%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU574^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:21 AM UTC 2026
% Result : Theorem 13.33s 3.16s
% Output : Refutation 13.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 31 unt; 0 typ; 7 def)
% Number of atoms : 1888 ( 497 equ; 0 cnn)
% Maximal formula atoms : 93 ( 24 avg)
% Number of connectives : 1208 ( 68 ~; 59 |; 280 &; 360 @)
% ( 9 <=>; 401 =>; 0 <=; 0 <~>)
% Maximal formula depth : 98 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 189 ( 185 usr; 102 con; 0-4 aty)
% ( 31 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 107 ( 37 ^; 64 !; 6 ?; 107 :)
% 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_126,type,
sK3: ( $i > $o ) > $i > $i ).
thf(func_def_127,type,
sK4: $i > ( $i > $o ) > $i ).
thf(func_def_128,type,
sK5: $i > $i ).
thf(func_def_129,type,
sK6: $i > $i ).
thf(func_def_130,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_131,type,
sK8: $i > $i > $i ).
thf(func_def_132,type,
sK9: $i > $i ).
thf(func_def_133,type,
sK10: $i > $i > $i ).
thf(func_def_134,type,
sK11: $i > $i > $i ).
thf(func_def_135,type,
sK12: $i > $i > $i ).
thf(func_def_136,type,
sK13: $i > $i > $i ).
thf(func_def_137,type,
sK14: $i > $i > $i ).
thf(func_def_138,type,
sK15: $i > $i > $i ).
thf(func_def_139,type,
sK16: $i > $i > $i > $i ).
thf(func_def_140,type,
sK17: $i > $i > $i ).
thf(func_def_141,type,
sK18: ( $i > $o ) > $i ).
thf(func_def_142,type,
sK19: ( $i > $o ) > $i ).
thf(func_def_143,type,
sK20: ( $i > $o ) > $i ).
thf(func_def_144,type,
sK21: $i > $i ).
thf(func_def_145,type,
sK22: ( $i > $o ) > $i > $i ).
thf(func_def_146,type,
sK23: $i > $i > $i ).
thf(func_def_147,type,
sK24: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_148,type,
sK25: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_149,type,
sK26: ( $i > $o ) > $i > $i ).
thf(func_def_150,type,
sK27: ( $i > $o ) > $i ).
thf(func_def_151,type,
sK28: ( $i > $o ) > $i > $i ).
thf(func_def_152,type,
sK29: ( $i > $i > $o ) > $i > $i ).
thf(func_def_153,type,
sK30: ( $i > $i > $o ) > $i > $i ).
thf(func_def_154,type,
sK31: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_155,type,
sK32: $i > $i > $i ).
thf(func_def_156,type,
sK33: $i > $i ).
thf(func_def_157,type,
sK34: ( $i > $o ) > $i > $i ).
thf(func_def_158,type,
sK35: ( $i > $o ) > $i ).
thf(func_def_159,type,
sK36: $o > $i > $i > $i ).
thf(func_def_160,type,
sK37: $i > $i ).
thf(func_def_161,type,
sK38: $i > ( $i > $o ) > $i ).
thf(func_def_162,type,
sK39: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_163,type,
sK40: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_164,type,
sK41: $i > ( $i > $o ) > $i ).
thf(func_def_165,type,
sK42: ( $i > $o ) > $i > $i ).
thf(func_def_166,type,
sK43: ( $i > $o ) > $i > $i ).
thf(func_def_167,type,
sK44: $i > ( $i > $o ) > $i ).
thf(func_def_168,type,
sK45: ( $i > $o ) > $i > $i ).
thf(func_def_169,type,
sK46: ( $i > $o ) > $i > $i ).
thf(func_def_170,type,
sK47: ( $i > $o ) > $i > $i ).
thf(func_def_171,type,
sK48: $i > $i ).
thf(func_def_172,type,
sK49: $i > ( $i > $o ) > $i ).
thf(func_def_173,type,
sK50: ( $i > $o ) > $i > $i ).
thf(func_def_174,type,
sK51: ( $i > $o ) > $i ).
thf(func_def_175,type,
sK52: ( $i > $o ) > $i > $i ).
thf(func_def_176,type,
sK53: $i > $i > $i ).
thf(func_def_177,type,
sK54: $i > $i > $i ).
thf(func_def_178,type,
sK55: $i > $i > $i ).
thf(func_def_179,type,
sK56: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_180,type,
sK57: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_181,type,
ph58:
!>[X0: $tType] : X0 ).
thf(func_def_182,type,
sK59: $i > $i ).
thf(func_def_183,type,
sK60: $i > $i ).
thf(func_def_184,type,
sK61: $i > $i > $i ).
thf(func_def_185,type,
sK62: $i > $i > $i ).
thf(func_def_186,type,
sK63: $i > $i > $i ).
thf(func_def_187,type,
sK64: $i > $i ).
thf(func_def_188,type,
sK65: $i > $i > $i ).
thf(func_def_189,type,
sK66: $i > $i > $i ).
thf(func_def_190,type,
sK67: $i > $i ).
thf(func_def_191,type,
sK68: $i > $i > $i ).
thf(func_def_192,type,
sK69: $i > $i > $i ).
thf(func_def_193,type,
sK70: $i > $i > $i ).
thf(func_def_194,type,
sK71: $i > $i > $i ).
thf(func_def_195,type,
sK72: $i > $i > $i ).
thf(func_def_196,type,
sK73: $i > $i > $i ).
thf(func_def_197,type,
sK74: $i > $i > $i ).
thf(func_def_198,type,
sK75: $i > $i > $i ).
thf(f3127,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1509,f1514,f1519,f1524,f2582,f3117,f3125,f3126]) ).
thf(f3126,plain,
( ( $false
!= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK0 ) )
| ( $true
!= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK0 ) )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f3125,plain,
( spl2_9
| spl2_1
| ~ spl2_7 ),
inference(avatar_split_clause,[status(thm)],[f2848,f2579,f1506,f3122]) ).
thf(f3122,definition,
( spl2_9
<=> ( $true
= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_9])],[avatar_definition]) ).
thf(f1506,definition,
( spl2_1
<=> ( sK0 = sK1 ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f2579,definition,
( spl2_7
<=> ( $false
= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_7])],[avatar_definition]) ).
thf(f2848,plain,
( ( $true
= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK0 ) )
| spl2_1
| ~ spl2_7 ),
inference(subsumption_resolution,[status(thm)],[f2834,f1508]) ).
thf(f1508,plain,
( ( sK0 != sK1 )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f1506]) ).
thf(f2834,plain,
( ( sK0 = sK1 )
| ( $true
= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK0 ) )
| ~ spl2_7 ),
inference(not_proxy_clausification,[status(thm)],[f2833]) ).
thf(f2833,plain,
( ( sK0 = sK1 )
| ( $false
= ( ~ ( in @ ( sK23 @ sK1 @ sK0 ) @ sK0 ) ) )
| ~ spl2_7 ),
inference(boolean_simplification,[status(thm)],[f2824]) ).
thf(f2824,plain,
( ( $false
= ( $false
= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK0 ) ) )
| ( sK0 = sK1 )
| ~ spl2_7 ),
inference(superposition,[status(thm)],[f987,f2581]) ).
thf(f2581,plain,
( ( $false
= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK1 ) )
| ~ spl2_7 ),
inference(avatar_component_clause,[status(thm)],[f2579]) ).
thf(f987,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ ( sK23 @ X1 @ X2 ) @ X1 )
= ( in @ ( sK23 @ X1 @ X2 ) @ X2 ) )
= $false )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f986]) ).
thf(f986,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ ( sK23 @ X1 @ X2 ) @ X1 )
= ( in @ ( sK23 @ X1 @ X2 ) @ X2 ) )
= $false )
| ( $true
= ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f985]) ).
thf(f985,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
= ( in @ Y0 @ X2 ) )
@ ( sK23 @ X1 @ X2 ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f984]) ).
thf(f984,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
= ( in @ Y0 @ X2 ) ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f983]) ).
thf(f983,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
= ( in @ Y0 @ X2 ) ) )
=> ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f982]) ).
thf(f982,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
= ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f981]) ).
thf(f981,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
= ( in @ Y1 @ Y0 ) ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f980]) ).
thf(f980,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
= ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f518]) ).
thf(f518,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
= ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f410,f296]) ).
thf(f296,plain,
( setextAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
= ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
thf(f111,plain,
( setextAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
= ( in @ Y2 @ Y1 ) ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f110]) ).
thf(f110,plain,
( setextAx
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
<=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setextAx
= ( ! [X4: $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
<=> ( in @ X1 @ X4 ) )
=> ( X3 = X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HoFUU0t9AD/DTF2THF_31518.p',setextAx) ).
thf(f410,plain,
setextAx = $true,
inference(cnf_transformation,[status(thm)],[f279]) ).
thf(f279,plain,
( ( descrp = $true )
& ( setadjoinSub = $true )
& ( setadjoinOr = $true )
& ( emptyI = $true )
& ( setadjoinIR = $true )
& ( setadjoinIL = $true )
& ( setext = $true )
& ( nonemptyI1 = $true )
& ( setunionE = $true )
& ( emptysetimpfalse = $true )
& ( in__Cong = $true )
& ( upairsetIR = $true )
& ( descr__Cong = $true )
& ( emptyInPowerset = $true )
& ( omegaSAx = $true )
& ( uniqinunit = $true )
& ( omega__Cong = $true )
& ( emptyinunitempty = $true )
& ( setadjoinAx = $true )
& ( notequalI2 = $true )
& ( emptyset__Cong = $true )
& ( powersetAx = $true )
& ( quantDeMorgan2 = $true )
& ( notdallE = $true )
& ( foundationAx = $true )
& ( dsetconstrI = $true )
& ( setunion__Cong = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan1 = $true )
& ( eqimpsubset2 = $true )
& ( eqimpsubset1 = $true )
& ( powersetI = $true )
& ( dsetconstrEL = $true )
& ( wellorderingAx = $true )
& ( exuEu = $true )
& ( subsetE = $true )
& ( emptysetAx = $true )
& ( exuE1 = $true )
& ( exuI2 = $true )
& ( setadjoinE = $true )
& ( replAx = $true )
& ( setextAx = $true )
& ( exuE3u = $true )
& ( setunionAx = $true )
& ( upairsetE = $true )
& ( exuE3e = $true )
& ( emptyinPowerset = $true )
& ( emptysetsubset = $true )
& ( quantDeMorgan4 = $true )
& ( prop2set2propI = $true )
& ( setadjoinSub2 = $true )
& ( prop2setE = $true )
& ( subsetRefl = $true )
& ( setadjoin__Cong = $true )
& ( inCongP = $true )
& ( subset2powerset = $true )
& ( notsubsetI = $true )
& ( exu__Cong = $true )
& ( notinsingleton = $true )
& ( nonemptyE1 = $true )
& ( upairsetIL = $true )
& ( setunionI = $true )
& ( omegaIndAx = $true )
& ( powersetE = $true )
& ( prop2setI = $true )
& ( exuI1 = $true )
& ( exuI3 = $true )
& ( singletonsswitch = $true )
& ( dsetconstr__Cong = $true )
& ( setoftrueEq = $true )
& ( noeltsimpempty = $true )
& ( subsetI2 = $true )
& ( vacuousDall = $true )
& ( notequalI1 = $true )
& ( powerset__Cong = $true )
& ( sK0 != sK1 )
& ( $true
= ( subset @ sK1 @ sK0 ) )
& ( $true
= ( subset @ sK0 @ sK1 ) )
& ( nonemptyImpWitness = $true )
& ( subsetI1 = $true )
& ( subPowSU = $true )
& ( notdexE = $true )
& ( emptyE1 = $true )
& ( setbeta = $true )
& ( nonemptyI = $true )
& ( subsetE2 = $true )
& ( dsetconstrER = $true )
& ( exuE2 = $true )
& ( emptysetE = $true )
& ( notinemptyset = $true )
& ( subsetTrans = $true )
& ( eqinunit = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f277,f278]) ).
thf(f278,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( $true
= ( subset @ X1 @ X0 ) )
& ( $true
= ( subset @ X0 @ X1 ) ) )
=> ( ( sK0 != sK1 )
& ( $true
= ( subset @ sK1 @ sK0 ) )
& ( $true
= ( subset @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f277,plain,
( ( descrp = $true )
& ( setadjoinSub = $true )
& ( setadjoinOr = $true )
& ( emptyI = $true )
& ( setadjoinIR = $true )
& ( setadjoinIL = $true )
& ( setext = $true )
& ( nonemptyI1 = $true )
& ( setunionE = $true )
& ( emptysetimpfalse = $true )
& ( in__Cong = $true )
& ( upairsetIR = $true )
& ( descr__Cong = $true )
& ( emptyInPowerset = $true )
& ( omegaSAx = $true )
& ( uniqinunit = $true )
& ( omega__Cong = $true )
& ( emptyinunitempty = $true )
& ( setadjoinAx = $true )
& ( notequalI2 = $true )
& ( emptyset__Cong = $true )
& ( powersetAx = $true )
& ( quantDeMorgan2 = $true )
& ( notdallE = $true )
& ( foundationAx = $true )
& ( dsetconstrI = $true )
& ( setunion__Cong = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan1 = $true )
& ( eqimpsubset2 = $true )
& ( eqimpsubset1 = $true )
& ( powersetI = $true )
& ( dsetconstrEL = $true )
& ( wellorderingAx = $true )
& ( exuEu = $true )
& ( subsetE = $true )
& ( emptysetAx = $true )
& ( exuE1 = $true )
& ( exuI2 = $true )
& ( setadjoinE = $true )
& ( replAx = $true )
& ( setextAx = $true )
& ( exuE3u = $true )
& ( setunionAx = $true )
& ( upairsetE = $true )
& ( exuE3e = $true )
& ( emptyinPowerset = $true )
& ( emptysetsubset = $true )
& ( quantDeMorgan4 = $true )
& ( prop2set2propI = $true )
& ( setadjoinSub2 = $true )
& ( prop2setE = $true )
& ( subsetRefl = $true )
& ( setadjoin__Cong = $true )
& ( inCongP = $true )
& ( subset2powerset = $true )
& ( notsubsetI = $true )
& ( exu__Cong = $true )
& ( notinsingleton = $true )
& ( nonemptyE1 = $true )
& ( upairsetIL = $true )
& ( setunionI = $true )
& ( omegaIndAx = $true )
& ( powersetE = $true )
& ( prop2setI = $true )
& ( exuI1 = $true )
& ( exuI3 = $true )
& ( singletonsswitch = $true )
& ( dsetconstr__Cong = $true )
& ( setoftrueEq = $true )
& ( noeltsimpempty = $true )
& ( subsetI2 = $true )
& ( vacuousDall = $true )
& ( notequalI1 = $true )
& ( powerset__Cong = $true )
& ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( $true
= ( subset @ X1 @ X0 ) )
& ( $true
= ( subset @ X0 @ X1 ) ) )
& ( nonemptyImpWitness = $true )
& ( subsetI1 = $true )
& ( subPowSU = $true )
& ( notdexE = $true )
& ( emptyE1 = $true )
& ( setbeta = $true )
& ( nonemptyI = $true )
& ( subsetE2 = $true )
& ( dsetconstrER = $true )
& ( exuE2 = $true )
& ( emptysetE = $true )
& ( notinemptyset = $true )
& ( subsetTrans = $true )
& ( eqinunit = $true ) ),
inference(flattening,[status(thm)],[f276]) ).
thf(f276,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( $true
= ( subset @ X0 @ X1 ) )
& ( $true
= ( subset @ X1 @ X0 ) ) )
& ( 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)],[f198]) ).
thf(f198,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 )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
=> ( ( $true
= ( subset @ X0 @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f197]) ).
thf(f197,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
=> ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( ( subset @ X0 @ X1 )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f94]) ).
thf(f94,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
=> ! [X4: $i,X3: $i] :
( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X3 )
=> ( X3 = X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f93]) ).
thf(f93,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
=> ! [X4: $i,X3: $i] :
( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X3 )
=> ( X3 = X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HoFUU0t9AD/DTF2THF_31518.p',setextsub) ).
thf(f3117,plain,
( spl2_8
| ~ spl2_2
| ~ spl2_7 ),
inference(avatar_split_clause,[status(thm)],[f2846,f2579,f1511,f2956]) ).
thf(f2956,definition,
( spl2_8
<=> ( $false
= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_8])],[avatar_definition]) ).
thf(f1511,definition,
( spl2_2
<=> ( $true
= ( subset @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f2846,plain,
( ( $false
= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK0 ) )
| ~ spl2_2
| ~ spl2_7 ),
inference(trivial_inequality_removal,[status(thm)],[f2826]) ).
thf(f2826,plain,
( ( $false
= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK0 ) )
| ( $true = $false )
| ~ spl2_2
| ~ spl2_7 ),
inference(superposition,[status(thm)],[f1806,f2581]) ).
thf(f1806,plain,
( ! [X0: $i] :
( ( $true
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f1792]) ).
thf(f1792,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f619,f1513]) ).
thf(f1513,plain,
( ( $true
= ( subset @ sK0 @ sK1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f1511]) ).
thf(f619,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X1 @ X3 ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( in @ X2 @ X3 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f618]) ).
thf(f618,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X3 )
= $true )
| ( ( ~ ( in @ X2 @ X1 ) )
= $true )
| ( $false
= ( subset @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f617]) ).
thf(f617,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( in @ X2 @ X3 ) ) )
| ( $false
= ( subset @ X1 @ X3 ) )
| ( ( ~ ( in @ X2 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f616]) ).
thf(f616,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X1 @ X3 ) )
| ( $true
= ( ~ ( in @ X2 @ X3 )
=> ~ ( in @ X2 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f615]) ).
thf(f615,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X1 @ X3 )
=> ( ~ ( in @ X2 @ X3 )
=> ~ ( in @ X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f614]) ).
thf(f614,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ~ ( in @ X2 @ Y0 )
=> ~ ( in @ X2 @ X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f613]) ).
thf(f613,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 )
=> ( ~ ( in @ X2 @ Y0 )
=> ~ ( in @ X2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f612]) ).
thf(f612,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y1 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ~ ( in @ Y0 @ X1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f611]) ).
thf(f611,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y1 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ~ ( in @ Y0 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f610]) ).
thf(f610,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ~ ( in @ Y1 @ Y2 )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f558]) ).
thf(f558,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ~ ( in @ Y1 @ Y2 )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f454,f366]) ).
thf(f366,plain,
subsetE2 = $true,
inference(cnf_transformation,[status(thm)],[f279]) ).
thf(f454,plain,
( subsetE2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ~ ( in @ Y1 @ Y2 )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
thf(f115,plain,
( subsetE2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y2 )
=> ( ~ ( in @ Y1 @ Y2 )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f114]) ).
thf(f114,plain,
( subsetE2
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X2 @ X0 )
=> ( ~ ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f84]) ).
thf(f84,axiom,
( subsetE2
= ( ! [X4: $i,X1: $i,X3: $i] :
( ( subset @ X3 @ X4 )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( in @ X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HoFUU0t9AD/DTF2THF_31518.p',subsetE2) ).
thf(f2582,plain,
( spl2_7
| spl2_1
| ~ spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f2577,f1521,f1506,f2579]) ).
thf(f1521,definition,
( spl2_4
<=> ( $true
= ( subset @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f2577,plain,
( ( $false
= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK1 ) )
| spl2_1
| ~ spl2_4 ),
inference(subsumption_resolution,[status(thm)],[f2565,f1508]) ).
thf(f2565,plain,
( ( $false
= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK1 ) )
| ( sK0 = sK1 )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f2559]) ).
thf(f2559,plain,
( ( sK0 = sK1 )
| ( $false
= ( in @ ( sK23 @ sK1 @ sK0 ) @ sK1 ) )
| ( $false != $false )
| ~ spl2_4 ),
inference(equality_factoring,[status(thm)],[f2464]) ).
thf(f2464,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK23 @ X0 @ sK0 ) @ sK1 ) )
| ( sK0 = X0 )
| ( $false
= ( in @ ( sK23 @ X0 @ sK0 ) @ X0 ) ) )
| ~ spl2_4 ),
inference(boolean_simplification,[status(thm)],[f2419]) ).
thf(f2419,plain,
( ! [X0: $i] :
( ( sK0 = X0 )
| ( $false
= ( in @ ( sK23 @ X0 @ sK0 ) @ sK1 ) )
| ( ( ( in @ ( sK23 @ X0 @ sK0 ) @ X0 )
= $true )
= $false ) )
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f987,f1802]) ).
thf(f1802,plain,
( ! [X0: $i] :
( ( $true
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f1793]) ).
thf(f1793,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( $true
= ( in @ X0 @ sK0 ) )
| ( $true = $false ) )
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f619,f1523]) ).
thf(f1523,plain,
( ( $true
= ( subset @ sK1 @ sK0 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f1521]) ).
thf(f1524,plain,
spl2_4,
inference(avatar_split_clause,[status(thm)],[f375,f1521]) ).
thf(f375,plain,
( $true
= ( subset @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f279]) ).
thf(f1519,plain,
~ spl2_3,
inference(avatar_split_clause,[status(thm)],[f95,f1516]) ).
thf(f1516,definition,
( spl2_3
<=> ( $true = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f95,plain,
$true != $false,
introduced(definition,[],[fool_axiom]) ).
thf(f1514,plain,
spl2_2,
inference(avatar_split_clause,[status(thm)],[f374,f1511]) ).
thf(f374,plain,
( $true
= ( subset @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f279]) ).
thf(f1509,plain,
~ spl2_1,
inference(avatar_split_clause,[status(thm)],[f376,f1506]) ).
thf(f376,plain,
sK0 != sK1,
inference(cnf_transformation,[status(thm)],[f279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU574^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n004.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:27:11 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEU574^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Set Theory
% 0.16/0.39 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : (! A:i.! B:i.subset A B -> subset B A -> A = B)
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.39 % Source : [Bro08]
% 0.16/0.39 % Names : ZFC076g [Bro08]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.71 v6.0.0, 0.57 v5.5.0, 0.83 v5.4.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 198 ( 92 unt; 105 typ; 92 def)
% 0.16/0.39 % Number of atoms : 503 ( 140 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 93 ( 5 avg)
% 0.16/0.39 % Number of connectives : 794 ( 29 ~; 5 |; 27 &; 489 @)
% 0.16/0.39 % ( 14 <=>; 230 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 97 ( 2 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 108 ( 105 usr; 94 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 280 ( 28 ^; 224 !; 28 ?; 280 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : http://mathgate.info/detsetitem.php?id=154
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(in_type,type,
% 0.16/0.39 in: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu_type,type,
% 0.16/0.39 exu: ( $i > $o ) > $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu,definition,
% 0.16/0.39 ( exu
% 0.16/0.39 = ( ^ [Xphi: $i > $o] :
% 0.16/0.39 ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setextAx_type,type,
% 0.16/0.39 setextAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setextAx,definition,
% 0.16/0.39 ( setextAx
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 <=> ( in @ Xx @ B ) )
% 0.16/0.39 => ( A = B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset_type,type,
% 0.16/0.39 emptyset: $i ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetAx_type,type,
% 0.16/0.39 emptysetAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetAx,definition,
% 0.16/0.39 ( emptysetAx
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin_type,type,
% 0.16/0.39 setadjoin: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinAx_type,type,
% 0.16/0.39 setadjoinAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinAx,definition,
% 0.16/0.39 ( setadjoinAx
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 <=> ( ( Xy = Xx )
% 0.16/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powerset_type,type,
% 0.16/0.39 powerset: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(powersetAx_type,type,
% 0.16/0.39 powersetAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetAx,definition,
% 0.16/0.39 ( powersetAx
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 <=> ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunion_type,type,
% 0.16/0.39 setunion: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setunionAx_type,type,
% 0.16/0.39 setunionAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionAx,definition,
% 0.16/0.39 ( setunionAx
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.39 <=> ? [B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 & ( in @ B @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omega_type,type,
% 0.16/0.39 omega: $i ).
% 0.16/0.39
% 0.16/0.39 thf(omega0Ax_type,type,
% 0.16/0.39 omega0Ax: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omega0Ax,definition,
% 0.16/0.39 ( omega0Ax
% 0.16/0.39 = ( in @ emptyset @ omega ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omegaSAx_type,type,
% 0.16/0.39 omegaSAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omegaSAx,definition,
% 0.16/0.39 ( omegaSAx
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ omega )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omegaIndAx_type,type,
% 0.16/0.39 omegaIndAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omegaIndAx,definition,
% 0.16/0.39 ( omegaIndAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( ( in @ emptyset @ A )
% 0.16/0.39 & ! [Xx: $i] :
% 0.16/0.39 ( ( ( in @ Xx @ omega )
% 0.16/0.39 & ( in @ Xx @ A ) )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ omega )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(replAx_type,type,
% 0.16/0.39 replAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(replAx,definition,
% 0.16/0.39 ( replAx
% 0.16/0.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.16/0.39 => ? [B: $i] :
% 0.16/0.39 ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 <=> ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(foundationAx_type,type,
% 0.16/0.39 foundationAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(foundationAx,definition,
% 0.16/0.39 ( foundationAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.39 => ? [B: $i] :
% 0.16/0.39 ( ( in @ B @ A )
% 0.16/0.39 & ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(wellorderingAx_type,type,
% 0.16/0.39 wellorderingAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(wellorderingAx,definition,
% 0.16/0.39 ( wellorderingAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ? [B: $i] :
% 0.16/0.39 ( ! [C: $i] :
% 0.16/0.39 ( ( in @ C @ B )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ A ) ) )
% 0.16/0.39 & ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( ( in @ Xx @ A )
% 0.16/0.39 & ( in @ Xy @ A ) )
% 0.16/0.39 => ( ! [C: $i] :
% 0.16/0.39 ( ( in @ C @ B )
% 0.16/0.39 => ( ( in @ Xx @ C )
% 0.16/0.39 <=> ( in @ Xy @ C ) ) )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 & ! [C: $i,D: $i] :
% 0.16/0.39 ( ( ( in @ C @ B )
% 0.16/0.39 & ( in @ D @ B ) )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ D ) )
% 0.16/0.39 | ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ D )
% 0.16/0.39 => ( in @ Xx @ C ) ) ) )
% 0.16/0.39 & ! [C: $i] :
% 0.16/0.39 ( ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.16/0.39 => ? [D: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ D @ B )
% 0.16/0.39 & ( in @ Xx @ C )
% 0.16/0.39 & ~ ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ D )
% 0.16/0.39 & ( in @ Xy @ C ) )
% 0.16/0.39 & ! [E: $i] :
% 0.16/0.39 ( ( in @ E @ B )
% 0.16/0.39 => ( ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ E )
% 0.16/0.39 => ( in @ Xy @ D ) )
% 0.16/0.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(descr_type,type,
% 0.16/0.39 descr: ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(descrp_type,type,
% 0.16/0.39 descrp: $o ).
% 0.16/0.39
% 0.16/0.39 thf(descrp,definition,
% 0.16/0.39 ( descrp
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ( Xphi
% 0.16/0.39 @ ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr_type,type,
% 0.16/0.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrI_type,type,
% 0.16/0.39 dsetconstrI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrI,definition,
% 0.16/0.39 ( dsetconstrI
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrEL_type,type,
% 0.16/0.39 dsetconstrEL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrEL,definition,
% 0.16/0.39 ( dsetconstrEL
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrER_type,type,
% 0.16/0.39 dsetconstrER: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrER,definition,
% 0.16/0.39 ( dsetconstrER
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE1_type,type,
% 0.16/0.39 exuE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE1,definition,
% 0.16/0.39 ( exuE1
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set_type,type,
% 0.16/0.39 prop2set: $o > $i ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setE_type,type,
% 0.16/0.39 prop2setE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setE,definition,
% 0.16/0.39 ( prop2setE
% 0.16/0.39 = ( ! [Xphi: $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.16/0.39 => Xphi ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetE_type,type,
% 0.16/0.39 emptysetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetE,definition,
% 0.16/0.39 ( emptysetE
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetimpfalse_type,type,
% 0.16/0.39 emptysetimpfalse: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetimpfalse,definition,
% 0.16/0.39 ( emptysetimpfalse
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => $false ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notinemptyset_type,type,
% 0.16/0.39 notinemptyset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notinemptyset,definition,
% 0.16/0.39 ( notinemptyset
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3e_type,type,
% 0.16/0.39 exuE3e: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3e,definition,
% 0.16/0.39 ( exuE3e
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setext_type,type,
% 0.16/0.39 setext: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setext,definition,
% 0.16/0.39 ( setext
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 => ( A = B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyI_type,type,
% 0.16/0.39 emptyI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyI,definition,
% 0.16/0.39 ( emptyI
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ A )
% 0.16/0.39 => ( A = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(noeltsimpempty_type,type,
% 0.16/0.39 noeltsimpempty: $o ).
% 0.16/0.39
% 0.16/0.39 thf(noeltsimpempty,definition,
% 0.16/0.39 ( noeltsimpempty
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ A )
% 0.16/0.39 => ( A = emptyset ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setbeta_type,type,
% 0.16/0.39 setbeta: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setbeta,definition,
% 0.16/0.39 ( setbeta
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonempty_type,type,
% 0.16/0.39 nonempty: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonempty,definition,
% 0.16/0.39 ( nonempty
% 0.16/0.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyE1_type,type,
% 0.16/0.39 nonemptyE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyE1,definition,
% 0.16/0.39 ( nonemptyE1
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( nonempty @ A )
% 0.16/0.39 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI_type,type,
% 0.16/0.39 nonemptyI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI,definition,
% 0.16/0.39 ( nonemptyI
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( nonempty
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI1_type,type,
% 0.16/0.39 nonemptyI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyI1,definition,
% 0.16/0.39 ( nonemptyI1
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.39 => ( nonempty @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIL_type,type,
% 0.16/0.39 setadjoinIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIL,definition,
% 0.16/0.39 ( setadjoinIL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinunitempty_type,type,
% 0.16/0.39 emptyinunitempty: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinunitempty,definition,
% 0.16/0.39 ( emptyinunitempty
% 0.16/0.39 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIR_type,type,
% 0.16/0.39 setadjoinIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinIR,definition,
% 0.16/0.39 ( setadjoinIR
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinE_type,type,
% 0.16/0.39 setadjoinE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinE,definition,
% 0.16/0.39 ( setadjoinE
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 => ! [Xphi: $o] :
% 0.16/0.39 ( ( ( Xy = Xx )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => ( ( ( in @ Xy @ A )
% 0.16/0.39 => Xphi )
% 0.16/0.39 => Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinOr_type,type,
% 0.16/0.39 setadjoinOr: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinOr,definition,
% 0.16/0.39 ( setadjoinOr
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 => ( ( Xy = Xx )
% 0.16/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setoftrueEq_type,type,
% 0.16/0.39 setoftrueEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setoftrueEq,definition,
% 0.16/0.39 ( setoftrueEq
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : $true )
% 0.16/0.39 = A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI_type,type,
% 0.16/0.39 powersetI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI,definition,
% 0.16/0.39 ( powersetI
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinPowerset_type,type,
% 0.16/0.39 emptyinPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyinPowerset,definition,
% 0.16/0.39 ( emptyinPowerset
% 0.16/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyInPowerset_type,type,
% 0.16/0.39 emptyInPowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyInPowerset,definition,
% 0.16/0.39 ( emptyInPowerset
% 0.16/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE_type,type,
% 0.16/0.39 powersetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetE,definition,
% 0.16/0.39 ( powersetE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 => ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionI_type,type,
% 0.16/0.39 setunionI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionI,definition,
% 0.16/0.39 ( setunionI
% 0.16/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( ( in @ B @ A )
% 0.16/0.39 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE_type,type,
% 0.16/0.39 setunionE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE,definition,
% 0.16/0.39 ( setunionE
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.39 => ! [Xphi: $o] :
% 0.16/0.39 ( ! [B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( ( in @ B @ A )
% 0.16/0.39 => Xphi ) )
% 0.16/0.39 => Xphi ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subPowSU_type,type,
% 0.16/0.39 subPowSU: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subPowSU,definition,
% 0.16/0.39 ( subPowSU
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE2_type,type,
% 0.16/0.39 exuE2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE2,definition,
% 0.16/0.39 ( exuE2
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyImpWitness_type,type,
% 0.16/0.39 nonemptyImpWitness: $o ).
% 0.16/0.39
% 0.16/0.39 thf(nonemptyImpWitness,definition,
% 0.16/0.39 ( nonemptyImpWitness
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( nonempty @ A )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & $true ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(uniqinunit_type,type,
% 0.16/0.39 uniqinunit: $o ).
% 0.16/0.39
% 0.16/0.39 thf(uniqinunit,definition,
% 0.16/0.39 ( uniqinunit
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notinsingleton_type,type,
% 0.16/0.39 notinsingleton: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notinsingleton,definition,
% 0.16/0.39 ( notinsingleton
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx != Xy )
% 0.16/0.39 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqinunit_type,type,
% 0.16/0.39 eqinunit: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqinunit,definition,
% 0.16/0.39 ( eqinunit
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsswitch_type,type,
% 0.16/0.39 singletonsswitch: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsswitch,definition,
% 0.16/0.39 ( singletonsswitch
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetE_type,type,
% 0.16/0.39 upairsetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetE,definition,
% 0.16/0.39 ( upairsetE
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.16/0.39 => ( ( Xz = Xx )
% 0.16/0.39 | ( Xz = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIL_type,type,
% 0.16/0.39 upairsetIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIL,definition,
% 0.16/0.39 ( upairsetIL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIR_type,type,
% 0.16/0.39 upairsetIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetIR,definition,
% 0.16/0.39 ( upairsetIR
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyE1_type,type,
% 0.16/0.39 emptyE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyE1,definition,
% 0.16/0.39 ( emptyE1
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ( ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = emptyset )
% 0.16/0.39 => $false ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(vacuousDall_type,type,
% 0.16/0.39 vacuousDall: $o ).
% 0.16/0.39
% 0.16/0.39 thf(vacuousDall,definition,
% 0.16/0.39 ( vacuousDall
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan1_type,type,
% 0.16/0.39 quantDeMorgan1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan1,definition,
% 0.16/0.39 ( quantDeMorgan1
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan2_type,type,
% 0.16/0.39 quantDeMorgan2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan2,definition,
% 0.16/0.39 ( quantDeMorgan2
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) )
% 0.16/0.39 => ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan3_type,type,
% 0.16/0.39 quantDeMorgan3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan3,definition,
% 0.16/0.39 ( quantDeMorgan3
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan4_type,type,
% 0.16/0.39 quantDeMorgan4: $o ).
% 0.16/0.39
% 0.16/0.39 thf(quantDeMorgan4,definition,
% 0.16/0.39 ( quantDeMorgan4
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) )
% 0.16/0.39 => ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setI_type,type,
% 0.16/0.39 prop2setI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setI,definition,
% 0.16/0.39 ( prop2setI
% 0.16/0.39 = ( ! [Xphi: $o] :
% 0.16/0.39 ( Xphi
% 0.16/0.39 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(set2prop_type,type,
% 0.16/0.39 set2prop: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set2propI_type,type,
% 0.16/0.39 prop2set2propI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set2propI,definition,
% 0.16/0.39 ( prop2set2propI
% 0.16/0.39 = ( ! [Xphi: $o] :
% 0.16/0.39 ( Xphi
% 0.16/0.39 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notdexE_type,type,
% 0.16/0.39 notdexE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notdexE,definition,
% 0.16/0.39 ( notdexE
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notdallE_type,type,
% 0.16/0.39 notdallE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notdallE,definition,
% 0.16/0.39 ( notdallE
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ~ ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI1_type,type,
% 0.16/0.39 exuI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI1,definition,
% 0.16/0.39 ( exuI1
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI3_type,type,
% 0.16/0.39 exuI3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI3,definition,
% 0.16/0.39 ( exuI3
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.16/0.39 => ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuI2_type,type,
% 0.16/0.39 exuI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuI2,definition,
% 0.16/0.39 ( exuI2
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 <=> ( Xy = Xx ) )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(inCongP_type,type,
% 0.16/0.39 inCongP: $o ).
% 0.16/0.39
% 0.16/0.39 thf(inCongP,definition,
% 0.16/0.39 ( inCongP
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(in__Cong_type,type,
% 0.16/0.39 in__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(in__Cong,definition,
% 0.16/0.39 ( in__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3u_type,type,
% 0.16/0.39 exuE3u: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3u,definition,
% 0.16/0.39 ( exuE3u
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exu__Cong_type,type,
% 0.16/0.39 exu__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu__Cong,definition,
% 0.16/0.39 ( exu__Cong
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 <=> ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset__Cong_type,type,
% 0.16/0.39 emptyset__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset__Cong,definition,
% 0.16/0.39 ( emptyset__Cong
% 0.16/0.39 = ( emptyset = emptyset ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin__Cong_type,type,
% 0.16/0.39 setadjoin__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin__Cong,definition,
% 0.16/0.39 ( setadjoin__Cong
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ! [Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( Xz = Xu )
% 0.16/0.39 => ( ( setadjoin @ Xx @ Xz )
% 0.16/0.39 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powerset__Cong_type,type,
% 0.16/0.39 powerset__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powerset__Cong,definition,
% 0.16/0.39 ( powerset__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( ( powerset @ A )
% 0.16/0.39 = ( powerset @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunion__Cong_type,type,
% 0.16/0.39 setunion__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunion__Cong,definition,
% 0.16/0.39 ( setunion__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( ( setunion @ A )
% 0.16/0.39 = ( setunion @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omega__Cong_type,type,
% 0.16/0.39 omega__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omega__Cong,definition,
% 0.16/0.39 ( omega__Cong
% 0.16/0.39 = ( omega = omega ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuEu_type,type,
% 0.16/0.39 exuEu: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuEu,definition,
% 0.16/0.39 ( exuEu
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(descr__Cong_type,type,
% 0.16/0.39 descr__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(descr__Cong,definition,
% 0.16/0.39 ( descr__Cong
% 0.16/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.16/0.39 => ( ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr__Cong_type,type,
% 0.16/0.39 dsetconstr__Cong: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr__Cong,definition,
% 0.16/0.39 ( dsetconstr__Cong
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( Xx = Xy )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.16/0.39 => ( ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 = ( dsetconstr @ B
% 0.16/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subset_type,type,
% 0.16/0.39 subset: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(disjoint_type,type,
% 0.16/0.39 disjoint: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(setsmeet_type,type,
% 0.16/0.39 setsmeet: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI1_type,type,
% 0.16/0.39 subsetI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI1,definition,
% 0.16/0.39 ( subsetI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset2_type,type,
% 0.16/0.39 eqimpsubset2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset2,definition,
% 0.16/0.39 ( eqimpsubset2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset1_type,type,
% 0.16/0.39 eqimpsubset1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(eqimpsubset1,definition,
% 0.16/0.39 ( eqimpsubset1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( A = B )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI2_type,type,
% 0.16/0.39 subsetI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetI2,definition,
% 0.16/0.39 ( subsetI2
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetsubset_type,type,
% 0.16/0.39 emptysetsubset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetsubset,definition,
% 0.16/0.39 ( emptysetsubset
% 0.16/0.39 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE_type,type,
% 0.16/0.39 subsetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE,definition,
% 0.16/0.39 ( subsetE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE2_type,type,
% 0.16/0.39 subsetE2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetE2,definition,
% 0.16/0.39 ( subsetE2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notsubsetI_type,type,
% 0.16/0.39 notsubsetI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notsubsetI,definition,
% 0.16/0.39 ( notsubsetI
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI1_type,type,
% 0.16/0.39 notequalI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI1,definition,
% 0.16/0.39 ( notequalI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ~ ( subset @ A @ B )
% 0.16/0.39 => ( A != B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI2_type,type,
% 0.16/0.39 notequalI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notequalI2,definition,
% 0.16/0.39 ( notequalI2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ( A != B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetRefl_type,type,
% 0.16/0.39 subsetRefl: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetRefl,definition,
% 0.16/0.39 ( subsetRefl
% 0.16/0.39 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subsetTrans_type,type,
% 0.16/0.39 subsetTrans: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subsetTrans,definition,
% 0.16/0.39 ( subsetTrans
% 0.16/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( subset @ B @ C )
% 0.16/0.39 => ( subset @ A @ C ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub_type,type,
% 0.16/0.39 setadjoinSub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub,definition,
% 0.16/0.39 ( setadjoinSub
% 0.16/0.39 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub2_type,type,
% 0.16/0.39 setadjoinSub2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinSub2,definition,
% 0.16/0.39 ( setadjoinSub2
% 0.16/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(subset2powerset_type,type,
% 0.16/0.39 subset2powerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(subset2powerset,definition,
% 0.16/0.39 ( subset2powerset
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setextsub,conjecture,
% 0.16/0.39 ( setextAx
% 0.16/0.39 => ( emptysetAx
% 0.16/0.39 => ( setadjoinAx
% 0.16/0.39 => ( powersetAx
% 0.16/0.39 => ( setunionAx
% 0.16/0.39 => ( omega0Ax
% 0.16/0.39 => ( omegaSAx
% 0.16/0.39 => ( omegaIndAx
% 0.16/0.39 => ( replAx
% 0.16/0.39 => ( foundationAx
% 0.16/0.39 => ( wellorderingAx
% 0.16/0.39 => ( descrp
% 0.16/0.39 => ( dsetconstrI
% 0.16/0.39 => ( dsetconstrEL
% 0.16/0.39 => ( dsetconstrER
% 0.16/0.39 => ( exuE1
% 0.16/0.39 => ( prop2setE
% 0.16/0.39 => ( emptysetE
% 0.16/0.39 => ( emptysetimpfalse
% 0.16/0.39 => ( notinemptyset
% 0.16/0.39 => ( exuE3e
% 0.16/0.39 => ( setext
% 0.16/0.39 => ( emptyI
% 0.16/0.39 => ( noeltsimpempty
% 0.16/0.39 => ( setbeta
% 0.16/0.39 => ( nonemptyE1
% 0.16/0.39 => ( nonemptyI
% 0.16/0.39 => ( nonemptyI1
% 0.16/0.39 => ( setadjoinIL
% 0.16/0.39 => ( emptyinunitempty
% 0.16/0.39 => ( setadjoinIR
% 0.16/0.39 => ( setadjoinE
% 0.16/0.39 => ( setadjoinOr
% 0.16/0.39 => ( setoftrueEq
% 0.16/0.39 => ( powersetI
% 0.16/0.39 => ( emptyinPowerset
% 0.16/0.39 => ( emptyInPowerset
% 0.16/0.39 => ( powersetE
% 0.16/0.39 => ( setunionI
% 0.16/0.39 => ( setunionE
% 0.16/0.39 => ( subPowSU
% 0.16/0.39 => ( exuE2
% 0.16/0.39 => ( nonemptyImpWitness
% 0.16/0.39 => ( uniqinunit
% 0.16/0.39 => ( notinsingleton
% 0.16/0.39 => ( eqinunit
% 0.16/0.39 => ( singletonsswitch
% 0.16/0.39 => ( upairsetE
% 0.16/0.39 => ( upairsetIL
% 0.16/0.39 => ( upairsetIR
% 0.16/0.39 => ( emptyE1
% 0.16/0.39 => ( vacuousDall
% 0.16/0.39 => ( quantDeMorgan1
% 0.16/0.39 => ( quantDeMorgan2
% 0.16/0.39 => ( quantDeMorgan3
% 0.16/0.39 => ( quantDeMorgan4
% 0.16/0.39 => ( prop2setI
% 0.16/0.39 => ( prop2set2propI
% 0.16/0.39 => ( notdexE
% 0.16/0.39 => ( notdallE
% 0.16/0.39 => ( exuI1
% 0.16/0.39 => ( exuI3
% 0.16/0.39 => ( exuI2
% 0.16/0.39 => ( inCongP
% 0.16/0.39 => ( in__Cong
% 0.16/0.39 => ( exuE3u
% 0.16/0.39 => ( exu__Cong
% 0.16/0.39 => ( emptyset__Cong
% 0.16/0.39 => ( setadjoin__Cong
% 0.16/0.39 => ( powerset__Cong
% 0.16/0.39 => ( setunion__Cong
% 0.16/0.39 => ( omega__Cong
% 0.16/0.39 => ( exuEu
% 0.16/0.39 => ( descr__Cong
% 0.16/0.39 => ( dsetconstr__Cong
% 0.16/0.39 => ( subsetI1
% 0.16/0.39 => ( eqimpsubset2
% 0.16/0.39 => ( eqimpsubset1
% 0.16/0.39 => ( subsetI2
% 0.16/0.39 => ( emptysetsubset
% 0.16/0.39 => ( subsetE
% 0.16/0.39 => ( subsetE2
% 0.16/0.39 => ( notsubsetI
% 0.16/0.39 => ( notequalI1
% 0.16/0.39 => ( notequalI2
% 0.16/0.39 => ( subsetRefl
% 0.16/0.39 => ( subsetTrans
% 0.16/0.39 => ( setadjoinSub
% 0.16/0.39 => ( setadjoinSub2
% 0.16/0.39 => ( subset2powerset
% 0.16/0.39 => ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ A @ B )
% 0.16/0.39 => ( ( subset @ B @ A )
% 0.16/0.39 => ( A = B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 2.44/1.54 ---- Embedded in THF ---
% 2.44/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.44/1.54 %%% Generated on Tue Feb 24 12:27:12 EST 2026
% 2.44/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 2.44/1.54 %%% Logic specification used:
% 2.44/1.54 %%% thf(spec, logic, $$dhol).
% 2.44/1.54
% 2.44/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.HoFUU0t9AD/DTF2DTF31518.p
% See solution above
% 2.44/1.54 ------------------------
% 2.44/1.56 ---- Cleaned THF ---
% 2.44/1.56 thf(in_type,type,
% 2.44/1.56 in: $i > $i > $o ).
% 2.44/1.56
% 2.44/1.56 thf(exu_type,type,
% 2.44/1.56 exu: ( $i > $o ) > $o ).
% 2.44/1.56
% 2.44/1.56 thf(exu,definition,
% 2.44/1.56 ( exu
% 2.44/1.56 = ( ^ [Xphi: $i > $o] :
% 2.44/1.56 ? [Xx: $i] :
% 2.44/1.56 ( ( Xphi @ Xx )
% 2.44/1.56 & ! [Xy: $i] :
% 2.44/1.56 ( ( Xphi @ Xy )
% 2.44/1.56 => ( Xx = Xy ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setextAx_type,type,
% 2.44/1.56 setextAx: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setextAx,definition,
% 2.44/1.56 ( setextAx
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 <=> ( in @ Xx @ B ) )
% 2.44/1.56 => ( A = B ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(emptyset_type,type,
% 2.44/1.56 emptyset: $i ).
% 2.44/1.56
% 2.44/1.56 thf(emptysetAx_type,type,
% 2.44/1.56 emptysetAx: $o ).
% 2.44/1.56
% 2.44/1.56 thf(emptysetAx,definition,
% 2.44/1.56 ( emptysetAx
% 2.44/1.56 = ( ! [Xx: $i] :
% 2.44/1.56 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoin_type,type,
% 2.44/1.56 setadjoin: $i > $i > $i ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinAx_type,type,
% 2.44/1.56 setadjoinAx: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinAx,definition,
% 2.44/1.56 ( setadjoinAx
% 2.44/1.56 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.44/1.56 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.44/1.56 <=> ( ( Xy = Xx )
% 2.44/1.56 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(powerset_type,type,
% 2.44/1.56 powerset: $i > $i ).
% 2.44/1.56
% 2.44/1.56 thf(powersetAx_type,type,
% 2.44/1.56 powersetAx: $o ).
% 2.44/1.56
% 2.44/1.56 thf(powersetAx,definition,
% 2.44/1.56 ( powersetAx
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ( in @ B @ ( powerset @ A ) )
% 2.44/1.56 <=> ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ B )
% 2.44/1.56 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setunion_type,type,
% 2.44/1.56 setunion: $i > $i ).
% 2.44/1.56
% 2.44/1.56 thf(setunionAx_type,type,
% 2.44/1.56 setunionAx: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setunionAx,definition,
% 2.44/1.56 ( setunionAx
% 2.44/1.56 = ( ! [A: $i,Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ ( setunion @ A ) )
% 2.44/1.56 <=> ? [B: $i] :
% 2.44/1.56 ( ( in @ Xx @ B )
% 2.44/1.56 & ( in @ B @ A ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(omega_type,type,
% 2.44/1.56 omega: $i ).
% 2.44/1.56
% 2.44/1.56 thf(omega0Ax_type,type,
% 2.44/1.56 omega0Ax: $o ).
% 2.44/1.56
% 2.44/1.56 thf(omega0Ax,definition,
% 2.44/1.56 ( omega0Ax
% 2.44/1.56 = ( in @ emptyset @ omega ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(omegaSAx_type,type,
% 2.44/1.56 omegaSAx: $o ).
% 2.44/1.56
% 2.44/1.56 thf(omegaSAx,definition,
% 2.44/1.56 ( omegaSAx
% 2.44/1.56 = ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ omega )
% 2.44/1.56 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(omegaIndAx_type,type,
% 2.44/1.56 omegaIndAx: $o ).
% 2.44/1.56
% 2.44/1.56 thf(omegaIndAx,definition,
% 2.44/1.56 ( omegaIndAx
% 2.44/1.56 = ( ! [A: $i] :
% 2.44/1.56 ( ( ( in @ emptyset @ A )
% 2.44/1.56 & ! [Xx: $i] :
% 2.44/1.56 ( ( ( in @ Xx @ omega )
% 2.44/1.56 & ( in @ Xx @ A ) )
% 2.44/1.56 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.44/1.56 => ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ omega )
% 2.44/1.56 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(replAx_type,type,
% 2.44/1.56 replAx: $o ).
% 2.44/1.56
% 2.44/1.56 thf(replAx,definition,
% 2.44/1.56 ( replAx
% 2.44/1.56 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.44/1.56 ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ( exu
% 2.44/1.56 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.44/1.56 => ? [B: $i] :
% 2.44/1.56 ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ B )
% 2.44/1.56 <=> ? [Xy: $i] :
% 2.44/1.56 ( ( in @ Xy @ A )
% 2.44/1.56 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(foundationAx_type,type,
% 2.44/1.56 foundationAx: $o ).
% 2.44/1.56
% 2.44/1.56 thf(foundationAx,definition,
% 2.44/1.56 ( foundationAx
% 2.44/1.56 = ( ! [A: $i] :
% 2.44/1.56 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.44/1.56 => ? [B: $i] :
% 2.44/1.56 ( ( in @ B @ A )
% 2.44/1.56 & ~ ? [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ B )
% 2.44/1.56 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(wellorderingAx_type,type,
% 2.44/1.56 wellorderingAx: $o ).
% 2.44/1.56
% 2.44/1.56 thf(wellorderingAx,definition,
% 2.44/1.56 ( wellorderingAx
% 2.44/1.56 = ( ! [A: $i] :
% 2.44/1.56 ? [B: $i] :
% 2.44/1.56 ( ! [C: $i] :
% 2.44/1.56 ( ( in @ C @ B )
% 2.44/1.56 => ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ C )
% 2.44/1.56 => ( in @ Xx @ A ) ) )
% 2.44/1.56 & ! [Xx: $i,Xy: $i] :
% 2.44/1.56 ( ( ( in @ Xx @ A )
% 2.44/1.56 & ( in @ Xy @ A ) )
% 2.44/1.56 => ( ! [C: $i] :
% 2.44/1.56 ( ( in @ C @ B )
% 2.44/1.56 => ( ( in @ Xx @ C )
% 2.44/1.56 <=> ( in @ Xy @ C ) ) )
% 2.44/1.56 => ( Xx = Xy ) ) )
% 2.44/1.56 & ! [C: $i,D: $i] :
% 2.44/1.56 ( ( ( in @ C @ B )
% 2.44/1.56 & ( in @ D @ B ) )
% 2.44/1.56 => ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ C )
% 2.44/1.56 => ( in @ Xx @ D ) )
% 2.44/1.56 | ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ D )
% 2.44/1.56 => ( in @ Xx @ C ) ) ) )
% 2.44/1.56 & ! [C: $i] :
% 2.44/1.56 ( ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ C )
% 2.44/1.56 => ( in @ Xx @ A ) )
% 2.44/1.56 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.44/1.56 => ? [D: $i,Xx: $i] :
% 2.44/1.56 ( ( in @ D @ B )
% 2.44/1.56 & ( in @ Xx @ C )
% 2.44/1.56 & ~ ? [Xy: $i] :
% 2.44/1.56 ( ( in @ Xy @ D )
% 2.44/1.56 & ( in @ Xy @ C ) )
% 2.44/1.56 & ! [E: $i] :
% 2.44/1.56 ( ( in @ E @ B )
% 2.44/1.56 => ( ! [Xy: $i] :
% 2.44/1.56 ( ( in @ Xy @ E )
% 2.44/1.56 => ( in @ Xy @ D ) )
% 2.44/1.56 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(descr_type,type,
% 2.44/1.56 descr: ( $i > $o ) > $i ).
% 2.44/1.56
% 2.44/1.56 thf(descrp_type,type,
% 2.44/1.56 descrp: $o ).
% 2.44/1.56
% 2.44/1.56 thf(descrp,definition,
% 2.44/1.56 ( descrp
% 2.44/1.56 = ( ! [Xphi: $i > $o] :
% 2.44/1.56 ( ( exu
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.56 => ( Xphi
% 2.44/1.56 @ ( descr
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(dsetconstr_type,type,
% 2.44/1.56 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.44/1.56
% 2.44/1.56 thf(dsetconstrI_type,type,
% 2.44/1.56 dsetconstrI: $o ).
% 2.44/1.56
% 2.44/1.56 thf(dsetconstrI,definition,
% 2.44/1.56 ( dsetconstrI
% 2.44/1.56 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ( ( Xphi @ Xx )
% 2.44/1.56 => ( in @ Xx
% 2.44/1.56 @ ( dsetconstr @ A
% 2.44/1.56 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(dsetconstrEL_type,type,
% 2.44/1.56 dsetconstrEL: $o ).
% 2.44/1.56
% 2.44/1.56 thf(dsetconstrEL,definition,
% 2.44/1.56 ( dsetconstrEL
% 2.44/1.56 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.44/1.56 ( ( in @ Xx
% 2.44/1.56 @ ( dsetconstr @ A
% 2.44/1.56 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.44/1.56 => ( in @ Xx @ A ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(dsetconstrER_type,type,
% 2.44/1.56 dsetconstrER: $o ).
% 2.44/1.56
% 2.44/1.56 thf(dsetconstrER,definition,
% 2.44/1.56 ( dsetconstrER
% 2.44/1.56 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.44/1.56 ( ( in @ Xx
% 2.44/1.56 @ ( dsetconstr @ A
% 2.44/1.56 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.44/1.56 => ( Xphi @ Xx ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(exuE1_type,type,
% 2.44/1.56 exuE1: $o ).
% 2.44/1.56
% 2.44/1.56 thf(exuE1,definition,
% 2.44/1.56 ( exuE1
% 2.44/1.56 = ( ! [Xphi: $i > $o] :
% 2.44/1.56 ( ( exu
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.56 => ? [Xx: $i] :
% 2.44/1.56 ( ( Xphi @ Xx )
% 2.44/1.56 & ! [Xy: $i] :
% 2.44/1.56 ( ( Xphi @ Xy )
% 2.44/1.56 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(prop2set_type,type,
% 2.44/1.56 prop2set: $o > $i ).
% 2.44/1.56
% 2.44/1.56 thf(prop2setE_type,type,
% 2.44/1.56 prop2setE: $o ).
% 2.44/1.56
% 2.44/1.56 thf(prop2setE,definition,
% 2.44/1.56 ( prop2setE
% 2.44/1.56 = ( ! [Xphi: $o,Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.44/1.56 => Xphi ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(emptysetE_type,type,
% 2.44/1.56 emptysetE: $o ).
% 2.44/1.56
% 2.44/1.56 thf(emptysetE,definition,
% 2.44/1.56 ( emptysetE
% 2.44/1.56 = ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ emptyset )
% 2.44/1.56 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(emptysetimpfalse_type,type,
% 2.44/1.56 emptysetimpfalse: $o ).
% 2.44/1.56
% 2.44/1.56 thf(emptysetimpfalse,definition,
% 2.44/1.56 ( emptysetimpfalse
% 2.44/1.56 = ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ emptyset )
% 2.44/1.56 => $false ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(notinemptyset_type,type,
% 2.44/1.56 notinemptyset: $o ).
% 2.44/1.56
% 2.44/1.56 thf(notinemptyset,definition,
% 2.44/1.56 ( notinemptyset
% 2.44/1.56 = ( ! [Xx: $i] :
% 2.44/1.56 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(exuE3e_type,type,
% 2.44/1.56 exuE3e: $o ).
% 2.44/1.56
% 2.44/1.56 thf(exuE3e,definition,
% 2.44/1.56 ( exuE3e
% 2.44/1.56 = ( ! [Xphi: $i > $o] :
% 2.44/1.56 ( ( exu
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.56 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setext_type,type,
% 2.44/1.56 setext: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setext,definition,
% 2.44/1.56 ( setext
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ( in @ Xx @ B ) )
% 2.44/1.56 => ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ B )
% 2.44/1.56 => ( in @ Xx @ A ) )
% 2.44/1.56 => ( A = B ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(emptyI_type,type,
% 2.44/1.56 emptyI: $o ).
% 2.44/1.56
% 2.44/1.56 thf(emptyI,definition,
% 2.44/1.56 ( emptyI
% 2.44/1.56 = ( ! [A: $i] :
% 2.44/1.56 ( ! [Xx: $i] :
% 2.44/1.56 ~ ( in @ Xx @ A )
% 2.44/1.56 => ( A = emptyset ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(noeltsimpempty_type,type,
% 2.44/1.56 noeltsimpempty: $o ).
% 2.44/1.56
% 2.44/1.56 thf(noeltsimpempty,definition,
% 2.44/1.56 ( noeltsimpempty
% 2.44/1.56 = ( ! [A: $i] :
% 2.44/1.56 ( ! [Xx: $i] :
% 2.44/1.56 ~ ( in @ Xx @ A )
% 2.44/1.56 => ( A = emptyset ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setbeta_type,type,
% 2.44/1.56 setbeta: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setbeta,definition,
% 2.44/1.56 ( setbeta
% 2.44/1.56 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ( ( in @ Xx
% 2.44/1.56 @ ( dsetconstr @ A
% 2.44/1.56 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.44/1.56 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(nonempty_type,type,
% 2.44/1.56 nonempty: $i > $o ).
% 2.44/1.56
% 2.44/1.56 thf(nonempty,definition,
% 2.44/1.56 ( nonempty
% 2.44/1.56 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(nonemptyE1_type,type,
% 2.44/1.56 nonemptyE1: $o ).
% 2.44/1.56
% 2.44/1.56 thf(nonemptyE1,definition,
% 2.44/1.56 ( nonemptyE1
% 2.44/1.56 = ( ! [A: $i] :
% 2.44/1.56 ( ( nonempty @ A )
% 2.44/1.56 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(nonemptyI_type,type,
% 2.44/1.56 nonemptyI: $o ).
% 2.44/1.56
% 2.44/1.56 thf(nonemptyI,definition,
% 2.44/1.56 ( nonemptyI
% 2.44/1.56 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ( ( Xphi @ Xx )
% 2.44/1.56 => ( nonempty
% 2.44/1.56 @ ( dsetconstr @ A
% 2.44/1.56 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(nonemptyI1_type,type,
% 2.44/1.56 nonemptyI1: $o ).
% 2.44/1.56
% 2.44/1.56 thf(nonemptyI1,definition,
% 2.44/1.56 ( nonemptyI1
% 2.44/1.56 = ( ! [A: $i] :
% 2.44/1.56 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.44/1.56 => ( nonempty @ A ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinIL_type,type,
% 2.44/1.56 setadjoinIL: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinIL,definition,
% 2.44/1.56 ( setadjoinIL
% 2.44/1.56 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(emptyinunitempty_type,type,
% 2.44/1.56 emptyinunitempty: $o ).
% 2.44/1.56
% 2.44/1.56 thf(emptyinunitempty,definition,
% 2.44/1.56 ( emptyinunitempty
% 2.44/1.56 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinIR_type,type,
% 2.44/1.56 setadjoinIR: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinIR,definition,
% 2.44/1.56 ( setadjoinIR
% 2.44/1.56 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.44/1.56 ( ( in @ Xy @ A )
% 2.44/1.56 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinE_type,type,
% 2.44/1.56 setadjoinE: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinE,definition,
% 2.44/1.56 ( setadjoinE
% 2.44/1.56 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.44/1.56 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.44/1.56 => ! [Xphi: $o] :
% 2.44/1.56 ( ( ( Xy = Xx )
% 2.44/1.56 => Xphi )
% 2.44/1.56 => ( ( ( in @ Xy @ A )
% 2.44/1.56 => Xphi )
% 2.44/1.56 => Xphi ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinOr_type,type,
% 2.44/1.56 setadjoinOr: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinOr,definition,
% 2.44/1.56 ( setadjoinOr
% 2.44/1.56 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.44/1.56 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.44/1.56 => ( ( Xy = Xx )
% 2.44/1.56 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setoftrueEq_type,type,
% 2.44/1.56 setoftrueEq: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setoftrueEq,definition,
% 2.44/1.56 ( setoftrueEq
% 2.44/1.56 = ( ! [A: $i] :
% 2.44/1.56 ( ( dsetconstr @ A
% 2.44/1.56 @ ^ [Xx: $i] : $true )
% 2.44/1.56 = A ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(powersetI_type,type,
% 2.44/1.56 powersetI: $o ).
% 2.44/1.56
% 2.44/1.56 thf(powersetI,definition,
% 2.44/1.56 ( powersetI
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ B )
% 2.44/1.56 => ( in @ Xx @ A ) )
% 2.44/1.56 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(emptyinPowerset_type,type,
% 2.44/1.56 emptyinPowerset: $o ).
% 2.44/1.56
% 2.44/1.56 thf(emptyinPowerset,definition,
% 2.44/1.56 ( emptyinPowerset
% 2.44/1.56 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(emptyInPowerset_type,type,
% 2.44/1.56 emptyInPowerset: $o ).
% 2.44/1.56
% 2.44/1.56 thf(emptyInPowerset,definition,
% 2.44/1.56 ( emptyInPowerset
% 2.44/1.56 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(powersetE_type,type,
% 2.44/1.56 powersetE: $o ).
% 2.44/1.56
% 2.44/1.56 thf(powersetE,definition,
% 2.44/1.56 ( powersetE
% 2.44/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.56 ( ( in @ B @ ( powerset @ A ) )
% 2.44/1.56 => ( ( in @ Xx @ B )
% 2.44/1.56 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setunionI_type,type,
% 2.44/1.56 setunionI: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setunionI,definition,
% 2.44/1.56 ( setunionI
% 2.44/1.56 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.44/1.56 ( ( in @ Xx @ B )
% 2.44/1.56 => ( ( in @ B @ A )
% 2.44/1.56 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setunionE_type,type,
% 2.44/1.56 setunionE: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setunionE,definition,
% 2.44/1.56 ( setunionE
% 2.44/1.56 = ( ! [A: $i,Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ ( setunion @ A ) )
% 2.44/1.56 => ! [Xphi: $o] :
% 2.44/1.56 ( ! [B: $i] :
% 2.44/1.56 ( ( in @ Xx @ B )
% 2.44/1.56 => ( ( in @ B @ A )
% 2.44/1.56 => Xphi ) )
% 2.44/1.56 => Xphi ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(subPowSU_type,type,
% 2.44/1.56 subPowSU: $o ).
% 2.44/1.56
% 2.44/1.56 thf(subPowSU,definition,
% 2.44/1.56 ( subPowSU
% 2.44/1.56 = ( ! [A: $i,Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(exuE2_type,type,
% 2.44/1.56 exuE2: $o ).
% 2.44/1.56
% 2.44/1.56 thf(exuE2,definition,
% 2.44/1.56 ( exuE2
% 2.44/1.56 = ( ! [Xphi: $i > $o] :
% 2.44/1.56 ( ( exu
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.56 => ? [Xx: $i] :
% 2.44/1.56 ! [Xy: $i] :
% 2.44/1.56 ( ( Xphi @ Xy )
% 2.44/1.56 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(nonemptyImpWitness_type,type,
% 2.44/1.56 nonemptyImpWitness: $o ).
% 2.44/1.56
% 2.44/1.56 thf(nonemptyImpWitness,definition,
% 2.44/1.56 ( nonemptyImpWitness
% 2.44/1.56 = ( ! [A: $i] :
% 2.44/1.56 ( ( nonempty @ A )
% 2.44/1.56 => ? [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 & $true ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(uniqinunit_type,type,
% 2.44/1.56 uniqinunit: $o ).
% 2.44/1.56
% 2.44/1.56 thf(uniqinunit,definition,
% 2.44/1.56 ( uniqinunit
% 2.44/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.44/1.56 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.44/1.56 => ( Xx = Xy ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(notinsingleton_type,type,
% 2.44/1.56 notinsingleton: $o ).
% 2.44/1.56
% 2.44/1.56 thf(notinsingleton,definition,
% 2.44/1.56 ( notinsingleton
% 2.44/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.44/1.56 ( ( Xx != Xy )
% 2.44/1.56 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(eqinunit_type,type,
% 2.44/1.56 eqinunit: $o ).
% 2.44/1.56
% 2.44/1.56 thf(eqinunit,definition,
% 2.44/1.56 ( eqinunit
% 2.44/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.44/1.56 ( ( Xx = Xy )
% 2.44/1.56 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(singletonsswitch_type,type,
% 2.44/1.56 singletonsswitch: $o ).
% 2.44/1.56
% 2.44/1.56 thf(singletonsswitch,definition,
% 2.44/1.56 ( singletonsswitch
% 2.44/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.44/1.56 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.44/1.56 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(upairsetE_type,type,
% 2.44/1.56 upairsetE: $o ).
% 2.44/1.56
% 2.44/1.56 thf(upairsetE,definition,
% 2.44/1.56 ( upairsetE
% 2.44/1.56 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.44/1.56 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.44/1.56 => ( ( Xz = Xx )
% 2.44/1.56 | ( Xz = Xy ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(upairsetIL_type,type,
% 2.44/1.56 upairsetIL: $o ).
% 2.44/1.56
% 2.44/1.56 thf(upairsetIL,definition,
% 2.44/1.56 ( upairsetIL
% 2.44/1.56 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(upairsetIR_type,type,
% 2.44/1.56 upairsetIR: $o ).
% 2.44/1.56
% 2.44/1.56 thf(upairsetIR,definition,
% 2.44/1.56 ( upairsetIR
% 2.44/1.56 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(emptyE1_type,type,
% 2.44/1.56 emptyE1: $o ).
% 2.44/1.56
% 2.44/1.56 thf(emptyE1,definition,
% 2.44/1.56 ( emptyE1
% 2.44/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.56 ( ? [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 & ( Xphi @ Xx ) )
% 2.44/1.56 => ( ( ( dsetconstr @ A
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.56 = emptyset )
% 2.44/1.56 => $false ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(vacuousDall_type,type,
% 2.44/1.56 vacuousDall: $o ).
% 2.44/1.56
% 2.44/1.56 thf(vacuousDall,definition,
% 2.44/1.56 ( vacuousDall
% 2.44/1.56 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ emptyset )
% 2.44/1.56 => ( Xphi @ Xx ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(quantDeMorgan1_type,type,
% 2.44/1.56 quantDeMorgan1: $o ).
% 2.44/1.56
% 2.44/1.56 thf(quantDeMorgan1,definition,
% 2.44/1.56 ( quantDeMorgan1
% 2.44/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.56 ( ~ ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ( Xphi @ Xx ) )
% 2.44/1.56 => ? [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(quantDeMorgan2_type,type,
% 2.44/1.56 quantDeMorgan2: $o ).
% 2.44/1.56
% 2.44/1.56 thf(quantDeMorgan2,definition,
% 2.44/1.56 ( quantDeMorgan2
% 2.44/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.56 ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ~ ( Xphi @ Xx ) )
% 2.44/1.56 => ~ ? [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(quantDeMorgan3_type,type,
% 2.44/1.56 quantDeMorgan3: $o ).
% 2.44/1.56
% 2.44/1.56 thf(quantDeMorgan3,definition,
% 2.44/1.56 ( quantDeMorgan3
% 2.44/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.56 ( ~ ? [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 & ( Xphi @ Xx ) )
% 2.44/1.56 => ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(quantDeMorgan4_type,type,
% 2.44/1.56 quantDeMorgan4: $o ).
% 2.44/1.56
% 2.44/1.56 thf(quantDeMorgan4,definition,
% 2.44/1.56 ( quantDeMorgan4
% 2.44/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.56 ( ? [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 & ~ ( Xphi @ Xx ) )
% 2.44/1.56 => ~ ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(prop2setI_type,type,
% 2.44/1.56 prop2setI: $o ).
% 2.44/1.56
% 2.44/1.56 thf(prop2setI,definition,
% 2.44/1.56 ( prop2setI
% 2.44/1.56 = ( ! [Xphi: $o] :
% 2.44/1.56 ( Xphi
% 2.44/1.56 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(set2prop_type,type,
% 2.44/1.56 set2prop: $i > $o ).
% 2.44/1.56
% 2.44/1.56 thf(prop2set2propI_type,type,
% 2.44/1.56 prop2set2propI: $o ).
% 2.44/1.56
% 2.44/1.56 thf(prop2set2propI,definition,
% 2.44/1.56 ( prop2set2propI
% 2.44/1.56 = ( ! [Xphi: $o] :
% 2.44/1.56 ( Xphi
% 2.44/1.56 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(notdexE_type,type,
% 2.44/1.56 notdexE: $o ).
% 2.44/1.56
% 2.44/1.56 thf(notdexE,definition,
% 2.44/1.56 ( notdexE
% 2.44/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.56 ( ~ ? [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 & ( Xphi @ Xx ) )
% 2.44/1.56 => ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(notdallE_type,type,
% 2.44/1.56 notdallE: $o ).
% 2.44/1.56
% 2.44/1.56 thf(notdallE,definition,
% 2.44/1.56 ( notdallE
% 2.44/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.44/1.56 ( ~ ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ( Xphi @ Xx ) )
% 2.44/1.56 => ? [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(exuI1_type,type,
% 2.44/1.56 exuI1: $o ).
% 2.44/1.56
% 2.44/1.56 thf(exuI1,definition,
% 2.44/1.56 ( exuI1
% 2.44/1.56 = ( ! [Xphi: $i > $o] :
% 2.44/1.56 ( ? [Xx: $i] :
% 2.44/1.56 ( ( Xphi @ Xx )
% 2.44/1.56 & ! [Xy: $i] :
% 2.44/1.56 ( ( Xphi @ Xy )
% 2.44/1.56 => ( Xx = Xy ) ) )
% 2.44/1.56 => ( exu
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(exuI3_type,type,
% 2.44/1.56 exuI3: $o ).
% 2.44/1.56
% 2.44/1.56 thf(exuI3,definition,
% 2.44/1.56 ( exuI3
% 2.44/1.56 = ( ! [Xphi: $i > $o] :
% 2.44/1.56 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.44/1.56 => ( ! [Xx: $i,Xy: $i] :
% 2.44/1.56 ( ( Xphi @ Xx )
% 2.44/1.56 => ( ( Xphi @ Xy )
% 2.44/1.56 => ( Xx = Xy ) ) )
% 2.44/1.56 => ( exu
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(exuI2_type,type,
% 2.44/1.56 exuI2: $o ).
% 2.44/1.56
% 2.44/1.56 thf(exuI2,definition,
% 2.44/1.56 ( exuI2
% 2.44/1.56 = ( ! [Xphi: $i > $o] :
% 2.44/1.56 ( ? [Xx: $i] :
% 2.44/1.56 ! [Xy: $i] :
% 2.44/1.56 ( ( Xphi @ Xy )
% 2.44/1.56 <=> ( Xy = Xx ) )
% 2.44/1.56 => ( exu
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(inCongP_type,type,
% 2.44/1.56 inCongP: $o ).
% 2.44/1.56
% 2.44/1.56 thf(inCongP,definition,
% 2.44/1.56 ( inCongP
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ( A = B )
% 2.44/1.56 => ! [Xx: $i,Xy: $i] :
% 2.44/1.56 ( ( Xx = Xy )
% 2.44/1.56 => ( ( in @ Xx @ A )
% 2.44/1.56 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(in__Cong_type,type,
% 2.44/1.56 in__Cong: $o ).
% 2.44/1.56
% 2.44/1.56 thf(in__Cong,definition,
% 2.44/1.56 ( in__Cong
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ( A = B )
% 2.44/1.56 => ! [Xx: $i,Xy: $i] :
% 2.44/1.56 ( ( Xx = Xy )
% 2.44/1.56 => ( ( in @ Xx @ A )
% 2.44/1.56 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(exuE3u_type,type,
% 2.44/1.56 exuE3u: $o ).
% 2.44/1.56
% 2.44/1.56 thf(exuE3u,definition,
% 2.44/1.56 ( exuE3u
% 2.44/1.56 = ( ! [Xphi: $i > $o] :
% 2.44/1.56 ( ( exu
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.56 => ! [Xx: $i,Xy: $i] :
% 2.44/1.56 ( ( Xphi @ Xx )
% 2.44/1.56 => ( ( Xphi @ Xy )
% 2.44/1.56 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(exu__Cong_type,type,
% 2.44/1.56 exu__Cong: $o ).
% 2.44/1.56
% 2.44/1.56 thf(exu__Cong,definition,
% 2.44/1.56 ( exu__Cong
% 2.44/1.56 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.44/1.56 ( ! [Xx: $i,Xy: $i] :
% 2.44/1.56 ( ( Xx = Xy )
% 2.44/1.56 => ( ( Xphi @ Xx )
% 2.44/1.56 <=> ( Xpsi @ Xy ) ) )
% 2.44/1.56 => ( ( exu
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.56 <=> ( exu
% 2.44/1.56 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(emptyset__Cong_type,type,
% 2.44/1.56 emptyset__Cong: $o ).
% 2.44/1.56
% 2.44/1.56 thf(emptyset__Cong,definition,
% 2.44/1.56 ( emptyset__Cong
% 2.44/1.56 = ( emptyset = emptyset ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoin__Cong_type,type,
% 2.44/1.56 setadjoin__Cong: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoin__Cong,definition,
% 2.44/1.56 ( setadjoin__Cong
% 2.44/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.44/1.56 ( ( Xx = Xy )
% 2.44/1.56 => ! [Xz: $i,Xu: $i] :
% 2.44/1.56 ( ( Xz = Xu )
% 2.44/1.56 => ( ( setadjoin @ Xx @ Xz )
% 2.44/1.56 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(powerset__Cong_type,type,
% 2.44/1.56 powerset__Cong: $o ).
% 2.44/1.56
% 2.44/1.56 thf(powerset__Cong,definition,
% 2.44/1.56 ( powerset__Cong
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ( A = B )
% 2.44/1.56 => ( ( powerset @ A )
% 2.44/1.56 = ( powerset @ B ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setunion__Cong_type,type,
% 2.44/1.56 setunion__Cong: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setunion__Cong,definition,
% 2.44/1.56 ( setunion__Cong
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ( A = B )
% 2.44/1.56 => ( ( setunion @ A )
% 2.44/1.56 = ( setunion @ B ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(omega__Cong_type,type,
% 2.44/1.56 omega__Cong: $o ).
% 2.44/1.56
% 2.44/1.56 thf(omega__Cong,definition,
% 2.44/1.56 ( omega__Cong
% 2.44/1.56 = ( omega = omega ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(exuEu_type,type,
% 2.44/1.56 exuEu: $o ).
% 2.44/1.56
% 2.44/1.56 thf(exuEu,definition,
% 2.44/1.56 ( exuEu
% 2.44/1.56 = ( ! [Xphi: $i > $o] :
% 2.44/1.56 ( ( exu
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.56 => ! [Xx: $i,Xy: $i] :
% 2.44/1.56 ( ( Xphi @ Xx )
% 2.44/1.56 => ( ( Xphi @ Xy )
% 2.44/1.56 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(descr__Cong_type,type,
% 2.44/1.56 descr__Cong: $o ).
% 2.44/1.56
% 2.44/1.56 thf(descr__Cong,definition,
% 2.44/1.56 ( descr__Cong
% 2.44/1.56 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.44/1.56 ( ! [Xx: $i,Xy: $i] :
% 2.44/1.56 ( ( Xx = Xy )
% 2.44/1.56 => ( ( Xphi @ Xx )
% 2.44/1.56 <=> ( Xpsi @ Xy ) ) )
% 2.44/1.56 => ( ( exu
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.56 => ( ( exu
% 2.44/1.56 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.44/1.56 => ( ( descr
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.56 = ( descr
% 2.44/1.56 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(dsetconstr__Cong_type,type,
% 2.44/1.56 dsetconstr__Cong: $o ).
% 2.44/1.56
% 2.44/1.56 thf(dsetconstr__Cong,definition,
% 2.44/1.56 ( dsetconstr__Cong
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ( A = B )
% 2.44/1.56 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.44/1.56 ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ! [Xy: $i] :
% 2.44/1.56 ( ( in @ Xy @ B )
% 2.44/1.56 => ( ( Xx = Xy )
% 2.44/1.56 => ( ( Xphi @ Xx )
% 2.44/1.56 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.44/1.56 => ( ( dsetconstr @ A
% 2.44/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.44/1.56 = ( dsetconstr @ B
% 2.44/1.56 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(subset_type,type,
% 2.44/1.56 subset: $i > $i > $o ).
% 2.44/1.56
% 2.44/1.56 thf(disjoint_type,type,
% 2.44/1.56 disjoint: $i > $i > $o ).
% 2.44/1.56
% 2.44/1.56 thf(setsmeet_type,type,
% 2.44/1.56 setsmeet: $i > $i > $o ).
% 2.44/1.56
% 2.44/1.56 thf(subsetI1_type,type,
% 2.44/1.56 subsetI1: $o ).
% 2.44/1.56
% 2.44/1.56 thf(subsetI1,definition,
% 2.44/1.56 ( subsetI1
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ( in @ Xx @ B ) )
% 2.44/1.56 => ( subset @ A @ B ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(eqimpsubset2_type,type,
% 2.44/1.56 eqimpsubset2: $o ).
% 2.44/1.56
% 2.44/1.56 thf(eqimpsubset2,definition,
% 2.44/1.56 ( eqimpsubset2
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ( A = B )
% 2.44/1.56 => ( subset @ B @ A ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(eqimpsubset1_type,type,
% 2.44/1.56 eqimpsubset1: $o ).
% 2.44/1.56
% 2.44/1.56 thf(eqimpsubset1,definition,
% 2.44/1.56 ( eqimpsubset1
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ( A = B )
% 2.44/1.56 => ( subset @ A @ B ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(subsetI2_type,type,
% 2.44/1.56 subsetI2: $o ).
% 2.44/1.56
% 2.44/1.56 thf(subsetI2,definition,
% 2.44/1.56 ( subsetI2
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ! [Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ( in @ Xx @ B ) )
% 2.44/1.56 => ( subset @ A @ B ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(emptysetsubset_type,type,
% 2.44/1.56 emptysetsubset: $o ).
% 2.44/1.56
% 2.44/1.56 thf(emptysetsubset,definition,
% 2.44/1.56 ( emptysetsubset
% 2.44/1.56 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(subsetE_type,type,
% 2.44/1.56 subsetE: $o ).
% 2.44/1.56
% 2.44/1.56 thf(subsetE,definition,
% 2.44/1.56 ( subsetE
% 2.44/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.56 ( ( subset @ A @ B )
% 2.44/1.56 => ( ( in @ Xx @ A )
% 2.44/1.56 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(subsetE2_type,type,
% 2.44/1.56 subsetE2: $o ).
% 2.44/1.56
% 2.44/1.56 thf(subsetE2,definition,
% 2.44/1.56 ( subsetE2
% 2.44/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.56 ( ( subset @ A @ B )
% 2.44/1.56 => ( ~ ( in @ Xx @ B )
% 2.44/1.56 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(notsubsetI_type,type,
% 2.44/1.56 notsubsetI: $o ).
% 2.44/1.56
% 2.44/1.56 thf(notsubsetI,definition,
% 2.44/1.56 ( notsubsetI
% 2.44/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ( ~ ( in @ Xx @ B )
% 2.44/1.56 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(notequalI1_type,type,
% 2.44/1.56 notequalI1: $o ).
% 2.44/1.56
% 2.44/1.56 thf(notequalI1,definition,
% 2.44/1.56 ( notequalI1
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ~ ( subset @ A @ B )
% 2.44/1.56 => ( A != B ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(notequalI2_type,type,
% 2.44/1.56 notequalI2: $o ).
% 2.44/1.56
% 2.44/1.56 thf(notequalI2,definition,
% 2.44/1.56 ( notequalI2
% 2.44/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.44/1.56 ( ( in @ Xx @ A )
% 2.44/1.56 => ( ~ ( in @ Xx @ B )
% 2.44/1.56 => ( A != B ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(subsetRefl_type,type,
% 2.44/1.56 subsetRefl: $o ).
% 2.44/1.56
% 2.44/1.56 thf(subsetRefl,definition,
% 2.44/1.56 ( subsetRefl
% 2.44/1.56 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(subsetTrans_type,type,
% 2.44/1.56 subsetTrans: $o ).
% 2.44/1.56
% 2.44/1.56 thf(subsetTrans,definition,
% 2.44/1.56 ( subsetTrans
% 2.44/1.56 = ( ! [A: $i,B: $i,C: $i] :
% 2.44/1.56 ( ( subset @ A @ B )
% 2.44/1.56 => ( ( subset @ B @ C )
% 2.44/1.56 => ( subset @ A @ C ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinSub_type,type,
% 2.44/1.56 setadjoinSub: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinSub,definition,
% 2.44/1.56 ( setadjoinSub
% 2.44/1.56 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinSub2_type,type,
% 2.44/1.56 setadjoinSub2: $o ).
% 2.44/1.56
% 2.44/1.56 thf(setadjoinSub2,definition,
% 2.44/1.56 ( setadjoinSub2
% 2.44/1.56 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.44/1.56 ( ( subset @ A @ B )
% 2.44/1.56 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(subset2powerset_type,type,
% 2.44/1.56 subset2powerset: $o ).
% 2.44/1.56
% 2.44/1.56 thf(subset2powerset,definition,
% 2.44/1.56 ( subset2powerset
% 2.44/1.56 = ( ! [A: $i,B: $i] :
% 2.44/1.56 ( ( subset @ A @ B )
% 2.44/1.56 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.44/1.56
% 2.44/1.56 thf(setextsub,conjecture,
% 2.44/1.56 ( setextAx
% 2.44/1.56 => ( emptysetAx
% 2.44/1.56 => ( setadjoinAx
% 2.44/1.56 => ( powersetAx
% 2.44/1.56 => ( setunionAx
% 2.44/1.56 => ( omega0Ax
% 2.44/1.56 => ( omegaSAx
% 2.44/1.56 => ( omegaIndAx
% 2.44/1.56 => ( replAx
% 2.44/1.56 => ( foundationAx
% 2.44/1.56 => ( wellorderingAx
% 2.44/1.56 => ( descrp
% 2.44/1.56 => ( dsetconstrI
% 2.44/1.56 => ( dsetconstrEL
% 2.44/1.56 => ( dsetconstrER
% 2.44/1.56 => ( exuE1
% 2.44/1.56 => ( prop2setE
% 2.44/1.56 => ( emptysetE
% 2.44/1.56 => ( emptysetimpfalse
% 2.44/1.56 => ( notinemptyset
% 2.44/1.56 => ( exuE3e
% 2.44/1.56 => ( setext
% 2.44/1.56 => ( emptyI
% 2.44/1.56 => ( noeltsimpempty
% 2.44/1.56 => ( setbeta
% 2.44/1.56 => ( nonemptyE1
% 2.44/1.56 => ( nonemptyI
% 2.44/1.56 => ( nonemptyI1
% 2.44/1.56 => ( setadjoinIL
% 2.44/1.56 => ( emptyinunitempty
% 2.44/1.56 => ( setadjoinIR
% 2.44/1.56 => ( setadjoinE
% 2.44/1.56 => ( setadjoinOr
% 2.44/1.56 => ( setoftrueEq
% 2.44/1.56 => ( powersetI
% 2.44/1.56 => ( emptyinPowerset
% 2.44/1.56 => ( emptyInPowerset
% 2.44/1.56 => ( powersetE
% 2.44/1.56 => ( setunionI
% 2.44/1.56 => ( setunionE
% 2.44/1.56 => ( subPowSU
% 2.44/1.56 => ( exuE2
% 2.44/1.56 => ( nonemptyImpWitness
% 2.44/1.56 => ( uniqinunit
% 2.44/1.56 => ( notinsingleton
% 2.44/1.56 => ( eqinunit
% 2.44/1.56 => ( singletonsswitch
% 2.44/1.56 => ( upairsetE
% 2.44/1.56 => ( upairsetIL
% 2.44/1.56 => ( upairsetIR
% 2.44/1.56 => ( emptyE1
% 2.44/1.56 => ( vacuousDall
% 2.44/1.56 => ( quantDeMorgan1
% 2.44/1.56 => ( quantDeMorgan2
% 2.44/1.56 => ( quantDeMorgan3
% 2.44/1.56 => ( quantDeMorgan4
% 2.44/1.56 => ( prop2setI
% 2.44/1.56 => ( prop2set2propI
% 2.44/1.56 => ( notdexE
% 2.44/1.56 => ( notdallE
% 2.44/1.56 => ( exuI1
% 2.44/1.56 => ( exuI3
% 2.44/1.56 => ( exuI2
% 2.44/1.56 => ( inCongP
% 2.44/1.56 => ( in__Cong
% 2.44/1.56 => ( exuE3u
% 2.44/1.56 => ( exu__Cong
% 2.44/1.56 => ( emptyset__Cong
% 2.44/1.56 => ( setadjoin__Cong
% 2.44/1.56 => ( powerset__Cong
% 2.44/1.56 => ( setunion__Cong
% 2.44/1.56 => ( omega__Cong
% 2.44/1.56 => ( exuEu
% 2.44/1.56 => ( descr__Cong
% 2.44/1.56 => ( dsetconstr__Cong
% 2.44/1.56 => ( subsetI1
% 2.44/1.56 => ( eqimpsubset2
% 2.44/1.56 => ( eqimpsubset1
% 2.44/1.56 => ( subsetI2
% 2.44/1.56 => ( emptysetsubset
% 2.44/1.56 => ( subsetE
% 2.44/1.56 => ( subsetE2
% 2.44/1.56 => ( notsubsetI
% 2.44/1.56 => ( notequalI1
% 2.44/1.56 => ( notequalI2
% 2.44/1.56 => ( subsetRefl
% 2.44/1.56 => ( subsetTrans
% 2.44/1.56 => ( setadjoinSub
% 2.44/1.56 => ( setadjoinSub2
% 2.44/1.56 => ( subset2powerset
% 2.44/1.56 => ! [A: $i,B: $i] :
% 2.44/1.56 ( ( subset @ A @ B )
% 2.44/1.56 => ( ( subset @ B @ A )
% 2.44/1.56 => ( A = B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.44/1.56 ------------------------
% 2.44/1.58 % (31619)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31518 for (2999ds/2Mi)
% 2.44/1.58 % (31621)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_31518 for (2999ds/275Mi)
% 2.44/1.58 % (31618)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_31518 for (2999ds/27Mi)
% 2.44/1.58 % (31620)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_31518 for (2999ds/2Mi)
% 2.44/1.58 % (31622)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31518 for (2999ds/18Mi)
% 2.44/1.58 % (31617)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_31518 for (2999ds/4Mi)
% 2.44/1.58 % (31616)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31518 for (2999ds/183Mi)
% 2.44/1.58 % (31619)Instruction limit reached!
% 2.44/1.58 % (31619)------------------------------
% 2.44/1.58 % (31619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.44/1.58 % (31619)Termination reason: Unknown
% 2.44/1.58 % (31619)Termination phase: shuffling
% 2.44/1.58
% 2.44/1.58 % (31620)Instruction limit reached!
% 2.44/1.58 % (31620)------------------------------
% 2.44/1.58 % (31620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.44/1.58 % (31620)Termination reason: Unknown
% 2.44/1.58 % (31620)Termination phase: shuffling
% 2.44/1.58
% 2.44/1.58 % (31620)Memory used [KB]: 1151
% 2.44/1.58 % (31620)Time elapsed: 0.003 s
% 2.44/1.58 % (31620)Instructions burned: 3 (million)
% 2.44/1.58 % (31620)------------------------------
% 2.44/1.58 % (31620)------------------------------
% 2.44/1.58 % (31619)Memory used [KB]: 1151
% 2.44/1.58 % (31619)Time elapsed: 0.003 s
% 2.44/1.59 % (31619)Instructions burned: 2 (million)
% 2.44/1.59 % (31619)------------------------------
% 2.44/1.59 % (31619)------------------------------
% 2.44/1.59 % (31617)Instruction limit reached!
% 2.44/1.59 % (31617)------------------------------
% 2.44/1.59 % (31617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.44/1.59 % (31617)Termination reason: Unknown
% 2.44/1.59 % (31617)Termination phase: shuffling
% 2.44/1.59
% 2.44/1.59 % (31617)Memory used [KB]: 1151
% 2.44/1.59 % (31617)Time elapsed: 0.003 s
% 2.44/1.59 % (31617)Instructions burned: 4 (million)
% 2.44/1.59 % (31617)------------------------------
% 2.44/1.59 % (31617)------------------------------
% 2.44/1.59 % (31622)Instruction limit reached!
% 2.44/1.59 % (31622)------------------------------
% 2.44/1.59 % (31622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.44/1.59 % (31622)Termination reason: Unknown
% 2.44/1.59 % (31622)Termination phase: Preprocessing 3
% 2.44/1.59
% 2.44/1.59 % (31622)Memory used [KB]: 1663
% 2.44/1.59 % (31622)Time elapsed: 0.011 s
% 2.44/1.59 % (31622)Instructions burned: 19 (million)
% 2.44/1.59 % (31622)------------------------------
% 2.44/1.59 % (31622)------------------------------
% 2.44/1.60 % (31618)Instruction limit reached!
% 2.44/1.60 % (31618)------------------------------
% 2.44/1.60 % (31618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.44/1.60 % (31618)Termination reason: Unknown
% 2.44/1.60 % (31618)Termination phase: Property scanning
% 2.44/1.60
% 2.44/1.60 % (31618)Memory used [KB]: 1407
% 2.44/1.60 % (31618)Time elapsed: 0.014 s
% 2.44/1.60 % (31618)Instructions burned: 28 (million)
% 2.44/1.60 % (31618)------------------------------
% 2.44/1.60 % (31618)------------------------------
% 2.51/1.60 % (31624)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_31518 for (2999ds/37Mi)
% 2.51/1.60 % (31623)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31518 for (2999ds/3Mi)
% 2.51/1.60 % (31625)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_31518 for (2999ds/15Mi)
% 2.51/1.60 % (31623)Instruction limit reached!
% 2.51/1.60 % (31623)------------------------------
% 2.51/1.60 % (31623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.60 % (31623)Termination reason: Unknown
% 2.51/1.60 % (31623)Termination phase: shuffling
% 2.51/1.60
% 2.51/1.60 % (31623)Memory used [KB]: 1151
% 2.51/1.60 % (31623)Time elapsed: 0.003 s
% 2.51/1.60 % (31623)Instructions burned: 3 (million)
% 2.51/1.60 % (31623)------------------------------
% 2.51/1.60 % (31623)------------------------------
% 2.51/1.61 % (31625)Instruction limit reached!
% 2.51/1.61 % (31625)------------------------------
% 2.51/1.61 % (31625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.61 % (31625)Termination reason: Unknown
% 2.51/1.61 % (31625)Termination phase: Preprocessing 3
% 2.51/1.61
% 2.51/1.61 % (31625)Memory used [KB]: 1535
% 2.51/1.61 % (31625)Time elapsed: 0.009 s
% 2.51/1.61 % (31625)Instructions burned: 16 (million)
% 2.51/1.61 % (31626)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_31518 for (2999ds/3Mi)
% 2.51/1.61 % (31625)------------------------------
% 2.51/1.61 % (31625)------------------------------
% 2.51/1.61 % (31626)Instruction limit reached!
% 2.51/1.61 % (31626)------------------------------
% 2.51/1.61 % (31626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.61 % (31626)Termination reason: Unknown
% 2.51/1.61 % (31626)Termination phase: shuffling
% 2.51/1.61
% 2.51/1.61 % (31626)Memory used [KB]: 1151
% 2.51/1.61 % (31626)Time elapsed: 0.003 s
% 2.51/1.61 % (31626)Instructions burned: 3 (million)
% 2.51/1.61 % (31626)------------------------------
% 2.51/1.61 % (31626)------------------------------
% 2.51/1.61 % (31627)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_31518 for (2999ds/1041Mi)
% 2.51/1.62 % (31624)Instruction limit reached!
% 2.51/1.62 % (31624)------------------------------
% 2.51/1.62 % (31624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.62 % (31624)Termination reason: Unknown
% 2.51/1.62 % (31624)Termination phase: Property scanning
% 2.51/1.62
% 2.51/1.62 % (31624)Memory used [KB]: 1535
% 2.51/1.62 % (31624)Time elapsed: 0.018 s
% 2.51/1.62 % (31624)Instructions burned: 38 (million)
% 2.51/1.62 % (31624)------------------------------
% 2.51/1.62 % (31624)------------------------------
% 2.51/1.62 % (31628)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_31518 for (2999ds/7Mi)
% 2.51/1.62 % (31628)Instruction limit reached!
% 2.51/1.62 % (31628)------------------------------
% 2.51/1.62 % (31628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.62 % (31628)Termination reason: Unknown
% 2.51/1.62 % (31628)Termination phase: shuffling
% 2.51/1.62
% 2.51/1.62 % (31628)Memory used [KB]: 1279
% 2.51/1.62 % (31628)Time elapsed: 0.005 s
% 2.51/1.62 % (31628)Instructions burned: 7 (million)
% 2.51/1.62 % (31628)------------------------------
% 2.51/1.62 % (31628)------------------------------
% 2.51/1.63 % (31629)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_31518 for (2999ds/16Mi)
% 2.51/1.63 % (31630)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_31518 for (2999ds/3Mi)
% 2.51/1.63 % (31630)Instruction limit reached!
% 2.51/1.63 % (31630)------------------------------
% 2.51/1.63 % (31630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.63 % (31630)Termination reason: Unknown
% 2.51/1.63 % (31630)Termination phase: shuffling
% 2.51/1.63
% 2.51/1.63 % (31630)Memory used [KB]: 1151
% 2.51/1.63 % (31630)Time elapsed: 0.003 s
% 2.51/1.63 % (31630)Instructions burned: 3 (million)
% 2.51/1.63 % (31630)------------------------------
% 2.51/1.63 % (31630)------------------------------
% 2.51/1.63 % (31629)Instruction limit reached!
% 2.51/1.63 % (31629)------------------------------
% 2.51/1.63 % (31629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.63 % (31629)Termination reason: Unknown
% 2.51/1.63 % (31629)Termination phase: Property scanning
% 2.51/1.63
% 2.51/1.63 % (31629)Memory used [KB]: 1407
% 2.51/1.63 % (31629)Time elapsed: 0.009 s
% 2.51/1.63 % (31629)Instructions burned: 17 (million)
% 2.51/1.63 % (31629)------------------------------
% 2.51/1.63 % (31629)------------------------------
% 2.51/1.63 % (31631)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_31518 for (2999ds/3Mi)
% 2.51/1.64 % (31631)Instruction limit reached!
% 2.51/1.64 % (31631)------------------------------
% 2.51/1.64 % (31631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.64 % (31631)Termination reason: Unknown
% 2.51/1.64 % (31631)Termination phase: shuffling
% 2.51/1.64
% 2.51/1.64 % (31631)Memory used [KB]: 1151
% 2.51/1.64 % (31631)Time elapsed: 0.003 s
% 2.51/1.64 % (31631)Instructions burned: 3 (million)
% 2.51/1.64 % (31631)------------------------------
% 2.51/1.64 % (31631)------------------------------
% 2.51/1.64 % (31632)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_31518 for (2999ds/7Mi)
% 2.51/1.64 % (31632)Instruction limit reached!
% 2.51/1.64 % (31632)------------------------------
% 2.51/1.64 % (31632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.64 % (31632)Termination reason: Unknown
% 2.51/1.64 % (31632)Termination phase: shuffling
% 2.51/1.64
% 2.51/1.64 % (31632)Memory used [KB]: 1279
% 2.51/1.64 % (31632)Time elapsed: 0.005 s
% 2.51/1.64 % (31632)Instructions burned: 8 (million)
% 2.51/1.64 % (31632)------------------------------
% 2.51/1.64 % (31632)------------------------------
% 2.51/1.64 % (31633)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_31518 for (2999ds/3Mi)
% 2.51/1.65 % (31633)Instruction limit reached!
% 2.51/1.65 % (31633)------------------------------
% 2.51/1.65 % (31633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.65 % (31633)Termination reason: Unknown
% 2.51/1.65 % (31633)Termination phase: shuffling
% 2.51/1.65
% 2.51/1.65 % (31633)Memory used [KB]: 1151
% 2.51/1.65 % (31633)Time elapsed: 0.003 s
% 2.51/1.65 % (31633)Instructions burned: 4 (million)
% 2.51/1.65 % (31633)------------------------------
% 2.51/1.65 % (31633)------------------------------
% 2.51/1.65 % (31634)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_31518 for (2999ds/4Mi)
% 2.51/1.65 % (31634)Instruction limit reached!
% 2.51/1.65 % (31634)------------------------------
% 2.51/1.65 % (31634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.65 % (31635)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_31518 for (2999ds/18Mi)
% 2.51/1.65 % (31634)Termination reason: Unknown
% 2.51/1.65 % (31634)Termination phase: shuffling
% 2.51/1.65
% 2.51/1.65 % (31634)Memory used [KB]: 1279
% 2.51/1.65 % (31634)Time elapsed: 0.004 s
% 2.51/1.65 % (31634)Instructions burned: 6 (million)
% 2.51/1.65 % (31634)------------------------------
% 2.51/1.65 % (31634)------------------------------
% 2.51/1.66 % (31636)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_31518 for (2999ds/710Mi)
% 2.51/1.66 % (31635)Instruction limit reached!
% 2.51/1.66 % (31635)------------------------------
% 2.51/1.66 % (31635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.66 % (31635)Termination reason: Unknown
% 2.51/1.66 % (31635)Termination phase: Property scanning
% 2.51/1.66
% 2.51/1.66 % (31635)Memory used [KB]: 1407
% 2.51/1.66 % (31635)Time elapsed: 0.010 s
% 2.51/1.66 % (31635)Instructions burned: 19 (million)
% 2.51/1.66 % (31635)------------------------------
% 2.51/1.66 % (31635)------------------------------
% 2.51/1.66 % (31637)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31518 for (2999ds/6Mi)
% 2.51/1.66 % (31637)Instruction limit reached!
% 2.51/1.66 % (31637)------------------------------
% 2.51/1.66 % (31637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.66 % (31637)Termination reason: Unknown
% 2.51/1.66 % (31637)Termination phase: shuffling
% 2.51/1.66
% 2.51/1.66 % (31637)Memory used [KB]: 1279
% 2.51/1.66 % (31637)Time elapsed: 0.004 s
% 2.51/1.66 % (31637)Instructions burned: 6 (million)
% 2.51/1.66 % (31637)------------------------------
% 2.51/1.66 % (31637)------------------------------
% 2.51/1.67 % (31638)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_31518 for (2999ds/902Mi)
% 2.51/1.67 % (31616)Instruction limit reached!
% 2.51/1.67 % (31616)------------------------------
% 2.51/1.67 % (31616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.67 % (31616)Termination reason: Unknown
% 2.51/1.67 % (31616)Termination phase: Saturation
% 2.51/1.67
% 2.51/1.67 % (31616)Memory used [KB]: 6908
% 2.51/1.67 % (31616)Time elapsed: 0.087 s
% 2.51/1.67 % (31616)Instructions burned: 183 (million)
% 2.51/1.67 % (31616)------------------------------
% 2.51/1.67 % (31616)------------------------------
% 2.51/1.68 % (31639)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_31518 for (2999ds/21Mi)
% 2.51/1.68 % (31640)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_31518 for (2999ds/5Mi)
% 2.51/1.68 % (31640)Instruction limit reached!
% 2.51/1.68 % (31640)------------------------------
% 2.51/1.68 % (31640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.68 % (31640)Termination reason: Unknown
% 2.51/1.68 % (31640)Termination phase: shuffling
% 2.51/1.68
% 2.51/1.68 % (31640)Memory used [KB]: 1279
% 2.51/1.68 % (31640)Time elapsed: 0.004 s
% 2.51/1.68 % (31640)Instructions burned: 6 (million)
% 2.51/1.68 % (31640)------------------------------
% 2.51/1.68 % (31640)------------------------------
% 2.51/1.69 % (31639)Instruction limit reached!
% 2.51/1.69 % (31639)------------------------------
% 2.51/1.69 % (31639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.69 % (31639)Termination reason: Unknown
% 2.51/1.69 % (31639)Termination phase: Property scanning
% 2.51/1.69
% 2.51/1.69 % (31639)Memory used [KB]: 1407
% 2.51/1.69 % (31639)Time elapsed: 0.011 s
% 2.51/1.69 % (31639)Instructions burned: 21 (million)
% 2.51/1.69 % (31639)------------------------------
% 2.51/1.69 % (31639)------------------------------
% 2.51/1.69 % (31641)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_31518 for (2999ds/6Mi)
% 2.51/1.69 % (31641)Instruction limit reached!
% 2.51/1.69 % (31641)------------------------------
% 2.51/1.69 % (31641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.69 % (31641)Termination reason: Unknown
% 2.51/1.69 % (31641)Termination phase: shuffling
% 2.51/1.69
% 2.51/1.69 % (31641)Memory used [KB]: 1279
% 2.51/1.69 % (31641)Time elapsed: 0.004 s
% 2.51/1.69 % (31641)Instructions burned: 6 (million)
% 2.51/1.69 % (31641)------------------------------
% 2.51/1.69 % (31641)------------------------------
% 2.51/1.70 % (31642)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_31518 for (2998ds/377Mi)
% 2.51/1.70 % (31643)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_31518 for (2998ds/779Mi)
% 2.51/1.70 % (31644)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_31518 for (2998ds/19Mi)
% 2.51/1.71 % (31644)Instruction limit reached!
% 2.51/1.71 % (31644)------------------------------
% 2.51/1.71 % (31644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.71 % (31644)Termination reason: Unknown
% 2.51/1.71 % (31644)Termination phase: Property scanning
% 2.51/1.71
% 2.51/1.71 % (31644)Memory used [KB]: 1407
% 2.51/1.71 % (31644)Time elapsed: 0.011 s
% 2.51/1.71 % (31644)Instructions burned: 20 (million)
% 2.51/1.71 % (31644)------------------------------
% 2.51/1.71 % (31644)------------------------------
% 2.51/1.71 % (31638)Refutation not found, incomplete strategy
% 2.51/1.71 % (31638)------------------------------
% 2.51/1.71 % (31638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.71 % (31638)Termination reason: Refutation not found, incomplete strategy
% 2.51/1.71
% 2.51/1.71
% 2.51/1.71 % (31638)Memory used [KB]: 6908
% 2.51/1.71 % (31638)Time elapsed: 0.047 s
% 2.51/1.71 % (31638)Instructions burned: 94 (million)
% 2.51/1.71 % (31638)------------------------------
% 2.51/1.71 % (31638)------------------------------
% 2.51/1.72 % (31621)Instruction limit reached!
% 2.51/1.72 % (31621)------------------------------
% 2.51/1.72 % (31621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.72 % (31621)Termination reason: Unknown
% 2.51/1.72 % (31621)Termination phase: Saturation
% 2.51/1.72
% 2.51/1.72 % (31621)Memory used [KB]: 7419
% 2.51/1.72 % (31621)Time elapsed: 0.138 s
% 2.51/1.72 % (31621)Instructions burned: 276 (million)
% 2.51/1.72 % (31621)------------------------------
% 2.51/1.72 % (31621)------------------------------
% 2.51/1.73 % (31645)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_31518 for (2998ds/879Mi)
% 2.51/1.73 % (31646)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_31518 for (2998ds/17Mi)
% 2.51/1.74 % (31647)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_31518 for (2998ds/3Mi)
% 2.51/1.74 % (31647)Instruction limit reached!
% 2.51/1.74 % (31647)------------------------------
% 2.51/1.74 % (31647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.74 % (31647)Termination reason: Unknown
% 2.51/1.74 % (31647)Termination phase: shuffling
% 2.51/1.74
% 2.51/1.74 % (31647)Memory used [KB]: 1151
% 2.51/1.74 % (31647)Time elapsed: 0.004 s
% 2.51/1.74 % (31647)Instructions burned: 5 (million)
% 2.51/1.74 % (31646)Instruction limit reached!
% 2.51/1.74 % (31646)------------------------------
% 2.51/1.74 % (31646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.74 % (31646)Termination reason: Unknown
% 2.51/1.74 % (31646)Termination phase: Property scanning
% 2.51/1.74
% 2.51/1.74 % (31646)Memory used [KB]: 1407
% 2.51/1.74 % (31646)Time elapsed: 0.010 s
% 2.51/1.74 % (31646)Instructions burned: 18 (million)
% 2.51/1.74 % (31646)------------------------------
% 2.51/1.74 % (31646)------------------------------
% 2.51/1.74 % (31647)------------------------------
% 2.51/1.74 % (31647)------------------------------
% 2.51/1.76 % (31649)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_31518 for (2998ds/127Mi)
% 2.51/1.76 % (31648)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_31518 for (2998ds/30Mi)
% 2.51/1.77 % (31648)Instruction limit reached!
% 2.51/1.77 % (31648)------------------------------
% 2.51/1.77 % (31648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.77 % (31648)Termination reason: Unknown
% 2.51/1.77 % (31648)Termination phase: Function definition elimination
% 2.51/1.77
% 2.51/1.77 % (31648)Memory used [KB]: 1407
% 2.51/1.77 % (31648)Time elapsed: 0.016 s
% 2.51/1.77 % (31648)Instructions burned: 31 (million)
% 2.51/1.77 % (31648)------------------------------
% 2.51/1.77 % (31648)------------------------------
% 2.51/1.79 % (31650)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_31518 for (2997ds/100Mi)
% 2.51/1.81 % (31649)Instruction limit reached!
% 2.51/1.81 % (31649)------------------------------
% 2.51/1.81 % (31649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.81 % (31649)Termination reason: Unknown
% 2.51/1.81 % (31649)Termination phase: Saturation
% 2.51/1.81
% 2.51/1.81 % (31649)Memory used [KB]: 6652
% 2.51/1.81 % (31649)Time elapsed: 0.061 s
% 2.51/1.81 % (31649)Instructions burned: 127 (million)
% 2.51/1.81 % (31649)------------------------------
% 2.51/1.81 % (31649)------------------------------
% 2.51/1.83 % (31651)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_31518 for (2997ds/3Mi)
% 2.51/1.83 % (31651)Instruction limit reached!
% 2.51/1.83 % (31651)------------------------------
% 2.51/1.83 % (31651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.83 % (31651)Termination reason: Unknown
% 2.51/1.83 % (31651)Termination phase: shuffling
% 2.51/1.83
% 2.51/1.83 % (31651)Memory used [KB]: 1151
% 2.51/1.83 % (31651)Time elapsed: 0.004 s
% 2.51/1.83 % (31651)Instructions burned: 4 (million)
% 2.51/1.83 % (31651)------------------------------
% 2.51/1.83 % (31651)------------------------------
% 2.51/1.84 % (31650)Instruction limit reached!
% 2.51/1.84 % (31650)------------------------------
% 2.51/1.84 % (31650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.84 % (31650)Termination reason: Unknown
% 2.51/1.84 % (31650)Termination phase: Saturation
% 2.51/1.84
% 2.51/1.84 % (31650)Memory used [KB]: 6268
% 2.51/1.84 % (31650)Time elapsed: 0.049 s
% 2.51/1.84 % (31650)Instructions burned: 101 (million)
% 2.51/1.84 % (31650)------------------------------
% 2.51/1.84 % (31650)------------------------------
% 2.51/1.85 % (31652)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_31518 for (2997ds/20Mi)
% 2.51/1.85 % (31653)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_31518 for (2997ds/86Mi)
% 2.51/1.86 % (31652)Instruction limit reached!
% 2.51/1.86 % (31652)------------------------------
% 2.51/1.86 % (31652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.86 % (31652)Termination reason: Unknown
% 2.51/1.86 % (31652)Termination phase: Preprocessing 3
% 2.51/1.86
% 2.51/1.86 % (31652)Memory used [KB]: 1535
% 2.51/1.86 % (31652)Time elapsed: 0.012 s
% 2.51/1.86 % (31652)Instructions burned: 21 (million)
% 2.51/1.86 % (31652)------------------------------
% 2.51/1.86 % (31652)------------------------------
% 2.51/1.88 % (31654)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_31518 for (2997ds/107Mi)
% 2.51/1.88 % (31642)Instruction limit reached!
% 2.51/1.88 % (31642)------------------------------
% 2.51/1.88 % (31642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.88 % (31642)Termination reason: Unknown
% 2.51/1.88 % (31642)Termination phase: Saturation
% 2.51/1.88
% 2.51/1.88 % (31642)Memory used [KB]: 7036
% 2.51/1.88 % (31642)Time elapsed: 0.204 s
% 2.51/1.88 % (31642)Instructions burned: 378 (million)
% 2.51/1.88 % (31642)------------------------------
% 2.51/1.88 % (31642)------------------------------
% 2.51/1.89 % (31653)Instruction limit reached!
% 2.51/1.89 % (31653)------------------------------
% 2.51/1.89 % (31653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.89 % (31653)Termination reason: Unknown
% 2.51/1.89 % (31653)Termination phase: Saturation
% 2.51/1.89
% 2.51/1.89 % (31653)Memory used [KB]: 6396
% 2.51/1.89 % (31653)Time elapsed: 0.041 s
% 2.51/1.89 % (31653)Instructions burned: 87 (million)
% 2.51/1.89 % (31653)------------------------------
% 2.51/1.89 % (31653)------------------------------
% 2.51/1.90 % (31655)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_31518 for (2996ds/39Mi)
% 2.51/1.91 % (31656)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_31518 for (2996ds/448Mi)
% 2.51/1.91 % (31655)Instruction limit reached!
% 2.51/1.91 % (31655)------------------------------
% 2.51/1.91 % (31655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.91 % (31655)Termination reason: Unknown
% 2.51/1.91 % (31655)Termination phase: Property scanning
% 2.51/1.91
% 2.51/1.91 % (31655)Memory used [KB]: 1535
% 2.51/1.91 % (31655)Time elapsed: 0.019 s
% 2.51/1.91 % (31655)Instructions burned: 39 (million)
% 2.51/1.91 % (31655)------------------------------
% 2.51/1.91 % (31655)------------------------------
% 2.51/1.92 % (31654)Instruction limit reached!
% 2.51/1.92 % (31654)------------------------------
% 2.51/1.92 % (31654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.93 % (31654)Termination reason: Unknown
% 2.51/1.93 % (31654)Termination phase: Saturation
% 2.51/1.93
% 2.51/1.93 % (31654)Memory used [KB]: 6524
% 2.51/1.93 % (31654)Time elapsed: 0.050 s
% 2.51/1.93 % (31654)Instructions burned: 107 (million)
% 2.51/1.93 % (31654)------------------------------
% 2.51/1.93 % (31654)------------------------------
% 2.51/1.93 % (31657)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_31518 for (2996ds/46Mi)
% 2.51/1.94 % (31658)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_31518 for (2996ds/98Mi)
% 2.51/1.95 % (31657)Instruction limit reached!
% 2.51/1.95 % (31657)------------------------------
% 2.51/1.95 % (31657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.95 % (31657)Termination reason: Unknown
% 2.51/1.95 % (31657)Termination phase: Property scanning
% 2.51/1.95
% 2.51/1.95 % (31657)Memory used [KB]: 1535
% 2.51/1.95 % (31657)Time elapsed: 0.022 s
% 2.51/1.95 % (31657)Instructions burned: 46 (million)
% 2.51/1.95 % (31657)------------------------------
% 2.51/1.95 % (31657)------------------------------
% 2.51/1.97 % (31659)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_31518 for (2996ds/507Mi)
% 2.51/1.98 % (31636)Refutation not found, non-redundant clauses discarded% (31636)------------------------------
% 2.51/1.98 % (31636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.98 % (31636)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.51/1.98
% 2.51/1.98 % (31636)Memory used [KB]: 8443
% 2.51/1.98 % (31636)Time elapsed: 0.320 s
% 2.51/1.98 % (31636)Instructions burned: 625 (million)
% 2.51/1.98 % (31636)------------------------------
% 2.51/1.98 % (31636)------------------------------
% 2.51/1.98 % (31658)Instruction limit reached!
% 2.51/1.98 % (31658)------------------------------
% 2.51/1.98 % (31658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.98 % (31658)Termination reason: Unknown
% 2.51/1.98 % (31658)Termination phase: Saturation
% 2.51/1.98
% 2.51/1.98 % (31658)Memory used [KB]: 1663
% 2.51/1.98 % (31658)Time elapsed: 0.043 s
% 2.51/1.98 % (31658)Instructions burned: 99 (million)
% 2.51/1.98 % (31658)------------------------------
% 2.51/1.98 % (31658)------------------------------
% 2.51/1.99 % (31660)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_31518 for (2995ds/149Mi)
% 2.51/2.00 % (31661)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_31518 for (2995ds/39Mi)
% 2.51/2.00 % (31627)Instruction limit reached!
% 2.51/2.00 % (31627)------------------------------
% 2.51/2.00 % (31627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/2.00 % (31627)Termination reason: Unknown
% 2.51/2.00 % (31627)Termination phase: Saturation
% 2.51/2.00
% 2.51/2.00 % (31627)Memory used [KB]: 7291
% 2.51/2.00 % (31627)Time elapsed: 0.391 s
% 2.51/2.00 % (31627)Instructions burned: 1042 (million)
% 2.51/2.00 % (31627)------------------------------
% 2.51/2.00 % (31627)------------------------------
% 2.51/2.02 % (31643)Instruction limit reached!
% 2.51/2.02 % (31643)------------------------------
% 2.51/2.02 % (31643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/2.02 % (31643)Termination reason: Unknown
% 2.51/2.02 % (31643)Termination phase: Saturation
% 2.51/2.02
% 2.51/2.02 % (31643)Memory used [KB]: 6908
% 2.51/2.02 % (31643)Time elapsed: 0.318 s
% 2.51/2.02 % (31643)Instructions burned: 780 (million)
% 2.51/2.02 % (31643)------------------------------
% 2.51/2.02 % (31643)------------------------------
% 2.51/2.02 % (31661)Instruction limit reached!
% 2.51/2.02 % (31661)------------------------------
% 2.51/2.02 % (31661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/2.02 % (31661)Termination reason: Unknown
% 2.51/2.02 % (31661)Termination phase: Property scanning
% 2.51/2.02
% 2.51/2.02 % (31661)Memory used [KB]: 1535
% 2.51/2.02 % (31661)Time elapsed: 0.020 s
% 2.51/2.02 % (31661)Instructions burned: 40 (million)
% 2.51/2.02 % (31661)------------------------------
% 2.51/2.02 % (31661)------------------------------
% 2.51/2.02 % (31662)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_31518 for (2995ds/6Mi)
% 2.51/2.02 % (31662)Instruction limit reached!
% 2.51/2.02 % (31662)------------------------------
% 2.51/2.02 % (31662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/2.02 % (31662)Termination reason: Unknown
% 2.51/2.02 % (31662)Termination phase: shuffling
% 2.51/2.02
% 2.51/2.02 % (31662)Memory used [KB]: 1279
% 2.51/2.02 % (31662)Time elapsed: 0.005 s
% 2.51/2.02 % (31662)Instructions burned: 7 (million)
% 2.51/2.02 % (31662)------------------------------
% 2.51/2.02 % (31662)------------------------------
% 5.63/2.04 % (31664)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_31518 for (2995ds/47Mi)
% 5.63/2.04 % (31663)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_31518 for (2995ds/1087Mi)
% 5.63/2.04 % (31665)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_31518 for (2995ds/44Mi)
% 5.63/2.06 % (31664)Instruction limit reached!
% 5.63/2.06 % (31664)------------------------------
% 5.63/2.06 % (31664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.06 % (31664)Termination reason: Unknown
% 5.63/2.06 % (31664)Termination phase: Saturation
% 5.63/2.06
% 5.63/2.06 % (31664)Memory used [KB]: 6012
% 5.63/2.06 % (31664)Time elapsed: 0.023 s
% 5.63/2.06 % (31664)Instructions burned: 47 (million)
% 5.63/2.06 % (31664)------------------------------
% 5.63/2.06 % (31664)------------------------------
% 5.63/2.06 % (31665)Instruction limit reached!
% 5.63/2.06 % (31665)------------------------------
% 5.63/2.06 % (31665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.06 % (31665)Termination reason: Unknown
% 5.63/2.06 % (31665)Termination phase: Property scanning
% 5.63/2.06
% 5.63/2.06 % (31665)Memory used [KB]: 1535
% 5.63/2.06 % (31665)Time elapsed: 0.021 s
% 5.63/2.06 % (31665)Instructions burned: 45 (million)
% 5.63/2.06 % (31665)------------------------------
% 5.63/2.06 % (31665)------------------------------
% 5.63/2.07 % (31660)Instruction limit reached!
% 5.63/2.07 % (31660)------------------------------
% 5.63/2.07 % (31660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.07 % (31660)Termination reason: Unknown
% 5.63/2.07 % (31660)Termination phase: Saturation
% 5.63/2.07
% 5.63/2.07 % (31660)Memory used [KB]: 6524
% 5.63/2.07 % (31660)Time elapsed: 0.075 s
% 5.63/2.07 % (31660)Instructions burned: 149 (million)
% 5.63/2.07 % (31660)------------------------------
% 5.63/2.07 % (31660)------------------------------
% 5.63/2.07 % (31667)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_31518 for (2995ds/62Mi)
% 5.63/2.07 % (31666)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_31518 for (2995ds/432Mi)
% 5.63/2.07 % (31656)Instruction limit reached!
% 5.63/2.07 % (31656)------------------------------
% 5.63/2.07 % (31656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.07 % (31656)Termination reason: Unknown
% 5.63/2.07 % (31656)Termination phase: Saturation
% 5.63/2.07
% 5.63/2.07 % (31656)Memory used [KB]: 6268
% 5.63/2.07 % (31656)Time elapsed: 0.167 s
% 5.63/2.07 % (31656)Instructions burned: 448 (million)
% 5.63/2.07 % (31656)------------------------------
% 5.63/2.07 % (31656)------------------------------
% 5.63/2.08 % (31668)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_31518 for (2995ds/31Mi)
% 5.63/2.09 % (31669)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_31518 for (2994ds/96Mi)
% 5.63/2.10 % (31668)Instruction limit reached!
% 5.63/2.10 % (31668)------------------------------
% 5.63/2.10 % (31668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.10 % (31668)Termination reason: Unknown
% 5.63/2.10 % (31668)Termination phase: Property scanning
% 5.63/2.10
% 5.63/2.10 % (31668)Memory used [KB]: 1407
% 5.63/2.10 % (31668)Time elapsed: 0.016 s
% 5.63/2.10 % (31668)Instructions burned: 31 (million)
% 5.63/2.10 % (31668)------------------------------
% 5.63/2.10 % (31668)------------------------------
% 5.63/2.10 % (31667)Instruction limit reached!
% 5.63/2.10 % (31667)------------------------------
% 5.63/2.10 % (31667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.10 % (31667)Termination reason: Unknown
% 5.63/2.10 % (31667)Termination phase: Saturation
% 5.63/2.10
% 5.63/2.10 % (31667)Memory used [KB]: 6012
% 5.63/2.10 % (31667)Time elapsed: 0.028 s
% 5.63/2.10 % (31667)Instructions burned: 62 (million)
% 5.63/2.10 % (31667)------------------------------
% 5.63/2.10 % (31667)------------------------------
% 5.63/2.11 % (31671)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_31518 for (2994ds/71Mi)
% 5.63/2.11 % (31670)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_31518 for (2994ds/453Mi)
% 6.11/2.13 % (31669)Instruction limit reached!
% 6.11/2.13 % (31669)------------------------------
% 6.11/2.13 % (31669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.13 % (31669)Termination reason: Unknown
% 6.11/2.13 % (31669)Termination phase: Saturation
% 6.11/2.13
% 6.11/2.13 % (31669)Memory used [KB]: 6524
% 6.11/2.13 % (31669)Time elapsed: 0.045 s
% 6.11/2.13 % (31669)Instructions burned: 96 (million)
% 6.11/2.13 % (31669)------------------------------
% 6.11/2.13 % (31669)------------------------------
% 6.11/2.15 % (31671)Instruction limit reached!
% 6.11/2.15 % (31671)------------------------------
% 6.11/2.15 % (31671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.15 % (31671)Termination reason: Unknown
% 6.11/2.15 % (31671)Termination phase: Saturation
% 6.11/2.15
% 6.11/2.15 % (31671)Memory used [KB]: 6268
% 6.11/2.15 % (31671)Time elapsed: 0.036 s
% 6.11/2.15 % (31671)Instructions burned: 72 (million)
% 6.11/2.15 % (31671)------------------------------
% 6.11/2.15 % (31671)------------------------------
% 6.11/2.15 % (31672)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_31518 for (2994ds/83Mi)
% 6.11/2.16 % (31673)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_31518 for (2994ds/11Mi)
% 6.11/2.17 % (31645)Instruction limit reached!
% 6.11/2.17 % (31645)------------------------------
% 6.11/2.17 % (31645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.17 % (31645)Termination reason: Unknown
% 6.11/2.17 % (31645)Termination phase: Saturation
% 6.11/2.17
% 6.11/2.17 % (31645)Memory used [KB]: 7291
% 6.11/2.17 % (31645)Time elapsed: 0.438 s
% 6.11/2.17 % (31645)Instructions burned: 879 (million)
% 6.11/2.17 % (31645)------------------------------
% 6.11/2.17 % (31645)------------------------------
% 6.11/2.17 % (31673)Instruction limit reached!
% 6.11/2.17 % (31673)------------------------------
% 6.11/2.17 % (31673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.17 % (31673)Termination reason: Unknown
% 6.11/2.17 % (31673)Termination phase: shuffling
% 6.11/2.17
% 6.11/2.17 % (31673)Memory used [KB]: 1407
% 6.11/2.17 % (31673)Time elapsed: 0.007 s
% 6.11/2.17 % (31673)Instructions burned: 12 (million)
% 6.11/2.17 % (31673)------------------------------
% 6.11/2.17 % (31673)------------------------------
% 6.11/2.18 % (31674)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_31518 for (2994ds/41Mi)
% 6.11/2.18 % (31675)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31518 for (2994ds/6Mi)
% 6.11/2.19 % (31672)Instruction limit reached!
% 6.11/2.19 % (31672)------------------------------
% 6.11/2.19 % (31672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.19 % (31672)Termination reason: Unknown
% 6.11/2.19 % (31672)Termination phase: Saturation
% 6.11/2.19
% 6.11/2.19 % (31672)Memory used [KB]: 6268
% 6.11/2.19 % (31672)Time elapsed: 0.039 s
% 6.11/2.19 % (31672)Instructions burned: 83 (million)
% 6.11/2.19 % (31672)------------------------------
% 6.11/2.19 % (31672)------------------------------
% 6.11/2.19 % (31675)Instruction limit reached!
% 6.11/2.19 % (31675)------------------------------
% 6.11/2.19 % (31675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.19 % (31675)Termination reason: Unknown
% 6.11/2.19 % (31675)Termination phase: shuffling
% 6.11/2.19
% 6.11/2.19 % (31675)Memory used [KB]: 1279
% 6.11/2.19 % (31675)Time elapsed: 0.004 s
% 6.11/2.19 % (31675)Instructions burned: 6 (million)
% 6.11/2.19 % (31675)------------------------------
% 6.11/2.19 % (31675)------------------------------
% 6.44/2.20 % (31674)Instruction limit reached!
% 6.44/2.20 % (31674)------------------------------
% 6.44/2.20 % (31674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.20 % (31674)Termination reason: Unknown
% 6.44/2.20 % (31674)Termination phase: Property scanning
% 6.44/2.20
% 6.44/2.20 % (31674)Memory used [KB]: 1535
% 6.44/2.20 % (31674)Time elapsed: 0.020 s
% 6.44/2.20 % (31674)Instructions burned: 42 (million)
% 6.44/2.20 % (31674)------------------------------
% 6.44/2.20 % (31674)------------------------------
% 6.44/2.20 % (31677)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_31518 for (2993ds/343Mi)
% 6.44/2.20 % (31676)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_31518 for (2993ds/150Mi)
% 6.44/2.21 % (31659)Instruction limit reached!
% 6.44/2.21 % (31659)------------------------------
% 6.44/2.21 % (31659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.21 % (31659)Termination reason: Unknown
% 6.44/2.21 % (31659)Termination phase: Saturation
% 6.44/2.21
% 6.44/2.21 % (31659)Memory used [KB]: 6780
% 6.44/2.21 % (31659)Time elapsed: 0.245 s
% 6.44/2.21 % (31659)Instructions burned: 508 (million)
% 6.44/2.21 % (31659)------------------------------
% 6.44/2.21 % (31659)------------------------------
% 6.44/2.22 % (31678)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_31518 for (2993ds/109Mi)
% 6.44/2.23 % (31679)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_31518 for (2993ds/253Mi)
% 6.44/2.24 % (31666)Instruction limit reached!
% 6.44/2.24 % (31666)------------------------------
% 6.44/2.24 % (31666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.24 % (31666)Termination reason: Unknown
% 6.44/2.24 % (31666)Termination phase: Saturation
% 6.44/2.24
% 6.44/2.24 % (31666)Memory used [KB]: 2430
% 6.44/2.24 % (31666)Time elapsed: 0.174 s
% 6.44/2.24 % (31666)Instructions burned: 433 (million)
% 6.44/2.24 % (31666)------------------------------
% 6.44/2.24 % (31666)------------------------------
% 6.44/2.26 % (31680)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_31518 for (2993ds/140Mi)
% 6.44/2.27 % (31678)Instruction limit reached!
% 6.44/2.27 % (31678)------------------------------
% 6.44/2.27 % (31678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.27 % (31678)Termination reason: Unknown
% 6.44/2.27 % (31678)Termination phase: Saturation
% 6.44/2.27
% 6.44/2.27 % (31678)Memory used [KB]: 6652
% 6.44/2.27 % (31678)Time elapsed: 0.050 s
% 6.44/2.27 % (31678)Instructions burned: 109 (million)
% 6.44/2.27 % (31678)------------------------------
% 6.44/2.27 % (31678)------------------------------
% 6.44/2.28 % (31676)Instruction limit reached!
% 6.44/2.28 % (31676)------------------------------
% 6.44/2.28 % (31676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.28 % (31676)Termination reason: Unknown
% 6.44/2.28 % (31676)Termination phase: Saturation
% 6.44/2.28
% 6.44/2.28 % (31676)Memory used [KB]: 7036
% 6.44/2.28 % (31676)Time elapsed: 0.101 s
% 6.44/2.28 % (31676)Instructions burned: 151 (million)
% 6.44/2.28 % (31676)------------------------------
% 6.44/2.28 % (31676)------------------------------
% 6.44/2.28 % (31681)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_31518 for (2992ds/614Mi)
% 6.44/2.29 % (31670)Instruction limit reached!
% 6.44/2.29 % (31670)------------------------------
% 6.44/2.29 % (31670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.29 % (31670)Termination reason: Unknown
% 6.44/2.29 % (31670)Termination phase: Saturation
% 6.44/2.29
% 6.44/2.29 % (31670)Memory used [KB]: 6140
% 6.44/2.29 % (31670)Time elapsed: 0.176 s
% 6.44/2.29 % (31670)Instructions burned: 454 (million)
% 6.44/2.29 % (31670)------------------------------
% 6.44/2.29 % (31670)------------------------------
% 7.02/2.30 % (31682)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_31518 for (2992ds/202Mi)
% 7.02/2.31 % (31683)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_31518 for (2992ds/339Mi)
% 7.02/2.31 % (31680)Refutation not found, incomplete strategy
% 7.02/2.31 % (31680)------------------------------
% 7.02/2.31 % (31680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.31 % (31680)Termination reason: Refutation not found, incomplete strategy
% 7.02/2.31
% 7.02/2.31
% 7.02/2.31 % (31680)Memory used [KB]: 6140
% 7.02/2.31 % (31680)Time elapsed: 0.073 s
% 7.02/2.31 % (31680)Instructions burned: 103 (million)
% 7.02/2.31 % (31680)------------------------------
% 7.02/2.31 % (31680)------------------------------
% 7.02/2.33 % (31684)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_31518 for (2992ds/283Mi)
% 7.02/2.35 % (31679)Instruction limit reached!
% 7.02/2.35 % (31679)------------------------------
% 7.02/2.35 % (31679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.35 % (31679)Termination reason: Unknown
% 7.02/2.35 % (31679)Termination phase: Saturation
% 7.02/2.35
% 7.02/2.35 % (31679)Memory used [KB]: 7547
% 7.02/2.35 % (31679)Time elapsed: 0.146 s
% 7.02/2.35 % (31679)Instructions burned: 253 (million)
% 7.02/2.35 % (31679)------------------------------
% 7.02/2.35 % (31679)------------------------------
% 7.02/2.36 % (31685)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_31518 for (2992ds/134Mi)
% 7.02/2.37 % (31677)Instruction limit reached!
% 7.02/2.37 % (31677)------------------------------
% 7.02/2.37 % (31677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.37 % (31677)Termination reason: Unknown
% 7.02/2.37 % (31677)Termination phase: Saturation
% 7.02/2.37
% 7.02/2.37 % (31677)Memory used [KB]: 7036
% 7.02/2.37 % (31677)Time elapsed: 0.187 s
% 7.02/2.37 % (31677)Instructions burned: 343 (million)
% 7.02/2.37 % (31677)------------------------------
% 7.02/2.37 % (31677)------------------------------
% 7.02/2.39 % (31686)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_31518 for (2991ds/298Mi)
% 7.41/2.40 % (31682)Instruction limit reached!
% 7.41/2.40 % (31682)------------------------------
% 7.41/2.40 % (31682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.40 % (31682)Termination reason: Unknown
% 7.41/2.40 % (31682)Termination phase: Saturation
% 7.41/2.40
% 7.41/2.40 % (31682)Memory used [KB]: 7291
% 7.41/2.40 % (31682)Time elapsed: 0.106 s
% 7.41/2.40 % (31682)Instructions burned: 202 (million)
% 7.41/2.40 % (31682)------------------------------
% 7.41/2.40 % (31682)------------------------------
% 7.41/2.42 % (31687)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_31518 for (2991ds/192Mi)
% 7.41/2.43 % (31685)Instruction limit reached!
% 7.41/2.43 % (31685)------------------------------
% 7.41/2.43 % (31685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.43 % (31685)Termination reason: Unknown
% 7.41/2.43 % (31685)Termination phase: Saturation
% 7.41/2.43
% 7.41/2.43 % (31685)Memory used [KB]: 6780
% 7.41/2.43 % (31685)Time elapsed: 0.065 s
% 7.41/2.43 % (31685)Instructions burned: 134 (million)
% 7.41/2.43 % (31685)------------------------------
% 7.41/2.43 % (31685)------------------------------
% 7.41/2.44 % (31684)Instruction limit reached!
% 7.41/2.44 % (31684)------------------------------
% 7.41/2.44 % (31684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.44 % (31684)Termination reason: Unknown
% 7.41/2.44 % (31684)Termination phase: Saturation
% 7.41/2.44
% 7.41/2.44 % (31684)Memory used [KB]: 7803
% 7.41/2.44 % (31684)Time elapsed: 0.115 s
% 7.41/2.44 % (31684)Instructions burned: 284 (million)
% 7.41/2.44 % (31684)------------------------------
% 7.41/2.44 % (31684)------------------------------
% 7.41/2.44 % (31688)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_31518 for (2991ds/258Mi)
% 7.41/2.46 % (31689)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_31518 for (2991ds/90Mi)
% 7.41/2.47 % (31683)Instruction limit reached!
% 7.41/2.47 % (31683)------------------------------
% 7.41/2.47 % (31683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.47 % (31683)Termination reason: Unknown
% 7.41/2.47 % (31683)Termination phase: Saturation
% 7.41/2.47
% 7.41/2.47 % (31683)Memory used [KB]: 7803
% 7.41/2.47 % (31683)Time elapsed: 0.164 s
% 7.41/2.47 % (31683)Instructions burned: 340 (million)
% 7.41/2.47 % (31683)------------------------------
% 7.41/2.47 % (31683)------------------------------
% 7.41/2.48 % (31690)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_31518 for (2990ds/231Mi)
% 7.92/2.50 % (31689)Instruction limit reached!
% 7.92/2.50 % (31689)------------------------------
% 7.92/2.50 % (31689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.50 % (31689)Termination reason: Unknown
% 7.92/2.50 % (31689)Termination phase: Saturation
% 7.92/2.50
% 7.92/2.50 % (31689)Memory used [KB]: 6524
% 7.92/2.50 % (31689)Time elapsed: 0.045 s
% 7.92/2.50 % (31689)Instructions burned: 91 (million)
% 7.92/2.50 % (31689)------------------------------
% 7.92/2.50 % (31689)------------------------------
% 7.92/2.51 % (31686)Instruction limit reached!
% 7.92/2.51 % (31686)------------------------------
% 7.92/2.51 % (31686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.51 % (31686)Termination reason: Unknown
% 7.92/2.51 % (31686)Termination phase: Saturation
% 7.92/2.51
% 7.92/2.51 % (31686)Memory used [KB]: 6396
% 7.92/2.51 % (31686)Time elapsed: 0.127 s
% 7.92/2.51 % (31686)Instructions burned: 298 (million)
% 7.92/2.51 % (31686)------------------------------
% 7.92/2.51 % (31686)------------------------------
% 7.92/2.51 % (31687)Instruction limit reached!
% 7.92/2.51 % (31687)------------------------------
% 7.92/2.51 % (31687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.51 % (31687)Termination reason: Unknown
% 7.92/2.51 % (31687)Termination phase: Saturation
% 7.92/2.51
% 7.92/2.51 % (31687)Memory used [KB]: 7036
% 7.92/2.51 % (31687)Time elapsed: 0.093 s
% 7.92/2.51 % (31687)Instructions burned: 192 (million)
% 7.92/2.51 % (31687)------------------------------
% 7.92/2.51 % (31687)------------------------------
% 7.92/2.52 % (31691)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_31518 for (2990ds/458Mi)
% 7.92/2.53 % (31693)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_31518 for (2990ds/297Mi)
% 7.92/2.53 % (31692)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_31518 for (2990ds/31Mi)
% 7.92/2.54 % (31692)Instruction limit reached!
% 7.92/2.54 % (31692)------------------------------
% 7.92/2.54 % (31692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.54 % (31692)Termination reason: Unknown
% 7.92/2.54 % (31692)Termination phase: Property scanning
% 7.92/2.54
% 7.92/2.54 % (31692)Memory used [KB]: 1407
% 7.92/2.54 % (31692)Time elapsed: 0.015 s
% 7.92/2.54 % (31692)Instructions burned: 31 (million)
% 7.92/2.54 % (31692)------------------------------
% 7.92/2.54 % (31692)------------------------------
% 7.92/2.56 % (31694)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_31518 for (2990ds/987Mi)
% 7.92/2.57 % (31688)Instruction limit reached!
% 7.92/2.57 % (31688)------------------------------
% 7.92/2.57 % (31688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.57 % (31688)Termination reason: Unknown
% 7.92/2.57 % (31688)Termination phase: Saturation
% 7.92/2.57
% 7.92/2.57 % (31688)Memory used [KB]: 6908
% 7.92/2.57 % (31688)Time elapsed: 0.125 s
% 7.92/2.57 % (31688)Instructions burned: 259 (million)
% 7.92/2.57 % (31688)------------------------------
% 7.92/2.57 % (31688)------------------------------
% 7.92/2.58 % (31663)Instruction limit reached!
% 7.92/2.58 % (31663)------------------------------
% 7.92/2.58 % (31663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.58 % (31663)Termination reason: Unknown
% 7.92/2.58 % (31663)Termination phase: Saturation
% 7.92/2.58
% 7.92/2.58 % (31663)Memory used [KB]: 9978
% 7.92/2.58 % (31663)Time elapsed: 0.551 s
% 7.92/2.58 % (31663)Instructions burned: 1088 (million)
% 7.92/2.58 % (31663)------------------------------
% 7.92/2.58 % (31663)------------------------------
% 7.92/2.58 % (31681)Instruction limit reached!
% 7.92/2.58 % (31681)------------------------------
% 7.92/2.58 % (31681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.58 % (31681)Termination reason: Unknown
% 7.92/2.58 % (31681)Termination phase: Saturation
% 7.92/2.58
% 7.92/2.58 % (31681)Memory used [KB]: 7419
% 7.92/2.58 % (31681)Time elapsed: 0.302 s
% 7.92/2.58 % (31681)Instructions burned: 614 (million)
% 7.92/2.58 % (31681)------------------------------
% 7.92/2.58 % (31681)------------------------------
% 7.92/2.58 % (31695)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_31518 for (2989ds/182Mi)
% 9.28/2.60 % (31690)Instruction limit reached!
% 9.28/2.60 % (31690)------------------------------
% 9.28/2.60 % (31690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.60 % (31690)Termination reason: Unknown
% 9.28/2.60 % (31690)Termination phase: Saturation
% 9.28/2.60
% 9.28/2.60 % (31690)Memory used [KB]: 9338
% 9.28/2.60 % (31690)Time elapsed: 0.117 s
% 9.28/2.60 % (31690)Instructions burned: 231 (million)
% 9.28/2.60 % (31690)------------------------------
% 9.28/2.60 % (31690)------------------------------
% 9.28/2.60 % (31697)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_31518 for (2989ds/154Mi)
% 9.28/2.60 % (31696)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_31518 for (2989ds/182Mi)
% 9.28/2.62 % (31698)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_31518 for (2989ds/79Mi)
% 9.28/2.64 % (31693)Instruction limit reached!
% 9.28/2.64 % (31693)------------------------------
% 9.28/2.64 % (31693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.64 % (31693)Termination reason: Unknown
% 9.28/2.64 % (31693)Termination phase: Saturation
% 9.28/2.64
% 9.28/2.64 % (31693)Memory used [KB]: 7036
% 9.28/2.64 % (31693)Time elapsed: 0.119 s
% 9.28/2.64 % (31693)Instructions burned: 297 (million)
% 9.28/2.64 % (31693)------------------------------
% 9.28/2.64 % (31693)------------------------------
% 9.28/2.65 % (31698)Instruction limit reached!
% 9.28/2.65 % (31698)------------------------------
% 9.28/2.65 % (31698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.65 % (31698)Termination reason: Unknown
% 9.28/2.65 % (31698)Termination phase: Saturation
% 9.28/2.65
% 9.28/2.65 % (31698)Memory used [KB]: 6268
% 9.28/2.65 % (31698)Time elapsed: 0.038 s
% 9.28/2.65 % (31698)Instructions burned: 79 (million)
% 9.28/2.65 % (31698)------------------------------
% 9.28/2.65 % (31698)------------------------------
% 9.28/2.66 % (31697)Instruction limit reached!
% 9.28/2.66 % (31697)------------------------------
% 9.28/2.66 % (31697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.66 % (31697)Termination reason: Unknown
% 9.28/2.66 % (31697)Termination phase: Saturation
% 9.28/2.66
% 9.28/2.66 % (31697)Memory used [KB]: 6140
% 9.28/2.66 % (31697)Time elapsed: 0.062 s
% 9.28/2.66 % (31697)Instructions burned: 156 (million)
% 9.28/2.66 % (31697)------------------------------
% 9.28/2.66 % (31697)------------------------------
% 9.28/2.66 % (31699)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_31518 for (2989ds/216Mi)
% 9.28/2.67 % (31700)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_31518 for (2989ds/114Mi)
% 9.28/2.67 % (31695)Instruction limit reached!
% 9.28/2.67 % (31695)------------------------------
% 9.28/2.67 % (31695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.67 % (31695)Termination reason: Unknown
% 9.28/2.67 % (31695)Termination phase: Saturation
% 9.28/2.67
% 9.28/2.67 % (31695)Memory used [KB]: 6780
% 9.28/2.67 % (31695)Time elapsed: 0.088 s
% 9.28/2.67 % (31695)Instructions burned: 183 (million)
% 9.28/2.67 % (31695)------------------------------
% 9.28/2.67 % (31695)------------------------------
% 9.28/2.68 % (31701)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_31518 for (2989ds/922Mi)
% 9.28/2.69 % (31702)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_31518 for (2988ds/182Mi)
% 9.28/2.69 % (31696)Instruction limit reached!
% 9.28/2.69 % (31696)------------------------------
% 9.28/2.69 % (31696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.69 % (31696)Termination reason: Unknown
% 9.28/2.69 % (31696)Termination phase: Saturation
% 9.28/2.69
% 9.28/2.69 % (31696)Memory used [KB]: 8315
% 9.28/2.69 % (31696)Time elapsed: 0.095 s
% 9.28/2.69 % (31696)Instructions burned: 182 (million)
% 9.28/2.69 % (31696)------------------------------
% 9.28/2.69 % (31696)------------------------------
% 9.88/2.71 % (31703)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_31518 for (2988ds/164Mi)
% 9.88/2.72 % (31700)Instruction limit reached!
% 9.88/2.72 % (31700)------------------------------
% 9.88/2.72 % (31700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.88/2.72 % (31700)Termination reason: Unknown
% 9.88/2.72 % (31700)Termination phase: Saturation
% 9.88/2.72
% 9.88/2.72 % (31700)Memory used [KB]: 6652
% 9.88/2.72 % (31700)Time elapsed: 0.055 s
% 9.88/2.72 % (31700)Instructions burned: 115 (million)
% 9.88/2.72 % (31700)------------------------------
% 9.88/2.72 % (31700)------------------------------
% 9.88/2.74 % (31704)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_31518 for (2988ds/50Mi)
% 9.88/2.74 % (31691)Instruction limit reached!
% 9.88/2.74 % (31691)------------------------------
% 9.88/2.74 % (31691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.88/2.74 % (31691)Termination reason: Unknown
% 9.88/2.74 % (31691)Termination phase: Saturation
% 9.88/2.74
% 9.88/2.74 % (31691)Memory used [KB]: 7419
% 9.88/2.74 % (31691)Time elapsed: 0.227 s
% 9.88/2.74 % (31691)Instructions burned: 459 (million)
% 9.88/2.74 % (31691)------------------------------
% 9.88/2.74 % (31691)------------------------------
% 9.88/2.75 % (31699)Instruction limit reached!
% 9.88/2.75 % (31699)------------------------------
% 9.88/2.75 % (31699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.88/2.75 % (31699)Termination reason: Unknown
% 9.88/2.75 % (31699)Termination phase: Saturation
% 9.88/2.75
% 9.88/2.75 % (31699)Memory used [KB]: 7164
% 9.88/2.75 % (31699)Time elapsed: 0.086 s
% 9.88/2.75 % (31699)Instructions burned: 217 (million)
% 9.88/2.75 % (31699)------------------------------
% 9.88/2.75 % (31699)------------------------------
% 9.88/2.76 % (31702)Instruction limit reached!
% 9.88/2.76 % (31702)------------------------------
% 9.88/2.76 % (31702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.88/2.76 % (31702)Termination reason: Unknown
% 9.88/2.76 % (31702)Termination phase: Saturation
% 9.88/2.76
% 9.88/2.76 % (31702)Memory used [KB]: 6140
% 9.88/2.76 % (31702)Time elapsed: 0.072 s
% 9.88/2.76 % (31702)Instructions burned: 182 (million)
% 9.88/2.76 % (31702)------------------------------
% 9.88/2.76 % (31702)------------------------------
% 9.88/2.76 % (31705)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_31518 for (2988ds/368Mi)
% 9.88/2.76 % (31706)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_31518 for (2988ds/1021Mi)
% 9.88/2.76 % (31704)Instruction limit reached!
% 9.88/2.76 % (31704)------------------------------
% 9.88/2.76 % (31704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.88/2.76 % (31704)Termination reason: Unknown
% 9.88/2.76 % (31704)Termination phase: Saturation
% 9.88/2.76
% 9.88/2.76 % (31704)Memory used [KB]: 10490
% 9.88/2.76 % (31704)Time elapsed: 0.025 s
% 9.88/2.76 % (31704)Instructions burned: 51 (million)
% 9.88/2.76 % (31704)------------------------------
% 9.88/2.76 % (31704)------------------------------
% 9.88/2.77 % (31707)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_31518 for (2988ds/267Mi)
% 9.88/2.78 % (31708)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_31518 for (2988ds/204Mi)
% 9.88/2.79 % (31703)Instruction limit reached!
% 9.88/2.79 % (31703)------------------------------
% 9.88/2.79 % (31703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.88/2.79 % (31703)Termination reason: Unknown
% 9.88/2.79 % (31703)Termination phase: Saturation
% 9.88/2.79
% 9.88/2.79 % (31703)Memory used [KB]: 1918
% 9.88/2.79 % (31703)Time elapsed: 0.079 s
% 9.88/2.79 % (31703)Instructions burned: 164 (million)
% 9.88/2.79 % (31703)------------------------------
% 9.88/2.79 % (31703)------------------------------
% 10.53/2.81 % (31709)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_31518 for (2987ds/26Mi)
% 10.53/2.82 % (31709)Instruction limit reached!
% 10.53/2.82 % (31709)------------------------------
% 10.53/2.82 % (31709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/2.82 % (31709)Termination reason: Unknown
% 10.53/2.82 % (31709)Termination phase: Property scanning
% 10.53/2.82
% 10.53/2.82 % (31709)Memory used [KB]: 1407
% 10.53/2.82 % (31709)Time elapsed: 0.014 s
% 10.53/2.82 % (31709)Instructions burned: 27 (million)
% 10.53/2.82 % (31709)------------------------------
% 10.53/2.82 % (31709)------------------------------
% 10.53/2.84 % (31710)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_31518 for (2987ds/53Mi)
% 10.53/2.86 % (31710)Instruction limit reached!
% 10.53/2.86 % (31710)------------------------------
% 10.53/2.86 % (31710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/2.86 % (31710)Termination reason: Unknown
% 10.53/2.86 % (31710)Termination phase: Saturation
% 10.53/2.86
% 10.53/2.86 % (31710)Memory used [KB]: 6012
% 10.53/2.86 % (31710)Time elapsed: 0.025 s
% 10.53/2.86 % (31710)Instructions burned: 54 (million)
% 10.53/2.86 % (31710)------------------------------
% 10.53/2.86 % (31710)------------------------------
% 10.53/2.87 % (31708)Instruction limit reached!
% 10.53/2.87 % (31708)------------------------------
% 10.53/2.87 % (31708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/2.87 % (31708)Termination reason: Unknown
% 10.53/2.87 % (31708)Termination phase: Saturation
% 10.53/2.87
% 10.53/2.87 % (31708)Memory used [KB]: 6780
% 10.53/2.87 % (31708)Time elapsed: 0.098 s
% 10.53/2.87 % (31708)Instructions burned: 204 (million)
% 10.53/2.88 % (31708)------------------------------
% 10.53/2.88 % (31708)------------------------------
% 10.53/2.88 % (31711)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_31518 for (2987ds/4436Mi)
% 10.53/2.88 % (31707)Instruction limit reached!
% 10.53/2.88 % (31707)------------------------------
% 10.53/2.88 % (31707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/2.88 % (31707)Termination reason: Unknown
% 10.53/2.88 % (31707)Termination phase: Saturation
% 10.53/2.88
% 10.53/2.88 % (31707)Memory used [KB]: 7803
% 10.53/2.88 % (31707)Time elapsed: 0.108 s
% 10.53/2.88 % (31707)Instructions burned: 267 (million)
% 10.53/2.88 % (31707)------------------------------
% 10.53/2.88 % (31707)------------------------------
% 10.53/2.89 % (31712)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_31518 for (2987ds/1539Mi)
% 10.53/2.90 % (31713)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_31518 for (2986ds/408Mi)
% 10.83/2.93 % (31694)Instruction limit reached!
% 10.83/2.93 % (31694)------------------------------
% 10.83/2.93 % (31694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.83/2.93 % (31694)Termination reason: Unknown
% 10.83/2.93 % (31694)Termination phase: Saturation
% 10.83/2.93
% 10.83/2.93 % (31694)Memory used [KB]: 7419
% 10.83/2.93 % (31694)Time elapsed: 0.371 s
% 10.83/2.93 % (31694)Instructions burned: 987 (million)
% 10.83/2.93 % (31694)------------------------------
% 10.83/2.93 % (31694)------------------------------
% 10.83/2.94 % (31705)Instruction limit reached!
% 10.83/2.94 % (31705)------------------------------
% 10.83/2.94 % (31705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.83/2.94 % (31705)Termination reason: Unknown
% 10.83/2.94 % (31705)Termination phase: Saturation
% 10.83/2.94
% 10.83/2.94 % (31705)Memory used [KB]: 7164
% 10.83/2.94 % (31705)Time elapsed: 0.182 s
% 10.83/2.94 % (31705)Instructions burned: 368 (million)
% 10.83/2.94 % (31705)------------------------------
% 10.83/2.94 % (31705)------------------------------
% 10.83/2.94 % (31714)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_31518 for (2986ds/5205Mi)
% 10.83/2.96 % (31715)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_31518 for (2986ds/1913Mi)
% 12.64/3.11 % (31713)Instruction limit reached!
% 12.64/3.11 % (31713)------------------------------
% 12.64/3.11 % (31713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.64/3.11 % (31713)Termination reason: Unknown
% 12.64/3.11 % (31713)Termination phase: Saturation
% 12.64/3.11
% 12.64/3.11 % (31713)Memory used [KB]: 8571
% 12.64/3.11 % (31713)Time elapsed: 0.237 s
% 12.64/3.11 % (31713)Instructions burned: 409 (million)
% 12.64/3.11 % (31713)------------------------------
% 12.64/3.11 % (31713)------------------------------
% 13.33/3.13 % (31716)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_31518 for (2984ds/4350Mi)
% 13.33/3.13 % (31701)Instruction limit reached!
% 13.33/3.13 % (31701)------------------------------
% 13.33/3.13 % (31701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.33/3.13 % (31701)Termination reason: Unknown
% 13.33/3.13 % (31701)Termination phase: Saturation
% 13.33/3.13
% 13.33/3.13 % (31701)Memory used [KB]: 8955
% 13.33/3.13 % (31701)Time elapsed: 0.452 s
% 13.33/3.13 % (31701)Instructions burned: 922 (million)
% 13.33/3.13 % (31701)------------------------------
% 13.33/3.13 % (31701)------------------------------
% 13.33/3.15 % (31717)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_31518 for (2984ds/68Mi)
% 13.33/3.15 % (31712)First to succeed.
% 13.33/3.16 % (31712)Refutation found. Thanks to Tanya!
% 13.33/3.16 % SZS status Theorem for DTF2THF_31518
% 13.33/3.16 % SZS output start Proof for DTF2THF_31518
% 13.33/3.16 thf(func_def_0, type, in: $i > $i > $o).
% 13.33/3.16 thf(func_def_1, type, exu: ($i > $o) > $o).
% 13.33/3.16 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 13.33/3.16 thf(func_def_8, type, powerset: $i > $i).
% 13.33/3.16 thf(func_def_10, type, setunion: $i > $i).
% 13.33/3.16 thf(func_def_19, type, descr: ($i > $o) > $i).
% 13.33/3.16 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 13.33/3.16 thf(func_def_26, type, prop2set: $o > $i).
% 13.33/3.16 thf(func_def_36, type, nonempty: $i > $o).
% 13.33/3.16 thf(func_def_69, type, set2prop: $i > $o).
% 13.33/3.16 thf(func_def_88, type, subset: $i > $i > $o).
% 13.33/3.16 thf(func_def_89, type, disjoint: $i > $i > $o).
% 13.33/3.16 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 13.33/3.16 thf(func_def_126, type, sK3: ($i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_127, type, sK4: $i > ($i > $o) > $i).
% 13.33/3.16 thf(func_def_128, type, sK5: $i > $i).
% 13.33/3.16 thf(func_def_129, type, sK6: $i > $i).
% 13.33/3.16 thf(func_def_130, type, sK7: ($i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_131, type, sK8: $i > $i > $i).
% 13.33/3.16 thf(func_def_132, type, sK9: $i > $i).
% 13.33/3.16 thf(func_def_133, type, sK10: $i > $i > $i).
% 13.33/3.16 thf(func_def_134, type, sK11: $i > $i > $i).
% 13.33/3.16 thf(func_def_135, type, sK12: $i > $i > $i).
% 13.33/3.16 thf(func_def_136, type, sK13: $i > $i > $i).
% 13.33/3.16 thf(func_def_137, type, sK14: $i > $i > $i).
% 13.33/3.16 thf(func_def_138, type, sK15: $i > $i > $i).
% 13.33/3.16 thf(func_def_139, type, sK16: $i > $i > $i > $i).
% 13.33/3.16 thf(func_def_140, type, sK17: $i > $i > $i).
% 13.33/3.16 thf(func_def_141, type, sK18: ($i > $o) > $i).
% 13.33/3.16 thf(func_def_142, type, sK19: ($i > $o) > $i).
% 13.33/3.16 thf(func_def_143, type, sK20: ($i > $o) > $i).
% 13.33/3.16 thf(func_def_144, type, sK21: $i > $i).
% 13.33/3.16 thf(func_def_145, type, sK22: ($i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_146, type, sK23: $i > $i > $i).
% 13.33/3.16 thf(func_def_147, type, sK24: ($i > $o) > ($i > $o) > $i).
% 13.33/3.16 thf(func_def_148, type, sK25: ($i > $o) > ($i > $o) > $i).
% 13.33/3.16 thf(func_def_149, type, sK26: ($i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_150, type, sK27: ($i > $o) > $i).
% 13.33/3.16 thf(func_def_151, type, sK28: ($i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_152, type, sK29: ($i > $i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_153, type, sK30: ($i > $i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_154, type, sK31: $i > ($i > $i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_155, type, sK32: $i > $i > $i).
% 13.33/3.16 thf(func_def_156, type, sK33: $i > $i).
% 13.33/3.16 thf(func_def_157, type, sK34: ($i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_158, type, sK35: ($i > $o) > $i).
% 13.33/3.16 thf(func_def_159, type, sK36: $o > $i > $i > $i).
% 13.33/3.16 thf(func_def_160, type, sK37: $i > $i).
% 13.33/3.16 thf(func_def_161, type, sK38: $i > ($i > $o) > $i).
% 13.33/3.16 thf(func_def_162, type, sK39: ($i > $o) > ($i > $o) > $i).
% 13.33/3.16 thf(func_def_163, type, sK40: ($i > $o) > ($i > $o) > $i).
% 13.33/3.16 thf(func_def_164, type, sK41: $i > ($i > $o) > $i).
% 13.33/3.16 thf(func_def_165, type, sK42: ($i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_166, type, sK43: ($i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_167, type, sK44: $i > ($i > $o) > $i).
% 13.33/3.16 thf(func_def_168, type, sK45: ($i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_169, type, sK46: ($i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_170, type, sK47: ($i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_171, type, sK48: $i > $i).
% 13.33/3.16 thf(func_def_172, type, sK49: $i > ($i > $o) > $i).
% 13.33/3.16 thf(func_def_173, type, sK50: ($i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_174, type, sK51: ($i > $o) > $i).
% 13.33/3.16 thf(func_def_175, type, sK52: ($i > $o) > $i > $i).
% 13.33/3.16 thf(func_def_176, type, sK53: $i > $i > $i).
% 13.33/3.16 thf(func_def_177, type, sK54: $i > $i > $i).
% 13.33/3.16 thf(func_def_178, type, sK55: $i > $i > $i).
% 13.33/3.16 thf(func_def_179, type, sK56: ($i > $o) > ($i > $o) > $i > $i > $i).
% 13.33/3.16 thf(func_def_180, type, sK57: $i > $i > ($i > $o) > ($i > $o) > $i).
% 13.33/3.16 thf(func_def_181, type, ph58: !>[X0: $tType]:(X0)).
% 13.33/3.16 thf(func_def_182, type, sK59: $i > $i).
% 13.33/3.16 thf(func_def_183, type, sK60: $i > $i).
% 13.33/3.16 thf(func_def_184, type, sK61: $i > $i > $i).
% 13.33/3.16 thf(func_def_185, type, sK62: $i > $i > $i).
% 13.33/3.16 thf(func_def_186, type, sK63: $i > $i > $i).
% 13.33/3.16 thf(func_def_187, type, sK64: $i > $i).
% 13.33/3.16 thf(func_def_188, type, sK65: $i > $i > $i).
% 13.33/3.16 thf(func_def_189, type, sK66: $i > $i > $i).
% 13.33/3.16 thf(func_def_190, type, sK67: $i > $i).
% 13.33/3.16 thf(func_def_191, type, sK68: $i > $i > $i).
% 13.33/3.16 thf(func_def_192, type, sK69: $i > $i > $i).
% 13.33/3.16 thf(func_def_193, type, sK70: $i > $i > $i).
% 13.33/3.16 thf(func_def_194, type, sK71: $i > $i > $i).
% 13.33/3.16 thf(func_def_195, type, sK72: $i > $i > $i).
% 13.33/3.16 thf(func_def_196, type, sK73: $i > $i > $i).
% 13.33/3.16 thf(func_def_197, type, sK74: $i > $i > $i).
% 13.33/3.16 thf(func_def_198, type, sK75: $i > $i > $i).
% 13.33/3.16 thf(f3127,plain,(
% 13.33/3.16 $false),
% 13.33/3.16 inference(avatar_sat_refutation,[status(thm)],[f1509,f1514,f1519,f1524,f2582,f3117,f3125,f3126])).
% 13.33/3.16 thf(f3126,plain,(
% 13.33/3.16 ($false != (in @ (sK23 @ sK1 @ sK0) @ sK0)) | ($true != (in @ (sK23 @ sK1 @ sK0) @ sK0)) | ($true = $false)),
% 13.33/3.16 introduced(definition,[],[theory_tautology_sat_conflict])).
% 13.33/3.16 thf(f3125,plain,(
% 13.33/3.16 spl2_9 | spl2_1 | ~spl2_7),
% 13.33/3.16 inference(avatar_split_clause,[status(thm)],[f2848,f2579,f1506,f3122])).
% 13.33/3.16 thf(f3122,definition,(
% 13.33/3.16 spl2_9 <=> ($true = (in @ (sK23 @ sK1 @ sK0) @ sK0))),
% 13.33/3.16 introduced(definition,[new_symbols(naming,[spl2_9])],[avatar_definition])).
% 13.33/3.16 thf(f1506,definition,(
% 13.33/3.16 spl2_1 <=> (sK0 = sK1)),
% 13.33/3.16 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 13.33/3.16 thf(f2579,definition,(
% 13.33/3.16 spl2_7 <=> ($false = (in @ (sK23 @ sK1 @ sK0) @ sK1))),
% 13.33/3.16 introduced(definition,[new_symbols(naming,[spl2_7])],[avatar_definition])).
% 13.33/3.16 thf(f2848,plain,(
% 13.33/3.16 ($true = (in @ (sK23 @ sK1 @ sK0) @ sK0)) | (spl2_1 | ~spl2_7)),
% 13.33/3.16 inference(subsumption_resolution,[status(thm)],[f2834,f1508])).
% 13.33/3.16 thf(f1508,plain,(
% 13.33/3.16 (sK0 != sK1) | spl2_1),
% 13.33/3.16 inference(avatar_component_clause,[status(thm)],[f1506])).
% 13.33/3.16 thf(f2834,plain,(
% 13.33/3.16 (sK0 = sK1) | ($true = (in @ (sK23 @ sK1 @ sK0) @ sK0)) | ~spl2_7),
% 13.33/3.16 inference(not_proxy_clausification,[status(thm)],[f2833])).
% 13.33/3.16 thf(f2833,plain,(
% 13.33/3.16 (sK0 = sK1) | ($false = (~ (in @ (sK23 @ sK1 @ sK0) @ sK0))) | ~spl2_7),
% 13.33/3.16 inference(boolean_simplification,[status(thm)],[f2824])).
% 13.33/3.16 thf(f2824,plain,(
% 13.33/3.16 ($false = ($false = (in @ (sK23 @ sK1 @ sK0) @ sK0))) | (sK0 = sK1) | ~spl2_7),
% 13.33/3.16 inference(superposition,[status(thm)],[f987,f2581])).
% 13.33/3.16 thf(f2581,plain,(
% 13.33/3.16 ($false = (in @ (sK23 @ sK1 @ sK0) @ sK1)) | ~spl2_7),
% 13.33/3.16 inference(avatar_component_clause,[status(thm)],[f2579])).
% 13.33/3.16 thf(f987,plain,(
% 13.33/3.16 ( ! [X2 : $i,X1 : $i] : ((((in @ (sK23 @ X1 @ X2) @ X1) = (in @ (sK23 @ X1 @ X2) @ X2)) = $false) | (X1 = X2)) )),
% 13.33/3.16 inference(equality_proxy_clausification,[status(thm)],[f986])).
% 13.33/3.16 thf(f986,plain,(
% 13.33/3.16 ( ! [X2 : $i,X1 : $i] : ((((in @ (sK23 @ X1 @ X2) @ X1) = (in @ (sK23 @ X1 @ X2) @ X2)) = $false) | ($true = (X2 = X1))) )),
% 13.33/3.16 inference(beta_eta_normalization,[status(thm)],[f985])).
% 13.33/3.16 thf(f985,plain,(
% 13.33/3.16 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((in @ Y0 @ X1) = (in @ Y0 @ X2))) @ (sK23 @ X1 @ X2))) | ($true = (X2 = X1))) )),
% 13.33/3.16 inference(sigma_clausification,[status(thm)],[f984])).
% 13.33/3.16 thf(f984,plain,(
% 13.33/3.16 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) = (in @ Y0 @ X2))))) | ($true = (X2 = X1))) )),
% 13.33/3.16 inference(binary_proxy_clausification,[status(thm)],[f983])).
% 13.33/3.16 thf(f983,plain,(
% 13.33/3.16 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) = (in @ Y0 @ X2)))) => (X2 = X1)))) )),
% 13.33/3.16 inference(beta_eta_normalization,[status(thm)],[f982])).
% 13.33/3.16 thf(f982,plain,(
% 13.33/3.16 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) = (in @ Y1 @ Y0)))) => (Y0 = X1))) @ X2))) )),
% 13.33/3.16 inference(pi_clausification,[status(thm)],[f981])).
% 13.33/3.16 thf(f981,plain,(
% 13.33/3.16 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) = (in @ Y1 @ Y0)))) => (Y0 = X1)))))) )),
% 13.33/3.16 inference(beta_eta_normalization,[status(thm)],[f980])).
% 13.33/3.16 thf(f980,plain,(
% 13.33/3.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0))))) @ X1))) )),
% 13.33/3.16 inference(pi_clausification,[status(thm)],[f518])).
% 13.33/3.16 thf(f518,plain,(
% 13.33/3.16 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))))),
% 13.33/3.16 inference(definition_unfolding,[status(thm)],[f410,f296])).
% 13.33/3.16 thf(f296,plain,(
% 13.33/3.16 (setextAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))))),
% 13.33/3.16 inference(cnf_transformation,[status(thm)],[f111])).
% 13.33/3.16 thf(f111,plain,(
% 13.33/3.16 (setextAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))))),
% 13.33/3.16 inference(fool_elimination,[status(thm)],[f110])).
% 13.33/3.16 thf(f110,plain,(
% 13.33/3.16 (setextAx = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) <=> (in @ X2 @ X0)) => (X0 = X1)))),
% 13.33/3.16 inference(rectify,[status(thm)],[f2])).
% 13.33/3.16 thf(f2,axiom,(
% 13.33/3.16 (setextAx = ! [X4 : $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) <=> (in @ X1 @ X4)) => (X3 = X4)))),
% 13.33/3.16 file('/export/starexec/sandbox/tmp/tmp.HoFUU0t9AD/DTF2THF_31518.p',setextAx)).
% 13.33/3.16 thf(f410,plain,(
% 13.33/3.16 (setextAx = $true)),
% 13.33/3.16 inference(cnf_transformation,[status(thm)],[f279])).
% 13.33/3.16 thf(f279,plain,(
% 13.33/3.16 (descrp = $true) & (setadjoinSub = $true) & (setadjoinOr = $true) & (emptyI = $true) & (setadjoinIR = $true) & (setadjoinIL = $true) & (setext = $true) & (nonemptyI1 = $true) & (setunionE = $true) & (emptysetimpfalse = $true) & (in__Cong = $true) & (upairsetIR = $true) & (descr__Cong = $true) & (emptyInPowerset = $true) & (omegaSAx = $true) & (uniqinunit = $true) & (omega__Cong = $true) & (emptyinunitempty = $true) & (setadjoinAx = $true) & (notequalI2 = $true) & (emptyset__Cong = $true) & (powersetAx = $true) & (quantDeMorgan2 = $true) & (notdallE = $true) & (foundationAx = $true) & (dsetconstrI = $true) & (setunion__Cong = $true) & (omega0Ax = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan1 = $true) & (eqimpsubset2 = $true) & (eqimpsubset1 = $true) & (powersetI = $true) & (dsetconstrEL = $true) & (wellorderingAx = $true) & (exuEu = $true) & (subsetE = $true) & (emptysetAx = $true) & (exuE1 = $true) & (exuI2 = $true) & (setadjoinE = $true) & (replAx = $true) & (setextAx = $true) & (exuE3u = $true) & (setunionAx = $true) & (upairsetE = $true) & (exuE3e = $true) & (emptyinPowerset = $true) & (emptysetsubset = $true) & (quantDeMorgan4 = $true) & (prop2set2propI = $true) & (setadjoinSub2 = $true) & (prop2setE = $true) & (subsetRefl = $true) & (setadjoin__Cong = $true) & (inCongP = $true) & (subset2powerset = $true) & (notsubsetI = $true) & (exu__Cong = $true) & (notinsingleton = $true) & (nonemptyE1 = $true) & (upairsetIL = $true) & (setunionI = $true) & (omegaIndAx = $true) & (powersetE = $true) & (prop2setI = $true) & (exuI1 = $true) & (exuI3 = $true) & (singletonsswitch = $true) & (dsetconstr__Cong = $true) & (setoftrueEq = $true) & (noeltsimpempty = $true) & (subsetI2 = $true) & (vacuousDall = $true) & (notequalI1 = $true) & (powerset__Cong = $true) & ((sK0 != sK1) & ($true = (subset @ sK1 @ sK0)) & ($true = (subset @ sK0 @ sK1))) & (nonemptyImpWitness = $true) & (subsetI1 = $true) & (subPowSU = $true) & (notdexE = $true) & (emptyE1 = $true) & (setbeta = $true) & (nonemptyI = $true) & (subsetE2 = $true) & (dsetconstrER = $true) & (exuE2 = $true) & (emptysetE = $true) & (notinemptyset = $true) & (subsetTrans = $true) & (eqinunit = $true)),
% 13.33/3.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f277,f278])).
% 13.33/3.16 thf(f278,plain,(
% 13.33/3.16 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ($true = (subset @ X1 @ X0)) & ($true = (subset @ X0 @ X1))) => ((sK0 != sK1) & ($true = (subset @ sK1 @ sK0)) & ($true = (subset @ sK0 @ sK1)))),
% 13.33/3.16 introduced(definition,[],[choice_axiom])).
% 13.33/3.16 thf(f277,plain,(
% 13.33/3.16 (descrp = $true) & (setadjoinSub = $true) & (setadjoinOr = $true) & (emptyI = $true) & (setadjoinIR = $true) & (setadjoinIL = $true) & (setext = $true) & (nonemptyI1 = $true) & (setunionE = $true) & (emptysetimpfalse = $true) & (in__Cong = $true) & (upairsetIR = $true) & (descr__Cong = $true) & (emptyInPowerset = $true) & (omegaSAx = $true) & (uniqinunit = $true) & (omega__Cong = $true) & (emptyinunitempty = $true) & (setadjoinAx = $true) & (notequalI2 = $true) & (emptyset__Cong = $true) & (powersetAx = $true) & (quantDeMorgan2 = $true) & (notdallE = $true) & (foundationAx = $true) & (dsetconstrI = $true) & (setunion__Cong = $true) & (omega0Ax = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan1 = $true) & (eqimpsubset2 = $true) & (eqimpsubset1 = $true) & (powersetI = $true) & (dsetconstrEL = $true) & (wellorderingAx = $true) & (exuEu = $true) & (subsetE = $true) & (emptysetAx = $true) & (exuE1 = $true) & (exuI2 = $true) & (setadjoinE = $true) & (replAx = $true) & (setextAx = $true) & (exuE3u = $true) & (setunionAx = $true) & (upairsetE = $true) & (exuE3e = $true) & (emptyinPowerset = $true) & (emptysetsubset = $true) & (quantDeMorgan4 = $true) & (prop2set2propI = $true) & (setadjoinSub2 = $true) & (prop2setE = $true) & (subsetRefl = $true) & (setadjoin__Cong = $true) & (inCongP = $true) & (subset2powerset = $true) & (notsubsetI = $true) & (exu__Cong = $true) & (notinsingleton = $true) & (nonemptyE1 = $true) & (upairsetIL = $true) & (setunionI = $true) & (omegaIndAx = $true) & (powersetE = $true) & (prop2setI = $true) & (exuI1 = $true) & (exuI3 = $true) & (singletonsswitch = $true) & (dsetconstr__Cong = $true) & (setoftrueEq = $true) & (noeltsimpempty = $true) & (subsetI2 = $true) & (vacuousDall = $true) & (notequalI1 = $true) & (powerset__Cong = $true) & ? [X0 : $i,X1 : $i] : ((X0 != X1) & ($true = (subset @ X1 @ X0)) & ($true = (subset @ X0 @ X1))) & (nonemptyImpWitness = $true) & (subsetI1 = $true) & (subPowSU = $true) & (notdexE = $true) & (emptyE1 = $true) & (setbeta = $true) & (nonemptyI = $true) & (subsetE2 = $true) & (dsetconstrER = $true) & (exuE2 = $true) & (emptysetE = $true) & (notinemptyset = $true) & (subsetTrans = $true) & (eqinunit = $true)),
% 13.33/3.16 inference(flattening,[status(thm)],[f276])).
% 13.33/3.16 thf(f276,plain,(
% 13.33/3.16 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (((X0 != X1) & ($true = (subset @ X0 @ X1))) & ($true = (subset @ X1 @ X0))) & (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)),
% 13.33/3.16 inference(ennf_transformation,[status(thm)],[f198])).
% 13.33/3.16 thf(f198,plain,(
% 13.33/3.16 ~((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) => ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) => (($true = (subset @ X0 @ X1)) => (X0 = X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.33/3.16 inference(fool_elimination,[status(thm)],[f197])).
% 13.33/3.16 thf(f197,plain,(
% 13.33/3.16 ~(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 => ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.33/3.16 inference(rectify,[status(thm)],[f94])).
% 13.33/3.16 thf(f94,negated_conjecture,(
% 13.33/3.16 ~(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 => ! [X4 : $i,X3 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X3) => (X3 = X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.33/3.16 inference(negated_conjecture,[status(cth)],[f93])).
% 13.33/3.16 thf(f93,conjecture,(
% 13.33/3.16 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 => ! [X4 : $i,X3 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X3) => (X3 = X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.33/3.16 file('/export/starexec/sandbox/tmp/tmp.HoFUU0t9AD/DTF2THF_31518.p',setextsub)).
% 13.33/3.16 thf(f3117,plain,(
% 13.33/3.16 spl2_8 | ~spl2_2 | ~spl2_7),
% 13.33/3.16 inference(avatar_split_clause,[status(thm)],[f2846,f2579,f1511,f2956])).
% 13.33/3.16 thf(f2956,definition,(
% 13.33/3.16 spl2_8 <=> ($false = (in @ (sK23 @ sK1 @ sK0) @ sK0))),
% 13.33/3.16 introduced(definition,[new_symbols(naming,[spl2_8])],[avatar_definition])).
% 13.33/3.16 thf(f1511,definition,(
% 13.33/3.16 spl2_2 <=> ($true = (subset @ sK0 @ sK1))),
% 13.33/3.16 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 13.33/3.16 thf(f2846,plain,(
% 13.33/3.16 ($false = (in @ (sK23 @ sK1 @ sK0) @ sK0)) | (~spl2_2 | ~spl2_7)),
% 13.33/3.16 inference(trivial_inequality_removal,[status(thm)],[f2826])).
% 13.33/3.16 thf(f2826,plain,(
% 13.33/3.16 ($false = (in @ (sK23 @ sK1 @ sK0) @ sK0)) | ($true = $false) | (~spl2_2 | ~spl2_7)),
% 13.33/3.16 inference(superposition,[status(thm)],[f1806,f2581])).
% 13.33/3.16 thf(f1806,plain,(
% 13.33/3.16 ( ! [X0 : $i] : (($true = (in @ X0 @ sK1)) | ($false = (in @ X0 @ sK0))) ) | ~spl2_2),
% 13.33/3.16 inference(trivial_inequality_removal,[status(thm)],[f1792])).
% 13.33/3.16 thf(f1792,plain,(
% 13.33/3.16 ( ! [X0 : $i] : (($true = $false) | ($true = (in @ X0 @ sK1)) | ($false = (in @ X0 @ sK0))) ) | ~spl2_2),
% 13.33/3.16 inference(superposition,[status(thm)],[f619,f1513])).
% 13.33/3.16 thf(f1513,plain,(
% 13.33/3.16 ($true = (subset @ sK0 @ sK1)) | ~spl2_2),
% 13.33/3.16 inference(avatar_component_clause,[status(thm)],[f1511])).
% 13.33/3.16 thf(f619,plain,(
% 13.33/3.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (subset @ X1 @ X3)) | ((in @ X2 @ X1) = $false) | ((in @ X2 @ X3) = $true)) )),
% 13.33/3.16 inference(not_proxy_clausification,[status(thm)],[f618])).
% 13.33/3.16 thf(f618,plain,(
% 13.33/3.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ X3) = $true) | ((~ (in @ X2 @ X1)) = $true) | ($false = (subset @ X1 @ X3))) )),
% 13.33/3.16 inference(not_proxy_clausification,[status(thm)],[f617])).
% 13.33/3.16 thf(f617,plain,(
% 13.33/3.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (~ (in @ X2 @ X3))) | ($false = (subset @ X1 @ X3)) | ((~ (in @ X2 @ X1)) = $true)) )),
% 13.33/3.16 inference(binary_proxy_clausification,[status(thm)],[f616])).
% 13.33/3.16 thf(f616,plain,(
% 13.33/3.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (subset @ X1 @ X3)) | ($true = ((~ (in @ X2 @ X3)) => (~ (in @ X2 @ X1))))) )),
% 13.33/3.16 inference(binary_proxy_clausification,[status(thm)],[f615])).
% 13.33/3.16 thf(f615,plain,(
% 13.33/3.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X1 @ X3) => ((~ (in @ X2 @ X3)) => (~ (in @ X2 @ X1)))))) )),
% 13.33/3.16 inference(beta_eta_normalization,[status(thm)],[f614])).
% 13.33/3.16 thf(f614,plain,(
% 13.33/3.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ X1 @ Y0) => ((~ (in @ X2 @ Y0)) => (~ (in @ X2 @ X1))))) @ X3))) )),
% 13.33/3.16 inference(pi_clausification,[status(thm)],[f613])).
% 13.33/3.16 thf(f613,plain,(
% 13.33/3.16 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ Y0) => ((~ (in @ X2 @ Y0)) => (~ (in @ X2 @ X1)))))))) )),
% 13.33/3.16 inference(beta_eta_normalization,[status(thm)],[f612])).
% 13.33/3.16 thf(f612,plain,(
% 13.33/3.16 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ X1))))))) @ X2) = $true)) )),
% 13.33/3.16 inference(pi_clausification,[status(thm)],[f611])).
% 13.33/3.16 thf(f611,plain,(
% 13.33/3.16 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ X1)))))))))) )),
% 13.33/3.16 inference(beta_eta_normalization,[status(thm)],[f610])).
% 13.33/3.16 thf(f610,plain,(
% 13.33/3.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0))))))))) @ X1))) )),
% 13.33/3.16 inference(pi_clausification,[status(thm)],[f558])).
% 13.33/3.16 thf(f558,plain,(
% 13.33/3.16 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))))),
% 13.33/3.16 inference(definition_unfolding,[status(thm)],[f454,f366])).
% 13.33/3.16 thf(f366,plain,(
% 13.33/3.16 (subsetE2 = $true)),
% 13.33/3.16 inference(cnf_transformation,[status(thm)],[f279])).
% 13.33/3.16 thf(f454,plain,(
% 13.33/3.16 (subsetE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))))),
% 13.33/3.16 inference(cnf_transformation,[status(thm)],[f115])).
% 13.33/3.16 thf(f115,plain,(
% 13.33/3.16 (subsetE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))))),
% 13.33/3.16 inference(fool_elimination,[status(thm)],[f114])).
% 13.33/3.16 thf(f114,plain,(
% 13.33/3.16 (subsetE2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X0) => (~(in @ X1 @ X0) => ~(in @ X1 @ X2))))),
% 13.33/3.16 inference(rectify,[status(thm)],[f84])).
% 13.33/3.16 thf(f84,axiom,(
% 13.33/3.16 (subsetE2 = ! [X4 : $i,X1 : $i,X3 : $i] : ((subset @ X3 @ X4) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3))))),
% 13.33/3.16 file('/export/starexec/sandbox/tmp/tmp.HoFUU0t9AD/DTF2THF_31518.p',subsetE2)).
% 13.33/3.16 thf(f2582,plain,(
% 13.33/3.16 spl2_7 | spl2_1 | ~spl2_4),
% 13.33/3.16 inference(avatar_split_clause,[status(thm)],[f2577,f1521,f1506,f2579])).
% 13.33/3.16 thf(f1521,definition,(
% 13.33/3.16 spl2_4 <=> ($true = (subset @ sK1 @ sK0))),
% 13.33/3.16 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 13.33/3.16 thf(f2577,plain,(
% 13.33/3.16 ($false = (in @ (sK23 @ sK1 @ sK0) @ sK1)) | (spl2_1 | ~spl2_4)),
% 13.33/3.16 inference(subsumption_resolution,[status(thm)],[f2565,f1508])).
% 13.33/3.16 thf(f2565,plain,(
% 13.33/3.16 ($false = (in @ (sK23 @ sK1 @ sK0) @ sK1)) | (sK0 = sK1) | ~spl2_4),
% 13.33/3.16 inference(trivial_inequality_removal,[status(thm)],[f2559])).
% 13.33/3.16 thf(f2559,plain,(
% 13.33/3.16 (sK0 = sK1) | ($false = (in @ (sK23 @ sK1 @ sK0) @ sK1)) | ($false != $false) | ~spl2_4),
% 13.33/3.16 inference(equality_factoring,[status(thm)],[f2464])).
% 13.33/3.16 thf(f2464,plain,(
% 13.33/3.16 ( ! [X0 : $i] : (($false = (in @ (sK23 @ X0 @ sK0) @ sK1)) | (sK0 = X0) | ($false = (in @ (sK23 @ X0 @ sK0) @ X0))) ) | ~spl2_4),
% 13.33/3.16 inference(boolean_simplification,[status(thm)],[f2419])).
% 13.33/3.16 thf(f2419,plain,(
% 13.33/3.16 ( ! [X0 : $i] : ((sK0 = X0) | ($false = (in @ (sK23 @ X0 @ sK0) @ sK1)) | (((in @ (sK23 @ X0 @ sK0) @ X0) = $true) = $false)) ) | ~spl2_4),
% 13.33/3.16 inference(superposition,[status(thm)],[f987,f1802])).
% 13.33/3.16 thf(f1802,plain,(
% 13.33/3.16 ( ! [X0 : $i] : (($true = (in @ X0 @ sK0)) | ($false = (in @ X0 @ sK1))) ) | ~spl2_4),
% 13.33/3.16 inference(trivial_inequality_removal,[status(thm)],[f1793])).
% 13.33/3.16 thf(f1793,plain,(
% 13.33/3.16 ( ! [X0 : $i] : (($false = (in @ X0 @ sK1)) | ($true = (in @ X0 @ sK0)) | ($true = $false)) ) | ~spl2_4),
% 13.33/3.16 inference(superposition,[status(thm)],[f619,f1523])).
% 13.33/3.16 thf(f1523,plain,(
% 13.33/3.16 ($true = (subset @ sK1 @ sK0)) | ~spl2_4),
% 13.33/3.16 inference(avatar_component_clause,[status(thm)],[f1521])).
% 13.33/3.16 thf(f1524,plain,(
% 13.33/3.16 spl2_4),
% 13.33/3.16 inference(avatar_split_clause,[status(thm)],[f375,f1521])).
% 13.33/3.16 thf(f375,plain,(
% 13.33/3.16 ($true = (subset @ sK1 @ sK0))),
% 13.33/3.16 inference(cnf_transformation,[status(thm)],[f279])).
% 13.33/3.16 thf(f1519,plain,(
% 13.33/3.16 ~spl2_3),
% 13.33/3.16 inference(avatar_split_clause,[status(thm)],[f95,f1516])).
% 13.33/3.16 thf(f1516,definition,(
% 13.33/3.16 spl2_3 <=> ($true = $false)),
% 13.33/3.16 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 13.33/3.16 thf(f95,plain,(
% 13.33/3.16 ($true != $false)),
% 13.33/3.16 introduced(definition,[],[fool_axiom])).
% 13.33/3.16 thf(f1514,plain,(
% 13.33/3.16 spl2_2),
% 13.33/3.16 inference(avatar_split_clause,[status(thm)],[f374,f1511])).
% 13.33/3.16 thf(f374,plain,(
% 13.33/3.16 ($true = (subset @ sK0 @ sK1))),
% 13.33/3.16 inference(cnf_transformation,[status(thm)],[f279])).
% 13.33/3.16 thf(f1509,plain,(
% 13.33/3.16 ~spl2_1),
% 13.33/3.16 inference(avatar_split_clause,[status(thm)],[f376,f1506])).
% 13.33/3.16 thf(f376,plain,(
% 13.33/3.16 (sK0 != sK1)),
% 13.33/3.16 inference(cnf_transformation,[status(thm)],[f279])).
% 13.33/3.16 % SZS output end Proof for DTF2THF_31518
% 13.33/3.16 % (31712)------------------------------
% 13.33/3.16 % (31712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.33/3.16 % (31712)Termination reason: Refutation
% 13.33/3.16
% 13.33/3.16 % (31712)Memory used [KB]: 7419
% 13.33/3.16 % (31712)Time elapsed: 0.266 s
% 13.33/3.16 % (31712)Instructions burned: 535 (million)
% 13.33/3.16 % (31712)------------------------------
% 13.33/3.16 % (31712)------------------------------
% 13.33/3.16 % (31615)Success in time 1.578 s
%------------------------------------------------------------------------------