%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU573^1 : 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 : n027.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 9.30s 2.60s
% Output : Refutation 9.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 88 ( 45 unt; 0 typ; 5 def)
% Number of atoms : 1838 ( 461 equ; 0 cnn)
% Maximal formula atoms : 91 ( 20 avg)
% Number of connectives : 1230 ( 41 ~; 44 |; 272 &; 408 @)
% ( 7 <=>; 414 =>; 0 <=; 0 <~>)
% Maximal formula depth : 96 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 197 ( 193 usr; 101 con; 0-4 aty)
% ( 44 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 124 ( 53 ^; 65 !; 6 ?; 124 :)
% 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_124,type,
sK3: ( $i > $o ) > $i ).
thf(func_def_125,type,
sK4: ( $i > $o ) > $i > $i ).
thf(func_def_126,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_127,type,
sK6: ( $i > $o ) > $i > $i ).
thf(func_def_128,type,
sK7: $i > $i > $i ).
thf(func_def_129,type,
sK8: ( $i > $o ) > $i > $i ).
thf(func_def_130,type,
sK9: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_131,type,
sK10: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_132,type,
sK11: $i > ( $i > $o ) > $i ).
thf(func_def_133,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_134,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_135,type,
sK14: $i > $i ).
thf(func_def_136,type,
sK15: $o > $i > $i > $i ).
thf(func_def_137,type,
sK16: ( $i > $o ) > $i > $i ).
thf(func_def_138,type,
sK17: ( $i > $o ) > $i > $i ).
thf(func_def_139,type,
sK18: ( $i > $o ) > $i ).
thf(func_def_140,type,
sK19: ( $i > $o ) > $i > $i ).
thf(func_def_141,type,
sK20: $i > $i ).
thf(func_def_142,type,
sK21: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_143,type,
sK22: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_144,type,
sK23: $i > $i > $i ).
thf(func_def_145,type,
sK24: $i > $i > $i ).
thf(func_def_146,type,
sK25: $i > $i > $i ).
thf(func_def_147,type,
sK26: $i > ( $i > $o ) > $i ).
thf(func_def_148,type,
sK27: $i > $i > $i ).
thf(func_def_149,type,
sK28: $i > ( $i > $i > $o ) > $i ).
thf(func_def_150,type,
sK29: $i > ( $i > $i > $o ) > $i ).
thf(func_def_151,type,
sK30: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_152,type,
sK31: $i > ( $i > $i > $o ) > $i ).
thf(func_def_153,type,
sK32: $i > ( $i > $i > $o ) > $i ).
thf(func_def_154,type,
sK33: ( $i > $o ) > $i > $i ).
thf(func_def_155,type,
sK34: ( $i > $o ) > $i ).
thf(func_def_156,type,
sK35: ( $i > $o ) > $i ).
thf(func_def_157,type,
sK36: ( $i > $o ) > $i ).
thf(func_def_158,type,
sK37: ( $i > $o ) > $i ).
thf(func_def_159,type,
sK38: ( $i > $o ) > $i ).
thf(func_def_160,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_161,type,
sK40: $i > $i ).
thf(func_def_162,type,
sK41: $i > $i ).
thf(func_def_163,type,
sK42: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_164,type,
sK43: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_165,type,
sK44: $i > $i ).
thf(func_def_166,type,
sK45: $i > $i > $i ).
thf(func_def_167,type,
sK46: ( $i > $o ) > $i > $i ).
thf(func_def_168,type,
sK47: $i > $i > $i ).
thf(func_def_169,type,
sK48: $i > $i ).
thf(func_def_170,type,
sK49: $i > ( $i > $o ) > $i ).
thf(func_def_171,type,
sK50: ( $i > $o ) > $i ).
thf(func_def_172,type,
sK51: ( $i > $o ) > $i > $i ).
thf(func_def_173,type,
sK52: ( $i > $o ) > $i > $i ).
thf(func_def_174,type,
sK53: $i > $i ).
thf(func_def_175,type,
sK54: $i > $i > $i > $i ).
thf(func_def_176,type,
sK55: $i > $i > $i ).
thf(func_def_177,type,
sK56: $i > $i > $i ).
thf(func_def_178,type,
sK57: $i > $i > $i ).
thf(func_def_179,type,
sK58: $i > $i > $i ).
thf(func_def_180,type,
sK59: ( $i > $o ) > $i ).
thf(func_def_181,type,
sK60: ( $i > $o ) > $i > $i ).
thf(func_def_182,type,
ph61:
!>[X0: $tType] : X0 ).
thf(func_def_183,type,
sK62: $i > $i > $i ).
thf(func_def_184,type,
sK63: $i > $i ).
thf(func_def_185,type,
sK64: $i > $i > $i ).
thf(func_def_186,type,
sK65: $i > $i > $i ).
thf(func_def_187,type,
sK66: $i > $i > $i ).
thf(func_def_188,type,
sK67: $i > $i > $i ).
thf(func_def_189,type,
sK68: $i > $i ).
thf(func_def_190,type,
sK69: $i > $i > $i ).
thf(func_def_191,type,
sK70: $i > $i > $i ).
thf(func_def_192,type,
sK71: $i > $i > $i ).
thf(func_def_193,type,
sK72: $i > $i > $i ).
thf(func_def_194,type,
sK73: $i > $i ).
thf(func_def_195,type,
sK74: $i > $i ).
thf(func_def_196,type,
sK75: $i > $i > $i ).
thf(func_def_197,type,
sK76: $i > $i > $i ).
thf(func_def_199,type,
sK78: $i > $i > $i ).
thf(func_def_200,type,
sK79: $i > $i > $i ).
thf(func_def_201,type,
sK80: $i > $i > $i ).
thf(func_def_202,type,
sK81: $i > $i > $i ).
thf(func_def_203,type,
sK82: $i > $i > $i ).
thf(func_def_204,type,
sK83: $i > $i > $i ).
thf(func_def_205,type,
sK84: $i > $i > $i ).
thf(func_def_206,type,
sK85: $i > $i > $i ).
thf(f3704,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1513,f1532,f1587,f3279,f3303,f3703]) ).
thf(f3703,plain,
( ~ spl2_2
| ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f3702]) ).
thf(f3702,plain,
( $false
| ~ spl2_2
| ~ spl2_7
| ~ spl2_8 ),
inference(trivial_inequality_removal,[status(thm)],[f3696]) ).
thf(f3696,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_7
| ~ spl2_8 ),
inference(backward_demodulation,[status(thm)],[f3302,f3682]) ).
thf(f3682,plain,
( ( $false
= ( in @ sK77 @ sK0 ) )
| ~ spl2_2
| ~ spl2_7 ),
inference(trivial_inequality_removal,[status(thm)],[f3673]) ).
thf(f3673,plain,
( ( $true = $false )
| ( $false
= ( in @ sK77 @ sK0 ) )
| ~ spl2_2
| ~ spl2_7 ),
inference(superposition,[status(thm)],[f1512,f3322]) ).
thf(f3322,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ sK1 )
= $false )
| ( ( in @ sK77 @ X0 )
= $false ) )
| ~ spl2_7 ),
inference(trivial_inequality_removal,[status(thm)],[f3305]) ).
thf(f3305,plain,
( ! [X0: $i] :
( ( ( subset @ X0 @ sK1 )
= $false )
| ( ( in @ sK77 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl2_7 ),
inference(superposition,[status(thm)],[f3278,f793]) ).
thf(f793,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X1 )
= $false )
| ( ( subset @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f792]) ).
thf(f792,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $false )
| ( ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f791]) ).
thf(f791,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( subset @ X1 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f790]) ).
thf(f790,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f789]) ).
thf(f789,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f788]) ).
thf(f788,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f787]) ).
thf(f787,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ X1 @ Y0 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f786]) ).
thf(f786,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f539]) ).
thf(f539,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f444,f395]) ).
thf(f395,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f276]) ).
thf(f276,plain,
( ( setadjoinSub = $true )
& ( nonemptyImpWitness = $true )
& ( omegaIndAx = $true )
& ( exu__Cong = $true )
& ( uniqinunit = $true )
& ( powersetE = $true )
& ( omega__Cong = $true )
& ( notinsingleton = $true )
& ( singletonsswitch = $true )
& ( dsetconstrI = $true )
& ( emptysetsubset = $true )
& ( prop2setE = $true )
& ( powersetI = $true )
& ( notdallE = $true )
& ( subsetRefl = $true )
& ( setext = $true )
& ( setunionAx = $true )
& ( emptyE1 = $true )
& ( exuEu = $true )
& ( emptysetE = $true )
& ( setunionE = $true )
& ( subsetE = $true )
& ( setextAx = $true )
& ( notinemptyset = $true )
& ( emptyI = $true )
& ( subsetI2 = $true )
& ( emptyinPowerset = $true )
& ( setadjoinOr = $true )
& ( setadjoinSub2 = $true )
& ( dsetconstr__Cong = $true )
& ( exuE2 = $true )
& ( notdexE = $true )
& ( exuI2 = $true )
& ( setadjoin__Cong = $true )
& ( exuI3 = $true )
& ( notsubsetI = $true )
& ( notequalI1 = $true )
& ( emptyinunitempty = $true )
& ( omegaSAx = $true )
& ( setoftrueEq = $true )
& ( setadjoinIL = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinE = $true )
& ( setunion__Cong = $true )
& ( vacuousDall = $true )
& ( subPowSU = $true )
& ( emptyset__Cong = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan4 = $true )
& ( descr__Cong = $true )
& ( exuI1 = $true )
& ( prop2setI = $true )
& ( upairsetIR = $true )
& ( powerset__Cong = $true )
& ( setadjoinAx = $true )
& ( nonemptyE1 = $true )
& ( subsetI1 = $true )
& ( subsetE2 = $true )
& ( dsetconstrER = $true )
& ( notequalI2 = $true )
& ( eqimpsubset2 = $true )
& ( emptyInPowerset = $true )
& ( subsetTrans = $true )
& ( setadjoinIR = $true )
& ( foundationAx = $true )
& ( quantDeMorgan3 = $true )
& ( in__Cong = $true )
& ( emptysetAx = $true )
& ( setunionI = $true )
& ( noeltsimpempty = $true )
& ( nonemptyI1 = $true )
& ( dsetconstrEL = $true )
& ( quantDeMorgan2 = $true )
& ( exuE3u = $true )
& ( descrp = $true )
& ( upairsetIL = $true )
& ( $true
!= ( in @ sK0 @ ( powerset @ sK1 ) ) )
& ( $true
= ( subset @ sK0 @ sK1 ) )
& ( eqinunit = $true )
& ( exuE1 = $true )
& ( emptysetimpfalse = $true )
& ( wellorderingAx = $true )
& ( replAx = $true )
& ( nonemptyI = $true )
& ( setbeta = $true )
& ( eqimpsubset1 = $true )
& ( prop2set2propI = $true )
& ( powersetAx = $true )
& ( inCongP = $true )
& ( upairsetE = $true )
& ( exuE3e = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f274,f275]) ).
thf(f275,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
& ( $true
= ( subset @ X0 @ X1 ) ) )
=> ( ( $true
!= ( in @ sK0 @ ( powerset @ sK1 ) ) )
& ( $true
= ( subset @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f274,plain,
( ( setadjoinSub = $true )
& ( nonemptyImpWitness = $true )
& ( omegaIndAx = $true )
& ( exu__Cong = $true )
& ( uniqinunit = $true )
& ( powersetE = $true )
& ( omega__Cong = $true )
& ( notinsingleton = $true )
& ( singletonsswitch = $true )
& ( dsetconstrI = $true )
& ( emptysetsubset = $true )
& ( prop2setE = $true )
& ( powersetI = $true )
& ( notdallE = $true )
& ( subsetRefl = $true )
& ( setext = $true )
& ( setunionAx = $true )
& ( emptyE1 = $true )
& ( exuEu = $true )
& ( emptysetE = $true )
& ( setunionE = $true )
& ( subsetE = $true )
& ( setextAx = $true )
& ( notinemptyset = $true )
& ( emptyI = $true )
& ( subsetI2 = $true )
& ( emptyinPowerset = $true )
& ( setadjoinOr = $true )
& ( setadjoinSub2 = $true )
& ( dsetconstr__Cong = $true )
& ( exuE2 = $true )
& ( notdexE = $true )
& ( exuI2 = $true )
& ( setadjoin__Cong = $true )
& ( exuI3 = $true )
& ( notsubsetI = $true )
& ( notequalI1 = $true )
& ( emptyinunitempty = $true )
& ( omegaSAx = $true )
& ( setoftrueEq = $true )
& ( setadjoinIL = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinE = $true )
& ( setunion__Cong = $true )
& ( vacuousDall = $true )
& ( subPowSU = $true )
& ( emptyset__Cong = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan4 = $true )
& ( descr__Cong = $true )
& ( exuI1 = $true )
& ( prop2setI = $true )
& ( upairsetIR = $true )
& ( powerset__Cong = $true )
& ( setadjoinAx = $true )
& ( nonemptyE1 = $true )
& ( subsetI1 = $true )
& ( subsetE2 = $true )
& ( dsetconstrER = $true )
& ( notequalI2 = $true )
& ( eqimpsubset2 = $true )
& ( emptyInPowerset = $true )
& ( subsetTrans = $true )
& ( setadjoinIR = $true )
& ( foundationAx = $true )
& ( quantDeMorgan3 = $true )
& ( in__Cong = $true )
& ( emptysetAx = $true )
& ( setunionI = $true )
& ( noeltsimpempty = $true )
& ( nonemptyI1 = $true )
& ( dsetconstrEL = $true )
& ( quantDeMorgan2 = $true )
& ( exuE3u = $true )
& ( descrp = $true )
& ( upairsetIL = $true )
& ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
& ( $true
= ( subset @ X0 @ X1 ) ) )
& ( eqinunit = $true )
& ( exuE1 = $true )
& ( emptysetimpfalse = $true )
& ( wellorderingAx = $true )
& ( replAx = $true )
& ( nonemptyI = $true )
& ( setbeta = $true )
& ( eqimpsubset1 = $true )
& ( prop2set2propI = $true )
& ( powersetAx = $true )
& ( inCongP = $true )
& ( upairsetE = $true )
& ( exuE3e = $true ) ),
inference(flattening,[status(thm)],[f273]) ).
thf(f273,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
& ( $true
= ( subset @ X0 @ X1 ) ) )
& ( 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)],[f207]) ).
thf(f207,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 )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
=> ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f206]) ).
thf(f206,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
=> ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f93]) ).
thf(f93,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
=> ! [X3: $i,X4: $i] :
( ( subset @ X3 @ X4 )
=> ( in @ X3 @ ( powerset @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f92]) ).
thf(f92,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
=> ! [X3: $i,X4: $i] :
( ( subset @ X3 @ X4 )
=> ( in @ X3 @ ( powerset @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBNDjAFKO7/DTF2THF_1757.p',subset2powerset) ).
thf(f444,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
thf(f205,plain,
( subsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f204]) ).
thf(f204,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X0 @ X1 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f83]) ).
thf(f83,axiom,
! [X1: $i,X4: $i,X3: $i] :
( ( ( subset @ X3 @ X4 )
=> ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X4 ) ) )
= subsetE ),
file('/export/starexec/sandbox/tmp/tmp.fBNDjAFKO7/DTF2THF_1757.p',subsetE) ).
thf(f3278,plain,
( ( ( in @ sK77 @ sK1 )
= $false )
| ~ spl2_7 ),
inference(avatar_component_clause,[status(thm)],[f3276]) ).
thf(f3276,definition,
( spl2_7
<=> ( ( in @ sK77 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_7])],[avatar_definition]) ).
thf(f1512,plain,
( ( $true
= ( subset @ sK0 @ sK1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f1510]) ).
thf(f1510,definition,
( spl2_2
<=> ( $true
= ( subset @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f3302,plain,
( ( $true
= ( in @ sK77 @ sK0 ) )
| ~ spl2_8 ),
inference(avatar_component_clause,[status(thm)],[f3300]) ).
thf(f3300,definition,
( spl2_8
<=> ( $true
= ( in @ sK77 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_8])],[avatar_definition]) ).
thf(f3303,plain,
( spl2_8
| ~ spl2_5 ),
inference(avatar_split_clause,[status(thm)],[f3204,f1584,f3300]) ).
thf(f1584,definition,
( spl2_5
<=> ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition]) ).
thf(f3204,plain,
( ( $true
= ( in @ sK77 @ sK0 ) )
| ~ spl2_5 ),
inference(binary_proxy_clausification,[status(thm)],[f3202]) ).
thf(f3202,plain,
( ( ( ( in @ sK77 @ sK0 )
=> ( in @ sK77 @ sK1 ) )
= $false )
| ~ spl2_5 ),
inference(beta_eta_normalization,[status(thm)],[f3201]) ).
thf(f3201,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( in @ Y0 @ sK1 ) )
@ sK77 )
= $false )
| ~ spl2_5 ),
inference(sigma_clausification,[status(thm)],[f3200]) ).
thf(f3200,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( in @ Y0 @ sK1 ) ) )
= $false )
| ~ spl2_5 ),
inference(not_proxy_clausification,[status(thm)],[f3199]) ).
thf(f3199,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( in @ Y0 @ sK1 ) ) ) )
= $true )
| ~ spl2_5 ),
inference(boolean_simplification,[status(thm)],[f3168]) ).
thf(f3168,plain,
( ( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( in @ Y0 @ sK1 ) ) ) )
= $true )
| ~ spl2_5 ),
inference(superposition,[status(thm)],[f1241,f1586]) ).
thf(f1586,plain,
( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false )
| ~ spl2_5 ),
inference(avatar_component_clause,[status(thm)],[f1584]) ).
thf(f1241,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1240]) ).
thf(f1240,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1239]) ).
thf(f1239,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1238]) ).
thf(f1238,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f535]) ).
thf(f535,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f440,f329]) ).
thf(f329,plain,
powersetAx = $true,
inference(cnf_transformation,[status(thm)],[f276]) ).
thf(f440,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
thf(f199,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f198]) ).
thf(f198,plain,
( powersetAx
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( powersetAx
= ( ! [X3: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
<=> ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBNDjAFKO7/DTF2THF_1757.p',powersetAx) ).
thf(f3279,plain,
( spl2_7
| ~ spl2_5 ),
inference(avatar_split_clause,[status(thm)],[f3203,f1584,f3276]) ).
thf(f3203,plain,
( ( ( in @ sK77 @ sK1 )
= $false )
| ~ spl2_5 ),
inference(binary_proxy_clausification,[status(thm)],[f3202]) ).
thf(f1587,plain,
( spl2_5
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f1579,f1529,f1584]) ).
thf(f1529,definition,
( spl2_4
<=> ( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f1579,plain,
( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false )
| spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f1569]) ).
thf(f1569,plain,
( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false )
| ( $true != $true )
| spl2_4 ),
inference(superposition,[status(thm)],[f1531,f1563]) ).
thf(f1563,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1561]) ).
thf(f1561,plain,
! [X0: $o] :
( ( $false = X0 )
| ( $true = $false )
| ( $true = X0 ) ),
inference(superposition,[status(thm)],[f617,f614]) ).
thf(f614,plain,
! [X2: $i,X1: $o] :
( ( ( in @ X2 @ ( prop2set @ X1 ) )
= $false )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f613]) ).
thf(f613,plain,
! [X2: $i,X1: $o] :
( $true
= ( ( in @ X2 @ ( prop2set @ X1 ) )
=> X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f612]) ).
thf(f612,plain,
! [X2: $i,X1: $o] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( prop2set @ X1 ) )
=> X1 )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f611]) ).
thf(f611,plain,
! [X1: $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( prop2set @ X1 ) )
=> X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f610]) ).
thf(f610,plain,
! [X1: $o] :
( $true
= ( ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( prop2set @ Y0 ) )
=> Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f533]) ).
thf(f533,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( prop2set @ Y0 ) )
=> Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f438,f405]) ).
thf(f405,plain,
prop2setE = $true,
inference(cnf_transformation,[status(thm)],[f276]) ).
thf(f438,plain,
( prop2setE
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( prop2set @ Y0 ) )
=> Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
thf(f193,plain,
( prop2setE
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( prop2set @ Y0 ) )
=> Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f192]) ).
thf(f192,plain,
! [X0: $i,X1: $o] :
( ( ( in @ X0 @ ( prop2set @ X1 ) )
=> X1 )
= prop2setE ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,axiom,
! [X1: $i,X0: $o] :
( ( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 )
= prop2setE ),
file('/export/starexec/sandbox/tmp/tmp.fBNDjAFKO7/DTF2THF_1757.p',prop2setE) ).
thf(f617,plain,
! [X1: $o] :
( ( $true
= ( in @ emptyset @ ( prop2set @ X1 ) ) )
| ( $false = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f616]) ).
thf(f616,plain,
! [X1: $o] :
( $true
= ( X1
=> ( in @ emptyset @ ( prop2set @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f615]) ).
thf(f615,plain,
! [X1: $o] :
( $true
= ( ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f490]) ).
thf(f490,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f365,f301]) ).
thf(f301,plain,
( prop2setI
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
thf(f133,plain,
( prop2setI
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f132]) ).
thf(f132,plain,
( prop2setI
= ( ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f59]) ).
thf(f59,axiom,
( prop2setI
= ( ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fBNDjAFKO7/DTF2THF_1757.p',prop2setI) ).
thf(f365,plain,
prop2setI = $true,
inference(cnf_transformation,[status(thm)],[f276]) ).
thf(f1531,plain,
( ( $true
!= ( in @ sK0 @ ( powerset @ sK1 ) ) )
| spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f1529]) ).
thf(f1532,plain,
~ spl2_4,
inference(avatar_split_clause,[status(thm)],[f340,f1529]) ).
thf(f340,plain,
( $true
!= ( in @ sK0 @ ( powerset @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f276]) ).
thf(f1513,plain,
spl2_2,
inference(avatar_split_clause,[status(thm)],[f339,f1510]) ).
thf(f339,plain,
( $true
= ( subset @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU573^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n027.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:27:37 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SEU573^1 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.47 % Domain : Set Theory
% 0.31/0.47 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English : (! A:i.! B:i.subset A B -> in A (powerset B))
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.47 % Source : [Bro08]
% 0.31/0.47 % Names : ZFC075g [Bro08]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.31/0.47 % Syntax : Number of formulae : 196 ( 91 unt; 104 typ; 91 def)
% 0.31/0.47 % Number of atoms : 497 ( 138 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 91 ( 5 avg)
% 0.31/0.47 % Number of connectives : 787 ( 29 ~; 5 |; 27 &; 485 @)
% 0.31/0.47 % ( 14 <=>; 227 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 95 ( 2 avg)
% 0.31/0.47 % Number of types : 2 ( 0 usr)
% 0.31/0.47 % Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 107 ( 104 usr; 93 con; 0-2 aty)
% 0.31/0.47 % Number of variables : 278 ( 28 ^; 222 !; 28 ?; 278 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : http://mathgate.info/detsetitem.php?id=153
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(in_type,type,
% 0.31/0.47 in: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu_type,type,
% 0.31/0.47 exu: ( $i > $o ) > $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu,definition,
% 0.31/0.47 ( exu
% 0.31/0.47 = ( ^ [Xphi: $i > $o] :
% 0.31/0.47 ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setextAx_type,type,
% 0.31/0.47 setextAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setextAx,definition,
% 0.31/0.47 ( setextAx
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 <=> ( in @ Xx @ B ) )
% 0.31/0.47 => ( A = B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset_type,type,
% 0.31/0.47 emptyset: $i ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetAx_type,type,
% 0.31/0.47 emptysetAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetAx,definition,
% 0.31/0.47 ( emptysetAx
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin_type,type,
% 0.31/0.47 setadjoin: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinAx_type,type,
% 0.31/0.47 setadjoinAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinAx,definition,
% 0.31/0.47 ( setadjoinAx
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 <=> ( ( Xy = Xx )
% 0.31/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powerset_type,type,
% 0.31/0.47 powerset: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(powersetAx_type,type,
% 0.31/0.47 powersetAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetAx,definition,
% 0.31/0.47 ( powersetAx
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.47 <=> ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunion_type,type,
% 0.31/0.47 setunion: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(setunionAx_type,type,
% 0.31/0.47 setunionAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunionAx,definition,
% 0.31/0.47 ( setunionAx
% 0.31/0.47 = ( ! [A: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/0.47 <=> ? [B: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omega_type,type,
% 0.31/0.47 omega: $i ).
% 0.31/0.47
% 0.31/0.47 thf(omega0Ax_type,type,
% 0.31/0.47 omega0Ax: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omega0Ax,definition,
% 0.31/0.47 ( omega0Ax
% 0.31/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omegaSAx_type,type,
% 0.31/0.47 omegaSAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omegaSAx,definition,
% 0.31/0.47 ( omegaSAx
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ omega )
% 0.31/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omegaIndAx_type,type,
% 0.31/0.47 omegaIndAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omegaIndAx,definition,
% 0.31/0.47 ( omegaIndAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( ( in @ emptyset @ A )
% 0.31/0.47 & ! [Xx: $i] :
% 0.31/0.47 ( ( ( in @ Xx @ omega )
% 0.31/0.47 & ( in @ Xx @ A ) )
% 0.31/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ omega )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(replAx_type,type,
% 0.31/0.47 replAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(replAx,definition,
% 0.31/0.47 ( replAx
% 0.31/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.31/0.47 => ? [B: $i] :
% 0.31/0.47 ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 <=> ? [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(foundationAx_type,type,
% 0.31/0.47 foundationAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(foundationAx,definition,
% 0.31/0.47 ( foundationAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/0.47 => ? [B: $i] :
% 0.31/0.47 ( ( in @ B @ A )
% 0.31/0.47 & ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(wellorderingAx_type,type,
% 0.31/0.47 wellorderingAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(wellorderingAx,definition,
% 0.31/0.47 ( wellorderingAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ? [B: $i] :
% 0.31/0.47 ( ! [C: $i] :
% 0.31/0.47 ( ( in @ C @ B )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ A ) ) )
% 0.31/0.47 & ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( ( in @ Xx @ A )
% 0.31/0.47 & ( in @ Xy @ A ) )
% 0.31/0.47 => ( ! [C: $i] :
% 0.31/0.47 ( ( in @ C @ B )
% 0.31/0.47 => ( ( in @ Xx @ C )
% 0.31/0.47 <=> ( in @ Xy @ C ) ) )
% 0.31/0.47 => ( Xx = Xy ) ) )
% 0.31/0.47 & ! [C: $i,D: $i] :
% 0.31/0.47 ( ( ( in @ C @ B )
% 0.31/0.47 & ( in @ D @ B ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ D ) )
% 0.31/0.47 | ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ D )
% 0.31/0.47 => ( in @ Xx @ C ) ) ) )
% 0.31/0.47 & ! [C: $i] :
% 0.31/0.47 ( ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.31/0.47 => ? [D: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ D @ B )
% 0.31/0.47 & ( in @ Xx @ C )
% 0.31/0.47 & ~ ? [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ D )
% 0.31/0.47 & ( in @ Xy @ C ) )
% 0.31/0.47 & ! [E: $i] :
% 0.31/0.47 ( ( in @ E @ B )
% 0.31/0.47 => ( ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ E )
% 0.31/0.47 => ( in @ Xy @ D ) )
% 0.31/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(descr_type,type,
% 0.31/0.47 descr: ( $i > $o ) > $i ).
% 0.31/0.47
% 0.31/0.47 thf(descrp_type,type,
% 0.31/0.47 descrp: $o ).
% 0.31/0.47
% 0.31/0.47 thf(descrp,definition,
% 0.31/0.47 ( descrp
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ( Xphi
% 0.31/0.47 @ ( descr
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr_type,type,
% 0.31/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrI_type,type,
% 0.31/0.47 dsetconstrI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrI,definition,
% 0.31/0.47 ( dsetconstrI
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrEL_type,type,
% 0.31/0.47 dsetconstrEL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrEL,definition,
% 0.31/0.47 ( dsetconstrEL
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrER_type,type,
% 0.31/0.47 dsetconstrER: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrER,definition,
% 0.31/0.47 ( dsetconstrER
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE1_type,type,
% 0.31/0.47 exuE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE1,definition,
% 0.31/0.47 ( exuE1
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set_type,type,
% 0.31/0.47 prop2set: $o > $i ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setE_type,type,
% 0.31/0.47 prop2setE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setE,definition,
% 0.31/0.47 ( prop2setE
% 0.31/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.31/0.47 => Xphi ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetE_type,type,
% 0.31/0.47 emptysetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetE,definition,
% 0.31/0.47 ( emptysetE
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetimpfalse_type,type,
% 0.31/0.47 emptysetimpfalse: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetimpfalse,definition,
% 0.31/0.47 ( emptysetimpfalse
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => $false ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notinemptyset_type,type,
% 0.31/0.47 notinemptyset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notinemptyset,definition,
% 0.31/0.47 ( notinemptyset
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3e_type,type,
% 0.31/0.47 exuE3e: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3e,definition,
% 0.31/0.47 ( exuE3e
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setext_type,type,
% 0.31/0.47 setext: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setext,definition,
% 0.31/0.47 ( setext
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 => ( A = B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyI_type,type,
% 0.31/0.47 emptyI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyI,definition,
% 0.31/0.47 ( emptyI
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ A )
% 0.31/0.47 => ( A = emptyset ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(noeltsimpempty_type,type,
% 0.31/0.47 noeltsimpempty: $o ).
% 0.31/0.47
% 0.31/0.47 thf(noeltsimpempty,definition,
% 0.31/0.47 ( noeltsimpempty
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ A )
% 0.31/0.47 => ( A = emptyset ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setbeta_type,type,
% 0.31/0.47 setbeta: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setbeta,definition,
% 0.31/0.47 ( setbeta
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonempty_type,type,
% 0.31/0.47 nonempty: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonempty,definition,
% 0.31/0.47 ( nonempty
% 0.31/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyE1_type,type,
% 0.31/0.47 nonemptyE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyE1,definition,
% 0.31/0.47 ( nonemptyE1
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( nonempty @ A )
% 0.31/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI_type,type,
% 0.31/0.47 nonemptyI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI,definition,
% 0.31/0.47 ( nonemptyI
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( nonempty
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI1_type,type,
% 0.31/0.47 nonemptyI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI1,definition,
% 0.31/0.47 ( nonemptyI1
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL_type,type,
% 0.31/0.47 setadjoinIL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL,definition,
% 0.31/0.47 ( setadjoinIL
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinunitempty_type,type,
% 0.31/0.47 emptyinunitempty: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinunitempty,definition,
% 0.31/0.47 ( emptyinunitempty
% 0.31/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIR_type,type,
% 0.31/0.47 setadjoinIR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIR,definition,
% 0.31/0.47 ( setadjoinIR
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinE_type,type,
% 0.31/0.47 setadjoinE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinE,definition,
% 0.31/0.47 ( setadjoinE
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 => ! [Xphi: $o] :
% 0.31/0.47 ( ( ( Xy = Xx )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => ( ( ( in @ Xy @ A )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinOr_type,type,
% 0.31/0.47 setadjoinOr: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinOr,definition,
% 0.31/0.47 ( setadjoinOr
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 => ( ( Xy = Xx )
% 0.31/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setoftrueEq_type,type,
% 0.31/0.47 setoftrueEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setoftrueEq,definition,
% 0.31/0.47 ( setoftrueEq
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : $true )
% 0.31/0.47 = A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI_type,type,
% 0.31/0.47 powersetI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI,definition,
% 0.31/0.47 ( powersetI
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinPowerset_type,type,
% 0.31/0.47 emptyinPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinPowerset,definition,
% 0.31/0.47 ( emptyinPowerset
% 0.31/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyInPowerset_type,type,
% 0.31/0.47 emptyInPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyInPowerset,definition,
% 0.31/0.47 ( emptyInPowerset
% 0.31/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetE_type,type,
% 0.31/0.47 powersetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetE,definition,
% 0.31/0.47 ( powersetE
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.47 => ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunionI_type,type,
% 0.31/0.47 setunionI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunionI,definition,
% 0.31/0.47 ( setunionI
% 0.31/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( ( in @ B @ A )
% 0.31/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunionE_type,type,
% 0.31/0.47 setunionE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunionE,definition,
% 0.31/0.47 ( setunionE
% 0.31/0.47 = ( ! [A: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/0.47 => ! [Xphi: $o] :
% 0.31/0.47 ( ! [B: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( ( in @ B @ A )
% 0.31/0.47 => Xphi ) )
% 0.31/0.47 => Xphi ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subPowSU_type,type,
% 0.31/0.47 subPowSU: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subPowSU,definition,
% 0.31/0.47 ( subPowSU
% 0.31/0.47 = ( ! [A: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE2_type,type,
% 0.31/0.47 exuE2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE2,definition,
% 0.31/0.47 ( exuE2
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyImpWitness_type,type,
% 0.31/0.47 nonemptyImpWitness: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyImpWitness,definition,
% 0.31/0.47 ( nonemptyImpWitness
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( nonempty @ A )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & $true ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(uniqinunit_type,type,
% 0.31/0.47 uniqinunit: $o ).
% 0.31/0.47
% 0.31/0.47 thf(uniqinunit,definition,
% 0.31/0.47 ( uniqinunit
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notinsingleton_type,type,
% 0.31/0.47 notinsingleton: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notinsingleton,definition,
% 0.31/0.47 ( notinsingleton
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx != Xy )
% 0.31/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eqinunit_type,type,
% 0.31/0.47 eqinunit: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eqinunit,definition,
% 0.31/0.47 ( eqinunit
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(singletonsswitch_type,type,
% 0.31/0.47 singletonsswitch: $o ).
% 0.31/0.47
% 0.31/0.47 thf(singletonsswitch,definition,
% 0.31/0.47 ( singletonsswitch
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetE_type,type,
% 0.31/0.47 upairsetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetE,definition,
% 0.31/0.47 ( upairsetE
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.31/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.31/0.47 => ( ( Xz = Xx )
% 0.31/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIL_type,type,
% 0.31/0.47 upairsetIL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIL,definition,
% 0.31/0.47 ( upairsetIL
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIR_type,type,
% 0.31/0.47 upairsetIR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIR,definition,
% 0.31/0.47 ( upairsetIR
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyE1_type,type,
% 0.31/0.47 emptyE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyE1,definition,
% 0.31/0.47 ( emptyE1
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) )
% 0.31/0.47 => ( ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 = emptyset )
% 0.31/0.47 => $false ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(vacuousDall_type,type,
% 0.31/0.47 vacuousDall: $o ).
% 0.31/0.47
% 0.31/0.47 thf(vacuousDall,definition,
% 0.31/0.47 ( vacuousDall
% 0.31/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan1_type,type,
% 0.31/0.47 quantDeMorgan1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan1,definition,
% 0.31/0.47 ( quantDeMorgan1
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan2_type,type,
% 0.31/0.47 quantDeMorgan2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan2,definition,
% 0.31/0.47 ( quantDeMorgan2
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ~ ( Xphi @ Xx ) )
% 0.31/0.47 => ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan3_type,type,
% 0.31/0.47 quantDeMorgan3: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan3,definition,
% 0.31/0.47 ( quantDeMorgan3
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan4_type,type,
% 0.31/0.47 quantDeMorgan4: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan4,definition,
% 0.31/0.47 ( quantDeMorgan4
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ~ ( Xphi @ Xx ) )
% 0.31/0.47 => ~ ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setI_type,type,
% 0.31/0.47 prop2setI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setI,definition,
% 0.31/0.47 ( prop2setI
% 0.31/0.47 = ( ! [Xphi: $o] :
% 0.31/0.47 ( Xphi
% 0.31/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(set2prop_type,type,
% 0.31/0.47 set2prop: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set2propI_type,type,
% 0.31/0.47 prop2set2propI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set2propI,definition,
% 0.31/0.47 ( prop2set2propI
% 0.31/0.47 = ( ! [Xphi: $o] :
% 0.31/0.47 ( Xphi
% 0.31/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notdexE_type,type,
% 0.31/0.47 notdexE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notdexE,definition,
% 0.31/0.47 ( notdexE
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notdallE_type,type,
% 0.31/0.47 notdallE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notdallE,definition,
% 0.31/0.47 ( notdallE
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuI1_type,type,
% 0.31/0.47 exuI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuI1,definition,
% 0.31/0.47 ( exuI1
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuI3_type,type,
% 0.31/0.47 exuI3: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuI3,definition,
% 0.31/0.47 ( exuI3
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.31/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 => ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuI2_type,type,
% 0.31/0.47 exuI2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuI2,definition,
% 0.31/0.47 ( exuI2
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 <=> ( Xy = Xx ) )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(inCongP_type,type,
% 0.31/0.47 inCongP: $o ).
% 0.31/0.47
% 0.31/0.47 thf(inCongP,definition,
% 0.31/0.47 ( inCongP
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(in__Cong_type,type,
% 0.31/0.47 in__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(in__Cong,definition,
% 0.31/0.47 ( in__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3u_type,type,
% 0.31/0.47 exuE3u: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3u,definition,
% 0.31/0.47 ( exuE3u
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 => ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exu__Cong_type,type,
% 0.31/0.47 exu__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu__Cong,definition,
% 0.31/0.47 ( exu__Cong
% 0.31/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.31/0.47 => ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 <=> ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset__Cong_type,type,
% 0.31/0.47 emptyset__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset__Cong,definition,
% 0.31/0.47 ( emptyset__Cong
% 0.31/0.47 = ( emptyset = emptyset ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin__Cong_type,type,
% 0.31/0.47 setadjoin__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin__Cong,definition,
% 0.31/0.47 ( setadjoin__Cong
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ! [Xz: $i,Xu: $i] :
% 0.31/0.47 ( ( Xz = Xu )
% 0.31/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.31/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powerset__Cong_type,type,
% 0.31/0.47 powerset__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powerset__Cong,definition,
% 0.31/0.47 ( powerset__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( powerset @ A )
% 0.31/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunion__Cong_type,type,
% 0.31/0.47 setunion__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunion__Cong,definition,
% 0.31/0.47 ( setunion__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( setunion @ A )
% 0.31/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omega__Cong_type,type,
% 0.31/0.47 omega__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omega__Cong,definition,
% 0.31/0.47 ( omega__Cong
% 0.31/0.47 = ( omega = omega ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuEu_type,type,
% 0.31/0.47 exuEu: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuEu,definition,
% 0.31/0.47 ( exuEu
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 => ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(descr__Cong_type,type,
% 0.31/0.47 descr__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(descr__Cong,definition,
% 0.31/0.47 ( descr__Cong
% 0.31/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.31/0.47 => ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.31/0.47 => ( ( descr
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 = ( descr
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr__Cong_type,type,
% 0.31/0.47 dsetconstr__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr__Cong,definition,
% 0.31/0.47 ( dsetconstr__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( Xx = Xy )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.31/0.47 => ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 = ( dsetconstr @ B
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subset_type,type,
% 0.31/0.47 subset: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(disjoint_type,type,
% 0.31/0.47 disjoint: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(setsmeet_type,type,
% 0.31/0.47 setsmeet: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI1_type,type,
% 0.31/0.47 subsetI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI1,definition,
% 0.31/0.47 ( subsetI1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) )
% 0.31/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset2_type,type,
% 0.31/0.47 eqimpsubset2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset2,definition,
% 0.31/0.47 ( eqimpsubset2
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset1_type,type,
% 0.31/0.47 eqimpsubset1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset1,definition,
% 0.31/0.47 ( eqimpsubset1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI2_type,type,
% 0.31/0.47 subsetI2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI2,definition,
% 0.31/0.47 ( subsetI2
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) )
% 0.31/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetsubset_type,type,
% 0.31/0.47 emptysetsubset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetsubset,definition,
% 0.31/0.47 ( emptysetsubset
% 0.31/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE_type,type,
% 0.31/0.47 subsetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE,definition,
% 0.31/0.47 ( subsetE
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE2_type,type,
% 0.31/0.47 subsetE2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE2,definition,
% 0.31/0.47 ( subsetE2
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ~ ( in @ Xx @ B )
% 0.31/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notsubsetI_type,type,
% 0.31/0.47 notsubsetI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notsubsetI,definition,
% 0.31/0.47 ( notsubsetI
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ~ ( in @ Xx @ B )
% 0.31/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notequalI1_type,type,
% 0.31/0.47 notequalI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notequalI1,definition,
% 0.31/0.47 ( notequalI1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ~ ( subset @ A @ B )
% 0.31/0.47 => ( A != B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notequalI2_type,type,
% 0.31/0.47 notequalI2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notequalI2,definition,
% 0.31/0.47 ( notequalI2
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ~ ( in @ Xx @ B )
% 0.31/0.47 => ( A != B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetRefl_type,type,
% 0.31/0.47 subsetRefl: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetRefl,definition,
% 0.31/0.47 ( subsetRefl
% 0.31/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetTrans_type,type,
% 0.31/0.47 subsetTrans: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetTrans,definition,
% 0.31/0.47 ( subsetTrans
% 0.31/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ( subset @ B @ C )
% 0.31/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinSub_type,type,
% 0.31/0.47 setadjoinSub: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinSub,definition,
% 0.31/0.47 ( setadjoinSub
% 0.31/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinSub2_type,type,
% 0.31/0.47 setadjoinSub2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinSub2,definition,
% 0.31/0.47 ( setadjoinSub2
% 0.31/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subset2powerset,conjecture,
% 0.31/0.47 ( setextAx
% 0.31/0.47 => ( emptysetAx
% 0.31/0.47 => ( setadjoinAx
% 0.31/0.47 => ( powersetAx
% 0.31/0.47 => ( setunionAx
% 0.31/0.47 => ( omega0Ax
% 0.31/0.47 => ( omegaSAx
% 0.31/0.47 => ( omegaIndAx
% 0.31/0.47 => ( replAx
% 0.31/0.47 => ( foundationAx
% 0.31/0.47 => ( wellorderingAx
% 0.31/0.47 => ( descrp
% 0.31/0.47 => ( dsetconstrI
% 0.31/0.47 => ( dsetconstrEL
% 0.31/0.47 => ( dsetconstrER
% 0.31/0.47 => ( exuE1
% 0.31/0.47 => ( prop2setE
% 0.31/0.47 => ( emptysetE
% 0.31/0.47 => ( emptysetimpfalse
% 0.31/0.47 => ( notinemptyset
% 0.31/0.47 => ( exuE3e
% 0.31/0.47 => ( setext
% 0.31/0.47 => ( emptyI
% 0.31/0.47 => ( noeltsimpempty
% 0.31/0.47 => ( setbeta
% 0.31/0.47 => ( nonemptyE1
% 0.31/0.47 => ( nonemptyI
% 0.31/0.47 => ( nonemptyI1
% 0.31/0.47 => ( setadjoinIL
% 0.31/0.47 => ( emptyinunitempty
% 0.31/0.47 => ( setadjoinIR
% 0.31/0.47 => ( setadjoinE
% 0.31/0.47 => ( setadjoinOr
% 0.31/0.47 => ( setoftrueEq
% 0.31/0.47 => ( powersetI
% 0.31/0.47 => ( emptyinPowerset
% 0.31/0.47 => ( emptyInPowerset
% 0.31/0.47 => ( powersetE
% 0.31/0.47 => ( setunionI
% 0.31/0.47 => ( setunionE
% 0.31/0.47 => ( subPowSU
% 0.31/0.47 => ( exuE2
% 0.31/0.47 => ( nonemptyImpWitness
% 0.31/0.47 => ( uniqinunit
% 0.31/0.47 => ( notinsingleton
% 0.31/0.47 => ( eqinunit
% 0.31/0.47 => ( singletonsswitch
% 0.31/0.47 => ( upairsetE
% 0.31/0.47 => ( upairsetIL
% 0.31/0.47 => ( upairsetIR
% 0.31/0.47 => ( emptyE1
% 0.31/0.47 => ( vacuousDall
% 0.31/0.47 => ( quantDeMorgan1
% 0.31/0.47 => ( quantDeMorgan2
% 0.31/0.47 => ( quantDeMorgan3
% 0.31/0.47 => ( quantDeMorgan4
% 0.31/0.47 => ( prop2setI
% 0.31/0.47 => ( prop2set2propI
% 0.31/0.47 => ( notdexE
% 0.31/0.47 => ( notdallE
% 0.31/0.47 => ( exuI1
% 0.31/0.47 => ( exuI3
% 0.31/0.47 => ( exuI2
% 0.31/0.47 => ( inCongP
% 0.31/0.47 => ( in__Cong
% 0.31/0.47 => ( exuE3u
% 0.31/0.47 => ( exu__Cong
% 0.31/0.47 => ( emptyset__Cong
% 0.31/0.47 => ( setadjoin__Cong
% 0.31/0.47 => ( powerset__Cong
% 0.31/0.47 => ( setunion__Cong
% 0.31/0.47 => ( omega__Cong
% 0.31/0.47 => ( exuEu
% 0.31/0.47 => ( descr__Cong
% 0.31/0.47 => ( dsetconstr__Cong
% 0.31/0.47 => ( subsetI1
% 0.31/0.47 => ( eqimpsubset2
% 0.31/0.47 => ( eqimpsubset1
% 0.31/0.47 => ( subsetI2
% 0.31/0.47 => ( emptysetsubset
% 0.31/0.47 => ( subsetE
% 0.31/0.47 => ( subsetE2
% 0.31/0.47 => ( notsubsetI
% 0.31/0.47 => ( notequalI1
% 0.31/0.47 => ( notequalI2
% 0.31/0.47 => ( subsetRefl
% 0.31/0.47 => ( subsetTrans
% 0.31/0.47 => ( setadjoinSub
% 0.31/0.47 => ( setadjoinSub2
% 0.31/0.47 => ! [A: $i,B: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 2.37/1.43 ---- Embedded in THF ---
% 2.37/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.37/1.43 %%% Generated on Tue Feb 24 12:27:38 EST 2026
% 2.37/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 2.37/1.43 %%% Logic specification used:
% 2.37/1.43 %%% thf(spec, logic, $$dhol).
% 2.37/1.43
% 2.37/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.fBNDjAFKO7/DTF2DTF1757.p
% See solution above
% 2.37/1.43 ------------------------
% 2.37/1.45 ---- Cleaned THF ---
% 2.37/1.45 thf(in_type,type,
% 2.37/1.45 in: $i > $i > $o ).
% 2.37/1.45
% 2.37/1.45 thf(exu_type,type,
% 2.37/1.45 exu: ( $i > $o ) > $o ).
% 2.37/1.45
% 2.37/1.45 thf(exu,definition,
% 2.37/1.45 ( exu
% 2.37/1.45 = ( ^ [Xphi: $i > $o] :
% 2.37/1.45 ? [Xx: $i] :
% 2.37/1.45 ( ( Xphi @ Xx )
% 2.37/1.45 & ! [Xy: $i] :
% 2.37/1.45 ( ( Xphi @ Xy )
% 2.37/1.45 => ( Xx = Xy ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(setextAx_type,type,
% 2.37/1.45 setextAx: $o ).
% 2.37/1.45
% 2.37/1.45 thf(setextAx,definition,
% 2.37/1.45 ( setextAx
% 2.37/1.45 = ( ! [A: $i,B: $i] :
% 2.37/1.45 ( ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ A )
% 2.37/1.45 <=> ( in @ Xx @ B ) )
% 2.37/1.45 => ( A = B ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(emptyset_type,type,
% 2.37/1.45 emptyset: $i ).
% 2.37/1.45
% 2.37/1.45 thf(emptysetAx_type,type,
% 2.37/1.45 emptysetAx: $o ).
% 2.37/1.45
% 2.37/1.45 thf(emptysetAx,definition,
% 2.37/1.45 ( emptysetAx
% 2.37/1.45 = ( ! [Xx: $i] :
% 2.37/1.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(setadjoin_type,type,
% 2.37/1.45 setadjoin: $i > $i > $i ).
% 2.37/1.45
% 2.37/1.45 thf(setadjoinAx_type,type,
% 2.37/1.45 setadjoinAx: $o ).
% 2.37/1.45
% 2.37/1.45 thf(setadjoinAx,definition,
% 2.37/1.45 ( setadjoinAx
% 2.37/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.37/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.37/1.45 <=> ( ( Xy = Xx )
% 2.37/1.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(powerset_type,type,
% 2.37/1.45 powerset: $i > $i ).
% 2.37/1.45
% 2.37/1.45 thf(powersetAx_type,type,
% 2.37/1.45 powersetAx: $o ).
% 2.37/1.45
% 2.37/1.45 thf(powersetAx,definition,
% 2.37/1.45 ( powersetAx
% 2.37/1.45 = ( ! [A: $i,B: $i] :
% 2.37/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.37/1.45 <=> ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ B )
% 2.37/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(setunion_type,type,
% 2.37/1.45 setunion: $i > $i ).
% 2.37/1.45
% 2.37/1.45 thf(setunionAx_type,type,
% 2.37/1.45 setunionAx: $o ).
% 2.37/1.45
% 2.37/1.45 thf(setunionAx,definition,
% 2.37/1.45 ( setunionAx
% 2.37/1.45 = ( ! [A: $i,Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.37/1.45 <=> ? [B: $i] :
% 2.37/1.45 ( ( in @ Xx @ B )
% 2.37/1.45 & ( in @ B @ A ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(omega_type,type,
% 2.37/1.45 omega: $i ).
% 2.37/1.45
% 2.37/1.45 thf(omega0Ax_type,type,
% 2.37/1.45 omega0Ax: $o ).
% 2.37/1.45
% 2.37/1.45 thf(omega0Ax,definition,
% 2.37/1.45 ( omega0Ax
% 2.37/1.45 = ( in @ emptyset @ omega ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(omegaSAx_type,type,
% 2.37/1.45 omegaSAx: $o ).
% 2.37/1.45
% 2.37/1.45 thf(omegaSAx,definition,
% 2.37/1.45 ( omegaSAx
% 2.37/1.45 = ( ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ omega )
% 2.37/1.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(omegaIndAx_type,type,
% 2.37/1.45 omegaIndAx: $o ).
% 2.37/1.45
% 2.37/1.45 thf(omegaIndAx,definition,
% 2.37/1.45 ( omegaIndAx
% 2.37/1.45 = ( ! [A: $i] :
% 2.37/1.45 ( ( ( in @ emptyset @ A )
% 2.37/1.45 & ! [Xx: $i] :
% 2.37/1.45 ( ( ( in @ Xx @ omega )
% 2.37/1.45 & ( in @ Xx @ A ) )
% 2.37/1.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.37/1.45 => ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ omega )
% 2.37/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(replAx_type,type,
% 2.37/1.45 replAx: $o ).
% 2.37/1.45
% 2.37/1.45 thf(replAx,definition,
% 2.37/1.45 ( replAx
% 2.37/1.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.37/1.45 ( ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ A )
% 2.37/1.45 => ( exu
% 2.37/1.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.37/1.45 => ? [B: $i] :
% 2.37/1.45 ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ B )
% 2.37/1.45 <=> ? [Xy: $i] :
% 2.37/1.45 ( ( in @ Xy @ A )
% 2.37/1.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(foundationAx_type,type,
% 2.37/1.45 foundationAx: $o ).
% 2.37/1.45
% 2.37/1.45 thf(foundationAx,definition,
% 2.37/1.45 ( foundationAx
% 2.37/1.45 = ( ! [A: $i] :
% 2.37/1.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.37/1.45 => ? [B: $i] :
% 2.37/1.45 ( ( in @ B @ A )
% 2.37/1.45 & ~ ? [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ B )
% 2.37/1.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(wellorderingAx_type,type,
% 2.37/1.45 wellorderingAx: $o ).
% 2.37/1.45
% 2.37/1.45 thf(wellorderingAx,definition,
% 2.37/1.45 ( wellorderingAx
% 2.37/1.45 = ( ! [A: $i] :
% 2.37/1.45 ? [B: $i] :
% 2.37/1.45 ( ! [C: $i] :
% 2.37/1.45 ( ( in @ C @ B )
% 2.37/1.45 => ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ C )
% 2.37/1.45 => ( in @ Xx @ A ) ) )
% 2.37/1.45 & ! [Xx: $i,Xy: $i] :
% 2.37/1.45 ( ( ( in @ Xx @ A )
% 2.37/1.45 & ( in @ Xy @ A ) )
% 2.37/1.45 => ( ! [C: $i] :
% 2.37/1.45 ( ( in @ C @ B )
% 2.37/1.45 => ( ( in @ Xx @ C )
% 2.37/1.45 <=> ( in @ Xy @ C ) ) )
% 2.37/1.45 => ( Xx = Xy ) ) )
% 2.37/1.45 & ! [C: $i,D: $i] :
% 2.37/1.45 ( ( ( in @ C @ B )
% 2.37/1.45 & ( in @ D @ B ) )
% 2.37/1.45 => ( ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ C )
% 2.37/1.45 => ( in @ Xx @ D ) )
% 2.37/1.45 | ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ D )
% 2.37/1.45 => ( in @ Xx @ C ) ) ) )
% 2.37/1.45 & ! [C: $i] :
% 2.37/1.45 ( ( ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ C )
% 2.37/1.45 => ( in @ Xx @ A ) )
% 2.37/1.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.37/1.45 => ? [D: $i,Xx: $i] :
% 2.37/1.45 ( ( in @ D @ B )
% 2.37/1.45 & ( in @ Xx @ C )
% 2.37/1.45 & ~ ? [Xy: $i] :
% 2.37/1.45 ( ( in @ Xy @ D )
% 2.37/1.45 & ( in @ Xy @ C ) )
% 2.37/1.45 & ! [E: $i] :
% 2.37/1.45 ( ( in @ E @ B )
% 2.37/1.45 => ( ! [Xy: $i] :
% 2.37/1.45 ( ( in @ Xy @ E )
% 2.37/1.45 => ( in @ Xy @ D ) )
% 2.37/1.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(descr_type,type,
% 2.37/1.45 descr: ( $i > $o ) > $i ).
% 2.37/1.45
% 2.37/1.45 thf(descrp_type,type,
% 2.37/1.45 descrp: $o ).
% 2.37/1.45
% 2.37/1.45 thf(descrp,definition,
% 2.37/1.45 ( descrp
% 2.37/1.45 = ( ! [Xphi: $i > $o] :
% 2.37/1.45 ( ( exu
% 2.37/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.37/1.45 => ( Xphi
% 2.37/1.45 @ ( descr
% 2.37/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(dsetconstr_type,type,
% 2.37/1.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.37/1.45
% 2.37/1.45 thf(dsetconstrI_type,type,
% 2.37/1.45 dsetconstrI: $o ).
% 2.37/1.45
% 2.37/1.45 thf(dsetconstrI,definition,
% 2.37/1.45 ( dsetconstrI
% 2.37/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ A )
% 2.37/1.45 => ( ( Xphi @ Xx )
% 2.37/1.45 => ( in @ Xx
% 2.37/1.45 @ ( dsetconstr @ A
% 2.37/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(dsetconstrEL_type,type,
% 2.37/1.45 dsetconstrEL: $o ).
% 2.37/1.45
% 2.37/1.45 thf(dsetconstrEL,definition,
% 2.37/1.45 ( dsetconstrEL
% 2.37/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.37/1.45 ( ( in @ Xx
% 2.37/1.45 @ ( dsetconstr @ A
% 2.37/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.37/1.45 => ( in @ Xx @ A ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(dsetconstrER_type,type,
% 2.37/1.45 dsetconstrER: $o ).
% 2.37/1.45
% 2.37/1.45 thf(dsetconstrER,definition,
% 2.37/1.45 ( dsetconstrER
% 2.37/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.37/1.45 ( ( in @ Xx
% 2.37/1.45 @ ( dsetconstr @ A
% 2.37/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.37/1.45 => ( Xphi @ Xx ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(exuE1_type,type,
% 2.37/1.45 exuE1: $o ).
% 2.37/1.45
% 2.37/1.45 thf(exuE1,definition,
% 2.37/1.45 ( exuE1
% 2.37/1.45 = ( ! [Xphi: $i > $o] :
% 2.37/1.45 ( ( exu
% 2.37/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.37/1.45 => ? [Xx: $i] :
% 2.37/1.45 ( ( Xphi @ Xx )
% 2.37/1.45 & ! [Xy: $i] :
% 2.37/1.45 ( ( Xphi @ Xy )
% 2.37/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(prop2set_type,type,
% 2.37/1.45 prop2set: $o > $i ).
% 2.37/1.45
% 2.37/1.45 thf(prop2setE_type,type,
% 2.37/1.45 prop2setE: $o ).
% 2.37/1.45
% 2.37/1.45 thf(prop2setE,definition,
% 2.37/1.45 ( prop2setE
% 2.37/1.45 = ( ! [Xphi: $o,Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.37/1.45 => Xphi ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(emptysetE_type,type,
% 2.37/1.45 emptysetE: $o ).
% 2.37/1.45
% 2.37/1.45 thf(emptysetE,definition,
% 2.37/1.45 ( emptysetE
% 2.37/1.45 = ( ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ emptyset )
% 2.37/1.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(emptysetimpfalse_type,type,
% 2.37/1.45 emptysetimpfalse: $o ).
% 2.37/1.45
% 2.37/1.45 thf(emptysetimpfalse,definition,
% 2.37/1.45 ( emptysetimpfalse
% 2.37/1.45 = ( ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ emptyset )
% 2.37/1.45 => $false ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(notinemptyset_type,type,
% 2.37/1.45 notinemptyset: $o ).
% 2.37/1.45
% 2.37/1.45 thf(notinemptyset,definition,
% 2.37/1.45 ( notinemptyset
% 2.37/1.45 = ( ! [Xx: $i] :
% 2.37/1.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(exuE3e_type,type,
% 2.37/1.45 exuE3e: $o ).
% 2.37/1.45
% 2.37/1.45 thf(exuE3e,definition,
% 2.37/1.45 ( exuE3e
% 2.37/1.45 = ( ! [Xphi: $i > $o] :
% 2.37/1.45 ( ( exu
% 2.37/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.37/1.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(setext_type,type,
% 2.37/1.45 setext: $o ).
% 2.37/1.45
% 2.37/1.45 thf(setext,definition,
% 2.37/1.45 ( setext
% 2.37/1.45 = ( ! [A: $i,B: $i] :
% 2.37/1.45 ( ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ A )
% 2.37/1.45 => ( in @ Xx @ B ) )
% 2.37/1.45 => ( ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ B )
% 2.37/1.45 => ( in @ Xx @ A ) )
% 2.37/1.45 => ( A = B ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(emptyI_type,type,
% 2.37/1.45 emptyI: $o ).
% 2.37/1.45
% 2.37/1.45 thf(emptyI,definition,
% 2.37/1.45 ( emptyI
% 2.37/1.45 = ( ! [A: $i] :
% 2.37/1.45 ( ! [Xx: $i] :
% 2.37/1.45 ~ ( in @ Xx @ A )
% 2.37/1.45 => ( A = emptyset ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(noeltsimpempty_type,type,
% 2.37/1.45 noeltsimpempty: $o ).
% 2.37/1.45
% 2.37/1.45 thf(noeltsimpempty,definition,
% 2.37/1.45 ( noeltsimpempty
% 2.37/1.45 = ( ! [A: $i] :
% 2.37/1.45 ( ! [Xx: $i] :
% 2.37/1.45 ~ ( in @ Xx @ A )
% 2.37/1.45 => ( A = emptyset ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(setbeta_type,type,
% 2.37/1.45 setbeta: $o ).
% 2.37/1.45
% 2.37/1.45 thf(setbeta,definition,
% 2.37/1.45 ( setbeta
% 2.37/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ A )
% 2.37/1.45 => ( ( in @ Xx
% 2.37/1.45 @ ( dsetconstr @ A
% 2.37/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.37/1.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(nonempty_type,type,
% 2.37/1.45 nonempty: $i > $o ).
% 2.37/1.45
% 2.37/1.45 thf(nonempty,definition,
% 2.37/1.45 ( nonempty
% 2.37/1.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(nonemptyE1_type,type,
% 2.37/1.45 nonemptyE1: $o ).
% 2.37/1.45
% 2.37/1.45 thf(nonemptyE1,definition,
% 2.37/1.45 ( nonemptyE1
% 2.37/1.45 = ( ! [A: $i] :
% 2.37/1.45 ( ( nonempty @ A )
% 2.37/1.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(nonemptyI_type,type,
% 2.37/1.45 nonemptyI: $o ).
% 2.37/1.45
% 2.37/1.45 thf(nonemptyI,definition,
% 2.37/1.45 ( nonemptyI
% 2.37/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ A )
% 2.37/1.45 => ( ( Xphi @ Xx )
% 2.37/1.45 => ( nonempty
% 2.37/1.45 @ ( dsetconstr @ A
% 2.37/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(nonemptyI1_type,type,
% 2.37/1.45 nonemptyI1: $o ).
% 2.37/1.45
% 2.37/1.45 thf(nonemptyI1,definition,
% 2.37/1.45 ( nonemptyI1
% 2.37/1.45 = ( ! [A: $i] :
% 2.37/1.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.37/1.45 => ( nonempty @ A ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(setadjoinIL_type,type,
% 2.37/1.45 setadjoinIL: $o ).
% 2.37/1.45
% 2.37/1.45 thf(setadjoinIL,definition,
% 2.37/1.45 ( setadjoinIL
% 2.37/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(emptyinunitempty_type,type,
% 2.37/1.45 emptyinunitempty: $o ).
% 2.37/1.45
% 2.37/1.45 thf(emptyinunitempty,definition,
% 2.37/1.45 ( emptyinunitempty
% 2.37/1.45 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(setadjoinIR_type,type,
% 2.37/1.45 setadjoinIR: $o ).
% 2.37/1.45
% 2.37/1.45 thf(setadjoinIR,definition,
% 2.37/1.45 ( setadjoinIR
% 2.37/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.37/1.45 ( ( in @ Xy @ A )
% 2.37/1.45 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(setadjoinE_type,type,
% 2.37/1.45 setadjoinE: $o ).
% 2.37/1.45
% 2.37/1.45 thf(setadjoinE,definition,
% 2.37/1.45 ( setadjoinE
% 2.37/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.37/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.37/1.45 => ! [Xphi: $o] :
% 2.37/1.45 ( ( ( Xy = Xx )
% 2.37/1.45 => Xphi )
% 2.37/1.45 => ( ( ( in @ Xy @ A )
% 2.37/1.45 => Xphi )
% 2.37/1.45 => Xphi ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(setadjoinOr_type,type,
% 2.37/1.45 setadjoinOr: $o ).
% 2.37/1.45
% 2.37/1.45 thf(setadjoinOr,definition,
% 2.37/1.45 ( setadjoinOr
% 2.37/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.37/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.37/1.45 => ( ( Xy = Xx )
% 2.37/1.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(setoftrueEq_type,type,
% 2.37/1.45 setoftrueEq: $o ).
% 2.37/1.45
% 2.37/1.45 thf(setoftrueEq,definition,
% 2.37/1.45 ( setoftrueEq
% 2.37/1.45 = ( ! [A: $i] :
% 2.37/1.45 ( ( dsetconstr @ A
% 2.37/1.45 @ ^ [Xx: $i] : $true )
% 2.37/1.45 = A ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(powersetI_type,type,
% 2.37/1.45 powersetI: $o ).
% 2.37/1.45
% 2.37/1.45 thf(powersetI,definition,
% 2.37/1.45 ( powersetI
% 2.37/1.45 = ( ! [A: $i,B: $i] :
% 2.37/1.45 ( ! [Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ B )
% 2.37/1.45 => ( in @ Xx @ A ) )
% 2.37/1.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(emptyinPowerset_type,type,
% 2.37/1.45 emptyinPowerset: $o ).
% 2.37/1.45
% 2.37/1.45 thf(emptyinPowerset,definition,
% 2.37/1.45 ( emptyinPowerset
% 2.37/1.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(emptyInPowerset_type,type,
% 2.37/1.45 emptyInPowerset: $o ).
% 2.37/1.45
% 2.37/1.45 thf(emptyInPowerset,definition,
% 2.37/1.45 ( emptyInPowerset
% 2.37/1.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(powersetE_type,type,
% 2.37/1.45 powersetE: $o ).
% 2.37/1.45
% 2.37/1.45 thf(powersetE,definition,
% 2.37/1.45 ( powersetE
% 2.37/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.37/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.37/1.45 => ( ( in @ Xx @ B )
% 2.37/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(setunionI_type,type,
% 2.37/1.45 setunionI: $o ).
% 2.37/1.45
% 2.37/1.45 thf(setunionI,definition,
% 2.37/1.45 ( setunionI
% 2.37/1.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.37/1.45 ( ( in @ Xx @ B )
% 2.37/1.45 => ( ( in @ B @ A )
% 2.37/1.45 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(setunionE_type,type,
% 2.37/1.45 setunionE: $o ).
% 2.37/1.45
% 2.37/1.45 thf(setunionE,definition,
% 2.37/1.45 ( setunionE
% 2.37/1.45 = ( ! [A: $i,Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.37/1.45 => ! [Xphi: $o] :
% 2.37/1.45 ( ! [B: $i] :
% 2.37/1.45 ( ( in @ Xx @ B )
% 2.37/1.45 => ( ( in @ B @ A )
% 2.37/1.45 => Xphi ) )
% 2.37/1.45 => Xphi ) ) ) ) ).
% 2.37/1.45
% 2.37/1.45 thf(subPowSU_type,type,
% 2.37/1.45 subPowSU: $o ).
% 2.37/1.45
% 2.37/1.45 thf(subPowSU,definition,
% 2.37/1.45 ( subPowSU
% 2.37/1.45 = ( ! [A: $i,Xx: $i] :
% 2.37/1.45 ( ( in @ Xx @ A )
% 2.37/1.45 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(exuE2_type,type,
% 2.37/1.46 exuE2: $o ).
% 2.37/1.46
% 2.37/1.46 thf(exuE2,definition,
% 2.37/1.46 ( exuE2
% 2.37/1.46 = ( ! [Xphi: $i > $o] :
% 2.37/1.46 ( ( exu
% 2.37/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.37/1.46 => ? [Xx: $i] :
% 2.37/1.46 ! [Xy: $i] :
% 2.37/1.46 ( ( Xphi @ Xy )
% 2.37/1.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(nonemptyImpWitness_type,type,
% 2.37/1.46 nonemptyImpWitness: $o ).
% 2.37/1.46
% 2.37/1.46 thf(nonemptyImpWitness,definition,
% 2.37/1.46 ( nonemptyImpWitness
% 2.37/1.46 = ( ! [A: $i] :
% 2.37/1.46 ( ( nonempty @ A )
% 2.37/1.46 => ? [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 & $true ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(uniqinunit_type,type,
% 2.37/1.46 uniqinunit: $o ).
% 2.37/1.46
% 2.37/1.46 thf(uniqinunit,definition,
% 2.37/1.46 ( uniqinunit
% 2.37/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.37/1.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.37/1.46 => ( Xx = Xy ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(notinsingleton_type,type,
% 2.37/1.46 notinsingleton: $o ).
% 2.37/1.46
% 2.37/1.46 thf(notinsingleton,definition,
% 2.37/1.46 ( notinsingleton
% 2.37/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.37/1.46 ( ( Xx != Xy )
% 2.37/1.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(eqinunit_type,type,
% 2.37/1.46 eqinunit: $o ).
% 2.37/1.46
% 2.37/1.46 thf(eqinunit,definition,
% 2.37/1.46 ( eqinunit
% 2.37/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.37/1.46 ( ( Xx = Xy )
% 2.37/1.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(singletonsswitch_type,type,
% 2.37/1.46 singletonsswitch: $o ).
% 2.37/1.46
% 2.37/1.46 thf(singletonsswitch,definition,
% 2.37/1.46 ( singletonsswitch
% 2.37/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.37/1.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.37/1.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(upairsetE_type,type,
% 2.37/1.46 upairsetE: $o ).
% 2.37/1.46
% 2.37/1.46 thf(upairsetE,definition,
% 2.37/1.46 ( upairsetE
% 2.37/1.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.37/1.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.37/1.46 => ( ( Xz = Xx )
% 2.37/1.46 | ( Xz = Xy ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(upairsetIL_type,type,
% 2.37/1.46 upairsetIL: $o ).
% 2.37/1.46
% 2.37/1.46 thf(upairsetIL,definition,
% 2.37/1.46 ( upairsetIL
% 2.37/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(upairsetIR_type,type,
% 2.37/1.46 upairsetIR: $o ).
% 2.37/1.46
% 2.37/1.46 thf(upairsetIR,definition,
% 2.37/1.46 ( upairsetIR
% 2.37/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(emptyE1_type,type,
% 2.37/1.46 emptyE1: $o ).
% 2.37/1.46
% 2.37/1.46 thf(emptyE1,definition,
% 2.37/1.46 ( emptyE1
% 2.37/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.37/1.46 ( ? [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 & ( Xphi @ Xx ) )
% 2.37/1.46 => ( ( ( dsetconstr @ A
% 2.37/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.37/1.46 = emptyset )
% 2.37/1.46 => $false ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(vacuousDall_type,type,
% 2.37/1.46 vacuousDall: $o ).
% 2.37/1.46
% 2.37/1.46 thf(vacuousDall,definition,
% 2.37/1.46 ( vacuousDall
% 2.37/1.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ emptyset )
% 2.37/1.46 => ( Xphi @ Xx ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(quantDeMorgan1_type,type,
% 2.37/1.46 quantDeMorgan1: $o ).
% 2.37/1.46
% 2.37/1.46 thf(quantDeMorgan1,definition,
% 2.37/1.46 ( quantDeMorgan1
% 2.37/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.37/1.46 ( ~ ! [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 => ( Xphi @ Xx ) )
% 2.37/1.46 => ? [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(quantDeMorgan2_type,type,
% 2.37/1.46 quantDeMorgan2: $o ).
% 2.37/1.46
% 2.37/1.46 thf(quantDeMorgan2,definition,
% 2.37/1.46 ( quantDeMorgan2
% 2.37/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.37/1.46 ( ! [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 => ~ ( Xphi @ Xx ) )
% 2.37/1.46 => ~ ? [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(quantDeMorgan3_type,type,
% 2.37/1.46 quantDeMorgan3: $o ).
% 2.37/1.46
% 2.37/1.46 thf(quantDeMorgan3,definition,
% 2.37/1.46 ( quantDeMorgan3
% 2.37/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.37/1.46 ( ~ ? [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 & ( Xphi @ Xx ) )
% 2.37/1.46 => ! [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(quantDeMorgan4_type,type,
% 2.37/1.46 quantDeMorgan4: $o ).
% 2.37/1.46
% 2.37/1.46 thf(quantDeMorgan4,definition,
% 2.37/1.46 ( quantDeMorgan4
% 2.37/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.37/1.46 ( ? [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 & ~ ( Xphi @ Xx ) )
% 2.37/1.46 => ~ ! [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(prop2setI_type,type,
% 2.37/1.46 prop2setI: $o ).
% 2.37/1.46
% 2.37/1.46 thf(prop2setI,definition,
% 2.37/1.46 ( prop2setI
% 2.37/1.46 = ( ! [Xphi: $o] :
% 2.37/1.46 ( Xphi
% 2.37/1.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(set2prop_type,type,
% 2.37/1.46 set2prop: $i > $o ).
% 2.37/1.46
% 2.37/1.46 thf(prop2set2propI_type,type,
% 2.37/1.46 prop2set2propI: $o ).
% 2.37/1.46
% 2.37/1.46 thf(prop2set2propI,definition,
% 2.37/1.46 ( prop2set2propI
% 2.37/1.46 = ( ! [Xphi: $o] :
% 2.37/1.46 ( Xphi
% 2.37/1.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(notdexE_type,type,
% 2.37/1.46 notdexE: $o ).
% 2.37/1.46
% 2.37/1.46 thf(notdexE,definition,
% 2.37/1.46 ( notdexE
% 2.37/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.37/1.46 ( ~ ? [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 & ( Xphi @ Xx ) )
% 2.37/1.46 => ! [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(notdallE_type,type,
% 2.37/1.46 notdallE: $o ).
% 2.37/1.46
% 2.37/1.46 thf(notdallE,definition,
% 2.37/1.46 ( notdallE
% 2.37/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.37/1.46 ( ~ ! [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 => ( Xphi @ Xx ) )
% 2.37/1.46 => ? [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(exuI1_type,type,
% 2.37/1.46 exuI1: $o ).
% 2.37/1.46
% 2.37/1.46 thf(exuI1,definition,
% 2.37/1.46 ( exuI1
% 2.37/1.46 = ( ! [Xphi: $i > $o] :
% 2.37/1.46 ( ? [Xx: $i] :
% 2.37/1.46 ( ( Xphi @ Xx )
% 2.37/1.46 & ! [Xy: $i] :
% 2.37/1.46 ( ( Xphi @ Xy )
% 2.37/1.46 => ( Xx = Xy ) ) )
% 2.37/1.46 => ( exu
% 2.37/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(exuI3_type,type,
% 2.37/1.46 exuI3: $o ).
% 2.37/1.46
% 2.37/1.46 thf(exuI3,definition,
% 2.37/1.46 ( exuI3
% 2.37/1.46 = ( ! [Xphi: $i > $o] :
% 2.37/1.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.37/1.46 => ( ! [Xx: $i,Xy: $i] :
% 2.37/1.46 ( ( Xphi @ Xx )
% 2.37/1.46 => ( ( Xphi @ Xy )
% 2.37/1.46 => ( Xx = Xy ) ) )
% 2.37/1.46 => ( exu
% 2.37/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(exuI2_type,type,
% 2.37/1.46 exuI2: $o ).
% 2.37/1.46
% 2.37/1.46 thf(exuI2,definition,
% 2.37/1.46 ( exuI2
% 2.37/1.46 = ( ! [Xphi: $i > $o] :
% 2.37/1.46 ( ? [Xx: $i] :
% 2.37/1.46 ! [Xy: $i] :
% 2.37/1.46 ( ( Xphi @ Xy )
% 2.37/1.46 <=> ( Xy = Xx ) )
% 2.37/1.46 => ( exu
% 2.37/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(inCongP_type,type,
% 2.37/1.46 inCongP: $o ).
% 2.37/1.46
% 2.37/1.46 thf(inCongP,definition,
% 2.37/1.46 ( inCongP
% 2.37/1.46 = ( ! [A: $i,B: $i] :
% 2.37/1.46 ( ( A = B )
% 2.37/1.46 => ! [Xx: $i,Xy: $i] :
% 2.37/1.46 ( ( Xx = Xy )
% 2.37/1.46 => ( ( in @ Xx @ A )
% 2.37/1.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(in__Cong_type,type,
% 2.37/1.46 in__Cong: $o ).
% 2.37/1.46
% 2.37/1.46 thf(in__Cong,definition,
% 2.37/1.46 ( in__Cong
% 2.37/1.46 = ( ! [A: $i,B: $i] :
% 2.37/1.46 ( ( A = B )
% 2.37/1.46 => ! [Xx: $i,Xy: $i] :
% 2.37/1.46 ( ( Xx = Xy )
% 2.37/1.46 => ( ( in @ Xx @ A )
% 2.37/1.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(exuE3u_type,type,
% 2.37/1.46 exuE3u: $o ).
% 2.37/1.46
% 2.37/1.46 thf(exuE3u,definition,
% 2.37/1.46 ( exuE3u
% 2.37/1.46 = ( ! [Xphi: $i > $o] :
% 2.37/1.46 ( ( exu
% 2.37/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.37/1.46 => ! [Xx: $i,Xy: $i] :
% 2.37/1.46 ( ( Xphi @ Xx )
% 2.37/1.46 => ( ( Xphi @ Xy )
% 2.37/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(exu__Cong_type,type,
% 2.37/1.46 exu__Cong: $o ).
% 2.37/1.46
% 2.37/1.46 thf(exu__Cong,definition,
% 2.37/1.46 ( exu__Cong
% 2.37/1.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.37/1.46 ( ! [Xx: $i,Xy: $i] :
% 2.37/1.46 ( ( Xx = Xy )
% 2.37/1.46 => ( ( Xphi @ Xx )
% 2.37/1.46 <=> ( Xpsi @ Xy ) ) )
% 2.37/1.46 => ( ( exu
% 2.37/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.37/1.46 <=> ( exu
% 2.37/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(emptyset__Cong_type,type,
% 2.37/1.46 emptyset__Cong: $o ).
% 2.37/1.46
% 2.37/1.46 thf(emptyset__Cong,definition,
% 2.37/1.46 ( emptyset__Cong
% 2.37/1.46 = ( emptyset = emptyset ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(setadjoin__Cong_type,type,
% 2.37/1.46 setadjoin__Cong: $o ).
% 2.37/1.46
% 2.37/1.46 thf(setadjoin__Cong,definition,
% 2.37/1.46 ( setadjoin__Cong
% 2.37/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.37/1.46 ( ( Xx = Xy )
% 2.37/1.46 => ! [Xz: $i,Xu: $i] :
% 2.37/1.46 ( ( Xz = Xu )
% 2.37/1.46 => ( ( setadjoin @ Xx @ Xz )
% 2.37/1.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(powerset__Cong_type,type,
% 2.37/1.46 powerset__Cong: $o ).
% 2.37/1.46
% 2.37/1.46 thf(powerset__Cong,definition,
% 2.37/1.46 ( powerset__Cong
% 2.37/1.46 = ( ! [A: $i,B: $i] :
% 2.37/1.46 ( ( A = B )
% 2.37/1.46 => ( ( powerset @ A )
% 2.37/1.46 = ( powerset @ B ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(setunion__Cong_type,type,
% 2.37/1.46 setunion__Cong: $o ).
% 2.37/1.46
% 2.37/1.46 thf(setunion__Cong,definition,
% 2.37/1.46 ( setunion__Cong
% 2.37/1.46 = ( ! [A: $i,B: $i] :
% 2.37/1.46 ( ( A = B )
% 2.37/1.46 => ( ( setunion @ A )
% 2.37/1.46 = ( setunion @ B ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(omega__Cong_type,type,
% 2.37/1.46 omega__Cong: $o ).
% 2.37/1.46
% 2.37/1.46 thf(omega__Cong,definition,
% 2.37/1.46 ( omega__Cong
% 2.37/1.46 = ( omega = omega ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(exuEu_type,type,
% 2.37/1.46 exuEu: $o ).
% 2.37/1.46
% 2.37/1.46 thf(exuEu,definition,
% 2.37/1.46 ( exuEu
% 2.37/1.46 = ( ! [Xphi: $i > $o] :
% 2.37/1.46 ( ( exu
% 2.37/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.37/1.46 => ! [Xx: $i,Xy: $i] :
% 2.37/1.46 ( ( Xphi @ Xx )
% 2.37/1.46 => ( ( Xphi @ Xy )
% 2.37/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(descr__Cong_type,type,
% 2.37/1.46 descr__Cong: $o ).
% 2.37/1.46
% 2.37/1.46 thf(descr__Cong,definition,
% 2.37/1.46 ( descr__Cong
% 2.37/1.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.37/1.46 ( ! [Xx: $i,Xy: $i] :
% 2.37/1.46 ( ( Xx = Xy )
% 2.37/1.46 => ( ( Xphi @ Xx )
% 2.37/1.46 <=> ( Xpsi @ Xy ) ) )
% 2.37/1.46 => ( ( exu
% 2.37/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.37/1.46 => ( ( exu
% 2.37/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.37/1.46 => ( ( descr
% 2.37/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.37/1.46 = ( descr
% 2.37/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(dsetconstr__Cong_type,type,
% 2.37/1.46 dsetconstr__Cong: $o ).
% 2.37/1.46
% 2.37/1.46 thf(dsetconstr__Cong,definition,
% 2.37/1.46 ( dsetconstr__Cong
% 2.37/1.46 = ( ! [A: $i,B: $i] :
% 2.37/1.46 ( ( A = B )
% 2.37/1.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.37/1.46 ( ! [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 => ! [Xy: $i] :
% 2.37/1.46 ( ( in @ Xy @ B )
% 2.37/1.46 => ( ( Xx = Xy )
% 2.37/1.46 => ( ( Xphi @ Xx )
% 2.37/1.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.37/1.46 => ( ( dsetconstr @ A
% 2.37/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.37/1.46 = ( dsetconstr @ B
% 2.37/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(subset_type,type,
% 2.37/1.46 subset: $i > $i > $o ).
% 2.37/1.46
% 2.37/1.46 thf(disjoint_type,type,
% 2.37/1.46 disjoint: $i > $i > $o ).
% 2.37/1.46
% 2.37/1.46 thf(setsmeet_type,type,
% 2.37/1.46 setsmeet: $i > $i > $o ).
% 2.37/1.46
% 2.37/1.46 thf(subsetI1_type,type,
% 2.37/1.46 subsetI1: $o ).
% 2.37/1.46
% 2.37/1.46 thf(subsetI1,definition,
% 2.37/1.46 ( subsetI1
% 2.37/1.46 = ( ! [A: $i,B: $i] :
% 2.37/1.46 ( ! [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 => ( in @ Xx @ B ) )
% 2.37/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(eqimpsubset2_type,type,
% 2.37/1.46 eqimpsubset2: $o ).
% 2.37/1.46
% 2.37/1.46 thf(eqimpsubset2,definition,
% 2.37/1.46 ( eqimpsubset2
% 2.37/1.46 = ( ! [A: $i,B: $i] :
% 2.37/1.46 ( ( A = B )
% 2.37/1.46 => ( subset @ B @ A ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(eqimpsubset1_type,type,
% 2.37/1.46 eqimpsubset1: $o ).
% 2.37/1.46
% 2.37/1.46 thf(eqimpsubset1,definition,
% 2.37/1.46 ( eqimpsubset1
% 2.37/1.46 = ( ! [A: $i,B: $i] :
% 2.37/1.46 ( ( A = B )
% 2.37/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(subsetI2_type,type,
% 2.37/1.46 subsetI2: $o ).
% 2.37/1.46
% 2.37/1.46 thf(subsetI2,definition,
% 2.37/1.46 ( subsetI2
% 2.37/1.46 = ( ! [A: $i,B: $i] :
% 2.37/1.46 ( ! [Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 => ( in @ Xx @ B ) )
% 2.37/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(emptysetsubset_type,type,
% 2.37/1.46 emptysetsubset: $o ).
% 2.37/1.46
% 2.37/1.46 thf(emptysetsubset,definition,
% 2.37/1.46 ( emptysetsubset
% 2.37/1.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(subsetE_type,type,
% 2.37/1.46 subsetE: $o ).
% 2.37/1.46
% 2.37/1.46 thf(subsetE,definition,
% 2.37/1.46 ( subsetE
% 2.37/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.37/1.46 ( ( subset @ A @ B )
% 2.37/1.46 => ( ( in @ Xx @ A )
% 2.37/1.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(subsetE2_type,type,
% 2.37/1.46 subsetE2: $o ).
% 2.37/1.46
% 2.37/1.46 thf(subsetE2,definition,
% 2.37/1.46 ( subsetE2
% 2.37/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.37/1.46 ( ( subset @ A @ B )
% 2.37/1.46 => ( ~ ( in @ Xx @ B )
% 2.37/1.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(notsubsetI_type,type,
% 2.37/1.46 notsubsetI: $o ).
% 2.37/1.46
% 2.37/1.46 thf(notsubsetI,definition,
% 2.37/1.46 ( notsubsetI
% 2.37/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 => ( ~ ( in @ Xx @ B )
% 2.37/1.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(notequalI1_type,type,
% 2.37/1.46 notequalI1: $o ).
% 2.37/1.46
% 2.37/1.46 thf(notequalI1,definition,
% 2.37/1.46 ( notequalI1
% 2.37/1.46 = ( ! [A: $i,B: $i] :
% 2.37/1.46 ( ~ ( subset @ A @ B )
% 2.37/1.46 => ( A != B ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(notequalI2_type,type,
% 2.37/1.46 notequalI2: $o ).
% 2.37/1.46
% 2.37/1.46 thf(notequalI2,definition,
% 2.37/1.46 ( notequalI2
% 2.37/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.37/1.46 ( ( in @ Xx @ A )
% 2.37/1.46 => ( ~ ( in @ Xx @ B )
% 2.37/1.46 => ( A != B ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(subsetRefl_type,type,
% 2.37/1.46 subsetRefl: $o ).
% 2.37/1.46
% 2.37/1.46 thf(subsetRefl,definition,
% 2.37/1.46 ( subsetRefl
% 2.37/1.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(subsetTrans_type,type,
% 2.37/1.46 subsetTrans: $o ).
% 2.37/1.46
% 2.37/1.46 thf(subsetTrans,definition,
% 2.37/1.46 ( subsetTrans
% 2.37/1.46 = ( ! [A: $i,B: $i,C: $i] :
% 2.37/1.46 ( ( subset @ A @ B )
% 2.37/1.46 => ( ( subset @ B @ C )
% 2.37/1.46 => ( subset @ A @ C ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(setadjoinSub_type,type,
% 2.37/1.46 setadjoinSub: $o ).
% 2.37/1.46
% 2.37/1.46 thf(setadjoinSub,definition,
% 2.37/1.46 ( setadjoinSub
% 2.37/1.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(setadjoinSub2_type,type,
% 2.37/1.46 setadjoinSub2: $o ).
% 2.37/1.46
% 2.37/1.46 thf(setadjoinSub2,definition,
% 2.37/1.46 ( setadjoinSub2
% 2.37/1.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.37/1.46 ( ( subset @ A @ B )
% 2.37/1.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.37/1.46
% 2.37/1.46 thf(subset2powerset,conjecture,
% 2.37/1.46 ( setextAx
% 2.37/1.46 => ( emptysetAx
% 2.37/1.46 => ( setadjoinAx
% 2.37/1.46 => ( powersetAx
% 2.37/1.46 => ( setunionAx
% 2.37/1.46 => ( omega0Ax
% 2.37/1.46 => ( omegaSAx
% 2.37/1.46 => ( omegaIndAx
% 2.37/1.46 => ( replAx
% 2.37/1.46 => ( foundationAx
% 2.37/1.46 => ( wellorderingAx
% 2.37/1.46 => ( descrp
% 2.37/1.46 => ( dsetconstrI
% 2.37/1.46 => ( dsetconstrEL
% 2.37/1.46 => ( dsetconstrER
% 2.37/1.46 => ( exuE1
% 2.37/1.46 => ( prop2setE
% 2.37/1.46 => ( emptysetE
% 2.37/1.46 => ( emptysetimpfalse
% 2.37/1.46 => ( notinemptyset
% 2.37/1.46 => ( exuE3e
% 2.37/1.46 => ( setext
% 2.37/1.46 => ( emptyI
% 2.37/1.46 => ( noeltsimpempty
% 2.37/1.46 => ( setbeta
% 2.37/1.46 => ( nonemptyE1
% 2.37/1.46 => ( nonemptyI
% 2.37/1.46 => ( nonemptyI1
% 2.37/1.46 => ( setadjoinIL
% 2.37/1.46 => ( emptyinunitempty
% 2.37/1.46 => ( setadjoinIR
% 2.37/1.46 => ( setadjoinE
% 2.37/1.46 => ( setadjoinOr
% 2.37/1.46 => ( setoftrueEq
% 2.37/1.46 => ( powersetI
% 2.37/1.46 => ( emptyinPowerset
% 2.37/1.46 => ( emptyInPowerset
% 2.37/1.46 => ( powersetE
% 2.37/1.46 => ( setunionI
% 2.37/1.46 => ( setunionE
% 2.37/1.46 => ( subPowSU
% 2.37/1.46 => ( exuE2
% 2.37/1.46 => ( nonemptyImpWitness
% 2.37/1.46 => ( uniqinunit
% 2.37/1.46 => ( notinsingleton
% 2.37/1.46 => ( eqinunit
% 2.37/1.46 => ( singletonsswitch
% 2.37/1.46 => ( upairsetE
% 2.37/1.46 => ( upairsetIL
% 2.37/1.46 => ( upairsetIR
% 2.37/1.46 => ( emptyE1
% 2.37/1.46 => ( vacuousDall
% 2.37/1.46 => ( quantDeMorgan1
% 2.37/1.46 => ( quantDeMorgan2
% 2.37/1.46 => ( quantDeMorgan3
% 2.37/1.46 => ( quantDeMorgan4
% 2.37/1.46 => ( prop2setI
% 2.37/1.46 => ( prop2set2propI
% 2.37/1.46 => ( notdexE
% 2.37/1.46 => ( notdallE
% 2.37/1.46 => ( exuI1
% 2.37/1.46 => ( exuI3
% 2.37/1.46 => ( exuI2
% 2.37/1.46 => ( inCongP
% 2.37/1.46 => ( in__Cong
% 2.37/1.46 => ( exuE3u
% 2.37/1.46 => ( exu__Cong
% 2.37/1.46 => ( emptyset__Cong
% 2.37/1.46 => ( setadjoin__Cong
% 2.37/1.46 => ( powerset__Cong
% 2.37/1.46 => ( setunion__Cong
% 2.37/1.46 => ( omega__Cong
% 2.37/1.46 => ( exuEu
% 2.37/1.46 => ( descr__Cong
% 2.37/1.46 => ( dsetconstr__Cong
% 2.37/1.46 => ( subsetI1
% 2.37/1.46 => ( eqimpsubset2
% 2.37/1.46 => ( eqimpsubset1
% 2.37/1.46 => ( subsetI2
% 2.37/1.46 => ( emptysetsubset
% 2.37/1.46 => ( subsetE
% 2.37/1.46 => ( subsetE2
% 2.37/1.46 => ( notsubsetI
% 2.37/1.46 => ( notequalI1
% 2.37/1.46 => ( notequalI2
% 2.37/1.46 => ( subsetRefl
% 2.37/1.46 => ( subsetTrans
% 2.37/1.46 => ( setadjoinSub
% 2.37/1.46 => ( setadjoinSub2
% 2.37/1.46 => ! [A: $i,B: $i] :
% 2.37/1.46 ( ( subset @ A @ B )
% 2.37/1.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.37/1.46 ------------------------
% 2.37/1.47 % (2099)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_1757 for (2999ds/27Mi)
% 2.37/1.47 % (2100)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/2Mi)
% 2.37/1.47 % (2103)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/18Mi)
% 2.37/1.48 % (2100)Instruction limit reached!
% 2.37/1.48 % (2100)------------------------------
% 2.37/1.48 % (2100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.48 % (2100)Termination reason: Unknown
% 2.37/1.48 % (2100)Termination phase: shuffling
% 2.37/1.48
% 2.37/1.48 % (2100)Memory used [KB]: 1151
% 2.37/1.48 % (2100)Time elapsed: 0.002 s
% 2.37/1.48 % (2100)Instructions burned: 3 (million)
% 2.37/1.48 % (2100)------------------------------
% 2.37/1.48 % (2100)------------------------------
% 2.37/1.48 % (2103)Instruction limit reached!
% 2.37/1.48 % (2103)------------------------------
% 2.37/1.48 % (2103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.48 % (2103)Termination reason: Unknown
% 2.37/1.48 % (2103)Termination phase: Preprocessing 3
% 2.37/1.48
% 2.37/1.48 % (2103)Memory used [KB]: 1535
% 2.37/1.48 % (2103)Time elapsed: 0.007 s
% 2.37/1.48 % (2103)Instructions burned: 18 (million)
% 2.37/1.48 % (2103)------------------------------
% 2.37/1.48 % (2103)------------------------------
% 2.37/1.48 % (2099)Instruction limit reached!
% 2.37/1.48 % (2099)------------------------------
% 2.37/1.48 % (2099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.48 % (2099)Termination reason: Unknown
% 2.37/1.48 % (2099)Termination phase: Property scanning
% 2.37/1.48
% 2.37/1.48 % (2099)Memory used [KB]: 1407
% 2.37/1.48 % (2099)Time elapsed: 0.009 s
% 2.37/1.48 % (2099)Instructions burned: 29 (million)
% 2.37/1.48 % (2099)------------------------------
% 2.37/1.48 % (2099)------------------------------
% 2.37/1.48 % (2097)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/183Mi)
% 2.37/1.48 % (2098)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_1757 for (2999ds/4Mi)
% 2.37/1.48 % (2101)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_1757 for (2999ds/2Mi)
% 2.37/1.48 % (2102)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_1757 for (2999ds/275Mi)
% 2.37/1.48 % (2101)Instruction limit reached!
% 2.37/1.48 % (2101)------------------------------
% 2.37/1.48 % (2101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.48 % (2101)Termination reason: Unknown
% 2.37/1.48 % (2101)Termination phase: shuffling
% 2.37/1.48
% 2.37/1.48 % (2101)Memory used [KB]: 1151
% 2.37/1.48 % (2101)Time elapsed: 0.003 s
% 2.37/1.48 % (2101)Instructions burned: 2 (million)
% 2.37/1.48 % (2101)------------------------------
% 2.37/1.48 % (2101)------------------------------
% 2.37/1.48 % (2098)Instruction limit reached!
% 2.37/1.48 % (2098)------------------------------
% 2.37/1.48 % (2098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.48 % (2098)Termination reason: Unknown
% 2.37/1.48 % (2098)Termination phase: shuffling
% 2.37/1.48
% 2.37/1.48 % (2098)Memory used [KB]: 1151
% 2.37/1.48 % (2098)Time elapsed: 0.005 s
% 2.37/1.48 % (2098)Instructions burned: 5 (million)
% 2.37/1.48 % (2098)------------------------------
% 2.37/1.48 % (2098)------------------------------
% 2.37/1.49 % (2104)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/3Mi)
% 2.37/1.49 % (2104)Instruction limit reached!
% 2.37/1.49 % (2104)------------------------------
% 2.37/1.49 % (2104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.49 % (2104)Termination reason: Unknown
% 2.37/1.49 % (2104)Termination phase: shuffling
% 2.37/1.49
% 2.37/1.49 % (2104)Memory used [KB]: 1151
% 2.37/1.49 % (2104)Time elapsed: 0.003 s
% 2.37/1.49 % (2104)Instructions burned: 4 (million)
% 2.37/1.49 % (2104)------------------------------
% 2.37/1.49 % (2104)------------------------------
% 2.37/1.49 % (2106)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_1757 for (2999ds/15Mi)
% 2.37/1.49 % (2105)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_1757 for (2999ds/37Mi)
% 2.37/1.50 % (2106)Instruction limit reached!
% 2.37/1.50 % (2106)------------------------------
% 2.37/1.50 % (2106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.50 % (2106)Termination reason: Unknown
% 2.37/1.50 % (2106)Termination phase: Preprocessing 3
% 2.37/1.50
% 2.37/1.50 % (2106)Memory used [KB]: 1535
% 2.37/1.50 % (2106)Time elapsed: 0.006 s
% 2.37/1.50 % (2106)Instructions burned: 16 (million)
% 2.37/1.50 % (2106)------------------------------
% 2.37/1.50 % (2106)------------------------------
% 2.47/1.50 % (2109)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/7Mi)
% 2.47/1.50 % (2109)Instruction limit reached!
% 2.47/1.50 % (2109)------------------------------
% 2.47/1.50 % (2109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.50 % (2109)Termination reason: Unknown
% 2.47/1.50 % (2109)Termination phase: shuffling
% 2.47/1.50
% 2.47/1.50 % (2109)Memory used [KB]: 1279
% 2.47/1.50 % (2109)Time elapsed: 0.004 s
% 2.47/1.50 % (2109)Instructions burned: 8 (million)
% 2.47/1.50 % (2109)------------------------------
% 2.47/1.50 % (2109)------------------------------
% 2.47/1.50 % (2107)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_1757 for (2999ds/3Mi)
% 2.47/1.50 % (2105)Instruction limit reached!
% 2.47/1.50 % (2105)------------------------------
% 2.47/1.50 % (2105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.50 % (2105)Termination reason: Unknown
% 2.47/1.50 % (2105)Termination phase: Property scanning
% 2.47/1.50
% 2.47/1.50 % (2105)Memory used [KB]: 1535
% 2.47/1.50 % (2105)Time elapsed: 0.012 s
% 2.47/1.50 % (2105)Instructions burned: 38 (million)
% 2.47/1.50 % (2105)------------------------------
% 2.47/1.50 % (2105)------------------------------
% 2.47/1.50 % (2108)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_1757 for (2999ds/1041Mi)
% 2.47/1.50 % (2107)Instruction limit reached!
% 2.47/1.50 % (2107)------------------------------
% 2.47/1.50 % (2107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.50 % (2107)Termination reason: Unknown
% 2.47/1.50 % (2107)Termination phase: shuffling
% 2.47/1.50
% 2.47/1.50 % (2107)Memory used [KB]: 1151
% 2.47/1.50 % (2107)Time elapsed: 0.004 s
% 2.47/1.50 % (2107)Instructions burned: 4 (million)
% 2.47/1.50 % (2107)------------------------------
% 2.47/1.50 % (2107)------------------------------
% 2.47/1.51 % (2110)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/16Mi)
% 2.47/1.51 % (2111)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_1757 for (2999ds/3Mi)
% 2.47/1.51 % (2110)Instruction limit reached!
% 2.47/1.51 % (2110)------------------------------
% 2.47/1.51 % (2110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.51 % (2110)Termination reason: Unknown
% 2.47/1.51 % (2110)Termination phase: Property scanning
% 2.47/1.51
% 2.47/1.51 % (2110)Memory used [KB]: 1407
% 2.47/1.51 % (2110)Time elapsed: 0.006 s
% 2.47/1.51 % (2110)Instructions burned: 19 (million)
% 2.47/1.51 % (2110)------------------------------
% 2.47/1.51 % (2110)------------------------------
% 2.47/1.51 % (2111)Instruction limit reached!
% 2.47/1.51 % (2111)------------------------------
% 2.47/1.51 % (2111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.51 % (2111)Termination reason: Unknown
% 2.47/1.51 % (2111)Termination phase: shuffling
% 2.47/1.51
% 2.47/1.51 % (2111)Memory used [KB]: 1151
% 2.47/1.51 % (2111)Time elapsed: 0.003 s
% 2.47/1.51 % (2111)Instructions burned: 4 (million)
% 2.47/1.51 % (2111)------------------------------
% 2.47/1.51 % (2111)------------------------------
% 2.47/1.51 % (2112)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_1757 for (2999ds/3Mi)
% 2.47/1.51 % (2112)Instruction limit reached!
% 2.47/1.51 % (2112)------------------------------
% 2.47/1.51 % (2112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.51 % (2112)Termination reason: Unknown
% 2.47/1.51 % (2112)Termination phase: shuffling
% 2.47/1.51
% 2.47/1.51 % (2112)Memory used [KB]: 1151
% 2.47/1.51 % (2112)Time elapsed: 0.003 s
% 2.47/1.51 % (2112)Instructions burned: 4 (million)
% 2.47/1.51 % (2112)------------------------------
% 2.47/1.51 % (2112)------------------------------
% 2.47/1.52 % (2114)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/3Mi)
% 2.47/1.52 % (2113)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/7Mi)
% 2.47/1.52 % (2114)Instruction limit reached!
% 2.47/1.52 % (2114)------------------------------
% 2.47/1.52 % (2114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.52 % (2114)Termination reason: Unknown
% 2.47/1.52 % (2114)Termination phase: shuffling
% 2.47/1.52
% 2.47/1.52 % (2114)Memory used [KB]: 1151
% 2.47/1.52 % (2114)Time elapsed: 0.002 s
% 2.47/1.52 % (2114)Instructions burned: 4 (million)
% 2.47/1.52 % (2114)------------------------------
% 2.47/1.52 % (2114)------------------------------
% 2.47/1.52 % (2115)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/4Mi)
% 2.47/1.52 % (2115)Instruction limit reached!
% 2.47/1.52 % (2115)------------------------------
% 2.47/1.52 % (2115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.52 % (2115)Termination reason: Unknown
% 2.47/1.52 % (2115)Termination phase: shuffling
% 2.47/1.52
% 2.47/1.52 % (2115)Memory used [KB]: 1151
% 2.47/1.52 % (2115)Time elapsed: 0.003 s
% 2.47/1.52 % (2115)Instructions burned: 4 (million)
% 2.47/1.52 % (2115)------------------------------
% 2.47/1.52 % (2115)------------------------------
% 2.47/1.52 % (2116)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/18Mi)
% 2.47/1.52 % (2113)Instruction limit reached!
% 2.47/1.52 % (2113)------------------------------
% 2.47/1.52 % (2113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.52 % (2113)Termination reason: Unknown
% 2.47/1.52 % (2113)Termination phase: shuffling
% 2.47/1.52
% 2.47/1.52 % (2113)Memory used [KB]: 1279
% 2.47/1.52 % (2113)Time elapsed: 0.006 s
% 2.47/1.52 % (2113)Instructions burned: 8 (million)
% 2.47/1.52 % (2113)------------------------------
% 2.47/1.52 % (2113)------------------------------
% 2.47/1.53 % (2116)Instruction limit reached!
% 2.47/1.53 % (2116)------------------------------
% 2.47/1.53 % (2116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.53 % (2116)Termination reason: Unknown
% 2.47/1.53 % (2116)Termination phase: Property scanning
% 2.47/1.53
% 2.47/1.53 % (2116)Memory used [KB]: 1407
% 2.47/1.53 % (2116)Time elapsed: 0.007 s
% 2.47/1.53 % (2116)Instructions burned: 19 (million)
% 2.47/1.53 % (2116)------------------------------
% 2.47/1.53 % (2116)------------------------------
% 2.47/1.53 % (2117)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/710Mi)
% 2.47/1.53 % (2118)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/6Mi)
% 2.47/1.53 % (2118)Instruction limit reached!
% 2.47/1.53 % (2118)------------------------------
% 2.47/1.53 % (2118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.53 % (2118)Termination reason: Unknown
% 2.47/1.53 % (2118)Termination phase: shuffling
% 2.47/1.53
% 2.47/1.53 % (2118)Memory used [KB]: 1279
% 2.47/1.53 % (2118)Time elapsed: 0.004 s
% 2.47/1.53 % (2118)Instructions burned: 8 (million)
% 2.47/1.53 % (2118)------------------------------
% 2.47/1.53 % (2118)------------------------------
% 2.47/1.54 % (2120)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_1757 for (2999ds/21Mi)
% 2.47/1.54 % (2119)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_1757 for (2999ds/902Mi)
% 2.47/1.54 % (2120)Instruction limit reached!
% 2.47/1.54 % (2120)------------------------------
% 2.47/1.54 % (2120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.54 % (2120)Termination reason: Unknown
% 2.47/1.54 % (2120)Termination phase: Property scanning
% 2.47/1.54
% 2.47/1.54 % (2120)Memory used [KB]: 1407
% 2.47/1.54 % (2120)Time elapsed: 0.007 s
% 2.47/1.54 % (2120)Instructions burned: 21 (million)
% 2.47/1.54 % (2120)------------------------------
% 2.47/1.54 % (2120)------------------------------
% 2.47/1.54 % (2121)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/5Mi)
% 2.47/1.55 % (2121)Instruction limit reached!
% 2.47/1.55 % (2121)------------------------------
% 2.47/1.55 % (2121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.55 % (2121)Termination reason: Unknown
% 2.47/1.55 % (2121)Termination phase: shuffling
% 2.47/1.55
% 2.47/1.55 % (2121)Memory used [KB]: 1151
% 2.47/1.55 % (2121)Time elapsed: 0.003 s
% 2.47/1.55 % (2121)Instructions burned: 5 (million)
% 2.47/1.55 % (2121)------------------------------
% 2.47/1.55 % (2121)------------------------------
% 2.47/1.55 % (2122)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_1757 for (2999ds/6Mi)
% 2.47/1.55 % (2122)Instruction limit reached!
% 2.47/1.55 % (2122)------------------------------
% 2.47/1.55 % (2122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.55 % (2122)Termination reason: Unknown
% 2.47/1.55 % (2122)Termination phase: shuffling
% 2.47/1.55
% 2.47/1.55 % (2122)Memory used [KB]: 1279
% 2.47/1.55 % (2122)Time elapsed: 0.003 s
% 2.47/1.55 % (2122)Instructions burned: 7 (million)
% 2.47/1.55 % (2122)------------------------------
% 2.47/1.55 % (2122)------------------------------
% 2.47/1.56 % (2123)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_1757 for (2999ds/377Mi)
% 2.47/1.56 % (2097)Instruction limit reached!
% 2.47/1.56 % (2097)------------------------------
% 2.47/1.56 % (2097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.56 % (2097)Termination reason: Unknown
% 2.47/1.56 % (2097)Termination phase: Saturation
% 2.47/1.56
% 2.47/1.56 % (2097)Memory used [KB]: 6908
% 2.47/1.56 % (2097)Time elapsed: 0.077 s
% 2.47/1.56 % (2097)Instructions burned: 185 (million)
% 2.47/1.56 % (2097)------------------------------
% 2.47/1.56 % (2097)------------------------------
% 2.47/1.56 % (2124)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_1757 for (2998ds/779Mi)
% 2.47/1.57 % (2125)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_1757 for (2998ds/19Mi)
% 2.47/1.57 % (2125)Instruction limit reached!
% 2.47/1.57 % (2125)------------------------------
% 2.47/1.57 % (2125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.57 % (2125)Termination reason: Unknown
% 2.47/1.57 % (2125)Termination phase: Property scanning
% 2.47/1.57
% 2.47/1.57 % (2125)Memory used [KB]: 1407
% 2.47/1.57 % (2125)Time elapsed: 0.007 s
% 2.47/1.57 % (2125)Instructions burned: 19 (million)
% 2.47/1.57 % (2125)------------------------------
% 2.47/1.57 % (2125)------------------------------
% 2.47/1.58 % (2127)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_1757 for (2998ds/879Mi)
% 2.47/1.60 % (2102)Instruction limit reached!
% 2.47/1.60 % (2102)------------------------------
% 2.47/1.60 % (2102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.60 % (2102)Termination reason: Unknown
% 2.47/1.60 % (2102)Termination phase: Saturation
% 2.47/1.60
% 2.47/1.60 % (2102)Memory used [KB]: 7419
% 2.47/1.60 % (2102)Time elapsed: 0.125 s
% 2.47/1.60 % (2102)Instructions burned: 277 (million)
% 2.47/1.60 % (2102)------------------------------
% 2.47/1.60 % (2102)------------------------------
% 2.47/1.62 % (2128)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_1757 for (2998ds/17Mi)
% 2.47/1.62 % (2128)Instruction limit reached!
% 2.47/1.62 % (2128)------------------------------
% 2.47/1.62 % (2128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.62 % (2128)Termination reason: Unknown
% 2.47/1.62 % (2128)Termination phase: Property scanning
% 2.47/1.62
% 2.47/1.62 % (2128)Memory used [KB]: 1407
% 2.47/1.62 % (2128)Time elapsed: 0.007 s
% 2.47/1.62 % (2128)Instructions burned: 18 (million)
% 2.47/1.62 % (2128)------------------------------
% 2.47/1.62 % (2128)------------------------------
% 2.47/1.63 % (2129)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1757 for (2998ds/3Mi)
% 2.47/1.63 % (2129)Instruction limit reached!
% 2.47/1.63 % (2129)------------------------------
% 2.47/1.63 % (2129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.63 % (2129)Termination reason: Unknown
% 2.47/1.63 % (2129)Termination phase: shuffling
% 2.47/1.63
% 2.47/1.63 % (2129)Memory used [KB]: 1279
% 2.47/1.63 % (2129)Time elapsed: 0.003 s
% 2.47/1.63 % (2129)Instructions burned: 5 (million)
% 2.47/1.63 % (2129)------------------------------
% 2.47/1.63 % (2129)------------------------------
% 2.47/1.64 % (2130)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_1757 for (2998ds/30Mi)
% 2.47/1.65 % (2130)Instruction limit reached!
% 2.47/1.65 % (2130)------------------------------
% 2.47/1.65 % (2130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.65 % (2130)Termination reason: Unknown
% 2.47/1.65 % (2130)Termination phase: Property scanning
% 2.47/1.65
% 2.47/1.65 % (2130)Memory used [KB]: 1407
% 2.47/1.65 % (2130)Time elapsed: 0.010 s
% 2.47/1.65 % (2130)Instructions burned: 30 (million)
% 2.47/1.65 % (2130)------------------------------
% 2.47/1.65 % (2130)------------------------------
% 2.47/1.66 % (2131)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_1757 for (2998ds/127Mi)
% 2.47/1.67 % (2123)Refutation not found, non-redundant clauses discarded% (2123)------------------------------
% 2.47/1.67 % (2123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.67 % (2123)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.47/1.67
% 2.47/1.67 % (2123)Memory used [KB]: 7036
% 2.47/1.67 % (2123)Time elapsed: 0.111 s
% 2.47/1.67 % (2123)Instructions burned: 362 (million)
% 2.47/1.67 % (2123)------------------------------
% 2.47/1.67 % (2123)------------------------------
% 2.47/1.68 % (2132)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_1757 for (2997ds/100Mi)
% 2.47/1.70 % (2131)Instruction limit reached!
% 2.47/1.70 % (2131)------------------------------
% 2.47/1.70 % (2131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.70 % (2131)Termination reason: Unknown
% 2.47/1.70 % (2131)Termination phase: Saturation
% 2.47/1.70
% 2.47/1.70 % (2131)Memory used [KB]: 6652
% 2.47/1.70 % (2131)Time elapsed: 0.041 s
% 2.47/1.70 % (2131)Instructions burned: 128 (million)
% 2.47/1.70 % (2131)------------------------------
% 2.47/1.70 % (2131)------------------------------
% 2.47/1.70 % (2132)Instruction limit reached!
% 2.47/1.70 % (2132)------------------------------
% 2.47/1.70 % (2132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.70 % (2132)Termination reason: Unknown
% 2.47/1.70 % (2132)Termination phase: Saturation
% 2.47/1.70
% 2.47/1.70 % (2132)Memory used [KB]: 6268
% 2.47/1.70 % (2132)Time elapsed: 0.029 s
% 2.47/1.70 % (2132)Instructions burned: 100 (million)
% 2.47/1.70 % (2132)------------------------------
% 2.47/1.70 % (2132)------------------------------
% 2.47/1.71 % (2133)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_1757 for (2997ds/3Mi)
% 2.47/1.71 % (2133)Instruction limit reached!
% 2.47/1.71 % (2133)------------------------------
% 2.47/1.71 % (2133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.71 % (2133)Termination reason: Unknown
% 2.47/1.71 % (2133)Termination phase: shuffling
% 2.47/1.71
% 2.47/1.71 % (2133)Memory used [KB]: 1151
% 2.47/1.71 % (2133)Time elapsed: 0.003 s
% 2.47/1.71 % (2133)Instructions burned: 5 (million)
% 2.47/1.71 % (2133)------------------------------
% 2.47/1.71 % (2133)------------------------------
% 2.47/1.71 % (2134)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_1757 for (2997ds/20Mi)
% 2.47/1.72 % (2134)Instruction limit reached!
% 2.47/1.72 % (2134)------------------------------
% 2.47/1.72 % (2134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.72 % (2134)Termination reason: Unknown
% 2.47/1.72 % (2134)Termination phase: Preprocessing 3
% 2.47/1.72
% 2.47/1.72 % (2134)Memory used [KB]: 1407
% 2.47/1.72 % (2134)Time elapsed: 0.007 s
% 2.47/1.72 % (2134)Instructions burned: 20 (million)
% 2.47/1.72 % (2134)------------------------------
% 2.47/1.72 % (2134)------------------------------
% 2.47/1.72 % (2135)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_1757 for (2997ds/86Mi)
% 2.47/1.73 % (2136)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_1757 for (2997ds/107Mi)
% 2.47/1.75 % (2135)Instruction limit reached!
% 2.47/1.75 % (2135)------------------------------
% 2.47/1.75 % (2135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.75 % (2135)Termination reason: Unknown
% 2.47/1.75 % (2135)Termination phase: Saturation
% 2.47/1.75
% 2.47/1.75 % (2135)Memory used [KB]: 6396
% 2.47/1.75 % (2135)Time elapsed: 0.027 s
% 2.47/1.75 % (2135)Instructions burned: 88 (million)
% 2.47/1.75 % (2135)------------------------------
% 2.47/1.75 % (2135)------------------------------
% 2.47/1.75 % (2124)Instruction limit reached!
% 2.47/1.75 % (2124)------------------------------
% 2.47/1.75 % (2124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.75 % (2124)Termination reason: Unknown
% 2.47/1.75 % (2124)Termination phase: Saturation
% 2.47/1.75
% 2.47/1.75 % (2124)Memory used [KB]: 6652
% 2.47/1.75 % (2124)Time elapsed: 0.185 s
% 2.47/1.75 % (2124)Instructions burned: 780 (million)
% 2.47/1.75 % (2124)------------------------------
% 2.47/1.75 % (2124)------------------------------
% 2.47/1.75 % (2117)Instruction limit reached!
% 2.47/1.75 % (2117)------------------------------
% 2.47/1.75 % (2117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.75 % (2117)Termination reason: Unknown
% 2.47/1.75 % (2117)Termination phase: Saturation
% 2.47/1.75
% 2.47/1.75 % (2117)Memory used [KB]: 8827
% 2.47/1.75 % (2117)Time elapsed: 0.244 s
% 2.47/1.75 % (2117)Instructions burned: 710 (million)
% 2.47/1.75 % (2117)------------------------------
% 2.47/1.75 % (2117)------------------------------
% 2.47/1.76 % (2137)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_1757 for (2997ds/39Mi)
% 2.47/1.76 % (2136)Instruction limit reached!
% 2.47/1.76 % (2136)------------------------------
% 2.47/1.76 % (2136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.76 % (2136)Termination reason: Unknown
% 2.47/1.76 % (2136)Termination phase: Saturation
% 2.47/1.76
% 2.47/1.76 % (2136)Memory used [KB]: 6524
% 2.47/1.76 % (2136)Time elapsed: 0.030 s
% 2.47/1.76 % (2136)Instructions burned: 107 (million)
% 2.47/1.76 % (2136)------------------------------
% 2.47/1.76 % (2136)------------------------------
% 2.47/1.76 % (2138)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_1757 for (2997ds/448Mi)
% 2.47/1.76 % (2139)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_1757 for (2997ds/46Mi)
% 2.47/1.77 % (2140)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_1757 for (2997ds/98Mi)
% 2.47/1.77 % (2137)Instruction limit reached!
% 2.47/1.77 % (2137)------------------------------
% 2.47/1.77 % (2137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.77 % (2137)Termination reason: Unknown
% 2.47/1.77 % (2137)Termination phase: Property scanning
% 2.47/1.77
% 2.47/1.77 % (2137)Memory used [KB]: 1535
% 2.47/1.77 % (2137)Time elapsed: 0.013 s
% 2.47/1.77 % (2137)Instructions burned: 42 (million)
% 2.47/1.77 % (2137)------------------------------
% 2.47/1.77 % (2137)------------------------------
% 2.47/1.77 % (2139)Instruction limit reached!
% 2.47/1.77 % (2139)------------------------------
% 2.47/1.77 % (2139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.77 % (2139)Termination reason: Unknown
% 2.47/1.77 % (2139)Termination phase: Property scanning
% 2.47/1.77
% 2.47/1.77 % (2139)Memory used [KB]: 1535
% 2.47/1.77 % (2139)Time elapsed: 0.013 s
% 2.47/1.77 % (2139)Instructions burned: 48 (million)
% 2.47/1.77 % (2139)------------------------------
% 2.47/1.77 % (2139)------------------------------
% 2.47/1.78 % (2141)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_1757 for (2996ds/507Mi)
% 2.47/1.78 % (2142)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_1757 for (2996ds/149Mi)
% 2.47/1.79 % (2140)Instruction limit reached!
% 2.47/1.79 % (2140)------------------------------
% 2.47/1.79 % (2140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.79 % (2140)Termination reason: Unknown
% 2.47/1.79 % (2140)Termination phase: Saturation
% 2.47/1.79
% 2.47/1.79 % (2140)Memory used [KB]: 1663
% 2.47/1.79 % (2140)Time elapsed: 0.025 s
% 2.47/1.79 % (2140)Instructions burned: 98 (million)
% 2.47/1.79 % (2140)------------------------------
% 2.47/1.79 % (2140)------------------------------
% 2.47/1.79 % (2108)Instruction limit reached!
% 2.47/1.79 % (2108)------------------------------
% 2.47/1.79 % (2108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.79 % (2108)Termination reason: Unknown
% 2.47/1.79 % (2108)Termination phase: Saturation
% 2.47/1.79
% 2.47/1.79 % (2108)Memory used [KB]: 7419
% 2.47/1.79 % (2108)Time elapsed: 0.293 s
% 2.47/1.79 % (2108)Instructions burned: 1043 (million)
% 2.47/1.79 % (2108)------------------------------
% 2.47/1.79 % (2108)------------------------------
% 2.47/1.80 % (2143)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_1757 for (2996ds/39Mi)
% 2.47/1.80 % (2144)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_1757 for (2996ds/6Mi)
% 2.47/1.81 % (2144)Instruction limit reached!
% 2.47/1.81 % (2144)------------------------------
% 2.47/1.81 % (2144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.81 % (2144)Termination reason: Unknown
% 2.47/1.81 % (2144)Termination phase: shuffling
% 2.47/1.81
% 2.47/1.81 % (2144)Memory used [KB]: 1279
% 2.47/1.81 % (2144)Time elapsed: 0.004 s
% 2.47/1.81 % (2144)Instructions burned: 8 (million)
% 2.47/1.81 % (2144)------------------------------
% 2.47/1.81 % (2144)------------------------------
% 2.47/1.81 % (2143)Instruction limit reached!
% 2.47/1.81 % (2143)------------------------------
% 2.47/1.81 % (2143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.81 % (2143)Termination reason: Unknown
% 2.47/1.81 % (2143)Termination phase: Property scanning
% 2.47/1.81
% 2.47/1.81 % (2143)Memory used [KB]: 1535
% 2.47/1.81 % (2143)Time elapsed: 0.011 s
% 2.47/1.81 % (2143)Instructions burned: 40 (million)
% 2.47/1.81 % (2143)------------------------------
% 2.47/1.81 % (2143)------------------------------
% 2.47/1.82 % (2145)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_1757 for (2996ds/1087Mi)
% 2.47/1.82 % (2146)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_1757 for (2996ds/47Mi)
% 2.47/1.83 % (2142)Instruction limit reached!
% 2.47/1.83 % (2142)------------------------------
% 2.47/1.83 % (2142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.83 % (2142)Termination reason: Unknown
% 2.47/1.83 % (2142)Termination phase: Saturation
% 2.47/1.83
% 2.47/1.83 % (2142)Memory used [KB]: 6652
% 2.47/1.83 % (2142)Time elapsed: 0.046 s
% 2.47/1.83 % (2142)Instructions burned: 149 (million)
% 2.47/1.83 % (2142)------------------------------
% 2.47/1.83 % (2142)------------------------------
% 2.47/1.83 % (2146)Instruction limit reached!
% 2.47/1.83 % (2146)------------------------------
% 2.47/1.83 % (2146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.83 % (2146)Termination reason: Unknown
% 2.47/1.83 % (2146)Termination phase: Saturation
% 2.47/1.83
% 2.47/1.83 % (2146)Memory used [KB]: 6012
% 2.47/1.83 % (2146)Time elapsed: 0.014 s
% 2.47/1.83 % (2146)Instructions burned: 49 (million)
% 2.47/1.83 % (2146)------------------------------
% 2.47/1.83 % (2146)------------------------------
% 2.47/1.83 % (2119)Instruction limit reached!
% 2.47/1.83 % (2119)------------------------------
% 2.47/1.83 % (2119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.83 % (2119)Termination reason: Unknown
% 2.47/1.83 % (2119)Termination phase: Saturation
% 2.47/1.83
% 2.47/1.83 % (2119)Memory used [KB]: 9338
% 2.47/1.83 % (2119)Time elapsed: 0.315 s
% 2.47/1.83 % (2119)Instructions burned: 904 (million)
% 2.47/1.83 % (2119)------------------------------
% 2.47/1.83 % (2119)------------------------------
% 2.47/1.84 % (2147)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_1757 for (2996ds/44Mi)
% 2.47/1.84 % (2148)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_1757 for (2996ds/432Mi)
% 2.47/1.84 % (2149)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_1757 for (2996ds/62Mi)
% 2.47/1.85 % (2147)Instruction limit reached!
% 2.47/1.85 % (2147)------------------------------
% 2.47/1.85 % (2147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.85 % (2147)Termination reason: Unknown
% 2.47/1.85 % (2147)Termination phase: Property scanning
% 2.47/1.85
% 2.47/1.85 % (2147)Memory used [KB]: 1535
% 2.47/1.85 % (2147)Time elapsed: 0.012 s
% 2.47/1.85 % (2147)Instructions burned: 45 (million)
% 2.47/1.85 % (2147)------------------------------
% 2.47/1.85 % (2147)------------------------------
% 2.47/1.86 % (2150)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_1757 for (2996ds/31Mi)
% 2.47/1.86 % (2149)Instruction limit reached!
% 2.47/1.86 % (2149)------------------------------
% 2.47/1.86 % (2149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.86 % (2149)Termination reason: Unknown
% 2.47/1.86 % (2149)Termination phase: Saturation
% 2.47/1.86
% 2.47/1.86 % (2149)Memory used [KB]: 6012
% 2.47/1.86 % (2149)Time elapsed: 0.019 s
% 2.47/1.86 % (2149)Instructions burned: 64 (million)
% 2.47/1.86 % (2149)------------------------------
% 2.47/1.86 % (2149)------------------------------
% 2.47/1.86 % (2138)Instruction limit reached!
% 2.47/1.86 % (2138)------------------------------
% 2.47/1.86 % (2138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.86 % (2138)Termination reason: Unknown
% 2.47/1.86 % (2138)Termination phase: Saturation
% 2.47/1.86
% 2.47/1.86 % (2138)Memory used [KB]: 6140
% 2.47/1.86 % (2138)Time elapsed: 0.105 s
% 2.47/1.86 % (2138)Instructions burned: 449 (million)
% 2.47/1.86 % (2138)------------------------------
% 2.47/1.86 % (2138)------------------------------
% 2.47/1.87 % (2150)Instruction limit reached!
% 2.47/1.87 % (2150)------------------------------
% 2.47/1.87 % (2150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.87 % (2150)Termination reason: Unknown
% 2.47/1.87 % (2150)Termination phase: Function definition elimination
% 2.47/1.87
% 2.47/1.87 % (2150)Memory used [KB]: 1535
% 2.47/1.87 % (2150)Time elapsed: 0.009 s
% 2.47/1.87 % (2150)Instructions burned: 32 (million)
% 2.47/1.87 % (2150)------------------------------
% 2.47/1.87 % (2150)------------------------------
% 2.47/1.87 % (2151)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_1757 for (2996ds/96Mi)
% 2.47/1.87 % (2152)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_1757 for (2996ds/453Mi)
% 2.47/1.87 % (2127)Refutation not found, non-redundant clauses discarded% (2127)------------------------------
% 2.47/1.87 % (2127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.87 % (2127)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.47/1.87
% 2.47/1.87 % (2127)Memory used [KB]: 7419
% 2.47/1.87 % (2127)Time elapsed: 0.293 s
% 2.47/1.87 % (2127)Instructions burned: 867 (million)
% 2.47/1.87 % (2127)------------------------------
% 2.47/1.87 % (2127)------------------------------
% 2.47/1.88 % (2153)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_1757 for (2996ds/71Mi)
% 2.47/1.88 % (2154)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_1757 for (2995ds/83Mi)
% 2.47/1.89 % (2153)Instruction limit reached!
% 2.47/1.89 % (2153)------------------------------
% 2.47/1.89 % (2153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.89 % (2153)Termination reason: Unknown
% 2.47/1.89 % (2153)Termination phase: Saturation
% 2.47/1.89
% 2.47/1.89 % (2153)Memory used [KB]: 6268
% 2.47/1.89 % (2153)Time elapsed: 0.021 s
% 2.47/1.89 % (2153)Instructions burned: 73 (million)
% 2.47/1.89 % (2153)------------------------------
% 2.47/1.89 % (2153)------------------------------
% 2.47/1.90 % (2151)Instruction limit reached!
% 2.47/1.90 % (2151)------------------------------
% 2.47/1.90 % (2151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.90 % (2151)Termination reason: Unknown
% 2.47/1.90 % (2151)Termination phase: Saturation
% 2.47/1.90
% 2.47/1.90 % (2151)Memory used [KB]: 6524
% 2.47/1.90 % (2151)Time elapsed: 0.027 s
% 2.47/1.90 % (2151)Instructions burned: 97 (million)
% 2.47/1.90 % (2151)------------------------------
% 2.47/1.90 % (2151)------------------------------
% 2.47/1.90 % (2155)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_1757 for (2995ds/11Mi)
% 2.47/1.90 % (2156)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_1757 for (2995ds/41Mi)
% 2.47/1.91 % (2154)Instruction limit reached!
% 2.47/1.91 % (2154)------------------------------
% 2.47/1.91 % (2154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.91 % (2154)Termination reason: Unknown
% 2.47/1.91 % (2154)Termination phase: Saturation
% 2.47/1.91
% 2.47/1.91 % (2154)Memory used [KB]: 6268
% 2.47/1.91 % (2154)Time elapsed: 0.023 s
% 2.47/1.91 % (2154)Instructions burned: 85 (million)
% 2.47/1.91 % (2154)------------------------------
% 2.47/1.91 % (2154)------------------------------
% 2.47/1.91 % (2155)Instruction limit reached!
% 2.47/1.91 % (2155)------------------------------
% 2.47/1.91 % (2155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.91 % (2155)Termination reason: Unknown
% 2.47/1.91 % (2155)Termination phase: shuffling
% 2.47/1.91
% 2.47/1.91 % (2155)Memory used [KB]: 1407
% 2.47/1.91 % (2155)Time elapsed: 0.004 s
% 2.47/1.91 % (2155)Instructions burned: 12 (million)
% 2.47/1.91 % (2155)------------------------------
% 2.47/1.91 % (2155)------------------------------
% 2.47/1.91 % (2156)Instruction limit reached!
% 2.47/1.91 % (2156)------------------------------
% 2.47/1.91 % (2156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.91 % (2156)Termination reason: Unknown
% 2.47/1.91 % (2156)Termination phase: Property scanning
% 2.47/1.91
% 2.47/1.91 % (2156)Memory used [KB]: 1535
% 2.47/1.91 % (2156)Time elapsed: 0.011 s
% 2.47/1.91 % (2156)Instructions burned: 41 (million)
% 2.47/1.91 % (2156)------------------------------
% 2.47/1.91 % (2156)------------------------------
% 2.47/1.91 % (2157)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1757 for (2995ds/6Mi)
% 2.47/1.92 % (2158)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_1757 for (2995ds/150Mi)
% 2.47/1.92 % (2157)Instruction limit reached!
% 2.47/1.92 % (2157)------------------------------
% 2.47/1.92 % (2157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.92 % (2157)Termination reason: Unknown
% 2.47/1.92 % (2157)Termination phase: shuffling
% 2.47/1.92
% 2.47/1.92 % (2157)Memory used [KB]: 1279
% 2.47/1.92 % (2157)Time elapsed: 0.003 s
% 2.47/1.92 % (2157)Instructions burned: 8 (million)
% 2.47/1.92 % (2157)------------------------------
% 2.47/1.92 % (2157)------------------------------
% 2.47/1.92 % (2159)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_1757 for (2995ds/343Mi)
% 2.47/1.93 % (2160)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_1757 for (2995ds/109Mi)
% 2.47/1.93 % (2141)Instruction limit reached!
% 2.47/1.93 % (2141)------------------------------
% 2.47/1.93 % (2141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.93 % (2141)Termination reason: Unknown
% 2.47/1.93 % (2141)Termination phase: Saturation
% 2.47/1.93
% 2.47/1.93 % (2141)Memory used [KB]: 6780
% 2.47/1.93 % (2141)Time elapsed: 0.152 s
% 2.47/1.93 % (2141)Instructions burned: 507 (million)
% 2.47/1.93 % (2141)------------------------------
% 2.47/1.93 % (2141)------------------------------
% 2.47/1.94 % (2161)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_1757 for (2995ds/253Mi)
% 2.47/1.95 % (2148)Instruction limit reached!
% 2.47/1.95 % (2148)------------------------------
% 2.47/1.95 % (2148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.95 % (2148)Termination reason: Unknown
% 2.47/1.95 % (2148)Termination phase: Saturation
% 2.47/1.95
% 2.47/1.95 % (2148)Memory used [KB]: 2430
% 2.47/1.95 % (2148)Time elapsed: 0.107 s
% 2.47/1.95 % (2148)Instructions burned: 432 (million)
% 2.47/1.95 % (2148)------------------------------
% 2.47/1.95 % (2148)------------------------------
% 2.47/1.96 % (2160)Instruction limit reached!
% 2.47/1.96 % (2160)------------------------------
% 2.47/1.96 % (2160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.96 % (2160)Termination reason: Unknown
% 2.47/1.96 % (2160)Termination phase: Saturation
% 2.47/1.96
% 2.47/1.96 % (2160)Memory used [KB]: 6652
% 2.47/1.96 % (2160)Time elapsed: 0.031 s
% 2.47/1.96 % (2160)Instructions burned: 111 (million)
% 2.47/1.96 % (2160)------------------------------
% 2.47/1.96 % (2160)------------------------------
% 2.47/1.96 % (2162)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_1757 for (2995ds/140Mi)
% 2.47/1.96 % (2158)Instruction limit reached!
% 2.47/1.96 % (2158)------------------------------
% 2.47/1.96 % (2158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.96 % (2158)Termination reason: Unknown
% 2.47/1.96 % (2158)Termination phase: Saturation
% 2.47/1.96
% 2.47/1.96 % (2158)Memory used [KB]: 7036
% 2.47/1.96 % (2158)Time elapsed: 0.070 s
% 2.47/1.96 % (2158)Instructions burned: 150 (million)
% 2.47/1.96 % (2158)------------------------------
% 2.47/1.96 % (2158)------------------------------
% 2.47/1.97 % (2163)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_1757 for (2994ds/614Mi)
% 2.47/1.97 % (2164)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_1757 for (2994ds/202Mi)
% 2.47/1.98 % (2152)Instruction limit reached!
% 2.47/1.98 % (2152)------------------------------
% 2.47/1.98 % (2152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.98 % (2152)Termination reason: Unknown
% 2.47/1.98 % (2152)Termination phase: Saturation
% 2.47/1.98
% 2.47/1.98 % (2152)Memory used [KB]: 6140
% 2.47/1.98 % (2152)Time elapsed: 0.112 s
% 2.47/1.98 % (2152)Instructions burned: 455 (million)
% 2.47/1.98 % (2152)------------------------------
% 2.47/1.98 % (2152)------------------------------
% 2.47/1.99 % (2162)Refutation not found, incomplete strategy
% 2.47/1.99 % (2162)------------------------------
% 2.47/1.99 % (2162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.99 % (2162)Termination reason: Refutation not found, incomplete strategy
% 2.47/1.99
% 2.47/1.99
% 2.47/1.99 % (2162)Memory used [KB]: 6140
% 2.47/1.99 % (2162)Time elapsed: 0.030 s
% 2.47/1.99 % (2162)Instructions burned: 104 (million)
% 2.47/1.99 % (2162)------------------------------
% 2.47/1.99 % (2162)------------------------------
% 2.47/1.99 % (2165)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_1757 for (2994ds/339Mi)
% 2.47/2.00 % (2166)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_1757 for (2994ds/283Mi)
% 6.22/2.03 % (2159)Instruction limit reached!
% 6.22/2.03 % (2159)------------------------------
% 6.22/2.03 % (2159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.03 % (2159)Termination reason: Unknown
% 6.22/2.03 % (2159)Termination phase: Saturation
% 6.22/2.03
% 6.22/2.03 % (2159)Memory used [KB]: 7036
% 6.22/2.03 % (2159)Time elapsed: 0.128 s
% 6.22/2.03 % (2159)Instructions burned: 343 (million)
% 6.22/2.03 % (2159)------------------------------
% 6.22/2.03 % (2159)------------------------------
% 6.22/2.03 % (2161)Instruction limit reached!
% 6.22/2.03 % (2161)------------------------------
% 6.22/2.03 % (2161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.03 % (2161)Termination reason: Unknown
% 6.22/2.03 % (2161)Termination phase: Saturation
% 6.22/2.03
% 6.22/2.03 % (2161)Memory used [KB]: 7547
% 6.22/2.03 % (2161)Time elapsed: 0.097 s
% 6.22/2.03 % (2161)Instructions burned: 253 (million)
% 6.22/2.03 % (2161)------------------------------
% 6.22/2.03 % (2161)------------------------------
% 6.22/2.04 % (2164)Instruction limit reached!
% 6.22/2.04 % (2164)------------------------------
% 6.22/2.04 % (2164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.04 % (2164)Termination reason: Unknown
% 6.22/2.04 % (2164)Termination phase: Saturation
% 6.22/2.04
% 6.22/2.04 % (2164)Memory used [KB]: 7419
% 6.22/2.04 % (2164)Time elapsed: 0.064 s
% 6.22/2.04 % (2164)Instructions burned: 203 (million)
% 6.22/2.04 % (2164)------------------------------
% 6.22/2.04 % (2164)------------------------------
% 6.22/2.04 % (2167)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_1757 for (2994ds/134Mi)
% 6.22/2.04 % (2169)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_1757 for (2994ds/192Mi)
% 6.22/2.05 % (2168)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_1757 for (2994ds/298Mi)
% 6.22/2.06 % (2166)Instruction limit reached!
% 6.22/2.06 % (2166)------------------------------
% 6.22/2.06 % (2166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.06 % (2166)Termination reason: Unknown
% 6.22/2.06 % (2166)Termination phase: Saturation
% 6.22/2.06
% 6.22/2.06 % (2166)Memory used [KB]: 7675
% 6.22/2.06 % (2166)Time elapsed: 0.070 s
% 6.22/2.06 % (2166)Instructions burned: 284 (million)
% 6.22/2.06 % (2166)------------------------------
% 6.22/2.06 % (2166)------------------------------
% 6.22/2.07 % (2170)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_1757 for (2994ds/258Mi)
% 6.22/2.08 % (2167)Instruction limit reached!
% 6.22/2.08 % (2167)------------------------------
% 6.22/2.08 % (2167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.08 % (2167)Termination reason: Unknown
% 6.22/2.08 % (2167)Termination phase: Saturation
% 6.22/2.08
% 6.22/2.08 % (2167)Memory used [KB]: 6780
% 6.22/2.08 % (2167)Time elapsed: 0.039 s
% 6.22/2.08 % (2167)Instructions burned: 134 (million)
% 6.22/2.08 % (2167)------------------------------
% 6.22/2.08 % (2167)------------------------------
% 6.22/2.08 % (2171)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_1757 for (2993ds/90Mi)
% 6.22/2.09 % (2165)Instruction limit reached!
% 6.22/2.09 % (2165)------------------------------
% 6.22/2.09 % (2165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.09 % (2165)Termination reason: Unknown
% 6.22/2.09 % (2165)Termination phase: Saturation
% 6.22/2.09
% 6.22/2.09 % (2165)Memory used [KB]: 7419
% 6.22/2.09 % (2165)Time elapsed: 0.099 s
% 6.22/2.09 % (2165)Instructions burned: 339 (million)
% 6.22/2.09 % (2165)------------------------------
% 6.22/2.09 % (2165)------------------------------
% 6.22/2.10 % (2172)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_1757 for (2993ds/231Mi)
% 6.22/2.10 % (2169)Instruction limit reached!
% 6.22/2.10 % (2169)------------------------------
% 6.22/2.10 % (2169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.10 % (2169)Termination reason: Unknown
% 6.22/2.10 % (2169)Termination phase: Saturation
% 6.22/2.10
% 6.22/2.10 % (2169)Memory used [KB]: 6908
% 6.22/2.10 % (2169)Time elapsed: 0.057 s
% 6.22/2.10 % (2169)Instructions burned: 194 (million)
% 6.22/2.10 % (2169)------------------------------
% 6.22/2.10 % (2169)------------------------------
% 6.22/2.11 % (2171)Instruction limit reached!
% 6.22/2.11 % (2171)------------------------------
% 6.22/2.11 % (2171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.11 % (2171)Termination reason: Unknown
% 6.22/2.11 % (2171)Termination phase: Saturation
% 6.22/2.11
% 6.22/2.11 % (2171)Memory used [KB]: 6524
% 6.22/2.11 % (2171)Time elapsed: 0.026 s
% 6.22/2.11 % (2171)Instructions burned: 90 (million)
% 6.22/2.11 % (2171)------------------------------
% 6.22/2.11 % (2171)------------------------------
% 6.22/2.11 % (2173)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_1757 for (2993ds/458Mi)
% 6.83/2.12 % (2174)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_1757 for (2993ds/31Mi)
% 6.83/2.13 % (2174)Instruction limit reached!
% 6.83/2.13 % (2174)------------------------------
% 6.83/2.13 % (2174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.13 % (2174)Termination reason: Unknown
% 6.83/2.13 % (2174)Termination phase: Function definition elimination
% 6.83/2.13
% 6.83/2.13 % (2174)Memory used [KB]: 1535
% 6.83/2.13 % (2174)Time elapsed: 0.010 s
% 6.83/2.13 % (2174)Instructions burned: 33 (million)
% 6.83/2.13 % (2174)------------------------------
% 6.83/2.13 % (2174)------------------------------
% 6.83/2.14 % (2175)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_1757 for (2993ds/297Mi)
% 6.83/2.15 % (2170)Instruction limit reached!
% 6.83/2.15 % (2170)------------------------------
% 6.83/2.15 % (2170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.15 % (2170)Termination reason: Unknown
% 6.83/2.15 % (2170)Termination phase: Saturation
% 6.83/2.15
% 6.83/2.15 % (2170)Memory used [KB]: 6908
% 6.83/2.15 % (2170)Time elapsed: 0.078 s
% 6.83/2.15 % (2170)Instructions burned: 258 (million)
% 6.83/2.15 % (2170)------------------------------
% 6.83/2.15 % (2170)------------------------------
% 6.83/2.16 % (2163)Instruction limit reached!
% 6.83/2.16 % (2163)------------------------------
% 6.83/2.16 % (2163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.16 % (2163)Termination reason: Unknown
% 6.83/2.16 % (2163)Termination phase: Saturation
% 6.83/2.16
% 6.83/2.16 % (2163)Memory used [KB]: 7931
% 6.83/2.16 % (2163)Time elapsed: 0.191 s
% 6.83/2.16 % (2163)Instructions burned: 615 (million)
% 6.83/2.16 % (2163)------------------------------
% 6.83/2.16 % (2163)------------------------------
% 6.83/2.16 % (2176)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_1757 for (2993ds/987Mi)
% 6.83/2.16 % (2145)Instruction limit reached!
% 6.83/2.16 % (2145)------------------------------
% 6.83/2.16 % (2145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.16 % (2145)Termination reason: Unknown
% 6.83/2.16 % (2145)Termination phase: Saturation
% 6.83/2.16
% 6.83/2.16 % (2145)Memory used [KB]: 9722
% 6.83/2.16 % (2145)Time elapsed: 0.349 s
% 6.83/2.16 % (2145)Instructions burned: 1088 (million)
% 6.83/2.16 % (2145)------------------------------
% 6.83/2.16 % (2145)------------------------------
% 6.83/2.16 % (2168)Instruction limit reached!
% 6.83/2.16 % (2168)------------------------------
% 6.83/2.16 % (2168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.16 % (2168)Termination reason: Unknown
% 6.83/2.16 % (2168)Termination phase: Saturation
% 6.83/2.16
% 6.83/2.16 % (2168)Memory used [KB]: 6396
% 6.83/2.16 % (2168)Time elapsed: 0.114 s
% 6.83/2.16 % (2168)Instructions burned: 298 (million)
% 6.83/2.16 % (2168)------------------------------
% 6.83/2.16 % (2168)------------------------------
% 6.83/2.17 % (2177)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_1757 for (2993ds/182Mi)
% 6.83/2.17 % (2172)Instruction limit reached!
% 6.83/2.17 % (2172)------------------------------
% 6.83/2.17 % (2172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.17 % (2172)Termination reason: Unknown
% 6.83/2.17 % (2172)Termination phase: Saturation
% 6.83/2.17
% 6.83/2.17 % (2172)Memory used [KB]: 9338
% 6.83/2.17 % (2172)Time elapsed: 0.092 s
% 6.83/2.17 % (2172)Instructions burned: 232 (million)
% 6.83/2.17 % (2172)------------------------------
% 6.83/2.17 % (2172)------------------------------
% 6.83/2.17 % (2179)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_1757 for (2993ds/154Mi)
% 6.83/2.17 % (2178)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_1757 for (2993ds/182Mi)
% 6.83/2.18 % (2180)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_1757 for (2992ds/79Mi)
% 7.25/2.20 % (2180)Instruction limit reached!
% 7.25/2.20 % (2180)------------------------------
% 7.25/2.20 % (2180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.20 % (2180)Termination reason: Unknown
% 7.25/2.20 % (2180)Termination phase: Saturation
% 7.25/2.20
% 7.25/2.20 % (2180)Memory used [KB]: 6268
% 7.25/2.20 % (2180)Time elapsed: 0.022 s
% 7.25/2.20 % (2180)Instructions burned: 79 (million)
% 7.25/2.20 % (2180)------------------------------
% 7.25/2.20 % (2180)------------------------------
% 7.25/2.21 % (2181)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_1757 for (2992ds/216Mi)
% 7.25/2.21 % (2179)Instruction limit reached!
% 7.25/2.21 % (2179)------------------------------
% 7.25/2.21 % (2179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.21 % (2179)Termination reason: Unknown
% 7.25/2.21 % (2179)Termination phase: Saturation
% 7.25/2.21
% 7.25/2.21 % (2179)Memory used [KB]: 6140
% 7.25/2.21 % (2179)Time elapsed: 0.038 s
% 7.25/2.21 % (2179)Instructions burned: 155 (million)
% 7.25/2.21 % (2179)------------------------------
% 7.25/2.21 % (2179)------------------------------
% 7.25/2.21 % (2175)Instruction limit reached!
% 7.25/2.21 % (2175)------------------------------
% 7.25/2.21 % (2175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.21 % (2175)Termination reason: Unknown
% 7.25/2.21 % (2175)Termination phase: Saturation
% 7.25/2.21
% 7.25/2.21 % (2175)Memory used [KB]: 7036
% 7.25/2.21 % (2175)Time elapsed: 0.075 s
% 7.25/2.21 % (2175)Instructions burned: 300 (million)
% 7.25/2.21 % (2175)------------------------------
% 7.25/2.21 % (2175)------------------------------
% 7.25/2.22 % (2177)Instruction limit reached!
% 7.25/2.22 % (2177)------------------------------
% 7.25/2.22 % (2177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.22 % (2177)Termination reason: Unknown
% 7.25/2.22 % (2177)Termination phase: Saturation
% 7.25/2.22
% 7.25/2.22 % (2177)Memory used [KB]: 6780
% 7.25/2.22 % (2177)Time elapsed: 0.054 s
% 7.25/2.22 % (2177)Instructions burned: 183 (million)
% 7.25/2.22 % (2177)------------------------------
% 7.25/2.22 % (2177)------------------------------
% 7.25/2.22 % (2182)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_1757 for (2992ds/114Mi)
% 7.25/2.22 % (2183)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_1757 for (2992ds/922Mi)
% 7.25/2.23 % (2184)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_1757 for (2992ds/182Mi)
% 7.25/2.24 % (2178)Instruction limit reached!
% 7.25/2.24 % (2178)------------------------------
% 7.25/2.24 % (2178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.24 % (2178)Termination reason: Unknown
% 7.25/2.24 % (2178)Termination phase: Saturation
% 7.25/2.24
% 7.25/2.24 % (2178)Memory used [KB]: 8315
% 7.25/2.24 % (2178)Time elapsed: 0.086 s
% 7.25/2.24 % (2178)Instructions burned: 182 (million)
% 7.25/2.24 % (2178)------------------------------
% 7.25/2.24 % (2178)------------------------------
% 7.25/2.25 % (2185)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_1757 for (2992ds/164Mi)
% 7.25/2.25 % (2173)Instruction limit reached!
% 7.25/2.25 % (2173)------------------------------
% 7.25/2.25 % (2173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.25 % (2173)Termination reason: Unknown
% 7.25/2.25 % (2173)Termination phase: Saturation
% 7.25/2.25
% 7.25/2.25 % (2173)Memory used [KB]: 7291
% 7.25/2.25 % (2173)Time elapsed: 0.162 s
% 7.25/2.25 % (2173)Instructions burned: 459 (million)
% 7.25/2.25 % (2173)------------------------------
% 7.25/2.25 % (2173)------------------------------
% 7.25/2.25 % (2182)Instruction limit reached!
% 7.25/2.25 % (2182)------------------------------
% 7.25/2.25 % (2182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.25 % (2182)Termination reason: Unknown
% 7.25/2.25 % (2182)Termination phase: Saturation
% 7.25/2.25
% 7.25/2.25 % (2182)Memory used [KB]: 6652
% 7.25/2.25 % (2182)Time elapsed: 0.033 s
% 7.25/2.25 % (2182)Instructions burned: 115 (million)
% 7.25/2.25 % (2182)------------------------------
% 7.25/2.25 % (2182)------------------------------
% 7.25/2.26 % (2186)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_1757 for (2992ds/50Mi)
% 7.25/2.26 % (2187)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_1757 for (2992ds/368Mi)
% 7.25/2.26 % (2181)Instruction limit reached!
% 7.25/2.26 % (2181)------------------------------
% 7.25/2.26 % (2181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.26 % (2181)Termination reason: Unknown
% 7.25/2.26 % (2181)Termination phase: Saturation
% 7.25/2.26
% 7.25/2.26 % (2181)Memory used [KB]: 7164
% 7.25/2.26 % (2181)Time elapsed: 0.054 s
% 7.25/2.26 % (2181)Instructions burned: 218 (million)
% 7.25/2.26 % (2181)------------------------------
% 7.25/2.26 % (2181)------------------------------
% 7.25/2.27 % (2188)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_1757 for (2991ds/1021Mi)
% 7.25/2.27 % (2184)Instruction limit reached!
% 7.25/2.27 % (2184)------------------------------
% 7.25/2.27 % (2184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.27 % (2184)Termination reason: Unknown
% 7.25/2.27 % (2184)Termination phase: Saturation
% 7.25/2.27
% 7.25/2.27 % (2184)Memory used [KB]: 6140
% 7.25/2.27 % (2184)Time elapsed: 0.046 s
% 7.25/2.27 % (2184)Instructions burned: 184 (million)
% 7.25/2.27 % (2184)------------------------------
% 7.25/2.27 % (2184)------------------------------
% 7.25/2.27 % (2186)Instruction limit reached!
% 7.25/2.27 % (2186)------------------------------
% 7.25/2.27 % (2186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.27 % (2186)Termination reason: Unknown
% 7.25/2.27 % (2186)Termination phase: Saturation
% 7.25/2.27
% 7.25/2.27 % (2186)Memory used [KB]: 10490
% 7.25/2.27 % (2186)Time elapsed: 0.015 s
% 7.25/2.27 % (2186)Instructions burned: 53 (million)
% 7.25/2.27 % (2186)------------------------------
% 7.25/2.27 % (2186)------------------------------
% 7.25/2.28 % (2189)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_1757 for (2991ds/267Mi)
% 7.25/2.28 % (2190)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_1757 for (2991ds/204Mi)
% 7.25/2.30 % (2185)Instruction limit reached!
% 7.25/2.30 % (2185)------------------------------
% 7.25/2.30 % (2185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.30 % (2185)Termination reason: Unknown
% 7.25/2.30 % (2185)Termination phase: Saturation
% 7.25/2.30
% 7.25/2.30 % (2185)Memory used [KB]: 2174
% 7.25/2.30 % (2185)Time elapsed: 0.052 s
% 7.25/2.30 % (2185)Instructions burned: 164 (million)
% 7.25/2.30 % (2185)------------------------------
% 7.25/2.30 % (2185)------------------------------
% 7.89/2.31 % (2191)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_1757 for (2991ds/26Mi)
% 7.89/2.33 % (2191)Instruction limit reached!
% 7.89/2.33 % (2191)------------------------------
% 7.89/2.33 % (2191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.33 % (2191)Termination reason: Unknown
% 7.89/2.33 % (2191)Termination phase: Property scanning
% 7.89/2.33
% 7.89/2.33 % (2191)Memory used [KB]: 1407
% 7.89/2.33 % (2191)Time elapsed: 0.015 s
% 7.89/2.33 % (2191)Instructions burned: 27 (million)
% 7.89/2.33 % (2191)------------------------------
% 7.89/2.33 % (2191)------------------------------
% 7.89/2.34 % (2190)Instruction limit reached!
% 7.89/2.34 % (2190)------------------------------
% 7.89/2.34 % (2190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.34 % (2190)Termination reason: Unknown
% 7.89/2.34 % (2190)Termination phase: Saturation
% 7.89/2.34
% 7.89/2.34 % (2190)Memory used [KB]: 6908
% 7.89/2.34 % (2190)Time elapsed: 0.062 s
% 7.89/2.34 % (2190)Instructions burned: 205 (million)
% 7.89/2.34 % (2190)------------------------------
% 7.89/2.34 % (2190)------------------------------
% 7.89/2.34 % (2192)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_1757 for (2991ds/53Mi)
% 7.89/2.35 % (2189)Instruction limit reached!
% 7.89/2.35 % (2189)------------------------------
% 7.89/2.35 % (2189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.35 % (2189)Termination reason: Unknown
% 7.89/2.35 % (2189)Termination phase: Saturation
% 7.89/2.35
% 7.89/2.35 % (2189)Memory used [KB]: 7803
% 7.89/2.35 % (2189)Time elapsed: 0.068 s
% 7.89/2.35 % (2189)Instructions burned: 268 (million)
% 7.89/2.35 % (2189)------------------------------
% 7.89/2.35 % (2189)------------------------------
% 7.89/2.35 % (2193)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_1757 for (2991ds/4436Mi)
% 7.89/2.35 % (2187)Instruction limit reached!
% 7.89/2.35 % (2187)------------------------------
% 7.89/2.35 % (2187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.35 % (2187)Termination reason: Unknown
% 7.89/2.35 % (2187)Termination phase: Saturation
% 7.89/2.35
% 7.89/2.35 % (2187)Memory used [KB]: 6908
% 7.89/2.35 % (2187)Time elapsed: 0.094 s
% 7.89/2.35 % (2187)Instructions burned: 368 (million)
% 7.89/2.35 % (2187)------------------------------
% 7.89/2.35 % (2187)------------------------------
% 7.89/2.36 % (2194)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_1757 for (2991ds/1539Mi)
% 7.89/2.36 % (2195)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_1757 for (2991ds/408Mi)
% 7.89/2.37 % (2192)Instruction limit reached!
% 7.89/2.37 % (2192)------------------------------
% 7.89/2.37 % (2192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.37 % (2192)Termination reason: Unknown
% 7.89/2.37 % (2192)Termination phase: Saturation
% 7.89/2.37
% 7.89/2.37 % (2192)Memory used [KB]: 6012
% 7.89/2.37 % (2192)Time elapsed: 0.027 s
% 7.89/2.37 % (2192)Instructions burned: 53 (million)
% 7.89/2.37 % (2192)------------------------------
% 7.89/2.37 % (2192)------------------------------
% 7.89/2.39 % (2196)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_1757 for (2990ds/5205Mi)
% 7.89/2.40 % (2176)Instruction limit reached!
% 7.89/2.40 % (2176)------------------------------
% 7.89/2.40 % (2176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.40 % (2176)Termination reason: Unknown
% 7.89/2.40 % (2176)Termination phase: Saturation
% 7.89/2.40
% 7.89/2.40 % (2176)Memory used [KB]: 7419
% 7.89/2.40 % (2176)Time elapsed: 0.258 s
% 7.89/2.40 % (2176)Instructions burned: 990 (million)
% 7.89/2.40 % (2176)------------------------------
% 7.89/2.40 % (2176)------------------------------
% 8.27/2.41 % (2197)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_1757 for (2990ds/1913Mi)
% 8.27/2.49 % (2195)Instruction limit reached!
% 8.27/2.49 % (2195)------------------------------
% 8.27/2.49 % (2195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.49 % (2195)Termination reason: Unknown
% 8.27/2.49 % (2195)Termination phase: Saturation
% 8.27/2.49
% 8.27/2.49 % (2195)Memory used [KB]: 8571
% 8.27/2.49 % (2195)Time elapsed: 0.129 s
% 8.27/2.49 % (2195)Instructions burned: 411 (million)
% 8.27/2.49 % (2195)------------------------------
% 8.27/2.49 % (2195)------------------------------
% 8.66/2.50 % (2198)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_1757 for (2989ds/4350Mi)
% 8.66/2.51 % (2183)Instruction limit reached!
% 8.66/2.51 % (2183)------------------------------
% 8.66/2.51 % (2183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.51 % (2183)Termination reason: Unknown
% 8.66/2.51 % (2183)Termination phase: Saturation
% 8.66/2.51
% 8.66/2.51 % (2183)Memory used [KB]: 8955
% 8.66/2.51 % (2183)Time elapsed: 0.286 s
% 8.66/2.51 % (2183)Instructions burned: 925 (million)
% 8.66/2.51 % (2183)------------------------------
% 8.66/2.51 % (2183)------------------------------
% 8.66/2.52 % (2199)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_1757 for (2989ds/68Mi)
% 8.66/2.53 % (2199)Instruction limit reached!
% 8.66/2.53 % (2199)------------------------------
% 8.66/2.53 % (2199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.53 % (2199)Termination reason: Unknown
% 8.66/2.53 % (2199)Termination phase: Saturation
% 8.66/2.53
% 8.66/2.53 % (2199)Memory used [KB]: 6268
% 8.66/2.53 % (2199)Time elapsed: 0.019 s
% 8.66/2.53 % (2199)Instructions burned: 69 (million)
% 8.66/2.53 % (2199)------------------------------
% 8.66/2.53 % (2199)------------------------------
% 8.66/2.54 % (2200)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_1757 for (2989ds/358Mi)
% 8.66/2.59 % (2188)Instruction limit reached!
% 8.66/2.59 % (2188)------------------------------
% 8.66/2.59 % (2188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.59 % (2188)Termination reason: Unknown
% 8.66/2.59 % (2188)Termination phase: Saturation
% 8.66/2.59
% 8.66/2.59 % (2188)Memory used [KB]: 9338
% 8.66/2.59 % (2188)Time elapsed: 0.316 s
% 8.66/2.59 % (2188)Instructions burned: 1022 (million)
% 8.66/2.59 % (2188)------------------------------
% 8.66/2.59 % (2188)------------------------------
% 9.30/2.60 % (2201)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_1757 for (2988ds/31Mi)
% 9.30/2.60 % (2194)First to succeed.
% 9.30/2.60 % (2194)Refutation found. Thanks to Tanya!
% 9.30/2.60 % SZS status Theorem for DTF2THF_1757
% 9.30/2.60 % SZS output start Proof for DTF2THF_1757
% 9.30/2.60 thf(func_def_0, type, in: $i > $i > $o).
% 9.30/2.60 thf(func_def_1, type, exu: ($i > $o) > $o).
% 9.30/2.60 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 9.30/2.60 thf(func_def_8, type, powerset: $i > $i).
% 9.30/2.60 thf(func_def_10, type, setunion: $i > $i).
% 9.30/2.60 thf(func_def_19, type, descr: ($i > $o) > $i).
% 9.30/2.60 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 9.30/2.60 thf(func_def_26, type, prop2set: $o > $i).
% 9.30/2.60 thf(func_def_36, type, nonempty: $i > $o).
% 9.30/2.60 thf(func_def_69, type, set2prop: $i > $o).
% 9.30/2.60 thf(func_def_88, type, subset: $i > $i > $o).
% 9.30/2.60 thf(func_def_89, type, disjoint: $i > $i > $o).
% 9.30/2.60 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 9.30/2.60 thf(func_def_124, type, sK3: ($i > $o) > $i).
% 9.30/2.60 thf(func_def_125, type, sK4: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_126, type, sK5: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_127, type, sK6: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_128, type, sK7: $i > $i > $i).
% 9.30/2.60 thf(func_def_129, type, sK8: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_130, type, sK9: ($i > $o) > ($i > $o) > $i).
% 9.30/2.60 thf(func_def_131, type, sK10: ($i > $o) > ($i > $o) > $i).
% 9.30/2.60 thf(func_def_132, type, sK11: $i > ($i > $o) > $i).
% 9.30/2.60 thf(func_def_133, type, sK12: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_134, type, sK13: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_135, type, sK14: $i > $i).
% 9.30/2.60 thf(func_def_136, type, sK15: $o > $i > $i > $i).
% 9.30/2.60 thf(func_def_137, type, sK16: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_138, type, sK17: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_139, type, sK18: ($i > $o) > $i).
% 9.30/2.60 thf(func_def_140, type, sK19: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_141, type, sK20: $i > $i).
% 9.30/2.60 thf(func_def_142, type, sK21: ($i > $o) > ($i > $o) > $i > $i > $i).
% 9.30/2.60 thf(func_def_143, type, sK22: $i > $i > ($i > $o) > ($i > $o) > $i).
% 9.30/2.60 thf(func_def_144, type, sK23: $i > $i > $i).
% 9.30/2.60 thf(func_def_145, type, sK24: $i > $i > $i).
% 9.30/2.60 thf(func_def_146, type, sK25: $i > $i > $i).
% 9.30/2.60 thf(func_def_147, type, sK26: $i > ($i > $o) > $i).
% 9.30/2.60 thf(func_def_148, type, sK27: $i > $i > $i).
% 9.30/2.60 thf(func_def_149, type, sK28: $i > ($i > $i > $o) > $i).
% 9.30/2.60 thf(func_def_150, type, sK29: $i > ($i > $i > $o) > $i).
% 9.30/2.60 thf(func_def_151, type, sK30: $i > ($i > $i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_152, type, sK31: $i > ($i > $i > $o) > $i).
% 9.30/2.60 thf(func_def_153, type, sK32: $i > ($i > $i > $o) > $i).
% 9.30/2.60 thf(func_def_154, type, sK33: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_155, type, sK34: ($i > $o) > $i).
% 9.30/2.60 thf(func_def_156, type, sK35: ($i > $o) > $i).
% 9.30/2.60 thf(func_def_157, type, sK36: ($i > $o) > $i).
% 9.30/2.60 thf(func_def_158, type, sK37: ($i > $o) > $i).
% 9.30/2.60 thf(func_def_159, type, sK38: ($i > $o) > $i).
% 9.30/2.60 thf(func_def_160, type, sK39: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_161, type, sK40: $i > $i).
% 9.30/2.60 thf(func_def_162, type, sK41: $i > $i).
% 9.30/2.60 thf(func_def_163, type, sK42: ($i > $o) > ($i > $o) > $i).
% 9.30/2.60 thf(func_def_164, type, sK43: ($i > $o) > ($i > $o) > $i).
% 9.30/2.60 thf(func_def_165, type, sK44: $i > $i).
% 9.30/2.60 thf(func_def_166, type, sK45: $i > $i > $i).
% 9.30/2.60 thf(func_def_167, type, sK46: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_168, type, sK47: $i > $i > $i).
% 9.30/2.60 thf(func_def_169, type, sK48: $i > $i).
% 9.30/2.60 thf(func_def_170, type, sK49: $i > ($i > $o) > $i).
% 9.30/2.60 thf(func_def_171, type, sK50: ($i > $o) > $i).
% 9.30/2.60 thf(func_def_172, type, sK51: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_173, type, sK52: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_174, type, sK53: $i > $i).
% 9.30/2.60 thf(func_def_175, type, sK54: $i > $i > $i > $i).
% 9.30/2.60 thf(func_def_176, type, sK55: $i > $i > $i).
% 9.30/2.60 thf(func_def_177, type, sK56: $i > $i > $i).
% 9.30/2.60 thf(func_def_178, type, sK57: $i > $i > $i).
% 9.30/2.60 thf(func_def_179, type, sK58: $i > $i > $i).
% 9.30/2.60 thf(func_def_180, type, sK59: ($i > $o) > $i).
% 9.30/2.60 thf(func_def_181, type, sK60: ($i > $o) > $i > $i).
% 9.30/2.60 thf(func_def_182, type, ph61: !>[X0: $tType]:(X0)).
% 9.30/2.60 thf(func_def_183, type, sK62: $i > $i > $i).
% 9.30/2.60 thf(func_def_184, type, sK63: $i > $i).
% 9.30/2.60 thf(func_def_185, type, sK64: $i > $i > $i).
% 9.30/2.60 thf(func_def_186, type, sK65: $i > $i > $i).
% 9.30/2.60 thf(func_def_187, type, sK66: $i > $i > $i).
% 9.30/2.60 thf(func_def_188, type, sK67: $i > $i > $i).
% 9.30/2.60 thf(func_def_189, type, sK68: $i > $i).
% 9.30/2.60 thf(func_def_190, type, sK69: $i > $i > $i).
% 9.30/2.60 thf(func_def_191, type, sK70: $i > $i > $i).
% 9.30/2.60 thf(func_def_192, type, sK71: $i > $i > $i).
% 9.30/2.60 thf(func_def_193, type, sK72: $i > $i > $i).
% 9.30/2.60 thf(func_def_194, type, sK73: $i > $i).
% 9.30/2.60 thf(func_def_195, type, sK74: $i > $i).
% 9.30/2.60 thf(func_def_196, type, sK75: $i > $i > $i).
% 9.30/2.60 thf(func_def_197, type, sK76: $i > $i > $i).
% 9.30/2.60 thf(func_def_199, type, sK78: $i > $i > $i).
% 9.30/2.60 thf(func_def_200, type, sK79: $i > $i > $i).
% 9.30/2.60 thf(func_def_201, type, sK80: $i > $i > $i).
% 9.30/2.60 thf(func_def_202, type, sK81: $i > $i > $i).
% 9.30/2.60 thf(func_def_203, type, sK82: $i > $i > $i).
% 9.30/2.60 thf(func_def_204, type, sK83: $i > $i > $i).
% 9.30/2.60 thf(func_def_205, type, sK84: $i > $i > $i).
% 9.30/2.60 thf(func_def_206, type, sK85: $i > $i > $i).
% 9.30/2.60 thf(f3704,plain,(
% 9.30/2.60 $false),
% 9.30/2.60 inference(avatar_sat_refutation,[status(thm)],[f1513,f1532,f1587,f3279,f3303,f3703])).
% 9.30/2.60 thf(f3703,plain,(
% 9.30/2.60 ~spl2_2 | ~spl2_7 | ~spl2_8),
% 9.30/2.60 inference(avatar_contradiction_clause,[status(thm)],[f3702])).
% 9.30/2.60 thf(f3702,plain,(
% 9.30/2.60 $false | (~spl2_2 | ~spl2_7 | ~spl2_8)),
% 9.30/2.60 inference(trivial_inequality_removal,[status(thm)],[f3696])).
% 9.30/2.60 thf(f3696,plain,(
% 9.30/2.60 ($true = $false) | (~spl2_2 | ~spl2_7 | ~spl2_8)),
% 9.30/2.60 inference(backward_demodulation,[status(thm)],[f3302,f3682])).
% 9.30/2.60 thf(f3682,plain,(
% 9.30/2.60 ($false = (in @ sK77 @ sK0)) | (~spl2_2 | ~spl2_7)),
% 9.30/2.60 inference(trivial_inequality_removal,[status(thm)],[f3673])).
% 9.30/2.60 thf(f3673,plain,(
% 9.30/2.60 ($true = $false) | ($false = (in @ sK77 @ sK0)) | (~spl2_2 | ~spl2_7)),
% 9.30/2.60 inference(superposition,[status(thm)],[f1512,f3322])).
% 9.30/2.60 thf(f3322,plain,(
% 9.30/2.60 ( ! [X0 : $i] : (((subset @ X0 @ sK1) = $false) | ((in @ sK77 @ X0) = $false)) ) | ~spl2_7),
% 9.30/2.60 inference(trivial_inequality_removal,[status(thm)],[f3305])).
% 9.30/2.60 thf(f3305,plain,(
% 9.30/2.60 ( ! [X0 : $i] : (((subset @ X0 @ sK1) = $false) | ((in @ sK77 @ X0) = $false) | ($true = $false)) ) | ~spl2_7),
% 9.30/2.60 inference(superposition,[status(thm)],[f3278,f793])).
% 9.30/2.60 thf(f793,plain,(
% 9.30/2.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (in @ X3 @ X2)) | ((in @ X3 @ X1) = $false) | ((subset @ X1 @ X2) = $false)) )),
% 9.30/2.60 inference(binary_proxy_clausification,[status(thm)],[f792])).
% 9.30/2.60 thf(f792,plain,(
% 9.30/2.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((subset @ X1 @ X2) = $false) | (((in @ X3 @ X1) => (in @ X3 @ X2)) = $true)) )),
% 9.30/2.60 inference(binary_proxy_clausification,[status(thm)],[f791])).
% 9.30/2.60 thf(f791,plain,(
% 9.30/2.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X1 @ X2) => ((in @ X3 @ X1) => (in @ X3 @ X2))))) )),
% 9.30/2.60 inference(beta_eta_normalization,[status(thm)],[f790])).
% 9.30/2.60 thf(f790,plain,(
% 9.30/2.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ X1 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) @ X3))) )),
% 9.30/2.60 inference(pi_clausification,[status(thm)],[f789])).
% 9.30/2.60 thf(f789,plain,(
% 9.30/2.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ X2))))))) )),
% 9.30/2.60 inference(beta_eta_normalization,[status(thm)],[f788])).
% 9.30/2.60 thf(f788,plain,(
% 9.30/2.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ Y0) => ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))))) @ X2))) )),
% 9.30/2.60 inference(pi_clausification,[status(thm)],[f787])).
% 9.30/2.60 thf(f787,plain,(
% 9.30/2.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ Y0) => ((in @ Y1 @ X1) => (in @ Y1 @ Y0))))))) = $true)) )),
% 9.30/2.60 inference(beta_eta_normalization,[status(thm)],[f786])).
% 9.30/2.60 thf(f786,plain,(
% 9.30/2.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))))))) @ X1))) )),
% 9.30/2.60 inference(pi_clausification,[status(thm)],[f539])).
% 9.30/2.60 thf(f539,plain,(
% 9.30/2.60 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))))),
% 9.30/2.60 inference(definition_unfolding,[status(thm)],[f444,f395])).
% 9.30/2.60 thf(f395,plain,(
% 9.30/2.60 (subsetE = $true)),
% 9.30/2.60 inference(cnf_transformation,[status(thm)],[f276])).
% 9.30/2.60 thf(f276,plain,(
% 9.30/2.60 (setadjoinSub = $true) & (nonemptyImpWitness = $true) & (omegaIndAx = $true) & (exu__Cong = $true) & (uniqinunit = $true) & (powersetE = $true) & (omega__Cong = $true) & (notinsingleton = $true) & (singletonsswitch = $true) & (dsetconstrI = $true) & (emptysetsubset = $true) & (prop2setE = $true) & (powersetI = $true) & (notdallE = $true) & (subsetRefl = $true) & (setext = $true) & (setunionAx = $true) & (emptyE1 = $true) & (exuEu = $true) & (emptysetE = $true) & (setunionE = $true) & (subsetE = $true) & (setextAx = $true) & (notinemptyset = $true) & (emptyI = $true) & (subsetI2 = $true) & (emptyinPowerset = $true) & (setadjoinOr = $true) & (setadjoinSub2 = $true) & (dsetconstr__Cong = $true) & (exuE2 = $true) & (notdexE = $true) & (exuI2 = $true) & (setadjoin__Cong = $true) & (exuI3 = $true) & (notsubsetI = $true) & (notequalI1 = $true) & (emptyinunitempty = $true) & (omegaSAx = $true) & (setoftrueEq = $true) & (setadjoinIL = $true) & (quantDeMorgan1 = $true) & (setadjoinE = $true) & (setunion__Cong = $true) & (vacuousDall = $true) & (subPowSU = $true) & (emptyset__Cong = $true) & (omega0Ax = $true) & (quantDeMorgan4 = $true) & (descr__Cong = $true) & (exuI1 = $true) & (prop2setI = $true) & (upairsetIR = $true) & (powerset__Cong = $true) & (setadjoinAx = $true) & (nonemptyE1 = $true) & (subsetI1 = $true) & (subsetE2 = $true) & (dsetconstrER = $true) & (notequalI2 = $true) & (eqimpsubset2 = $true) & (emptyInPowerset = $true) & (subsetTrans = $true) & (setadjoinIR = $true) & (foundationAx = $true) & (quantDeMorgan3 = $true) & (in__Cong = $true) & (emptysetAx = $true) & (setunionI = $true) & (noeltsimpempty = $true) & (nonemptyI1 = $true) & (dsetconstrEL = $true) & (quantDeMorgan2 = $true) & (exuE3u = $true) & (descrp = $true) & (upairsetIL = $true) & (($true != (in @ sK0 @ (powerset @ sK1))) & ($true = (subset @ sK0 @ sK1))) & (eqinunit = $true) & (exuE1 = $true) & (emptysetimpfalse = $true) & (wellorderingAx = $true) & (replAx = $true) & (nonemptyI = $true) & (setbeta = $true) & (eqimpsubset1 = $true) & (prop2set2propI = $true) & (powersetAx = $true) & (inCongP = $true) & (upairsetE = $true) & (exuE3e = $true)),
% 9.30/2.60 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f274,f275])).
% 9.30/2.60 thf(f275,plain,(
% 9.30/2.60 ? [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) & ($true = (subset @ X0 @ X1))) => (($true != (in @ sK0 @ (powerset @ sK1))) & ($true = (subset @ sK0 @ sK1)))),
% 9.30/2.60 introduced(definition,[],[choice_axiom])).
% 9.30/2.60 thf(f274,plain,(
% 9.30/2.60 (setadjoinSub = $true) & (nonemptyImpWitness = $true) & (omegaIndAx = $true) & (exu__Cong = $true) & (uniqinunit = $true) & (powersetE = $true) & (omega__Cong = $true) & (notinsingleton = $true) & (singletonsswitch = $true) & (dsetconstrI = $true) & (emptysetsubset = $true) & (prop2setE = $true) & (powersetI = $true) & (notdallE = $true) & (subsetRefl = $true) & (setext = $true) & (setunionAx = $true) & (emptyE1 = $true) & (exuEu = $true) & (emptysetE = $true) & (setunionE = $true) & (subsetE = $true) & (setextAx = $true) & (notinemptyset = $true) & (emptyI = $true) & (subsetI2 = $true) & (emptyinPowerset = $true) & (setadjoinOr = $true) & (setadjoinSub2 = $true) & (dsetconstr__Cong = $true) & (exuE2 = $true) & (notdexE = $true) & (exuI2 = $true) & (setadjoin__Cong = $true) & (exuI3 = $true) & (notsubsetI = $true) & (notequalI1 = $true) & (emptyinunitempty = $true) & (omegaSAx = $true) & (setoftrueEq = $true) & (setadjoinIL = $true) & (quantDeMorgan1 = $true) & (setadjoinE = $true) & (setunion__Cong = $true) & (vacuousDall = $true) & (subPowSU = $true) & (emptyset__Cong = $true) & (omega0Ax = $true) & (quantDeMorgan4 = $true) & (descr__Cong = $true) & (exuI1 = $true) & (prop2setI = $true) & (upairsetIR = $true) & (powerset__Cong = $true) & (setadjoinAx = $true) & (nonemptyE1 = $true) & (subsetI1 = $true) & (subsetE2 = $true) & (dsetconstrER = $true) & (notequalI2 = $true) & (eqimpsubset2 = $true) & (emptyInPowerset = $true) & (subsetTrans = $true) & (setadjoinIR = $true) & (foundationAx = $true) & (quantDeMorgan3 = $true) & (in__Cong = $true) & (emptysetAx = $true) & (setunionI = $true) & (noeltsimpempty = $true) & (nonemptyI1 = $true) & (dsetconstrEL = $true) & (quantDeMorgan2 = $true) & (exuE3u = $true) & (descrp = $true) & (upairsetIL = $true) & ? [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) & ($true = (subset @ X0 @ X1))) & (eqinunit = $true) & (exuE1 = $true) & (emptysetimpfalse = $true) & (wellorderingAx = $true) & (replAx = $true) & (nonemptyI = $true) & (setbeta = $true) & (eqimpsubset1 = $true) & (prop2set2propI = $true) & (powersetAx = $true) & (inCongP = $true) & (upairsetE = $true) & (exuE3e = $true)),
% 9.30/2.60 inference(flattening,[status(thm)],[f273])).
% 9.30/2.60 thf(f273,plain,(
% 9.30/2.60 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) & ($true = (subset @ X0 @ X1))) & (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)),
% 9.30/2.60 inference(ennf_transformation,[status(thm)],[f207])).
% 9.30/2.60 thf(f207,plain,(
% 9.30/2.60 ~((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) => ! [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) => ($true = (in @ X0 @ (powerset @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.30/2.60 inference(fool_elimination,[status(thm)],[f206])).
% 9.30/2.60 thf(f206,plain,(
% 9.30/2.60 ~(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 => ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.30/2.60 inference(rectify,[status(thm)],[f93])).
% 9.30/2.60 thf(f93,negated_conjecture,(
% 9.30/2.60 ~(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 => ! [X3 : $i,X4 : $i] : ((subset @ X3 @ X4) => (in @ X3 @ (powerset @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.30/2.60 inference(negated_conjecture,[status(cth)],[f92])).
% 9.30/2.60 thf(f92,conjecture,(
% 9.30/2.60 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 => ! [X3 : $i,X4 : $i] : ((subset @ X3 @ X4) => (in @ X3 @ (powerset @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.30/2.60 file('/export/starexec/sandbox/tmp/tmp.fBNDjAFKO7/DTF2THF_1757.p',subset2powerset)).
% 9.30/2.60 thf(f444,plain,(
% 9.30/2.60 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))))),
% 9.30/2.60 inference(cnf_transformation,[status(thm)],[f205])).
% 9.30/2.60 thf(f205,plain,(
% 9.30/2.60 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))))),
% 9.30/2.60 inference(fool_elimination,[status(thm)],[f204])).
% 9.30/2.60 thf(f204,plain,(
% 9.30/2.60 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ X1))) = subsetE)),
% 9.30/2.60 inference(rectify,[status(thm)],[f83])).
% 9.30/2.60 thf(f83,axiom,(
% 9.30/2.60 (! [X1 : $i,X4 : $i,X3 : $i] : ((subset @ X3 @ X4) => ((in @ X1 @ X3) => (in @ X1 @ X4))) = subsetE)),
% 9.30/2.60 file('/export/starexec/sandbox/tmp/tmp.fBNDjAFKO7/DTF2THF_1757.p',subsetE)).
% 9.30/2.60 thf(f3278,plain,(
% 9.30/2.60 ((in @ sK77 @ sK1) = $false) | ~spl2_7),
% 9.30/2.60 inference(avatar_component_clause,[status(thm)],[f3276])).
% 9.30/2.60 thf(f3276,definition,(
% 9.30/2.60 spl2_7 <=> ((in @ sK77 @ sK1) = $false)),
% 9.30/2.60 introduced(definition,[new_symbols(naming,[spl2_7])],[avatar_definition])).
% 9.30/2.60 thf(f1512,plain,(
% 9.30/2.60 ($true = (subset @ sK0 @ sK1)) | ~spl2_2),
% 9.30/2.60 inference(avatar_component_clause,[status(thm)],[f1510])).
% 9.30/2.60 thf(f1510,definition,(
% 9.30/2.60 spl2_2 <=> ($true = (subset @ sK0 @ sK1))),
% 9.30/2.60 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 9.30/2.60 thf(f3302,plain,(
% 9.30/2.60 ($true = (in @ sK77 @ sK0)) | ~spl2_8),
% 9.30/2.60 inference(avatar_component_clause,[status(thm)],[f3300])).
% 9.30/2.60 thf(f3300,definition,(
% 9.30/2.60 spl2_8 <=> ($true = (in @ sK77 @ sK0))),
% 9.30/2.60 introduced(definition,[new_symbols(naming,[spl2_8])],[avatar_definition])).
% 9.30/2.60 thf(f3303,plain,(
% 9.30/2.60 spl2_8 | ~spl2_5),
% 9.30/2.60 inference(avatar_split_clause,[status(thm)],[f3204,f1584,f3300])).
% 9.30/2.60 thf(f1584,definition,(
% 9.30/2.60 spl2_5 <=> ((in @ sK0 @ (powerset @ sK1)) = $false)),
% 9.30/2.60 introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition])).
% 9.30/2.60 thf(f3204,plain,(
% 9.30/2.60 ($true = (in @ sK77 @ sK0)) | ~spl2_5),
% 9.30/2.60 inference(binary_proxy_clausification,[status(thm)],[f3202])).
% 9.30/2.60 thf(f3202,plain,(
% 9.30/2.60 (((in @ sK77 @ sK0) => (in @ sK77 @ sK1)) = $false) | ~spl2_5),
% 9.30/2.60 inference(beta_eta_normalization,[status(thm)],[f3201])).
% 9.30/2.60 thf(f3201,plain,(
% 9.30/2.60 (((^[Y0 : $i]: ((in @ Y0 @ sK0) => (in @ Y0 @ sK1))) @ sK77) = $false) | ~spl2_5),
% 9.30/2.60 inference(sigma_clausification,[status(thm)],[f3200])).
% 9.30/2.60 thf(f3200,plain,(
% 9.30/2.60 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (in @ Y0 @ sK1)))) = $false) | ~spl2_5),
% 9.30/2.60 inference(not_proxy_clausification,[status(thm)],[f3199])).
% 9.30/2.60 thf(f3199,plain,(
% 9.30/2.60 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (in @ Y0 @ sK1))))) = $true) | ~spl2_5),
% 9.30/2.60 inference(boolean_simplification,[status(thm)],[f3168])).
% 9.30/2.60 thf(f3168,plain,(
% 9.30/2.60 (($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (in @ Y0 @ sK1))))) = $true) | ~spl2_5),
% 9.30/2.60 inference(superposition,[status(thm)],[f1241,f1586])).
% 9.30/2.60 thf(f1586,plain,(
% 9.30/2.60 ((in @ sK0 @ (powerset @ sK1)) = $false) | ~spl2_5),
% 9.30/2.60 inference(avatar_component_clause,[status(thm)],[f1584])).
% 9.30/2.60 thf(f1241,plain,(
% 9.30/2.60 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X1 @ (powerset @ X2)) = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))))))) )),
% 9.30/2.60 inference(beta_eta_normalization,[status(thm)],[f1240])).
% 9.30/2.60 thf(f1240,plain,(
% 9.30/2.60 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))))) @ X2) = $true)) )),
% 9.30/2.60 inference(pi_clausification,[status(thm)],[f1239])).
% 9.30/2.60 thf(f1239,plain,(
% 9.30/2.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0))))))))) )),
% 9.30/2.60 inference(beta_eta_normalization,[status(thm)],[f1238])).
% 9.30/2.60 thf(f1238,plain,(
% 9.30/2.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))))))) @ X1))) )),
% 9.30/2.60 inference(pi_clausification,[status(thm)],[f535])).
% 9.30/2.60 thf(f535,plain,(
% 9.30/2.60 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))))),
% 9.30/2.60 inference(definition_unfolding,[status(thm)],[f440,f329])).
% 9.30/2.60 thf(f329,plain,(
% 9.30/2.60 (powersetAx = $true)),
% 9.30/2.60 inference(cnf_transformation,[status(thm)],[f276])).
% 9.30/2.60 thf(f440,plain,(
% 9.30/2.60 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))))),
% 9.30/2.60 inference(cnf_transformation,[status(thm)],[f199])).
% 9.30/2.60 thf(f199,plain,(
% 9.30/2.60 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))))),
% 9.30/2.60 inference(fool_elimination,[status(thm)],[f198])).
% 9.30/2.60 thf(f198,plain,(
% 9.30/2.60 (powersetAx = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) <=> ! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 9.30/2.60 inference(rectify,[status(thm)],[f5])).
% 9.30/2.60 thf(f5,axiom,(
% 9.30/2.60 (powersetAx = ! [X3 : $i,X4 : $i] : ((in @ X4 @ (powerset @ X3)) <=> ! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3))))),
% 9.30/2.60 file('/export/starexec/sandbox/tmp/tmp.fBNDjAFKO7/DTF2THF_1757.p',powersetAx)).
% 9.30/2.60 thf(f3279,plain,(
% 9.30/2.60 spl2_7 | ~spl2_5),
% 9.30/2.60 inference(avatar_split_clause,[status(thm)],[f3203,f1584,f3276])).
% 9.30/2.60 thf(f3203,plain,(
% 9.30/2.60 ((in @ sK77 @ sK1) = $false) | ~spl2_5),
% 9.30/2.60 inference(binary_proxy_clausification,[status(thm)],[f3202])).
% 9.30/2.60 thf(f1587,plain,(
% 9.30/2.60 spl2_5 | spl2_4),
% 9.30/2.60 inference(avatar_split_clause,[status(thm)],[f1579,f1529,f1584])).
% 9.30/2.60 thf(f1529,definition,(
% 9.30/2.60 spl2_4 <=> ($true = (in @ sK0 @ (powerset @ sK1)))),
% 9.30/2.60 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 9.30/2.60 thf(f1579,plain,(
% 9.30/2.60 ((in @ sK0 @ (powerset @ sK1)) = $false) | spl2_4),
% 9.30/2.60 inference(trivial_inequality_removal,[status(thm)],[f1569])).
% 9.30/2.60 thf(f1569,plain,(
% 9.30/2.60 ((in @ sK0 @ (powerset @ sK1)) = $false) | ($true != $true) | spl2_4),
% 9.30/2.60 inference(superposition,[status(thm)],[f1531,f1563])).
% 9.30/2.60 thf(f1563,plain,(
% 9.30/2.60 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 9.30/2.60 inference(trivial_inequality_removal,[status(thm)],[f1561])).
% 9.30/2.60 thf(f1561,plain,(
% 9.30/2.60 ( ! [X0 : $o] : (($false = X0) | ($true = $false) | ($true = X0)) )),
% 9.30/2.60 inference(superposition,[status(thm)],[f617,f614])).
% 9.30/2.60 thf(f614,plain,(
% 9.30/2.60 ( ! [X2 : $i,X1 : $o] : (((in @ X2 @ (prop2set @ X1)) = $false) | ($true = X1)) )),
% 9.30/2.60 inference(binary_proxy_clausification,[status(thm)],[f613])).
% 9.30/2.60 thf(f613,plain,(
% 9.30/2.60 ( ! [X2 : $i,X1 : $o] : (($true = ((in @ X2 @ (prop2set @ X1)) => X1))) )),
% 9.30/2.60 inference(beta_eta_normalization,[status(thm)],[f612])).
% 9.30/2.60 thf(f612,plain,(
% 9.30/2.60 ( ! [X2 : $i,X1 : $o] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (prop2set @ X1)) => X1)) @ X2))) )),
% 9.30/2.60 inference(pi_clausification,[status(thm)],[f611])).
% 9.30/2.60 thf(f611,plain,(
% 9.30/2.60 ( ! [X1 : $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (prop2set @ X1)) => X1))))) )),
% 9.30/2.60 inference(beta_eta_normalization,[status(thm)],[f610])).
% 9.30/2.60 thf(f610,plain,(
% 9.30/2.60 ( ! [X1 : $o] : (($true = ((^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0)))) @ X1))) )),
% 9.30/2.60 inference(pi_clausification,[status(thm)],[f533])).
% 9.30/2.60 thf(f533,plain,(
% 9.30/2.60 ($true = (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0))))))),
% 9.30/2.60 inference(definition_unfolding,[status(thm)],[f438,f405])).
% 9.30/2.60 thf(f405,plain,(
% 9.30/2.60 (prop2setE = $true)),
% 9.30/2.60 inference(cnf_transformation,[status(thm)],[f276])).
% 9.30/2.60 thf(f438,plain,(
% 9.30/2.60 (prop2setE = (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0))))))),
% 9.30/2.60 inference(cnf_transformation,[status(thm)],[f193])).
% 9.30/2.60 thf(f193,plain,(
% 9.30/2.60 (prop2setE = (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0))))))),
% 9.30/2.60 inference(fool_elimination,[status(thm)],[f192])).
% 9.30/2.60 thf(f192,plain,(
% 9.30/2.60 (! [X0 : $i,X1 : $o] : ((in @ X0 @ (prop2set @ X1)) => X1) = prop2setE)),
% 9.30/2.60 inference(rectify,[status(thm)],[f18])).
% 9.30/2.60 thf(f18,axiom,(
% 9.30/2.60 (! [X1 : $i,X0 : $o] : ((in @ X1 @ (prop2set @ X0)) => X0) = prop2setE)),
% 9.30/2.60 file('/export/starexec/sandbox/tmp/tmp.fBNDjAFKO7/DTF2THF_1757.p',prop2setE)).
% 9.30/2.60 thf(f617,plain,(
% 9.30/2.60 ( ! [X1 : $o] : (($true = (in @ emptyset @ (prop2set @ X1))) | ($false = X1)) )),
% 9.30/2.60 inference(binary_proxy_clausification,[status(thm)],[f616])).
% 9.30/2.60 thf(f616,plain,(
% 9.30/2.60 ( ! [X1 : $o] : (($true = (X1 => (in @ emptyset @ (prop2set @ X1))))) )),
% 9.30/2.60 inference(beta_eta_normalization,[status(thm)],[f615])).
% 9.30/2.60 thf(f615,plain,(
% 9.30/2.60 ( ! [X1 : $o] : (($true = ((^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0)))) @ X1))) )),
% 9.30/2.60 inference(pi_clausification,[status(thm)],[f490])).
% 9.30/2.60 thf(f490,plain,(
% 9.30/2.60 ($true = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))),
% 9.30/2.60 inference(definition_unfolding,[status(thm)],[f365,f301])).
% 9.30/2.60 thf(f301,plain,(
% 9.30/2.60 (prop2setI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))),
% 9.30/2.60 inference(cnf_transformation,[status(thm)],[f133])).
% 9.30/2.60 thf(f133,plain,(
% 9.30/2.60 (prop2setI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))),
% 9.30/2.60 inference(fool_elimination,[status(thm)],[f132])).
% 9.30/2.60 thf(f132,plain,(
% 9.30/2.60 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 9.30/2.60 inference(rectify,[status(thm)],[f59])).
% 9.30/2.60 thf(f59,axiom,(
% 9.30/2.60 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 9.30/2.60 file('/export/starexec/sandbox/tmp/tmp.fBNDjAFKO7/DTF2THF_1757.p',prop2setI)).
% 9.30/2.60 thf(f365,plain,(
% 9.30/2.60 (prop2setI = $true)),
% 9.30/2.60 inference(cnf_transformation,[status(thm)],[f276])).
% 9.30/2.60 thf(f1531,plain,(
% 9.30/2.60 ($true != (in @ sK0 @ (powerset @ sK1))) | spl2_4),
% 9.30/2.60 inference(avatar_component_clause,[status(thm)],[f1529])).
% 9.30/2.60 thf(f1532,plain,(
% 9.30/2.60 ~spl2_4),
% 9.30/2.60 inference(avatar_split_clause,[status(thm)],[f340,f1529])).
% 9.30/2.60 thf(f340,plain,(
% 9.30/2.60 ($true != (in @ sK0 @ (powerset @ sK1)))),
% 9.30/2.60 inference(cnf_transformation,[status(thm)],[f276])).
% 9.30/2.60 thf(f1513,plain,(
% 9.30/2.60 spl2_2),
% 9.30/2.60 inference(avatar_split_clause,[status(thm)],[f339,f1510])).
% 9.30/2.60 thf(f339,plain,(
% 9.30/2.60 ($true = (subset @ sK0 @ sK1))),
% 9.30/2.60 inference(cnf_transformation,[status(thm)],[f276])).
% 9.30/2.60 % SZS output end Proof for DTF2THF_1757
% 9.30/2.60 % (2194)------------------------------
% 9.30/2.60 % (2194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.30/2.60 % (2194)Termination reason: Refutation
% 9.30/2.60
% 9.30/2.60 % (2194)Memory used [KB]: 8059
% 9.30/2.60 % (2194)Time elapsed: 0.245 s
% 9.30/2.60 % (2194)Instructions burned: 772 (million)
% 9.30/2.60 % (2194)------------------------------
% 9.30/2.60 % (2194)------------------------------
% 9.30/2.60 % (2096)Success in time 1.143 s
%------------------------------------------------------------------------------