%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU524^1 : 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 : n019.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 09:35:04 AM UTC 2026
% Result : Theorem 9.15s 2.64s
% Output : Refutation 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 104 ( 50 unt; 0 typ; 7 def)
% Number of atoms : 1224 ( 305 equ; 0 cnn)
% Maximal formula atoms : 42 ( 11 avg)
% Number of connectives : 1180 ( 49 ~; 64 |; 125 &; 592 @)
% ( 9 <=>; 275 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 133 ( 129 usr; 53 con; 0-3 aty)
% ( 66 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 199 ( 78 ^; 115 !; 6 ?; 199 :)
% 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_71,type,
sK3: $i > $i ).
thf(func_def_72,type,
sK4: $i > $i ).
thf(func_def_73,type,
sK5: $i > $i > $i ).
thf(func_def_74,type,
sK6: $i > $i > $i ).
thf(func_def_75,type,
sK7: $i > $i > $i ).
thf(func_def_76,type,
sK8: ( $i > $o ) > $i > $i ).
thf(func_def_77,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_78,type,
sK10: $i > ( $i > $i > $o ) > $i ).
thf(func_def_79,type,
sK11: $i > ( $i > $i > $o ) > $i ).
thf(func_def_80,type,
sK12: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_81,type,
sK13: $i > $i ).
thf(func_def_82,type,
sK14: $i > $i ).
thf(func_def_83,type,
sK15: ( $i > $o ) > $i > $i ).
thf(func_def_84,type,
sK16: $i > $i > $i ).
thf(func_def_85,type,
sK17: $i > $i ).
thf(func_def_86,type,
sK18: $i > $i > $i ).
thf(func_def_87,type,
sK19: $o > $i > $i > $i ).
thf(func_def_88,type,
sK20: $i > $i ).
thf(func_def_89,type,
sK21: $i > $i > $i ).
thf(func_def_90,type,
sK22: $i > $i > $i ).
thf(func_def_91,type,
sK23: $i > $i > $i ).
thf(func_def_92,type,
sK24: $i > $i > $i > $i ).
thf(func_def_93,type,
ph25:
!>[X0: $tType] : X0 ).
thf(func_def_94,type,
sK26: $i > $i > $i ).
thf(func_def_95,type,
sK27: $i > $i > $i ).
thf(func_def_96,type,
sK28: $i > $i > $i ).
thf(func_def_97,type,
sK29: $i > $i > $i ).
thf(func_def_98,type,
sK30: $i > $i > $i ).
thf(func_def_99,type,
sK31: $i > $i > $i ).
thf(func_def_100,type,
sK32: $i > $i > $i ).
thf(func_def_101,type,
sK33: $i > $i > $i ).
thf(func_def_102,type,
sK34: $i > $i > $i ).
thf(func_def_103,type,
sK35: $i > $i > $i ).
thf(func_def_104,type,
sK36: $i > $i > $i ).
thf(func_def_105,type,
sK37: $i > $i ).
thf(func_def_106,type,
sK38: $i > $i > $i ).
thf(func_def_107,type,
sK39: $i > $i > $i ).
thf(func_def_108,type,
sK40: $i > $i ).
thf(func_def_109,type,
sK41: $i > $i > $i ).
thf(func_def_110,type,
sK42: $i > $i ).
thf(func_def_111,type,
sK43: $i > $i ).
thf(func_def_112,type,
sK44: $i > $i ).
thf(func_def_113,type,
sK45: $i > $i ).
thf(func_def_114,type,
sK46: $i > $i > $i ).
thf(func_def_115,type,
sK47: $i > $i > $i ).
thf(func_def_116,type,
sK48: $i > $i > $i ).
thf(func_def_117,type,
sK49: $i > $i > $i ).
thf(func_def_118,type,
sK50: $i > $i > $i ).
thf(func_def_119,type,
sK51: $i > $i > $i ).
thf(func_def_122,type,
sK54: $i > $i > $i ).
thf(func_def_123,type,
sK55: $i > $i ).
thf(func_def_124,type,
sK56: $i > $i ).
thf(func_def_125,type,
sK57: $i > $i ).
thf(func_def_126,type,
sK58: $i > $i ).
thf(func_def_127,type,
sK59: $i > $i ).
thf(func_def_128,type,
sK60: $i > $i ).
thf(func_def_129,type,
sK61: $i > $i ).
thf(func_def_130,type,
sK62: $i > $i ).
thf(func_def_131,type,
sK63: $i > $i ).
thf(func_def_132,type,
sK64: $i > $i ).
thf(func_def_135,type,
sK67: $i > $i ).
thf(func_def_136,type,
sK68: $i > $i > $i ).
thf(func_def_137,type,
sK69: $i > $i > $i ).
thf(func_def_138,type,
sK70: $i > $i > $i ).
thf(func_def_139,type,
sK71: $i > $i > $i ).
thf(func_def_140,type,
sK72: $i > $i ).
thf(func_def_141,type,
sK73: $i > $i > $i ).
thf(func_def_142,type,
sK74: $i > $i > $i ).
thf(func_def_143,type,
sK75: $i > $i ).
thf(func_def_144,type,
sK76: $i > $i > $i ).
thf(f5161,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f659,f676,f718,f838,f1892,f3503,f3851,f5160]) ).
thf(f5160,plain,
( ~ spl2_2
| ~ spl2_18
| ~ spl2_21 ),
inference(avatar_contradiction_clause,[status(thm)],[f5159]) ).
thf(f5159,plain,
( $false
| ~ spl2_2
| ~ spl2_18
| ~ spl2_21 ),
inference(trivial_inequality_removal,[status(thm)],[f5153]) ).
thf(f5153,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_18
| ~ spl2_21 ),
inference(backward_demodulation,[status(thm)],[f658,f5058]) ).
thf(f5058,plain,
( ( ( in @ sK1 @ sK0 )
= $false )
| ~ spl2_18
| ~ spl2_21 ),
inference(trivial_inequality_removal,[status(thm)],[f5007]) ).
thf(f5007,plain,
( ( $false = $true )
| ( ( in @ sK1 @ sK0 )
= $false )
| ~ spl2_18
| ~ spl2_21 ),
inference(superposition,[status(thm)],[f3502,f3909]) ).
thf(f3909,plain,
( ! [X0: $i] :
( ( $false
= ( in @ sK53 @ X0 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) )
| ~ spl2_21 ),
inference(trivial_inequality_removal,[status(thm)],[f3906]) ).
thf(f3906,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( in @ sK53 @ X0 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) )
| ~ spl2_21 ),
inference(superposition,[status(thm)],[f310,f3850]) ).
thf(f3850,plain,
( ( ( in @ sK53 @ ( setunion @ sK0 ) )
= $false )
| ~ spl2_21 ),
inference(avatar_component_clause,[status(thm)],[f3848]) ).
thf(f3848,definition,
( spl2_21
<=> ( ( in @ sK53 @ ( setunion @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_21])],[avatar_definition]) ).
thf(f310,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( setunion @ X3 ) )
= $true )
| ( ( in @ X1 @ X2 )
= $false )
| ( ( in @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f309]) ).
thf(f309,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $false )
| ( $true
= ( ( in @ X2 @ X3 )
=> ( in @ X1 @ ( setunion @ X3 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f308]) ).
thf(f308,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X3 )
=> ( in @ X1 @ ( setunion @ X3 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f307]) ).
thf(f307,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ Y0 )
=> ( in @ X1 @ ( setunion @ Y0 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f306]) ).
thf(f306,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ Y0 )
=> ( in @ X1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f305]) ).
thf(f305,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ X1 @ ( setunion @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f304]) ).
thf(f304,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ X1 @ ( setunion @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f303]) ).
thf(f303,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y0 @ ( setunion @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f226]) ).
thf(f226,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y0 @ ( setunion @ Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f155,f138]) ).
thf(f138,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y0 @ ( setunion @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
thf(f90,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y0 @ ( setunion @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f89]) ).
thf(f89,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ( ( in @ X1 @ X0 )
=> ( in @ X2 @ ( setunion @ X0 ) ) ) )
= setunionI ),
inference(rectify,[status(thm)],[f42]) ).
thf(f42,axiom,
! [X3: $i,X4: $i,X1: $i] :
( ( ( in @ X1 @ X4 )
=> ( ( in @ X4 @ X3 )
=> ( in @ X1 @ ( setunion @ X3 ) ) ) )
= setunionI ),
file('/export/starexec/sandbox/tmp/tmp.QB27Oebfrm/DTF2THF_29480.p',setunionI) ).
thf(f155,plain,
setunionI = $true,
inference(cnf_transformation,[status(thm)],[f133]) ).
thf(f133,plain,
( ( $true
!= ( in @ sK1 @ ( powerset @ ( setunion @ sK0 ) ) ) )
& ( ( in @ sK1 @ sK0 )
= $true )
& ( powersetE = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( prop2setE = $true )
& ( powersetAx = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( emptyI = $true )
& ( omega0Ax = $true )
& ( emptyinunitempty = $true )
& ( setadjoinOr = $true )
& ( nonemptyI = $true )
& ( descrp = $true )
& ( emptyinPowerset = $true )
& ( exuE1 = $true )
& ( setunionE = $true )
& ( replAx = $true )
& ( setadjoinIL = $true )
& ( setextAx = $true )
& ( dsetconstrI = $true )
& ( emptyInPowerset = $true )
& ( setbeta = $true )
& ( setext = $true )
& ( notinemptyset = $true )
& ( wellorderingAx = $true )
& ( exuE3e = $true )
& ( nonemptyE1 = $true )
& ( setunionI = $true )
& ( setadjoinAx = $true )
& ( nonemptyI1 = $true )
& ( emptysetAx = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinE = $true )
& ( setoftrueEq = $true )
& ( foundationAx = $true )
& ( noeltsimpempty = $true )
& ( setunionAx = $true )
& ( powersetI = $true )
& ( emptysetE = $true )
& ( setadjoinIR = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f131,f132]) ).
thf(f132,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ ( setunion @ X0 ) ) ) )
& ( ( in @ X1 @ X0 )
= $true ) )
=> ( ( $true
!= ( in @ sK1 @ ( powerset @ ( setunion @ sK0 ) ) ) )
& ( ( in @ sK1 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f131,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ ( setunion @ X0 ) ) ) )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( powersetE = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( prop2setE = $true )
& ( powersetAx = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( emptyI = $true )
& ( omega0Ax = $true )
& ( emptyinunitempty = $true )
& ( setadjoinOr = $true )
& ( nonemptyI = $true )
& ( descrp = $true )
& ( emptyinPowerset = $true )
& ( exuE1 = $true )
& ( setunionE = $true )
& ( replAx = $true )
& ( setadjoinIL = $true )
& ( setextAx = $true )
& ( dsetconstrI = $true )
& ( emptyInPowerset = $true )
& ( setbeta = $true )
& ( setext = $true )
& ( notinemptyset = $true )
& ( wellorderingAx = $true )
& ( exuE3e = $true )
& ( nonemptyE1 = $true )
& ( setunionI = $true )
& ( setadjoinAx = $true )
& ( nonemptyI1 = $true )
& ( emptysetAx = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinE = $true )
& ( setoftrueEq = $true )
& ( foundationAx = $true )
& ( noeltsimpempty = $true )
& ( setunionAx = $true )
& ( powersetI = $true )
& ( emptysetE = $true )
& ( setadjoinIR = $true ) ),
inference(flattening,[status(thm)],[f130]) ).
thf(f130,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ ( setunion @ X0 ) ) ) )
& ( ( in @ X1 @ X0 )
= $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)],[f120]) ).
thf(f120,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 )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( $true
= ( in @ X1 @ ( powerset @ ( setunion @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f119]) ).
thf(f119,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ ( setunion @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f45]) ).
thf(f45,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
=> ! [X3: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ ( powerset @ ( setunion @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
thf(f44,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
=> ! [X3: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ ( powerset @ ( setunion @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QB27Oebfrm/DTF2THF_29480.p',subPowSU) ).
thf(f3502,plain,
( ( ( in @ sK53 @ sK1 )
= $true )
| ~ spl2_18 ),
inference(avatar_component_clause,[status(thm)],[f3500]) ).
thf(f3500,definition,
( spl2_18
<=> ( ( in @ sK53 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_18])],[avatar_definition]) ).
thf(f658,plain,
( ( ( in @ sK1 @ sK0 )
= $true )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f656]) ).
thf(f656,definition,
( spl2_2
<=> ( ( in @ sK1 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f3851,plain,
( spl2_21
| ~ spl2_11 ),
inference(avatar_split_clause,[status(thm)],[f2892,f835,f3848]) ).
thf(f835,definition,
( spl2_11
<=> ( $false
= ( in @ sK1 @ ( powerset @ ( setunion @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_11])],[avatar_definition]) ).
thf(f2892,plain,
( ( ( in @ sK53 @ ( setunion @ sK0 ) )
= $false )
| ~ spl2_11 ),
inference(binary_proxy_clausification,[status(thm)],[f2891]) ).
thf(f2891,plain,
( ( $false
= ( ( in @ sK53 @ sK1 )
=> ( in @ sK53 @ ( setunion @ sK0 ) ) ) )
| ~ spl2_11 ),
inference(beta_eta_normalization,[status(thm)],[f2890]) ).
thf(f2890,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( in @ Y0 @ ( setunion @ sK0 ) ) )
@ sK53 ) )
| ~ spl2_11 ),
inference(sigma_clausification,[status(thm)],[f2889]) ).
thf(f2889,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( in @ Y0 @ ( setunion @ sK0 ) ) ) )
= $false )
| ~ spl2_11 ),
inference(not_proxy_clausification,[status(thm)],[f2888]) ).
thf(f2888,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( in @ Y0 @ ( setunion @ sK0 ) ) ) ) ) )
| ~ spl2_11 ),
inference(boolean_simplification,[status(thm)],[f2808]) ).
thf(f2808,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( in @ Y0 @ ( setunion @ sK0 ) ) ) )
= $false ) )
| ~ spl2_11 ),
inference(superposition,[status(thm)],[f347,f837]) ).
thf(f837,plain,
( ( $false
= ( in @ sK1 @ ( powerset @ ( setunion @ sK0 ) ) ) )
| ~ spl2_11 ),
inference(avatar_component_clause,[status(thm)],[f835]) ).
thf(f347,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= ( in @ X2 @ ( powerset @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f346]) ).
thf(f346,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
= ( in @ Y0 @ ( powerset @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f345]) ).
thf(f345,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
= ( in @ Y0 @ ( powerset @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f344]) ).
thf(f344,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f256]) ).
thf(f256,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f215,f178]) ).
thf(f178,plain,
powersetAx = $true,
inference(cnf_transformation,[status(thm)],[f133]) ).
thf(f215,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
thf(f102,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f101]) ).
thf(f101,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
<=> ( in @ X0 @ ( powerset @ X1 ) ) )
= powersetAx ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X4: $i,X3: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
<=> ( in @ X4 @ ( powerset @ X3 ) ) )
= powersetAx ),
file('/export/starexec/sandbox/tmp/tmp.QB27Oebfrm/DTF2THF_29480.p',powersetAx) ).
thf(f3503,plain,
( spl2_18
| ~ spl2_11 ),
inference(avatar_split_clause,[status(thm)],[f2893,f835,f3500]) ).
thf(f2893,plain,
( ( ( in @ sK53 @ sK1 )
= $true )
| ~ spl2_11 ),
inference(binary_proxy_clausification,[status(thm)],[f2891]) ).
thf(f1892,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[status(thm)],[f1891]) ).
thf(f1891,plain,
( $false
| ~ spl2_8 ),
inference(trivial_inequality_removal,[status(thm)],[f1878]) ).
thf(f1878,plain,
( ( $false = $true )
| ~ spl2_8 ),
inference(backward_demodulation,[status(thm)],[f509,f717]) ).
thf(f717,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( $false
= ( in @ X3 @ ( setadjoin @ X2 @ X1 ) ) )
| ~ spl2_8 ),
inference(avatar_component_clause,[status(thm)],[f716]) ).
thf(f716,definition,
( spl2_8
<=> ! [X2: $i,X1: $i,X3: $i] :
( $false
= ( in @ X3 @ ( setadjoin @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_8])],[avatar_definition]) ).
thf(f509,plain,
! [X2: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f508]) ).
thf(f508,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f507]) ).
thf(f507,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f506]) ).
thf(f506,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f241]) ).
thf(f241,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f199,f165]) ).
thf(f165,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f133]) ).
thf(f199,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
thf(f110,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f109]) ).
thf(f109,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= setadjoinIL ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,axiom,
! [X2: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
= setadjoinIL ),
file('/export/starexec/sandbox/tmp/tmp.QB27Oebfrm/DTF2THF_29480.p',setadjoinIL) ).
thf(f838,plain,
( spl2_11
| spl2_4
| ~ spl2_6 ),
inference(avatar_split_clause,[status(thm)],[f726,f697,f673,f835]) ).
thf(f673,definition,
( spl2_4
<=> ( $true
= ( in @ sK1 @ ( powerset @ ( setunion @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f697,definition,
( spl2_6
<=> ! [X3: $o] :
( ( $true = X3 )
| ( $false = X3 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition]) ).
thf(f726,plain,
( ( $false
= ( in @ sK1 @ ( powerset @ ( setunion @ sK0 ) ) ) )
| spl2_4
| ~ spl2_6 ),
inference(trivial_inequality_removal,[status(thm)],[f724]) ).
thf(f724,plain,
( ( $true != $true )
| ( $false
= ( in @ sK1 @ ( powerset @ ( setunion @ sK0 ) ) ) )
| spl2_4
| ~ spl2_6 ),
inference(superposition,[status(thm)],[f675,f698]) ).
thf(f698,plain,
( ! [X3: $o] :
( ( $true = X3 )
| ( $false = X3 ) )
| ~ spl2_6 ),
inference(avatar_component_clause,[status(thm)],[f697]) ).
thf(f675,plain,
( ( $true
!= ( in @ sK1 @ ( powerset @ ( setunion @ sK0 ) ) ) )
| spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f673]) ).
thf(f718,plain,
( spl2_8
| spl2_6 ),
inference(avatar_split_clause,[status(thm)],[f407,f697,f716]) ).
thf(f407,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false = X4 )
| ( $true = X4 )
| ( $false
= ( in @ X3 @ ( setadjoin @ X2 @ X1 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f405]) ).
thf(f405,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false = X4 )
| ( $false
= ( in @ X3 @ ( setadjoin @ X2 @ X1 ) ) )
| ( $false = X4 )
| ( $true = X4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f404]) ).
thf(f404,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X3 @ ( setadjoin @ X2 @ X1 ) ) )
| ( $false = X4 )
| ( $false
= ( ( in @ X3 @ X1 )
=> X4 ) )
| ( $true = X4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f398]) ).
thf(f398,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false = X4 )
| ( $false
= ( in @ X3 @ ( setadjoin @ X2 @ X1 ) ) )
| ( ( ( ( in @ X3 @ X1 )
=> X4 )
=> X4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f397]) ).
thf(f397,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( ( X3 = X2 )
=> X4 )
= $false )
| ( ( ( ( in @ X3 @ X1 )
=> X4 )
=> X4 )
= $true )
| ( $false
= ( in @ X3 @ ( setadjoin @ X2 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f396]) ).
thf(f396,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X3 @ ( setadjoin @ X2 @ X1 ) ) )
| ( ( ( ( X3 = X2 )
=> X4 )
=> ( ( ( in @ X3 @ X1 )
=> X4 )
=> X4 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f395]) ).
thf(f395,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $false
= ( in @ X3 @ ( setadjoin @ X2 @ X1 ) ) )
| ( ( ^ [Y0: $o] :
( ( ( X3 = X2 )
=> Y0 )
=> ( ( ( in @ X3 @ X1 )
=> Y0 )
=> Y0 ) )
@ X4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f394]) ).
thf(f394,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( ( X3 = X2 )
=> Y0 )
=> ( ( ( in @ X3 @ X1 )
=> Y0 )
=> Y0 ) ) ) )
| ( $false
= ( in @ X3 @ ( setadjoin @ X2 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f393]) ).
thf(f393,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X3 @ ( setadjoin @ X2 @ X1 ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( ( ( X3 = X2 )
=> Y0 )
=> ( ( ( in @ X3 @ X1 )
=> Y0 )
=> Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f392]) ).
thf(f392,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X2 @ X1 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( Y0 = X2 )
=> Y1 )
=> ( ( ( in @ Y0 @ X1 )
=> Y1 )
=> Y1 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f391]) ).
thf(f391,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X2 @ X1 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( Y0 = X2 )
=> Y1 )
=> ( ( ( in @ Y0 @ X1 )
=> Y1 )
=> Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f390]) ).
thf(f390,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ X1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( Y1 = Y0 )
=> Y2 )
=> ( ( ( in @ Y1 @ X1 )
=> Y2 )
=> Y2 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f389]) ).
thf(f389,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ X1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( Y1 = Y0 )
=> Y2 )
=> ( ( ( in @ Y1 @ X1 )
=> Y2 )
=> Y2 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f388]) ).
thf(f388,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y1 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( Y2 = Y1 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y0 )
=> Y3 )
=> Y3 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f252]) ).
thf(f252,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y1 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( Y2 = Y1 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y0 )
=> Y3 )
=> Y3 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f211,f150]) ).
thf(f150,plain,
setadjoinE = $true,
inference(cnf_transformation,[status(thm)],[f133]) ).
thf(f211,plain,
( setadjoinE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y1 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( Y2 = Y1 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y0 )
=> Y3 )
=> Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
thf(f124,plain,
( setadjoinE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y1 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( Y2 = Y1 )
=> Y3 )
=> ( ( ( in @ Y2 @ Y0 )
=> Y3 )
=> Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f123]) ).
thf(f123,plain,
( setadjoinE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
=> ! [X3: $o] :
( ( ( X0 = X1 )
=> X3 )
=> ( ( ( in @ X0 @ X2 )
=> X3 )
=> X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,axiom,
( setadjoinE
= ( ! [X2: $i,X1: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
=> ! [X0: $o] :
( ( ( X1 = X2 )
=> X0 )
=> ( ( ( in @ X2 @ X3 )
=> X0 )
=> X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QB27Oebfrm/DTF2THF_29480.p',setadjoinE) ).
thf(f676,plain,
~ spl2_4,
inference(avatar_split_clause,[status(thm)],[f184,f673]) ).
thf(f184,plain,
( $true
!= ( in @ sK1 @ ( powerset @ ( setunion @ sK0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
thf(f659,plain,
spl2_2,
inference(avatar_split_clause,[status(thm)],[f183,f656]) ).
thf(f183,plain,
( ( in @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU524^1 : 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
% 0.17/0.34 % Computer : n019.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:25:39 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEU524^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.47 % Domain : Set Theory
% 0.28/0.47 % Problem : Preliminary Notions - Power Sets and Unions
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English : (! A:i.! x:i.in x A -> in x (powerset (setunion A)))
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.47 % Source : [Bro08]
% 0.28/0.47 % Names : ZFC026g [Bro08]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.22 v9.1.0, 0.25 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, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.67 v4.0.0, 1.00 v3.7.0
% 0.28/0.47 % Syntax : Number of formulae : 95 ( 43 unt; 51 typ; 43 def)
% 0.28/0.47 % Number of atoms : 242 ( 55 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 42 ( 5 avg)
% 0.28/0.47 % Number of connectives : 403 ( 7 ~; 4 |; 18 &; 265 @)
% 0.28/0.47 % ( 7 <=>; 102 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 47 ( 2 avg)
% 0.28/0.47 % Number of types : 2 ( 0 usr)
% 0.28/0.47 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 54 ( 51 usr; 44 con; 0-2 aty)
% 0.28/0.47 % Number of variables : 132 ( 15 ^; 101 !; 16 ?; 132 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : http://mathgate.info/detsetitem.php?id=473
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(in_type,type,
% 0.28/0.47 in: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(exu_type,type,
% 0.28/0.47 exu: ( $i > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(exu,definition,
% 0.28/0.47 ( exu
% 0.28/0.47 = ( ^ [Xphi: $i > $o] :
% 0.28/0.47 ? [Xx: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 & ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setextAx_type,type,
% 0.28/0.47 setextAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setextAx,definition,
% 0.28/0.47 ( setextAx
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 <=> ( in @ Xx @ B ) )
% 0.28/0.47 => ( A = B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset_type,type,
% 0.28/0.47 emptyset: $i ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetAx_type,type,
% 0.28/0.47 emptysetAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetAx,definition,
% 0.28/0.47 ( emptysetAx
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin_type,type,
% 0.28/0.47 setadjoin: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinAx_type,type,
% 0.28/0.47 setadjoinAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinAx,definition,
% 0.28/0.47 ( setadjoinAx
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 <=> ( ( Xy = Xx )
% 0.28/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powerset_type,type,
% 0.28/0.47 powerset: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(powersetAx_type,type,
% 0.28/0.47 powersetAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetAx,definition,
% 0.28/0.47 ( powersetAx
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 <=> ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunion_type,type,
% 0.28/0.47 setunion: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setunionAx_type,type,
% 0.28/0.47 setunionAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionAx,definition,
% 0.28/0.47 ( setunionAx
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 <=> ? [B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omega_type,type,
% 0.28/0.47 omega: $i ).
% 0.28/0.47
% 0.28/0.47 thf(omega0Ax_type,type,
% 0.28/0.47 omega0Ax: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omega0Ax,definition,
% 0.28/0.47 ( omega0Ax
% 0.28/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omegaSAx_type,type,
% 0.28/0.47 omegaSAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omegaSAx,definition,
% 0.28/0.47 ( omegaSAx
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ omega )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omegaIndAx_type,type,
% 0.28/0.47 omegaIndAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omegaIndAx,definition,
% 0.28/0.47 ( omegaIndAx
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( ( in @ emptyset @ A )
% 0.28/0.47 & ! [Xx: $i] :
% 0.28/0.47 ( ( ( in @ Xx @ omega )
% 0.28/0.47 & ( in @ Xx @ A ) )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ omega )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(replAx_type,type,
% 0.28/0.47 replAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(replAx,definition,
% 0.28/0.47 ( replAx
% 0.28/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.28/0.47 => ? [B: $i] :
% 0.28/0.47 ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 <=> ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(foundationAx_type,type,
% 0.28/0.47 foundationAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(foundationAx,definition,
% 0.28/0.47 ( foundationAx
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.47 => ? [B: $i] :
% 0.28/0.47 ( ( in @ B @ A )
% 0.28/0.47 & ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(wellorderingAx_type,type,
% 0.28/0.47 wellorderingAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(wellorderingAx,definition,
% 0.28/0.47 ( wellorderingAx
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ? [B: $i] :
% 0.28/0.47 ( ! [C: $i] :
% 0.28/0.47 ( ( in @ C @ B )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ C )
% 0.28/0.47 => ( in @ Xx @ A ) ) )
% 0.28/0.47 & ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( ( in @ Xx @ A )
% 0.28/0.47 & ( in @ Xy @ A ) )
% 0.28/0.47 => ( ! [C: $i] :
% 0.28/0.47 ( ( in @ C @ B )
% 0.28/0.47 => ( ( in @ Xx @ C )
% 0.28/0.47 <=> ( in @ Xy @ C ) ) )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 & ! [C: $i,D: $i] :
% 0.28/0.47 ( ( ( in @ C @ B )
% 0.28/0.47 & ( in @ D @ B ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ C )
% 0.28/0.47 => ( in @ Xx @ D ) )
% 0.28/0.47 | ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ D )
% 0.28/0.47 => ( in @ Xx @ C ) ) ) )
% 0.28/0.47 & ! [C: $i] :
% 0.28/0.47 ( ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ C )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.28/0.47 => ? [D: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ D @ B )
% 0.28/0.47 & ( in @ Xx @ C )
% 0.28/0.47 & ~ ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ D )
% 0.28/0.47 & ( in @ Xy @ C ) )
% 0.28/0.47 & ! [E: $i] :
% 0.28/0.47 ( ( in @ E @ B )
% 0.28/0.47 => ( ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ E )
% 0.28/0.47 => ( in @ Xy @ D ) )
% 0.28/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(descr_type,type,
% 0.28/0.47 descr: ( $i > $o ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(descrp_type,type,
% 0.28/0.47 descrp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(descrp,definition,
% 0.28/0.47 ( descrp
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ( Xphi
% 0.28/0.47 @ ( descr
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr_type,type,
% 0.28/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrI_type,type,
% 0.28/0.47 dsetconstrI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrI,definition,
% 0.28/0.47 ( dsetconstrI
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrEL_type,type,
% 0.28/0.47 dsetconstrEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrEL,definition,
% 0.28/0.47 ( dsetconstrEL
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrER_type,type,
% 0.28/0.47 dsetconstrER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrER,definition,
% 0.28/0.47 ( dsetconstrER
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE1_type,type,
% 0.28/0.47 exuE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE1,definition,
% 0.28/0.47 ( exuE1
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 & ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set_type,type,
% 0.28/0.47 prop2set: $o > $i ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set,definition,
% 0.28/0.47 ( prop2set
% 0.28/0.47 = ( ^ [Xphi: $o] :
% 0.28/0.47 ( dsetconstr @ ( powerset @ emptyset )
% 0.28/0.47 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setE_type,type,
% 0.28/0.47 prop2setE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setE,definition,
% 0.28/0.47 ( prop2setE
% 0.28/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetE_type,type,
% 0.28/0.47 emptysetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetE,definition,
% 0.28/0.47 ( emptysetE
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetimpfalse_type,type,
% 0.28/0.47 emptysetimpfalse: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetimpfalse,definition,
% 0.28/0.47 ( emptysetimpfalse
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => $false ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notinemptyset_type,type,
% 0.28/0.47 notinemptyset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notinemptyset,definition,
% 0.28/0.47 ( notinemptyset
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3e_type,type,
% 0.28/0.47 exuE3e: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3e,definition,
% 0.28/0.47 ( exuE3e
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setext_type,type,
% 0.28/0.47 setext: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setext,definition,
% 0.28/0.47 ( setext
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 => ( A = B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyI_type,type,
% 0.28/0.47 emptyI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyI,definition,
% 0.28/0.47 ( emptyI
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ A )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(noeltsimpempty_type,type,
% 0.28/0.47 noeltsimpempty: $o ).
% 0.28/0.47
% 0.28/0.47 thf(noeltsimpempty,definition,
% 0.28/0.47 ( noeltsimpempty
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ A )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setbeta_type,type,
% 0.28/0.47 setbeta: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setbeta,definition,
% 0.28/0.47 ( setbeta
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonempty_type,type,
% 0.28/0.47 nonempty: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonempty,definition,
% 0.28/0.47 ( nonempty
% 0.28/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyE1_type,type,
% 0.28/0.47 nonemptyE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyE1,definition,
% 0.28/0.47 ( nonemptyE1
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( nonempty @ A )
% 0.28/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI_type,type,
% 0.28/0.47 nonemptyI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI,definition,
% 0.28/0.47 ( nonemptyI
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( nonempty
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI1_type,type,
% 0.28/0.47 nonemptyI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI1,definition,
% 0.28/0.47 ( nonemptyI1
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIL_type,type,
% 0.28/0.47 setadjoinIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIL,definition,
% 0.28/0.47 ( setadjoinIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinunitempty_type,type,
% 0.28/0.47 emptyinunitempty: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinunitempty,definition,
% 0.28/0.47 ( emptyinunitempty
% 0.28/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIR_type,type,
% 0.28/0.47 setadjoinIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIR,definition,
% 0.28/0.47 ( setadjoinIR
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinE_type,type,
% 0.28/0.47 setadjoinE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinE,definition,
% 0.28/0.47 ( setadjoinE
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ( ( Xy = Xx )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => ( ( ( in @ Xy @ A )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinOr_type,type,
% 0.28/0.47 setadjoinOr: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinOr,definition,
% 0.28/0.47 ( setadjoinOr
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 => ( ( Xy = Xx )
% 0.28/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setoftrueEq_type,type,
% 0.28/0.47 setoftrueEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setoftrueEq,definition,
% 0.28/0.47 ( setoftrueEq
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : $true )
% 0.28/0.47 = A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI_type,type,
% 0.28/0.47 powersetI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI,definition,
% 0.28/0.47 ( powersetI
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinPowerset_type,type,
% 0.28/0.47 emptyinPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinPowerset,definition,
% 0.28/0.47 ( emptyinPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyInPowerset_type,type,
% 0.28/0.47 emptyInPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyInPowerset,definition,
% 0.28/0.47 ( emptyInPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE_type,type,
% 0.28/0.47 powersetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE,definition,
% 0.28/0.47 ( powersetE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionI_type,type,
% 0.28/0.47 setunionI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionI,definition,
% 0.28/0.47 ( setunionI
% 0.28/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( ( in @ B @ A )
% 0.28/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE_type,type,
% 0.28/0.47 setunionE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE,definition,
% 0.28/0.47 ( setunionE
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ! [B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( ( in @ B @ A )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subPowSU,conjecture,
% 0.28/0.47 ( setextAx
% 0.28/0.47 => ( emptysetAx
% 0.28/0.47 => ( setadjoinAx
% 0.28/0.47 => ( powersetAx
% 0.28/0.47 => ( setunionAx
% 0.28/0.47 => ( omega0Ax
% 0.28/0.47 => ( omegaSAx
% 0.28/0.47 => ( omegaIndAx
% 0.28/0.47 => ( replAx
% 0.28/0.47 => ( foundationAx
% 0.28/0.47 => ( wellorderingAx
% 0.28/0.47 => ( descrp
% 0.28/0.47 => ( dsetconstrI
% 0.28/0.47 => ( dsetconstrEL
% 0.28/0.47 => ( dsetconstrER
% 0.28/0.47 => ( exuE1
% 0.28/0.47 => ( prop2setE
% 0.28/0.47 => ( emptysetE
% 0.28/0.47 => ( emptysetimpfalse
% 0.28/0.47 => ( notinemptyset
% 0.28/0.47 => ( exuE3e
% 0.28/0.47 => ( setext
% 0.28/0.47 => ( emptyI
% 0.28/0.47 => ( noeltsimpempty
% 0.28/0.47 => ( setbeta
% 0.28/0.47 => ( nonemptyE1
% 0.28/0.47 => ( nonemptyI
% 0.28/0.47 => ( nonemptyI1
% 0.28/0.47 => ( setadjoinIL
% 0.28/0.47 => ( emptyinunitempty
% 0.28/0.47 => ( setadjoinIR
% 0.28/0.47 => ( setadjoinE
% 0.28/0.47 => ( setadjoinOr
% 0.28/0.47 => ( setoftrueEq
% 0.28/0.47 => ( powersetI
% 0.28/0.47 => ( emptyinPowerset
% 0.28/0.47 => ( emptyInPowerset
% 0.28/0.47 => ( powersetE
% 0.28/0.47 => ( setunionI
% 0.28/0.47 => ( setunionE
% 0.28/0.47 => ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.85/1.36 ---- Embedded in THF ---
% 1.85/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.85/1.36 %%% Generated on Tue Feb 24 12:25:40 EST 2026
% 1.85/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.85/1.36 %%% Logic specification used:
% 1.85/1.36 %%% thf(spec, logic, $$dhol).
% 1.85/1.36
% 1.85/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QB27Oebfrm/DTF2DTF29480.p
% See solution above
% 1.85/1.36 ------------------------
% 1.85/1.38 ---- Cleaned THF ---
% 1.85/1.38 thf(in_type,type,
% 1.85/1.38 in: $i > $i > $o ).
% 1.85/1.38
% 1.85/1.38 thf(exu_type,type,
% 1.85/1.38 exu: ( $i > $o ) > $o ).
% 1.85/1.38
% 1.85/1.38 thf(exu,definition,
% 1.85/1.38 ( exu
% 1.85/1.38 = ( ^ [Xphi: $i > $o] :
% 1.85/1.38 ? [Xx: $i] :
% 1.85/1.38 ( ( Xphi @ Xx )
% 1.85/1.38 & ! [Xy: $i] :
% 1.85/1.38 ( ( Xphi @ Xy )
% 1.85/1.38 => ( Xx = Xy ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(setextAx_type,type,
% 1.85/1.38 setextAx: $o ).
% 1.85/1.38
% 1.85/1.38 thf(setextAx,definition,
% 1.85/1.38 ( setextAx
% 1.85/1.38 = ( ! [A: $i,B: $i] :
% 1.85/1.38 ( ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ A )
% 1.85/1.38 <=> ( in @ Xx @ B ) )
% 1.85/1.38 => ( A = B ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(emptyset_type,type,
% 1.85/1.38 emptyset: $i ).
% 1.85/1.38
% 1.85/1.38 thf(emptysetAx_type,type,
% 1.85/1.38 emptysetAx: $o ).
% 1.85/1.38
% 1.85/1.38 thf(emptysetAx,definition,
% 1.85/1.38 ( emptysetAx
% 1.85/1.38 = ( ! [Xx: $i] :
% 1.85/1.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(setadjoin_type,type,
% 1.85/1.38 setadjoin: $i > $i > $i ).
% 1.85/1.38
% 1.85/1.38 thf(setadjoinAx_type,type,
% 1.85/1.38 setadjoinAx: $o ).
% 1.85/1.38
% 1.85/1.38 thf(setadjoinAx,definition,
% 1.85/1.38 ( setadjoinAx
% 1.85/1.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.85/1.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.85/1.38 <=> ( ( Xy = Xx )
% 1.85/1.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(powerset_type,type,
% 1.85/1.38 powerset: $i > $i ).
% 1.85/1.38
% 1.85/1.38 thf(powersetAx_type,type,
% 1.85/1.38 powersetAx: $o ).
% 1.85/1.38
% 1.85/1.38 thf(powersetAx,definition,
% 1.85/1.38 ( powersetAx
% 1.85/1.38 = ( ! [A: $i,B: $i] :
% 1.85/1.38 ( ( in @ B @ ( powerset @ A ) )
% 1.85/1.38 <=> ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ B )
% 1.85/1.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(setunion_type,type,
% 1.85/1.38 setunion: $i > $i ).
% 1.85/1.38
% 1.85/1.38 thf(setunionAx_type,type,
% 1.85/1.38 setunionAx: $o ).
% 1.85/1.38
% 1.85/1.38 thf(setunionAx,definition,
% 1.85/1.38 ( setunionAx
% 1.85/1.38 = ( ! [A: $i,Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ ( setunion @ A ) )
% 1.85/1.38 <=> ? [B: $i] :
% 1.85/1.38 ( ( in @ Xx @ B )
% 1.85/1.38 & ( in @ B @ A ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(omega_type,type,
% 1.85/1.38 omega: $i ).
% 1.85/1.38
% 1.85/1.38 thf(omega0Ax_type,type,
% 1.85/1.38 omega0Ax: $o ).
% 1.85/1.38
% 1.85/1.38 thf(omega0Ax,definition,
% 1.85/1.38 ( omega0Ax
% 1.85/1.38 = ( in @ emptyset @ omega ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(omegaSAx_type,type,
% 1.85/1.38 omegaSAx: $o ).
% 1.85/1.38
% 1.85/1.38 thf(omegaSAx,definition,
% 1.85/1.38 ( omegaSAx
% 1.85/1.38 = ( ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ omega )
% 1.85/1.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(omegaIndAx_type,type,
% 1.85/1.38 omegaIndAx: $o ).
% 1.85/1.38
% 1.85/1.38 thf(omegaIndAx,definition,
% 1.85/1.38 ( omegaIndAx
% 1.85/1.38 = ( ! [A: $i] :
% 1.85/1.38 ( ( ( in @ emptyset @ A )
% 1.85/1.38 & ! [Xx: $i] :
% 1.85/1.38 ( ( ( in @ Xx @ omega )
% 1.85/1.38 & ( in @ Xx @ A ) )
% 1.85/1.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.85/1.38 => ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ omega )
% 1.85/1.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(replAx_type,type,
% 1.85/1.38 replAx: $o ).
% 1.85/1.38
% 1.85/1.38 thf(replAx,definition,
% 1.85/1.38 ( replAx
% 1.85/1.38 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.85/1.38 ( ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ A )
% 1.85/1.38 => ( exu
% 1.85/1.38 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.85/1.38 => ? [B: $i] :
% 1.85/1.38 ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ B )
% 1.85/1.38 <=> ? [Xy: $i] :
% 1.85/1.38 ( ( in @ Xy @ A )
% 1.85/1.38 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(foundationAx_type,type,
% 1.85/1.38 foundationAx: $o ).
% 1.85/1.38
% 1.85/1.38 thf(foundationAx,definition,
% 1.85/1.38 ( foundationAx
% 1.85/1.38 = ( ! [A: $i] :
% 1.85/1.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.85/1.38 => ? [B: $i] :
% 1.85/1.38 ( ( in @ B @ A )
% 1.85/1.38 & ~ ? [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ B )
% 1.85/1.38 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(wellorderingAx_type,type,
% 1.85/1.38 wellorderingAx: $o ).
% 1.85/1.38
% 1.85/1.38 thf(wellorderingAx,definition,
% 1.85/1.38 ( wellorderingAx
% 1.85/1.38 = ( ! [A: $i] :
% 1.85/1.38 ? [B: $i] :
% 1.85/1.38 ( ! [C: $i] :
% 1.85/1.38 ( ( in @ C @ B )
% 1.85/1.38 => ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ C )
% 1.85/1.38 => ( in @ Xx @ A ) ) )
% 1.85/1.38 & ! [Xx: $i,Xy: $i] :
% 1.85/1.38 ( ( ( in @ Xx @ A )
% 1.85/1.38 & ( in @ Xy @ A ) )
% 1.85/1.38 => ( ! [C: $i] :
% 1.85/1.38 ( ( in @ C @ B )
% 1.85/1.38 => ( ( in @ Xx @ C )
% 1.85/1.38 <=> ( in @ Xy @ C ) ) )
% 1.85/1.38 => ( Xx = Xy ) ) )
% 1.85/1.38 & ! [C: $i,D: $i] :
% 1.85/1.38 ( ( ( in @ C @ B )
% 1.85/1.38 & ( in @ D @ B ) )
% 1.85/1.38 => ( ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ C )
% 1.85/1.38 => ( in @ Xx @ D ) )
% 1.85/1.38 | ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ D )
% 1.85/1.38 => ( in @ Xx @ C ) ) ) )
% 1.85/1.38 & ! [C: $i] :
% 1.85/1.38 ( ( ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ C )
% 1.85/1.38 => ( in @ Xx @ A ) )
% 1.85/1.38 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.85/1.38 => ? [D: $i,Xx: $i] :
% 1.85/1.38 ( ( in @ D @ B )
% 1.85/1.38 & ( in @ Xx @ C )
% 1.85/1.38 & ~ ? [Xy: $i] :
% 1.85/1.38 ( ( in @ Xy @ D )
% 1.85/1.38 & ( in @ Xy @ C ) )
% 1.85/1.38 & ! [E: $i] :
% 1.85/1.38 ( ( in @ E @ B )
% 1.85/1.38 => ( ! [Xy: $i] :
% 1.85/1.38 ( ( in @ Xy @ E )
% 1.85/1.38 => ( in @ Xy @ D ) )
% 1.85/1.38 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(descr_type,type,
% 1.85/1.38 descr: ( $i > $o ) > $i ).
% 1.85/1.38
% 1.85/1.38 thf(descrp_type,type,
% 1.85/1.38 descrp: $o ).
% 1.85/1.38
% 1.85/1.38 thf(descrp,definition,
% 1.85/1.38 ( descrp
% 1.85/1.38 = ( ! [Xphi: $i > $o] :
% 1.85/1.38 ( ( exu
% 1.85/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.85/1.38 => ( Xphi
% 1.85/1.38 @ ( descr
% 1.85/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(dsetconstr_type,type,
% 1.85/1.38 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.85/1.38
% 1.85/1.38 thf(dsetconstrI_type,type,
% 1.85/1.38 dsetconstrI: $o ).
% 1.85/1.38
% 1.85/1.38 thf(dsetconstrI,definition,
% 1.85/1.38 ( dsetconstrI
% 1.85/1.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ A )
% 1.85/1.38 => ( ( Xphi @ Xx )
% 1.85/1.38 => ( in @ Xx
% 1.85/1.38 @ ( dsetconstr @ A
% 1.85/1.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(dsetconstrEL_type,type,
% 1.85/1.38 dsetconstrEL: $o ).
% 1.85/1.38
% 1.85/1.38 thf(dsetconstrEL,definition,
% 1.85/1.38 ( dsetconstrEL
% 1.85/1.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.85/1.38 ( ( in @ Xx
% 1.85/1.38 @ ( dsetconstr @ A
% 1.85/1.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.85/1.38 => ( in @ Xx @ A ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(dsetconstrER_type,type,
% 1.85/1.38 dsetconstrER: $o ).
% 1.85/1.38
% 1.85/1.38 thf(dsetconstrER,definition,
% 1.85/1.38 ( dsetconstrER
% 1.85/1.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.85/1.38 ( ( in @ Xx
% 1.85/1.38 @ ( dsetconstr @ A
% 1.85/1.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.85/1.38 => ( Xphi @ Xx ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(exuE1_type,type,
% 1.85/1.38 exuE1: $o ).
% 1.85/1.38
% 1.85/1.38 thf(exuE1,definition,
% 1.85/1.38 ( exuE1
% 1.85/1.38 = ( ! [Xphi: $i > $o] :
% 1.85/1.38 ( ( exu
% 1.85/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.85/1.38 => ? [Xx: $i] :
% 1.85/1.38 ( ( Xphi @ Xx )
% 1.85/1.38 & ! [Xy: $i] :
% 1.85/1.38 ( ( Xphi @ Xy )
% 1.85/1.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(prop2set_type,type,
% 1.85/1.38 prop2set: $o > $i ).
% 1.85/1.38
% 1.85/1.38 thf(prop2set,definition,
% 1.85/1.38 ( prop2set
% 1.85/1.38 = ( ^ [Xphi: $o] :
% 1.85/1.38 ( dsetconstr @ ( powerset @ emptyset )
% 1.85/1.38 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(prop2setE_type,type,
% 1.85/1.38 prop2setE: $o ).
% 1.85/1.38
% 1.85/1.38 thf(prop2setE,definition,
% 1.85/1.38 ( prop2setE
% 1.85/1.38 = ( ! [Xphi: $o,Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.85/1.38 => Xphi ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(emptysetE_type,type,
% 1.85/1.38 emptysetE: $o ).
% 1.85/1.38
% 1.85/1.38 thf(emptysetE,definition,
% 1.85/1.38 ( emptysetE
% 1.85/1.38 = ( ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ emptyset )
% 1.85/1.38 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(emptysetimpfalse_type,type,
% 1.85/1.38 emptysetimpfalse: $o ).
% 1.85/1.38
% 1.85/1.38 thf(emptysetimpfalse,definition,
% 1.85/1.38 ( emptysetimpfalse
% 1.85/1.38 = ( ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ emptyset )
% 1.85/1.38 => $false ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(notinemptyset_type,type,
% 1.85/1.38 notinemptyset: $o ).
% 1.85/1.38
% 1.85/1.38 thf(notinemptyset,definition,
% 1.85/1.38 ( notinemptyset
% 1.85/1.38 = ( ! [Xx: $i] :
% 1.85/1.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(exuE3e_type,type,
% 1.85/1.38 exuE3e: $o ).
% 1.85/1.38
% 1.85/1.38 thf(exuE3e,definition,
% 1.85/1.38 ( exuE3e
% 1.85/1.38 = ( ! [Xphi: $i > $o] :
% 1.85/1.38 ( ( exu
% 1.85/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.85/1.38 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(setext_type,type,
% 1.85/1.38 setext: $o ).
% 1.85/1.38
% 1.85/1.38 thf(setext,definition,
% 1.85/1.38 ( setext
% 1.85/1.38 = ( ! [A: $i,B: $i] :
% 1.85/1.38 ( ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ A )
% 1.85/1.38 => ( in @ Xx @ B ) )
% 1.85/1.38 => ( ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ B )
% 1.85/1.38 => ( in @ Xx @ A ) )
% 1.85/1.38 => ( A = B ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(emptyI_type,type,
% 1.85/1.38 emptyI: $o ).
% 1.85/1.38
% 1.85/1.38 thf(emptyI,definition,
% 1.85/1.38 ( emptyI
% 1.85/1.38 = ( ! [A: $i] :
% 1.85/1.38 ( ! [Xx: $i] :
% 1.85/1.38 ~ ( in @ Xx @ A )
% 1.85/1.38 => ( A = emptyset ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(noeltsimpempty_type,type,
% 1.85/1.38 noeltsimpempty: $o ).
% 1.85/1.38
% 1.85/1.38 thf(noeltsimpempty,definition,
% 1.85/1.38 ( noeltsimpempty
% 1.85/1.38 = ( ! [A: $i] :
% 1.85/1.38 ( ! [Xx: $i] :
% 1.85/1.38 ~ ( in @ Xx @ A )
% 1.85/1.38 => ( A = emptyset ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(setbeta_type,type,
% 1.85/1.38 setbeta: $o ).
% 1.85/1.38
% 1.85/1.38 thf(setbeta,definition,
% 1.85/1.38 ( setbeta
% 1.85/1.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ A )
% 1.85/1.38 => ( ( in @ Xx
% 1.85/1.38 @ ( dsetconstr @ A
% 1.85/1.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.85/1.38 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(nonempty_type,type,
% 1.85/1.38 nonempty: $i > $o ).
% 1.85/1.38
% 1.85/1.38 thf(nonempty,definition,
% 1.85/1.38 ( nonempty
% 1.85/1.38 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(nonemptyE1_type,type,
% 1.85/1.38 nonemptyE1: $o ).
% 1.85/1.38
% 1.85/1.38 thf(nonemptyE1,definition,
% 1.85/1.38 ( nonemptyE1
% 1.85/1.38 = ( ! [A: $i] :
% 1.85/1.38 ( ( nonempty @ A )
% 1.85/1.38 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(nonemptyI_type,type,
% 1.85/1.38 nonemptyI: $o ).
% 1.85/1.38
% 1.85/1.38 thf(nonemptyI,definition,
% 1.85/1.38 ( nonemptyI
% 1.85/1.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ A )
% 1.85/1.38 => ( ( Xphi @ Xx )
% 1.85/1.38 => ( nonempty
% 1.85/1.38 @ ( dsetconstr @ A
% 1.85/1.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(nonemptyI1_type,type,
% 1.85/1.38 nonemptyI1: $o ).
% 1.85/1.38
% 1.85/1.38 thf(nonemptyI1,definition,
% 1.85/1.38 ( nonemptyI1
% 1.85/1.38 = ( ! [A: $i] :
% 1.85/1.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.85/1.38 => ( nonempty @ A ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(setadjoinIL_type,type,
% 1.85/1.38 setadjoinIL: $o ).
% 1.85/1.38
% 1.85/1.38 thf(setadjoinIL,definition,
% 1.85/1.38 ( setadjoinIL
% 1.85/1.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(emptyinunitempty_type,type,
% 1.85/1.38 emptyinunitempty: $o ).
% 1.85/1.38
% 1.85/1.38 thf(emptyinunitempty,definition,
% 1.85/1.38 ( emptyinunitempty
% 1.85/1.38 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(setadjoinIR_type,type,
% 1.85/1.38 setadjoinIR: $o ).
% 1.85/1.38
% 1.85/1.38 thf(setadjoinIR,definition,
% 1.85/1.38 ( setadjoinIR
% 1.85/1.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.85/1.38 ( ( in @ Xy @ A )
% 1.85/1.38 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(setadjoinE_type,type,
% 1.85/1.38 setadjoinE: $o ).
% 1.85/1.38
% 1.85/1.38 thf(setadjoinE,definition,
% 1.85/1.38 ( setadjoinE
% 1.85/1.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.85/1.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.85/1.38 => ! [Xphi: $o] :
% 1.85/1.38 ( ( ( Xy = Xx )
% 1.85/1.38 => Xphi )
% 1.85/1.38 => ( ( ( in @ Xy @ A )
% 1.85/1.38 => Xphi )
% 1.85/1.38 => Xphi ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(setadjoinOr_type,type,
% 1.85/1.38 setadjoinOr: $o ).
% 1.85/1.38
% 1.85/1.38 thf(setadjoinOr,definition,
% 1.85/1.38 ( setadjoinOr
% 1.85/1.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.85/1.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.85/1.38 => ( ( Xy = Xx )
% 1.85/1.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(setoftrueEq_type,type,
% 1.85/1.38 setoftrueEq: $o ).
% 1.85/1.38
% 1.85/1.38 thf(setoftrueEq,definition,
% 1.85/1.38 ( setoftrueEq
% 1.85/1.38 = ( ! [A: $i] :
% 1.85/1.38 ( ( dsetconstr @ A
% 1.85/1.38 @ ^ [Xx: $i] : $true )
% 1.85/1.38 = A ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(powersetI_type,type,
% 1.85/1.38 powersetI: $o ).
% 1.85/1.38
% 1.85/1.38 thf(powersetI,definition,
% 1.85/1.38 ( powersetI
% 1.85/1.38 = ( ! [A: $i,B: $i] :
% 1.85/1.38 ( ! [Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ B )
% 1.85/1.38 => ( in @ Xx @ A ) )
% 1.85/1.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(emptyinPowerset_type,type,
% 1.85/1.38 emptyinPowerset: $o ).
% 1.85/1.38
% 1.85/1.38 thf(emptyinPowerset,definition,
% 1.85/1.38 ( emptyinPowerset
% 1.85/1.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(emptyInPowerset_type,type,
% 1.85/1.38 emptyInPowerset: $o ).
% 1.85/1.38
% 1.85/1.38 thf(emptyInPowerset,definition,
% 1.85/1.38 ( emptyInPowerset
% 1.85/1.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(powersetE_type,type,
% 1.85/1.38 powersetE: $o ).
% 1.85/1.38
% 1.85/1.38 thf(powersetE,definition,
% 1.85/1.38 ( powersetE
% 1.85/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.85/1.38 ( ( in @ B @ ( powerset @ A ) )
% 1.85/1.38 => ( ( in @ Xx @ B )
% 1.85/1.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(setunionI_type,type,
% 1.85/1.38 setunionI: $o ).
% 1.85/1.38
% 1.85/1.38 thf(setunionI,definition,
% 1.85/1.38 ( setunionI
% 1.85/1.38 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.85/1.38 ( ( in @ Xx @ B )
% 1.85/1.38 => ( ( in @ B @ A )
% 1.85/1.38 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(setunionE_type,type,
% 1.85/1.38 setunionE: $o ).
% 1.85/1.38
% 1.85/1.38 thf(setunionE,definition,
% 1.85/1.38 ( setunionE
% 1.85/1.38 = ( ! [A: $i,Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ ( setunion @ A ) )
% 1.85/1.38 => ! [Xphi: $o] :
% 1.85/1.38 ( ! [B: $i] :
% 1.85/1.38 ( ( in @ Xx @ B )
% 1.85/1.38 => ( ( in @ B @ A )
% 1.85/1.38 => Xphi ) )
% 1.85/1.38 => Xphi ) ) ) ) ).
% 1.85/1.38
% 1.85/1.38 thf(subPowSU,conjecture,
% 1.85/1.38 ( setextAx
% 1.85/1.38 => ( emptysetAx
% 1.85/1.38 => ( setadjoinAx
% 1.85/1.38 => ( powersetAx
% 1.85/1.38 => ( setunionAx
% 1.85/1.38 => ( omega0Ax
% 1.85/1.38 => ( omegaSAx
% 1.85/1.38 => ( omegaIndAx
% 1.85/1.38 => ( replAx
% 1.85/1.38 => ( foundationAx
% 1.85/1.38 => ( wellorderingAx
% 1.85/1.38 => ( descrp
% 1.85/1.38 => ( dsetconstrI
% 1.85/1.38 => ( dsetconstrEL
% 1.85/1.38 => ( dsetconstrER
% 1.85/1.38 => ( exuE1
% 1.85/1.38 => ( prop2setE
% 1.85/1.38 => ( emptysetE
% 1.85/1.38 => ( emptysetimpfalse
% 1.85/1.38 => ( notinemptyset
% 1.85/1.38 => ( exuE3e
% 1.85/1.38 => ( setext
% 1.85/1.38 => ( emptyI
% 1.85/1.38 => ( noeltsimpempty
% 1.85/1.38 => ( setbeta
% 1.85/1.38 => ( nonemptyE1
% 1.85/1.38 => ( nonemptyI
% 1.85/1.38 => ( nonemptyI1
% 1.85/1.38 => ( setadjoinIL
% 1.85/1.38 => ( emptyinunitempty
% 1.85/1.38 => ( setadjoinIR
% 1.85/1.38 => ( setadjoinE
% 1.85/1.38 => ( setadjoinOr
% 1.85/1.38 => ( setoftrueEq
% 1.85/1.38 => ( powersetI
% 1.85/1.38 => ( emptyinPowerset
% 1.85/1.38 => ( emptyInPowerset
% 1.85/1.38 => ( powersetE
% 1.85/1.38 => ( setunionI
% 1.85/1.38 => ( setunionE
% 1.85/1.38 => ! [A: $i,Xx: $i] :
% 1.85/1.38 ( ( in @ Xx @ A )
% 1.85/1.38 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.85/1.38 ------------------------
% 1.85/1.39 % (29768)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/18Mi)
% 1.85/1.39 % (29767)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_29480 for (2999ds/275Mi)
% 2.01/1.40 % (29768)Instruction limit reached!
% 2.01/1.40 % (29768)------------------------------
% 2.01/1.40 % (29768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.40 % (29768)Termination reason: Unknown
% 2.01/1.40 % (29768)Termination phase: Property scanning
% 2.01/1.40
% 2.01/1.40 % (29768)Memory used [KB]: 1535
% 2.01/1.40 % (29768)Time elapsed: 0.007 s
% 2.01/1.40 % (29768)Instructions burned: 20 (million)
% 2.01/1.40 % (29768)------------------------------
% 2.01/1.40 % (29768)------------------------------
% 2.01/1.40 % (29762)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/183Mi)
% 2.01/1.40 % (29763)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_29480 for (2999ds/4Mi)
% 2.01/1.40 % (29765)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/2Mi)
% 2.01/1.40 % (29766)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_29480 for (2999ds/2Mi)
% 2.01/1.40 % (29764)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_29480 for (2999ds/27Mi)
% 2.01/1.40 % (29765)Instruction limit reached!
% 2.01/1.40 % (29765)------------------------------
% 2.01/1.40 % (29765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.40 % (29765)Termination reason: Unknown
% 2.01/1.40 % (29765)Termination phase: shuffling
% 2.01/1.40
% 2.01/1.40 % (29765)Memory used [KB]: 1023
% 2.01/1.40 % (29765)Time elapsed: 0.003 s
% 2.01/1.40 % (29765)Instructions burned: 2 (million)
% 2.01/1.40 % (29765)------------------------------
% 2.01/1.40 % (29765)------------------------------
% 2.01/1.40 % (29766)Instruction limit reached!
% 2.01/1.40 % (29766)------------------------------
% 2.01/1.40 % (29766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.40 % (29766)Termination reason: Unknown
% 2.01/1.40 % (29766)Termination phase: shuffling
% 2.01/1.40
% 2.01/1.40 % (29766)Memory used [KB]: 1023
% 2.01/1.40 % (29766)Time elapsed: 0.003 s
% 2.01/1.40 % (29766)Instructions burned: 2 (million)
% 2.01/1.40 % (29766)------------------------------
% 2.01/1.40 % (29766)------------------------------
% 2.01/1.40 % (29763)Instruction limit reached!
% 2.01/1.40 % (29763)------------------------------
% 2.01/1.40 % (29763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.40 % (29763)Termination reason: Unknown
% 2.01/1.40 % (29763)Termination phase: shuffling
% 2.01/1.40
% 2.01/1.40 % (29763)Memory used [KB]: 1151
% 2.01/1.40 % (29763)Time elapsed: 0.004 s
% 2.01/1.40 % (29763)Instructions burned: 4 (million)
% 2.01/1.40 % (29763)------------------------------
% 2.01/1.40 % (29763)------------------------------
% 2.01/1.41 % (29769)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/3Mi)
% 2.01/1.41 % (29769)Instruction limit reached!
% 2.01/1.41 % (29769)------------------------------
% 2.01/1.41 % (29769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.41 % (29769)Termination reason: Unknown
% 2.01/1.41 % (29769)Termination phase: shuffling
% 2.01/1.41
% 2.01/1.41 % (29769)Memory used [KB]: 1023
% 2.01/1.41 % (29769)Time elapsed: 0.002 s
% 2.01/1.41 % (29769)Instructions burned: 4 (million)
% 2.01/1.41 % (29769)------------------------------
% 2.01/1.41 % (29769)------------------------------
% 2.01/1.42 % (29764)Instruction limit reached!
% 2.01/1.42 % (29764)------------------------------
% 2.01/1.42 % (29764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.42 % (29764)Termination reason: Unknown
% 2.01/1.42 % (29764)Termination phase: Saturation
% 2.01/1.42
% 2.01/1.42 % (29764)Memory used [KB]: 5756
% 2.01/1.42 % (29764)Time elapsed: 0.016 s
% 2.01/1.42 % (29764)Instructions burned: 28 (million)
% 2.01/1.42 % (29764)------------------------------
% 2.01/1.42 % (29764)------------------------------
% 2.01/1.42 % (29773)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_29480 for (2999ds/1041Mi)
% 2.01/1.42 % (29770)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_29480 for (2999ds/37Mi)
% 2.01/1.42 % (29771)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_29480 for (2999ds/15Mi)
% 2.01/1.42 % (29772)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_29480 for (2999ds/3Mi)
% 2.01/1.42 % (29772)Instruction limit reached!
% 2.01/1.42 % (29772)------------------------------
% 2.01/1.42 % (29772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.42 % (29772)Termination reason: Unknown
% 2.01/1.42 % (29772)Termination phase: shuffling
% 2.01/1.42
% 2.01/1.42 % (29772)Memory used [KB]: 1151
% 2.01/1.42 % (29772)Time elapsed: 0.004 s
% 2.01/1.42 % (29772)Instructions burned: 4 (million)
% 2.01/1.42 % (29772)------------------------------
% 2.01/1.42 % (29772)------------------------------
% 2.01/1.43 % (29771)Instruction limit reached!
% 2.01/1.43 % (29771)------------------------------
% 2.01/1.43 % (29771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.43 % (29771)Termination reason: Unknown
% 2.01/1.43 % (29771)Termination phase: Preprocessing 3
% 2.01/1.43
% 2.01/1.43 % (29771)Memory used [KB]: 1535
% 2.01/1.43 % (29771)Time elapsed: 0.011 s
% 2.01/1.43 % (29771)Instructions burned: 16 (million)
% 2.01/1.43 % (29771)------------------------------
% 2.01/1.43 % (29771)------------------------------
% 2.01/1.43 % (29774)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/7Mi)
% 2.01/1.44 % (29770)Instruction limit reached!
% 2.01/1.44 % (29770)------------------------------
% 2.01/1.44 % (29770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.44 % (29770)Termination reason: Unknown
% 2.01/1.44 % (29770)Termination phase: Saturation
% 2.01/1.44
% 2.01/1.44 % (29770)Memory used [KB]: 6012
% 2.01/1.44 % (29770)Time elapsed: 0.018 s
% 2.01/1.44 % (29770)Instructions burned: 39 (million)
% 2.01/1.44 % (29770)------------------------------
% 2.01/1.44 % (29770)------------------------------
% 2.01/1.44 % (29774)Instruction limit reached!
% 2.01/1.44 % (29774)------------------------------
% 2.01/1.44 % (29774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.44 % (29774)Termination reason: Unknown
% 2.01/1.44 % (29774)Termination phase: Property scanning
% 2.01/1.44
% 2.01/1.44 % (29774)Memory used [KB]: 1151
% 2.01/1.44 % (29774)Time elapsed: 0.006 s
% 2.01/1.44 % (29774)Instructions burned: 8 (million)
% 2.01/1.44 % (29774)------------------------------
% 2.01/1.44 % (29774)------------------------------
% 2.01/1.44 % (29775)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/16Mi)
% 2.01/1.45 % (29776)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_29480 for (2999ds/3Mi)
% 2.01/1.45 % (29777)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_29480 for (2999ds/3Mi)
% 2.01/1.45 % (29775)Instruction limit reached!
% 2.01/1.45 % (29775)------------------------------
% 2.01/1.45 % (29775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.45 % (29775)Termination reason: Unknown
% 2.01/1.45 % (29775)Termination phase: Function definition elimination
% 2.01/1.45
% 2.01/1.45 % (29775)Memory used [KB]: 1151
% 2.01/1.45 % (29775)Time elapsed: 0.010 s
% 2.01/1.45 % (29775)Instructions burned: 17 (million)
% 2.01/1.45 % (29775)------------------------------
% 2.01/1.45 % (29775)------------------------------
% 2.01/1.45 % (29777)Instruction limit reached!
% 2.01/1.45 % (29777)------------------------------
% 2.01/1.45 % (29777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.45 % (29777)Termination reason: Unknown
% 2.01/1.45 % (29777)Termination phase: shuffling
% 2.01/1.45
% 2.01/1.45 % (29777)Memory used [KB]: 1151
% 2.01/1.45 % (29777)Time elapsed: 0.003 s
% 2.01/1.45 % (29777)Instructions burned: 6 (million)
% 2.01/1.45 % (29777)------------------------------
% 2.01/1.45 % (29777)------------------------------
% 2.01/1.45 % (29776)Instruction limit reached!
% 2.01/1.45 % (29776)------------------------------
% 2.01/1.45 % (29776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.45 % (29776)Termination reason: Unknown
% 2.01/1.45 % (29776)Termination phase: shuffling
% 2.01/1.45
% 2.01/1.45 % (29776)Memory used [KB]: 1151
% 2.01/1.45 % (29776)Time elapsed: 0.004 s
% 2.01/1.45 % (29776)Instructions burned: 4 (million)
% 2.01/1.45 % (29776)------------------------------
% 2.01/1.45 % (29776)------------------------------
% 2.01/1.46 % (29778)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/7Mi)
% 2.01/1.46 % (29779)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/3Mi)
% 2.01/1.46 % (29778)Instruction limit reached!
% 2.01/1.46 % (29778)------------------------------
% 2.01/1.46 % (29778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.46 % (29778)Termination reason: Unknown
% 2.01/1.46 % (29778)Termination phase: Property scanning
% 2.01/1.46
% 2.01/1.46 % (29778)Memory used [KB]: 1151
% 2.01/1.46 % (29778)Time elapsed: 0.006 s
% 2.01/1.46 % (29778)Instructions burned: 8 (million)
% 2.01/1.46 % (29778)------------------------------
% 2.01/1.46 % (29778)------------------------------
% 2.01/1.46 % (29779)Instruction limit reached!
% 2.01/1.46 % (29779)------------------------------
% 2.01/1.46 % (29779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.46 % (29779)Termination reason: Unknown
% 2.01/1.46 % (29779)Termination phase: shuffling
% 2.01/1.46
% 2.01/1.46 % (29779)Memory used [KB]: 1151
% 2.01/1.46 % (29779)Time elapsed: 0.003 s
% 2.01/1.46 % (29779)Instructions burned: 5 (million)
% 2.01/1.46 % (29779)------------------------------
% 2.01/1.46 % (29779)------------------------------
% 2.01/1.47 % (29780)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/4Mi)
% 2.01/1.47 % (29781)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/18Mi)
% 2.01/1.47 % (29780)Instruction limit reached!
% 2.01/1.47 % (29780)------------------------------
% 2.01/1.47 % (29780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.47 % (29780)Termination reason: Unknown
% 2.01/1.47 % (29780)Termination phase: shuffling
% 2.01/1.47
% 2.01/1.47 % (29780)Memory used [KB]: 1023
% 2.01/1.47 % (29780)Time elapsed: 0.003 s
% 2.01/1.47 % (29780)Instructions burned: 4 (million)
% 2.01/1.47 % (29780)------------------------------
% 2.01/1.47 % (29780)------------------------------
% 2.01/1.47 % (29783)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/6Mi)
% 2.01/1.47 % (29783)Instruction limit reached!
% 2.01/1.47 % (29783)------------------------------
% 2.01/1.47 % (29783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.47 % (29783)Termination reason: Unknown
% 2.01/1.47 % (29783)Termination phase: Property scanning
% 2.01/1.47
% 2.01/1.47 % (29783)Memory used [KB]: 1151
% 2.01/1.47 % (29783)Time elapsed: 0.004 s
% 2.01/1.47 % (29783)Instructions burned: 8 (million)
% 2.01/1.47 % (29783)------------------------------
% 2.01/1.47 % (29783)------------------------------
% 2.01/1.47 % (29762)Instruction limit reached!
% 2.01/1.47 % (29762)------------------------------
% 2.01/1.47 % (29762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.47 % (29762)Termination reason: Unknown
% 2.01/1.47 % (29762)Termination phase: Saturation
% 2.01/1.47
% 2.01/1.47 % (29762)Memory used [KB]: 6908
% 2.01/1.47 % (29762)Time elapsed: 0.074 s
% 2.01/1.47 % (29762)Instructions burned: 183 (million)
% 2.01/1.47 % (29762)------------------------------
% 2.01/1.47 % (29762)------------------------------
% 2.01/1.48 % (29781)Instruction limit reached!
% 2.01/1.48 % (29781)------------------------------
% 2.01/1.48 % (29781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.48 % (29781)Termination reason: Unknown
% 2.01/1.48 % (29781)Termination phase: Saturation
% 2.01/1.48
% 2.01/1.48 % (29781)Memory used [KB]: 5756
% 2.01/1.48 % (29781)Time elapsed: 0.011 s
% 2.01/1.48 % (29781)Instructions burned: 18 (million)
% 2.01/1.48 % (29781)------------------------------
% 2.01/1.48 % (29781)------------------------------
% 2.01/1.48 % (29782)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/710Mi)
% 2.01/1.48 % (29784)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_29480 for (2999ds/902Mi)
% 2.01/1.48 % (29785)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_29480 for (2999ds/21Mi)
% 2.01/1.48 % (29786)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/5Mi)
% 2.01/1.48 % (29786)Instruction limit reached!
% 2.01/1.48 % (29786)------------------------------
% 2.01/1.48 % (29786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.48 % (29786)Termination reason: Unknown
% 2.01/1.48 % (29786)Termination phase: shuffling
% 2.01/1.48
% 2.01/1.48 % (29786)Memory used [KB]: 1151
% 2.01/1.48 % (29786)Time elapsed: 0.003 s
% 2.01/1.48 % (29786)Instructions burned: 5 (million)
% 2.01/1.48 % (29786)------------------------------
% 2.01/1.48 % (29786)------------------------------
% 2.01/1.49 % (29767)Instruction limit reached!
% 2.01/1.49 % (29767)------------------------------
% 2.01/1.49 % (29767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.49 % (29767)Termination reason: Unknown
% 2.01/1.49 % (29767)Termination phase: Saturation
% 2.01/1.49
% 2.01/1.49 % (29767)Memory used [KB]: 7036
% 2.01/1.49 % (29767)Time elapsed: 0.093 s
% 2.01/1.49 % (29767)Instructions burned: 275 (million)
% 2.01/1.49 % (29767)------------------------------
% 2.01/1.49 % (29767)------------------------------
% 2.01/1.49 % (29785)Instruction limit reached!
% 2.01/1.49 % (29785)------------------------------
% 2.01/1.49 % (29785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.49 % (29785)Termination reason: Unknown
% 2.01/1.49 % (29785)Termination phase: Property scanning
% 2.01/1.49
% 2.01/1.49 % (29785)Memory used [KB]: 1279
% 2.01/1.49 % (29785)Time elapsed: 0.008 s
% 2.01/1.49 % (29785)Instructions burned: 23 (million)
% 2.01/1.49 % (29785)------------------------------
% 2.01/1.49 % (29785)------------------------------
% 2.01/1.49 % (29787)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_29480 for (2999ds/6Mi)
% 2.01/1.49 % (29787)Instruction limit reached!
% 2.01/1.49 % (29787)------------------------------
% 2.01/1.49 % (29787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.49 % (29787)Termination reason: Unknown
% 2.01/1.49 % (29787)Termination phase: shuffling
% 2.01/1.49
% 2.01/1.49 % (29787)Memory used [KB]: 1151
% 2.01/1.49 % (29787)Time elapsed: 0.004 s
% 2.01/1.49 % (29787)Instructions burned: 7 (million)
% 2.01/1.49 % (29787)------------------------------
% 2.01/1.49 % (29787)------------------------------
% 2.01/1.49 % (29788)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29480 for (2999ds/377Mi)
% 2.01/1.50 % (29789)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_29480 for (2999ds/779Mi)
% 2.01/1.50 % (29790)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_29480 for (2999ds/19Mi)
% 2.01/1.50 % (29790)Instruction limit reached!
% 2.01/1.50 % (29790)------------------------------
% 2.01/1.50 % (29790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.50 % (29790)Termination reason: Unknown
% 2.01/1.50 % (29790)Termination phase: Function definition elimination
% 2.01/1.50
% 2.01/1.50 % (29790)Memory used [KB]: 1279
% 2.01/1.50 % (29790)Time elapsed: 0.007 s
% 2.01/1.50 % (29790)Instructions burned: 19 (million)
% 2.01/1.50 % (29790)------------------------------
% 2.01/1.50 % (29790)------------------------------
% 2.01/1.51 % (29791)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_29480 for (2998ds/879Mi)
% 2.01/1.51 % (29792)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_29480 for (2998ds/17Mi)
% 2.01/1.52 % (29792)Instruction limit reached!
% 2.01/1.52 % (29792)------------------------------
% 2.01/1.52 % (29792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.52 % (29792)Termination reason: Unknown
% 2.01/1.52 % (29792)Termination phase: Property scanning
% 2.01/1.52
% 2.01/1.52 % (29792)Memory used [KB]: 1151
% 2.01/1.52 % (29792)Time elapsed: 0.007 s
% 2.01/1.52 % (29792)Instructions burned: 19 (million)
% 2.01/1.52 % (29792)------------------------------
% 2.01/1.52 % (29792)------------------------------
% 2.01/1.53 % (29793)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_29480 for (2998ds/3Mi)
% 2.01/1.53 % (29793)Instruction limit reached!
% 2.01/1.53 % (29793)------------------------------
% 2.01/1.53 % (29793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.53 % (29793)Termination reason: Unknown
% 2.01/1.53 % (29793)Termination phase: shuffling
% 2.01/1.53
% 2.01/1.53 % (29793)Memory used [KB]: 1151
% 2.01/1.53 % (29793)Time elapsed: 0.003 s
% 2.01/1.53 % (29793)Instructions burned: 5 (million)
% 2.01/1.53 % (29793)------------------------------
% 2.01/1.53 % (29793)------------------------------
% 2.01/1.54 % (29794)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_29480 for (2998ds/30Mi)
% 2.01/1.55 % (29794)Instruction limit reached!
% 2.01/1.55 % (29794)------------------------------
% 2.01/1.55 % (29794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.55 % (29794)Termination reason: Unknown
% 2.01/1.55 % (29794)Termination phase: Saturation
% 2.01/1.55
% 2.01/1.55 % (29794)Memory used [KB]: 5756
% 2.01/1.55 % (29794)Time elapsed: 0.011 s
% 2.01/1.55 % (29794)Instructions burned: 31 (million)
% 2.01/1.55 % (29794)------------------------------
% 2.01/1.55 % (29794)------------------------------
% 2.01/1.56 % (29795)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_29480 for (2998ds/127Mi)
% 2.01/1.60 % (29795)Instruction limit reached!
% 2.01/1.60 % (29795)------------------------------
% 2.01/1.60 % (29795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.60 % (29795)Termination reason: Unknown
% 2.01/1.60 % (29795)Termination phase: Saturation
% 2.01/1.60
% 2.01/1.60 % (29795)Memory used [KB]: 6396
% 2.01/1.60 % (29795)Time elapsed: 0.065 s
% 2.01/1.60 % (29795)Instructions burned: 127 (million)
% 2.01/1.60 % (29795)------------------------------
% 2.01/1.60 % (29795)------------------------------
% 2.01/1.61 % (29796)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_29480 for (2997ds/100Mi)
% 2.01/1.62 % (29788)Instruction limit reached!
% 2.01/1.62 % (29788)------------------------------
% 2.01/1.62 % (29788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.62 % (29788)Termination reason: Unknown
% 2.01/1.62 % (29788)Termination phase: Saturation
% 2.01/1.62
% 2.01/1.62 % (29788)Memory used [KB]: 6652
% 2.01/1.62 % (29788)Time elapsed: 0.127 s
% 2.01/1.62 % (29788)Instructions burned: 378 (million)
% 2.01/1.62 % (29788)------------------------------
% 2.01/1.62 % (29788)------------------------------
% 2.01/1.63 % (29797)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_29480 for (2997ds/3Mi)
% 2.01/1.63 % (29797)Instruction limit reached!
% 2.01/1.63 % (29797)------------------------------
% 2.01/1.63 % (29797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.63 % (29797)Termination reason: Unknown
% 2.01/1.63 % (29797)Termination phase: shuffling
% 2.01/1.63
% 2.01/1.63 % (29797)Memory used [KB]: 1151
% 2.01/1.63 % (29797)Time elapsed: 0.003 s
% 2.01/1.63 % (29797)Instructions burned: 5 (million)
% 2.01/1.63 % (29797)------------------------------
% 2.01/1.63 % (29797)------------------------------
% 2.01/1.64 % (29798)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_29480 for (2997ds/20Mi)
% 2.01/1.64 % (29796)Instruction limit reached!
% 2.01/1.64 % (29796)------------------------------
% 2.01/1.64 % (29796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.64 % (29796)Termination reason: Unknown
% 2.01/1.64 % (29796)Termination phase: Saturation
% 2.01/1.64
% 2.01/1.64 % (29796)Memory used [KB]: 6012
% 2.01/1.64 % (29796)Time elapsed: 0.033 s
% 2.01/1.64 % (29796)Instructions burned: 100 (million)
% 2.01/1.64 % (29796)------------------------------
% 2.01/1.64 % (29796)------------------------------
% 2.01/1.65 % (29798)Instruction limit reached!
% 2.01/1.65 % (29798)------------------------------
% 2.01/1.65 % (29798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.65 % (29798)Termination reason: Unknown
% 2.01/1.65 % (29798)Termination phase: Property scanning
% 2.01/1.65
% 2.01/1.65 % (29798)Memory used [KB]: 1535
% 2.01/1.65 % (29798)Time elapsed: 0.008 s
% 2.01/1.65 % (29798)Instructions burned: 20 (million)
% 2.01/1.65 % (29798)------------------------------
% 2.01/1.65 % (29798)------------------------------
% 2.01/1.65 % (29799)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_29480 for (2997ds/86Mi)
% 2.01/1.66 % (29800)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_29480 for (2997ds/107Mi)
% 2.01/1.68 % (29799)Instruction limit reached!
% 2.01/1.68 % (29799)------------------------------
% 2.01/1.68 % (29799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.68 % (29799)Termination reason: Unknown
% 2.01/1.68 % (29799)Termination phase: Saturation
% 2.01/1.68
% 2.01/1.68 % (29799)Memory used [KB]: 6268
% 2.01/1.68 % (29799)Time elapsed: 0.054 s
% 2.01/1.68 % (29799)Instructions burned: 88 (million)
% 2.01/1.68 % (29799)------------------------------
% 2.01/1.68 % (29799)------------------------------
% 2.01/1.69 % (29801)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_29480 for (2997ds/39Mi)
% 2.01/1.69 % (29800)Instruction limit reached!
% 2.01/1.69 % (29800)------------------------------
% 2.01/1.69 % (29800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.69 % (29800)Termination reason: Unknown
% 2.01/1.69 % (29800)Termination phase: Saturation
% 2.01/1.69
% 2.01/1.69 % (29800)Memory used [KB]: 6268
% 2.01/1.69 % (29800)Time elapsed: 0.060 s
% 2.01/1.69 % (29800)Instructions burned: 108 (million)
% 2.01/1.69 % (29800)------------------------------
% 2.01/1.69 % (29800)------------------------------
% 2.01/1.70 % (29801)Instruction limit reached!
% 2.01/1.70 % (29801)------------------------------
% 2.01/1.70 % (29801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.70 % (29801)Termination reason: Unknown
% 2.01/1.70 % (29801)Termination phase: Saturation
% 2.01/1.70
% 2.01/1.70 % (29801)Memory used [KB]: 6012
% 2.01/1.70 % (29801)Time elapsed: 0.013 s
% 2.01/1.70 % (29801)Instructions burned: 41 (million)
% 2.01/1.70 % (29801)------------------------------
% 2.01/1.70 % (29801)------------------------------
% 2.01/1.70 % (29802)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_29480 for (2997ds/448Mi)
% 2.01/1.70 % (29789)Instruction limit reached!
% 2.01/1.70 % (29789)------------------------------
% 2.01/1.70 % (29789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.70 % (29789)Termination reason: Unknown
% 2.01/1.70 % (29789)Termination phase: Saturation
% 2.01/1.70
% 2.01/1.70 % (29789)Memory used [KB]: 6780
% 2.01/1.70 % (29789)Time elapsed: 0.209 s
% 2.01/1.70 % (29789)Instructions burned: 780 (million)
% 2.01/1.70 % (29789)------------------------------
% 2.01/1.70 % (29789)------------------------------
% 2.01/1.71 % (29773)Instruction limit reached!
% 2.01/1.71 % (29773)------------------------------
% 2.01/1.71 % (29773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.71 % (29773)Termination reason: Unknown
% 2.01/1.71 % (29773)Termination phase: Saturation
% 2.01/1.71
% 2.01/1.71 % (29773)Memory used [KB]: 8187
% 2.01/1.71 % (29773)Time elapsed: 0.290 s
% 2.01/1.71 % (29773)Instructions burned: 1042 (million)
% 2.01/1.71 % (29773)------------------------------
% 2.01/1.71 % (29773)------------------------------
% 2.01/1.71 % (29803)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_29480 for (2996ds/46Mi)
% 2.01/1.71 % (29804)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_29480 for (2996ds/98Mi)
% 2.01/1.72 % (29805)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_29480 for (2996ds/507Mi)
% 2.01/1.73 % (29803)Instruction limit reached!
% 2.01/1.73 % (29803)------------------------------
% 2.01/1.73 % (29803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.73 % (29803)Termination reason: Unknown
% 2.01/1.73 % (29803)Termination phase: Saturation
% 2.01/1.73
% 2.01/1.73 % (29803)Memory used [KB]: 5884
% 2.01/1.73 % (29803)Time elapsed: 0.015 s
% 2.01/1.73 % (29803)Instructions burned: 47 (million)
% 2.01/1.73 % (29803)------------------------------
% 2.01/1.73 % (29803)------------------------------
% 2.01/1.73 % (29782)Instruction limit reached!
% 2.01/1.73 % (29782)------------------------------
% 2.01/1.73 % (29782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.73 % (29782)Termination reason: Unknown
% 2.01/1.73 % (29782)Termination phase: Saturation
% 2.01/1.73
% 2.01/1.73 % (29782)Memory used [KB]: 8059
% 2.01/1.73 % (29782)Time elapsed: 0.253 s
% 2.01/1.73 % (29782)Instructions burned: 710 (million)
% 2.01/1.73 % (29782)------------------------------
% 2.01/1.73 % (29782)------------------------------
% 2.01/1.74 % (29806)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_29480 for (2996ds/149Mi)
% 2.01/1.74 % (29807)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_29480 for (2996ds/39Mi)
% 2.01/1.74 % (29804)Instruction limit reached!
% 2.01/1.74 % (29804)------------------------------
% 2.01/1.74 % (29804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.74 % (29804)Termination reason: Unknown
% 2.01/1.74 % (29804)Termination phase: Saturation
% 2.01/1.74
% 2.01/1.74 % (29804)Memory used [KB]: 1279
% 2.01/1.74 % (29804)Time elapsed: 0.026 s
% 2.01/1.74 % (29804)Instructions burned: 99 (million)
% 2.01/1.74 % (29804)------------------------------
% 2.01/1.74 % (29804)------------------------------
% 2.01/1.75 % (29808)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_29480 for (2996ds/6Mi)
% 2.01/1.75 % (29807)Instruction limit reached!
% 2.01/1.75 % (29807)------------------------------
% 2.01/1.75 % (29807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.75 % (29807)Termination reason: Unknown
% 2.01/1.75 % (29807)Termination phase: Saturation
% 2.01/1.75
% 2.01/1.75 % (29807)Memory used [KB]: 5884
% 2.01/1.75 % (29807)Time elapsed: 0.013 s
% 2.01/1.75 % (29807)Instructions burned: 40 (million)
% 2.01/1.75 % (29807)------------------------------
% 2.01/1.75 % (29807)------------------------------
% 2.01/1.75 % (29808)Instruction limit reached!
% 2.01/1.75 % (29808)------------------------------
% 2.01/1.75 % (29808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.75 % (29808)Termination reason: Unknown
% 2.01/1.75 % (29808)Termination phase: Property scanning
% 2.01/1.75
% 2.01/1.75 % (29808)Memory used [KB]: 1151
% 2.01/1.75 % (29808)Time elapsed: 0.003 s
% 2.01/1.75 % (29808)Instructions burned: 8 (million)
% 2.01/1.75 % (29808)------------------------------
% 2.01/1.75 % (29808)------------------------------
% 2.01/1.76 % (29810)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_29480 for (2996ds/47Mi)
% 2.01/1.76 % (29809)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_29480 for (2996ds/1087Mi)
% 2.01/1.77 % (29784)Instruction limit reached!
% 2.01/1.77 % (29784)------------------------------
% 2.01/1.77 % (29784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.77 % (29784)Termination reason: Unknown
% 2.01/1.77 % (29784)Termination phase: Saturation
% 2.01/1.77
% 2.01/1.77 % (29784)Memory used [KB]: 8315
% 2.01/1.77 % (29784)Time elapsed: 0.291 s
% 2.01/1.77 % (29784)Instructions burned: 903 (million)
% 2.01/1.77 % (29784)------------------------------
% 2.01/1.77 % (29784)------------------------------
% 2.01/1.77 % (29810)Instruction limit reached!
% 2.01/1.77 % (29810)------------------------------
% 2.01/1.77 % (29810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.77 % (29810)Termination reason: Unknown
% 2.01/1.77 % (29810)Termination phase: Saturation
% 2.01/1.77
% 2.01/1.77 % (29810)Memory used [KB]: 5884
% 2.01/1.77 % (29810)Time elapsed: 0.015 s
% 2.01/1.77 % (29810)Instructions burned: 49 (million)
% 2.01/1.77 % (29810)------------------------------
% 2.01/1.77 % (29810)------------------------------
% 2.01/1.78 % (29811)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_29480 for (2996ds/44Mi)
% 2.01/1.78 % (29812)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_29480 for (2996ds/432Mi)
% 2.01/1.78 % (29806)Instruction limit reached!
% 2.01/1.78 % (29806)------------------------------
% 2.01/1.78 % (29806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.78 % (29806)Termination reason: Unknown
% 2.01/1.78 % (29806)Termination phase: Saturation
% 2.01/1.78
% 2.01/1.78 % (29806)Memory used [KB]: 6140
% 2.01/1.78 % (29806)Time elapsed: 0.051 s
% 2.01/1.78 % (29806)Instructions burned: 151 (million)
% 2.01/1.78 % (29806)------------------------------
% 2.01/1.78 % (29806)------------------------------
% 2.01/1.79 % (29791)Instruction limit reached!
% 2.01/1.79 % (29791)------------------------------
% 2.01/1.79 % (29791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.79 % (29791)Termination reason: Unknown
% 2.01/1.79 % (29791)Termination phase: Saturation
% 2.01/1.79
% 2.01/1.79 % (29791)Memory used [KB]: 7547
% 2.01/1.79 % (29791)Time elapsed: 0.305 s
% 2.01/1.79 % (29791)Instructions burned: 881 (million)
% 2.01/1.79 % (29791)------------------------------
% 2.01/1.79 % (29791)------------------------------
% 2.01/1.79 % (29811)Instruction limit reached!
% 2.01/1.79 % (29811)------------------------------
% 2.01/1.79 % (29811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.79 % (29811)Termination reason: Unknown
% 2.01/1.79 % (29811)Termination phase: Saturation
% 2.01/1.79
% 2.01/1.79 % (29811)Memory used [KB]: 1279
% 2.01/1.79 % (29811)Time elapsed: 0.014 s
% 2.01/1.79 % (29811)Instructions burned: 46 (million)
% 2.01/1.79 % (29811)------------------------------
% 2.01/1.79 % (29811)------------------------------
% 2.01/1.79 % (29813)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_29480 for (2995ds/62Mi)
% 2.01/1.80 % (29814)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_29480 for (2995ds/31Mi)
% 2.01/1.80 % (29815)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_29480 for (2995ds/96Mi)
% 2.01/1.81 % (29814)Instruction limit reached!
% 2.01/1.81 % (29814)------------------------------
% 2.01/1.81 % (29814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.81 % (29814)Termination reason: Unknown
% 2.01/1.81 % (29814)Termination phase: Saturation
% 2.01/1.81
% 2.01/1.81 % (29814)Memory used [KB]: 5756
% 2.01/1.81 % (29814)Time elapsed: 0.011 s
% 2.01/1.81 % (29814)Instructions burned: 33 (million)
% 2.01/1.81 % (29814)------------------------------
% 2.01/1.81 % (29814)------------------------------
% 2.01/1.81 % (29813)Instruction limit reached!
% 2.01/1.81 % (29813)------------------------------
% 2.01/1.81 % (29813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.81 % (29813)Termination reason: Unknown
% 2.01/1.81 % (29813)Termination phase: Saturation
% 2.01/1.81
% 2.01/1.81 % (29813)Memory used [KB]: 6140
% 2.01/1.81 % (29813)Time elapsed: 0.019 s
% 2.01/1.81 % (29813)Instructions burned: 63 (million)
% 2.01/1.81 % (29813)------------------------------
% 2.01/1.81 % (29813)------------------------------
% 2.01/1.82 % (29816)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_29480 for (2995ds/453Mi)
% 2.01/1.82 % (29817)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_29480 for (2995ds/71Mi)
% 2.01/1.83 % (29815)Instruction limit reached!
% 2.01/1.83 % (29815)------------------------------
% 2.01/1.83 % (29815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.83 % (29815)Termination reason: Unknown
% 2.01/1.83 % (29815)Termination phase: Saturation
% 2.01/1.83
% 2.01/1.83 % (29815)Memory used [KB]: 6140
% 2.01/1.83 % (29815)Time elapsed: 0.032 s
% 2.01/1.83 % (29815)Instructions burned: 96 (million)
% 2.01/1.83 % (29815)------------------------------
% 2.01/1.83 % (29815)------------------------------
% 2.01/1.84 % (29802)Instruction limit reached!
% 2.01/1.84 % (29802)------------------------------
% 2.01/1.84 % (29802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.84 % (29802)Termination reason: Unknown
% 2.01/1.84 % (29802)Termination phase: Saturation
% 2.01/1.84
% 2.01/1.84 % (29802)Memory used [KB]: 6652
% 2.01/1.84 % (29802)Time elapsed: 0.165 s
% 2.01/1.84 % (29802)Instructions burned: 450 (million)
% 2.01/1.84 % (29802)------------------------------
% 2.01/1.84 % (29802)------------------------------
% 2.01/1.84 % (29818)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_29480 for (2995ds/83Mi)
% 2.01/1.84 % (29817)Instruction limit reached!
% 2.01/1.84 % (29817)------------------------------
% 2.01/1.84 % (29817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.84 % (29817)Termination reason: Unknown
% 2.01/1.84 % (29817)Termination phase: Saturation
% 2.01/1.84
% 2.01/1.84 % (29817)Memory used [KB]: 6012
% 2.01/1.84 % (29817)Time elapsed: 0.023 s
% 2.01/1.84 % (29817)Instructions burned: 74 (million)
% 2.01/1.84 % (29817)------------------------------
% 2.01/1.84 % (29817)------------------------------
% 2.01/1.85 % (29819)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_29480 for (2995ds/11Mi)
% 2.01/1.85 % (29819)Instruction limit reached!
% 2.01/1.85 % (29819)------------------------------
% 2.01/1.85 % (29819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.85 % (29819)Termination reason: Unknown
% 2.01/1.85 % (29819)Termination phase: Property scanning
% 2.01/1.85
% 2.01/1.85 % (29819)Memory used [KB]: 1151
% 2.01/1.85 % (29819)Time elapsed: 0.004 s
% 2.01/1.85 % (29819)Instructions burned: 12 (million)
% 2.01/1.85 % (29819)------------------------------
% 2.01/1.85 % (29819)------------------------------
% 2.01/1.85 % (29820)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_29480 for (2995ds/41Mi)
% 2.01/1.86 % (29821)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29480 for (2995ds/6Mi)
% 2.01/1.86 % (29821)Instruction limit reached!
% 2.01/1.86 % (29821)------------------------------
% 2.01/1.86 % (29821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.86 % (29821)Termination reason: Unknown
% 2.01/1.86 % (29821)Termination phase: shuffling
% 2.01/1.86
% 2.01/1.86 % (29821)Memory used [KB]: 1151
% 2.01/1.86 % (29821)Time elapsed: 0.003 s
% 2.01/1.86 % (29821)Instructions burned: 7 (million)
% 2.01/1.86 % (29821)------------------------------
% 2.01/1.86 % (29821)------------------------------
% 2.01/1.86 % (29820)Instruction limit reached!
% 2.01/1.86 % (29820)------------------------------
% 2.01/1.86 % (29820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.86 % (29820)Termination reason: Unknown
% 2.01/1.86 % (29820)Termination phase: Saturation
% 2.01/1.86
% 2.01/1.86 % (29820)Memory used [KB]: 6012
% 2.01/1.86 % (29820)Time elapsed: 0.012 s
% 2.01/1.86 % (29820)Instructions burned: 43 (million)
% 2.01/1.86 % (29820)------------------------------
% 2.01/1.86 % (29820)------------------------------
% 2.01/1.87 % (29818)Instruction limit reached!
% 2.01/1.87 % (29818)------------------------------
% 2.01/1.87 % (29818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.87 % (29818)Termination reason: Unknown
% 2.01/1.87 % (29818)Termination phase: Saturation
% 2.01/1.87
% 2.01/1.87 % (29818)Memory used [KB]: 6140
% 2.01/1.87 % (29818)Time elapsed: 0.028 s
% 2.01/1.87 % (29818)Instructions burned: 85 (million)
% 2.01/1.87 % (29818)------------------------------
% 2.01/1.87 % (29818)------------------------------
% 2.01/1.87 % (29822)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_29480 for (2995ds/150Mi)
% 2.01/1.87 % (29823)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_29480 for (2995ds/343Mi)
% 2.01/1.87 % (29805)Instruction limit reached!
% 2.01/1.87 % (29805)------------------------------
% 2.01/1.87 % (29805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.87 % (29805)Termination reason: Unknown
% 2.01/1.87 % (29805)Termination phase: Saturation
% 2.01/1.87
% 2.01/1.87 % (29805)Memory used [KB]: 6908
% 2.01/1.87 % (29805)Time elapsed: 0.157 s
% 2.01/1.87 % (29805)Instructions burned: 507 (million)
% 2.01/1.87 % (29805)------------------------------
% 2.01/1.87 % (29805)------------------------------
% 2.01/1.88 % (29824)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_29480 for (2995ds/109Mi)
% 2.01/1.88 % (29825)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_29480 for (2995ds/253Mi)
% 2.01/1.89 % (29812)Instruction limit reached!
% 2.01/1.89 % (29812)------------------------------
% 2.01/1.89 % (29812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.89 % (29812)Termination reason: Unknown
% 2.01/1.89 % (29812)Termination phase: Saturation
% 2.01/1.89
% 2.01/1.89 % (29812)Memory used [KB]: 1918
% 2.01/1.89 % (29812)Time elapsed: 0.111 s
% 2.01/1.89 % (29812)Instructions burned: 435 (million)
% 2.01/1.89 % (29812)------------------------------
% 2.01/1.89 % (29812)------------------------------
% 2.01/1.90 % (29826)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_29480 for (2994ds/140Mi)
% 2.01/1.91 % (29824)Instruction limit reached!
% 2.01/1.91 % (29824)------------------------------
% 2.01/1.91 % (29824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.91 % (29824)Termination reason: Unknown
% 2.01/1.91 % (29824)Termination phase: Saturation
% 2.01/1.91
% 2.01/1.91 % (29824)Memory used [KB]: 6396
% 2.01/1.91 % (29824)Time elapsed: 0.033 s
% 2.01/1.91 % (29824)Instructions burned: 110 (million)
% 2.01/1.91 % (29824)------------------------------
% 2.01/1.91 % (29824)------------------------------
% 2.01/1.91 % (29826)Refutation not found, incomplete strategy
% 2.01/1.91 % (29826)------------------------------
% 2.01/1.91 % (29826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.91 % (29826)Termination reason: Refutation not found, incomplete strategy
% 2.01/1.91
% 2.01/1.91
% 2.01/1.91 % (29826)Memory used [KB]: 5756
% 2.01/1.91 % (29826)Time elapsed: 0.013 s
% 2.01/1.91 % (29826)Instructions burned: 44 (million)
% 2.01/1.91 % (29826)------------------------------
% 2.01/1.91 % (29826)------------------------------
% 2.01/1.92 % (29827)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_29480 for (2994ds/614Mi)
% 2.01/1.92 % (29822)Instruction limit reached!
% 2.01/1.92 % (29822)------------------------------
% 2.01/1.92 % (29822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.92 % (29822)Termination reason: Unknown
% 2.01/1.92 % (29822)Termination phase: Saturation
% 2.01/1.92
% 2.01/1.92 % (29822)Memory used [KB]: 6524
% 2.01/1.92 % (29822)Time elapsed: 0.048 s
% 2.01/1.92 % (29822)Instructions burned: 151 (million)
% 2.01/1.92 % (29822)------------------------------
% 2.01/1.92 % (29822)------------------------------
% 2.01/1.92 % (29828)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_29480 for (2994ds/202Mi)
% 2.01/1.93 % (29829)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_29480 for (2994ds/339Mi)
% 2.01/1.96 % (29816)Instruction limit reached!
% 2.01/1.96 % (29816)------------------------------
% 2.01/1.96 % (29816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.96 % (29816)Termination reason: Unknown
% 2.01/1.96 % (29816)Termination phase: Saturation
% 2.01/1.96
% 2.01/1.96 % (29816)Memory used [KB]: 6396
% 2.01/1.96 % (29816)Time elapsed: 0.140 s
% 2.01/1.96 % (29816)Instructions burned: 455 (million)
% 2.01/1.96 % (29816)------------------------------
% 2.01/1.96 % (29816)------------------------------
% 2.01/1.96 % (29825)Instruction limit reached!
% 2.01/1.96 % (29825)------------------------------
% 2.01/1.96 % (29825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.96 % (29825)Termination reason: Unknown
% 2.01/1.96 % (29825)Termination phase: Saturation
% 2.01/1.96
% 2.01/1.96 % (29825)Memory used [KB]: 7036
% 2.01/1.96 % (29825)Time elapsed: 0.079 s
% 2.01/1.96 % (29825)Instructions burned: 255 (million)
% 2.01/1.96 % (29825)------------------------------
% 2.01/1.96 % (29825)------------------------------
% 2.01/1.97 % (29830)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_29480 for (2994ds/283Mi)
% 2.01/1.97 % (29831)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_29480 for (2994ds/134Mi)
% 2.01/1.98 % (29823)Instruction limit reached!
% 2.01/1.98 % (29823)------------------------------
% 2.01/1.98 % (29823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.98 % (29823)Termination reason: Unknown
% 2.01/1.98 % (29823)Termination phase: Saturation
% 2.01/1.98
% 2.01/1.98 % (29823)Memory used [KB]: 6908
% 2.01/1.98 % (29823)Time elapsed: 0.106 s
% 2.01/1.98 % (29823)Instructions burned: 345 (million)
% 2.01/1.98 % (29823)------------------------------
% 2.01/1.98 % (29823)------------------------------
% 2.01/1.99 % (29828)Instruction limit reached!
% 2.01/1.99 % (29828)------------------------------
% 2.01/1.99 % (29828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.01/1.99 % (29828)Termination reason: Unknown
% 2.01/1.99 % (29828)Termination phase: Saturation
% 2.01/1.99
% 2.01/1.99 % (29828)Memory used [KB]: 6780
% 2.01/1.99 % (29828)Time elapsed: 0.063 s
% 2.01/1.99 % (29828)Instructions burned: 204 (million)
% 2.01/1.99 % (29828)------------------------------
% 2.01/1.99 % (29828)------------------------------
% 2.01/1.99 % (29832)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_29480 for (2994ds/298Mi)
% 2.01/2.00 % (29833)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_29480 for (2994ds/192Mi)
% 6.36/2.01 % (29831)Instruction limit reached!
% 6.36/2.01 % (29831)------------------------------
% 6.36/2.01 % (29831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.36/2.01 % (29831)Termination reason: Unknown
% 6.36/2.01 % (29831)Termination phase: Saturation
% 6.36/2.01
% 6.36/2.01 % (29831)Memory used [KB]: 6268
% 6.36/2.01 % (29831)Time elapsed: 0.042 s
% 6.36/2.01 % (29831)Instructions burned: 135 (million)
% 6.36/2.01 % (29831)------------------------------
% 6.36/2.01 % (29831)------------------------------
% 6.36/2.02 % (29834)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_29480 for (2993ds/258Mi)
% 6.36/2.03 % (29829)Instruction limit reached!
% 6.36/2.03 % (29829)------------------------------
% 6.36/2.03 % (29829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.36/2.03 % (29829)Termination reason: Unknown
% 6.36/2.03 % (29829)Termination phase: Saturation
% 6.36/2.03
% 6.36/2.03 % (29829)Memory used [KB]: 7419
% 6.36/2.03 % (29829)Time elapsed: 0.099 s
% 6.36/2.03 % (29829)Instructions burned: 340 (million)
% 6.36/2.03 % (29829)------------------------------
% 6.36/2.03 % (29829)------------------------------
% 6.36/2.04 % (29835)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_29480 for (2993ds/90Mi)
% 6.36/2.04 % (29830)Instruction limit reached!
% 6.36/2.04 % (29830)------------------------------
% 6.36/2.04 % (29830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.36/2.04 % (29830)Termination reason: Unknown
% 6.36/2.04 % (29830)Termination phase: Saturation
% 6.36/2.04
% 6.36/2.04 % (29830)Memory used [KB]: 6268
% 6.36/2.04 % (29830)Time elapsed: 0.074 s
% 6.36/2.04 % (29830)Instructions burned: 284 (million)
% 6.36/2.04 % (29830)------------------------------
% 6.36/2.04 % (29830)------------------------------
% 6.36/2.05 % (29836)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_29480 for (2993ds/231Mi)
% 6.36/2.05 % (29833)Instruction limit reached!
% 6.36/2.05 % (29833)------------------------------
% 6.36/2.05 % (29833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.36/2.05 % (29833)Termination reason: Unknown
% 6.36/2.05 % (29833)Termination phase: Saturation
% 6.36/2.05
% 6.36/2.05 % (29833)Memory used [KB]: 6396
% 6.36/2.05 % (29833)Time elapsed: 0.060 s
% 6.36/2.05 % (29833)Instructions burned: 194 (million)
% 6.36/2.05 % (29833)------------------------------
% 6.36/2.05 % (29833)------------------------------
% 6.36/2.06 % (29832)Instruction limit reached!
% 6.36/2.06 % (29832)------------------------------
% 6.36/2.06 % (29832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.36/2.06 % (29832)Termination reason: Unknown
% 6.36/2.06 % (29832)Termination phase: Saturation
% 6.36/2.06
% 6.36/2.06 % (29832)Memory used [KB]: 6012
% 6.36/2.06 % (29832)Time elapsed: 0.073 s
% 6.36/2.06 % (29832)Instructions burned: 299 (million)
% 6.36/2.06 % (29832)------------------------------
% 6.36/2.06 % (29832)------------------------------
% 6.36/2.06 % (29835)Instruction limit reached!
% 6.36/2.06 % (29835)------------------------------
% 6.36/2.06 % (29835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.36/2.06 % (29835)Termination reason: Unknown
% 6.36/2.06 % (29835)Termination phase: Saturation
% 6.36/2.06
% 6.36/2.06 % (29835)Memory used [KB]: 6268
% 6.36/2.06 % (29835)Time elapsed: 0.028 s
% 6.36/2.06 % (29835)Instructions burned: 91 (million)
% 6.36/2.06 % (29835)------------------------------
% 6.36/2.06 % (29835)------------------------------
% 6.36/2.06 % (29837)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_29480 for (2993ds/458Mi)
% 6.36/2.07 % (29838)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_29480 for (2993ds/31Mi)
% 6.36/2.07 % (29839)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_29480 for (2993ds/297Mi)
% 6.36/2.08 % (29838)Instruction limit reached!
% 6.36/2.08 % (29838)------------------------------
% 6.36/2.08 % (29838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.36/2.08 % (29838)Termination reason: Unknown
% 6.36/2.08 % (29838)Termination phase: Saturation
% 6.36/2.08
% 6.36/2.08 % (29838)Memory used [KB]: 5756
% 6.36/2.08 % (29838)Time elapsed: 0.009 s
% 6.36/2.08 % (29838)Instructions burned: 31 (million)
% 6.36/2.08 % (29838)------------------------------
% 6.36/2.08 % (29838)------------------------------
% 6.36/2.09 % (29840)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_29480 for (2993ds/987Mi)
% 6.36/2.10 % (29834)Instruction limit reached!
% 6.36/2.10 % (29834)------------------------------
% 6.36/2.10 % (29834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.36/2.10 % (29834)Termination reason: Unknown
% 6.36/2.10 % (29834)Termination phase: Saturation
% 6.36/2.10
% 6.36/2.10 % (29834)Memory used [KB]: 6396
% 6.36/2.10 % (29834)Time elapsed: 0.079 s
% 6.36/2.10 % (29834)Instructions burned: 260 (million)
% 6.36/2.10 % (29834)------------------------------
% 6.36/2.10 % (29834)------------------------------
% 6.36/2.10 % (29827)Instruction limit reached!
% 6.36/2.10 % (29827)------------------------------
% 6.36/2.10 % (29827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.36/2.10 % (29827)Termination reason: Unknown
% 6.36/2.10 % (29827)Termination phase: Saturation
% 6.36/2.10
% 6.36/2.10 % (29827)Memory used [KB]: 7036
% 6.36/2.10 % (29827)Time elapsed: 0.185 s
% 6.36/2.10 % (29827)Instructions burned: 614 (million)
% 6.36/2.10 % (29827)------------------------------
% 6.36/2.10 % (29827)------------------------------
% 6.36/2.11 % (29841)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_29480 for (2992ds/182Mi)
% 6.87/2.11 % (29842)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_29480 for (2992ds/182Mi)
% 6.87/2.12 % (29836)Instruction limit reached!
% 6.87/2.12 % (29836)------------------------------
% 6.87/2.12 % (29836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.12 % (29836)Termination reason: Unknown
% 6.87/2.12 % (29836)Termination phase: Saturation
% 6.87/2.12
% 6.87/2.12 % (29836)Memory used [KB]: 7803
% 6.87/2.12 % (29836)Time elapsed: 0.078 s
% 6.87/2.12 % (29836)Instructions burned: 232 (million)
% 6.87/2.12 % (29836)------------------------------
% 6.87/2.12 % (29836)------------------------------
% 6.87/2.13 % (29843)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_29480 for (2992ds/154Mi)
% 6.87/2.15 % (29839)Instruction limit reached!
% 6.87/2.15 % (29839)------------------------------
% 6.87/2.15 % (29839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.15 % (29839)Termination reason: Unknown
% 6.87/2.15 % (29839)Termination phase: Saturation
% 6.87/2.15
% 6.87/2.15 % (29839)Memory used [KB]: 6268
% 6.87/2.15 % (29839)Time elapsed: 0.080 s
% 6.87/2.15 % (29839)Instructions burned: 298 (million)
% 6.87/2.15 % (29839)------------------------------
% 6.87/2.15 % (29839)------------------------------
% 6.87/2.16 % (29844)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_29480 for (2992ds/79Mi)
% 6.87/2.16 % (29841)Instruction limit reached!
% 6.87/2.16 % (29841)------------------------------
% 6.87/2.16 % (29841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.16 % (29841)Termination reason: Unknown
% 6.87/2.16 % (29841)Termination phase: Saturation
% 6.87/2.16
% 6.87/2.16 % (29841)Memory used [KB]: 6652
% 6.87/2.16 % (29841)Time elapsed: 0.055 s
% 6.87/2.16 % (29841)Instructions burned: 183 (million)
% 6.87/2.16 % (29841)------------------------------
% 6.87/2.16 % (29841)------------------------------
% 6.87/2.17 % (29809)Instruction limit reached!
% 6.87/2.17 % (29809)------------------------------
% 6.87/2.17 % (29809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.17 % (29809)Termination reason: Unknown
% 6.87/2.17 % (29809)Termination phase: Saturation
% 6.87/2.17
% 6.87/2.17 % (29809)Memory used [KB]: 8187
% 6.87/2.17 % (29809)Time elapsed: 0.411 s
% 6.87/2.17 % (29809)Instructions burned: 1088 (million)
% 6.87/2.17 % (29809)------------------------------
% 6.87/2.17 % (29809)------------------------------
% 6.87/2.17 % (29842)Instruction limit reached!
% 6.87/2.17 % (29842)------------------------------
% 6.87/2.17 % (29842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.17 % (29842)Termination reason: Unknown
% 6.87/2.17 % (29842)Termination phase: Saturation
% 6.87/2.17
% 6.87/2.17 % (29842)Memory used [KB]: 7164
% 6.87/2.17 % (29842)Time elapsed: 0.060 s
% 6.87/2.17 % (29842)Instructions burned: 182 (million)
% 6.87/2.17 % (29842)------------------------------
% 6.87/2.17 % (29842)------------------------------
% 6.87/2.17 % (29845)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_29480 for (2992ds/216Mi)
% 6.87/2.18 % (29843)Instruction limit reached!
% 6.87/2.18 % (29843)------------------------------
% 6.87/2.18 % (29843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.18 % (29843)Termination reason: Unknown
% 6.87/2.18 % (29843)Termination phase: Saturation
% 6.87/2.18
% 6.87/2.18 % (29843)Memory used [KB]: 6012
% 6.87/2.18 % (29843)Time elapsed: 0.044 s
% 6.87/2.18 % (29843)Instructions burned: 156 (million)
% 6.87/2.18 % (29843)------------------------------
% 6.87/2.18 % (29843)------------------------------
% 6.87/2.18 % (29846)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_29480 for (2992ds/114Mi)
% 6.87/2.18 % (29847)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_29480 for (2992ds/922Mi)
% 6.87/2.19 % (29844)Instruction limit reached!
% 6.87/2.19 % (29844)------------------------------
% 6.87/2.19 % (29844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.19 % (29844)Termination reason: Unknown
% 6.87/2.19 % (29844)Termination phase: Saturation
% 6.87/2.19
% 6.87/2.19 % (29844)Memory used [KB]: 6140
% 6.87/2.19 % (29844)Time elapsed: 0.025 s
% 6.87/2.19 % (29844)Instructions burned: 81 (million)
% 6.87/2.19 % (29844)------------------------------
% 6.87/2.19 % (29844)------------------------------
% 6.87/2.19 % (29848)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_29480 for (2992ds/182Mi)
% 6.87/2.19 % (29849)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_29480 for (2992ds/164Mi)
% 7.31/2.20 % (29837)Instruction limit reached!
% 7.31/2.20 % (29837)------------------------------
% 7.31/2.20 % (29837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.20 % (29837)Termination reason: Unknown
% 7.31/2.20 % (29837)Termination phase: Saturation
% 7.31/2.20
% 7.31/2.20 % (29837)Memory used [KB]: 6908
% 7.31/2.20 % (29837)Time elapsed: 0.142 s
% 7.31/2.20 % (29837)Instructions burned: 458 (million)
% 7.31/2.20 % (29837)------------------------------
% 7.31/2.20 % (29837)------------------------------
% 7.31/2.21 % (29850)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_29480 for (2991ds/50Mi)
% 7.31/2.22 % (29846)Instruction limit reached!
% 7.31/2.22 % (29846)------------------------------
% 7.31/2.22 % (29846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.22 % (29846)Termination reason: Unknown
% 7.31/2.22 % (29846)Termination phase: Saturation
% 7.31/2.22
% 7.31/2.22 % (29846)Memory used [KB]: 6396
% 7.31/2.22 % (29846)Time elapsed: 0.038 s
% 7.31/2.22 % (29846)Instructions burned: 115 (million)
% 7.31/2.22 % (29846)------------------------------
% 7.31/2.22 % (29846)------------------------------
% 7.31/2.23 % (29851)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_29480 for (2991ds/368Mi)
% 7.31/2.23 % (29845)Instruction limit reached!
% 7.31/2.23 % (29845)------------------------------
% 7.31/2.23 % (29845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.23 % (29845)Termination reason: Unknown
% 7.31/2.23 % (29845)Termination phase: Saturation
% 7.31/2.23
% 7.31/2.23 % (29845)Memory used [KB]: 6140
% 7.31/2.23 % (29845)Time elapsed: 0.055 s
% 7.31/2.23 % (29845)Instructions burned: 216 (million)
% 7.31/2.23 % (29845)------------------------------
% 7.31/2.23 % (29845)------------------------------
% 7.31/2.23 % (29850)Instruction limit reached!
% 7.31/2.23 % (29850)------------------------------
% 7.31/2.23 % (29850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.23 % (29850)Termination reason: Unknown
% 7.31/2.23 % (29850)Termination phase: Saturation
% 7.31/2.23
% 7.31/2.23 % (29850)Memory used [KB]: 10234
% 7.31/2.23 % (29850)Time elapsed: 0.014 s
% 7.31/2.23 % (29850)Instructions burned: 50 (million)
% 7.31/2.23 % (29850)------------------------------
% 7.31/2.23 % (29850)------------------------------
% 7.31/2.24 % (29848)Instruction limit reached!
% 7.31/2.24 % (29848)------------------------------
% 7.31/2.24 % (29848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.24 % (29848)Termination reason: Unknown
% 7.31/2.24 % (29848)Termination phase: Saturation
% 7.31/2.24
% 7.31/2.24 % (29848)Memory used [KB]: 6140
% 7.31/2.24 % (29848)Time elapsed: 0.050 s
% 7.31/2.24 % (29848)Instructions burned: 182 (million)
% 7.31/2.24 % (29848)------------------------------
% 7.31/2.24 % (29848)------------------------------
% 7.31/2.24 % (29852)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_29480 for (2991ds/1021Mi)
% 7.31/2.24 % (29853)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_29480 for (2991ds/267Mi)
% 7.31/2.24 % (29849)Instruction limit reached!
% 7.31/2.24 % (29849)------------------------------
% 7.31/2.24 % (29849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.24 % (29849)Termination reason: Unknown
% 7.31/2.24 % (29849)Termination phase: Saturation
% 7.31/2.24
% 7.31/2.24 % (29849)Memory used [KB]: 1663
% 7.31/2.24 % (29849)Time elapsed: 0.047 s
% 7.31/2.24 % (29849)Instructions burned: 166 (million)
% 7.31/2.24 % (29849)------------------------------
% 7.31/2.24 % (29849)------------------------------
% 7.31/2.25 % (29855)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_29480 for (2991ds/26Mi)
% 7.31/2.25 % (29854)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_29480 for (2991ds/204Mi)
% 7.31/2.26 % (29855)Instruction limit reached!
% 7.31/2.26 % (29855)------------------------------
% 7.31/2.26 % (29855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.26 % (29855)Termination reason: Unknown
% 7.31/2.26 % (29855)Termination phase: Saturation
% 7.31/2.26
% 7.31/2.26 % (29855)Memory used [KB]: 5884
% 7.31/2.26 % (29855)Time elapsed: 0.009 s
% 7.31/2.26 % (29855)Instructions burned: 29 (million)
% 7.31/2.26 % (29855)------------------------------
% 7.31/2.26 % (29855)------------------------------
% 7.31/2.27 % (29856)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_29480 for (2991ds/53Mi)
% 7.31/2.28 % (29856)Instruction limit reached!
% 7.31/2.28 % (29856)------------------------------
% 7.31/2.28 % (29856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.28 % (29856)Termination reason: Unknown
% 7.31/2.28 % (29856)Termination phase: Saturation
% 7.31/2.28
% 7.31/2.28 % (29856)Memory used [KB]: 6140
% 7.31/2.28 % (29856)Time elapsed: 0.015 s
% 7.31/2.28 % (29856)Instructions burned: 54 (million)
% 7.31/2.28 % (29856)------------------------------
% 7.31/2.28 % (29856)------------------------------
% 7.31/2.29 % (29857)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_29480 for (2991ds/4436Mi)
% 7.75/2.31 % (29853)Instruction limit reached!
% 7.75/2.31 % (29853)------------------------------
% 7.75/2.31 % (29853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.31 % (29853)Termination reason: Unknown
% 7.75/2.31 % (29853)Termination phase: Saturation
% 7.75/2.31
% 7.75/2.31 % (29853)Memory used [KB]: 6268
% 7.75/2.31 % (29853)Time elapsed: 0.091 s
% 7.75/2.31 % (29853)Instructions burned: 267 (million)
% 7.75/2.31 % (29853)------------------------------
% 7.75/2.31 % (29853)------------------------------
% 7.75/2.31 % (29858)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_29480 for (2990ds/1539Mi)
% 7.75/2.33 % (29854)Instruction limit reached!
% 7.75/2.33 % (29854)------------------------------
% 7.75/2.33 % (29854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.33 % (29854)Termination reason: Unknown
% 7.75/2.33 % (29854)Termination phase: Saturation
% 7.75/2.33
% 7.75/2.33 % (29854)Memory used [KB]: 6268
% 7.75/2.33 % (29854)Time elapsed: 0.101 s
% 7.75/2.33 % (29854)Instructions burned: 204 (million)
% 7.75/2.33 % (29854)------------------------------
% 7.75/2.33 % (29854)------------------------------
% 7.75/2.34 % (29859)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_29480 for (2990ds/408Mi)
% 7.75/2.35 % (29840)Instruction limit reached!
% 7.75/2.35 % (29840)------------------------------
% 7.75/2.35 % (29840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.35 % (29840)Termination reason: Unknown
% 7.75/2.35 % (29840)Termination phase: Saturation
% 7.75/2.35
% 7.75/2.35 % (29840)Memory used [KB]: 6780
% 7.75/2.35 % (29840)Time elapsed: 0.262 s
% 7.75/2.35 % (29840)Instructions burned: 988 (million)
% 7.75/2.35 % (29840)------------------------------
% 7.75/2.35 % (29840)------------------------------
% 7.75/2.35 % (29851)Instruction limit reached!
% 7.75/2.35 % (29851)------------------------------
% 7.75/2.35 % (29851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.35 % (29851)Termination reason: Unknown
% 7.75/2.35 % (29851)Termination phase: Saturation
% 7.75/2.35
% 7.75/2.35 % (29851)Memory used [KB]: 6908
% 7.75/2.35 % (29851)Time elapsed: 0.124 s
% 7.75/2.35 % (29851)Instructions burned: 369 (million)
% 7.75/2.35 % (29851)------------------------------
% 7.75/2.35 % (29851)------------------------------
% 7.75/2.36 % (29860)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_29480 for (2990ds/5205Mi)
% 7.75/2.36 % (29861)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_29480 for (2990ds/1913Mi)
% 8.33/2.47 % (29859)Instruction limit reached!
% 8.33/2.47 % (29859)------------------------------
% 8.33/2.47 % (29859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.47 % (29859)Termination reason: Unknown
% 8.33/2.47 % (29859)Termination phase: Saturation
% 8.33/2.47
% 8.33/2.47 % (29859)Memory used [KB]: 7036
% 8.33/2.47 % (29859)Time elapsed: 0.151 s
% 8.33/2.47 % (29859)Instructions burned: 408 (million)
% 8.33/2.47 % (29859)------------------------------
% 8.33/2.47 % (29859)------------------------------
% 8.33/2.47 % (29847)Instruction limit reached!
% 8.33/2.47 % (29847)------------------------------
% 8.33/2.47 % (29847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.47 % (29847)Termination reason: Unknown
% 8.33/2.47 % (29847)Termination phase: Saturation
% 8.33/2.47
% 8.33/2.47 % (29847)Memory used [KB]: 8187
% 8.33/2.47 % (29847)Time elapsed: 0.289 s
% 8.33/2.47 % (29847)Instructions burned: 925 (million)
% 8.33/2.47 % (29847)------------------------------
% 8.33/2.47 % (29847)------------------------------
% 8.33/2.47 % (29862)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_29480 for (2989ds/4350Mi)
% 8.33/2.48 % (29863)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_29480 for (2989ds/68Mi)
% 8.77/2.50 % (29863)Instruction limit reached!
% 8.77/2.50 % (29863)------------------------------
% 8.77/2.50 % (29863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.50 % (29863)Termination reason: Unknown
% 8.77/2.50 % (29863)Termination phase: Saturation
% 8.77/2.50
% 8.77/2.50 % (29863)Memory used [KB]: 6140
% 8.77/2.50 % (29863)Time elapsed: 0.020 s
% 8.77/2.50 % (29863)Instructions burned: 68 (million)
% 8.77/2.50 % (29863)------------------------------
% 8.77/2.50 % (29863)------------------------------
% 8.77/2.51 % (29864)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_29480 for (2988ds/358Mi)
% 8.77/2.55 % (29852)Instruction limit reached!
% 8.77/2.55 % (29852)------------------------------
% 8.77/2.55 % (29852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.55 % (29852)Termination reason: Unknown
% 8.77/2.55 % (29852)Termination phase: Saturation
% 8.77/2.55
% 8.77/2.55 % (29852)Memory used [KB]: 8443
% 8.77/2.55 % (29852)Time elapsed: 0.318 s
% 8.77/2.55 % (29852)Instructions burned: 1024 (million)
% 8.77/2.55 % (29852)------------------------------
% 8.77/2.55 % (29852)------------------------------
% 8.77/2.56 % (29865)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_29480 for (2988ds/31Mi)
% 8.77/2.57 % (29865)Instruction limit reached!
% 8.77/2.57 % (29865)------------------------------
% 8.77/2.57 % (29865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.57 % (29865)Termination reason: Unknown
% 8.77/2.57 % (29865)Termination phase: Saturation
% 8.77/2.57
% 8.77/2.57 % (29865)Memory used [KB]: 5756
% 8.77/2.57 % (29865)Time elapsed: 0.010 s
% 8.77/2.57 % (29865)Instructions burned: 32 (million)
% 8.77/2.57 % (29865)------------------------------
% 8.77/2.57 % (29865)------------------------------
% 8.77/2.58 % (29866)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_29480 for (2988ds/279Mi)
% 9.15/2.62 % (29864)Instruction limit reached!
% 9.15/2.62 % (29864)------------------------------
% 9.15/2.62 % (29864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/2.62 % (29864)Termination reason: Unknown
% 9.15/2.62 % (29864)Termination phase: Saturation
% 9.15/2.62
% 9.15/2.62 % (29864)Memory used [KB]: 6524
% 9.15/2.62 % (29864)Time elapsed: 0.113 s
% 9.15/2.62 % (29864)Instructions burned: 360 (million)
% 9.15/2.62 % (29864)------------------------------
% 9.15/2.62 % (29864)------------------------------
% 9.15/2.63 % (29867)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_29480 for (2987ds/258Mi)
% 9.15/2.64 % (29858)First to succeed.
% 9.15/2.64 % (29858)Refutation found. Thanks to Tanya!
% 9.15/2.64 % SZS status Theorem for DTF2THF_29480
% 9.15/2.64 % SZS output start Proof for DTF2THF_29480
% 9.15/2.64 thf(func_def_0, type, in: $i > $i > $o).
% 9.15/2.64 thf(func_def_1, type, exu: ($i > $o) > $o).
% 9.15/2.64 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 9.15/2.64 thf(func_def_8, type, powerset: $i > $i).
% 9.15/2.64 thf(func_def_10, type, setunion: $i > $i).
% 9.15/2.64 thf(func_def_19, type, descr: ($i > $o) > $i).
% 9.15/2.64 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 9.15/2.64 thf(func_def_26, type, prop2set: $o > $i).
% 9.15/2.64 thf(func_def_36, type, nonempty: $i > $o).
% 9.15/2.64 thf(func_def_71, type, sK3: $i > $i).
% 9.15/2.64 thf(func_def_72, type, sK4: $i > $i).
% 9.15/2.64 thf(func_def_73, type, sK5: $i > $i > $i).
% 9.15/2.64 thf(func_def_74, type, sK6: $i > $i > $i).
% 9.15/2.64 thf(func_def_75, type, sK7: $i > $i > $i).
% 9.15/2.64 thf(func_def_76, type, sK8: ($i > $o) > $i > $i).
% 9.15/2.64 thf(func_def_77, type, sK9: ($i > $o) > $i).
% 9.15/2.64 thf(func_def_78, type, sK10: $i > ($i > $i > $o) > $i).
% 9.15/2.64 thf(func_def_79, type, sK11: $i > ($i > $i > $o) > $i).
% 9.15/2.64 thf(func_def_80, type, sK12: $i > $i > ($i > $i > $o) > $i).
% 9.15/2.64 thf(func_def_81, type, sK13: $i > $i).
% 9.15/2.64 thf(func_def_82, type, sK14: $i > $i).
% 9.15/2.64 thf(func_def_83, type, sK15: ($i > $o) > $i > $i).
% 9.15/2.64 thf(func_def_84, type, sK16: $i > $i > $i).
% 9.15/2.64 thf(func_def_85, type, sK17: $i > $i).
% 9.15/2.64 thf(func_def_86, type, sK18: $i > $i > $i).
% 9.15/2.64 thf(func_def_87, type, sK19: $o > $i > $i > $i).
% 9.15/2.64 thf(func_def_88, type, sK20: $i > $i).
% 9.15/2.64 thf(func_def_89, type, sK21: $i > $i > $i).
% 9.15/2.64 thf(func_def_90, type, sK22: $i > $i > $i).
% 9.15/2.64 thf(func_def_91, type, sK23: $i > $i > $i).
% 9.15/2.64 thf(func_def_92, type, sK24: $i > $i > $i > $i).
% 9.15/2.64 thf(func_def_93, type, ph25: !>[X0: $tType]:(X0)).
% 9.15/2.64 thf(func_def_94, type, sK26: $i > $i > $i).
% 9.15/2.64 thf(func_def_95, type, sK27: $i > $i > $i).
% 9.15/2.64 thf(func_def_96, type, sK28: $i > $i > $i).
% 9.15/2.64 thf(func_def_97, type, sK29: $i > $i > $i).
% 9.15/2.64 thf(func_def_98, type, sK30: $i > $i > $i).
% 9.15/2.64 thf(func_def_99, type, sK31: $i > $i > $i).
% 9.15/2.64 thf(func_def_100, type, sK32: $i > $i > $i).
% 9.15/2.64 thf(func_def_101, type, sK33: $i > $i > $i).
% 9.15/2.64 thf(func_def_102, type, sK34: $i > $i > $i).
% 9.15/2.64 thf(func_def_103, type, sK35: $i > $i > $i).
% 9.15/2.64 thf(func_def_104, type, sK36: $i > $i > $i).
% 9.15/2.64 thf(func_def_105, type, sK37: $i > $i).
% 9.15/2.64 thf(func_def_106, type, sK38: $i > $i > $i).
% 9.15/2.64 thf(func_def_107, type, sK39: $i > $i > $i).
% 9.15/2.64 thf(func_def_108, type, sK40: $i > $i).
% 9.15/2.64 thf(func_def_109, type, sK41: $i > $i > $i).
% 9.15/2.64 thf(func_def_110, type, sK42: $i > $i).
% 9.15/2.64 thf(func_def_111, type, sK43: $i > $i).
% 9.15/2.64 thf(func_def_112, type, sK44: $i > $i).
% 9.15/2.64 thf(func_def_113, type, sK45: $i > $i).
% 9.15/2.64 thf(func_def_114, type, sK46: $i > $i > $i).
% 9.15/2.64 thf(func_def_115, type, sK47: $i > $i > $i).
% 9.15/2.64 thf(func_def_116, type, sK48: $i > $i > $i).
% 9.15/2.64 thf(func_def_117, type, sK49: $i > $i > $i).
% 9.15/2.64 thf(func_def_118, type, sK50: $i > $i > $i).
% 9.15/2.64 thf(func_def_119, type, sK51: $i > $i > $i).
% 9.15/2.64 thf(func_def_122, type, sK54: $i > $i > $i).
% 9.15/2.64 thf(func_def_123, type, sK55: $i > $i).
% 9.15/2.64 thf(func_def_124, type, sK56: $i > $i).
% 9.15/2.64 thf(func_def_125, type, sK57: $i > $i).
% 9.15/2.64 thf(func_def_126, type, sK58: $i > $i).
% 9.15/2.64 thf(func_def_127, type, sK59: $i > $i).
% 9.15/2.64 thf(func_def_128, type, sK60: $i > $i).
% 9.15/2.64 thf(func_def_129, type, sK61: $i > $i).
% 9.15/2.64 thf(func_def_130, type, sK62: $i > $i).
% 9.15/2.64 thf(func_def_131, type, sK63: $i > $i).
% 9.15/2.64 thf(func_def_132, type, sK64: $i > $i).
% 9.15/2.64 thf(func_def_135, type, sK67: $i > $i).
% 9.15/2.64 thf(func_def_136, type, sK68: $i > $i > $i).
% 9.15/2.64 thf(func_def_137, type, sK69: $i > $i > $i).
% 9.15/2.64 thf(func_def_138, type, sK70: $i > $i > $i).
% 9.15/2.64 thf(func_def_139, type, sK71: $i > $i > $i).
% 9.15/2.64 thf(func_def_140, type, sK72: $i > $i).
% 9.15/2.64 thf(func_def_141, type, sK73: $i > $i > $i).
% 9.15/2.64 thf(func_def_142, type, sK74: $i > $i > $i).
% 9.15/2.64 thf(func_def_143, type, sK75: $i > $i).
% 9.15/2.64 thf(func_def_144, type, sK76: $i > $i > $i).
% 9.15/2.64 thf(f5161,plain,(
% 9.15/2.64 $false),
% 9.15/2.64 inference(avatar_sat_refutation,[status(thm)],[f659,f676,f718,f838,f1892,f3503,f3851,f5160])).
% 9.15/2.64 thf(f5160,plain,(
% 9.15/2.64 ~spl2_2 | ~spl2_18 | ~spl2_21),
% 9.15/2.64 inference(avatar_contradiction_clause,[status(thm)],[f5159])).
% 9.15/2.64 thf(f5159,plain,(
% 9.15/2.64 $false | (~spl2_2 | ~spl2_18 | ~spl2_21)),
% 9.15/2.64 inference(trivial_inequality_removal,[status(thm)],[f5153])).
% 9.15/2.64 thf(f5153,plain,(
% 9.15/2.64 ($false = $true) | (~spl2_2 | ~spl2_18 | ~spl2_21)),
% 9.15/2.64 inference(backward_demodulation,[status(thm)],[f658,f5058])).
% 9.15/2.64 thf(f5058,plain,(
% 9.15/2.64 ((in @ sK1 @ sK0) = $false) | (~spl2_18 | ~spl2_21)),
% 9.15/2.64 inference(trivial_inequality_removal,[status(thm)],[f5007])).
% 9.15/2.64 thf(f5007,plain,(
% 9.15/2.64 ($false = $true) | ((in @ sK1 @ sK0) = $false) | (~spl2_18 | ~spl2_21)),
% 9.15/2.64 inference(superposition,[status(thm)],[f3502,f3909])).
% 9.15/2.64 thf(f3909,plain,(
% 9.15/2.64 ( ! [X0 : $i] : (($false = (in @ sK53 @ X0)) | ($false = (in @ X0 @ sK0))) ) | ~spl2_21),
% 9.15/2.64 inference(trivial_inequality_removal,[status(thm)],[f3906])).
% 9.15/2.64 thf(f3906,plain,(
% 9.15/2.64 ( ! [X0 : $i] : (($false = $true) | ($false = (in @ sK53 @ X0)) | ($false = (in @ X0 @ sK0))) ) | ~spl2_21),
% 9.15/2.64 inference(superposition,[status(thm)],[f310,f3850])).
% 9.15/2.64 thf(f3850,plain,(
% 9.15/2.64 ((in @ sK53 @ (setunion @ sK0)) = $false) | ~spl2_21),
% 9.15/2.64 inference(avatar_component_clause,[status(thm)],[f3848])).
% 9.15/2.64 thf(f3848,definition,(
% 9.15/2.64 spl2_21 <=> ((in @ sK53 @ (setunion @ sK0)) = $false)),
% 9.15/2.64 introduced(definition,[new_symbols(naming,[spl2_21])],[avatar_definition])).
% 9.15/2.64 thf(f310,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X1 @ (setunion @ X3)) = $true) | ((in @ X1 @ X2) = $false) | ((in @ X2 @ X3) = $false)) )),
% 9.15/2.64 inference(binary_proxy_clausification,[status(thm)],[f309])).
% 9.15/2.64 thf(f309,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X1 @ X2) = $false) | ($true = ((in @ X2 @ X3) => (in @ X1 @ (setunion @ X3))))) )),
% 9.15/2.64 inference(binary_proxy_clausification,[status(thm)],[f308])).
% 9.15/2.64 thf(f308,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ X2) => ((in @ X2 @ X3) => (in @ X1 @ (setunion @ X3)))) = $true)) )),
% 9.15/2.64 inference(beta_eta_normalization,[status(thm)],[f307])).
% 9.15/2.64 thf(f307,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ X2) => ((in @ X2 @ Y0) => (in @ X1 @ (setunion @ Y0))))) @ X3) = $true)) )),
% 9.15/2.64 inference(pi_clausification,[status(thm)],[f306])).
% 9.15/2.64 thf(f306,plain,(
% 9.15/2.64 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ X2) => ((in @ X2 @ Y0) => (in @ X1 @ (setunion @ Y0)))))))) )),
% 9.15/2.64 inference(beta_eta_normalization,[status(thm)],[f305])).
% 9.15/2.64 thf(f305,plain,(
% 9.15/2.64 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y0) => ((in @ Y0 @ Y1) => (in @ X1 @ (setunion @ Y1))))))) @ X2) = $true)) )),
% 9.15/2.64 inference(pi_clausification,[status(thm)],[f304])).
% 9.15/2.64 thf(f304,plain,(
% 9.15/2.64 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y0) => ((in @ Y0 @ Y1) => (in @ X1 @ (setunion @ Y1)))))))))) )),
% 9.15/2.64 inference(beta_eta_normalization,[status(thm)],[f303])).
% 9.15/2.64 thf(f303,plain,(
% 9.15/2.64 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2))))))))) @ X1))) )),
% 9.15/2.64 inference(pi_clausification,[status(thm)],[f226])).
% 9.15/2.64 thf(f226,plain,(
% 9.15/2.64 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) = $true)),
% 9.15/2.64 inference(definition_unfolding,[status(thm)],[f155,f138])).
% 9.15/2.64 thf(f138,plain,(
% 9.15/2.64 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))))),
% 9.15/2.64 inference(cnf_transformation,[status(thm)],[f90])).
% 9.15/2.64 thf(f90,plain,(
% 9.15/2.64 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))))),
% 9.15/2.64 inference(fool_elimination,[status(thm)],[f89])).
% 9.15/2.64 thf(f89,plain,(
% 9.15/2.64 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ((in @ X1 @ X0) => (in @ X2 @ (setunion @ X0)))) = setunionI)),
% 9.15/2.64 inference(rectify,[status(thm)],[f42])).
% 9.15/2.64 thf(f42,axiom,(
% 9.15/2.64 (! [X3 : $i,X4 : $i,X1 : $i] : ((in @ X1 @ X4) => ((in @ X4 @ X3) => (in @ X1 @ (setunion @ X3)))) = setunionI)),
% 9.15/2.64 file('/export/starexec/sandbox/tmp/tmp.QB27Oebfrm/DTF2THF_29480.p',setunionI)).
% 9.15/2.64 thf(f155,plain,(
% 9.15/2.64 (setunionI = $true)),
% 9.15/2.64 inference(cnf_transformation,[status(thm)],[f133])).
% 9.15/2.64 thf(f133,plain,(
% 9.15/2.64 (($true != (in @ sK1 @ (powerset @ (setunion @ sK0)))) & ((in @ sK1 @ sK0) = $true)) & (powersetE = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (prop2setE = $true) & (powersetAx = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (emptyI = $true) & (omega0Ax = $true) & (emptyinunitempty = $true) & (setadjoinOr = $true) & (nonemptyI = $true) & (descrp = $true) & (emptyinPowerset = $true) & (exuE1 = $true) & (setunionE = $true) & (replAx = $true) & (setadjoinIL = $true) & (setextAx = $true) & (dsetconstrI = $true) & (emptyInPowerset = $true) & (setbeta = $true) & (setext = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (exuE3e = $true) & (nonemptyE1 = $true) & (setunionI = $true) & (setadjoinAx = $true) & (nonemptyI1 = $true) & (emptysetAx = $true) & (emptysetimpfalse = $true) & (setadjoinE = $true) & (setoftrueEq = $true) & (foundationAx = $true) & (noeltsimpempty = $true) & (setunionAx = $true) & (powersetI = $true) & (emptysetE = $true) & (setadjoinIR = $true)),
% 9.15/2.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f131,f132])).
% 9.15/2.64 thf(f132,plain,(
% 9.15/2.64 ? [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ (setunion @ X0)))) & ((in @ X1 @ X0) = $true)) => (($true != (in @ sK1 @ (powerset @ (setunion @ sK0)))) & ((in @ sK1 @ sK0) = $true))),
% 9.15/2.64 introduced(definition,[],[choice_axiom])).
% 9.15/2.64 thf(f131,plain,(
% 9.15/2.64 ? [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ (setunion @ X0)))) & ((in @ X1 @ X0) = $true)) & (powersetE = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (prop2setE = $true) & (powersetAx = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (emptyI = $true) & (omega0Ax = $true) & (emptyinunitempty = $true) & (setadjoinOr = $true) & (nonemptyI = $true) & (descrp = $true) & (emptyinPowerset = $true) & (exuE1 = $true) & (setunionE = $true) & (replAx = $true) & (setadjoinIL = $true) & (setextAx = $true) & (dsetconstrI = $true) & (emptyInPowerset = $true) & (setbeta = $true) & (setext = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (exuE3e = $true) & (nonemptyE1 = $true) & (setunionI = $true) & (setadjoinAx = $true) & (nonemptyI1 = $true) & (emptysetAx = $true) & (emptysetimpfalse = $true) & (setadjoinE = $true) & (setoftrueEq = $true) & (foundationAx = $true) & (noeltsimpempty = $true) & (setunionAx = $true) & (powersetI = $true) & (emptysetE = $true) & (setadjoinIR = $true)),
% 9.15/2.64 inference(flattening,[status(thm)],[f130])).
% 9.15/2.64 thf(f130,plain,(
% 9.15/2.64 (((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ (setunion @ X0)))) & ((in @ X1 @ X0) = $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)),
% 9.15/2.64 inference(ennf_transformation,[status(thm)],[f120])).
% 9.15/2.64 thf(f120,plain,(
% 9.15/2.64 ~((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) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ X0) = $true) => ($true = (in @ X1 @ (powerset @ (setunion @ X0)))))))))))))))))))))))))))))))))))))))))))))),
% 9.15/2.64 inference(fool_elimination,[status(thm)],[f119])).
% 9.15/2.64 thf(f119,plain,(
% 9.15/2.64 ~(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 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (powerset @ (setunion @ X0))))))))))))))))))))))))))))))))))))))))))))),
% 9.15/2.64 inference(rectify,[status(thm)],[f45])).
% 9.15/2.64 thf(f45,negated_conjecture,(
% 9.15/2.64 ~(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 => ! [X3 : $i,X1 : $i] : ((in @ X1 @ X3) => (in @ X1 @ (powerset @ (setunion @ X3))))))))))))))))))))))))))))))))))))))))))))),
% 9.15/2.64 inference(negated_conjecture,[status(cth)],[f44])).
% 9.15/2.64 thf(f44,conjecture,(
% 9.15/2.64 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 => ! [X3 : $i,X1 : $i] : ((in @ X1 @ X3) => (in @ X1 @ (powerset @ (setunion @ X3)))))))))))))))))))))))))))))))))))))))))))),
% 9.15/2.64 file('/export/starexec/sandbox/tmp/tmp.QB27Oebfrm/DTF2THF_29480.p',subPowSU)).
% 9.15/2.64 thf(f3502,plain,(
% 9.15/2.64 ((in @ sK53 @ sK1) = $true) | ~spl2_18),
% 9.15/2.64 inference(avatar_component_clause,[status(thm)],[f3500])).
% 9.15/2.64 thf(f3500,definition,(
% 9.15/2.64 spl2_18 <=> ((in @ sK53 @ sK1) = $true)),
% 9.15/2.64 introduced(definition,[new_symbols(naming,[spl2_18])],[avatar_definition])).
% 9.15/2.64 thf(f658,plain,(
% 9.15/2.64 ((in @ sK1 @ sK0) = $true) | ~spl2_2),
% 9.15/2.64 inference(avatar_component_clause,[status(thm)],[f656])).
% 9.15/2.64 thf(f656,definition,(
% 9.15/2.64 spl2_2 <=> ((in @ sK1 @ sK0) = $true)),
% 9.15/2.64 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 9.15/2.64 thf(f3851,plain,(
% 9.15/2.64 spl2_21 | ~spl2_11),
% 9.15/2.64 inference(avatar_split_clause,[status(thm)],[f2892,f835,f3848])).
% 9.15/2.64 thf(f835,definition,(
% 9.15/2.64 spl2_11 <=> ($false = (in @ sK1 @ (powerset @ (setunion @ sK0))))),
% 9.15/2.64 introduced(definition,[new_symbols(naming,[spl2_11])],[avatar_definition])).
% 9.15/2.64 thf(f2892,plain,(
% 9.15/2.64 ((in @ sK53 @ (setunion @ sK0)) = $false) | ~spl2_11),
% 9.15/2.64 inference(binary_proxy_clausification,[status(thm)],[f2891])).
% 9.15/2.64 thf(f2891,plain,(
% 9.15/2.64 ($false = ((in @ sK53 @ sK1) => (in @ sK53 @ (setunion @ sK0)))) | ~spl2_11),
% 9.15/2.64 inference(beta_eta_normalization,[status(thm)],[f2890])).
% 9.15/2.64 thf(f2890,plain,(
% 9.15/2.64 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK1) => (in @ Y0 @ (setunion @ sK0)))) @ sK53)) | ~spl2_11),
% 9.15/2.64 inference(sigma_clausification,[status(thm)],[f2889])).
% 9.15/2.64 thf(f2889,plain,(
% 9.15/2.64 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (in @ Y0 @ (setunion @ sK0))))) = $false) | ~spl2_11),
% 9.15/2.64 inference(not_proxy_clausification,[status(thm)],[f2888])).
% 9.15/2.64 thf(f2888,plain,(
% 9.15/2.64 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (in @ Y0 @ (setunion @ sK0))))))) | ~spl2_11),
% 9.15/2.64 inference(boolean_simplification,[status(thm)],[f2808])).
% 9.15/2.64 thf(f2808,plain,(
% 9.15/2.64 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (in @ Y0 @ (setunion @ sK0))))) = $false)) | ~spl2_11),
% 9.15/2.64 inference(superposition,[status(thm)],[f347,f837])).
% 9.15/2.64 thf(f837,plain,(
% 9.15/2.64 ($false = (in @ sK1 @ (powerset @ (setunion @ sK0)))) | ~spl2_11),
% 9.15/2.64 inference(avatar_component_clause,[status(thm)],[f835])).
% 9.15/2.64 thf(f347,plain,(
% 9.15/2.64 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) = (in @ X2 @ (powerset @ X1))) = $true)) )),
% 9.15/2.64 inference(beta_eta_normalization,[status(thm)],[f346])).
% 9.15/2.64 thf(f346,plain,(
% 9.15/2.64 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) = (in @ Y0 @ (powerset @ X1)))) @ X2) = $true)) )),
% 9.15/2.64 inference(pi_clausification,[status(thm)],[f345])).
% 9.15/2.64 thf(f345,plain,(
% 9.15/2.64 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) = (in @ Y0 @ (powerset @ X1))))))) )),
% 9.15/2.64 inference(beta_eta_normalization,[status(thm)],[f344])).
% 9.15/2.64 thf(f344,plain,(
% 9.15/2.64 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0)))))) @ X1) = $true)) )),
% 9.15/2.64 inference(pi_clausification,[status(thm)],[f256])).
% 9.15/2.64 thf(f256,plain,(
% 9.15/2.64 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) = $true)),
% 9.15/2.64 inference(definition_unfolding,[status(thm)],[f215,f178])).
% 9.15/2.64 thf(f178,plain,(
% 9.15/2.64 (powersetAx = $true)),
% 9.15/2.64 inference(cnf_transformation,[status(thm)],[f133])).
% 9.15/2.64 thf(f215,plain,(
% 9.15/2.64 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))))),
% 9.15/2.64 inference(cnf_transformation,[status(thm)],[f102])).
% 9.15/2.64 thf(f102,plain,(
% 9.15/2.64 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))))),
% 9.15/2.64 inference(fool_elimination,[status(thm)],[f101])).
% 9.15/2.64 thf(f101,plain,(
% 9.15/2.64 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) <=> (in @ X0 @ (powerset @ X1))) = powersetAx)),
% 9.15/2.64 inference(rectify,[status(thm)],[f5])).
% 9.15/2.64 thf(f5,axiom,(
% 9.15/2.64 (! [X4 : $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3)) <=> (in @ X4 @ (powerset @ X3))) = powersetAx)),
% 9.15/2.64 file('/export/starexec/sandbox/tmp/tmp.QB27Oebfrm/DTF2THF_29480.p',powersetAx)).
% 9.15/2.64 thf(f3503,plain,(
% 9.15/2.64 spl2_18 | ~spl2_11),
% 9.15/2.64 inference(avatar_split_clause,[status(thm)],[f2893,f835,f3500])).
% 9.15/2.64 thf(f2893,plain,(
% 9.15/2.64 ((in @ sK53 @ sK1) = $true) | ~spl2_11),
% 9.15/2.64 inference(binary_proxy_clausification,[status(thm)],[f2891])).
% 9.15/2.64 thf(f1892,plain,(
% 9.15/2.64 ~spl2_8),
% 9.15/2.64 inference(avatar_contradiction_clause,[status(thm)],[f1891])).
% 9.15/2.64 thf(f1891,plain,(
% 9.15/2.64 $false | ~spl2_8),
% 9.15/2.64 inference(trivial_inequality_removal,[status(thm)],[f1878])).
% 9.15/2.64 thf(f1878,plain,(
% 9.15/2.64 ($false = $true) | ~spl2_8),
% 9.15/2.64 inference(backward_demodulation,[status(thm)],[f509,f717])).
% 9.15/2.64 thf(f717,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X3 @ (setadjoin @ X2 @ X1)))) ) | ~spl2_8),
% 9.15/2.64 inference(avatar_component_clause,[status(thm)],[f716])).
% 9.15/2.64 thf(f716,definition,(
% 9.15/2.64 spl2_8 <=> ! [X2 : $i,X1 : $i,X3 : $i] : ($false = (in @ X3 @ (setadjoin @ X2 @ X1)))),
% 9.15/2.64 introduced(definition,[new_symbols(naming,[spl2_8])],[avatar_definition])).
% 9.15/2.64 thf(f509,plain,(
% 9.15/2.64 ( ! [X2 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X1 @ X2)) = $true)) )),
% 9.15/2.64 inference(beta_eta_normalization,[status(thm)],[f508])).
% 9.15/2.64 thf(f508,plain,(
% 9.15/2.64 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (in @ X1 @ (setadjoin @ X1 @ Y0))) @ X2) = $true)) )),
% 9.15/2.64 inference(pi_clausification,[status(thm)],[f507])).
% 9.15/2.64 thf(f507,plain,(
% 9.15/2.64 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ X1 @ (setadjoin @ X1 @ Y0)))))) )),
% 9.15/2.64 inference(beta_eta_normalization,[status(thm)],[f506])).
% 9.15/2.64 thf(f506,plain,(
% 9.15/2.64 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1))))) @ X1))) )),
% 9.15/2.64 inference(pi_clausification,[status(thm)],[f241])).
% 9.15/2.64 thf(f241,plain,(
% 9.15/2.64 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) = $true)),
% 9.15/2.64 inference(definition_unfolding,[status(thm)],[f199,f165])).
% 9.15/2.64 thf(f165,plain,(
% 9.15/2.64 (setadjoinIL = $true)),
% 9.15/2.64 inference(cnf_transformation,[status(thm)],[f133])).
% 9.15/2.64 thf(f199,plain,(
% 9.15/2.64 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 9.15/2.64 inference(cnf_transformation,[status(thm)],[f110])).
% 9.15/2.64 thf(f110,plain,(
% 9.15/2.64 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 9.15/2.64 inference(fool_elimination,[status(thm)],[f109])).
% 9.15/2.64 thf(f109,plain,(
% 9.15/2.64 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X0)) = setadjoinIL)),
% 9.15/2.64 inference(rectify,[status(thm)],[f32])).
% 9.15/2.64 thf(f32,axiom,(
% 9.15/2.64 (! [X2 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X2)) = setadjoinIL)),
% 9.15/2.64 file('/export/starexec/sandbox/tmp/tmp.QB27Oebfrm/DTF2THF_29480.p',setadjoinIL)).
% 9.15/2.64 thf(f838,plain,(
% 9.15/2.64 spl2_11 | spl2_4 | ~spl2_6),
% 9.15/2.64 inference(avatar_split_clause,[status(thm)],[f726,f697,f673,f835])).
% 9.15/2.64 thf(f673,definition,(
% 9.15/2.64 spl2_4 <=> ($true = (in @ sK1 @ (powerset @ (setunion @ sK0))))),
% 9.15/2.64 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 9.15/2.64 thf(f697,definition,(
% 9.15/2.64 spl2_6 <=> ! [X3 : $o] : (($true = X3) | ($false = X3))),
% 9.15/2.64 introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition])).
% 9.15/2.64 thf(f726,plain,(
% 9.15/2.64 ($false = (in @ sK1 @ (powerset @ (setunion @ sK0)))) | (spl2_4 | ~spl2_6)),
% 9.15/2.64 inference(trivial_inequality_removal,[status(thm)],[f724])).
% 9.15/2.64 thf(f724,plain,(
% 9.15/2.64 ($true != $true) | ($false = (in @ sK1 @ (powerset @ (setunion @ sK0)))) | (spl2_4 | ~spl2_6)),
% 9.15/2.64 inference(superposition,[status(thm)],[f675,f698])).
% 9.15/2.64 thf(f698,plain,(
% 9.15/2.64 ( ! [X3 : $o] : (($true = X3) | ($false = X3)) ) | ~spl2_6),
% 9.15/2.64 inference(avatar_component_clause,[status(thm)],[f697])).
% 9.15/2.64 thf(f675,plain,(
% 9.15/2.64 ($true != (in @ sK1 @ (powerset @ (setunion @ sK0)))) | spl2_4),
% 9.15/2.64 inference(avatar_component_clause,[status(thm)],[f673])).
% 9.15/2.64 thf(f718,plain,(
% 9.15/2.64 spl2_8 | spl2_6),
% 9.15/2.64 inference(avatar_split_clause,[status(thm)],[f407,f697,f716])).
% 9.15/2.64 thf(f407,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($false = X4) | ($true = X4) | ($false = (in @ X3 @ (setadjoin @ X2 @ X1)))) )),
% 9.15/2.64 inference(duplicate_literal_removal,[status(thm)],[f405])).
% 9.15/2.64 thf(f405,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($false = X4) | ($false = (in @ X3 @ (setadjoin @ X2 @ X1))) | ($false = X4) | ($true = X4)) )),
% 9.15/2.64 inference(binary_proxy_clausification,[status(thm)],[f404])).
% 9.15/2.64 thf(f404,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($false = (in @ X3 @ (setadjoin @ X2 @ X1))) | ($false = X4) | ($false = ((in @ X3 @ X1) => X4)) | ($true = X4)) )),
% 9.15/2.64 inference(binary_proxy_clausification,[status(thm)],[f398])).
% 9.15/2.64 thf(f398,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($false = X4) | ($false = (in @ X3 @ (setadjoin @ X2 @ X1))) | ((((in @ X3 @ X1) => X4) => X4) = $true)) )),
% 9.15/2.64 inference(binary_proxy_clausification,[status(thm)],[f397])).
% 9.15/2.64 thf(f397,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : ((((X3 = X2) => X4) = $false) | ((((in @ X3 @ X1) => X4) => X4) = $true) | ($false = (in @ X3 @ (setadjoin @ X2 @ X1)))) )),
% 9.15/2.64 inference(binary_proxy_clausification,[status(thm)],[f396])).
% 9.15/2.64 thf(f396,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($false = (in @ X3 @ (setadjoin @ X2 @ X1))) | ((((X3 = X2) => X4) => (((in @ X3 @ X1) => X4) => X4)) = $true)) )),
% 9.15/2.64 inference(beta_eta_normalization,[status(thm)],[f395])).
% 9.15/2.64 thf(f395,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($false = (in @ X3 @ (setadjoin @ X2 @ X1))) | (((^[Y0 : $o]: (((X3 = X2) => Y0) => (((in @ X3 @ X1) => Y0) => Y0))) @ X4) = $true)) )),
% 9.15/2.64 inference(pi_clausification,[status(thm)],[f394])).
% 9.15/2.64 thf(f394,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $o @ (^[Y0 : $o]: (((X3 = X2) => Y0) => (((in @ X3 @ X1) => Y0) => Y0))))) | ($false = (in @ X3 @ (setadjoin @ X2 @ X1)))) )),
% 9.15/2.64 inference(binary_proxy_clausification,[status(thm)],[f393])).
% 9.15/2.64 thf(f393,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ (setadjoin @ X2 @ X1)) => (!! @ $o @ (^[Y0 : $o]: (((X3 = X2) => Y0) => (((in @ X3 @ X1) => Y0) => Y0))))))) )),
% 9.15/2.64 inference(beta_eta_normalization,[status(thm)],[f392])).
% 9.15/2.64 thf(f392,plain,(
% 9.15/2.64 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X2 @ X1)) => (!! @ $o @ (^[Y1 : $o]: (((Y0 = X2) => Y1) => (((in @ Y0 @ X1) => Y1) => Y1)))))) @ X3) = $true)) )),
% 9.15/2.64 inference(pi_clausification,[status(thm)],[f391])).
% 9.15/2.64 thf(f391,plain,(
% 9.15/2.64 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X2 @ X1)) => (!! @ $o @ (^[Y1 : $o]: (((Y0 = X2) => Y1) => (((in @ Y0 @ X1) => Y1) => Y1))))))) = $true)) )),
% 9.15/2.64 inference(beta_eta_normalization,[status(thm)],[f390])).
% 9.15/2.64 thf(f390,plain,(
% 9.15/2.64 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ X1)) => (!! @ $o @ (^[Y2 : $o]: (((Y1 = Y0) => Y2) => (((in @ Y1 @ X1) => Y2) => Y2)))))))) @ X2))) )),
% 9.15/2.64 inference(pi_clausification,[status(thm)],[f389])).
% 9.15/2.64 thf(f389,plain,(
% 9.15/2.64 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ X1)) => (!! @ $o @ (^[Y2 : $o]: (((Y1 = Y0) => Y2) => (((in @ Y1 @ X1) => Y2) => Y2))))))))) = $true)) )),
% 9.15/2.64 inference(beta_eta_normalization,[status(thm)],[f388])).
% 9.15/2.64 thf(f388,plain,(
% 9.15/2.64 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3)))))))))) @ X1))) )),
% 9.15/2.64 inference(pi_clausification,[status(thm)],[f252])).
% 9.15/2.64 thf(f252,plain,(
% 9.15/2.64 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) = $true)),
% 9.15/2.64 inference(definition_unfolding,[status(thm)],[f211,f150])).
% 9.15/2.64 thf(f150,plain,(
% 9.15/2.64 (setadjoinE = $true)),
% 9.15/2.64 inference(cnf_transformation,[status(thm)],[f133])).
% 9.15/2.64 thf(f211,plain,(
% 9.15/2.64 (setadjoinE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))))),
% 9.15/2.64 inference(cnf_transformation,[status(thm)],[f124])).
% 9.15/2.64 thf(f124,plain,(
% 9.15/2.64 (setadjoinE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))))),
% 9.15/2.64 inference(fool_elimination,[status(thm)],[f123])).
% 9.15/2.64 thf(f123,plain,(
% 9.15/2.64 (setadjoinE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setadjoin @ X1 @ X2)) => ! [X3 : $o] : (((X0 = X1) => X3) => (((in @ X0 @ X2) => X3) => X3))))),
% 9.15/2.64 inference(rectify,[status(thm)],[f35])).
% 9.15/2.64 thf(f35,axiom,(
% 9.15/2.64 (setadjoinE = ! [X2 : $i,X1 : $i,X3 : $i] : ((in @ X2 @ (setadjoin @ X1 @ X3)) => ! [X0 : $o] : (((X1 = X2) => X0) => (((in @ X2 @ X3) => X0) => X0))))),
% 9.15/2.64 file('/export/starexec/sandbox/tmp/tmp.QB27Oebfrm/DTF2THF_29480.p',setadjoinE)).
% 9.15/2.64 thf(f676,plain,(
% 9.15/2.64 ~spl2_4),
% 9.15/2.64 inference(avatar_split_clause,[status(thm)],[f184,f673])).
% 9.15/2.64 thf(f184,plain,(
% 9.15/2.64 ($true != (in @ sK1 @ (powerset @ (setunion @ sK0))))),
% 9.15/2.64 inference(cnf_transformation,[status(thm)],[f133])).
% 9.15/2.64 thf(f659,plain,(
% 9.15/2.64 spl2_2),
% 9.15/2.64 inference(avatar_split_clause,[status(thm)],[f183,f656])).
% 9.15/2.64 thf(f183,plain,(
% 9.15/2.64 ((in @ sK1 @ sK0) = $true)),
% 9.15/2.64 inference(cnf_transformation,[status(thm)],[f133])).
% 9.15/2.64 % SZS output end Proof for DTF2THF_29480
% 9.15/2.64 % (29858)------------------------------
% 9.15/2.64 % (29858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/2.64 % (29858)Termination reason: Refutation
% 9.15/2.64
% 9.15/2.64 % (29858)Memory used [KB]: 8187
% 9.15/2.64 % (29858)Time elapsed: 0.352 s
% 9.15/2.64 % (29858)Instructions burned: 1051 (million)
% 9.15/2.64 % (29858)------------------------------
% 9.15/2.64 % (29858)------------------------------
% 9.15/2.64 % (29761)Success in time 1.266 s
%------------------------------------------------------------------------------