%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU577^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 09:35:22 AM UTC 2026
% Result : Theorem 2.26s 1.61s
% Output : Refutation 2.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 76 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 2233 ( 613 equ; 0 cnn)
% Maximal formula atoms : 95 ( 29 avg)
% Number of connectives : 1392 ( 125 ~; 99 |; 327 &; 432 @)
% ( 9 <=>; 400 =>; 0 <=; 0 <~>)
% Maximal formula depth : 100 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 214 ( 211 usr; 106 con; 0-4 aty)
% Number of variables : 146 ( 0 ^; 109 !; 37 ?; 146 :)
% 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_122,type,
sP1: $i > $i > $o ).
thf(func_def_123,type,
sP2: $i > $o ).
thf(func_def_124,type,
sP3: $i > $i > $o ).
thf(func_def_125,type,
sP4: $i > $i > $o ).
thf(func_def_133,type,
sK12: $i > $o ).
thf(func_def_135,type,
sK14: ( $i > $o ) > $i > $i ).
thf(func_def_140,type,
sK19: $i > $o ).
thf(func_def_142,type,
sK21: ( $i > $o ) > $i > $i ).
thf(func_def_143,type,
sK22: $i > ( $i > $o ) > $i ).
thf(func_def_144,type,
sK23: $i > $o ).
thf(func_def_159,type,
sK38: $i > $o ).
thf(func_def_160,type,
sK39: $i > $o ).
thf(func_def_161,type,
sK40: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_162,type,
sK41: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_164,type,
sK43: $i > $i > $o ).
thf(func_def_165,type,
sK44: $i > $i ).
thf(func_def_166,type,
sK45: $i > $i ).
thf(func_def_167,type,
sK46: ( $i > $i > $o ) > $i > $i ).
thf(func_def_168,type,
sK47: ( $i > $i > $o ) > $i > $i ).
thf(func_def_169,type,
sK48: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_175,type,
sK54: $o > $i > $i > $i ).
thf(func_def_176,type,
sK55: $i > $i > $i ).
thf(func_def_185,type,
sK64: $i > $o ).
thf(func_def_186,type,
sK65: $i > ( $i > $o ) > $i ).
thf(func_def_187,type,
sK66: $i > $o ).
thf(func_def_189,type,
sK68: $i > $o ).
thf(func_def_193,type,
sK72: $i > $i ).
thf(func_def_196,type,
sK75: $i > $i > $i ).
thf(func_def_197,type,
sK76: $i > $i > $i ).
thf(func_def_198,type,
sK77: $i > $i > $i ).
thf(func_def_199,type,
sK78: $i > $i > $i ).
thf(func_def_200,type,
sK79: $i > $i > $i ).
thf(func_def_201,type,
sK80: $i > $i > $i > $i ).
thf(func_def_202,type,
sK81: $i > $i ).
thf(func_def_203,type,
sK82: $i > $i ).
thf(func_def_204,type,
sK83: $i > $i ).
thf(func_def_205,type,
sK84: $i > $i ).
thf(func_def_206,type,
sK85: $i > $i > $i ).
thf(func_def_207,type,
sK86: $i > $i > $i > $i ).
thf(func_def_208,type,
sK87: $i > $i > $i > $i ).
thf(func_def_209,type,
sK88: $i > $i > $i ).
thf(func_def_210,type,
sK89: $i > $i > $i ).
thf(func_def_212,type,
sK91: $i > $i ).
thf(func_def_213,type,
sK92: $i > $i ).
thf(func_def_214,type,
sK93: $i > $i ).
thf(func_def_215,type,
sK94: $i > ( $i > $o ) > $i ).
thf(func_def_216,type,
sK95: $i > $o ).
thf(func_def_223,type,
sK102: $i > $i > $i ).
thf(func_def_227,type,
sK106: $i > $i > $i ).
thf(func_def_232,type,
sK111: $i > $i > $i ).
thf(func_def_233,type,
sK112: $i > $i > $i ).
thf(func_def_234,type,
sK113: $i > $o ).
thf(func_def_238,type,
sK117: $i > $o ).
thf(func_def_245,type,
sK124: ( $i > $o ) > $i ).
thf(func_def_246,type,
sK125: $i > $o ).
thf(func_def_247,type,
sK126: $i > $i ).
thf(func_def_248,type,
sK127: $i > $o ).
thf(func_def_249,type,
sK128: ( $i > $o ) > $i ).
thf(func_def_261,type,
sK140: $i > $i ).
thf(func_def_262,type,
sK141: ( $i > $o ) > $i ).
thf(func_def_263,type,
sK142: $i > $o ).
thf(func_def_264,type,
sK143: $i > $i ).
thf(func_def_266,type,
sK145: $i > $i ).
thf(func_def_273,type,
sK152: $i > $o ).
thf(func_def_277,type,
sK156: $i > $o ).
thf(func_def_280,type,
sK159: $i > ( $i > $o ) > $i ).
thf(func_def_281,type,
sK160: $i > $i ).
thf(func_def_283,type,
sK162: $i > $i ).
thf(func_def_293,type,
sK172: $i > $o ).
thf(func_def_296,type,
sK175: $i > $i ).
thf(func_def_304,type,
sK183: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_305,type,
sK184: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_306,type,
sK185: $i > $o ).
thf(func_def_307,type,
sK186: $i > $o ).
thf(func_def_310,type,
sK189: $i > $o ).
thf(func_def_316,type,
sK195: $i > $i > $i ).
thf(func_def_321,type,
sK200: $i > $o ).
thf(func_def_326,type,
sK205: $i > $o ).
thf(func_def_328,type,
sK207: $i > $o ).
thf(func_def_331,type,
sK210: $i > ( $i > $o ) > $i ).
thf(func_def_332,type,
sK211: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_333,type,
sK212: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_334,type,
sK213: $i > $o ).
thf(func_def_335,type,
sK214: $i > $o ).
thf(func_def_337,type,
sK216: $i > $i ).
thf(func_def_347,type,
sK226: $i > $o ).
thf(func_def_350,type,
sK229: ( $i > $o ) > $i ).
thf(func_def_351,type,
sK230: ( $i > $o ) > $i ).
thf(func_def_352,type,
sK231: $i > $o ).
thf(func_def_361,type,
sK240: $i > $i > $i ).
thf(func_def_371,type,
sK250: $i > $i > $i ).
thf(func_def_380,type,
sK259: $i > ( $i > $o ) > $i ).
thf(func_def_381,type,
sK260: $i > $o ).
thf(func_def_385,type,
ph264:
!>[X0: $tType] : X0 ).
thf(f2073,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f2066]) ).
thf(f2066,plain,
$true != $true,
inference(superposition,[status(thm)],[f1538,f2022]) ).
thf(f2022,plain,
( ( subset @ sK60 @ sK61 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f2021]) ).
thf(f2021,plain,
( ( ( subset @ sK60 @ sK61 )
= $true )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f2016,f1020]) ).
thf(f1020,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f503]) ).
thf(f503,plain,
( ( emptysetE = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetAx = $true )
& ( emptyinPowerset = $true )
& ( notequalI1 = $true )
& ( inCongP = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( ( in @ sK60 @ ( powerset @ sK61 ) )
= $true )
& ( ( subset @ sK60 @ sK61 )
!= $true )
& ( setadjoin__Cong = $true )
& ( exuE2 = $true )
& ( eqimpsubset2 = $true )
& ( setadjoinSub = $true )
& ( emptyinunitempty = $true )
& ( subset2powerset = $true )
& ( exuI2 = $true )
& ( notinsingleton = $true )
& ( eqimpsubset1 = $true )
& ( emptysetimpfalse = $true )
& ( setunionI = $true )
& ( subsetI1 = $true )
& ( setunionE = $true )
& ( subsetE2 = $true )
& ( setadjoinIL = $true )
& ( notsubsetI = $true )
& ( powersetE = $true )
& ( noeltsimpempty = $true )
& ( notdexE = $true )
& ( subsetI2 = $true )
& ( quantDeMorgan1 = $true )
& ( emptyInPowerset = $true )
& ( setadjoinSub2 = $true )
& ( omega__Cong = $true )
& ( setextsub = $true )
& ( exuE1 = $true )
& ( exuI3 = $true )
& ( subsetRefl = $true )
& ( emptyI = $true )
& ( replAx = $true )
& ( upairsetE = $true )
& ( subsetE = $true )
& ( dsetconstr__Cong = $true )
& ( notinemptyset = $true )
& ( emptysetsubset = $true )
& ( descrp = $true )
& ( notdallE = $true )
& ( omegaIndAx = $true )
& ( subPowSU = $true )
& ( dsetconstrEL = $true )
& ( descr__Cong = $true )
& ( setadjoinOr = $true )
& ( notequalI2 = $true )
& ( setunionAx = $true )
& ( subsetTrans = $true )
& ( emptyE1 = $true )
& ( powersetI = $true )
& ( exuI1 = $true )
& ( dsetconstrI = $true )
& ( uniqinunit = $true )
& ( prop2set2propI = $true )
& ( setadjoinIR = $true )
& ( setbeta = $true )
& ( exu__Cong = $true )
& ( prop2setI = $true )
& ( in__Cong = $true )
& ( exuE3e = $true )
& ( nonemptyImpWitness = $true )
& ( omega0Ax = $true )
& ( subsetemptysetimpeq = $true )
& ( singletonsswitch = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI = $true )
& ( setoftrueEq = $true )
& ( setadjoinAx = $true )
& ( wellorderingAx = $true )
& ( omegaSAx = $true )
& ( upairsetIR = $true )
& ( nonemptyI1 = $true )
& ( setextAx = $true )
& ( exuEu = $true )
& ( dsetconstrER = $true )
& ( emptyset__Cong = $true )
& ( powersetI1 = $true )
& ( setext = $true )
& ( upairsetIL = $true )
& ( exuE3u = $true )
& ( quantDeMorgan4 = $true )
& ( powerset__Cong = $true )
& ( powersetAx = $true )
& ( setadjoinE = $true )
& ( eqinunit = $true )
& ( quantDeMorgan3 = $true )
& ( vacuousDall = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60,sK61])],[f383,f502]) ).
thf(f502,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X0 @ X1 )
!= $true ) )
=> ( ( ( in @ sK60 @ ( powerset @ sK61 ) )
= $true )
& ( ( subset @ sK60 @ sK61 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f383,plain,
( ( emptysetE = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetAx = $true )
& ( emptyinPowerset = $true )
& ( notequalI1 = $true )
& ( inCongP = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X0 @ X1 )
!= $true ) )
& ( setadjoin__Cong = $true )
& ( exuE2 = $true )
& ( eqimpsubset2 = $true )
& ( setadjoinSub = $true )
& ( emptyinunitempty = $true )
& ( subset2powerset = $true )
& ( exuI2 = $true )
& ( notinsingleton = $true )
& ( eqimpsubset1 = $true )
& ( emptysetimpfalse = $true )
& ( setunionI = $true )
& ( subsetI1 = $true )
& ( setunionE = $true )
& ( subsetE2 = $true )
& ( setadjoinIL = $true )
& ( notsubsetI = $true )
& ( powersetE = $true )
& ( noeltsimpempty = $true )
& ( notdexE = $true )
& ( subsetI2 = $true )
& ( quantDeMorgan1 = $true )
& ( emptyInPowerset = $true )
& ( setadjoinSub2 = $true )
& ( omega__Cong = $true )
& ( setextsub = $true )
& ( exuE1 = $true )
& ( exuI3 = $true )
& ( subsetRefl = $true )
& ( emptyI = $true )
& ( replAx = $true )
& ( upairsetE = $true )
& ( subsetE = $true )
& ( dsetconstr__Cong = $true )
& ( notinemptyset = $true )
& ( emptysetsubset = $true )
& ( descrp = $true )
& ( notdallE = $true )
& ( omegaIndAx = $true )
& ( subPowSU = $true )
& ( dsetconstrEL = $true )
& ( descr__Cong = $true )
& ( setadjoinOr = $true )
& ( notequalI2 = $true )
& ( setunionAx = $true )
& ( subsetTrans = $true )
& ( emptyE1 = $true )
& ( powersetI = $true )
& ( exuI1 = $true )
& ( dsetconstrI = $true )
& ( uniqinunit = $true )
& ( prop2set2propI = $true )
& ( setadjoinIR = $true )
& ( setbeta = $true )
& ( exu__Cong = $true )
& ( prop2setI = $true )
& ( in__Cong = $true )
& ( exuE3e = $true )
& ( nonemptyImpWitness = $true )
& ( omega0Ax = $true )
& ( subsetemptysetimpeq = $true )
& ( singletonsswitch = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI = $true )
& ( setoftrueEq = $true )
& ( setadjoinAx = $true )
& ( wellorderingAx = $true )
& ( omegaSAx = $true )
& ( upairsetIR = $true )
& ( nonemptyI1 = $true )
& ( setextAx = $true )
& ( exuEu = $true )
& ( dsetconstrER = $true )
& ( emptyset__Cong = $true )
& ( powersetI1 = $true )
& ( setext = $true )
& ( upairsetIL = $true )
& ( exuE3u = $true )
& ( quantDeMorgan4 = $true )
& ( powerset__Cong = $true )
& ( powersetAx = $true )
& ( setadjoinE = $true )
& ( eqinunit = $true )
& ( quantDeMorgan3 = $true )
& ( vacuousDall = $true ) ),
inference(flattening,[status(thm)],[f382]) ).
thf(f382,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X0 @ X1 )
!= $true ) )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $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)],[f114]) ).
thf(f114,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 )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ( ( subset @ X0 @ X1 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f113]) ).
thf(f113,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
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f97]) ).
thf(f97,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ! [X4: $i,X3: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ( subset @ X4 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
thf(f96,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ! [X4: $i,X3: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ( subset @ X4 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JqQVLhIiKp/DTF2THF_18696.p',powersetE1) ).
thf(f2016,plain,
( ( ( subset @ sK60 @ sK61 )
= $true )
| ( subsetI1 != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2015]) ).
thf(f2015,plain,
( ( ( subset @ sK60 @ sK61 )
= $true )
| ( subsetI1 != $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f2008]) ).
thf(f2008,plain,
( ( $true != $true )
| ( subsetI1 != $true )
| ( ( subset @ sK60 @ sK61 )
= $true )
| ( ( subset @ sK60 @ sK61 )
= $true ) ),
inference(superposition,[status(thm)],[f1628,f1128]) ).
thf(f1128,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK106 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( subset @ X0 @ X1 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f589]) ).
thf(f589,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( ( in @ ( sK106 @ X1 @ X0 ) @ X1 )
!= $true )
& ( ( in @ ( sK106 @ X1 @ X0 ) @ X0 )
= $true ) )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ( ! [X5: $i] :
( ( $true
= ( in @ X5 @ sK108 ) )
| ( ( in @ X5 @ sK107 )
!= $true ) )
& ( ( subset @ sK107 @ sK108 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK106,sK107,sK108])],[f586,f588,f587]) ).
thf(f587,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( ( in @ ( sK106 @ X1 @ X0 ) @ X1 )
!= $true )
& ( ( in @ ( sK106 @ X1 @ X0 ) @ X0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f588,plain,
( ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( $true
!= ( in @ X5 @ X3 ) ) )
& ( ( subset @ X3 @ X4 )
!= $true ) )
=> ( ! [X5: $i] :
( ( $true
= ( in @ X5 @ sK108 ) )
| ( ( in @ X5 @ sK107 )
!= $true ) )
& ( ( subset @ sK107 @ sK108 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f586,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( $true
!= ( in @ X5 @ X3 ) ) )
& ( ( subset @ X3 @ X4 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f585]) ).
thf(f585,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( subsetI1 != $true ) )
& ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( subset @ X0 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f391]) ).
thf(f391,plain,
( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( ( subset @ X0 @ X1 )
= $true ) )
<=> ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f244]) ).
thf(f244,plain,
( ( subsetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( subset @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f243]) ).
thf(f243,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
inference(rectify,[status(thm)],[f78]) ).
thf(f78,axiom,
! [X3: $i,X4: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ X4 ) )
=> ( subset @ X3 @ X4 ) )
= subsetI1 ),
file('/export/starexec/sandbox2/tmp/tmp.JqQVLhIiKp/DTF2THF_18696.p',subsetI1) ).
thf(f1628,plain,
! [X0: $i] :
( ( ( in @ ( sK106 @ sK61 @ X0 ) @ sK60 )
!= $true )
| ( ( subset @ X0 @ sK61 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1627]) ).
thf(f1627,plain,
! [X0: $i] :
( ( ( subset @ X0 @ sK61 )
= $true )
| ( ( in @ ( sK106 @ sK61 @ X0 ) @ sK60 )
!= $true )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f1597,f1020]) ).
thf(f1597,plain,
! [X0: $i] :
( ( subsetI1 != $true )
| ( ( subset @ X0 @ sK61 )
= $true )
| ( ( in @ ( sK106 @ sK61 @ X0 ) @ sK60 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1577]) ).
thf(f1577,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( subset @ X0 @ sK61 )
= $true )
| ( subsetI1 != $true )
| ( ( in @ ( sK106 @ sK61 @ X0 ) @ sK60 )
!= $true ) ),
inference(superposition,[status(thm)],[f1129,f1451]) ).
thf(f1451,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK61 )
= $true )
| ( ( in @ X0 @ sK60 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1450]) ).
thf(f1450,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK60 )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ sK61 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f1446,f1015]) ).
thf(f1015,plain,
powersetE = $true,
inference(cnf_transformation,[status(thm)],[f503]) ).
thf(f1446,plain,
! [X0: $i] :
( ( powersetE != $true )
| ( ( in @ X0 @ sK61 )
= $true )
| ( ( in @ X0 @ sK60 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1443]) ).
thf(f1443,plain,
! [X0: $i] :
( ( $true != $true )
| ( powersetE != $true )
| ( ( in @ X0 @ sK60 )
!= $true )
| ( ( in @ X0 @ sK61 )
= $true ) ),
inference(superposition,[status(thm)],[f1147,f1033]) ).
thf(f1033,plain,
( ( in @ sK60 @ ( powerset @ sK61 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f503]) ).
thf(f1147,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( powersetE != $true )
| ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f611]) ).
thf(f611,plain,
( ( ( powersetE = $true )
| ( ( ( in @ sK121 @ sK122 )
= $true )
& ( ( in @ sK122 @ ( powerset @ sK123 ) )
= $true )
& ( ( in @ sK121 @ sK123 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X3 @ X5 )
= $true ) )
| ( powersetE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK121,sK122,sK123])],[f609,f610]) ).
thf(f610,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) )
& ( ( in @ X0 @ X2 )
!= $true ) )
=> ( ( ( in @ sK121 @ sK122 )
= $true )
& ( ( in @ sK122 @ ( powerset @ sK123 ) )
= $true )
& ( ( in @ sK121 @ sK123 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f609,plain,
( ( ( powersetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) )
& ( ( in @ X0 @ X2 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X3 @ X5 )
= $true ) )
| ( powersetE != $true ) ) ),
inference(rectify,[status(thm)],[f608]) ).
thf(f608,plain,
( ( ( powersetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) )
& ( ( in @ X0 @ X2 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( powersetE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f333]) ).
thf(f333,plain,
( ( powersetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( ( in @ X0 @ X2 )
= $true ) ) ),
inference(flattening,[status(thm)],[f332]) ).
thf(f332,plain,
( ( powersetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true
!= ( in @ X1 @ ( powerset @ X2 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f138]) ).
thf(f138,plain,
( ( powersetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) )
=> ( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f137]) ).
thf(f137,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) ) )
= powersetE ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,axiom,
! [X1: $i,X4: $i,X3: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
=> ( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) ) )
= powersetE ),
file('/export/starexec/sandbox2/tmp/tmp.JqQVLhIiKp/DTF2THF_18696.p',powersetE) ).
thf(f1129,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK106 @ X1 @ X0 ) @ X1 )
!= $true )
| ( subsetI1 != $true )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f589]) ).
thf(f1538,plain,
( ( subset @ sK60 @ sK61 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1537]) ).
thf(f1537,plain,
( ( $true != $true )
| ( ( subset @ sK60 @ sK61 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f1478,f1004]) ).
thf(f1004,plain,
subsetRefl = $true,
inference(cnf_transformation,[status(thm)],[f503]) ).
thf(f1478,plain,
( ( ( subset @ sK60 @ sK61 )
!= $true )
| ( subsetRefl != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1456]) ).
thf(f1456,plain,
( ( subsetRefl != $true )
| ( ( subset @ sK60 @ sK61 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1441,f1280]) ).
thf(f1280,plain,
! [X1: $i] :
( ( ( subset @ X1 @ X1 )
= $true )
| ( subsetRefl != $true ) ),
inference(cnf_transformation,[status(thm)],[f787]) ).
thf(f787,plain,
( ( ( subsetRefl = $true )
| ( ( subset @ sK217 @ sK217 )
!= $true ) )
& ( ! [X1: $i] :
( ( subset @ X1 @ X1 )
= $true )
| ( subsetRefl != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK217])],[f785,f786]) ).
thf(f786,plain,
( ? [X0: $i] :
( ( subset @ X0 @ X0 )
!= $true )
=> ( ( subset @ sK217 @ sK217 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f785,plain,
( ( ( subsetRefl = $true )
| ? [X0: $i] :
( ( subset @ X0 @ X0 )
!= $true ) )
& ( ! [X1: $i] :
( ( subset @ X1 @ X1 )
= $true )
| ( subsetRefl != $true ) ) ),
inference(rectify,[status(thm)],[f784]) ).
thf(f784,plain,
( ( ( subsetRefl = $true )
| ? [X0: $i] :
( ( subset @ X0 @ X0 )
!= $true ) )
& ( ! [X0: $i] :
( ( subset @ X0 @ X0 )
= $true )
| ( subsetRefl != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f136]) ).
thf(f136,plain,
( ( subsetRefl = $true )
<=> ! [X0: $i] :
( ( subset @ X0 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f135]) ).
thf(f135,plain,
! [X0: $i] :
( ( subset @ X0 @ X0 )
= subsetRefl ),
inference(rectify,[status(thm)],[f88]) ).
thf(f88,axiom,
! [X3: $i] :
( ( subset @ X3 @ X3 )
= subsetRefl ),
file('/export/starexec/sandbox2/tmp/tmp.JqQVLhIiKp/DTF2THF_18696.p',subsetRefl) ).
thf(f1441,plain,
! [X0: $i] :
( ( ( subset @ sK60 @ X0 )
!= $true )
| ( ( subset @ X0 @ sK61 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1440]) ).
thf(f1440,plain,
! [X0: $i] :
( ( ( subset @ sK60 @ X0 )
!= $true )
| ( ( subset @ X0 @ sK61 )
!= $true )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f1439,f987]) ).
thf(f987,plain,
subsetTrans = $true,
inference(cnf_transformation,[status(thm)],[f503]) ).
thf(f1439,plain,
! [X0: $i] :
( ( subsetTrans != $true )
| ( ( subset @ X0 @ sK61 )
!= $true )
| ( ( subset @ sK60 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1438]) ).
thf(f1438,plain,
! [X0: $i] :
( ( ( subset @ X0 @ sK61 )
!= $true )
| ( $true != $true )
| ( ( subset @ sK60 @ X0 )
!= $true )
| ( subsetTrans != $true ) ),
inference(superposition,[status(thm)],[f1032,f1193]) ).
thf(f1193,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X5 )
= $true )
| ( ( subset @ X3 @ X4 )
!= $true )
| ( ( subset @ X4 @ X5 )
!= $true )
| ( subsetTrans != $true ) ),
inference(cnf_transformation,[status(thm)],[f675]) ).
thf(f675,plain,
( ( ( subsetTrans = $true )
| ( ( ( subset @ sK153 @ sK155 )
!= $true )
& ( ( subset @ sK153 @ sK154 )
= $true )
& ( ( subset @ sK154 @ sK155 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X5 )
= $true )
| ( ( subset @ X3 @ X4 )
!= $true )
| ( ( subset @ X4 @ X5 )
!= $true ) )
| ( subsetTrans != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK153,sK154,sK155])],[f673,f674]) ).
thf(f674,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
& ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X1 @ X2 )
= $true ) )
=> ( ( ( subset @ sK153 @ sK155 )
!= $true )
& ( ( subset @ sK153 @ sK154 )
= $true )
& ( ( subset @ sK154 @ sK155 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f673,plain,
( ( ( subsetTrans = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
& ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X1 @ X2 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X5 )
= $true )
| ( ( subset @ X3 @ X4 )
!= $true )
| ( ( subset @ X4 @ X5 )
!= $true ) )
| ( subsetTrans != $true ) ) ),
inference(rectify,[status(thm)],[f672]) ).
thf(f672,plain,
( ( ( subsetTrans = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
& ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X1 @ X2 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X2 )
!= $true ) )
| ( subsetTrans != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f350]) ).
thf(f350,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
= $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f349]) ).
thf(f349,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
= $true )
| ( ( subset @ X1 @ X2 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f240]) ).
thf(f240,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( ( subset @ X1 @ X2 )
= $true )
=> ( ( subset @ X0 @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f239]) ).
thf(f239,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X0 @ X2 ) ) )
= subsetTrans ),
inference(rectify,[status(thm)],[f89]) ).
thf(f89,axiom,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ X3 @ X5 ) ) )
= subsetTrans ),
file('/export/starexec/sandbox2/tmp/tmp.JqQVLhIiKp/DTF2THF_18696.p',subsetTrans) ).
thf(f1032,plain,
( ( subset @ sK60 @ sK61 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f503]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU577^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n018.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:27:16 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : SEU577^1 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.46 % Domain : Set Theory
% 0.27/0.46 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English : (! A:i.! B:i.in B (powerset A) -> subset B A)
% 0.27/0.46
% 0.27/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.46 % Source : [Bro08]
% 0.27/0.46 % Names : ZFC079g [Bro08]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.27/0.46 % Syntax : Number of formulae : 204 ( 95 unt; 108 typ; 95 def)
% 0.27/0.46 % Number of atoms : 518 ( 144 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 95 ( 5 avg)
% 0.27/0.46 % Number of connectives : 812 ( 29 ~; 5 |; 27 &; 501 @)
% 0.27/0.46 % ( 14 <=>; 236 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 99 ( 2 avg)
% 0.27/0.46 % Number of types : 2 ( 0 usr)
% 0.27/0.46 % Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 111 ( 108 usr; 97 con; 0-2 aty)
% 0.27/0.46 % Number of variables : 285 ( 28 ^; 229 !; 28 ?; 285 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : http://mathgate.info/detsetitem.php?id=257
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(in_type,type,
% 0.27/0.46 in: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(exu_type,type,
% 0.27/0.46 exu: ( $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(exu,definition,
% 0.27/0.46 ( exu
% 0.27/0.46 = ( ^ [Xphi: $i > $o] :
% 0.27/0.46 ? [Xx: $i] :
% 0.27/0.46 ( ( Xphi @ Xx )
% 0.27/0.46 & ! [Xy: $i] :
% 0.27/0.46 ( ( Xphi @ Xy )
% 0.27/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setextAx_type,type,
% 0.27/0.46 setextAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setextAx,definition,
% 0.27/0.46 ( setextAx
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 <=> ( in @ Xx @ B ) )
% 0.27/0.46 => ( A = B ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptyset_type,type,
% 0.27/0.46 emptyset: $i ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetAx_type,type,
% 0.27/0.46 emptysetAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetAx,definition,
% 0.27/0.46 ( emptysetAx
% 0.27/0.46 = ( ! [Xx: $i] :
% 0.27/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoin_type,type,
% 0.27/0.46 setadjoin: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinAx_type,type,
% 0.27/0.46 setadjoinAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinAx,definition,
% 0.27/0.46 ( setadjoinAx
% 0.27/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.46 <=> ( ( Xy = Xx )
% 0.27/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(powerset_type,type,
% 0.27/0.46 powerset: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(powersetAx_type,type,
% 0.27/0.46 powersetAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(powersetAx,definition,
% 0.27/0.46 ( powersetAx
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.46 <=> ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setunion_type,type,
% 0.27/0.46 setunion: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(setunionAx_type,type,
% 0.27/0.46 setunionAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setunionAx,definition,
% 0.27/0.46 ( setunionAx
% 0.27/0.46 = ( ! [A: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.46 <=> ? [B: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(omega_type,type,
% 0.27/0.46 omega: $i ).
% 0.27/0.46
% 0.27/0.46 thf(omega0Ax_type,type,
% 0.27/0.46 omega0Ax: $o ).
% 0.27/0.46
% 0.27/0.46 thf(omega0Ax,definition,
% 0.27/0.46 ( omega0Ax
% 0.27/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(omegaSAx_type,type,
% 0.27/0.46 omegaSAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(omegaSAx,definition,
% 0.27/0.46 ( omegaSAx
% 0.27/0.46 = ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ omega )
% 0.27/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(omegaIndAx_type,type,
% 0.27/0.46 omegaIndAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(omegaIndAx,definition,
% 0.27/0.46 ( omegaIndAx
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ( ( in @ emptyset @ A )
% 0.27/0.46 & ! [Xx: $i] :
% 0.27/0.46 ( ( ( in @ Xx @ omega )
% 0.27/0.46 & ( in @ Xx @ A ) )
% 0.27/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.27/0.46 => ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ omega )
% 0.27/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(replAx_type,type,
% 0.27/0.46 replAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(replAx,definition,
% 0.27/0.46 ( replAx
% 0.27/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( exu
% 0.27/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.27/0.46 => ? [B: $i] :
% 0.27/0.46 ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 <=> ? [Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ A )
% 0.27/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(foundationAx_type,type,
% 0.27/0.46 foundationAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(foundationAx,definition,
% 0.27/0.46 ( foundationAx
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.27/0.46 => ? [B: $i] :
% 0.27/0.46 ( ( in @ B @ A )
% 0.27/0.46 & ~ ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(wellorderingAx_type,type,
% 0.27/0.46 wellorderingAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(wellorderingAx,definition,
% 0.27/0.46 ( wellorderingAx
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ? [B: $i] :
% 0.27/0.46 ( ! [C: $i] :
% 0.27/0.46 ( ( in @ C @ B )
% 0.27/0.46 => ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ C )
% 0.27/0.46 => ( in @ Xx @ A ) ) )
% 0.27/0.46 & ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( ( in @ Xx @ A )
% 0.27/0.46 & ( in @ Xy @ A ) )
% 0.27/0.46 => ( ! [C: $i] :
% 0.27/0.46 ( ( in @ C @ B )
% 0.27/0.46 => ( ( in @ Xx @ C )
% 0.27/0.46 <=> ( in @ Xy @ C ) ) )
% 0.27/0.46 => ( Xx = Xy ) ) )
% 0.27/0.46 & ! [C: $i,D: $i] :
% 0.27/0.46 ( ( ( in @ C @ B )
% 0.27/0.46 & ( in @ D @ B ) )
% 0.27/0.46 => ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ C )
% 0.27/0.46 => ( in @ Xx @ D ) )
% 0.27/0.46 | ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ D )
% 0.27/0.46 => ( in @ Xx @ C ) ) ) )
% 0.27/0.46 & ! [C: $i] :
% 0.27/0.46 ( ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ C )
% 0.27/0.46 => ( in @ Xx @ A ) )
% 0.27/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.27/0.46 => ? [D: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ D @ B )
% 0.27/0.46 & ( in @ Xx @ C )
% 0.27/0.46 & ~ ? [Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ D )
% 0.27/0.46 & ( in @ Xy @ C ) )
% 0.27/0.46 & ! [E: $i] :
% 0.27/0.46 ( ( in @ E @ B )
% 0.27/0.46 => ( ! [Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ E )
% 0.27/0.46 => ( in @ Xy @ D ) )
% 0.27/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(descr_type,type,
% 0.27/0.46 descr: ( $i > $o ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(descrp_type,type,
% 0.27/0.46 descrp: $o ).
% 0.27/0.46
% 0.27/0.46 thf(descrp,definition,
% 0.27/0.46 ( descrp
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 => ( Xphi
% 0.27/0.46 @ ( descr
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstr_type,type,
% 0.27/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrI_type,type,
% 0.27/0.46 dsetconstrI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrI,definition,
% 0.27/0.46 ( dsetconstrI
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( ( Xphi @ Xx )
% 0.27/0.46 => ( in @ Xx
% 0.27/0.46 @ ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrEL_type,type,
% 0.27/0.46 dsetconstrEL: $o ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrEL,definition,
% 0.27/0.46 ( dsetconstrEL
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx
% 0.27/0.46 @ ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrER_type,type,
% 0.27/0.46 dsetconstrER: $o ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrER,definition,
% 0.27/0.46 ( dsetconstrER
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx
% 0.27/0.46 @ ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exuE1_type,type,
% 0.27/0.46 exuE1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exuE1,definition,
% 0.27/0.46 ( exuE1
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 => ? [Xx: $i] :
% 0.27/0.46 ( ( Xphi @ Xx )
% 0.27/0.46 & ! [Xy: $i] :
% 0.27/0.46 ( ( Xphi @ Xy )
% 0.27/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(prop2set_type,type,
% 0.27/0.46 prop2set: $o > $i ).
% 0.27/0.46
% 0.27/0.46 thf(prop2setE_type,type,
% 0.27/0.46 prop2setE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(prop2setE,definition,
% 0.27/0.46 ( prop2setE
% 0.27/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.27/0.46 => Xphi ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetE_type,type,
% 0.27/0.46 emptysetE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetE,definition,
% 0.27/0.46 ( emptysetE
% 0.27/0.46 = ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ emptyset )
% 0.27/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetimpfalse_type,type,
% 0.27/0.46 emptysetimpfalse: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetimpfalse,definition,
% 0.27/0.46 ( emptysetimpfalse
% 0.27/0.46 = ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ emptyset )
% 0.27/0.46 => $false ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(notinemptyset_type,type,
% 0.27/0.46 notinemptyset: $o ).
% 0.27/0.46
% 0.27/0.46 thf(notinemptyset,definition,
% 0.27/0.46 ( notinemptyset
% 0.27/0.46 = ( ! [Xx: $i] :
% 0.27/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exuE3e_type,type,
% 0.27/0.46 exuE3e: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exuE3e,definition,
% 0.27/0.46 ( exuE3e
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setext_type,type,
% 0.27/0.46 setext: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setext,definition,
% 0.27/0.46 ( setext
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( in @ Xx @ B ) )
% 0.27/0.46 => ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 => ( in @ Xx @ A ) )
% 0.27/0.46 => ( A = B ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptyI_type,type,
% 0.27/0.46 emptyI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptyI,definition,
% 0.27/0.46 ( emptyI
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ~ ( in @ Xx @ A )
% 0.27/0.46 => ( A = emptyset ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(noeltsimpempty_type,type,
% 0.27/0.46 noeltsimpempty: $o ).
% 0.27/0.46
% 0.27/0.46 thf(noeltsimpempty,definition,
% 0.27/0.46 ( noeltsimpempty
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ~ ( in @ Xx @ A )
% 0.27/0.46 => ( A = emptyset ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setbeta_type,type,
% 0.27/0.46 setbeta: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setbeta,definition,
% 0.27/0.46 ( setbeta
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( ( in @ Xx
% 0.27/0.46 @ ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(nonempty_type,type,
% 0.27/0.46 nonempty: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(nonempty,definition,
% 0.27/0.46 ( nonempty
% 0.27/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyE1_type,type,
% 0.27/0.46 nonemptyE1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyE1,definition,
% 0.27/0.46 ( nonemptyE1
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ( nonempty @ A )
% 0.27/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyI_type,type,
% 0.27/0.46 nonemptyI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyI,definition,
% 0.27/0.46 ( nonemptyI
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( ( Xphi @ Xx )
% 0.27/0.46 => ( nonempty
% 0.27/0.46 @ ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyI1_type,type,
% 0.27/0.46 nonemptyI1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyI1,definition,
% 0.27/0.46 ( nonemptyI1
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.27/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinIL_type,type,
% 0.27/0.46 setadjoinIL: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinIL,definition,
% 0.27/0.46 ( setadjoinIL
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptyinunitempty_type,type,
% 0.27/0.46 emptyinunitempty: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptyinunitempty,definition,
% 0.27/0.46 ( emptyinunitempty
% 0.27/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinIR_type,type,
% 0.27/0.46 setadjoinIR: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinIR,definition,
% 0.27/0.46 ( setadjoinIR
% 0.27/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ A )
% 0.27/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinE_type,type,
% 0.27/0.46 setadjoinE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinE,definition,
% 0.27/0.46 ( setadjoinE
% 0.27/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.46 => ! [Xphi: $o] :
% 0.27/0.46 ( ( ( Xy = Xx )
% 0.27/0.46 => Xphi )
% 0.27/0.46 => ( ( ( in @ Xy @ A )
% 0.27/0.46 => Xphi )
% 0.27/0.46 => Xphi ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinOr_type,type,
% 0.27/0.46 setadjoinOr: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinOr,definition,
% 0.27/0.46 ( setadjoinOr
% 0.27/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.46 => ( ( Xy = Xx )
% 0.27/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setoftrueEq_type,type,
% 0.27/0.46 setoftrueEq: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setoftrueEq,definition,
% 0.27/0.46 ( setoftrueEq
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xx: $i] : $true )
% 0.27/0.46 = A ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(powersetI_type,type,
% 0.27/0.46 powersetI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(powersetI,definition,
% 0.27/0.46 ( powersetI
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 => ( in @ Xx @ A ) )
% 0.27/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptyinPowerset_type,type,
% 0.27/0.46 emptyinPowerset: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptyinPowerset,definition,
% 0.27/0.46 ( emptyinPowerset
% 0.27/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptyInPowerset_type,type,
% 0.27/0.46 emptyInPowerset: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptyInPowerset,definition,
% 0.27/0.46 ( emptyInPowerset
% 0.27/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(powersetE_type,type,
% 0.27/0.46 powersetE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(powersetE,definition,
% 0.27/0.46 ( powersetE
% 0.27/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.46 => ( ( in @ Xx @ B )
% 0.27/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setunionI_type,type,
% 0.27/0.46 setunionI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setunionI,definition,
% 0.27/0.46 ( setunionI
% 0.27/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 => ( ( in @ B @ A )
% 0.27/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setunionE_type,type,
% 0.27/0.46 setunionE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setunionE,definition,
% 0.27/0.46 ( setunionE
% 0.27/0.46 = ( ! [A: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.46 => ! [Xphi: $o] :
% 0.27/0.46 ( ! [B: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 => ( ( in @ B @ A )
% 0.27/0.46 => Xphi ) )
% 0.27/0.46 => Xphi ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(subPowSU_type,type,
% 0.27/0.46 subPowSU: $o ).
% 0.27/0.46
% 0.27/0.46 thf(subPowSU,definition,
% 0.27/0.46 ( subPowSU
% 0.27/0.46 = ( ! [A: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exuE2_type,type,
% 0.27/0.46 exuE2: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exuE2,definition,
% 0.27/0.46 ( exuE2
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 => ? [Xx: $i] :
% 0.27/0.46 ! [Xy: $i] :
% 0.27/0.46 ( ( Xphi @ Xy )
% 0.27/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyImpWitness_type,type,
% 0.27/0.46 nonemptyImpWitness: $o ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyImpWitness,definition,
% 0.27/0.46 ( nonemptyImpWitness
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ( nonempty @ A )
% 0.27/0.46 => ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & $true ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(uniqinunit_type,type,
% 0.27/0.46 uniqinunit: $o ).
% 0.27/0.46
% 0.27/0.46 thf(uniqinunit,definition,
% 0.27/0.46 ( uniqinunit
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(notinsingleton_type,type,
% 0.27/0.46 notinsingleton: $o ).
% 0.27/0.46
% 0.27/0.46 thf(notinsingleton,definition,
% 0.27/0.46 ( notinsingleton
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( Xx != Xy )
% 0.27/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(eqinunit_type,type,
% 0.27/0.46 eqinunit: $o ).
% 0.27/0.46
% 0.27/0.46 thf(eqinunit,definition,
% 0.27/0.46 ( eqinunit
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( Xx = Xy )
% 0.27/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(singletonsswitch_type,type,
% 0.27/0.46 singletonsswitch: $o ).
% 0.27/0.46
% 0.27/0.46 thf(singletonsswitch,definition,
% 0.27/0.46 ( singletonsswitch
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(upairsetE_type,type,
% 0.27/0.46 upairsetE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(upairsetE,definition,
% 0.27/0.46 ( upairsetE
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.27/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.27/0.46 => ( ( Xz = Xx )
% 0.27/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(upairsetIL_type,type,
% 0.27/0.46 upairsetIL: $o ).
% 0.27/0.46
% 0.27/0.46 thf(upairsetIL,definition,
% 0.27/0.46 ( upairsetIL
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(upairsetIR_type,type,
% 0.27/0.46 upairsetIR: $o ).
% 0.27/0.46
% 0.27/0.46 thf(upairsetIR,definition,
% 0.27/0.46 ( upairsetIR
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptyE1_type,type,
% 0.27/0.46 emptyE1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptyE1,definition,
% 0.27/0.46 ( emptyE1
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ( Xphi @ Xx ) )
% 0.27/0.46 => ( ( ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 = emptyset )
% 0.27/0.46 => $false ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(vacuousDall_type,type,
% 0.27/0.46 vacuousDall: $o ).
% 0.27/0.46
% 0.27/0.46 thf(vacuousDall,definition,
% 0.27/0.46 ( vacuousDall
% 0.27/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ emptyset )
% 0.27/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan1_type,type,
% 0.27/0.46 quantDeMorgan1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan1,definition,
% 0.27/0.46 ( quantDeMorgan1
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ~ ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( Xphi @ Xx ) )
% 0.27/0.46 => ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan2_type,type,
% 0.27/0.46 quantDeMorgan2: $o ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan2,definition,
% 0.27/0.46 ( quantDeMorgan2
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ~ ( Xphi @ Xx ) )
% 0.27/0.46 => ~ ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan3_type,type,
% 0.27/0.46 quantDeMorgan3: $o ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan3,definition,
% 0.27/0.46 ( quantDeMorgan3
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ~ ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ( Xphi @ Xx ) )
% 0.27/0.46 => ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan4_type,type,
% 0.27/0.46 quantDeMorgan4: $o ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan4,definition,
% 0.27/0.46 ( quantDeMorgan4
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ~ ( Xphi @ Xx ) )
% 0.27/0.46 => ~ ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(prop2setI_type,type,
% 0.27/0.46 prop2setI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(prop2setI,definition,
% 0.27/0.46 ( prop2setI
% 0.27/0.46 = ( ! [Xphi: $o] :
% 0.27/0.46 ( Xphi
% 0.27/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(set2prop_type,type,
% 0.27/0.46 set2prop: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(prop2set2propI_type,type,
% 0.27/0.46 prop2set2propI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(prop2set2propI,definition,
% 0.27/0.46 ( prop2set2propI
% 0.27/0.46 = ( ! [Xphi: $o] :
% 0.27/0.46 ( Xphi
% 0.27/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(notdexE_type,type,
% 0.27/0.46 notdexE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(notdexE,definition,
% 0.27/0.46 ( notdexE
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ~ ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ( Xphi @ Xx ) )
% 0.27/0.46 => ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(notdallE_type,type,
% 0.27/0.46 notdallE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(notdallE,definition,
% 0.27/0.46 ( notdallE
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ~ ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( Xphi @ Xx ) )
% 0.27/0.46 => ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exuI1_type,type,
% 0.27/0.46 exuI1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exuI1,definition,
% 0.27/0.46 ( exuI1
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ? [Xx: $i] :
% 0.27/0.46 ( ( Xphi @ Xx )
% 0.27/0.46 & ! [Xy: $i] :
% 0.27/0.46 ( ( Xphi @ Xy )
% 0.27/0.46 => ( Xx = Xy ) ) )
% 0.27/0.46 => ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exuI3_type,type,
% 0.27/0.46 exuI3: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exuI3,definition,
% 0.27/0.46 ( exuI3
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.27/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( Xphi @ Xx )
% 0.27/0.47 => ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) )
% 0.27/0.47 => ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exuI2_type,type,
% 0.27/0.47 exuI2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exuI2,definition,
% 0.27/0.47 ( exuI2
% 0.27/0.47 = ( ! [Xphi: $i > $o] :
% 0.27/0.47 ( ? [Xx: $i] :
% 0.27/0.47 ! [Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xy )
% 0.27/0.47 <=> ( Xy = Xx ) )
% 0.27/0.47 => ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(inCongP_type,type,
% 0.27/0.47 inCongP: $o ).
% 0.27/0.47
% 0.27/0.47 thf(inCongP,definition,
% 0.27/0.47 ( inCongP
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx = Xy )
% 0.27/0.47 => ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(in__Cong_type,type,
% 0.27/0.47 in__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(in__Cong,definition,
% 0.27/0.47 ( in__Cong
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx = Xy )
% 0.27/0.47 => ( ( in @ Xx @ A )
% 0.27/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exuE3u_type,type,
% 0.27/0.47 exuE3u: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exuE3u,definition,
% 0.27/0.47 ( exuE3u
% 0.27/0.47 = ( ! [Xphi: $i > $o] :
% 0.27/0.47 ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 => ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xx )
% 0.27/0.47 => ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exu__Cong_type,type,
% 0.27/0.47 exu__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exu__Cong,definition,
% 0.27/0.47 ( exu__Cong
% 0.27/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx = Xy )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.27/0.47 => ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 <=> ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(emptyset__Cong_type,type,
% 0.27/0.47 emptyset__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(emptyset__Cong,definition,
% 0.27/0.47 ( emptyset__Cong
% 0.27/0.47 = ( emptyset = emptyset ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoin__Cong_type,type,
% 0.27/0.47 setadjoin__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoin__Cong,definition,
% 0.27/0.47 ( setadjoin__Cong
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx = Xy )
% 0.27/0.47 => ! [Xz: $i,Xu: $i] :
% 0.27/0.47 ( ( Xz = Xu )
% 0.27/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.27/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powerset__Cong_type,type,
% 0.27/0.47 powerset__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powerset__Cong,definition,
% 0.27/0.47 ( powerset__Cong
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ( ( powerset @ A )
% 0.27/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setunion__Cong_type,type,
% 0.27/0.47 setunion__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setunion__Cong,definition,
% 0.27/0.47 ( setunion__Cong
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ( ( setunion @ A )
% 0.27/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(omega__Cong_type,type,
% 0.27/0.47 omega__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(omega__Cong,definition,
% 0.27/0.47 ( omega__Cong
% 0.27/0.47 = ( omega = omega ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exuEu_type,type,
% 0.27/0.47 exuEu: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exuEu,definition,
% 0.27/0.47 ( exuEu
% 0.27/0.47 = ( ! [Xphi: $i > $o] :
% 0.27/0.47 ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 => ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xx )
% 0.27/0.47 => ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(descr__Cong_type,type,
% 0.27/0.47 descr__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(descr__Cong,definition,
% 0.27/0.47 ( descr__Cong
% 0.27/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx = Xy )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.27/0.47 => ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 => ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.27/0.47 => ( ( descr
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 = ( descr
% 0.27/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(dsetconstr__Cong_type,type,
% 0.27/0.47 dsetconstr__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(dsetconstr__Cong,definition,
% 0.27/0.47 ( dsetconstr__Cong
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( Xx = Xy )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.27/0.47 => ( ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 = ( dsetconstr @ B
% 0.27/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subset_type,type,
% 0.27/0.47 subset: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(disjoint_type,type,
% 0.27/0.47 disjoint: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(setsmeet_type,type,
% 0.27/0.47 setsmeet: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetI1_type,type,
% 0.27/0.47 subsetI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetI1,definition,
% 0.27/0.47 ( subsetI1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xx @ B ) )
% 0.27/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(eqimpsubset2_type,type,
% 0.27/0.47 eqimpsubset2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(eqimpsubset2,definition,
% 0.27/0.47 ( eqimpsubset2
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(eqimpsubset1_type,type,
% 0.27/0.47 eqimpsubset1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(eqimpsubset1,definition,
% 0.27/0.47 ( eqimpsubset1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetI2_type,type,
% 0.27/0.47 subsetI2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetI2,definition,
% 0.27/0.47 ( subsetI2
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xx @ B ) )
% 0.27/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(emptysetsubset_type,type,
% 0.27/0.47 emptysetsubset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(emptysetsubset,definition,
% 0.27/0.47 ( emptysetsubset
% 0.27/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetE_type,type,
% 0.27/0.47 subsetE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetE,definition,
% 0.27/0.47 ( subsetE
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetE2_type,type,
% 0.27/0.47 subsetE2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetE2,definition,
% 0.27/0.47 ( subsetE2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(notsubsetI_type,type,
% 0.27/0.47 notsubsetI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(notsubsetI,definition,
% 0.27/0.47 ( notsubsetI
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(notequalI1_type,type,
% 0.27/0.47 notequalI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(notequalI1,definition,
% 0.27/0.47 ( notequalI1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ~ ( subset @ A @ B )
% 0.27/0.47 => ( A != B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(notequalI2_type,type,
% 0.27/0.47 notequalI2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(notequalI2,definition,
% 0.27/0.47 ( notequalI2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ( A != B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetRefl_type,type,
% 0.27/0.47 subsetRefl: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetRefl,definition,
% 0.27/0.47 ( subsetRefl
% 0.27/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetTrans_type,type,
% 0.27/0.47 subsetTrans: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetTrans,definition,
% 0.27/0.47 ( subsetTrans
% 0.27/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ( subset @ B @ C )
% 0.27/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinSub_type,type,
% 0.27/0.47 setadjoinSub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinSub,definition,
% 0.27/0.47 ( setadjoinSub
% 0.27/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinSub2_type,type,
% 0.27/0.47 setadjoinSub2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinSub2,definition,
% 0.27/0.47 ( setadjoinSub2
% 0.27/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subset2powerset_type,type,
% 0.27/0.47 subset2powerset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subset2powerset,definition,
% 0.27/0.47 ( subset2powerset
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setextsub_type,type,
% 0.27/0.47 setextsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setextsub,definition,
% 0.27/0.47 ( setextsub
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ( subset @ B @ A )
% 0.27/0.47 => ( A = B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetemptysetimpeq_type,type,
% 0.27/0.47 subsetemptysetimpeq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetemptysetimpeq,definition,
% 0.27/0.47 ( subsetemptysetimpeq
% 0.27/0.47 = ( ! [A: $i] :
% 0.27/0.47 ( ( subset @ A @ emptyset )
% 0.27/0.47 => ( A = emptyset ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetI1_type,type,
% 0.27/0.47 powersetI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetI1,definition,
% 0.27/0.47 ( powersetI1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ B @ A )
% 0.27/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetE1,conjecture,
% 0.27/0.47 ( setextAx
% 0.27/0.47 => ( emptysetAx
% 0.27/0.47 => ( setadjoinAx
% 0.27/0.47 => ( powersetAx
% 0.27/0.47 => ( setunionAx
% 0.27/0.47 => ( omega0Ax
% 0.27/0.47 => ( omegaSAx
% 0.27/0.47 => ( omegaIndAx
% 0.27/0.47 => ( replAx
% 0.27/0.47 => ( foundationAx
% 0.27/0.47 => ( wellorderingAx
% 0.27/0.47 => ( descrp
% 0.27/0.47 => ( dsetconstrI
% 0.27/0.47 => ( dsetconstrEL
% 0.27/0.47 => ( dsetconstrER
% 0.27/0.47 => ( exuE1
% 0.27/0.47 => ( prop2setE
% 0.27/0.47 => ( emptysetE
% 0.27/0.47 => ( emptysetimpfalse
% 0.27/0.47 => ( notinemptyset
% 0.27/0.47 => ( exuE3e
% 0.27/0.47 => ( setext
% 0.27/0.47 => ( emptyI
% 0.27/0.47 => ( noeltsimpempty
% 0.27/0.47 => ( setbeta
% 0.27/0.47 => ( nonemptyE1
% 0.27/0.47 => ( nonemptyI
% 0.27/0.47 => ( nonemptyI1
% 0.27/0.47 => ( setadjoinIL
% 0.27/0.47 => ( emptyinunitempty
% 0.27/0.47 => ( setadjoinIR
% 0.27/0.47 => ( setadjoinE
% 0.27/0.47 => ( setadjoinOr
% 0.27/0.47 => ( setoftrueEq
% 0.27/0.47 => ( powersetI
% 0.27/0.47 => ( emptyinPowerset
% 0.27/0.47 => ( emptyInPowerset
% 0.27/0.47 => ( powersetE
% 0.27/0.47 => ( setunionI
% 0.27/0.47 => ( setunionE
% 0.27/0.47 => ( subPowSU
% 0.27/0.47 => ( exuE2
% 0.27/0.47 => ( nonemptyImpWitness
% 0.27/0.47 => ( uniqinunit
% 0.27/0.47 => ( notinsingleton
% 0.27/0.47 => ( eqinunit
% 0.27/0.47 => ( singletonsswitch
% 0.27/0.47 => ( upairsetE
% 0.27/0.47 => ( upairsetIL
% 0.27/0.47 => ( upairsetIR
% 0.27/0.47 => ( emptyE1
% 0.27/0.47 => ( vacuousDall
% 0.27/0.47 => ( quantDeMorgan1
% 0.27/0.47 => ( quantDeMorgan2
% 0.27/0.47 => ( quantDeMorgan3
% 0.27/0.47 => ( quantDeMorgan4
% 0.27/0.47 => ( prop2setI
% 0.27/0.47 => ( prop2set2propI
% 0.27/0.47 => ( notdexE
% 0.27/0.47 => ( notdallE
% 0.27/0.47 => ( exuI1
% 0.27/0.47 => ( exuI3
% 0.27/0.47 => ( exuI2
% 0.27/0.47 => ( inCongP
% 0.27/0.47 => ( in__Cong
% 0.27/0.47 => ( exuE3u
% 0.27/0.47 => ( exu__Cong
% 0.27/0.47 => ( emptyset__Cong
% 0.27/0.47 => ( setadjoin__Cong
% 0.27/0.47 => ( powerset__Cong
% 0.27/0.47 => ( setunion__Cong
% 0.27/0.47 => ( omega__Cong
% 0.27/0.47 => ( exuEu
% 0.27/0.47 => ( descr__Cong
% 0.27/0.47 => ( dsetconstr__Cong
% 0.27/0.47 => ( subsetI1
% 0.27/0.47 => ( eqimpsubset2
% 0.27/0.47 => ( eqimpsubset1
% 0.27/0.47 => ( subsetI2
% 0.27/0.47 => ( emptysetsubset
% 0.27/0.47 => ( subsetE
% 0.27/0.47 => ( subsetE2
% 0.27/0.47 => ( notsubsetI
% 0.27/0.47 => ( notequalI1
% 0.27/0.47 => ( notequalI2
% 0.27/0.47 => ( subsetRefl
% 0.27/0.47 => ( subsetTrans
% 0.27/0.47 => ( setadjoinSub
% 0.27/0.47 => ( setadjoinSub2
% 0.27/0.47 => ( subset2powerset
% 0.27/0.47 => ( setextsub
% 0.27/0.47 => ( subsetemptysetimpeq
% 0.27/0.47 => ( powersetI1
% 0.27/0.47 => ! [A: $i,B: $i] :
% 0.27/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.47 => ( subset @ B @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 2.15/1.43 ---- Embedded in THF ---
% 2.15/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.15/1.43 %%% Generated on Tue Feb 24 12:27:17 EST 2026
% 2.15/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 2.15/1.43 %%% Logic specification used:
% 2.15/1.43 %%% thf(spec, logic, $$dhol).
% 2.15/1.43
% 2.15/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.JqQVLhIiKp/DTF2DTF18696.p
% See solution above
% 2.15/1.43 ------------------------
% 2.15/1.46 ---- Cleaned THF ---
% 2.15/1.46 thf(in_type,type,
% 2.15/1.46 in: $i > $i > $o ).
% 2.15/1.46
% 2.15/1.46 thf(exu_type,type,
% 2.15/1.46 exu: ( $i > $o ) > $o ).
% 2.15/1.46
% 2.15/1.46 thf(exu,definition,
% 2.15/1.46 ( exu
% 2.15/1.46 = ( ^ [Xphi: $i > $o] :
% 2.15/1.46 ? [Xx: $i] :
% 2.15/1.46 ( ( Xphi @ Xx )
% 2.15/1.46 & ! [Xy: $i] :
% 2.15/1.46 ( ( Xphi @ Xy )
% 2.15/1.46 => ( Xx = Xy ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setextAx_type,type,
% 2.15/1.46 setextAx: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setextAx,definition,
% 2.15/1.46 ( setextAx
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 <=> ( in @ Xx @ B ) )
% 2.15/1.46 => ( A = B ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(emptyset_type,type,
% 2.15/1.46 emptyset: $i ).
% 2.15/1.46
% 2.15/1.46 thf(emptysetAx_type,type,
% 2.15/1.46 emptysetAx: $o ).
% 2.15/1.46
% 2.15/1.46 thf(emptysetAx,definition,
% 2.15/1.46 ( emptysetAx
% 2.15/1.46 = ( ! [Xx: $i] :
% 2.15/1.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoin_type,type,
% 2.15/1.46 setadjoin: $i > $i > $i ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinAx_type,type,
% 2.15/1.46 setadjoinAx: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinAx,definition,
% 2.15/1.46 ( setadjoinAx
% 2.15/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.15/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.15/1.46 <=> ( ( Xy = Xx )
% 2.15/1.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(powerset_type,type,
% 2.15/1.46 powerset: $i > $i ).
% 2.15/1.46
% 2.15/1.46 thf(powersetAx_type,type,
% 2.15/1.46 powersetAx: $o ).
% 2.15/1.46
% 2.15/1.46 thf(powersetAx,definition,
% 2.15/1.46 ( powersetAx
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ( in @ B @ ( powerset @ A ) )
% 2.15/1.46 <=> ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ B )
% 2.15/1.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setunion_type,type,
% 2.15/1.46 setunion: $i > $i ).
% 2.15/1.46
% 2.15/1.46 thf(setunionAx_type,type,
% 2.15/1.46 setunionAx: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setunionAx,definition,
% 2.15/1.46 ( setunionAx
% 2.15/1.46 = ( ! [A: $i,Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ ( setunion @ A ) )
% 2.15/1.46 <=> ? [B: $i] :
% 2.15/1.46 ( ( in @ Xx @ B )
% 2.15/1.46 & ( in @ B @ A ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(omega_type,type,
% 2.15/1.46 omega: $i ).
% 2.15/1.46
% 2.15/1.46 thf(omega0Ax_type,type,
% 2.15/1.46 omega0Ax: $o ).
% 2.15/1.46
% 2.15/1.46 thf(omega0Ax,definition,
% 2.15/1.46 ( omega0Ax
% 2.15/1.46 = ( in @ emptyset @ omega ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(omegaSAx_type,type,
% 2.15/1.46 omegaSAx: $o ).
% 2.15/1.46
% 2.15/1.46 thf(omegaSAx,definition,
% 2.15/1.46 ( omegaSAx
% 2.15/1.46 = ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ omega )
% 2.15/1.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(omegaIndAx_type,type,
% 2.15/1.46 omegaIndAx: $o ).
% 2.15/1.46
% 2.15/1.46 thf(omegaIndAx,definition,
% 2.15/1.46 ( omegaIndAx
% 2.15/1.46 = ( ! [A: $i] :
% 2.15/1.46 ( ( ( in @ emptyset @ A )
% 2.15/1.46 & ! [Xx: $i] :
% 2.15/1.46 ( ( ( in @ Xx @ omega )
% 2.15/1.46 & ( in @ Xx @ A ) )
% 2.15/1.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.15/1.46 => ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ omega )
% 2.15/1.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(replAx_type,type,
% 2.15/1.46 replAx: $o ).
% 2.15/1.46
% 2.15/1.46 thf(replAx,definition,
% 2.15/1.46 ( replAx
% 2.15/1.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.15/1.46 ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ( exu
% 2.15/1.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.15/1.46 => ? [B: $i] :
% 2.15/1.46 ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ B )
% 2.15/1.46 <=> ? [Xy: $i] :
% 2.15/1.46 ( ( in @ Xy @ A )
% 2.15/1.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(foundationAx_type,type,
% 2.15/1.46 foundationAx: $o ).
% 2.15/1.46
% 2.15/1.46 thf(foundationAx,definition,
% 2.15/1.46 ( foundationAx
% 2.15/1.46 = ( ! [A: $i] :
% 2.15/1.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.15/1.46 => ? [B: $i] :
% 2.15/1.46 ( ( in @ B @ A )
% 2.15/1.46 & ~ ? [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ B )
% 2.15/1.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(wellorderingAx_type,type,
% 2.15/1.46 wellorderingAx: $o ).
% 2.15/1.46
% 2.15/1.46 thf(wellorderingAx,definition,
% 2.15/1.46 ( wellorderingAx
% 2.15/1.46 = ( ! [A: $i] :
% 2.15/1.46 ? [B: $i] :
% 2.15/1.46 ( ! [C: $i] :
% 2.15/1.46 ( ( in @ C @ B )
% 2.15/1.46 => ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ C )
% 2.15/1.46 => ( in @ Xx @ A ) ) )
% 2.15/1.46 & ! [Xx: $i,Xy: $i] :
% 2.15/1.46 ( ( ( in @ Xx @ A )
% 2.15/1.46 & ( in @ Xy @ A ) )
% 2.15/1.46 => ( ! [C: $i] :
% 2.15/1.46 ( ( in @ C @ B )
% 2.15/1.46 => ( ( in @ Xx @ C )
% 2.15/1.46 <=> ( in @ Xy @ C ) ) )
% 2.15/1.46 => ( Xx = Xy ) ) )
% 2.15/1.46 & ! [C: $i,D: $i] :
% 2.15/1.46 ( ( ( in @ C @ B )
% 2.15/1.46 & ( in @ D @ B ) )
% 2.15/1.46 => ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ C )
% 2.15/1.46 => ( in @ Xx @ D ) )
% 2.15/1.46 | ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ D )
% 2.15/1.46 => ( in @ Xx @ C ) ) ) )
% 2.15/1.46 & ! [C: $i] :
% 2.15/1.46 ( ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ C )
% 2.15/1.46 => ( in @ Xx @ A ) )
% 2.15/1.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.15/1.46 => ? [D: $i,Xx: $i] :
% 2.15/1.46 ( ( in @ D @ B )
% 2.15/1.46 & ( in @ Xx @ C )
% 2.15/1.46 & ~ ? [Xy: $i] :
% 2.15/1.46 ( ( in @ Xy @ D )
% 2.15/1.46 & ( in @ Xy @ C ) )
% 2.15/1.46 & ! [E: $i] :
% 2.15/1.46 ( ( in @ E @ B )
% 2.15/1.46 => ( ! [Xy: $i] :
% 2.15/1.46 ( ( in @ Xy @ E )
% 2.15/1.46 => ( in @ Xy @ D ) )
% 2.15/1.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(descr_type,type,
% 2.15/1.46 descr: ( $i > $o ) > $i ).
% 2.15/1.46
% 2.15/1.46 thf(descrp_type,type,
% 2.15/1.46 descrp: $o ).
% 2.15/1.46
% 2.15/1.46 thf(descrp,definition,
% 2.15/1.46 ( descrp
% 2.15/1.46 = ( ! [Xphi: $i > $o] :
% 2.15/1.46 ( ( exu
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.15/1.46 => ( Xphi
% 2.15/1.46 @ ( descr
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(dsetconstr_type,type,
% 2.15/1.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.15/1.46
% 2.15/1.46 thf(dsetconstrI_type,type,
% 2.15/1.46 dsetconstrI: $o ).
% 2.15/1.46
% 2.15/1.46 thf(dsetconstrI,definition,
% 2.15/1.46 ( dsetconstrI
% 2.15/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ( ( Xphi @ Xx )
% 2.15/1.46 => ( in @ Xx
% 2.15/1.46 @ ( dsetconstr @ A
% 2.15/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(dsetconstrEL_type,type,
% 2.15/1.46 dsetconstrEL: $o ).
% 2.15/1.46
% 2.15/1.46 thf(dsetconstrEL,definition,
% 2.15/1.46 ( dsetconstrEL
% 2.15/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.15/1.46 ( ( in @ Xx
% 2.15/1.46 @ ( dsetconstr @ A
% 2.15/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.15/1.46 => ( in @ Xx @ A ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(dsetconstrER_type,type,
% 2.15/1.46 dsetconstrER: $o ).
% 2.15/1.46
% 2.15/1.46 thf(dsetconstrER,definition,
% 2.15/1.46 ( dsetconstrER
% 2.15/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.15/1.46 ( ( in @ Xx
% 2.15/1.46 @ ( dsetconstr @ A
% 2.15/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.15/1.46 => ( Xphi @ Xx ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(exuE1_type,type,
% 2.15/1.46 exuE1: $o ).
% 2.15/1.46
% 2.15/1.46 thf(exuE1,definition,
% 2.15/1.46 ( exuE1
% 2.15/1.46 = ( ! [Xphi: $i > $o] :
% 2.15/1.46 ( ( exu
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.15/1.46 => ? [Xx: $i] :
% 2.15/1.46 ( ( Xphi @ Xx )
% 2.15/1.46 & ! [Xy: $i] :
% 2.15/1.46 ( ( Xphi @ Xy )
% 2.15/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(prop2set_type,type,
% 2.15/1.46 prop2set: $o > $i ).
% 2.15/1.46
% 2.15/1.46 thf(prop2setE_type,type,
% 2.15/1.46 prop2setE: $o ).
% 2.15/1.46
% 2.15/1.46 thf(prop2setE,definition,
% 2.15/1.46 ( prop2setE
% 2.15/1.46 = ( ! [Xphi: $o,Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.15/1.46 => Xphi ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(emptysetE_type,type,
% 2.15/1.46 emptysetE: $o ).
% 2.15/1.46
% 2.15/1.46 thf(emptysetE,definition,
% 2.15/1.46 ( emptysetE
% 2.15/1.46 = ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ emptyset )
% 2.15/1.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(emptysetimpfalse_type,type,
% 2.15/1.46 emptysetimpfalse: $o ).
% 2.15/1.46
% 2.15/1.46 thf(emptysetimpfalse,definition,
% 2.15/1.46 ( emptysetimpfalse
% 2.15/1.46 = ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ emptyset )
% 2.15/1.46 => $false ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(notinemptyset_type,type,
% 2.15/1.46 notinemptyset: $o ).
% 2.15/1.46
% 2.15/1.46 thf(notinemptyset,definition,
% 2.15/1.46 ( notinemptyset
% 2.15/1.46 = ( ! [Xx: $i] :
% 2.15/1.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(exuE3e_type,type,
% 2.15/1.46 exuE3e: $o ).
% 2.15/1.46
% 2.15/1.46 thf(exuE3e,definition,
% 2.15/1.46 ( exuE3e
% 2.15/1.46 = ( ! [Xphi: $i > $o] :
% 2.15/1.46 ( ( exu
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.15/1.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setext_type,type,
% 2.15/1.46 setext: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setext,definition,
% 2.15/1.46 ( setext
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ( in @ Xx @ B ) )
% 2.15/1.46 => ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ B )
% 2.15/1.46 => ( in @ Xx @ A ) )
% 2.15/1.46 => ( A = B ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(emptyI_type,type,
% 2.15/1.46 emptyI: $o ).
% 2.15/1.46
% 2.15/1.46 thf(emptyI,definition,
% 2.15/1.46 ( emptyI
% 2.15/1.46 = ( ! [A: $i] :
% 2.15/1.46 ( ! [Xx: $i] :
% 2.15/1.46 ~ ( in @ Xx @ A )
% 2.15/1.46 => ( A = emptyset ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(noeltsimpempty_type,type,
% 2.15/1.46 noeltsimpempty: $o ).
% 2.15/1.46
% 2.15/1.46 thf(noeltsimpempty,definition,
% 2.15/1.46 ( noeltsimpempty
% 2.15/1.46 = ( ! [A: $i] :
% 2.15/1.46 ( ! [Xx: $i] :
% 2.15/1.46 ~ ( in @ Xx @ A )
% 2.15/1.46 => ( A = emptyset ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setbeta_type,type,
% 2.15/1.46 setbeta: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setbeta,definition,
% 2.15/1.46 ( setbeta
% 2.15/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ( ( in @ Xx
% 2.15/1.46 @ ( dsetconstr @ A
% 2.15/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.15/1.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(nonempty_type,type,
% 2.15/1.46 nonempty: $i > $o ).
% 2.15/1.46
% 2.15/1.46 thf(nonempty,definition,
% 2.15/1.46 ( nonempty
% 2.15/1.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(nonemptyE1_type,type,
% 2.15/1.46 nonemptyE1: $o ).
% 2.15/1.46
% 2.15/1.46 thf(nonemptyE1,definition,
% 2.15/1.46 ( nonemptyE1
% 2.15/1.46 = ( ! [A: $i] :
% 2.15/1.46 ( ( nonempty @ A )
% 2.15/1.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(nonemptyI_type,type,
% 2.15/1.46 nonemptyI: $o ).
% 2.15/1.46
% 2.15/1.46 thf(nonemptyI,definition,
% 2.15/1.46 ( nonemptyI
% 2.15/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ( ( Xphi @ Xx )
% 2.15/1.46 => ( nonempty
% 2.15/1.46 @ ( dsetconstr @ A
% 2.15/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(nonemptyI1_type,type,
% 2.15/1.46 nonemptyI1: $o ).
% 2.15/1.46
% 2.15/1.46 thf(nonemptyI1,definition,
% 2.15/1.46 ( nonemptyI1
% 2.15/1.46 = ( ! [A: $i] :
% 2.15/1.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.15/1.46 => ( nonempty @ A ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinIL_type,type,
% 2.15/1.46 setadjoinIL: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinIL,definition,
% 2.15/1.46 ( setadjoinIL
% 2.15/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(emptyinunitempty_type,type,
% 2.15/1.46 emptyinunitempty: $o ).
% 2.15/1.46
% 2.15/1.46 thf(emptyinunitempty,definition,
% 2.15/1.46 ( emptyinunitempty
% 2.15/1.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinIR_type,type,
% 2.15/1.46 setadjoinIR: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinIR,definition,
% 2.15/1.46 ( setadjoinIR
% 2.15/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.15/1.46 ( ( in @ Xy @ A )
% 2.15/1.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinE_type,type,
% 2.15/1.46 setadjoinE: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinE,definition,
% 2.15/1.46 ( setadjoinE
% 2.15/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.15/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.15/1.46 => ! [Xphi: $o] :
% 2.15/1.46 ( ( ( Xy = Xx )
% 2.15/1.46 => Xphi )
% 2.15/1.46 => ( ( ( in @ Xy @ A )
% 2.15/1.46 => Xphi )
% 2.15/1.46 => Xphi ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinOr_type,type,
% 2.15/1.46 setadjoinOr: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinOr,definition,
% 2.15/1.46 ( setadjoinOr
% 2.15/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.15/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.15/1.46 => ( ( Xy = Xx )
% 2.15/1.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setoftrueEq_type,type,
% 2.15/1.46 setoftrueEq: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setoftrueEq,definition,
% 2.15/1.46 ( setoftrueEq
% 2.15/1.46 = ( ! [A: $i] :
% 2.15/1.46 ( ( dsetconstr @ A
% 2.15/1.46 @ ^ [Xx: $i] : $true )
% 2.15/1.46 = A ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(powersetI_type,type,
% 2.15/1.46 powersetI: $o ).
% 2.15/1.46
% 2.15/1.46 thf(powersetI,definition,
% 2.15/1.46 ( powersetI
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ B )
% 2.15/1.46 => ( in @ Xx @ A ) )
% 2.15/1.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(emptyinPowerset_type,type,
% 2.15/1.46 emptyinPowerset: $o ).
% 2.15/1.46
% 2.15/1.46 thf(emptyinPowerset,definition,
% 2.15/1.46 ( emptyinPowerset
% 2.15/1.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(emptyInPowerset_type,type,
% 2.15/1.46 emptyInPowerset: $o ).
% 2.15/1.46
% 2.15/1.46 thf(emptyInPowerset,definition,
% 2.15/1.46 ( emptyInPowerset
% 2.15/1.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(powersetE_type,type,
% 2.15/1.46 powersetE: $o ).
% 2.15/1.46
% 2.15/1.46 thf(powersetE,definition,
% 2.15/1.46 ( powersetE
% 2.15/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.15/1.46 ( ( in @ B @ ( powerset @ A ) )
% 2.15/1.46 => ( ( in @ Xx @ B )
% 2.15/1.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setunionI_type,type,
% 2.15/1.46 setunionI: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setunionI,definition,
% 2.15/1.46 ( setunionI
% 2.15/1.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.15/1.46 ( ( in @ Xx @ B )
% 2.15/1.46 => ( ( in @ B @ A )
% 2.15/1.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setunionE_type,type,
% 2.15/1.46 setunionE: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setunionE,definition,
% 2.15/1.46 ( setunionE
% 2.15/1.46 = ( ! [A: $i,Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ ( setunion @ A ) )
% 2.15/1.46 => ! [Xphi: $o] :
% 2.15/1.46 ( ! [B: $i] :
% 2.15/1.46 ( ( in @ Xx @ B )
% 2.15/1.46 => ( ( in @ B @ A )
% 2.15/1.46 => Xphi ) )
% 2.15/1.46 => Xphi ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(subPowSU_type,type,
% 2.15/1.46 subPowSU: $o ).
% 2.15/1.46
% 2.15/1.46 thf(subPowSU,definition,
% 2.15/1.46 ( subPowSU
% 2.15/1.46 = ( ! [A: $i,Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(exuE2_type,type,
% 2.15/1.46 exuE2: $o ).
% 2.15/1.46
% 2.15/1.46 thf(exuE2,definition,
% 2.15/1.46 ( exuE2
% 2.15/1.46 = ( ! [Xphi: $i > $o] :
% 2.15/1.46 ( ( exu
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.15/1.46 => ? [Xx: $i] :
% 2.15/1.46 ! [Xy: $i] :
% 2.15/1.46 ( ( Xphi @ Xy )
% 2.15/1.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(nonemptyImpWitness_type,type,
% 2.15/1.46 nonemptyImpWitness: $o ).
% 2.15/1.46
% 2.15/1.46 thf(nonemptyImpWitness,definition,
% 2.15/1.46 ( nonemptyImpWitness
% 2.15/1.46 = ( ! [A: $i] :
% 2.15/1.46 ( ( nonempty @ A )
% 2.15/1.46 => ? [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 & $true ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(uniqinunit_type,type,
% 2.15/1.46 uniqinunit: $o ).
% 2.15/1.46
% 2.15/1.46 thf(uniqinunit,definition,
% 2.15/1.46 ( uniqinunit
% 2.15/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.15/1.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.15/1.46 => ( Xx = Xy ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(notinsingleton_type,type,
% 2.15/1.46 notinsingleton: $o ).
% 2.15/1.46
% 2.15/1.46 thf(notinsingleton,definition,
% 2.15/1.46 ( notinsingleton
% 2.15/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.15/1.46 ( ( Xx != Xy )
% 2.15/1.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(eqinunit_type,type,
% 2.15/1.46 eqinunit: $o ).
% 2.15/1.46
% 2.15/1.46 thf(eqinunit,definition,
% 2.15/1.46 ( eqinunit
% 2.15/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.15/1.46 ( ( Xx = Xy )
% 2.15/1.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(singletonsswitch_type,type,
% 2.15/1.46 singletonsswitch: $o ).
% 2.15/1.46
% 2.15/1.46 thf(singletonsswitch,definition,
% 2.15/1.46 ( singletonsswitch
% 2.15/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.15/1.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.15/1.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(upairsetE_type,type,
% 2.15/1.46 upairsetE: $o ).
% 2.15/1.46
% 2.15/1.46 thf(upairsetE,definition,
% 2.15/1.46 ( upairsetE
% 2.15/1.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.15/1.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.15/1.46 => ( ( Xz = Xx )
% 2.15/1.46 | ( Xz = Xy ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(upairsetIL_type,type,
% 2.15/1.46 upairsetIL: $o ).
% 2.15/1.46
% 2.15/1.46 thf(upairsetIL,definition,
% 2.15/1.46 ( upairsetIL
% 2.15/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(upairsetIR_type,type,
% 2.15/1.46 upairsetIR: $o ).
% 2.15/1.46
% 2.15/1.46 thf(upairsetIR,definition,
% 2.15/1.46 ( upairsetIR
% 2.15/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(emptyE1_type,type,
% 2.15/1.46 emptyE1: $o ).
% 2.15/1.46
% 2.15/1.46 thf(emptyE1,definition,
% 2.15/1.46 ( emptyE1
% 2.15/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.15/1.46 ( ? [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 & ( Xphi @ Xx ) )
% 2.15/1.46 => ( ( ( dsetconstr @ A
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.15/1.46 = emptyset )
% 2.15/1.46 => $false ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(vacuousDall_type,type,
% 2.15/1.46 vacuousDall: $o ).
% 2.15/1.46
% 2.15/1.46 thf(vacuousDall,definition,
% 2.15/1.46 ( vacuousDall
% 2.15/1.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ emptyset )
% 2.15/1.46 => ( Xphi @ Xx ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(quantDeMorgan1_type,type,
% 2.15/1.46 quantDeMorgan1: $o ).
% 2.15/1.46
% 2.15/1.46 thf(quantDeMorgan1,definition,
% 2.15/1.46 ( quantDeMorgan1
% 2.15/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.15/1.46 ( ~ ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ( Xphi @ Xx ) )
% 2.15/1.46 => ? [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(quantDeMorgan2_type,type,
% 2.15/1.46 quantDeMorgan2: $o ).
% 2.15/1.46
% 2.15/1.46 thf(quantDeMorgan2,definition,
% 2.15/1.46 ( quantDeMorgan2
% 2.15/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.15/1.46 ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ~ ( Xphi @ Xx ) )
% 2.15/1.46 => ~ ? [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(quantDeMorgan3_type,type,
% 2.15/1.46 quantDeMorgan3: $o ).
% 2.15/1.46
% 2.15/1.46 thf(quantDeMorgan3,definition,
% 2.15/1.46 ( quantDeMorgan3
% 2.15/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.15/1.46 ( ~ ? [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 & ( Xphi @ Xx ) )
% 2.15/1.46 => ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(quantDeMorgan4_type,type,
% 2.15/1.46 quantDeMorgan4: $o ).
% 2.15/1.46
% 2.15/1.46 thf(quantDeMorgan4,definition,
% 2.15/1.46 ( quantDeMorgan4
% 2.15/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.15/1.46 ( ? [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 & ~ ( Xphi @ Xx ) )
% 2.15/1.46 => ~ ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(prop2setI_type,type,
% 2.15/1.46 prop2setI: $o ).
% 2.15/1.46
% 2.15/1.46 thf(prop2setI,definition,
% 2.15/1.46 ( prop2setI
% 2.15/1.46 = ( ! [Xphi: $o] :
% 2.15/1.46 ( Xphi
% 2.15/1.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(set2prop_type,type,
% 2.15/1.46 set2prop: $i > $o ).
% 2.15/1.46
% 2.15/1.46 thf(prop2set2propI_type,type,
% 2.15/1.46 prop2set2propI: $o ).
% 2.15/1.46
% 2.15/1.46 thf(prop2set2propI,definition,
% 2.15/1.46 ( prop2set2propI
% 2.15/1.46 = ( ! [Xphi: $o] :
% 2.15/1.46 ( Xphi
% 2.15/1.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(notdexE_type,type,
% 2.15/1.46 notdexE: $o ).
% 2.15/1.46
% 2.15/1.46 thf(notdexE,definition,
% 2.15/1.46 ( notdexE
% 2.15/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.15/1.46 ( ~ ? [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 & ( Xphi @ Xx ) )
% 2.15/1.46 => ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(notdallE_type,type,
% 2.15/1.46 notdallE: $o ).
% 2.15/1.46
% 2.15/1.46 thf(notdallE,definition,
% 2.15/1.46 ( notdallE
% 2.15/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.15/1.46 ( ~ ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ( Xphi @ Xx ) )
% 2.15/1.46 => ? [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(exuI1_type,type,
% 2.15/1.46 exuI1: $o ).
% 2.15/1.46
% 2.15/1.46 thf(exuI1,definition,
% 2.15/1.46 ( exuI1
% 2.15/1.46 = ( ! [Xphi: $i > $o] :
% 2.15/1.46 ( ? [Xx: $i] :
% 2.15/1.46 ( ( Xphi @ Xx )
% 2.15/1.46 & ! [Xy: $i] :
% 2.15/1.46 ( ( Xphi @ Xy )
% 2.15/1.46 => ( Xx = Xy ) ) )
% 2.15/1.46 => ( exu
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(exuI3_type,type,
% 2.15/1.46 exuI3: $o ).
% 2.15/1.46
% 2.15/1.46 thf(exuI3,definition,
% 2.15/1.46 ( exuI3
% 2.15/1.46 = ( ! [Xphi: $i > $o] :
% 2.15/1.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.15/1.46 => ( ! [Xx: $i,Xy: $i] :
% 2.15/1.46 ( ( Xphi @ Xx )
% 2.15/1.46 => ( ( Xphi @ Xy )
% 2.15/1.46 => ( Xx = Xy ) ) )
% 2.15/1.46 => ( exu
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(exuI2_type,type,
% 2.15/1.46 exuI2: $o ).
% 2.15/1.46
% 2.15/1.46 thf(exuI2,definition,
% 2.15/1.46 ( exuI2
% 2.15/1.46 = ( ! [Xphi: $i > $o] :
% 2.15/1.46 ( ? [Xx: $i] :
% 2.15/1.46 ! [Xy: $i] :
% 2.15/1.46 ( ( Xphi @ Xy )
% 2.15/1.46 <=> ( Xy = Xx ) )
% 2.15/1.46 => ( exu
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(inCongP_type,type,
% 2.15/1.46 inCongP: $o ).
% 2.15/1.46
% 2.15/1.46 thf(inCongP,definition,
% 2.15/1.46 ( inCongP
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ( A = B )
% 2.15/1.46 => ! [Xx: $i,Xy: $i] :
% 2.15/1.46 ( ( Xx = Xy )
% 2.15/1.46 => ( ( in @ Xx @ A )
% 2.15/1.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(in__Cong_type,type,
% 2.15/1.46 in__Cong: $o ).
% 2.15/1.46
% 2.15/1.46 thf(in__Cong,definition,
% 2.15/1.46 ( in__Cong
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ( A = B )
% 2.15/1.46 => ! [Xx: $i,Xy: $i] :
% 2.15/1.46 ( ( Xx = Xy )
% 2.15/1.46 => ( ( in @ Xx @ A )
% 2.15/1.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(exuE3u_type,type,
% 2.15/1.46 exuE3u: $o ).
% 2.15/1.46
% 2.15/1.46 thf(exuE3u,definition,
% 2.15/1.46 ( exuE3u
% 2.15/1.46 = ( ! [Xphi: $i > $o] :
% 2.15/1.46 ( ( exu
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.15/1.46 => ! [Xx: $i,Xy: $i] :
% 2.15/1.46 ( ( Xphi @ Xx )
% 2.15/1.46 => ( ( Xphi @ Xy )
% 2.15/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(exu__Cong_type,type,
% 2.15/1.46 exu__Cong: $o ).
% 2.15/1.46
% 2.15/1.46 thf(exu__Cong,definition,
% 2.15/1.46 ( exu__Cong
% 2.15/1.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.15/1.46 ( ! [Xx: $i,Xy: $i] :
% 2.15/1.46 ( ( Xx = Xy )
% 2.15/1.46 => ( ( Xphi @ Xx )
% 2.15/1.46 <=> ( Xpsi @ Xy ) ) )
% 2.15/1.46 => ( ( exu
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.15/1.46 <=> ( exu
% 2.15/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(emptyset__Cong_type,type,
% 2.15/1.46 emptyset__Cong: $o ).
% 2.15/1.46
% 2.15/1.46 thf(emptyset__Cong,definition,
% 2.15/1.46 ( emptyset__Cong
% 2.15/1.46 = ( emptyset = emptyset ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoin__Cong_type,type,
% 2.15/1.46 setadjoin__Cong: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoin__Cong,definition,
% 2.15/1.46 ( setadjoin__Cong
% 2.15/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.15/1.46 ( ( Xx = Xy )
% 2.15/1.46 => ! [Xz: $i,Xu: $i] :
% 2.15/1.46 ( ( Xz = Xu )
% 2.15/1.46 => ( ( setadjoin @ Xx @ Xz )
% 2.15/1.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(powerset__Cong_type,type,
% 2.15/1.46 powerset__Cong: $o ).
% 2.15/1.46
% 2.15/1.46 thf(powerset__Cong,definition,
% 2.15/1.46 ( powerset__Cong
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ( A = B )
% 2.15/1.46 => ( ( powerset @ A )
% 2.15/1.46 = ( powerset @ B ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setunion__Cong_type,type,
% 2.15/1.46 setunion__Cong: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setunion__Cong,definition,
% 2.15/1.46 ( setunion__Cong
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ( A = B )
% 2.15/1.46 => ( ( setunion @ A )
% 2.15/1.46 = ( setunion @ B ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(omega__Cong_type,type,
% 2.15/1.46 omega__Cong: $o ).
% 2.15/1.46
% 2.15/1.46 thf(omega__Cong,definition,
% 2.15/1.46 ( omega__Cong
% 2.15/1.46 = ( omega = omega ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(exuEu_type,type,
% 2.15/1.46 exuEu: $o ).
% 2.15/1.46
% 2.15/1.46 thf(exuEu,definition,
% 2.15/1.46 ( exuEu
% 2.15/1.46 = ( ! [Xphi: $i > $o] :
% 2.15/1.46 ( ( exu
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.15/1.46 => ! [Xx: $i,Xy: $i] :
% 2.15/1.46 ( ( Xphi @ Xx )
% 2.15/1.46 => ( ( Xphi @ Xy )
% 2.15/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(descr__Cong_type,type,
% 2.15/1.46 descr__Cong: $o ).
% 2.15/1.46
% 2.15/1.46 thf(descr__Cong,definition,
% 2.15/1.46 ( descr__Cong
% 2.15/1.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.15/1.46 ( ! [Xx: $i,Xy: $i] :
% 2.15/1.46 ( ( Xx = Xy )
% 2.15/1.46 => ( ( Xphi @ Xx )
% 2.15/1.46 <=> ( Xpsi @ Xy ) ) )
% 2.15/1.46 => ( ( exu
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.15/1.46 => ( ( exu
% 2.15/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.15/1.46 => ( ( descr
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.15/1.46 = ( descr
% 2.15/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(dsetconstr__Cong_type,type,
% 2.15/1.46 dsetconstr__Cong: $o ).
% 2.15/1.46
% 2.15/1.46 thf(dsetconstr__Cong,definition,
% 2.15/1.46 ( dsetconstr__Cong
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ( A = B )
% 2.15/1.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.15/1.46 ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ! [Xy: $i] :
% 2.15/1.46 ( ( in @ Xy @ B )
% 2.15/1.46 => ( ( Xx = Xy )
% 2.15/1.46 => ( ( Xphi @ Xx )
% 2.15/1.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.15/1.46 => ( ( dsetconstr @ A
% 2.15/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.15/1.46 = ( dsetconstr @ B
% 2.15/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(subset_type,type,
% 2.15/1.46 subset: $i > $i > $o ).
% 2.15/1.46
% 2.15/1.46 thf(disjoint_type,type,
% 2.15/1.46 disjoint: $i > $i > $o ).
% 2.15/1.46
% 2.15/1.46 thf(setsmeet_type,type,
% 2.15/1.46 setsmeet: $i > $i > $o ).
% 2.15/1.46
% 2.15/1.46 thf(subsetI1_type,type,
% 2.15/1.46 subsetI1: $o ).
% 2.15/1.46
% 2.15/1.46 thf(subsetI1,definition,
% 2.15/1.46 ( subsetI1
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ( in @ Xx @ B ) )
% 2.15/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(eqimpsubset2_type,type,
% 2.15/1.46 eqimpsubset2: $o ).
% 2.15/1.46
% 2.15/1.46 thf(eqimpsubset2,definition,
% 2.15/1.46 ( eqimpsubset2
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ( A = B )
% 2.15/1.46 => ( subset @ B @ A ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(eqimpsubset1_type,type,
% 2.15/1.46 eqimpsubset1: $o ).
% 2.15/1.46
% 2.15/1.46 thf(eqimpsubset1,definition,
% 2.15/1.46 ( eqimpsubset1
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ( A = B )
% 2.15/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(subsetI2_type,type,
% 2.15/1.46 subsetI2: $o ).
% 2.15/1.46
% 2.15/1.46 thf(subsetI2,definition,
% 2.15/1.46 ( subsetI2
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ! [Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ( in @ Xx @ B ) )
% 2.15/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(emptysetsubset_type,type,
% 2.15/1.46 emptysetsubset: $o ).
% 2.15/1.46
% 2.15/1.46 thf(emptysetsubset,definition,
% 2.15/1.46 ( emptysetsubset
% 2.15/1.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(subsetE_type,type,
% 2.15/1.46 subsetE: $o ).
% 2.15/1.46
% 2.15/1.46 thf(subsetE,definition,
% 2.15/1.46 ( subsetE
% 2.15/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.15/1.46 ( ( subset @ A @ B )
% 2.15/1.46 => ( ( in @ Xx @ A )
% 2.15/1.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(subsetE2_type,type,
% 2.15/1.46 subsetE2: $o ).
% 2.15/1.46
% 2.15/1.46 thf(subsetE2,definition,
% 2.15/1.46 ( subsetE2
% 2.15/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.15/1.46 ( ( subset @ A @ B )
% 2.15/1.46 => ( ~ ( in @ Xx @ B )
% 2.15/1.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(notsubsetI_type,type,
% 2.15/1.46 notsubsetI: $o ).
% 2.15/1.46
% 2.15/1.46 thf(notsubsetI,definition,
% 2.15/1.46 ( notsubsetI
% 2.15/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ( ~ ( in @ Xx @ B )
% 2.15/1.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(notequalI1_type,type,
% 2.15/1.46 notequalI1: $o ).
% 2.15/1.46
% 2.15/1.46 thf(notequalI1,definition,
% 2.15/1.46 ( notequalI1
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ~ ( subset @ A @ B )
% 2.15/1.46 => ( A != B ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(notequalI2_type,type,
% 2.15/1.46 notequalI2: $o ).
% 2.15/1.46
% 2.15/1.46 thf(notequalI2,definition,
% 2.15/1.46 ( notequalI2
% 2.15/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.15/1.46 ( ( in @ Xx @ A )
% 2.15/1.46 => ( ~ ( in @ Xx @ B )
% 2.15/1.46 => ( A != B ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(subsetRefl_type,type,
% 2.15/1.46 subsetRefl: $o ).
% 2.15/1.46
% 2.15/1.46 thf(subsetRefl,definition,
% 2.15/1.46 ( subsetRefl
% 2.15/1.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(subsetTrans_type,type,
% 2.15/1.46 subsetTrans: $o ).
% 2.15/1.46
% 2.15/1.46 thf(subsetTrans,definition,
% 2.15/1.46 ( subsetTrans
% 2.15/1.46 = ( ! [A: $i,B: $i,C: $i] :
% 2.15/1.46 ( ( subset @ A @ B )
% 2.15/1.46 => ( ( subset @ B @ C )
% 2.15/1.46 => ( subset @ A @ C ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinSub_type,type,
% 2.15/1.46 setadjoinSub: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinSub,definition,
% 2.15/1.46 ( setadjoinSub
% 2.15/1.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinSub2_type,type,
% 2.15/1.46 setadjoinSub2: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setadjoinSub2,definition,
% 2.15/1.46 ( setadjoinSub2
% 2.15/1.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.15/1.46 ( ( subset @ A @ B )
% 2.15/1.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(subset2powerset_type,type,
% 2.15/1.46 subset2powerset: $o ).
% 2.15/1.46
% 2.15/1.46 thf(subset2powerset,definition,
% 2.15/1.46 ( subset2powerset
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ( subset @ A @ B )
% 2.15/1.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(setextsub_type,type,
% 2.15/1.46 setextsub: $o ).
% 2.15/1.46
% 2.15/1.46 thf(setextsub,definition,
% 2.15/1.46 ( setextsub
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ( subset @ A @ B )
% 2.15/1.46 => ( ( subset @ B @ A )
% 2.15/1.46 => ( A = B ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(subsetemptysetimpeq_type,type,
% 2.15/1.46 subsetemptysetimpeq: $o ).
% 2.15/1.46
% 2.15/1.46 thf(subsetemptysetimpeq,definition,
% 2.15/1.46 ( subsetemptysetimpeq
% 2.15/1.46 = ( ! [A: $i] :
% 2.15/1.46 ( ( subset @ A @ emptyset )
% 2.15/1.46 => ( A = emptyset ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(powersetI1_type,type,
% 2.15/1.46 powersetI1: $o ).
% 2.15/1.46
% 2.15/1.46 thf(powersetI1,definition,
% 2.15/1.46 ( powersetI1
% 2.15/1.46 = ( ! [A: $i,B: $i] :
% 2.15/1.46 ( ( subset @ B @ A )
% 2.15/1.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.15/1.46
% 2.15/1.46 thf(powersetE1,conjecture,
% 2.15/1.46 ( setextAx
% 2.15/1.46 => ( emptysetAx
% 2.15/1.46 => ( setadjoinAx
% 2.15/1.46 => ( powersetAx
% 2.15/1.46 => ( setunionAx
% 2.15/1.46 => ( omega0Ax
% 2.15/1.46 => ( omegaSAx
% 2.15/1.46 => ( omegaIndAx
% 2.15/1.46 => ( replAx
% 2.15/1.46 => ( foundationAx
% 2.15/1.46 => ( wellorderingAx
% 2.15/1.46 => ( descrp
% 2.15/1.46 => ( dsetconstrI
% 2.15/1.46 => ( dsetconstrEL
% 2.15/1.46 => ( dsetconstrER
% 2.15/1.46 => ( exuE1
% 2.15/1.46 => ( prop2setE
% 2.15/1.46 => ( emptysetE
% 2.15/1.46 => ( emptysetimpfalse
% 2.15/1.46 => ( notinemptyset
% 2.15/1.46 => ( exuE3e
% 2.15/1.46 => ( setext
% 2.15/1.46 => ( emptyI
% 2.15/1.46 => ( noeltsimpempty
% 2.15/1.46 => ( setbeta
% 2.15/1.46 => ( nonemptyE1
% 2.15/1.46 => ( nonemptyI
% 2.15/1.46 => ( nonemptyI1
% 2.15/1.46 => ( setadjoinIL
% 2.15/1.46 => ( emptyinunitempty
% 2.15/1.46 => ( setadjoinIR
% 2.15/1.46 => ( setadjoinE
% 2.15/1.46 => ( setadjoinOr
% 2.15/1.46 => ( setoftrueEq
% 2.15/1.46 => ( powersetI
% 2.15/1.46 => ( emptyinPowerset
% 2.15/1.46 => ( emptyInPowerset
% 2.15/1.46 => ( powersetE
% 2.15/1.46 => ( setunionI
% 2.15/1.46 => ( setunionE
% 2.15/1.46 => ( subPowSU
% 2.15/1.46 => ( exuE2
% 2.15/1.46 => ( nonemptyImpWitness
% 2.15/1.46 => ( uniqinunit
% 2.15/1.46 => ( notinsingleton
% 2.15/1.46 => ( eqinunit
% 2.15/1.46 => ( singletonsswitch
% 2.15/1.46 => ( upairsetE
% 2.15/1.46 => ( upairsetIL
% 2.15/1.46 => ( upairsetIR
% 2.15/1.46 => ( emptyE1
% 2.15/1.46 => ( vacuousDall
% 2.15/1.46 => ( quantDeMorgan1
% 2.15/1.46 => ( quantDeMorgan2
% 2.15/1.46 => ( quantDeMorgan3
% 2.15/1.46 => ( quantDeMorgan4
% 2.15/1.46 => ( prop2setI
% 2.15/1.46 => ( prop2set2propI
% 2.15/1.46 => ( notdexE
% 2.15/1.46 => ( notdallE
% 2.15/1.46 => ( exuI1
% 2.15/1.46 => ( exuI3
% 2.15/1.46 => ( exuI2
% 2.15/1.46 => ( inCongP
% 2.15/1.46 => ( in__Cong
% 2.15/1.46 => ( exuE3u
% 2.15/1.46 => ( exu__Cong
% 2.15/1.46 => ( emptyset__Cong
% 2.15/1.46 => ( setadjoin__Cong
% 2.15/1.46 => ( powerset__Cong
% 2.15/1.46 => ( setunion__Cong
% 2.15/1.46 => ( omega__Cong
% 2.15/1.46 => ( exuEu
% 2.15/1.46 => ( descr__Cong
% 2.15/1.46 => ( dsetconstr__Cong
% 2.15/1.46 => ( subsetI1
% 2.15/1.46 => ( eqimpsubset2
% 2.15/1.46 => ( eqimpsubset1
% 2.15/1.46 => ( subsetI2
% 2.15/1.46 => ( emptysetsubset
% 2.15/1.46 => ( subsetE
% 2.15/1.46 => ( subsetE2
% 2.15/1.46 => ( notsubsetI
% 2.15/1.46 => ( notequalI1
% 2.15/1.46 => ( notequalI2
% 2.15/1.46 => ( subsetRefl
% 2.15/1.46 => ( subsetTrans
% 2.15/1.46 => ( setadjoinSub
% 2.15/1.46 => ( setadjoinSub2
% 2.15/1.46 => ( subset2powerset
% 2.15/1.46 => ( setextsub
% 2.15/1.46 => ( subsetemptysetimpeq
% 2.15/1.46 => ( powersetI1
% 2.15/1.46 => ! [A: $i,B: $i] :
% 2.15/1.46 ( ( in @ B @ ( powerset @ A ) )
% 2.15/1.46 => ( subset @ B @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.15/1.46 ------------------------
% 2.15/1.48 % (18968)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/183Mi)
% 2.15/1.48 % (18970)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_18696 for (2999ds/27Mi)
% 2.15/1.49 % (18969)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_18696 for (2999ds/4Mi)
% 2.15/1.49 % (18971)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/2Mi)
% 2.15/1.49 % (18972)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_18696 for (2999ds/2Mi)
% 2.15/1.49 % (18974)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/18Mi)
% 2.15/1.49 % (18973)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_18696 for (2999ds/275Mi)
% 2.15/1.49 % (18971)Instruction limit reached!
% 2.15/1.49 % (18971)------------------------------
% 2.15/1.49 % (18971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.49 % (18971)Termination reason: Unknown
% 2.15/1.49 % (18971)Termination phase: shuffling
% 2.15/1.49
% 2.15/1.49 % (18971)Memory used [KB]: 1151
% 2.15/1.49 % (18971)Time elapsed: 0.003 s
% 2.15/1.49 % (18971)Instructions burned: 2 (million)
% 2.15/1.49 % (18971)------------------------------
% 2.15/1.49 % (18971)------------------------------
% 2.15/1.49 % (18972)Instruction limit reached!
% 2.15/1.49 % (18972)------------------------------
% 2.15/1.49 % (18972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.49 % (18972)Termination reason: Unknown
% 2.15/1.49 % (18972)Termination phase: shuffling
% 2.15/1.49
% 2.15/1.49 % (18972)Memory used [KB]: 1151
% 2.15/1.49 % (18972)Time elapsed: 0.003 s
% 2.15/1.49 % (18972)Instructions burned: 2 (million)
% 2.15/1.49 % (18972)------------------------------
% 2.15/1.49 % (18972)------------------------------
% 2.15/1.49 % (18969)Instruction limit reached!
% 2.15/1.49 % (18969)------------------------------
% 2.15/1.49 % (18969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.49 % (18969)Termination reason: Unknown
% 2.15/1.49 % (18969)Termination phase: shuffling
% 2.15/1.49
% 2.15/1.49 % (18969)Memory used [KB]: 1151
% 2.15/1.49 % (18969)Time elapsed: 0.004 s
% 2.15/1.49 % (18969)Instructions burned: 4 (million)
% 2.15/1.49 % (18969)------------------------------
% 2.15/1.49 % (18969)------------------------------
% 2.26/1.50 % (18970)Instruction limit reached!
% 2.26/1.50 % (18970)------------------------------
% 2.26/1.50 % (18970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.50 % (18970)Termination reason: Unknown
% 2.26/1.50 % (18970)Termination phase: Property scanning
% 2.26/1.50
% 2.26/1.50 % (18970)Memory used [KB]: 1407
% 2.26/1.50 % (18970)Time elapsed: 0.015 s
% 2.26/1.50 % (18970)Instructions burned: 27 (million)
% 2.26/1.50 % (18970)------------------------------
% 2.26/1.50 % (18970)------------------------------
% 2.26/1.50 % (18974)Instruction limit reached!
% 2.26/1.50 % (18974)------------------------------
% 2.26/1.50 % (18974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.50 % (18974)Termination reason: Unknown
% 2.26/1.50 % (18974)Termination phase: Preprocessing 3
% 2.26/1.50
% 2.26/1.50 % (18974)Memory used [KB]: 1535
% 2.26/1.50 % (18974)Time elapsed: 0.013 s
% 2.26/1.50 % (18974)Instructions burned: 19 (million)
% 2.26/1.50 % (18974)------------------------------
% 2.26/1.50 % (18974)------------------------------
% 2.26/1.51 % (18975)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/3Mi)
% 2.26/1.51 % (18977)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_18696 for (2999ds/15Mi)
% 2.26/1.51 % (18976)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_18696 for (2999ds/37Mi)
% 2.26/1.51 % (18975)Instruction limit reached!
% 2.26/1.51 % (18975)------------------------------
% 2.26/1.51 % (18975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.51 % (18975)Termination reason: Unknown
% 2.26/1.51 % (18975)Termination phase: shuffling
% 2.26/1.51
% 2.26/1.51 % (18975)Memory used [KB]: 1151
% 2.26/1.51 % (18975)Time elapsed: 0.004 s
% 2.26/1.51 % (18975)Instructions burned: 4 (million)
% 2.26/1.51 % (18975)------------------------------
% 2.26/1.51 % (18975)------------------------------
% 2.26/1.51 % (18978)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_18696 for (2999ds/3Mi)
% 2.26/1.51 % (18978)Instruction limit reached!
% 2.26/1.51 % (18978)------------------------------
% 2.26/1.51 % (18978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.51 % (18978)Termination reason: Unknown
% 2.26/1.51 % (18978)Termination phase: shuffling
% 2.26/1.51
% 2.26/1.51 % (18978)Memory used [KB]: 1151
% 2.26/1.51 % (18978)Time elapsed: 0.002 s
% 2.26/1.51 % (18978)Instructions burned: 4 (million)
% 2.26/1.51 % (18978)------------------------------
% 2.26/1.51 % (18978)------------------------------
% 2.26/1.52 % (18977)Instruction limit reached!
% 2.26/1.52 % (18977)------------------------------
% 2.26/1.52 % (18977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.52 % (18977)Termination reason: Unknown
% 2.26/1.52 % (18977)Termination phase: Preprocessing 3
% 2.26/1.52
% 2.26/1.52 % (18977)Memory used [KB]: 1535
% 2.26/1.52 % (18977)Time elapsed: 0.011 s
% 2.26/1.52 % (18977)Instructions burned: 16 (million)
% 2.26/1.52 % (18977)------------------------------
% 2.26/1.52 % (18977)------------------------------
% 2.26/1.52 % (18979)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_18696 for (2999ds/1041Mi)
% 2.26/1.52 % (18981)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/16Mi)
% 2.26/1.52 % (18981)Instruction limit reached!
% 2.26/1.52 % (18981)------------------------------
% 2.26/1.52 % (18981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.52 % (18981)Termination reason: Unknown
% 2.26/1.52 % (18981)Termination phase: Property scanning
% 2.26/1.52
% 2.26/1.52 % (18981)Memory used [KB]: 1407
% 2.26/1.52 % (18981)Time elapsed: 0.006 s
% 2.26/1.52 % (18981)Instructions burned: 18 (million)
% 2.26/1.52 % (18981)------------------------------
% 2.26/1.52 % (18981)------------------------------
% 2.26/1.52 % (18976)Instruction limit reached!
% 2.26/1.52 % (18976)------------------------------
% 2.26/1.52 % (18976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.52 % (18976)Termination reason: Unknown
% 2.26/1.52 % (18976)Termination phase: Property scanning
% 2.26/1.52
% 2.26/1.52 % (18976)Memory used [KB]: 1535
% 2.26/1.52 % (18976)Time elapsed: 0.019 s
% 2.26/1.52 % (18976)Instructions burned: 37 (million)
% 2.26/1.52 % (18976)------------------------------
% 2.26/1.52 % (18976)------------------------------
% 2.26/1.53 % (18980)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/7Mi)
% 2.26/1.53 % (18980)Instruction limit reached!
% 2.26/1.53 % (18980)------------------------------
% 2.26/1.53 % (18980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.53 % (18980)Termination reason: Unknown
% 2.26/1.53 % (18980)Termination phase: shuffling
% 2.26/1.53
% 2.26/1.53 % (18980)Memory used [KB]: 1279
% 2.26/1.53 % (18980)Time elapsed: 0.006 s
% 2.26/1.53 % (18980)Instructions burned: 8 (million)
% 2.26/1.53 % (18980)------------------------------
% 2.26/1.53 % (18980)------------------------------
% 2.26/1.53 % (18982)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_18696 for (2999ds/3Mi)
% 2.26/1.53 % (18982)Instruction limit reached!
% 2.26/1.53 % (18982)------------------------------
% 2.26/1.53 % (18982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.53 % (18982)Termination reason: Unknown
% 2.26/1.53 % (18982)Termination phase: shuffling
% 2.26/1.53
% 2.26/1.53 % (18982)Memory used [KB]: 1151
% 2.26/1.53 % (18982)Time elapsed: 0.003 s
% 2.26/1.53 % (18982)Instructions burned: 3 (million)
% 2.26/1.53 % (18982)------------------------------
% 2.26/1.53 % (18982)------------------------------
% 2.26/1.53 % (18983)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_18696 for (2999ds/3Mi)
% 2.26/1.53 % (18983)Instruction limit reached!
% 2.26/1.53 % (18983)------------------------------
% 2.26/1.53 % (18983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.53 % (18983)Termination reason: Unknown
% 2.26/1.53 % (18983)Termination phase: shuffling
% 2.26/1.53
% 2.26/1.53 % (18983)Memory used [KB]: 1151
% 2.26/1.53 % (18983)Time elapsed: 0.002 s
% 2.26/1.53 % (18983)Instructions burned: 3 (million)
% 2.26/1.53 % (18983)------------------------------
% 2.26/1.53 % (18983)------------------------------
% 2.26/1.54 % (18968)Instruction limit reached!
% 2.26/1.54 % (18968)------------------------------
% 2.26/1.54 % (18968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.54 % (18968)Termination reason: Unknown
% 2.26/1.54 % (18968)Termination phase: Saturation
% 2.26/1.54
% 2.26/1.54 % (18968)Memory used [KB]: 6908
% 2.26/1.54 % (18968)Time elapsed: 0.059 s
% 2.26/1.54 % (18968)Instructions burned: 184 (million)
% 2.26/1.54 % (18968)------------------------------
% 2.26/1.54 % (18968)------------------------------
% 2.26/1.54 % (18984)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/7Mi)
% 2.26/1.54 % (18987)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/18Mi)
% 2.26/1.55 % (18984)Instruction limit reached!
% 2.26/1.55 % (18984)------------------------------
% 2.26/1.55 % (18984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.55 % (18984)Termination reason: Unknown
% 2.26/1.55 % (18984)Termination phase: shuffling
% 2.26/1.55
% 2.26/1.55 % (18984)Memory used [KB]: 1279
% 2.26/1.55 % (18984)Time elapsed: 0.006 s
% 2.26/1.55 % (18984)Instructions burned: 8 (million)
% 2.26/1.55 % (18984)------------------------------
% 2.26/1.55 % (18984)------------------------------
% 2.26/1.55 % (18985)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/3Mi)
% 2.26/1.55 % (18986)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/4Mi)
% 2.26/1.55 % (18988)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/710Mi)
% 2.26/1.55 % (18987)Instruction limit reached!
% 2.26/1.55 % (18987)------------------------------
% 2.26/1.55 % (18987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.55 % (18987)Termination reason: Unknown
% 2.26/1.55 % (18987)Termination phase: Property scanning
% 2.26/1.55
% 2.26/1.55 % (18987)Memory used [KB]: 1407
% 2.26/1.55 % (18987)Time elapsed: 0.006 s
% 2.26/1.55 % (18987)Instructions burned: 19 (million)
% 2.26/1.55 % (18987)------------------------------
% 2.26/1.55 % (18987)------------------------------
% 2.26/1.55 % (18986)Instruction limit reached!
% 2.26/1.55 % (18986)------------------------------
% 2.26/1.55 % (18986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.55 % (18986)Termination reason: Unknown
% 2.26/1.55 % (18986)Termination phase: shuffling
% 2.26/1.55
% 2.26/1.55 % (18986)Memory used [KB]: 1151
% 2.26/1.55 % (18986)Time elapsed: 0.003 s
% 2.26/1.55 % (18986)Instructions burned: 4 (million)
% 2.26/1.55 % (18986)------------------------------
% 2.26/1.55 % (18986)------------------------------
% 2.26/1.55 % (18985)Instruction limit reached!
% 2.26/1.55 % (18985)------------------------------
% 2.26/1.55 % (18985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.55 % (18985)Termination reason: Unknown
% 2.26/1.55 % (18985)Termination phase: shuffling
% 2.26/1.55
% 2.26/1.55 % (18985)Memory used [KB]: 1151
% 2.26/1.55 % (18985)Time elapsed: 0.004 s
% 2.26/1.55 % (18985)Instructions burned: 4 (million)
% 2.26/1.55 % (18985)------------------------------
% 2.26/1.55 % (18985)------------------------------
% 2.26/1.56 % (18991)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_18696 for (2999ds/21Mi)
% 2.26/1.56 % (18990)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_18696 for (2999ds/902Mi)
% 2.26/1.56 % (18989)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/6Mi)
% 2.26/1.56 % (18991)Instruction limit reached!
% 2.26/1.56 % (18991)------------------------------
% 2.26/1.56 % (18991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.56 % (18991)Termination reason: Unknown
% 2.26/1.56 % (18991)Termination phase: shuffling
% 2.26/1.56
% 2.26/1.56 % (18991)Memory used [KB]: 1407
% 2.26/1.56 % (18991)Time elapsed: 0.007 s
% 2.26/1.56 % (18991)Instructions burned: 23 (million)
% 2.26/1.56 % (18991)------------------------------
% 2.26/1.56 % (18991)------------------------------
% 2.26/1.57 % (18992)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/5Mi)
% 2.26/1.57 % (18989)Instruction limit reached!
% 2.26/1.57 % (18989)------------------------------
% 2.26/1.57 % (18989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.57 % (18989)Termination reason: Unknown
% 2.26/1.57 % (18989)Termination phase: shuffling
% 2.26/1.57
% 2.26/1.57 % (18989)Memory used [KB]: 1279
% 2.26/1.57 % (18989)Time elapsed: 0.005 s
% 2.26/1.57 % (18989)Instructions burned: 6 (million)
% 2.26/1.57 % (18989)------------------------------
% 2.26/1.57 % (18989)------------------------------
% 2.26/1.57 % (18992)Instruction limit reached!
% 2.26/1.57 % (18992)------------------------------
% 2.26/1.57 % (18992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.57 % (18992)Termination reason: Unknown
% 2.26/1.57 % (18992)Termination phase: shuffling
% 2.26/1.57
% 2.26/1.57 % (18992)Memory used [KB]: 1279
% 2.26/1.57 % (18992)Time elapsed: 0.005 s
% 2.26/1.57 % (18992)Instructions burned: 8 (million)
% 2.26/1.57 % (18992)------------------------------
% 2.26/1.57 % (18992)------------------------------
% 2.26/1.57 % (18993)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_18696 for (2999ds/6Mi)
% 2.26/1.57 % (18993)Instruction limit reached!
% 2.26/1.57 % (18993)------------------------------
% 2.26/1.57 % (18993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.57 % (18993)Termination reason: Unknown
% 2.26/1.57 % (18993)Termination phase: shuffling
% 2.26/1.57
% 2.26/1.57 % (18993)Memory used [KB]: 1279
% 2.26/1.57 % (18993)Time elapsed: 0.003 s
% 2.26/1.57 % (18993)Instructions burned: 7 (million)
% 2.26/1.57 % (18993)------------------------------
% 2.26/1.57 % (18993)------------------------------
% 2.26/1.58 % (18995)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_18696 for (2999ds/779Mi)
% 2.26/1.58 % (18994)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_18696 for (2999ds/377Mi)
% 2.26/1.58 % (18996)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_18696 for (2999ds/19Mi)
% 2.26/1.59 % (18996)Instruction limit reached!
% 2.26/1.59 % (18996)------------------------------
% 2.26/1.59 % (18996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.59 % (18996)Termination reason: Unknown
% 2.26/1.59 % (18996)Termination phase: Property scanning
% 2.26/1.59
% 2.26/1.59 % (18996)Memory used [KB]: 1407
% 2.26/1.59 % (18996)Time elapsed: 0.007 s
% 2.26/1.59 % (18996)Instructions burned: 22 (million)
% 2.26/1.59 % (18996)------------------------------
% 2.26/1.59 % (18996)------------------------------
% 2.26/1.60 % (18997)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_18696 for (2998ds/879Mi)
% 2.26/1.61 % (18990)First to succeed.
% 2.26/1.61 % (18990)Refutation found. Thanks to Tanya!
% 2.26/1.61 % SZS status Theorem for DTF2THF_18696
% 2.26/1.61 % SZS output start Proof for DTF2THF_18696
% 2.26/1.61 thf(func_def_0, type, in: $i > $i > $o).
% 2.26/1.61 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.26/1.61 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.26/1.61 thf(func_def_8, type, powerset: $i > $i).
% 2.26/1.61 thf(func_def_10, type, setunion: $i > $i).
% 2.26/1.61 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.26/1.61 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.26/1.61 thf(func_def_26, type, prop2set: $o > $i).
% 2.26/1.61 thf(func_def_36, type, nonempty: $i > $o).
% 2.26/1.61 thf(func_def_69, type, set2prop: $i > $o).
% 2.26/1.61 thf(func_def_88, type, subset: $i > $i > $o).
% 2.26/1.61 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.26/1.61 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.26/1.61 thf(func_def_122, type, sP1: $i > $i > $o).
% 2.26/1.61 thf(func_def_123, type, sP2: $i > $o).
% 2.26/1.61 thf(func_def_124, type, sP3: $i > $i > $o).
% 2.26/1.61 thf(func_def_125, type, sP4: $i > $i > $o).
% 2.26/1.61 thf(func_def_133, type, sK12: $i > $o).
% 2.26/1.61 thf(func_def_135, type, sK14: ($i > $o) > $i > $i).
% 2.26/1.61 thf(func_def_140, type, sK19: $i > $o).
% 2.26/1.61 thf(func_def_142, type, sK21: ($i > $o) > $i > $i).
% 2.26/1.61 thf(func_def_143, type, sK22: $i > ($i > $o) > $i).
% 2.26/1.61 thf(func_def_144, type, sK23: $i > $o).
% 2.26/1.61 thf(func_def_159, type, sK38: $i > $o).
% 2.26/1.61 thf(func_def_160, type, sK39: $i > $o).
% 2.26/1.61 thf(func_def_161, type, sK40: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.26/1.61 thf(func_def_162, type, sK41: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.26/1.61 thf(func_def_164, type, sK43: $i > $i > $o).
% 2.26/1.61 thf(func_def_165, type, sK44: $i > $i).
% 2.26/1.61 thf(func_def_166, type, sK45: $i > $i).
% 2.26/1.61 thf(func_def_167, type, sK46: ($i > $i > $o) > $i > $i).
% 2.26/1.61 thf(func_def_168, type, sK47: ($i > $i > $o) > $i > $i).
% 2.26/1.61 thf(func_def_169, type, sK48: $i > ($i > $i > $o) > $i > $i).
% 2.26/1.61 thf(func_def_175, type, sK54: $o > $i > $i > $i).
% 2.26/1.61 thf(func_def_176, type, sK55: $i > $i > $i).
% 2.26/1.61 thf(func_def_185, type, sK64: $i > $o).
% 2.26/1.61 thf(func_def_186, type, sK65: $i > ($i > $o) > $i).
% 2.26/1.61 thf(func_def_187, type, sK66: $i > $o).
% 2.26/1.61 thf(func_def_189, type, sK68: $i > $o).
% 2.26/1.61 thf(func_def_193, type, sK72: $i > $i).
% 2.26/1.61 thf(func_def_196, type, sK75: $i > $i > $i).
% 2.26/1.61 thf(func_def_197, type, sK76: $i > $i > $i).
% 2.26/1.61 thf(func_def_198, type, sK77: $i > $i > $i).
% 2.26/1.61 thf(func_def_199, type, sK78: $i > $i > $i).
% 2.26/1.61 thf(func_def_200, type, sK79: $i > $i > $i).
% 2.26/1.61 thf(func_def_201, type, sK80: $i > $i > $i > $i).
% 2.26/1.61 thf(func_def_202, type, sK81: $i > $i).
% 2.26/1.61 thf(func_def_203, type, sK82: $i > $i).
% 2.26/1.61 thf(func_def_204, type, sK83: $i > $i).
% 2.26/1.61 thf(func_def_205, type, sK84: $i > $i).
% 2.26/1.61 thf(func_def_206, type, sK85: $i > $i > $i).
% 2.26/1.61 thf(func_def_207, type, sK86: $i > $i > $i > $i).
% 2.26/1.61 thf(func_def_208, type, sK87: $i > $i > $i > $i).
% 2.26/1.61 thf(func_def_209, type, sK88: $i > $i > $i).
% 2.26/1.61 thf(func_def_210, type, sK89: $i > $i > $i).
% 2.26/1.61 thf(func_def_212, type, sK91: $i > $i).
% 2.26/1.61 thf(func_def_213, type, sK92: $i > $i).
% 2.26/1.61 thf(func_def_214, type, sK93: $i > $i).
% 2.26/1.61 thf(func_def_215, type, sK94: $i > ($i > $o) > $i).
% 2.26/1.61 thf(func_def_216, type, sK95: $i > $o).
% 2.26/1.61 thf(func_def_223, type, sK102: $i > $i > $i).
% 2.26/1.61 thf(func_def_227, type, sK106: $i > $i > $i).
% 2.26/1.61 thf(func_def_232, type, sK111: $i > $i > $i).
% 2.26/1.61 thf(func_def_233, type, sK112: $i > $i > $i).
% 2.26/1.61 thf(func_def_234, type, sK113: $i > $o).
% 2.26/1.61 thf(func_def_238, type, sK117: $i > $o).
% 2.26/1.61 thf(func_def_245, type, sK124: ($i > $o) > $i).
% 2.26/1.61 thf(func_def_246, type, sK125: $i > $o).
% 2.26/1.61 thf(func_def_247, type, sK126: $i > $i).
% 2.26/1.61 thf(func_def_248, type, sK127: $i > $o).
% 2.26/1.61 thf(func_def_249, type, sK128: ($i > $o) > $i).
% 2.26/1.61 thf(func_def_261, type, sK140: $i > $i).
% 2.26/1.61 thf(func_def_262, type, sK141: ($i > $o) > $i).
% 2.26/1.61 thf(func_def_263, type, sK142: $i > $o).
% 2.26/1.61 thf(func_def_264, type, sK143: $i > $i).
% 2.26/1.61 thf(func_def_266, type, sK145: $i > $i).
% 2.26/1.61 thf(func_def_273, type, sK152: $i > $o).
% 2.26/1.61 thf(func_def_277, type, sK156: $i > $o).
% 2.26/1.61 thf(func_def_280, type, sK159: $i > ($i > $o) > $i).
% 2.26/1.61 thf(func_def_281, type, sK160: $i > $i).
% 2.26/1.61 thf(func_def_283, type, sK162: $i > $i).
% 2.26/1.61 thf(func_def_293, type, sK172: $i > $o).
% 2.26/1.61 thf(func_def_296, type, sK175: $i > $i).
% 2.26/1.61 thf(func_def_304, type, sK183: ($i > $o) > ($i > $o) > $i).
% 2.26/1.61 thf(func_def_305, type, sK184: ($i > $o) > ($i > $o) > $i).
% 2.26/1.61 thf(func_def_306, type, sK185: $i > $o).
% 2.26/1.61 thf(func_def_307, type, sK186: $i > $o).
% 2.26/1.61 thf(func_def_310, type, sK189: $i > $o).
% 2.26/1.61 thf(func_def_316, type, sK195: $i > $i > $i).
% 2.26/1.61 thf(func_def_321, type, sK200: $i > $o).
% 2.26/1.61 thf(func_def_326, type, sK205: $i > $o).
% 2.26/1.61 thf(func_def_328, type, sK207: $i > $o).
% 2.26/1.61 thf(func_def_331, type, sK210: $i > ($i > $o) > $i).
% 2.26/1.61 thf(func_def_332, type, sK211: ($i > $o) > ($i > $o) > $i).
% 2.26/1.61 thf(func_def_333, type, sK212: ($i > $o) > ($i > $o) > $i).
% 2.26/1.61 thf(func_def_334, type, sK213: $i > $o).
% 2.26/1.61 thf(func_def_335, type, sK214: $i > $o).
% 2.26/1.61 thf(func_def_337, type, sK216: $i > $i).
% 2.26/1.61 thf(func_def_347, type, sK226: $i > $o).
% 2.26/1.61 thf(func_def_350, type, sK229: ($i > $o) > $i).
% 2.26/1.61 thf(func_def_351, type, sK230: ($i > $o) > $i).
% 2.26/1.61 thf(func_def_352, type, sK231: $i > $o).
% 2.26/1.61 thf(func_def_361, type, sK240: $i > $i > $i).
% 2.26/1.61 thf(func_def_371, type, sK250: $i > $i > $i).
% 2.26/1.61 thf(func_def_380, type, sK259: $i > ($i > $o) > $i).
% 2.26/1.61 thf(func_def_381, type, sK260: $i > $o).
% 2.26/1.61 thf(func_def_385, type, ph264: !>[X0: $tType]:(X0)).
% 2.26/1.61 thf(f2073,plain,(
% 2.26/1.61 $false),
% 2.26/1.61 inference(trivial_inequality_removal,[status(thm)],[f2066])).
% 2.26/1.61 thf(f2066,plain,(
% 2.26/1.61 ($true != $true)),
% 2.26/1.61 inference(superposition,[status(thm)],[f1538,f2022])).
% 2.26/1.61 thf(f2022,plain,(
% 2.26/1.61 ((subset @ sK60 @ sK61) = $true)),
% 2.26/1.61 inference(trivial_inequality_removal,[status(thm)],[f2021])).
% 2.26/1.61 thf(f2021,plain,(
% 2.26/1.61 ((subset @ sK60 @ sK61) = $true) | ($true != $true)),
% 2.26/1.61 inference(forward_demodulation,[status(thm)],[f2016,f1020])).
% 2.26/1.61 thf(f1020,plain,(
% 2.26/1.61 (subsetI1 = $true)),
% 2.26/1.61 inference(cnf_transformation,[status(thm)],[f503])).
% 2.26/1.61 thf(f503,plain,(
% 2.26/1.61 (emptysetE = $true) & (setunion__Cong = $true) & (quantDeMorgan2 = $true) & (emptysetAx = $true) & (emptyinPowerset = $true) & (notequalI1 = $true) & (inCongP = $true) & (foundationAx = $true) & (prop2setE = $true) & (((in @ sK60 @ (powerset @ sK61)) = $true) & ((subset @ sK60 @ sK61) != $true)) & (setadjoin__Cong = $true) & (exuE2 = $true) & (eqimpsubset2 = $true) & (setadjoinSub = $true) & (emptyinunitempty = $true) & (subset2powerset = $true) & (exuI2 = $true) & (notinsingleton = $true) & (eqimpsubset1 = $true) & (emptysetimpfalse = $true) & (setunionI = $true) & (subsetI1 = $true) & (setunionE = $true) & (subsetE2 = $true) & (setadjoinIL = $true) & (notsubsetI = $true) & (powersetE = $true) & (noeltsimpempty = $true) & (notdexE = $true) & (subsetI2 = $true) & (quantDeMorgan1 = $true) & (emptyInPowerset = $true) & (setadjoinSub2 = $true) & (omega__Cong = $true) & (setextsub = $true) & (exuE1 = $true) & (exuI3 = $true) & (subsetRefl = $true) & (emptyI = $true) & (replAx = $true) & (upairsetE = $true) & (subsetE = $true) & (dsetconstr__Cong = $true) & (notinemptyset = $true) & (emptysetsubset = $true) & (descrp = $true) & (notdallE = $true) & (omegaIndAx = $true) & (subPowSU = $true) & (dsetconstrEL = $true) & (descr__Cong = $true) & (setadjoinOr = $true) & (notequalI2 = $true) & (setunionAx = $true) & (subsetTrans = $true) & (emptyE1 = $true) & (powersetI = $true) & (exuI1 = $true) & (dsetconstrI = $true) & (uniqinunit = $true) & (prop2set2propI = $true) & (setadjoinIR = $true) & (setbeta = $true) & (exu__Cong = $true) & (prop2setI = $true) & (in__Cong = $true) & (exuE3e = $true) & (nonemptyImpWitness = $true) & (omega0Ax = $true) & (subsetemptysetimpeq = $true) & (singletonsswitch = $true) & (nonemptyE1 = $true) & (nonemptyI = $true) & (setoftrueEq = $true) & (setadjoinAx = $true) & (wellorderingAx = $true) & (omegaSAx = $true) & (upairsetIR = $true) & (nonemptyI1 = $true) & (setextAx = $true) & (exuEu = $true) & (dsetconstrER = $true) & (emptyset__Cong = $true) & (powersetI1 = $true) & (setext = $true) & (upairsetIL = $true) & (exuE3u = $true) & (quantDeMorgan4 = $true) & (powerset__Cong = $true) & (powersetAx = $true) & (setadjoinE = $true) & (eqinunit = $true) & (quantDeMorgan3 = $true) & (vacuousDall = $true)),
% 2.26/1.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK60,sK61])],[f383,f502])).
% 2.26/1.61 thf(f502,plain,(
% 2.26/1.61 ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ((subset @ X0 @ X1) != $true)) => (((in @ sK60 @ (powerset @ sK61)) = $true) & ((subset @ sK60 @ sK61) != $true))),
% 2.26/1.61 introduced(definition,[],[choice_axiom])).
% 2.26/1.61 thf(f383,plain,(
% 2.26/1.61 (emptysetE = $true) & (setunion__Cong = $true) & (quantDeMorgan2 = $true) & (emptysetAx = $true) & (emptyinPowerset = $true) & (notequalI1 = $true) & (inCongP = $true) & (foundationAx = $true) & (prop2setE = $true) & ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ((subset @ X0 @ X1) != $true)) & (setadjoin__Cong = $true) & (exuE2 = $true) & (eqimpsubset2 = $true) & (setadjoinSub = $true) & (emptyinunitempty = $true) & (subset2powerset = $true) & (exuI2 = $true) & (notinsingleton = $true) & (eqimpsubset1 = $true) & (emptysetimpfalse = $true) & (setunionI = $true) & (subsetI1 = $true) & (setunionE = $true) & (subsetE2 = $true) & (setadjoinIL = $true) & (notsubsetI = $true) & (powersetE = $true) & (noeltsimpempty = $true) & (notdexE = $true) & (subsetI2 = $true) & (quantDeMorgan1 = $true) & (emptyInPowerset = $true) & (setadjoinSub2 = $true) & (omega__Cong = $true) & (setextsub = $true) & (exuE1 = $true) & (exuI3 = $true) & (subsetRefl = $true) & (emptyI = $true) & (replAx = $true) & (upairsetE = $true) & (subsetE = $true) & (dsetconstr__Cong = $true) & (notinemptyset = $true) & (emptysetsubset = $true) & (descrp = $true) & (notdallE = $true) & (omegaIndAx = $true) & (subPowSU = $true) & (dsetconstrEL = $true) & (descr__Cong = $true) & (setadjoinOr = $true) & (notequalI2 = $true) & (setunionAx = $true) & (subsetTrans = $true) & (emptyE1 = $true) & (powersetI = $true) & (exuI1 = $true) & (dsetconstrI = $true) & (uniqinunit = $true) & (prop2set2propI = $true) & (setadjoinIR = $true) & (setbeta = $true) & (exu__Cong = $true) & (prop2setI = $true) & (in__Cong = $true) & (exuE3e = $true) & (nonemptyImpWitness = $true) & (omega0Ax = $true) & (subsetemptysetimpeq = $true) & (singletonsswitch = $true) & (nonemptyE1 = $true) & (nonemptyI = $true) & (setoftrueEq = $true) & (setadjoinAx = $true) & (wellorderingAx = $true) & (omegaSAx = $true) & (upairsetIR = $true) & (nonemptyI1 = $true) & (setextAx = $true) & (exuEu = $true) & (dsetconstrER = $true) & (emptyset__Cong = $true) & (powersetI1 = $true) & (setext = $true) & (upairsetIL = $true) & (exuE3u = $true) & (quantDeMorgan4 = $true) & (powerset__Cong = $true) & (powersetAx = $true) & (setadjoinE = $true) & (eqinunit = $true) & (quantDeMorgan3 = $true) & (vacuousDall = $true)),
% 2.26/1.61 inference(flattening,[status(thm)],[f382])).
% 2.26/1.61 thf(f382,plain,(
% 2.26/1.61 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ((subset @ X0 @ X1) != $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $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)),
% 2.26/1.61 inference(ennf_transformation,[status(thm)],[f114])).
% 2.26/1.61 thf(f114,plain,(
% 2.26/1.61 ~((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) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ((subset @ X0 @ X1) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.26/1.61 inference(fool_elimination,[status(thm)],[f113])).
% 2.26/1.61 thf(f113,plain,(
% 2.26/1.61 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.26/1.61 inference(rectify,[status(thm)],[f97])).
% 2.26/1.61 thf(f97,negated_conjecture,(
% 2.26/1.61 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => ! [X4 : $i,X3 : $i] : ((in @ X4 @ (powerset @ X3)) => (subset @ X4 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.26/1.61 inference(negated_conjecture,[status(cth)],[f96])).
% 2.26/1.61 thf(f96,conjecture,(
% 2.26/1.61 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => ! [X4 : $i,X3 : $i] : ((in @ X4 @ (powerset @ X3)) => (subset @ X4 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.26/1.61 file('/export/starexec/sandbox2/tmp/tmp.JqQVLhIiKp/DTF2THF_18696.p',powersetE1)).
% 2.26/1.61 thf(f2016,plain,(
% 2.26/1.61 ((subset @ sK60 @ sK61) = $true) | (subsetI1 != $true)),
% 2.26/1.61 inference(trivial_inequality_removal,[status(thm)],[f2015])).
% 2.26/1.61 thf(f2015,plain,(
% 2.26/1.61 ((subset @ sK60 @ sK61) = $true) | (subsetI1 != $true) | ($true != $true)),
% 2.26/1.61 inference(duplicate_literal_removal,[status(thm)],[f2008])).
% 2.26/1.61 thf(f2008,plain,(
% 2.26/1.61 ($true != $true) | (subsetI1 != $true) | ((subset @ sK60 @ sK61) = $true) | ((subset @ sK60 @ sK61) = $true)),
% 2.26/1.61 inference(superposition,[status(thm)],[f1628,f1128])).
% 2.26/1.61 thf(f1128,plain,(
% 2.26/1.61 ( ! [X0 : $i,X1 : $i] : (((in @ (sK106 @ X1 @ X0) @ X0) = $true) | ((subset @ X0 @ X1) = $true) | (subsetI1 != $true)) )),
% 2.26/1.61 inference(cnf_transformation,[status(thm)],[f589])).
% 2.26/1.61 thf(f589,plain,(
% 2.26/1.61 (! [X0 : $i,X1 : $i] : ((((in @ (sK106 @ X1 @ X0) @ X1) != $true) & ((in @ (sK106 @ X1 @ X0) @ X0) = $true)) | ((subset @ X0 @ X1) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | (! [X5 : $i] : (($true = (in @ X5 @ sK108)) | ((in @ X5 @ sK107) != $true)) & ((subset @ sK107 @ sK108) != $true)))),
% 2.26/1.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK106,sK107,sK108])],[f586,f588,f587])).
% 2.26/1.61 thf(f587,plain,(
% 2.26/1.61 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) => (((in @ (sK106 @ X1 @ X0) @ X1) != $true) & ((in @ (sK106 @ X1 @ X0) @ X0) = $true)))),
% 2.26/1.61 introduced(definition,[],[choice_axiom])).
% 2.26/1.61 thf(f588,plain,(
% 2.26/1.61 ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) = $true) | ($true != (in @ X5 @ X3))) & ((subset @ X3 @ X4) != $true)) => (! [X5 : $i] : (($true = (in @ X5 @ sK108)) | ((in @ X5 @ sK107) != $true)) & ((subset @ sK107 @ sK108) != $true))),
% 2.26/1.61 introduced(definition,[],[choice_axiom])).
% 2.26/1.61 thf(f586,plain,(
% 2.26/1.61 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) | ((subset @ X0 @ X1) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) = $true) | ($true != (in @ X5 @ X3))) & ((subset @ X3 @ X4) != $true)))),
% 2.26/1.61 inference(rectify,[status(thm)],[f585])).
% 2.26/1.61 thf(f585,plain,(
% 2.26/1.61 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) | ((subset @ X0 @ X1) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) & ((subset @ X0 @ X1) != $true)))),
% 2.26/1.61 inference(nnf_transformation,[status(thm)],[f391])).
% 2.26/1.61 thf(f391,plain,(
% 2.26/1.61 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) | ((subset @ X0 @ X1) = $true)) <=> (subsetI1 = $true)),
% 2.26/1.61 inference(ennf_transformation,[status(thm)],[f244])).
% 2.26/1.61 thf(f244,plain,(
% 2.26/1.61 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((subset @ X0 @ X1) = $true))),
% 2.26/1.61 inference(fool_elimination,[status(thm)],[f243])).
% 2.26/1.61 thf(f243,plain,(
% 2.26/1.61 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 2.26/1.61 inference(rectify,[status(thm)],[f78])).
% 2.26/1.61 thf(f78,axiom,(
% 2.26/1.61 (! [X3 : $i,X4 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)) = subsetI1)),
% 2.26/1.61 file('/export/starexec/sandbox2/tmp/tmp.JqQVLhIiKp/DTF2THF_18696.p',subsetI1)).
% 2.26/1.61 thf(f1628,plain,(
% 2.26/1.61 ( ! [X0 : $i] : (((in @ (sK106 @ sK61 @ X0) @ sK60) != $true) | ((subset @ X0 @ sK61) = $true)) )),
% 2.26/1.61 inference(trivial_inequality_removal,[status(thm)],[f1627])).
% 2.26/1.61 thf(f1627,plain,(
% 2.26/1.61 ( ! [X0 : $i] : (((subset @ X0 @ sK61) = $true) | ((in @ (sK106 @ sK61 @ X0) @ sK60) != $true) | ($true != $true)) )),
% 2.26/1.61 inference(forward_demodulation,[status(thm)],[f1597,f1020])).
% 2.26/1.61 thf(f1597,plain,(
% 2.26/1.61 ( ! [X0 : $i] : ((subsetI1 != $true) | ((subset @ X0 @ sK61) = $true) | ((in @ (sK106 @ sK61 @ X0) @ sK60) != $true)) )),
% 2.26/1.61 inference(trivial_inequality_removal,[status(thm)],[f1577])).
% 2.26/1.61 thf(f1577,plain,(
% 2.26/1.61 ( ! [X0 : $i] : (($true != $true) | ((subset @ X0 @ sK61) = $true) | (subsetI1 != $true) | ((in @ (sK106 @ sK61 @ X0) @ sK60) != $true)) )),
% 2.26/1.61 inference(superposition,[status(thm)],[f1129,f1451])).
% 2.26/1.61 thf(f1451,plain,(
% 2.26/1.61 ( ! [X0 : $i] : (((in @ X0 @ sK61) = $true) | ((in @ X0 @ sK60) != $true)) )),
% 2.26/1.61 inference(trivial_inequality_removal,[status(thm)],[f1450])).
% 2.26/1.61 thf(f1450,plain,(
% 2.26/1.61 ( ! [X0 : $i] : (((in @ X0 @ sK60) != $true) | ($true != $true) | ((in @ X0 @ sK61) = $true)) )),
% 2.26/1.61 inference(forward_demodulation,[status(thm)],[f1446,f1015])).
% 2.26/1.61 thf(f1015,plain,(
% 2.26/1.61 (powersetE = $true)),
% 2.26/1.61 inference(cnf_transformation,[status(thm)],[f503])).
% 2.26/1.61 thf(f1446,plain,(
% 2.26/1.61 ( ! [X0 : $i] : ((powersetE != $true) | ((in @ X0 @ sK61) = $true) | ((in @ X0 @ sK60) != $true)) )),
% 2.26/1.61 inference(trivial_inequality_removal,[status(thm)],[f1443])).
% 2.26/1.61 thf(f1443,plain,(
% 2.26/1.61 ( ! [X0 : $i] : (($true != $true) | (powersetE != $true) | ((in @ X0 @ sK60) != $true) | ((in @ X0 @ sK61) = $true)) )),
% 2.26/1.61 inference(superposition,[status(thm)],[f1147,f1033])).
% 2.26/1.61 thf(f1033,plain,(
% 2.26/1.61 ((in @ sK60 @ (powerset @ sK61)) = $true)),
% 2.26/1.61 inference(cnf_transformation,[status(thm)],[f503])).
% 2.26/1.61 thf(f1147,plain,(
% 2.26/1.61 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (powerset @ X5)) != $true) | (powersetE != $true) | ((in @ X3 @ X5) = $true) | ((in @ X3 @ X4) != $true)) )),
% 2.26/1.61 inference(cnf_transformation,[status(thm)],[f611])).
% 2.26/1.61 thf(f611,plain,(
% 2.26/1.61 ((powersetE = $true) | (((in @ sK121 @ sK122) = $true) & ((in @ sK122 @ (powerset @ sK123)) = $true) & ((in @ sK121 @ sK123) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) | ((in @ X4 @ (powerset @ X5)) != $true) | ((in @ X3 @ X5) = $true)) | (powersetE != $true))),
% 2.26/1.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK121,sK122,sK123])],[f609,f610])).
% 2.26/1.61 thf(f610,plain,(
% 2.26/1.61 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) & ($true = (in @ X1 @ (powerset @ X2))) & ((in @ X0 @ X2) != $true)) => (((in @ sK121 @ sK122) = $true) & ((in @ sK122 @ (powerset @ sK123)) = $true) & ((in @ sK121 @ sK123) != $true))),
% 2.26/1.61 introduced(definition,[],[choice_axiom])).
% 2.26/1.61 thf(f609,plain,(
% 2.26/1.61 ((powersetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) & ($true = (in @ X1 @ (powerset @ X2))) & ((in @ X0 @ X2) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) | ((in @ X4 @ (powerset @ X5)) != $true) | ((in @ X3 @ X5) = $true)) | (powersetE != $true))),
% 2.26/1.61 inference(rectify,[status(thm)],[f608])).
% 2.26/1.61 thf(f608,plain,(
% 2.26/1.61 ((powersetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) & ($true = (in @ X1 @ (powerset @ X2))) & ((in @ X0 @ X2) != $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) | ($true != (in @ X1 @ (powerset @ X2))) | ((in @ X0 @ X2) = $true)) | (powersetE != $true))),
% 2.26/1.61 inference(nnf_transformation,[status(thm)],[f333])).
% 2.26/1.61 thf(f333,plain,(
% 2.26/1.61 (powersetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) | ($true != (in @ X1 @ (powerset @ X2))) | ((in @ X0 @ X2) = $true))),
% 2.26/1.61 inference(flattening,[status(thm)],[f332])).
% 2.26/1.61 thf(f332,plain,(
% 2.26/1.61 (powersetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) != $true)) | ($true != (in @ X1 @ (powerset @ X2))))),
% 2.26/1.61 inference(ennf_transformation,[status(thm)],[f138])).
% 2.26/1.61 thf(f138,plain,(
% 2.26/1.61 (powersetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (powerset @ X2))) => (((in @ X0 @ X1) = $true) => ((in @ X0 @ X2) = $true)))),
% 2.26/1.61 inference(fool_elimination,[status(thm)],[f137])).
% 2.26/1.61 thf(f137,plain,(
% 2.26/1.61 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (powerset @ X2)) => ((in @ X0 @ X1) => (in @ X0 @ X2))) = powersetE)),
% 2.26/1.61 inference(rectify,[status(thm)],[f40])).
% 2.26/1.61 thf(f40,axiom,(
% 2.26/1.61 (! [X1 : $i,X4 : $i,X3 : $i] : ((in @ X4 @ (powerset @ X3)) => ((in @ X1 @ X4) => (in @ X1 @ X3))) = powersetE)),
% 2.26/1.61 file('/export/starexec/sandbox2/tmp/tmp.JqQVLhIiKp/DTF2THF_18696.p',powersetE)).
% 2.26/1.61 thf(f1129,plain,(
% 2.26/1.61 ( ! [X0 : $i,X1 : $i] : (((in @ (sK106 @ X1 @ X0) @ X1) != $true) | (subsetI1 != $true) | ((subset @ X0 @ X1) = $true)) )),
% 2.26/1.61 inference(cnf_transformation,[status(thm)],[f589])).
% 2.26/1.61 thf(f1538,plain,(
% 2.26/1.61 ((subset @ sK60 @ sK61) != $true)),
% 2.26/1.61 inference(trivial_inequality_removal,[status(thm)],[f1537])).
% 2.26/1.61 thf(f1537,plain,(
% 2.26/1.61 ($true != $true) | ((subset @ sK60 @ sK61) != $true)),
% 2.26/1.61 inference(forward_demodulation,[status(thm)],[f1478,f1004])).
% 2.26/1.61 thf(f1004,plain,(
% 2.26/1.61 (subsetRefl = $true)),
% 2.26/1.61 inference(cnf_transformation,[status(thm)],[f503])).
% 2.26/1.61 thf(f1478,plain,(
% 2.26/1.61 ((subset @ sK60 @ sK61) != $true) | (subsetRefl != $true)),
% 2.26/1.61 inference(trivial_inequality_removal,[status(thm)],[f1456])).
% 2.26/1.61 thf(f1456,plain,(
% 2.26/1.61 (subsetRefl != $true) | ((subset @ sK60 @ sK61) != $true) | ($true != $true)),
% 2.26/1.61 inference(superposition,[status(thm)],[f1441,f1280])).
% 2.26/1.61 thf(f1280,plain,(
% 2.26/1.61 ( ! [X1 : $i] : (((subset @ X1 @ X1) = $true) | (subsetRefl != $true)) )),
% 2.26/1.61 inference(cnf_transformation,[status(thm)],[f787])).
% 2.26/1.61 thf(f787,plain,(
% 2.26/1.61 ((subsetRefl = $true) | ((subset @ sK217 @ sK217) != $true)) & (! [X1 : $i] : ((subset @ X1 @ X1) = $true) | (subsetRefl != $true))),
% 2.26/1.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK217])],[f785,f786])).
% 2.26/1.61 thf(f786,plain,(
% 2.26/1.61 ? [X0 : $i] : ((subset @ X0 @ X0) != $true) => ((subset @ sK217 @ sK217) != $true)),
% 2.26/1.61 introduced(definition,[],[choice_axiom])).
% 2.26/1.61 thf(f785,plain,(
% 2.26/1.61 ((subsetRefl = $true) | ? [X0 : $i] : ((subset @ X0 @ X0) != $true)) & (! [X1 : $i] : ((subset @ X1 @ X1) = $true) | (subsetRefl != $true))),
% 2.26/1.61 inference(rectify,[status(thm)],[f784])).
% 2.26/1.61 thf(f784,plain,(
% 2.26/1.61 ((subsetRefl = $true) | ? [X0 : $i] : ((subset @ X0 @ X0) != $true)) & (! [X0 : $i] : ((subset @ X0 @ X0) = $true) | (subsetRefl != $true))),
% 2.26/1.61 inference(nnf_transformation,[status(thm)],[f136])).
% 2.26/1.61 thf(f136,plain,(
% 2.26/1.61 (subsetRefl = $true) <=> ! [X0 : $i] : ((subset @ X0 @ X0) = $true)),
% 2.26/1.61 inference(fool_elimination,[status(thm)],[f135])).
% 2.26/1.61 thf(f135,plain,(
% 2.26/1.61 (! [X0 : $i] : (subset @ X0 @ X0) = subsetRefl)),
% 2.26/1.61 inference(rectify,[status(thm)],[f88])).
% 2.26/1.61 thf(f88,axiom,(
% 2.26/1.61 (! [X3 : $i] : (subset @ X3 @ X3) = subsetRefl)),
% 2.26/1.61 file('/export/starexec/sandbox2/tmp/tmp.JqQVLhIiKp/DTF2THF_18696.p',subsetRefl)).
% 2.26/1.61 thf(f1441,plain,(
% 2.26/1.61 ( ! [X0 : $i] : (((subset @ sK60 @ X0) != $true) | ((subset @ X0 @ sK61) != $true)) )),
% 2.26/1.61 inference(trivial_inequality_removal,[status(thm)],[f1440])).
% 2.26/1.61 thf(f1440,plain,(
% 2.26/1.61 ( ! [X0 : $i] : (((subset @ sK60 @ X0) != $true) | ((subset @ X0 @ sK61) != $true) | ($true != $true)) )),
% 2.26/1.61 inference(forward_demodulation,[status(thm)],[f1439,f987])).
% 2.26/1.61 thf(f987,plain,(
% 2.26/1.61 (subsetTrans = $true)),
% 2.26/1.61 inference(cnf_transformation,[status(thm)],[f503])).
% 2.26/1.61 thf(f1439,plain,(
% 2.26/1.61 ( ! [X0 : $i] : ((subsetTrans != $true) | ((subset @ X0 @ sK61) != $true) | ((subset @ sK60 @ X0) != $true)) )),
% 2.26/1.61 inference(trivial_inequality_removal,[status(thm)],[f1438])).
% 2.26/1.61 thf(f1438,plain,(
% 2.26/1.61 ( ! [X0 : $i] : (((subset @ X0 @ sK61) != $true) | ($true != $true) | ((subset @ sK60 @ X0) != $true) | (subsetTrans != $true)) )),
% 2.26/1.61 inference(superposition,[status(thm)],[f1032,f1193])).
% 2.26/1.61 thf(f1193,plain,(
% 2.26/1.61 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X3 @ X5) = $true) | ((subset @ X3 @ X4) != $true) | ((subset @ X4 @ X5) != $true) | (subsetTrans != $true)) )),
% 2.26/1.61 inference(cnf_transformation,[status(thm)],[f675])).
% 2.26/1.61 thf(f675,plain,(
% 2.26/1.61 ((subsetTrans = $true) | (((subset @ sK153 @ sK155) != $true) & ((subset @ sK153 @ sK154) = $true) & ((subset @ sK154 @ sK155) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X3 @ X5) = $true) | ((subset @ X3 @ X4) != $true) | ((subset @ X4 @ X5) != $true)) | (subsetTrans != $true))),
% 2.26/1.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK153,sK154,sK155])],[f673,f674])).
% 2.26/1.61 thf(f674,plain,(
% 2.26/1.61 ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X2) != $true) & ((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X2) = $true)) => (((subset @ sK153 @ sK155) != $true) & ((subset @ sK153 @ sK154) = $true) & ((subset @ sK154 @ sK155) = $true))),
% 2.26/1.61 introduced(definition,[],[choice_axiom])).
% 2.26/1.61 thf(f673,plain,(
% 2.26/1.61 ((subsetTrans = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X2) != $true) & ((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X2) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X3 @ X5) = $true) | ((subset @ X3 @ X4) != $true) | ((subset @ X4 @ X5) != $true)) | (subsetTrans != $true))),
% 2.26/1.61 inference(rectify,[status(thm)],[f672])).
% 2.26/1.61 thf(f672,plain,(
% 2.26/1.61 ((subsetTrans = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X2) != $true) & ((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X2) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X2) = $true) | ((subset @ X0 @ X1) != $true) | ((subset @ X1 @ X2) != $true)) | (subsetTrans != $true))),
% 2.26/1.61 inference(nnf_transformation,[status(thm)],[f350])).
% 2.26/1.61 thf(f350,plain,(
% 2.26/1.61 (subsetTrans = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X2) = $true) | ((subset @ X0 @ X1) != $true) | ((subset @ X1 @ X2) != $true))),
% 2.26/1.61 inference(flattening,[status(thm)],[f349])).
% 2.26/1.61 thf(f349,plain,(
% 2.26/1.61 (subsetTrans = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X0 @ X2) = $true) | ((subset @ X1 @ X2) != $true)) | ((subset @ X0 @ X1) != $true))),
% 2.26/1.61 inference(ennf_transformation,[status(thm)],[f240])).
% 2.26/1.61 thf(f240,plain,(
% 2.26/1.61 (subsetTrans = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X1) = $true) => (((subset @ X1 @ X2) = $true) => ((subset @ X0 @ X2) = $true)))),
% 2.26/1.61 inference(fool_elimination,[status(thm)],[f239])).
% 2.26/1.61 thf(f239,plain,(
% 2.26/1.61 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X2) => (subset @ X0 @ X2))) = subsetTrans)),
% 2.26/1.61 inference(rectify,[status(thm)],[f89])).
% 2.26/1.61 thf(f89,axiom,(
% 2.26/1.61 (! [X3 : $i,X4 : $i,X5 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X5) => (subset @ X3 @ X5))) = subsetTrans)),
% 2.26/1.61 file('/export/starexec/sandbox2/tmp/tmp.JqQVLhIiKp/DTF2THF_18696.p',subsetTrans)).
% 2.26/1.61 thf(f1032,plain,(
% 2.26/1.61 ((subset @ sK60 @ sK61) != $true)),
% 2.26/1.61 inference(cnf_transformation,[status(thm)],[f503])).
% 2.26/1.61 % SZS output end Proof for DTF2THF_18696
% 2.26/1.61 % (18990)------------------------------
% 2.26/1.61 % (18990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.26/1.61 % (18990)Termination reason: Refutation
% 2.26/1.61
% 2.26/1.61 % (18990)Memory used [KB]: 7164
% 2.26/1.61 % (18990)Time elapsed: 0.051 s
% 2.26/1.61 % (18990)Instructions burned: 145 (million)
% 2.26/1.61 % (18990)------------------------------
% 2.26/1.61 % (18990)------------------------------
% 2.26/1.61 % (18967)Success in time 0.133 s
%------------------------------------------------------------------------------