s
% 2.62/1.73 % (30893)Instructions burned: 3 (million)
% 2.62/1.73 % (30893)------------------------------
% 2.62/1.73 % (30893)------------------------------
% 2.62/1.74 % (30894)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/7Mi)
% 2.62/1.74 % (30894)Instruction limit reached!
% 2.62/1.74 % (30894)------------------------------
% 2.62/1.74 % (30894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.74 % (30894)Termination reason: Unknown
% 2.62/1.74 % (30894)Termination phase: shuffling
% 2.62/1.74
% 2.62/1.74 % (30894)Memory used [KB]: 1279
% 2.62/1.74 % (30894)Time elapsed: 0.005 s
% 2.62/1.74 % (30894)Instructions burned: 7 (million)
% 2.62/1.74 % (30894)------------------------------
% 2.62/1.74 % (30894)------------------------------
% 2.62/1.74 % (30895)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/3Mi)
% 2.62/1.74 % (30895)Instruction limit reached!
% 2.62/1.74 % (30895)------------------------------
% 2.62/1.74 % (30895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.74 % (30895)Termination reason: Unknown
% 2.62/1.74 % (30895)Termination phase: shuffling
% 2.62/1.74
% 2.62/1.74 % (30895)Memory used [KB]: 1151
% 2.62/1.74 % (30895)Time elapsed: 0.003 s
% 2.62/1.74 % (30895)Instructions burned: 3 (million)
% 2.62/1.74 % (30895)------------------------------
% 2.62/1.74 % (30895)------------------------------
% 2.62/1.75 % (30896)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/4Mi)
% 2.62/1.75 % (30896)Instruction limit reached!
% 2.62/1.75 % (30896)------------------------------
% 2.62/1.75 % (30896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.75 % (30896)Termination reason: Unknown
% 2.62/1.75 % (30896)Termination phase: shuffling
% 2.62/1.75
% 2.62/1.75 % (30896)Memory used [KB]: 1151
% 2.62/1.75 % (30896)Time elapsed: 0.003 s
% 2.62/1.75 % (30896)Instructions burned: 4 (million)
% 2.62/1.75 % (30896)------------------------------
% 2.62/1.75 % (30896)------------------------------
% 2.62/1.75 % (30897)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/18Mi)
% 2.62/1.75 % (30898)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/710Mi)
% 2.62/1.76 % (30897)Instruction limit reached!
% 2.62/1.76 % (30897)------------------------------
% 2.62/1.76 % (30897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.76 % (30897)Termination reason: Unknown
% 2.62/1.76 % (30897)Termination phase: Property scanning
% 2.62/1.76
% 2.62/1.76 % (30897)Memory used [KB]: 1407
% 2.62/1.76 % (30897)Time elapsed: 0.010 s
% 2.62/1.76 % (30897)Instructions burned: 19 (million)
% 2.62/1.76 % (30897)------------------------------
% 2.62/1.76 % (30897)------------------------------
% 2.62/1.76 % (30899)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/6Mi)
% 2.62/1.76 % (30899)Instruction limit reached!
% 2.62/1.76 % (30899)------------------------------
% 2.62/1.76 % (30899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.76 % (30899)Termination reason: Unknown
% 2.62/1.76 % (30899)Termination phase: shuffling
% 2.62/1.76
% 2.62/1.76 % (30899)Memory used [KB]: 1279
% 2.62/1.76 % (30899)Time elapsed: 0.005 s
% 2.62/1.76 % (30899)Instructions burned: 8 (million)
% 2.62/1.76 % (30899)------------------------------
% 2.62/1.76 % (30899)------------------------------
% 2.62/1.76 % (30900)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/902Mi)
% 2.62/1.77 % (30878)Instruction limit reached!
% 2.62/1.77 % (30878)------------------------------
% 2.62/1.77 % (30878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.77 % (30878)Termination reason: Unknown
% 2.62/1.77 % (30878)Termination phase: Saturation
% 2.62/1.77
% 2.62/1.77 % (30878)Memory used [KB]: 6780
% 2.62/1.77 % (30878)Time elapsed: 0.089 s
% 2.62/1.77 % (30878)Instructions burned: 184 (million)
% 2.62/1.77 % (30878)------------------------------
% 2.62/1.77 % (30878)------------------------------
% 2.62/1.77 % (30901)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/21Mi)
% 2.62/1.78 % (30902)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/5Mi)
% 2.62/1.78 % (30902)Instruction limit reached!
% 2.62/1.78 % (30902)------------------------------
% 2.62/1.78 % (30902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.78 % (30902)Termination reason: Unknown
% 2.62/1.78 % (30902)Termination phase: shuffling
% 2.62/1.78
% 2.62/1.78 % (30902)Memory used [KB]: 1151
% 2.62/1.78 % (30902)Time elapsed: 0.004 s
% 2.62/1.78 % (30902)Instructions burned: 6 (million)
% 2.62/1.78 % (30902)------------------------------
% 2.62/1.78 % (30902)------------------------------
% 2.62/1.78 % (30901)Instruction limit reached!
% 2.62/1.78 % (30901)------------------------------
% 2.62/1.78 % (30901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.78 % (30901)Termination reason: Unknown
% 2.62/1.78 % (30901)Termination phase: SInE selection
% 2.62/1.78
% 2.62/1.78 % (30901)Memory used [KB]: 1407
% 2.62/1.78 % (30901)Time elapsed: 0.011 s
% 2.62/1.78 % (30901)Instructions burned: 21 (million)
% 2.62/1.78 % (30901)------------------------------
% 2.62/1.78 % (30901)------------------------------
% 2.62/1.78 % (30903)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_30771 for (2999ds/6Mi)
% 2.62/1.79 % (30903)Instruction limit reached!
% 2.62/1.79 % (30903)------------------------------
% 2.62/1.79 % (30903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.79 % (30903)Termination reason: Unknown
% 2.62/1.79 % (30903)Termination phase: shuffling
% 2.62/1.79
% 2.62/1.79 % (30903)Memory used [KB]: 1279
% 2.62/1.79 % (30903)Time elapsed: 0.005 s
% 2.62/1.79 % (30903)Instructions burned: 8 (million)
% 2.62/1.79 % (30903)------------------------------
% 2.62/1.79 % (30903)------------------------------
% 2.62/1.80 % (30904)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_30771 for (2998ds/377Mi)
% 2.62/1.80 % (30905)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_30771 for (2998ds/779Mi)
% 2.62/1.80 % (30906)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_30771 for (2998ds/19Mi)
% 2.62/1.81 % (30906)Instruction limit reached!
% 2.62/1.81 % (30906)------------------------------
% 2.62/1.81 % (30906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.81 % (30906)Termination reason: Unknown
% 2.62/1.81 % (30906)Termination phase: Property scanning
% 2.62/1.81
% 2.62/1.81 % (30906)Memory used [KB]: 1407
% 2.62/1.81 % (30906)Time elapsed: 0.010 s
% 2.62/1.81 % (30906)Instructions burned: 19 (million)
% 2.62/1.81 % (30906)------------------------------
% 2.62/1.81 % (30906)------------------------------
% 2.62/1.82 % (30883)Instruction limit reached!
% 2.62/1.82 % (30883)------------------------------
% 2.62/1.82 % (30883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.82 % (30883)Termination reason: Unknown
% 2.62/1.82 % (30883)Termination phase: Saturation
% 2.62/1.82
% 2.62/1.82 % (30883)Memory used [KB]: 7419
% 2.62/1.82 % (30883)Time elapsed: 0.138 s
% 2.62/1.82 % (30883)Instructions burned: 275 (million)
% 2.62/1.82 % (30883)------------------------------
% 2.62/1.82 % (30883)------------------------------
% 2.62/1.83 % (30907)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_30771 for (2998ds/879Mi)
% 2.62/1.83 % (30908)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_30771 for (2998ds/17Mi)
% 2.62/1.84 % (30908)Instruction limit reached!
% 2.62/1.84 % (30908)------------------------------
% 2.62/1.84 % (30908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.84 % (30908)Termination reason: Unknown
% 2.62/1.84 % (30908)Termination phase: Property scanning
% 2.62/1.84
% 2.62/1.84 % (30908)Memory used [KB]: 1407
% 2.62/1.84 % (30908)Time elapsed: 0.010 s
% 2.62/1.84 % (30908)Instructions burned: 19 (million)
% 2.62/1.84 % (30908)------------------------------
% 2.62/1.84 % (30908)------------------------------
% 2.62/1.84 % (30900)First to succeed.
% 2.62/1.85 % (30900)Refutation found. Thanks to Tanya!
% 2.62/1.85 % SZS status Theorem for DTF2THF_30771
% 2.62/1.85 % SZS output start Proof for DTF2THF_30771
% 2.62/1.85 thf(func_def_0, type, in: $i > $i > $o).
% 2.62/1.85 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.62/1.85 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.62/1.85 thf(func_def_8, type, powerset: $i > $i).
% 2.62/1.85 thf(func_def_10, type, setunion: $i > $i).
% 2.62/1.85 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.62/1.85 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.62/1.85 thf(func_def_26, type, prop2set: $o > $i).
% 2.62/1.85 thf(func_def_36, type, nonempty: $i > $o).
% 2.62/1.85 thf(func_def_69, type, set2prop: $i > $o).
% 2.62/1.85 thf(func_def_88, type, subset: $i > $i > $o).
% 2.62/1.85 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.62/1.85 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.62/1.85 thf(func_def_111, type, sP1: $i > $i > $o).
% 2.62/1.85 thf(func_def_112, type, sP2: $i > $o).
% 2.62/1.85 thf(func_def_113, type, sP3: $i > $i > $o).
% 2.62/1.85 thf(func_def_114, type, sP4: $i > $i > $o).
% 2.62/1.85 thf(func_def_116, type, sK6: $i > $o).
% 2.62/1.85 thf(func_def_118, type, sK8: $i > $o).
% 2.62/1.85 thf(func_def_124, type, sK14: $i > $o).
% 2.62/1.85 thf(func_def_129, type, sK19: $i > $i).
% 2.62/1.85 thf(func_def_139, type, sK29: $i > $o).
% 2.62/1.85 thf(func_def_143, type, sK33: $i > $o).
% 2.62/1.85 thf(func_def_149, type, sK39: $i > $i > $i).
% 2.62/1.85 thf(func_def_157, type, sK47: ($i > $o) > $i > $i).
% 2.62/1.85 thf(func_def_159, type, sK49: $i > $o).
% 2.62/1.85 thf(func_def_163, type, sK53: $i > $i).
% 2.62/1.85 thf(func_def_166, type, sK56: $i > $i > $i).
% 2.62/1.85 thf(func_def_167, type, sK57: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.62/1.85 thf(func_def_168, type, sK58: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.62/1.85 thf(func_def_171, type, sK61: $i > $o).
% 2.62/1.85 thf(func_def_172, type, sK62: $i > $o).
% 2.62/1.85 thf(func_def_173, type, sK63: ($i > $o) > ($i > $o) > $i).
% 2.62/1.85 thf(func_def_174, type, sK64: ($i > $o) > ($i > $o) > $i).
% 2.62/1.85 thf(func_def_175, type, sK65: $i > $o).
% 2.62/1.85 thf(func_def_176, type, sK66: $i > $o).
% 2.62/1.85 thf(func_def_177, type, sK67: $i > $o).
% 2.62/1.85 thf(func_def_184, type, sK74: $i > $o).
% 2.62/1.85 thf(func_def_186, type, sK76: $i > $i > $i).
% 2.62/1.85 thf(func_def_187, type, sK77: $i > $i > $i).
% 2.62/1.85 thf(func_def_190, type, sK80: $i > ($i > $o) > $i).
% 2.62/1.85 thf(func_def_191, type, sK81: $i > $o).
% 2.62/1.85 thf(func_def_194, type, sK84: $i > $i > $i).
% 2.62/1.85 thf(func_def_199, type, sK89: ($i > $o) > $i).
% 2.62/1.85 thf(func_def_200, type, sK90: $i > $o).
% 2.62/1.85 thf(func_def_201, type, sK91: $i > $i).
% 2.62/1.85 thf(func_def_204, type, sK94: ($i > $o) > ($i > $o) > $i).
% 2.62/1.85 thf(func_def_205, type, sK95: ($i > $o) > ($i > $o) > $i).
% 2.62/1.85 thf(func_def_206, type, sK96: $i > $o).
% 2.62/1.85 thf(func_def_207, type, sK97: $i > $o).
% 2.62/1.85 thf(func_def_215, type, sK105: ($i > $o) > $i).
% 2.62/1.85 thf(func_def_216, type, sK106: ($i > $o) > $i).
% 2.62/1.85 thf(func_def_217, type, sK107: $i > $o).
% 2.62/1.85 thf(func_def_219, type, sK109: $i > $o).
% 2.62/1.85 thf(func_def_221, type, sK111: $i > ($i > $o) > $i).
% 2.62/1.85 thf(func_def_223, type, sK113: $i > $o).
% 2.62/1.85 thf(func_def_229, type, sK119: $i > $o).
% 2.62/1.85 thf(func_def_232, type, sK122: $i > ($i > $o) > $i).
% 2.62/1.85 thf(func_def_238, type, sK128: $i > $i).
% 2.62/1.85 thf(func_def_240, type, sK130: $i > $i > $i).
% 2.62/1.85 thf(func_def_248, type, sK138: $i > $o).
% 2.62/1.85 thf(func_def_250, type, sK140: $i > $i > $o).
% 2.62/1.85 thf(func_def_252, type, sK142: $i > $i).
% 2.62/1.85 thf(func_def_253, type, sK143: $i > $i).
% 2.62/1.85 thf(func_def_254, type, sK144: $i > ($i > $i > $o) > $i).
% 2.62/1.85 thf(func_def_255, type, sK145: $i > $i > ($i > $i > $o) > $i).
% 2.62/1.85 thf(func_def_256, type, sK146: $i > ($i > $i > $o) > $i).
% 2.62/1.85 thf(func_def_258, type, sK148: $i > $o).
% 2.62/1.85 thf(func_def_260, type, sK150: ($i > $o) > $i > $i).
% 2.62/1.85 thf(func_def_263, type, sK153: $i > $i).
% 2.62/1.85 thf(func_def_264, type, sK154: $i > $i > $i).
% 2.62/1.85 thf(func_def_268, type, sK158: $i > $o).
% 2.62/1.85 thf(func_def_269, type, sK159: ($i > $o) > $i).
% 2.62/1.85 thf(func_def_273, type, sK163: $i > ($i > $o) > $i).
% 2.62/1.85 thf(func_def_274, type, sK164: $i > $o).
% 2.62/1.85 thf(func_def_279, type, sK169: $i > $i > $i).
% 2.62/1.85 thf(func_def_285, type, sK175: $i > $o).
% 2.62/1.85 thf(func_def_287, type, sK177: $i > ($i > $o) > $i).
% 2.62/1.85 thf(func_def_288, type, sK178: $i > $i).
% 2.62/1.85 thf(func_def_293, type, sK183: $i > $i).
% 2.62/1.85 thf(func_def_295, type, sK185: $i > $i).
% 2.62/1.85 thf(func_def_306, type, sK196: $i > ($i > $o) > $i).
% 2.62/1.85 thf(func_def_307, type, sK197: $i > $o).
% 2.62/1.85 thf(func_def_312, type, sK202: $i > $o).
% 2.62/1.85 thf(func_def_314, type, sK204: $i > $o).
% 2.62/1.85 thf(func_def_315, type, sK205: $i > $i).
% 2.62/1.85 thf(func_def_316, type, sK206: ($i > $o) > $i).
% 2.62/1.85 thf(func_def_323, type, sK213: $i > $i > $i).
% 2.62/1.85 thf(func_def_324, type, sK214: $i > $i > $i).
% 2.62/1.85 thf(func_def_325, type, sK215: $i > $i > $i).
% 2.62/1.85 thf(func_def_326, type, sK216: $i > $i > $i).
% 2.62/1.85 thf(func_def_327, type, sK217: $i > $i > $i).
% 2.62/1.85 thf(func_def_328, type, sK218: $i > $i > $i > $i).
% 2.62/1.85 thf(func_def_329, type, sK219: $i > $i).
% 2.62/1.85 thf(func_def_330, type, sK220: $i > $i).
% 2.62/1.85 thf(func_def_331, type, sK221: $i > $i).
% 2.62/1.85 thf(func_def_332, type, sK222: $i > $i).
% 2.62/1.85 thf(func_def_333, type, sK223: $i > $i > $i).
% 2.62/1.85 thf(func_def_334, type, sK224: $i > $i > $i > $i).
% 2.62/1.85 thf(func_def_335, type, sK225: $i > $i > $i > $i).
% 2.62/1.85 thf(func_def_336, type, sK226: $i > $i > $i).
% 2.62/1.85 thf(func_def_337, type, sK227: $i > $i > $i).
% 2.62/1.85 thf(func_def_338, type, sK228: $i > $i).
% 2.62/1.85 thf(func_def_340, type, sK230: $i > $i).
% 2.62/1.85 thf(func_def_341, type, sK231: $i > $i).
% 2.62/1.85 thf(func_def_345, type, sK235: $o > $i > $i > $i).
% 2.62/1.85 thf(func_def_351, type, ph241: !>[X0: $tType]:(X0)).
% 2.62/1.85 thf(f2040,plain,(
% 2.62/1.85 $false),
% 2.62/1.85 inference(trivial_inequality_removal,[status(thm)],[f2031])).
% 2.62/1.85 thf(f2031,plain,(
% 2.62/1.85 ($true != $true)),
% 2.62/1.85 inference(superposition,[status(thm)],[f1319,f1108])).
% 2.62/1.85 thf(f1108,plain,(
% 2.62/1.85 ((in @ sK207 @ sK209) = $true)),
% 2.62/1.85 inference(cnf_transformation,[status(thm)],[f731])).
% 2.62/1.85 thf(f731,plain,(
% 2.62/1.85 (replAx = $true) & (eqimpsubset2 = $true) & (omegaSAx = $true) & (setunionI = $true) & (quantDeMorgan3 = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (noeltsimpempty = $true) & (uniqinunit = $true) & (quantDeMorgan4 = $true) & (nonemptyI = $true) & (setadjoinAx = $true) & (exuE1 = $true) & (vacuousDall = $true) & (setunionAx = $true) & (exuI1 = $true) & (exuE2 = $true) & (eqinunit = $true) & (emptysetsubset = $true) & (quantDeMorgan2 = $true) & (nonemptyI1 = $true) & (emptyinPowerset = $true) & (inCongP = $true) & (notinemptyset = $true) & (setadjoinIR = $true) & (exuE3e = $true) & (subPowSU = $true) & (setunion__Cong = $true) & (exuE3u = $true) & (omegaIndAx = $true) & (setadjoin__Cong = $true) & (notdexE = $true) & (upairsetIL = $true) & (emptysetAx = $true) & (wellorderingAx = $true) & (notdallE = $true) & (dsetconstrER = $true) & (subsetI2 = $true) & (subsetE2 = $true) & (emptyE1 = $true) & (emptysetE = $true) & (descr__Cong = $true) & (powerset__Cong = $true) & (exuI3 = $true) & (powersetI = $true) & (prop2setE = $true) & (nonemptyImpWitness = $true) & (quantDeMorgan1 = $true) & (in__Cong = $true) & (prop2setI = $true) & (emptyinunitempty = $true) & (omega0Ax = $true) & (dsetconstrEL = $true) & (((subset @ sK209 @ sK208) = $true) & ((in @ sK207 @ sK208) != $true) & ((in @ sK207 @ sK209) = $true)) & (prop2set2propI = $true) & (powersetE = $true) & (descrp = $true) & (exuI2 = $true) & (exu__Cong = $true) & (setextAx = $true) & (emptyInPowerset = $true) & (subsetI1 = $true) & (setadjoinE = $true) & (emptyI = $true) & (setbeta = $true) & (setoftrueEq = $true) & (subsetE = $true) & (setadjoinOr = $true) & (emptyset__Cong = $true) & (nonemptyE1 = $true) & (exuEu = $true) & (emptysetimpfalse = $true) & (dsetconstrI = $true) & (setext = $true) & (notinsingleton = $true) & (powersetAx = $true) & (dsetconstr__Cong = $true) & (setunionE = $true) & (upairsetIR = $true) & (omega__Cong = $true) & (foundationAx = $true) & (eqimpsubset1 = $true) & (setadjoinIL = $true)),
% 2.62/1.85 inference(skolemisation,[status(esa),new_symbols(skolem,[sK207,sK208,sK209])],[f345,f730])).
% 2.62/1.85 thf(f730,plain,(
% 2.62/1.85 ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X1) = $true) & ((in @ X0 @ X1) != $true) & ((in @ X0 @ X2) = $true)) => (((subset @ sK209 @ sK208) = $true) & ((in @ sK207 @ sK208) != $true) & ((in @ sK207 @ sK209) = $true))),
% 2.62/1.85 introduced(definition,[],[choice_axiom])).
% 2.62/1.85 thf(f345,plain,(
% 2.62/1.85 (replAx = $true) & (eqimpsubset2 = $true) & (omegaSAx = $true) & (setunionI = $true) & (quantDeMorgan3 = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (noeltsimpempty = $true) & (uniqinunit = $true) & (quantDeMorgan4 = $true) & (nonemptyI = $true) & (setadjoinAx = $true) & (exuE1 = $true) & (vacuousDall = $true) & (setunionAx = $true) & (exuI1 = $true) & (exuE2 = $true) & (eqinunit = $true) & (emptysetsubset = $true) & (quantDeMorgan2 = $true) & (nonemptyI1 = $true) & (emptyinPowerset = $true) & (inCongP = $true) & (notinemptyset = $true) & (setadjoinIR = $true) & (exuE3e = $true) & (subPowSU = $true) & (setunion__Cong = $true) & (exuE3u = $true) & (omegaIndAx = $true) & (setadjoin__Cong = $true) & (notdexE = $true) & (upairsetIL = $true) & (emptysetAx = $true) & (wellorderingAx = $true) & (notdallE = $true) & (dsetconstrER = $true) & (subsetI2 = $true) & (subsetE2 = $true) & (emptyE1 = $true) & (emptysetE = $true) & (descr__Cong = $true) & (powerset__Cong = $true) & (exuI3 = $true) & (powersetI = $true) & (prop2setE = $true) & (nonemptyImpWitness = $true) & (quantDeMorgan1 = $true) & (in__Cong = $true) & (prop2setI = $true) & (emptyinunitempty = $true) & (omega0Ax = $true) & (dsetconstrEL = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X1) = $true) & ((in @ X0 @ X1) != $true) & ((in @ X0 @ X2) = $true)) & (prop2set2propI = $true) & (powersetE = $true) & (descrp = $true) & (exuI2 = $true) & (exu__Cong = $true) & (setextAx = $true) & (emptyInPowerset = $true) & (subsetI1 = $true) & (setadjoinE = $true) & (emptyI = $true) & (setbeta = $true) & (setoftrueEq = $true) & (subsetE = $true) & (setadjoinOr = $true) & (emptyset__Cong = $true) & (nonemptyE1 = $true) & (exuEu = $true) & (emptysetimpfalse = $true) & (dsetconstrI = $true) & (setext = $true) & (notinsingleton = $true) & (powersetAx = $true) & (dsetconstr__Cong = $true) & (setunionE = $true) & (upairsetIR = $true) & (omega__Cong = $true) & (foundationAx = $true) & (eqimpsubset1 = $true) & (setadjoinIL = $true)),
% 2.62/1.85 inference(flattening,[status(thm)],[f344])).
% 2.62/1.85 thf(f344,plain,(
% 2.62/1.85 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X2 @ X1) = $true) & ((in @ X0 @ X1) != $true)) & ((in @ X0 @ X2) = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.62/1.85 inference(ennf_transformation,[status(thm)],[f256])).
% 2.62/1.85 thf(f256,plain,(
% 2.62/1.85 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) => (((in @ X0 @ X1) != $true) => ((subset @ X2 @ X1) != $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.62/1.85 inference(flattening,[status(thm)],[f128])).
% 2.62/1.85 thf(f128,plain,(
% 2.62/1.85 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) => (~((in @ X0 @ X1) = $true) => ~((subset @ X2 @ X1) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.62/1.85 inference(fool_elimination,[status(thm)],[f127])).
% 2.62/1.85 thf(f127,plain,(
% 2.62/1.85 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (~(in @ X0 @ X1) => ~(subset @ X2 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.62/1.85 inference(rectify,[status(thm)],[f86])).
% 2.62/1.85 thf(f86,negated_conjecture,(
% 2.62/1.85 ~(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 => ! [X1 : $i,X4 : $i,X3 : $i] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => ~(subset @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.62/1.85 inference(negated_conjecture,[status(cth)],[f85])).
% 2.62/1.85 thf(f85,conjecture,(
% 2.62/1.85 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 => ! [X1 : $i,X4 : $i,X3 : $i] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => ~(subset @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.62/1.85 file('/export/starexec/sandbox/tmp/tmp.nkEZQ3bEXD/DTF2THF_30771.p',notsubsetI)).
% 2.62/1.85 thf(f1319,plain,(
% 2.62/1.85 ((in @ sK207 @ sK209) != $true)),
% 2.62/1.85 inference(trivial_inequality_removal,[status(thm)],[f1313])).
% 2.62/1.85 thf(f1313,plain,(
% 2.62/1.85 ((in @ sK207 @ sK209) != $true) | ($true != $true)),
% 2.62/1.85 inference(superposition,[status(thm)],[f1310,f1110])).
% 2.62/1.85 thf(f1110,plain,(
% 2.62/1.85 ((subset @ sK209 @ sK208) = $true)),
% 2.62/1.85 inference(cnf_transformation,[status(thm)],[f731])).
% 2.62/1.85 thf(f1310,plain,(
% 2.62/1.85 ( ! [X0 : $i] : (((subset @ X0 @ sK208) != $true) | ((in @ sK207 @ X0) != $true)) )),
% 2.62/1.85 inference(trivial_inequality_removal,[status(thm)],[f1309])).
% 2.62/1.85 thf(f1309,plain,(
% 2.62/1.85 ( ! [X0 : $i] : (((in @ sK207 @ X0) != $true) | ($true != $true) | ((subset @ X0 @ sK208) != $true)) )),
% 2.62/1.85 inference(forward_demodulation,[status(thm)],[f1307,f1125])).
% 2.62/1.85 thf(f1125,plain,(
% 2.62/1.85 (subsetE2 = $true)),
% 2.62/1.85 inference(cnf_transformation,[status(thm)],[f731])).
% 2.62/1.85 thf(f1307,plain,(
% 2.62/1.85 ( ! [X0 : $i] : ((subsetE2 != $true) | ((in @ sK207 @ X0) != $true) | ((subset @ X0 @ sK208) != $true)) )),
% 2.62/1.85 inference(trivial_inequality_removal,[status(thm)],[f1304])).
% 2.62/1.85 thf(f1304,plain,(
% 2.62/1.85 ( ! [X0 : $i] : (($true != $true) | (subsetE2 != $true) | ((in @ sK207 @ X0) != $true) | ((subset @ X0 @ sK208) != $true)) )),
% 2.62/1.85 inference(superposition,[status(thm)],[f1109,f829])).
% 2.62/1.85 thf(f829,plain,(
% 2.62/1.85 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) | (subsetE2 != $true) | ((subset @ X3 @ X4) != $true) | ((in @ X5 @ X3) != $true)) )),
% 2.62/1.85 inference(cnf_transformation,[status(thm)],[f442])).
% 2.62/1.85 thf(f442,plain,(
% 2.62/1.85 ((subsetE2 = $true) | (((in @ sK44 @ sK42) = $true) & ($true != (in @ sK44 @ sK43)) & ((subset @ sK42 @ sK43) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ((in @ X5 @ X4) = $true) | ((subset @ X3 @ X4) != $true)) | (subsetE2 != $true))),
% 2.62/1.85 inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43,sK44])],[f440,f441])).
% 2.62/1.85 thf(f441,plain,(
% 2.62/1.85 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true) & ((subset @ X0 @ X1) = $true)) => (((in @ sK44 @ sK42) = $true) & ($true != (in @ sK44 @ sK43)) & ((subset @ sK42 @ sK43) = $true))),
% 2.62/1.85 introduced(definition,[],[choice_axiom])).
% 2.62/1.85 thf(f440,plain,(
% 2.62/1.85 ((subsetE2 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true) & ((subset @ X0 @ X1) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ((in @ X5 @ X4) = $true) | ((subset @ X3 @ X4) != $true)) | (subsetE2 != $true))),
% 2.62/1.85 inference(rectify,[status(thm)],[f439])).
% 2.62/1.85 thf(f439,plain,(
% 2.62/1.85 ((subsetE2 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true) & ((subset @ X0 @ X1) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true) | ((subset @ X0 @ X1) != $true)) | (subsetE2 != $true))),
% 2.62/1.85 inference(nnf_transformation,[status(thm)],[f324])).
% 2.62/1.85 thf(f324,plain,(
% 2.62/1.85 (subsetE2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true) | ((subset @ X0 @ X1) != $true))),
% 2.62/1.85 inference(flattening,[status(thm)],[f323])).
% 2.62/1.85 thf(f323,plain,(
% 2.62/1.85 (subsetE2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true)) | ((subset @ X0 @ X1) != $true))),
% 2.62/1.85 inference(ennf_transformation,[status(thm)],[f254])).
% 2.62/1.85 thf(f254,plain,(
% 2.62/1.85 (subsetE2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X1) = $true) => (((in @ X2 @ X1) != $true) => ((in @ X2 @ X0) != $true)))),
% 2.62/1.85 inference(flattening,[status(thm)],[f110])).
% 2.62/1.85 thf(f110,plain,(
% 2.62/1.85 ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X1) = $true) => (~((in @ X2 @ X1) = $true) => ~((in @ X2 @ X0) = $true))) <=> (subsetE2 = $true)),
% 2.62/1.85 inference(fool_elimination,[status(thm)],[f109])).
% 2.62/1.85 thf(f109,plain,(
% 2.62/1.85 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => (~(in @ X2 @ X1) => ~(in @ X2 @ X0))) = subsetE2)),
% 2.62/1.85 inference(rectify,[status(thm)],[f84])).
% 2.62/1.85 thf(f84,axiom,(
% 2.62/1.85 (! [X3 : $i,X4 : $i,X1 : $i] : ((subset @ X3 @ X4) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3))) = subsetE2)),
% 2.62/1.85 file('/export/starexec/sandbox/tmp/tmp.nkEZQ3bEXD/DTF2THF_30771.p',subsetE2)).
% 2.62/1.85 thf(f1109,plain,(
% 2.62/1.85 ((in @ sK207 @ sK208) != $true)),
% 2.62/1.85 inference(cnf_transformation,[status(thm)],[f731])).
% 2.62/1.85 % SZS output end Proof for DTF2THF_30771
% 2.62/1.85 % (30900)------------------------------
% 2.62/1.85 % (30900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.85 % (30900)Termination reason: Refutation
% 2.62/1.85
% 2.62/1.85 % (30900)Memory used [KB]: 7164
% 2.62/1.85 % (30900)Time elapsed: 0.083 s
% 2.62/1.85 % (30900)Instructions burned: 161 (million)
% 2.62/1.85 % (30900)------------------------------
% 2.62/1.85 % (30900)------------------------------
% 2.62/1.85 % (30877)Success in time 0.168 s
%------------------------------------------------------------------------------