%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU550^1 : TPTP v9.2.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 09:35:13 AM UTC 2026
% Result : Theorem 0.32s 1.49s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 141 ( 9 unt; 0 typ; 8 def)
% Number of atoms : 2107 ( 608 equ; 0 cnn)
% Maximal formula atoms : 69 ( 14 avg)
% Number of connectives : 1521 ( 158 ~; 268 |; 234 &; 457 @)
% ( 14 <=>; 335 =>; 0 <=; 0 <~>)
% Maximal formula depth : 76 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 146 ( 141 usr; 80 con; 0-3 aty)
% ( 41 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 218 ( 93 ^; 117 !; 8 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_95,type,
sK0: $i > $o ).
thf(func_def_96,type,
sK1: $i > $o ).
thf(func_def_98,type,
sK3: ( $i > $o ) > $i > $i ).
thf(func_def_99,type,
sK4: $i > $i > $i ).
thf(func_def_100,type,
sK5: $i > $i > $i ).
thf(func_def_101,type,
sK6: $i > $i > $i ).
thf(func_def_102,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_103,type,
sK8: $i > $i ).
thf(func_def_104,type,
sK9: $i > $i > $i > $i ).
thf(func_def_105,type,
sK10: $i > $i > $i ).
thf(func_def_106,type,
sK11: $i > $i > $i ).
thf(func_def_107,type,
sK12: $i > $i > $i ).
thf(func_def_108,type,
sK13: $i > $i > $i ).
thf(func_def_109,type,
sK14: $i > $i > $i ).
thf(func_def_110,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_111,type,
sK16: ( $i > $o ) > $i > $i ).
thf(func_def_112,type,
sK17: $i > $i > $i ).
thf(func_def_113,type,
sK18: $i > $i ).
thf(func_def_114,type,
sK19: $i > $i ).
thf(func_def_115,type,
sK20: $i > $i ).
thf(func_def_118,type,
sK23: $i > $i ).
thf(func_def_119,type,
sK24: $i > $i ).
thf(func_def_120,type,
sK25: ( $i > $o ) > $i ).
thf(func_def_121,type,
sK26: ( $i > $o ) > $i > $i ).
thf(func_def_122,type,
sK27: ( $i > $o ) > $i > $i ).
thf(func_def_123,type,
sK28: $i > ( $i > $o ) > $i ).
thf(func_def_124,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_125,type,
sK30: $i > $i ).
thf(func_def_126,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_127,type,
sK32: ( $i > $o ) > $i ).
thf(func_def_128,type,
sK33: ( $i > $o ) > $i > $i ).
thf(func_def_129,type,
sK34: $i > $i > $i ).
thf(func_def_130,type,
sK35: $i > ( $i > $i > $o ) > $i ).
thf(func_def_131,type,
sK36: $i > ( $i > $i > $o ) > $i ).
thf(func_def_132,type,
sK37: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_133,type,
sK38: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_134,type,
sK39: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_135,type,
sK40: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_136,type,
sK41: $i > ( $i > $i > $o ) > $i ).
thf(func_def_137,type,
sK42: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_138,type,
sK43: ( $i > $o ) > $i ).
thf(func_def_139,type,
sK44: ( $i > $o ) > $i > $i ).
thf(func_def_140,type,
sK45: ( $i > $o ) > $i > $i ).
thf(func_def_141,type,
sK46: ( $i > $o ) > $i > $i ).
thf(func_def_142,type,
sK47: ( $i > $o ) > $i > $i ).
thf(func_def_143,type,
sK48: $i > $i > $i ).
thf(func_def_144,type,
sK49: $i > $i ).
thf(func_def_145,type,
sK50: $i > $i ).
thf(func_def_146,type,
sK51: $o > $i > $i > $i ).
thf(func_def_147,type,
sK52: ( $i > $o ) > $i ).
thf(func_def_148,type,
sK53: ( $i > $o ) > $i ).
thf(func_def_149,type,
sK54: ( $i > $o ) > $i ).
thf(func_def_150,type,
sK55: ( $i > $o ) > $i ).
thf(func_def_151,type,
sK56: ( $i > $o ) > $i ).
thf(func_def_152,type,
sK57: $i > ( $i > $o ) > $i ).
thf(f1583,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1326,f1330,f1334,f1335,f1342,f1346,f1350,f1351,f1423,f1459,f1485,f1539,f1582]) ).
thf(f1582,plain,
( ~ spl2_9
| ~ spl2_11
| ~ spl2_13
| ~ spl2_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f1581]) ).
thf(f1581,plain,
( $false
| ~ spl2_9
| ~ spl2_11
| ~ spl2_13
| ~ spl2_15 ),
inference(subsumption_resolution,[status(thm)],[f1572,f1555]) ).
thf(f1555,plain,
( ( sK22
!= ( sK19 @ sK22 ) )
| ~ spl2_9
| ~ spl2_13 ),
inference(trivial_inequality_removal,[status(thm)],[f1550]) ).
thf(f1550,plain,
( ( sK22
!= ( sK19 @ sK22 ) )
| ( $false = $true )
| ~ spl2_9
| ~ spl2_13 ),
inference(superposition,[status(thm)],[f1341,f1546]) ).
thf(f1546,plain,
( ( ( sK1 @ sK22 )
= $true )
| ~ spl2_9 ),
inference(trivial_inequality_removal,[status(thm)],[f1542]) ).
thf(f1542,plain,
( ( $false = $true )
| ( ( sK1 @ sK22 )
= $true )
| ~ spl2_9 ),
inference(superposition,[status(thm)],[f1325,f798]) ).
thf(f798,plain,
! [X3: $i] :
( ( $false
= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f414]) ).
thf(f414,plain,
! [X3: $i] :
( ( sK1 @ X3 )
= ( sK0 @ X3 ) ),
inference(equality_resolution,[status(thm)],[f277]) ).
thf(f277,plain,
! [X2: $i,X3: $i] :
( ( ( sK1 @ X2 )
= ( sK0 @ X3 ) )
| ( X2 != X3 ) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
thf(f209,plain,
( ( emptysetE = $true )
& ( foundationAx = $true )
& ( descrp = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan1 = $true )
& ( subPowSU = $true )
& ( nonemptyE1 = $true )
& ! [X2: $i,X3: $i] :
( ( ( sK1 @ X2 )
= ( sK0 @ X3 ) )
| ( X2 != X3 ) )
& ( ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ( prop2set2propI = $true )
& ( exuE3e = $true )
& ( in__Cong = $true )
& ( omegaIndAx = $true )
& ( upairsetE = $true )
& ( emptyinunitempty = $true )
& ( powersetE = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( emptysetimpfalse = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( singletonsswitch = $true )
& ( emptyE1 = $true )
& ( setadjoinAx = $true )
& ( setunionE = $true )
& ( powersetI = $true )
& ( emptyinPowerset = $true )
& ( notdallE = $true )
& ( exuE3u = $true )
& ( exuI2 = $true )
& ( quantDeMorgan2 = $true )
& ( notdexE = $true )
& ( emptysetAx = $true )
& ( quantDeMorgan3 = $true )
& ( dsetconstrI = $true )
& ( nonemptyI = $true )
& ( exuE2 = $true )
& ( nonemptyI1 = $true )
& ( setunionI = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( noeltsimpempty = $true )
& ( vacuousDall = $true )
& ( upairsetIL = $true )
& ( exuE1 = $true )
& ( setext = $true )
& ( uniqinunit = $true )
& ( wellorderingAx = $true )
& ( setunionAx = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( emptyInPowerset = $true )
& ( prop2setE = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setadjoinIL = $true )
& ( emptyI = $true )
& ( exuI1 = $true )
& ( setbeta = $true )
& ( setadjoinIR = $true )
& ( quantDeMorgan4 = $true )
& ( exuI3 = $true )
& ( prop2setI = $true )
& ( notinemptyset = $true )
& ( inCongP = $true )
& ( setextAx = $true )
& ( upairsetIR = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f207,f208]) ).
thf(f208,plain,
( ? [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X0 @ X3 ) )
| ( X2 != X3 ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
=> ( ! [X3: $i,X2: $i] :
( ( ( sK1 @ X2 )
= ( sK0 @ X3 ) )
| ( X2 != X3 ) )
& ( ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f207,plain,
( ( emptysetE = $true )
& ( foundationAx = $true )
& ( descrp = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan1 = $true )
& ( subPowSU = $true )
& ( nonemptyE1 = $true )
& ? [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X0 @ X3 ) )
| ( X2 != X3 ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
& ( prop2set2propI = $true )
& ( exuE3e = $true )
& ( in__Cong = $true )
& ( omegaIndAx = $true )
& ( upairsetE = $true )
& ( emptyinunitempty = $true )
& ( powersetE = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( emptysetimpfalse = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( singletonsswitch = $true )
& ( emptyE1 = $true )
& ( setadjoinAx = $true )
& ( setunionE = $true )
& ( powersetI = $true )
& ( emptyinPowerset = $true )
& ( notdallE = $true )
& ( exuE3u = $true )
& ( exuI2 = $true )
& ( quantDeMorgan2 = $true )
& ( notdexE = $true )
& ( emptysetAx = $true )
& ( quantDeMorgan3 = $true )
& ( dsetconstrI = $true )
& ( nonemptyI = $true )
& ( exuE2 = $true )
& ( nonemptyI1 = $true )
& ( setunionI = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( noeltsimpempty = $true )
& ( vacuousDall = $true )
& ( upairsetIL = $true )
& ( exuE1 = $true )
& ( setext = $true )
& ( uniqinunit = $true )
& ( wellorderingAx = $true )
& ( setunionAx = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( emptyInPowerset = $true )
& ( prop2setE = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setadjoinIL = $true )
& ( emptyI = $true )
& ( exuI1 = $true )
& ( setbeta = $true )
& ( setadjoinIR = $true )
& ( quantDeMorgan4 = $true )
& ( exuI3 = $true )
& ( prop2setI = $true )
& ( notinemptyset = $true )
& ( inCongP = $true )
& ( setextAx = $true )
& ( upairsetIR = $true ) ),
inference(flattening,[status(thm)],[f206]) ).
thf(f206,plain,
( ? [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X0 @ X3 ) )
| ( X2 != X3 ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f85]) ).
thf(f85,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
= ( X0 @ X3 ) ) )
=> ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f84]) ).
thf(f84,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X0 @ X3 ) ) )
=> ( ( exu
@ ^ [X4: $i] : ( X0 @ X4 ) )
<=> ( exu
@ ^ [X5: $i] : ( X1 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f70]) ).
thf(f70,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ! [X9: $i > $o,X0: $i > $o] :
( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( X0 @ X1 )
<=> ( X9 @ X2 ) ) )
=> ( ( exu
@ ^ [X1: $i] : ( X9 @ X1 ) )
<=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f69]) ).
thf(f69,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ! [X9: $i > $o,X0: $i > $o] :
( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( X0 @ X1 )
<=> ( X9 @ X2 ) ) )
=> ( ( exu
@ ^ [X1: $i] : ( X9 @ X1 ) )
<=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wcL8QCezj3/DTF2THF_7859.p',exu__Cong) ).
thf(f1325,plain,
( ( ( sK0 @ sK22 )
= $true )
| ~ spl2_9 ),
inference(avatar_component_clause,[status(thm)],[f1323]) ).
thf(f1323,definition,
( spl2_9
<=> ( ( sK0 @ sK22 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_9])],[avatar_definition]) ).
thf(f1341,plain,
( ! [X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK19 @ X1 )
!= X1 ) )
| ~ spl2_13 ),
inference(avatar_component_clause,[status(thm)],[f1340]) ).
thf(f1340,definition,
( spl2_13
<=> ! [X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK19 @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_13])],[avatar_definition]) ).
thf(f1572,plain,
( ( sK22
= ( sK19 @ sK22 ) )
| ~ spl2_9
| ~ spl2_11
| ~ spl2_15 ),
inference(trivial_inequality_removal,[status(thm)],[f1571]) ).
thf(f1571,plain,
( ( $false = $true )
| ( sK22
= ( sK19 @ sK22 ) )
| ~ spl2_9
| ~ spl2_11
| ~ spl2_15 ),
inference(superposition,[status(thm)],[f1546,f1564]) ).
thf(f1564,plain,
( ! [X0: $i] :
( ( ( sK1 @ X0 )
= $false )
| ( ( sK19 @ X0 )
= sK22 ) )
| ~ spl2_11
| ~ spl2_15 ),
inference(trivial_inequality_removal,[status(thm)],[f1557]) ).
thf(f1557,plain,
( ! [X0: $i] :
( ( ( sK19 @ X0 )
= sK22 )
| ( $false = $true )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl2_11
| ~ spl2_15 ),
inference(superposition,[status(thm)],[f1526,f1333]) ).
thf(f1333,plain,
( ! [X1: $i] :
( ( ( sK0 @ X1 )
= $false )
| ( sK22 = X1 ) )
| ~ spl2_11 ),
inference(avatar_component_clause,[status(thm)],[f1332]) ).
thf(f1332,definition,
( spl2_11
<=> ! [X1: $i] :
( ( sK22 = X1 )
| ( ( sK0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl2_11])],[avatar_definition]) ).
thf(f1526,plain,
( ! [X0: $i] :
( ( ( sK0 @ ( sK19 @ X0 ) )
= $true )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl2_15 ),
inference(trivial_inequality_removal,[status(thm)],[f1521]) ).
thf(f1521,plain,
( ! [X0: $i] :
( ( ( sK0 @ ( sK19 @ X0 ) )
= $true )
| ( $false = $true )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl2_15 ),
inference(superposition,[status(thm)],[f799,f1349]) ).
thf(f1349,plain,
( ! [X1: $i] :
( ( ( sK1 @ ( sK19 @ X1 ) )
= $true )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl2_15 ),
inference(avatar_component_clause,[status(thm)],[f1348]) ).
thf(f1348,definition,
( spl2_15
<=> ! [X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK1 @ ( sK19 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl2_15])],[avatar_definition]) ).
thf(f799,plain,
! [X3: $i] :
( ( ( sK1 @ X3 )
= $false )
| ( ( sK0 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f414]) ).
thf(f1539,plain,
( ~ spl2_8
| ~ spl2_10
| ~ spl2_13
| ~ spl2_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f1538]) ).
thf(f1538,plain,
( $false
| ~ spl2_8
| ~ spl2_10
| ~ spl2_13
| ~ spl2_15 ),
inference(trivial_inequality_removal,[status(thm)],[f1534]) ).
thf(f1534,plain,
( ( $false = $true )
| ~ spl2_8
| ~ spl2_10
| ~ spl2_13
| ~ spl2_15 ),
inference(superposition,[status(thm)],[f1321,f1531]) ).
thf(f1531,plain,
( ( ( sK1 @ sK21 )
= $false )
| ~ spl2_8
| ~ spl2_10
| ~ spl2_13
| ~ spl2_15 ),
inference(trivial_inequality_removal,[status(thm)],[f1528]) ).
thf(f1528,plain,
( ( ( sK1 @ sK21 )
= $false )
| ( sK21 != sK21 )
| ~ spl2_8
| ~ spl2_10
| ~ spl2_13
| ~ spl2_15 ),
inference(superposition,[status(thm)],[f1511,f1527]) ).
thf(f1527,plain,
( ! [X0: $i] :
( ( sK21
= ( sK19 @ X0 ) )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl2_10
| ~ spl2_15 ),
inference(trivial_inequality_removal,[status(thm)],[f1517]) ).
thf(f1517,plain,
( ! [X0: $i] :
( ( sK21
= ( sK19 @ X0 ) )
| ( ( sK1 @ X0 )
= $false )
| ( $false = $true ) )
| ~ spl2_10
| ~ spl2_15 ),
inference(superposition,[status(thm)],[f1349,f1329]) ).
thf(f1329,plain,
( ! [X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( sK21 = X1 ) )
| ~ spl2_10 ),
inference(avatar_component_clause,[status(thm)],[f1328]) ).
thf(f1328,definition,
( spl2_10
<=> ! [X1: $i] :
( ( sK21 = X1 )
| ( ( sK1 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl2_10])],[avatar_definition]) ).
thf(f1511,plain,
( ( ( sK19 @ sK21 )
!= sK21 )
| ~ spl2_8
| ~ spl2_13 ),
inference(trivial_inequality_removal,[status(thm)],[f1508]) ).
thf(f1508,plain,
( ( $false = $true )
| ( ( sK19 @ sK21 )
!= sK21 )
| ~ spl2_8
| ~ spl2_13 ),
inference(superposition,[status(thm)],[f1321,f1341]) ).
thf(f1321,plain,
( ( ( sK1 @ sK21 )
= $true )
| ~ spl2_8 ),
inference(avatar_component_clause,[status(thm)],[f1319]) ).
thf(f1319,definition,
( spl2_8
<=> ( ( sK1 @ sK21 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_8])],[avatar_definition]) ).
thf(f1485,plain,
( ~ spl2_9
| ~ spl2_11
| ~ spl2_12
| ~ spl2_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f1484]) ).
thf(f1484,plain,
( $false
| ~ spl2_9
| ~ spl2_11
| ~ spl2_12
| ~ spl2_14 ),
inference(subsumption_resolution,[status(thm)],[f1478,f1442]) ).
thf(f1442,plain,
( ( ( sK20 @ sK22 )
!= sK22 )
| ~ spl2_9
| ~ spl2_12 ),
inference(trivial_inequality_removal,[status(thm)],[f1436]) ).
thf(f1436,plain,
( ( $false = $true )
| ( ( sK20 @ sK22 )
!= sK22 )
| ~ spl2_9
| ~ spl2_12 ),
inference(superposition,[status(thm)],[f1338,f1325]) ).
thf(f1338,plain,
( ! [X2: $i] :
( ( ( sK0 @ X2 )
= $false )
| ( ( sK20 @ X2 )
!= X2 ) )
| ~ spl2_12 ),
inference(avatar_component_clause,[status(thm)],[f1337]) ).
thf(f1337,definition,
( spl2_12
<=> ! [X2: $i] :
( ( ( sK20 @ X2 )
!= X2 )
| ( ( sK0 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl2_12])],[avatar_definition]) ).
thf(f1478,plain,
( ( ( sK20 @ sK22 )
= sK22 )
| ~ spl2_9
| ~ spl2_11
| ~ spl2_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1473]) ).
thf(f1473,plain,
( ( ( sK20 @ sK22 )
= sK22 )
| ( $false = $true )
| ~ spl2_9
| ~ spl2_11
| ~ spl2_14 ),
inference(superposition,[status(thm)],[f1467,f1325]) ).
thf(f1467,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK20 @ X0 )
= sK22 ) )
| ~ spl2_11
| ~ spl2_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1463]) ).
thf(f1463,plain,
( ! [X0: $i] :
( ( ( sK20 @ X0 )
= sK22 )
| ( ( sK0 @ X0 )
= $false )
| ( $false = $true ) )
| ~ spl2_11
| ~ spl2_14 ),
inference(superposition,[status(thm)],[f1345,f1333]) ).
thf(f1345,plain,
( ! [X2: $i] :
( ( ( sK0 @ ( sK20 @ X2 ) )
= $true )
| ( ( sK0 @ X2 )
= $false ) )
| ~ spl2_14 ),
inference(avatar_component_clause,[status(thm)],[f1344]) ).
thf(f1344,definition,
( spl2_14
<=> ! [X2: $i] :
( ( ( sK0 @ X2 )
= $false )
| ( ( sK0 @ ( sK20 @ X2 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl2_14])],[avatar_definition]) ).
thf(f1459,plain,
( spl2_8
| ~ spl2_9
| ~ spl2_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f1458]) ).
thf(f1458,plain,
( $false
| spl2_8
| ~ spl2_9
| ~ spl2_10 ),
inference(subsumption_resolution,[status(thm)],[f1455,f1320]) ).
thf(f1320,plain,
( ( ( sK1 @ sK21 )
!= $true )
| spl2_8 ),
inference(avatar_component_clause,[status(thm)],[f1319]) ).
thf(f1455,plain,
( ( ( sK1 @ sK21 )
= $true )
| ~ spl2_9
| ~ spl2_10 ),
inference(superposition,[status(thm)],[f1443,f1454]) ).
thf(f1454,plain,
( ( sK21 = sK22 )
| ~ spl2_9
| ~ spl2_10 ),
inference(trivial_inequality_removal,[status(thm)],[f1448]) ).
thf(f1448,plain,
( ( $false = $true )
| ( sK21 = sK22 )
| ~ spl2_9
| ~ spl2_10 ),
inference(superposition,[status(thm)],[f1443,f1329]) ).
thf(f1443,plain,
( ( ( sK1 @ sK22 )
= $true )
| ~ spl2_9 ),
inference(trivial_inequality_removal,[status(thm)],[f1434]) ).
thf(f1434,plain,
( ( ( sK1 @ sK22 )
= $true )
| ( $false = $true )
| ~ spl2_9 ),
inference(superposition,[status(thm)],[f1325,f798]) ).
thf(f1423,plain,
( ~ spl2_8
| ~ spl2_10
| ~ spl2_12
| ~ spl2_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f1422]) ).
thf(f1422,plain,
( $false
| ~ spl2_8
| ~ spl2_10
| ~ spl2_12
| ~ spl2_14 ),
inference(subsumption_resolution,[status(thm)],[f1417,f1388]) ).
thf(f1388,plain,
( ( ( sK20 @ sK21 )
!= sK21 )
| ~ spl2_8
| ~ spl2_12 ),
inference(trivial_inequality_removal,[status(thm)],[f1386]) ).
thf(f1386,plain,
( ( $false = $true )
| ( ( sK20 @ sK21 )
!= sK21 )
| ~ spl2_8
| ~ spl2_12 ),
inference(superposition,[status(thm)],[f1372,f1338]) ).
thf(f1372,plain,
( ( ( sK0 @ sK21 )
= $true )
| ~ spl2_8 ),
inference(trivial_inequality_removal,[status(thm)],[f1368]) ).
thf(f1368,plain,
( ( ( sK0 @ sK21 )
= $true )
| ( $false = $true )
| ~ spl2_8 ),
inference(superposition,[status(thm)],[f799,f1321]) ).
thf(f1417,plain,
( ( ( sK20 @ sK21 )
= sK21 )
| ~ spl2_8
| ~ spl2_10
| ~ spl2_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1410]) ).
thf(f1410,plain,
( ( ( sK20 @ sK21 )
= sK21 )
| ( $false = $true )
| ~ spl2_8
| ~ spl2_10
| ~ spl2_14 ),
inference(superposition,[status(thm)],[f1408,f1372]) ).
thf(f1408,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK20 @ X0 )
= sK21 ) )
| ~ spl2_10
| ~ spl2_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1405]) ).
thf(f1405,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK20 @ X0 )
= sK21 ) )
| ~ spl2_10
| ~ spl2_14 ),
inference(superposition,[status(thm)],[f1329,f1401]) ).
thf(f1401,plain,
( ! [X0: $i] :
( ( ( sK1 @ ( sK20 @ X0 ) )
= $true )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1397]) ).
thf(f1397,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ ( sK20 @ X0 ) )
= $true )
| ( $false = $true ) )
| ~ spl2_14 ),
inference(superposition,[status(thm)],[f798,f1345]) ).
thf(f1351,plain,
( spl2_15
| spl2_14 ),
inference(avatar_split_clause,[status(thm)],[f684,f1344,f1348]) ).
thf(f684,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ X2 )
= $false )
| ( ( sK1 @ ( sK19 @ X1 ) )
= $true )
| ( ( sK0 @ ( sK20 @ X2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f682]) ).
thf(f682,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK0 @ ( sK20 @ X2 ) )
=> ( X2
= ( sK20 @ X2 ) ) )
= $false )
| ( ( sK0 @ X2 )
= $false )
| ( ( sK1 @ ( sK19 @ X1 ) )
= $true )
| ( ( sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f680]) ).
thf(f680,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 )
= $false )
| ( ( ( sK1 @ ( sK19 @ X1 ) )
=> ( X1
= ( sK19 @ X1 ) ) )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( ( ( sK0 @ ( sK20 @ X2 ) )
=> ( X2
= ( sK20 @ X2 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f679]) ).
thf(f679,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X2 = Y0 ) )
@ ( sK20 @ X2 ) )
= $false )
| ( ( ( sK1 @ ( sK19 @ X1 ) )
=> ( X1
= ( sK19 @ X1 ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f678]) ).
thf(f678,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X2 = Y0 ) ) )
= $false )
| ( ( ( sK1 @ ( sK19 @ X1 ) )
=> ( X1
= ( sK19 @ X1 ) ) )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ X2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f677]) ).
thf(f677,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X2 = Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK19 @ X1 ) )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ X2 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f676]) ).
thf(f676,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X1 = Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X2 = Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f675]) ).
thf(f675,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X2 = Y0 ) ) )
& ( sK0 @ X2 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X1 = Y0 ) ) )
= $false )
| ( ( sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f674]) ).
thf(f674,plain,
! [X2: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X1 = Y0 ) ) )
& ( sK1 @ X1 ) )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X2 = Y0 ) ) )
& ( sK0 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f673]) ).
thf(f673,plain,
! [X2: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X1 = Y0 ) ) )
& ( sK1 @ X1 ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f672]) ).
thf(f672,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X1 = Y0 ) ) )
& ( sK1 @ X1 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f671]) ).
thf(f671,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK1 @ Y0 ) )
@ X1 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f670]) ).
thf(f670,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK1 @ Y0 ) ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f668]) ).
thf(f668,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) )
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f347]) ).
thf(f347,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) )
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f276,f286,f286]) ).
thf(f286,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
thf(f179,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f178]) ).
thf(f178,plain,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) )
= exu ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) )
= exu ),
file('/export/starexec/sandbox/tmp/tmp.wcL8QCezj3/DTF2THF_7859.p',exu) ).
thf(f276,plain,
( ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
thf(f1350,plain,
( spl2_12
| spl2_15 ),
inference(avatar_split_clause,[status(thm)],[f685,f1348,f1337]) ).
thf(f685,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK20 @ X2 )
!= X2 )
| ( ( sK0 @ X2 )
= $false )
| ( ( sK1 @ ( sK19 @ X1 ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f683]) ).
thf(f683,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ ( sK19 @ X1 ) )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ X2 )
= $false )
| ( ( X2
= ( sK20 @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f682]) ).
thf(f1346,plain,
( spl2_14
| spl2_13 ),
inference(avatar_split_clause,[status(thm)],[f688,f1340,f1344]) ).
thf(f688,plain,
! [X2: $i,X1: $i] :
( ( ( sK19 @ X1 )
!= X1 )
| ( ( sK0 @ X2 )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ ( sK20 @ X2 ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f687]) ).
thf(f687,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ ( sK20 @ X2 ) )
= $true )
| ( ( X1
= ( sK19 @ X1 ) )
= $false )
| ( ( sK0 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f681]) ).
thf(f681,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 )
= $false )
| ( ( ( sK0 @ ( sK20 @ X2 ) )
=> ( X2
= ( sK20 @ X2 ) ) )
= $false )
| ( ( X1
= ( sK19 @ X1 ) )
= $false )
| ( ( sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f680]) ).
thf(f1342,plain,
( spl2_12
| spl2_13 ),
inference(avatar_split_clause,[status(thm)],[f690,f1340,f1337]) ).
thf(f690,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK20 @ X2 )
!= X2 )
| ( ( sK19 @ X1 )
!= X1 )
| ( ( sK0 @ X2 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f689]) ).
thf(f689,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ X2 )
= $false )
| ( ( sK20 @ X2 )
!= X2 )
| ( ( X1
= ( sK19 @ X1 ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f686]) ).
thf(f686,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( X2
= ( sK20 @ X2 ) )
= $false )
| ( ( X1
= ( sK19 @ X1 ) )
= $false )
| ( ( sK0 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f681]) ).
thf(f1335,plain,
( spl2_11
| spl2_10 ),
inference(avatar_split_clause,[status(thm)],[f706,f1328,f1332]) ).
thf(f706,plain,
! [X2: $i,X1: $i] :
( ( sK22 = X1 )
| ( ( sK1 @ X2 )
= $false )
| ( ( sK0 @ X1 )
= $false )
| ( sK21 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f705]) ).
thf(f705,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X2 )
= $false )
| ( ( sK22 = X1 )
= $true )
| ( ( sK0 @ X1 )
= $false )
| ( sK21 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f704]) ).
thf(f704,plain,
! [X2: $i,X1: $i] :
( ( ( sK21 = X2 )
= $true )
| ( ( sK1 @ X2 )
= $false )
| ( ( sK0 @ X1 )
= $false )
| ( ( sK22 = X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f703]) ).
thf(f703,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK1 @ X2 )
=> ( sK21 = X2 ) )
= $true )
| ( ( sK0 @ X1 )
= $false )
| ( ( sK22 = X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f702]) ).
thf(f702,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK0 @ X1 )
=> ( sK22 = X1 ) )
= $true )
| ( ( ( sK1 @ X2 )
=> ( sK21 = X2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f701]) ).
thf(f701,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK21 = Y0 ) )
@ X2 )
= $true )
| ( ( ( sK0 @ X1 )
=> ( sK22 = X1 ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f700]) ).
thf(f700,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK21 = Y0 ) ) )
= $true )
| ( ( ( sK0 @ X1 )
=> ( sK22 = X1 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f699]) ).
thf(f699,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK22 = Y0 ) )
@ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK21 = Y0 ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f698]) ).
thf(f698,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK22 = Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK21 = Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f696]) ).
thf(f696,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK21 = Y0 ) ) )
& ( sK1 @ sK21 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK22 = Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f694]) ).
thf(f694,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK22 = Y0 ) ) )
& ( sK0 @ sK22 ) )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK21 = Y0 ) ) )
& ( sK1 @ sK21 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f693]) ).
thf(f693,plain,
( ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) )
@ sK22 )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK21 = Y0 ) ) )
& ( sK1 @ sK21 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f692]) ).
thf(f692,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK21 = Y0 ) ) )
& ( sK1 @ sK21 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f691]) ).
thf(f691,plain,
( ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK1 @ Y0 ) )
@ sK21 )
= $true )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f669]) ).
thf(f669,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK1 @ Y0 ) ) )
= $true )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f668]) ).
thf(f1334,plain,
( spl2_8
| spl2_11 ),
inference(avatar_split_clause,[status(thm)],[f710,f1332,f1319]) ).
thf(f710,plain,
! [X1: $i] :
( ( sK22 = X1 )
| ( ( sK0 @ X1 )
= $false )
| ( ( sK1 @ sK21 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f709]) ).
thf(f709,plain,
! [X1: $i] :
( ( ( sK22 = X1 )
= $true )
| ( ( sK0 @ X1 )
= $false )
| ( ( sK1 @ sK21 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f708]) ).
thf(f708,plain,
! [X1: $i] :
( ( ( ( sK0 @ X1 )
=> ( sK22 = X1 ) )
= $true )
| ( ( sK1 @ sK21 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f707]) ).
thf(f707,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK22 = Y0 ) )
@ X1 )
= $true )
| ( ( sK1 @ sK21 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f697]) ).
thf(f697,plain,
( ( ( sK1 @ sK21 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK22 = Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f696]) ).
thf(f1330,plain,
( spl2_10
| spl2_9 ),
inference(avatar_split_clause,[status(thm)],[f716,f1323,f1328]) ).
thf(f716,plain,
! [X1: $i] :
( ( sK21 = X1 )
| ( ( sK0 @ sK22 )
= $true )
| ( ( sK1 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f715]) ).
thf(f715,plain,
! [X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK21 = X1 )
= $true )
| ( ( sK0 @ sK22 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f714]) ).
thf(f714,plain,
! [X1: $i] :
( ( ( sK0 @ sK22 )
= $true )
| ( ( ( sK1 @ X1 )
=> ( sK21 = X1 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f713]) ).
thf(f713,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK21 = Y0 ) )
@ X1 )
= $true )
| ( ( sK0 @ sK22 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f712]) ).
thf(f712,plain,
( ( ( sK0 @ sK22 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK21 = Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f695]) ).
thf(f695,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK21 = Y0 ) ) )
& ( sK1 @ sK21 ) )
= $true )
| ( ( sK0 @ sK22 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f694]) ).
thf(f1326,plain,
( spl2_8
| spl2_9 ),
inference(avatar_split_clause,[status(thm)],[f711,f1323,f1319]) ).
thf(f711,plain,
( ( ( sK0 @ sK22 )
= $true )
| ( ( sK1 @ sK21 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f695]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU550^1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n009.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:26:40 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU550^1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : A simple congruence property of exu
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : (forall phi:i>o.forall psi:i>o.(forall x:i.forall y:i.x = y ->
% 0.30/0.46 % (phi x <-> psi y)) -> (exu (lambda x:i.phi x) <->
% 0.30/0.46 % exu (lambda x:i.psi x)))
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC052g [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.50 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 1.00 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 147 ( 68 unt; 78 typ; 68 def)
% 0.30/0.46 % Number of atoms : 374 ( 96 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 69 ( 5 avg)
% 0.30/0.46 % Number of connectives : 620 ( 21 ~; 5 |; 27 &; 386 @)
% 0.30/0.46 % ( 12 <=>; 169 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 75 ( 2 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 81 ( 78 usr; 70 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 214 ( 21 ^; 165 !; 28 ?; 214 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=10
% 0.30/0.46 % Bugfixes : v4.0.0 - Adding missing type delaration for in
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu_type,type,
% 0.30/0.46 exu: ( $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu,definition,
% 0.30/0.46 ( exu
% 0.30/0.46 = ( ^ [Xphi: $i > $o] :
% 0.30/0.46 ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setextAx_type,type,
% 0.30/0.46 setextAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setextAx,definition,
% 0.30/0.46 ( setextAx
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 <=> ( in @ Xx @ B ) )
% 0.30/0.46 => ( A = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset_type,type,
% 0.30/0.46 emptyset: $i ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetAx_type,type,
% 0.30/0.46 emptysetAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetAx,definition,
% 0.30/0.46 ( emptysetAx
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin_type,type,
% 0.30/0.46 setadjoin: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinAx_type,type,
% 0.30/0.46 setadjoinAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinAx,definition,
% 0.30/0.46 ( setadjoinAx
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 <=> ( ( Xy = Xx )
% 0.30/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powerset_type,type,
% 0.30/0.46 powerset: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx_type,type,
% 0.30/0.46 powersetAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx,definition,
% 0.30/0.46 ( powersetAx
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 <=> ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunion_type,type,
% 0.30/0.46 setunion: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setunionAx_type,type,
% 0.30/0.46 setunionAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionAx,definition,
% 0.30/0.46 ( setunionAx
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 <=> ? [B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omega_type,type,
% 0.30/0.46 omega: $i ).
% 0.30/0.46
% 0.30/0.46 thf(omega0Ax_type,type,
% 0.30/0.46 omega0Ax: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omega0Ax,definition,
% 0.30/0.46 ( omega0Ax
% 0.30/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omegaSAx_type,type,
% 0.30/0.46 omegaSAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omegaSAx,definition,
% 0.30/0.46 ( omegaSAx
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ omega )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omegaIndAx_type,type,
% 0.30/0.46 omegaIndAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omegaIndAx,definition,
% 0.30/0.46 ( omegaIndAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( ( in @ emptyset @ A )
% 0.30/0.46 & ! [Xx: $i] :
% 0.30/0.46 ( ( ( in @ Xx @ omega )
% 0.30/0.46 & ( in @ Xx @ A ) )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ omega )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(replAx_type,type,
% 0.30/0.46 replAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(replAx,definition,
% 0.30/0.46 ( replAx
% 0.30/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.30/0.46 => ? [B: $i] :
% 0.30/0.46 ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 <=> ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(foundationAx_type,type,
% 0.30/0.46 foundationAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(foundationAx,definition,
% 0.30/0.46 ( foundationAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.46 => ? [B: $i] :
% 0.30/0.46 ( ( in @ B @ A )
% 0.30/0.46 & ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(wellorderingAx_type,type,
% 0.30/0.46 wellorderingAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(wellorderingAx,definition,
% 0.30/0.46 ( wellorderingAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ? [B: $i] :
% 0.30/0.46 ( ! [C: $i] :
% 0.30/0.46 ( ( in @ C @ B )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ A ) ) )
% 0.30/0.46 & ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( ( in @ Xx @ A )
% 0.30/0.46 & ( in @ Xy @ A ) )
% 0.30/0.46 => ( ! [C: $i] :
% 0.30/0.46 ( ( in @ C @ B )
% 0.30/0.46 => ( ( in @ Xx @ C )
% 0.30/0.46 <=> ( in @ Xy @ C ) ) )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 & ! [C: $i,D: $i] :
% 0.30/0.46 ( ( ( in @ C @ B )
% 0.30/0.46 & ( in @ D @ B ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ D ) )
% 0.30/0.46 | ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ D )
% 0.30/0.46 => ( in @ Xx @ C ) ) ) )
% 0.30/0.46 & ! [C: $i] :
% 0.30/0.46 ( ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.30/0.46 => ? [D: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ D @ B )
% 0.30/0.46 & ( in @ Xx @ C )
% 0.30/0.46 & ~ ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ D )
% 0.30/0.46 & ( in @ Xy @ C ) )
% 0.30/0.46 & ! [E: $i] :
% 0.30/0.46 ( ( in @ E @ B )
% 0.30/0.46 => ( ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ E )
% 0.30/0.46 => ( in @ Xy @ D ) )
% 0.30/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(descr_type,type,
% 0.30/0.46 descr: ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(descrp_type,type,
% 0.30/0.46 descrp: $o ).
% 0.30/0.46
% 0.30/0.46 thf(descrp,definition,
% 0.30/0.46 ( descrp
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ( Xphi
% 0.30/0.46 @ ( descr
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr_type,type,
% 0.30/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI_type,type,
% 0.30/0.46 dsetconstrI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI,definition,
% 0.30/0.46 ( dsetconstrI
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrEL_type,type,
% 0.30/0.46 dsetconstrEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrEL,definition,
% 0.30/0.46 ( dsetconstrEL
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER_type,type,
% 0.30/0.46 dsetconstrER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER,definition,
% 0.30/0.46 ( dsetconstrER
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE1_type,type,
% 0.30/0.46 exuE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE1,definition,
% 0.30/0.46 ( exuE1
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(prop2set_type,type,
% 0.30/0.46 prop2set: $o > $i ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setE_type,type,
% 0.30/0.46 prop2setE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setE,definition,
% 0.30/0.46 ( prop2setE
% 0.30/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.30/0.46 => Xphi ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetE_type,type,
% 0.30/0.46 emptysetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetE,definition,
% 0.30/0.46 ( emptysetE
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetimpfalse_type,type,
% 0.30/0.46 emptysetimpfalse: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetimpfalse,definition,
% 0.30/0.46 ( emptysetimpfalse
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => $false ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notinemptyset_type,type,
% 0.30/0.46 notinemptyset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notinemptyset,definition,
% 0.30/0.46 ( notinemptyset
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3e_type,type,
% 0.30/0.46 exuE3e: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3e,definition,
% 0.30/0.46 ( exuE3e
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setext_type,type,
% 0.30/0.46 setext: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setext,definition,
% 0.30/0.46 ( setext
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 => ( A = B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyI_type,type,
% 0.30/0.46 emptyI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyI,definition,
% 0.30/0.46 ( emptyI
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ A )
% 0.30/0.46 => ( A = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(noeltsimpempty_type,type,
% 0.30/0.46 noeltsimpempty: $o ).
% 0.30/0.46
% 0.30/0.46 thf(noeltsimpempty,definition,
% 0.30/0.46 ( noeltsimpempty
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ A )
% 0.30/0.46 => ( A = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setbeta_type,type,
% 0.30/0.46 setbeta: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setbeta,definition,
% 0.30/0.46 ( setbeta
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonempty_type,type,
% 0.30/0.46 nonempty: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonempty,definition,
% 0.30/0.46 ( nonempty
% 0.30/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyE1_type,type,
% 0.30/0.46 nonemptyE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyE1,definition,
% 0.30/0.46 ( nonemptyE1
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( nonempty @ A )
% 0.30/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI_type,type,
% 0.30/0.46 nonemptyI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI,definition,
% 0.30/0.46 ( nonemptyI
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( nonempty
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI1_type,type,
% 0.30/0.46 nonemptyI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI1,definition,
% 0.30/0.46 ( nonemptyI1
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIL_type,type,
% 0.30/0.46 setadjoinIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIL,definition,
% 0.30/0.46 ( setadjoinIL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinunitempty_type,type,
% 0.30/0.46 emptyinunitempty: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinunitempty,definition,
% 0.30/0.46 ( emptyinunitempty
% 0.30/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinIR_type,type,
% 0.30/0.47 setadjoinIR: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinIR,definition,
% 0.30/0.47 ( setadjoinIR
% 0.30/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinE_type,type,
% 0.30/0.47 setadjoinE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinE,definition,
% 0.30/0.47 ( setadjoinE
% 0.30/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.47 => ! [Xphi: $o] :
% 0.30/0.47 ( ( ( Xy = Xx )
% 0.30/0.47 => Xphi )
% 0.30/0.47 => ( ( ( in @ Xy @ A )
% 0.30/0.47 => Xphi )
% 0.30/0.47 => Xphi ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinOr_type,type,
% 0.30/0.47 setadjoinOr: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinOr,definition,
% 0.30/0.47 ( setadjoinOr
% 0.30/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.47 => ( ( Xy = Xx )
% 0.30/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setoftrueEq_type,type,
% 0.30/0.47 setoftrueEq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setoftrueEq,definition,
% 0.30/0.47 ( setoftrueEq
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xx: $i] : $true )
% 0.30/0.47 = A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powersetI_type,type,
% 0.30/0.47 powersetI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetI,definition,
% 0.30/0.47 ( powersetI
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ A ) )
% 0.30/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyinPowerset_type,type,
% 0.30/0.47 emptyinPowerset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyinPowerset,definition,
% 0.30/0.47 ( emptyinPowerset
% 0.30/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyInPowerset_type,type,
% 0.30/0.47 emptyInPowerset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyInPowerset,definition,
% 0.30/0.47 ( emptyInPowerset
% 0.30/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powersetE_type,type,
% 0.30/0.47 powersetE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetE,definition,
% 0.30/0.47 ( powersetE
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.47 => ( ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunionI_type,type,
% 0.30/0.47 setunionI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunionI,definition,
% 0.30/0.47 ( setunionI
% 0.30/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( ( in @ B @ A )
% 0.30/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunionE_type,type,
% 0.30/0.47 setunionE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunionE,definition,
% 0.30/0.47 ( setunionE
% 0.30/0.47 = ( ! [A: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.47 => ! [Xphi: $o] :
% 0.30/0.47 ( ! [B: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( ( in @ B @ A )
% 0.30/0.47 => Xphi ) )
% 0.30/0.47 => Xphi ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subPowSU_type,type,
% 0.30/0.47 subPowSU: $o ).
% 0.30/0.47
% 0.30/0.47 thf(subPowSU,definition,
% 0.30/0.47 ( subPowSU
% 0.30/0.47 = ( ! [A: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuE2_type,type,
% 0.30/0.47 exuE2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuE2,definition,
% 0.30/0.47 ( exuE2
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ! [Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xy )
% 0.30/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyImpWitness_type,type,
% 0.30/0.47 nonemptyImpWitness: $o ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyImpWitness,definition,
% 0.30/0.47 ( nonemptyImpWitness
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ( nonempty @ A )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & $true ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(uniqinunit_type,type,
% 0.30/0.47 uniqinunit: $o ).
% 0.30/0.47
% 0.30/0.47 thf(uniqinunit,definition,
% 0.30/0.47 ( uniqinunit
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notinsingleton_type,type,
% 0.30/0.47 notinsingleton: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notinsingleton,definition,
% 0.30/0.47 ( notinsingleton
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx != Xy )
% 0.30/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(eqinunit_type,type,
% 0.30/0.47 eqinunit: $o ).
% 0.30/0.47
% 0.30/0.47 thf(eqinunit,definition,
% 0.30/0.47 ( eqinunit
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(singletonsswitch_type,type,
% 0.30/0.47 singletonsswitch: $o ).
% 0.30/0.47
% 0.30/0.47 thf(singletonsswitch,definition,
% 0.30/0.47 ( singletonsswitch
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetE_type,type,
% 0.30/0.47 upairsetE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetE,definition,
% 0.30/0.47 ( upairsetE
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/0.47 => ( ( Xz = Xx )
% 0.30/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetIL_type,type,
% 0.30/0.47 upairsetIL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetIL,definition,
% 0.30/0.47 ( upairsetIL
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetIR_type,type,
% 0.30/0.47 upairsetIR: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetIR,definition,
% 0.30/0.47 ( upairsetIR
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyE1_type,type,
% 0.30/0.47 emptyE1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyE1,definition,
% 0.30/0.47 ( emptyE1
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) )
% 0.30/0.47 => ( ( ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 = emptyset )
% 0.30/0.47 => $false ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(vacuousDall_type,type,
% 0.30/0.47 vacuousDall: $o ).
% 0.30/0.47
% 0.30/0.47 thf(vacuousDall,definition,
% 0.30/0.47 ( vacuousDall
% 0.30/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ emptyset )
% 0.30/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan1_type,type,
% 0.30/0.47 quantDeMorgan1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan1,definition,
% 0.30/0.47 ( quantDeMorgan1
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ~ ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan2_type,type,
% 0.30/0.47 quantDeMorgan2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan2,definition,
% 0.30/0.47 ( quantDeMorgan2
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ~ ( Xphi @ Xx ) )
% 0.30/0.47 => ~ ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan3_type,type,
% 0.30/0.47 quantDeMorgan3: $o ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan3,definition,
% 0.30/0.47 ( quantDeMorgan3
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ~ ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan4_type,type,
% 0.30/0.47 quantDeMorgan4: $o ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan4,definition,
% 0.30/0.47 ( quantDeMorgan4
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ~ ( Xphi @ Xx ) )
% 0.30/0.47 => ~ ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(prop2setI_type,type,
% 0.30/0.47 prop2setI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(prop2setI,definition,
% 0.30/0.47 ( prop2setI
% 0.30/0.47 = ( ! [Xphi: $o] :
% 0.30/0.47 ( Xphi
% 0.30/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(set2prop_type,type,
% 0.30/0.47 set2prop: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(prop2set2propI_type,type,
% 0.30/0.47 prop2set2propI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(prop2set2propI,definition,
% 0.30/0.47 ( prop2set2propI
% 0.30/0.47 = ( ! [Xphi: $o] :
% 0.30/0.47 ( Xphi
% 0.30/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notdexE_type,type,
% 0.30/0.47 notdexE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notdexE,definition,
% 0.30/0.47 ( notdexE
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ~ ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notdallE_type,type,
% 0.30/0.47 notdallE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notdallE,definition,
% 0.30/0.47 ( notdallE
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ~ ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuI1_type,type,
% 0.30/0.47 exuI1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuI1,definition,
% 0.30/0.47 ( exuI1
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ? [Xx: $i] :
% 0.30/0.47 ( ( Xphi @ Xx )
% 0.30/0.47 & ! [Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) )
% 0.30/0.47 => ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuI3_type,type,
% 0.30/0.47 exuI3: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuI3,definition,
% 0.30/0.47 ( exuI3
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.30/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xx )
% 0.30/0.47 => ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) )
% 0.30/0.47 => ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuI2_type,type,
% 0.30/0.47 exuI2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuI2,definition,
% 0.30/0.47 ( exuI2
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ? [Xx: $i] :
% 0.30/0.47 ! [Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xy )
% 0.30/0.47 <=> ( Xy = Xx ) )
% 0.30/0.47 => ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(inCongP_type,type,
% 0.30/0.47 inCongP: $o ).
% 0.30/0.47
% 0.30/0.47 thf(inCongP,definition,
% 0.30/0.47 ( inCongP
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( A = B )
% 0.30/0.47 => ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(in__Cong_type,type,
% 0.30/0.47 in__Cong: $o ).
% 0.30/0.47
% 0.30/0.47 thf(in__Cong,definition,
% 0.30/0.47 ( in__Cong
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( A = B )
% 0.30/0.47 => ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ( ( in @ Xx @ A )
% 0.30/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuE3u_type,type,
% 0.30/0.47 exuE3u: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuE3u,definition,
% 0.30/0.47 ( exuE3u
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xx )
% 0.30/0.47 => ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exu__Cong,conjecture,
% 0.30/0.47 ( setextAx
% 0.30/0.47 => ( emptysetAx
% 0.30/0.47 => ( setadjoinAx
% 0.30/0.47 => ( powersetAx
% 0.30/0.47 => ( setunionAx
% 0.30/0.47 => ( omega0Ax
% 0.30/0.47 => ( omegaSAx
% 0.30/0.47 => ( omegaIndAx
% 0.30/0.47 => ( replAx
% 0.30/0.47 => ( foundationAx
% 0.30/0.47 => ( wellorderingAx
% 0.30/0.47 => ( descrp
% 0.30/0.47 => ( dsetconstrI
% 0.30/0.47 => ( dsetconstrEL
% 0.30/0.47 => ( dsetconstrER
% 0.30/0.47 => ( exuE1
% 0.30/0.47 => ( prop2setE
% 0.30/0.47 => ( emptysetE
% 0.30/0.47 => ( emptysetimpfalse
% 0.30/0.47 => ( notinemptyset
% 0.30/0.47 => ( exuE3e
% 0.30/0.47 => ( setext
% 0.30/0.47 => ( emptyI
% 0.30/0.47 => ( noeltsimpempty
% 0.30/0.47 => ( setbeta
% 0.30/0.47 => ( nonemptyE1
% 0.30/0.47 => ( nonemptyI
% 0.30/0.47 => ( nonemptyI1
% 0.30/0.47 => ( setadjoinIL
% 0.30/0.47 => ( emptyinunitempty
% 0.30/0.47 => ( setadjoinIR
% 0.30/0.47 => ( setadjoinE
% 0.30/0.47 => ( setadjoinOr
% 0.30/0.47 => ( setoftrueEq
% 0.30/0.47 => ( powersetI
% 0.30/0.47 => ( emptyinPowerset
% 0.30/0.47 => ( emptyInPowerset
% 0.30/0.47 => ( powersetE
% 0.30/0.47 => ( setunionI
% 0.30/0.47 => ( setunionE
% 0.30/0.47 => ( subPowSU
% 0.30/0.47 => ( exuE2
% 0.30/0.47 => ( nonemptyImpWitness
% 0.30/0.47 => ( uniqinunit
% 0.30/0.47 => ( notinsingleton
% 0.30/0.47 => ( eqinunit
% 0.30/0.47 => ( singletonsswitch
% 0.30/0.47 => ( upairsetE
% 0.30/0.47 => ( upairsetIL
% 0.30/0.47 => ( upairsetIR
% 0.30/0.47 => ( emptyE1
% 0.30/0.47 => ( vacuousDall
% 0.30/0.47 => ( quantDeMorgan1
% 0.30/0.47 => ( quantDeMorgan2
% 0.30/0.47 => ( quantDeMorgan3
% 0.30/0.47 => ( quantDeMorgan4
% 0.30/0.47 => ( prop2setI
% 0.30/0.47 => ( prop2set2propI
% 0.30/0.47 => ( notdexE
% 0.30/0.47 => ( notdallE
% 0.30/0.47 => ( exuI1
% 0.30/0.47 => ( exuI3
% 0.30/0.47 => ( exuI2
% 0.30/0.47 => ( inCongP
% 0.30/0.47 => ( in__Cong
% 0.30/0.47 => ( exuE3u
% 0.30/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ( ( Xphi @ Xx )
% 0.30/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.30/0.47 => ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 <=> ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 0.32/1.40 ---- Embedded in THF ---
% 0.32/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.40 %%% Generated on Tue Feb 24 12:26:41 EST 2026
% 0.32/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.40 %%% Logic specification used:
% 0.32/1.40 %%% thf(spec, logic, $$dhol).
% 0.32/1.40
% 0.32/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.wcL8QCezj3/DTF2DTF7859.p
% See solution above
% 0.32/1.40 ------------------------
% 0.32/1.42 ---- Cleaned THF ---
% 0.32/1.42 thf(in_type,type,
% 0.32/1.42 in: $i > $i > $o ).
% 0.32/1.42
% 0.32/1.42 thf(exu_type,type,
% 0.32/1.42 exu: ( $i > $o ) > $o ).
% 0.32/1.42
% 0.32/1.42 thf(exu,definition,
% 0.32/1.42 ( exu
% 0.32/1.42 = ( ^ [Xphi: $i > $o] :
% 0.32/1.42 ? [Xx: $i] :
% 0.32/1.42 ( ( Xphi @ Xx )
% 0.32/1.42 & ! [Xy: $i] :
% 0.32/1.42 ( ( Xphi @ Xy )
% 0.32/1.42 => ( Xx = Xy ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setextAx_type,type,
% 0.32/1.42 setextAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setextAx,definition,
% 0.32/1.42 ( setextAx
% 0.32/1.42 = ( ! [A: $i,B: $i] :
% 0.32/1.42 ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 <=> ( in @ Xx @ B ) )
% 0.32/1.42 => ( A = B ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(emptyset_type,type,
% 0.32/1.42 emptyset: $i ).
% 0.32/1.42
% 0.32/1.42 thf(emptysetAx_type,type,
% 0.32/1.42 emptysetAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(emptysetAx,definition,
% 0.32/1.42 ( emptysetAx
% 0.32/1.42 = ( ! [Xx: $i] :
% 0.32/1.42 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoin_type,type,
% 0.32/1.42 setadjoin: $i > $i > $i ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinAx_type,type,
% 0.32/1.42 setadjoinAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinAx,definition,
% 0.32/1.42 ( setadjoinAx
% 0.32/1.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/1.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/1.42 <=> ( ( Xy = Xx )
% 0.32/1.42 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(powerset_type,type,
% 0.32/1.42 powerset: $i > $i ).
% 0.32/1.42
% 0.32/1.42 thf(powersetAx_type,type,
% 0.32/1.42 powersetAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(powersetAx,definition,
% 0.32/1.42 ( powersetAx
% 0.32/1.42 = ( ! [A: $i,B: $i] :
% 0.32/1.42 ( ( in @ B @ ( powerset @ A ) )
% 0.32/1.42 <=> ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ B )
% 0.32/1.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setunion_type,type,
% 0.32/1.42 setunion: $i > $i ).
% 0.32/1.42
% 0.32/1.42 thf(setunionAx_type,type,
% 0.32/1.42 setunionAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setunionAx,definition,
% 0.32/1.42 ( setunionAx
% 0.32/1.42 = ( ! [A: $i,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ ( setunion @ A ) )
% 0.32/1.42 <=> ? [B: $i] :
% 0.32/1.42 ( ( in @ Xx @ B )
% 0.32/1.42 & ( in @ B @ A ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(omega_type,type,
% 0.32/1.42 omega: $i ).
% 0.32/1.42
% 0.32/1.42 thf(omega0Ax_type,type,
% 0.32/1.42 omega0Ax: $o ).
% 0.32/1.42
% 0.32/1.42 thf(omega0Ax,definition,
% 0.32/1.42 ( omega0Ax
% 0.32/1.42 = ( in @ emptyset @ omega ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(omegaSAx_type,type,
% 0.32/1.42 omegaSAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(omegaSAx,definition,
% 0.32/1.42 ( omegaSAx
% 0.32/1.42 = ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ omega )
% 0.32/1.42 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(omegaIndAx_type,type,
% 0.32/1.42 omegaIndAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(omegaIndAx,definition,
% 0.32/1.42 ( omegaIndAx
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ( ( in @ emptyset @ A )
% 0.32/1.42 & ! [Xx: $i] :
% 0.32/1.42 ( ( ( in @ Xx @ omega )
% 0.32/1.42 & ( in @ Xx @ A ) )
% 0.32/1.42 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.32/1.42 => ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ omega )
% 0.32/1.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(replAx_type,type,
% 0.32/1.42 replAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(replAx,definition,
% 0.32/1.42 ( replAx
% 0.32/1.42 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.32/1.42 ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( exu
% 0.32/1.42 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.32/1.42 => ? [B: $i] :
% 0.32/1.42 ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ B )
% 0.32/1.42 <=> ? [Xy: $i] :
% 0.32/1.42 ( ( in @ Xy @ A )
% 0.32/1.42 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(foundationAx_type,type,
% 0.32/1.42 foundationAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(foundationAx,definition,
% 0.32/1.42 ( foundationAx
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.32/1.42 => ? [B: $i] :
% 0.32/1.42 ( ( in @ B @ A )
% 0.32/1.42 & ~ ? [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ B )
% 0.32/1.42 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(wellorderingAx_type,type,
% 0.32/1.42 wellorderingAx: $o ).
% 0.32/1.42
% 0.32/1.42 thf(wellorderingAx,definition,
% 0.32/1.42 ( wellorderingAx
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ? [B: $i] :
% 0.32/1.42 ( ! [C: $i] :
% 0.32/1.42 ( ( in @ C @ B )
% 0.32/1.42 => ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ C )
% 0.32/1.42 => ( in @ Xx @ A ) ) )
% 0.32/1.42 & ! [Xx: $i,Xy: $i] :
% 0.32/1.42 ( ( ( in @ Xx @ A )
% 0.32/1.42 & ( in @ Xy @ A ) )
% 0.32/1.42 => ( ! [C: $i] :
% 0.32/1.42 ( ( in @ C @ B )
% 0.32/1.42 => ( ( in @ Xx @ C )
% 0.32/1.42 <=> ( in @ Xy @ C ) ) )
% 0.32/1.42 => ( Xx = Xy ) ) )
% 0.32/1.42 & ! [C: $i,D: $i] :
% 0.32/1.42 ( ( ( in @ C @ B )
% 0.32/1.42 & ( in @ D @ B ) )
% 0.32/1.42 => ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ C )
% 0.32/1.42 => ( in @ Xx @ D ) )
% 0.32/1.42 | ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ D )
% 0.32/1.42 => ( in @ Xx @ C ) ) ) )
% 0.32/1.42 & ! [C: $i] :
% 0.32/1.42 ( ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ C )
% 0.32/1.42 => ( in @ Xx @ A ) )
% 0.32/1.42 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.32/1.42 => ? [D: $i,Xx: $i] :
% 0.32/1.42 ( ( in @ D @ B )
% 0.32/1.42 & ( in @ Xx @ C )
% 0.32/1.42 & ~ ? [Xy: $i] :
% 0.32/1.42 ( ( in @ Xy @ D )
% 0.32/1.42 & ( in @ Xy @ C ) )
% 0.32/1.42 & ! [E: $i] :
% 0.32/1.42 ( ( in @ E @ B )
% 0.32/1.42 => ( ! [Xy: $i] :
% 0.32/1.42 ( ( in @ Xy @ E )
% 0.32/1.42 => ( in @ Xy @ D ) )
% 0.32/1.42 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(descr_type,type,
% 0.32/1.42 descr: ( $i > $o ) > $i ).
% 0.32/1.42
% 0.32/1.42 thf(descrp_type,type,
% 0.32/1.42 descrp: $o ).
% 0.32/1.42
% 0.32/1.42 thf(descrp,definition,
% 0.32/1.42 ( descrp
% 0.32/1.42 = ( ! [Xphi: $i > $o] :
% 0.32/1.42 ( ( exu
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.42 => ( Xphi
% 0.32/1.42 @ ( descr
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstr_type,type,
% 0.32/1.42 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstrI_type,type,
% 0.32/1.42 dsetconstrI: $o ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstrI,definition,
% 0.32/1.42 ( dsetconstrI
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( ( Xphi @ Xx )
% 0.32/1.42 => ( in @ Xx
% 0.32/1.42 @ ( dsetconstr @ A
% 0.32/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstrEL_type,type,
% 0.32/1.42 dsetconstrEL: $o ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstrEL,definition,
% 0.32/1.42 ( dsetconstrEL
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx
% 0.32/1.42 @ ( dsetconstr @ A
% 0.32/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/1.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstrER_type,type,
% 0.32/1.42 dsetconstrER: $o ).
% 0.32/1.42
% 0.32/1.42 thf(dsetconstrER,definition,
% 0.32/1.42 ( dsetconstrER
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx
% 0.32/1.42 @ ( dsetconstr @ A
% 0.32/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/1.42 => ( Xphi @ Xx ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(exuE1_type,type,
% 0.32/1.42 exuE1: $o ).
% 0.32/1.42
% 0.32/1.42 thf(exuE1,definition,
% 0.32/1.42 ( exuE1
% 0.32/1.42 = ( ! [Xphi: $i > $o] :
% 0.32/1.42 ( ( exu
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.42 => ? [Xx: $i] :
% 0.32/1.42 ( ( Xphi @ Xx )
% 0.32/1.42 & ! [Xy: $i] :
% 0.32/1.42 ( ( Xphi @ Xy )
% 0.32/1.42 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(prop2set_type,type,
% 0.32/1.42 prop2set: $o > $i ).
% 0.32/1.42
% 0.32/1.42 thf(prop2setE_type,type,
% 0.32/1.42 prop2setE: $o ).
% 0.32/1.42
% 0.32/1.42 thf(prop2setE,definition,
% 0.32/1.42 ( prop2setE
% 0.32/1.42 = ( ! [Xphi: $o,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.32/1.42 => Xphi ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(emptysetE_type,type,
% 0.32/1.42 emptysetE: $o ).
% 0.32/1.42
% 0.32/1.42 thf(emptysetE,definition,
% 0.32/1.42 ( emptysetE
% 0.32/1.42 = ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ emptyset )
% 0.32/1.42 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(emptysetimpfalse_type,type,
% 0.32/1.42 emptysetimpfalse: $o ).
% 0.32/1.42
% 0.32/1.42 thf(emptysetimpfalse,definition,
% 0.32/1.42 ( emptysetimpfalse
% 0.32/1.42 = ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ emptyset )
% 0.32/1.42 => $false ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(notinemptyset_type,type,
% 0.32/1.42 notinemptyset: $o ).
% 0.32/1.42
% 0.32/1.42 thf(notinemptyset,definition,
% 0.32/1.42 ( notinemptyset
% 0.32/1.42 = ( ! [Xx: $i] :
% 0.32/1.42 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(exuE3e_type,type,
% 0.32/1.42 exuE3e: $o ).
% 0.32/1.42
% 0.32/1.42 thf(exuE3e,definition,
% 0.32/1.42 ( exuE3e
% 0.32/1.42 = ( ! [Xphi: $i > $o] :
% 0.32/1.42 ( ( exu
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.42 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setext_type,type,
% 0.32/1.42 setext: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setext,definition,
% 0.32/1.42 ( setext
% 0.32/1.42 = ( ! [A: $i,B: $i] :
% 0.32/1.42 ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( in @ Xx @ B ) )
% 0.32/1.42 => ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ B )
% 0.32/1.42 => ( in @ Xx @ A ) )
% 0.32/1.42 => ( A = B ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(emptyI_type,type,
% 0.32/1.42 emptyI: $o ).
% 0.32/1.42
% 0.32/1.42 thf(emptyI,definition,
% 0.32/1.42 ( emptyI
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ! [Xx: $i] :
% 0.32/1.42 ~ ( in @ Xx @ A )
% 0.32/1.42 => ( A = emptyset ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(noeltsimpempty_type,type,
% 0.32/1.42 noeltsimpempty: $o ).
% 0.32/1.42
% 0.32/1.42 thf(noeltsimpempty,definition,
% 0.32/1.42 ( noeltsimpempty
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ! [Xx: $i] :
% 0.32/1.42 ~ ( in @ Xx @ A )
% 0.32/1.42 => ( A = emptyset ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setbeta_type,type,
% 0.32/1.42 setbeta: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setbeta,definition,
% 0.32/1.42 ( setbeta
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( ( in @ Xx
% 0.32/1.42 @ ( dsetconstr @ A
% 0.32/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/1.42 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(nonempty_type,type,
% 0.32/1.42 nonempty: $i > $o ).
% 0.32/1.42
% 0.32/1.42 thf(nonempty,definition,
% 0.32/1.42 ( nonempty
% 0.32/1.42 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyE1_type,type,
% 0.32/1.42 nonemptyE1: $o ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyE1,definition,
% 0.32/1.42 ( nonemptyE1
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ( nonempty @ A )
% 0.32/1.42 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyI_type,type,
% 0.32/1.42 nonemptyI: $o ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyI,definition,
% 0.32/1.42 ( nonemptyI
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( ( Xphi @ Xx )
% 0.32/1.42 => ( nonempty
% 0.32/1.42 @ ( dsetconstr @ A
% 0.32/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyI1_type,type,
% 0.32/1.42 nonemptyI1: $o ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyI1,definition,
% 0.32/1.42 ( nonemptyI1
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.32/1.42 => ( nonempty @ A ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinIL_type,type,
% 0.32/1.42 setadjoinIL: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinIL,definition,
% 0.32/1.42 ( setadjoinIL
% 0.32/1.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(emptyinunitempty_type,type,
% 0.32/1.42 emptyinunitempty: $o ).
% 0.32/1.42
% 0.32/1.42 thf(emptyinunitempty,definition,
% 0.32/1.42 ( emptyinunitempty
% 0.32/1.42 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinIR_type,type,
% 0.32/1.42 setadjoinIR: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinIR,definition,
% 0.32/1.42 ( setadjoinIR
% 0.32/1.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/1.42 ( ( in @ Xy @ A )
% 0.32/1.42 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinE_type,type,
% 0.32/1.42 setadjoinE: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinE,definition,
% 0.32/1.42 ( setadjoinE
% 0.32/1.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/1.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/1.42 => ! [Xphi: $o] :
% 0.32/1.42 ( ( ( Xy = Xx )
% 0.32/1.42 => Xphi )
% 0.32/1.42 => ( ( ( in @ Xy @ A )
% 0.32/1.42 => Xphi )
% 0.32/1.42 => Xphi ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinOr_type,type,
% 0.32/1.42 setadjoinOr: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setadjoinOr,definition,
% 0.32/1.42 ( setadjoinOr
% 0.32/1.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/1.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/1.42 => ( ( Xy = Xx )
% 0.32/1.42 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setoftrueEq_type,type,
% 0.32/1.42 setoftrueEq: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setoftrueEq,definition,
% 0.32/1.42 ( setoftrueEq
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ( dsetconstr @ A
% 0.32/1.42 @ ^ [Xx: $i] : $true )
% 0.32/1.42 = A ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(powersetI_type,type,
% 0.32/1.42 powersetI: $o ).
% 0.32/1.42
% 0.32/1.42 thf(powersetI,definition,
% 0.32/1.42 ( powersetI
% 0.32/1.42 = ( ! [A: $i,B: $i] :
% 0.32/1.42 ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ B )
% 0.32/1.42 => ( in @ Xx @ A ) )
% 0.32/1.42 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(emptyinPowerset_type,type,
% 0.32/1.42 emptyinPowerset: $o ).
% 0.32/1.42
% 0.32/1.42 thf(emptyinPowerset,definition,
% 0.32/1.42 ( emptyinPowerset
% 0.32/1.42 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(emptyInPowerset_type,type,
% 0.32/1.42 emptyInPowerset: $o ).
% 0.32/1.42
% 0.32/1.42 thf(emptyInPowerset,definition,
% 0.32/1.42 ( emptyInPowerset
% 0.32/1.42 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(powersetE_type,type,
% 0.32/1.42 powersetE: $o ).
% 0.32/1.42
% 0.32/1.42 thf(powersetE,definition,
% 0.32/1.42 ( powersetE
% 0.32/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.42 ( ( in @ B @ ( powerset @ A ) )
% 0.32/1.42 => ( ( in @ Xx @ B )
% 0.32/1.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setunionI_type,type,
% 0.32/1.42 setunionI: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setunionI,definition,
% 0.32/1.42 ( setunionI
% 0.32/1.42 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.32/1.42 ( ( in @ Xx @ B )
% 0.32/1.42 => ( ( in @ B @ A )
% 0.32/1.42 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(setunionE_type,type,
% 0.32/1.42 setunionE: $o ).
% 0.32/1.42
% 0.32/1.42 thf(setunionE,definition,
% 0.32/1.42 ( setunionE
% 0.32/1.42 = ( ! [A: $i,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ ( setunion @ A ) )
% 0.32/1.42 => ! [Xphi: $o] :
% 0.32/1.42 ( ! [B: $i] :
% 0.32/1.42 ( ( in @ Xx @ B )
% 0.32/1.42 => ( ( in @ B @ A )
% 0.32/1.42 => Xphi ) )
% 0.32/1.42 => Xphi ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(subPowSU_type,type,
% 0.32/1.42 subPowSU: $o ).
% 0.32/1.42
% 0.32/1.42 thf(subPowSU,definition,
% 0.32/1.42 ( subPowSU
% 0.32/1.42 = ( ! [A: $i,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(exuE2_type,type,
% 0.32/1.42 exuE2: $o ).
% 0.32/1.42
% 0.32/1.42 thf(exuE2,definition,
% 0.32/1.42 ( exuE2
% 0.32/1.42 = ( ! [Xphi: $i > $o] :
% 0.32/1.42 ( ( exu
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.42 => ? [Xx: $i] :
% 0.32/1.42 ! [Xy: $i] :
% 0.32/1.42 ( ( Xphi @ Xy )
% 0.32/1.42 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyImpWitness_type,type,
% 0.32/1.42 nonemptyImpWitness: $o ).
% 0.32/1.42
% 0.32/1.42 thf(nonemptyImpWitness,definition,
% 0.32/1.42 ( nonemptyImpWitness
% 0.32/1.42 = ( ! [A: $i] :
% 0.32/1.42 ( ( nonempty @ A )
% 0.32/1.42 => ? [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 & $true ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(uniqinunit_type,type,
% 0.32/1.42 uniqinunit: $o ).
% 0.32/1.42
% 0.32/1.42 thf(uniqinunit,definition,
% 0.32/1.42 ( uniqinunit
% 0.32/1.42 = ( ! [Xx: $i,Xy: $i] :
% 0.32/1.42 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.32/1.42 => ( Xx = Xy ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(notinsingleton_type,type,
% 0.32/1.42 notinsingleton: $o ).
% 0.32/1.42
% 0.32/1.42 thf(notinsingleton,definition,
% 0.32/1.42 ( notinsingleton
% 0.32/1.42 = ( ! [Xx: $i,Xy: $i] :
% 0.32/1.42 ( ( Xx != Xy )
% 0.32/1.42 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(eqinunit_type,type,
% 0.32/1.42 eqinunit: $o ).
% 0.32/1.42
% 0.32/1.42 thf(eqinunit,definition,
% 0.32/1.42 ( eqinunit
% 0.32/1.42 = ( ! [Xx: $i,Xy: $i] :
% 0.32/1.42 ( ( Xx = Xy )
% 0.32/1.42 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(singletonsswitch_type,type,
% 0.32/1.42 singletonsswitch: $o ).
% 0.32/1.42
% 0.32/1.42 thf(singletonsswitch,definition,
% 0.32/1.42 ( singletonsswitch
% 0.32/1.42 = ( ! [Xx: $i,Xy: $i] :
% 0.32/1.42 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.32/1.42 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(upairsetE_type,type,
% 0.32/1.42 upairsetE: $o ).
% 0.32/1.42
% 0.32/1.42 thf(upairsetE,definition,
% 0.32/1.42 ( upairsetE
% 0.32/1.42 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.32/1.42 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.32/1.42 => ( ( Xz = Xx )
% 0.32/1.42 | ( Xz = Xy ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(upairsetIL_type,type,
% 0.32/1.42 upairsetIL: $o ).
% 0.32/1.42
% 0.32/1.42 thf(upairsetIL,definition,
% 0.32/1.42 ( upairsetIL
% 0.32/1.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(upairsetIR_type,type,
% 0.32/1.42 upairsetIR: $o ).
% 0.32/1.42
% 0.32/1.42 thf(upairsetIR,definition,
% 0.32/1.42 ( upairsetIR
% 0.32/1.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(emptyE1_type,type,
% 0.32/1.42 emptyE1: $o ).
% 0.32/1.42
% 0.32/1.42 thf(emptyE1,definition,
% 0.32/1.42 ( emptyE1
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.42 ( ? [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 & ( Xphi @ Xx ) )
% 0.32/1.42 => ( ( ( dsetconstr @ A
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.42 = emptyset )
% 0.32/1.42 => $false ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(vacuousDall_type,type,
% 0.32/1.42 vacuousDall: $o ).
% 0.32/1.42
% 0.32/1.42 thf(vacuousDall,definition,
% 0.32/1.42 ( vacuousDall
% 0.32/1.42 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ emptyset )
% 0.32/1.42 => ( Xphi @ Xx ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(quantDeMorgan1_type,type,
% 0.32/1.42 quantDeMorgan1: $o ).
% 0.32/1.42
% 0.32/1.42 thf(quantDeMorgan1,definition,
% 0.32/1.42 ( quantDeMorgan1
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.42 ( ~ ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( Xphi @ Xx ) )
% 0.32/1.42 => ? [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(quantDeMorgan2_type,type,
% 0.32/1.42 quantDeMorgan2: $o ).
% 0.32/1.42
% 0.32/1.42 thf(quantDeMorgan2,definition,
% 0.32/1.42 ( quantDeMorgan2
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.42 ( ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ~ ( Xphi @ Xx ) )
% 0.32/1.42 => ~ ? [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(quantDeMorgan3_type,type,
% 0.32/1.42 quantDeMorgan3: $o ).
% 0.32/1.42
% 0.32/1.42 thf(quantDeMorgan3,definition,
% 0.32/1.42 ( quantDeMorgan3
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.42 ( ~ ? [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 & ( Xphi @ Xx ) )
% 0.32/1.42 => ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(quantDeMorgan4_type,type,
% 0.32/1.42 quantDeMorgan4: $o ).
% 0.32/1.42
% 0.32/1.42 thf(quantDeMorgan4,definition,
% 0.32/1.42 ( quantDeMorgan4
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.42 ( ? [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 & ~ ( Xphi @ Xx ) )
% 0.32/1.42 => ~ ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(prop2setI_type,type,
% 0.32/1.42 prop2setI: $o ).
% 0.32/1.42
% 0.32/1.42 thf(prop2setI,definition,
% 0.32/1.42 ( prop2setI
% 0.32/1.42 = ( ! [Xphi: $o] :
% 0.32/1.42 ( Xphi
% 0.32/1.42 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(set2prop_type,type,
% 0.32/1.42 set2prop: $i > $o ).
% 0.32/1.42
% 0.32/1.42 thf(prop2set2propI_type,type,
% 0.32/1.42 prop2set2propI: $o ).
% 0.32/1.42
% 0.32/1.42 thf(prop2set2propI,definition,
% 0.32/1.42 ( prop2set2propI
% 0.32/1.42 = ( ! [Xphi: $o] :
% 0.32/1.42 ( Xphi
% 0.32/1.42 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(notdexE_type,type,
% 0.32/1.42 notdexE: $o ).
% 0.32/1.42
% 0.32/1.42 thf(notdexE,definition,
% 0.32/1.42 ( notdexE
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.42 ( ~ ? [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 & ( Xphi @ Xx ) )
% 0.32/1.42 => ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(notdallE_type,type,
% 0.32/1.42 notdallE: $o ).
% 0.32/1.42
% 0.32/1.42 thf(notdallE,definition,
% 0.32/1.42 ( notdallE
% 0.32/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.42 ( ~ ! [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 => ( Xphi @ Xx ) )
% 0.32/1.42 => ? [Xx: $i] :
% 0.32/1.42 ( ( in @ Xx @ A )
% 0.32/1.42 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(exuI1_type,type,
% 0.32/1.42 exuI1: $o ).
% 0.32/1.42
% 0.32/1.42 thf(exuI1,definition,
% 0.32/1.42 ( exuI1
% 0.32/1.42 = ( ! [Xphi: $i > $o] :
% 0.32/1.42 ( ? [Xx: $i] :
% 0.32/1.42 ( ( Xphi @ Xx )
% 0.32/1.42 & ! [Xy: $i] :
% 0.32/1.42 ( ( Xphi @ Xy )
% 0.32/1.42 => ( Xx = Xy ) ) )
% 0.32/1.42 => ( exu
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(exuI3_type,type,
% 0.32/1.42 exuI3: $o ).
% 0.32/1.42
% 0.32/1.42 thf(exuI3,definition,
% 0.32/1.42 ( exuI3
% 0.32/1.42 = ( ! [Xphi: $i > $o] :
% 0.32/1.42 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.32/1.42 => ( ! [Xx: $i,Xy: $i] :
% 0.32/1.42 ( ( Xphi @ Xx )
% 0.32/1.42 => ( ( Xphi @ Xy )
% 0.32/1.42 => ( Xx = Xy ) ) )
% 0.32/1.42 => ( exu
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(exuI2_type,type,
% 0.32/1.42 exuI2: $o ).
% 0.32/1.42
% 0.32/1.42 thf(exuI2,definition,
% 0.32/1.42 ( exuI2
% 0.32/1.42 = ( ! [Xphi: $i > $o] :
% 0.32/1.42 ( ? [Xx: $i] :
% 0.32/1.42 ! [Xy: $i] :
% 0.32/1.42 ( ( Xphi @ Xy )
% 0.32/1.42 <=> ( Xy = Xx ) )
% 0.32/1.42 => ( exu
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(inCongP_type,type,
% 0.32/1.42 inCongP: $o ).
% 0.32/1.42
% 0.32/1.42 thf(inCongP,definition,
% 0.32/1.42 ( inCongP
% 0.32/1.42 = ( ! [A: $i,B: $i] :
% 0.32/1.42 ( ( A = B )
% 0.32/1.42 => ! [Xx: $i,Xy: $i] :
% 0.32/1.42 ( ( Xx = Xy )
% 0.32/1.42 => ( ( in @ Xx @ A )
% 0.32/1.42 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(in__Cong_type,type,
% 0.32/1.42 in__Cong: $o ).
% 0.32/1.42
% 0.32/1.42 thf(in__Cong,definition,
% 0.32/1.42 ( in__Cong
% 0.32/1.42 = ( ! [A: $i,B: $i] :
% 0.32/1.42 ( ( A = B )
% 0.32/1.42 => ! [Xx: $i,Xy: $i] :
% 0.32/1.42 ( ( Xx = Xy )
% 0.32/1.42 => ( ( in @ Xx @ A )
% 0.32/1.42 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(exuE3u_type,type,
% 0.32/1.42 exuE3u: $o ).
% 0.32/1.42
% 0.32/1.42 thf(exuE3u,definition,
% 0.32/1.42 ( exuE3u
% 0.32/1.42 = ( ! [Xphi: $i > $o] :
% 0.32/1.42 ( ( exu
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.42 => ! [Xx: $i,Xy: $i] :
% 0.32/1.42 ( ( Xphi @ Xx )
% 0.32/1.42 => ( ( Xphi @ Xy )
% 0.32/1.42 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.32/1.42
% 0.32/1.42 thf(exu__Cong,conjecture,
% 0.32/1.42 ( setextAx
% 0.32/1.42 => ( emptysetAx
% 0.32/1.42 => ( setadjoinAx
% 0.32/1.42 => ( powersetAx
% 0.32/1.42 => ( setunionAx
% 0.32/1.42 => ( omega0Ax
% 0.32/1.42 => ( omegaSAx
% 0.32/1.42 => ( omegaIndAx
% 0.32/1.42 => ( replAx
% 0.32/1.42 => ( foundationAx
% 0.32/1.42 => ( wellorderingAx
% 0.32/1.42 => ( descrp
% 0.32/1.42 => ( dsetconstrI
% 0.32/1.42 => ( dsetconstrEL
% 0.32/1.42 => ( dsetconstrER
% 0.32/1.42 => ( exuE1
% 0.32/1.42 => ( prop2setE
% 0.32/1.42 => ( emptysetE
% 0.32/1.42 => ( emptysetimpfalse
% 0.32/1.42 => ( notinemptyset
% 0.32/1.42 => ( exuE3e
% 0.32/1.42 => ( setext
% 0.32/1.42 => ( emptyI
% 0.32/1.42 => ( noeltsimpempty
% 0.32/1.42 => ( setbeta
% 0.32/1.42 => ( nonemptyE1
% 0.32/1.42 => ( nonemptyI
% 0.32/1.42 => ( nonemptyI1
% 0.32/1.42 => ( setadjoinIL
% 0.32/1.42 => ( emptyinunitempty
% 0.32/1.42 => ( setadjoinIR
% 0.32/1.42 => ( setadjoinE
% 0.32/1.42 => ( setadjoinOr
% 0.32/1.42 => ( setoftrueEq
% 0.32/1.42 => ( powersetI
% 0.32/1.42 => ( emptyinPowerset
% 0.32/1.42 => ( emptyInPowerset
% 0.32/1.42 => ( powersetE
% 0.32/1.42 => ( setunionI
% 0.32/1.42 => ( setunionE
% 0.32/1.42 => ( subPowSU
% 0.32/1.42 => ( exuE2
% 0.32/1.42 => ( nonemptyImpWitness
% 0.32/1.42 => ( uniqinunit
% 0.32/1.42 => ( notinsingleton
% 0.32/1.42 => ( eqinunit
% 0.32/1.42 => ( singletonsswitch
% 0.32/1.42 => ( upairsetE
% 0.32/1.42 => ( upairsetIL
% 0.32/1.42 => ( upairsetIR
% 0.32/1.42 => ( emptyE1
% 0.32/1.42 => ( vacuousDall
% 0.32/1.42 => ( quantDeMorgan1
% 0.32/1.42 => ( quantDeMorgan2
% 0.32/1.42 => ( quantDeMorgan3
% 0.32/1.42 => ( quantDeMorgan4
% 0.32/1.42 => ( prop2setI
% 0.32/1.42 => ( prop2set2propI
% 0.32/1.42 => ( notdexE
% 0.32/1.42 => ( notdallE
% 0.32/1.42 => ( exuI1
% 0.32/1.42 => ( exuI3
% 0.32/1.42 => ( exuI2
% 0.32/1.42 => ( inCongP
% 0.32/1.42 => ( in__Cong
% 0.32/1.42 => ( exuE3u
% 0.32/1.42 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.32/1.42 ( ! [Xx: $i,Xy: $i] :
% 0.32/1.42 ( ( Xx = Xy )
% 0.32/1.42 => ( ( Xphi @ Xx )
% 0.32/1.42 <=> ( Xpsi @ Xy ) ) )
% 0.32/1.42 => ( ( exu
% 0.32/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.42 <=> ( exu
% 0.32/1.42 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/1.42 ------------------------
% 0.32/1.44 % (7979)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7859 for (2999ds/2Mi)
% 0.32/1.44 % (7979)Instruction limit reached!
% 0.32/1.44 % (7979)------------------------------
% 0.32/1.44 % (7979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.44 % (7979)Termination reason: Unknown
% 0.32/1.44 % (7979)Termination phase: shuffling
% 0.32/1.44
% 0.32/1.44 % (7979)Memory used [KB]: 1151
% 0.32/1.44 % (7979)Time elapsed: 0.002 s
% 0.32/1.44 % (7979)Instructions burned: 3 (million)
% 0.32/1.44 % (7979)------------------------------
% 0.32/1.44 % (7979)------------------------------
% 0.32/1.44 % (7976)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7859 for (2999ds/183Mi)
% 0.32/1.45 % (7977)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_7859 for (2999ds/4Mi)
% 0.32/1.45 % (7978)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_7859 for (2999ds/27Mi)
% 0.32/1.45 % (7980)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_7859 for (2999ds/2Mi)
% 0.32/1.45 % (7981)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_7859 for (2999ds/275Mi)
% 0.32/1.45 % (7982)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7859 for (2999ds/18Mi)
% 0.32/1.45 % (7980)Instruction limit reached!
% 0.32/1.45 % (7980)------------------------------
% 0.32/1.45 % (7980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.45 % (7980)Termination reason: Unknown
% 0.32/1.45 % (7980)Termination phase: shuffling
% 0.32/1.45
% 0.32/1.45 % (7980)Memory used [KB]: 1023
% 0.32/1.45 % (7980)Time elapsed: 0.003 s
% 0.32/1.45 % (7980)Instructions burned: 2 (million)
% 0.32/1.45 % (7980)------------------------------
% 0.32/1.45 % (7980)------------------------------
% 0.32/1.45 % (7977)Instruction limit reached!
% 0.32/1.45 % (7977)------------------------------
% 0.32/1.45 % (7977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.45 % (7977)Termination reason: Unknown
% 0.32/1.45 % (7977)Termination phase: shuffling
% 0.32/1.45
% 0.32/1.45 % (7977)Memory used [KB]: 1151
% 0.32/1.45 % (7977)Time elapsed: 0.004 s
% 0.32/1.45 % (7977)Instructions burned: 4 (million)
% 0.32/1.45 % (7977)------------------------------
% 0.32/1.45 % (7977)------------------------------
% 0.32/1.45 % (7983)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7859 for (2999ds/3Mi)
% 0.32/1.45 % (7983)Instruction limit reached!
% 0.32/1.45 % (7983)------------------------------
% 0.32/1.45 % (7983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.45 % (7983)Termination reason: Unknown
% 0.32/1.45 % (7983)Termination phase: shuffling
% 0.32/1.45
% 0.32/1.45 % (7983)Memory used [KB]: 1151
% 0.32/1.45 % (7983)Time elapsed: 0.002 s
% 0.32/1.45 % (7983)Instructions burned: 4 (million)
% 0.32/1.45 % (7983)------------------------------
% 0.32/1.45 % (7983)------------------------------
% 0.32/1.46 % (7982)Instruction limit reached!
% 0.32/1.46 % (7982)------------------------------
% 0.32/1.46 % (7982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.46 % (7982)Termination reason: Unknown
% 0.32/1.46 % (7982)Termination phase: Preprocessing 3
% 0.32/1.46
% 0.32/1.46 % (7982)Memory used [KB]: 1663
% 0.32/1.46 % (7982)Time elapsed: 0.012 s
% 0.32/1.46 % (7982)Instructions burned: 18 (million)
% 0.32/1.46 % (7982)------------------------------
% 0.32/1.46 % (7982)------------------------------
% 0.32/1.46 % (7978)Instruction limit reached!
% 0.32/1.46 % (7978)------------------------------
% 0.32/1.46 % (7978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.46 % (7978)Termination reason: Unknown
% 0.32/1.46 % (7978)Termination phase: Property scanning
% 0.32/1.46
% 0.32/1.46 % (7978)Memory used [KB]: 1407
% 0.32/1.46 % (7978)Time elapsed: 0.016 s
% 0.32/1.46 % (7978)Instructions burned: 28 (million)
% 0.32/1.46 % (7978)------------------------------
% 0.32/1.46 % (7978)------------------------------
% 0.32/1.46 % (7986)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_7859 for (2999ds/3Mi)
% 0.32/1.46 % (7986)Instruction limit reached!
% 0.32/1.46 % (7986)------------------------------
% 0.32/1.46 % (7986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.46 % (7986)Termination reason: Unknown
% 0.32/1.46 % (7986)Termination phase: shuffling
% 0.32/1.46
% 0.32/1.46 % (7986)Memory used [KB]: 1151
% 0.32/1.46 % (7986)Time elapsed: 0.002 s
% 0.32/1.46 % (7986)Instructions burned: 3 (million)
% 0.32/1.46 % (7986)------------------------------
% 0.32/1.46 % (7986)------------------------------
% 0.32/1.47 % (7984)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_7859 for (2999ds/37Mi)
% 0.32/1.47 % (7985)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_7859 for (2999ds/15Mi)
% 0.32/1.47 % (7989)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7859 for (2999ds/16Mi)
% 0.32/1.48 % (7987)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_7859 for (2999ds/1041Mi)
% 0.32/1.48 % (7985)Instruction limit reached!
% 0.32/1.48 % (7985)------------------------------
% 0.32/1.48 % (7985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.48 % (7985)Termination reason: Unknown
% 0.32/1.48 % (7985)Termination phase: Preprocessing 3
% 0.32/1.48
% 0.32/1.48 % (7985)Memory used [KB]: 1535
% 0.32/1.48 % (7985)Time elapsed: 0.011 s
% 0.32/1.48 % (7985)Instructions burned: 16 (million)
% 0.32/1.48 % (7985)------------------------------
% 0.32/1.48 % (7985)------------------------------
% 0.32/1.48 % (7988)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7859 for (2999ds/7Mi)
% 0.32/1.48 % (7989)Instruction limit reached!
% 0.32/1.48 % (7989)------------------------------
% 0.32/1.48 % (7989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.48 % (7989)Termination reason: Unknown
% 0.32/1.48 % (7989)Termination phase: Property scanning
% 0.32/1.48
% 0.32/1.48 % (7989)Memory used [KB]: 1407
% 0.32/1.48 % (7989)Time elapsed: 0.006 s
% 0.32/1.48 % (7989)Instructions burned: 19 (million)
% 0.32/1.48 % (7989)------------------------------
% 0.32/1.48 % (7989)------------------------------
% 0.32/1.48 % (7988)Instruction limit reached!
% 0.32/1.48 % (7988)------------------------------
% 0.32/1.48 % (7988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.48 % (7988)Termination reason: Unknown
% 0.32/1.48 % (7988)Termination phase: shuffling
% 0.32/1.48
% 0.32/1.48 % (7988)Memory used [KB]: 1279
% 0.32/1.48 % (7988)Time elapsed: 0.005 s
% 0.32/1.48 % (7988)Instructions burned: 9 (million)
% 0.32/1.48 % (7988)------------------------------
% 0.32/1.48 % (7988)------------------------------
% 0.32/1.48 % (7976)First to succeed.
% 0.32/1.48 % (7984)Instruction limit reached!
% 0.32/1.48 % (7984)------------------------------
% 0.32/1.48 % (7984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.48 % (7984)Termination reason: Unknown
% 0.32/1.48 % (7984)Termination phase: Saturation
% 0.32/1.48
% 0.32/1.48 % (7984)Memory used [KB]: 5884
% 0.32/1.48 % (7984)Time elapsed: 0.020 s
% 0.32/1.48 % (7984)Instructions burned: 39 (million)
% 0.32/1.48 % (7984)------------------------------
% 0.32/1.48 % (7984)------------------------------
% 0.32/1.49 % (7991)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_7859 for (2999ds/3Mi)
% 0.32/1.49 % (7976)Refutation found. Thanks to Tanya!
% 0.32/1.49 % SZS status Theorem for DTF2THF_7859
% 0.32/1.49 % SZS output start Proof for DTF2THF_7859
% 0.32/1.49 thf(func_def_0, type, in: $i > $i > $o).
% 0.32/1.49 thf(func_def_1, type, exu: ($i > $o) > $o).
% 0.32/1.49 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 0.32/1.49 thf(func_def_8, type, powerset: $i > $i).
% 0.32/1.49 thf(func_def_10, type, setunion: $i > $i).
% 0.32/1.49 thf(func_def_19, type, descr: ($i > $o) > $i).
% 0.32/1.49 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 0.32/1.49 thf(func_def_26, type, prop2set: $o > $i).
% 0.32/1.49 thf(func_def_36, type, nonempty: $i > $o).
% 0.32/1.49 thf(func_def_69, type, set2prop: $i > $o).
% 0.32/1.49 thf(func_def_95, type, sK0: $i > $o).
% 0.32/1.49 thf(func_def_96, type, sK1: $i > $o).
% 0.32/1.49 thf(func_def_98, type, sK3: ($i > $o) > $i > $i).
% 0.32/1.49 thf(func_def_99, type, sK4: $i > $i > $i).
% 0.32/1.49 thf(func_def_100, type, sK5: $i > $i > $i).
% 0.32/1.49 thf(func_def_101, type, sK6: $i > $i > $i).
% 0.32/1.49 thf(func_def_102, type, sK7: ($i > $o) > $i > $i).
% 0.32/1.49 thf(func_def_103, type, sK8: $i > $i).
% 0.32/1.49 thf(func_def_104, type, sK9: $i > $i > $i > $i).
% 0.32/1.49 thf(func_def_105, type, sK10: $i > $i > $i).
% 0.32/1.49 thf(func_def_106, type, sK11: $i > $i > $i).
% 0.32/1.49 thf(func_def_107, type, sK12: $i > $i > $i).
% 0.32/1.49 thf(func_def_108, type, sK13: $i > $i > $i).
% 0.32/1.49 thf(func_def_109, type, sK14: $i > $i > $i).
% 0.32/1.49 thf(func_def_110, type, sK15: ($i > $o) > $i).
% 0.32/1.49 thf(func_def_111, type, sK16: ($i > $o) > $i > $i).
% 0.32/1.49 thf(func_def_112, type, sK17: $i > $i > $i).
% 0.32/1.49 thf(func_def_113, type, sK18: $i > $i).
% 0.32/1.49 thf(func_def_114, type, sK19: $i > $i).
% 0.32/1.49 thf(func_def_115, type, sK20: $i > $i).
% 0.32/1.49 thf(func_def_118, type, sK23: $i > $i).
% 0.32/1.49 thf(func_def_119, type, sK24: $i > $i).
% 0.32/1.49 thf(func_def_120, type, sK25: ($i > $o) > $i).
% 0.32/1.49 thf(func_def_121, type, sK26: ($i > $o) > $i > $i).
% 0.32/1.49 thf(func_def_122, type, sK27: ($i > $o) > $i > $i).
% 0.32/1.49 thf(func_def_123, type, sK28: $i > ($i > $o) > $i).
% 0.32/1.49 thf(func_def_124, type, sK29: ($i > $o) > $i > $i).
% 0.32/1.49 thf(func_def_125, type, sK30: $i > $i).
% 0.32/1.49 thf(func_def_126, type, sK31: ($i > $o) > $i > $i).
% 0.32/1.49 thf(func_def_127, type, sK32: ($i > $o) > $i).
% 0.32/1.49 thf(func_def_128, type, sK33: ($i > $o) > $i > $i).
% 0.32/1.49 thf(func_def_129, type, sK34: $i > $i > $i).
% 0.32/1.49 thf(func_def_130, type, sK35: $i > ($i > $i > $o) > $i).
% 0.32/1.49 thf(func_def_131, type, sK36: $i > ($i > $i > $o) > $i).
% 0.32/1.49 thf(func_def_132, type, sK37: $i > $i > ($i > $i > $o) > $i).
% 0.32/1.49 thf(func_def_133, type, sK38: $i > $i > ($i > $i > $o) > $i).
% 0.32/1.49 thf(func_def_134, type, sK39: $i > $i > ($i > $i > $o) > $i).
% 0.32/1.49 thf(func_def_135, type, sK40: $i > $i > ($i > $i > $o) > $i).
% 0.32/1.49 thf(func_def_136, type, sK41: $i > ($i > $i > $o) > $i).
% 0.32/1.49 thf(func_def_137, type, sK42: $i > $i > ($i > $i > $o) > $i).
% 0.32/1.49 thf(func_def_138, type, sK43: ($i > $o) > $i).
% 0.32/1.49 thf(func_def_139, type, sK44: ($i > $o) > $i > $i).
% 0.32/1.49 thf(func_def_140, type, sK45: ($i > $o) > $i > $i).
% 0.32/1.49 thf(func_def_141, type, sK46: ($i > $o) > $i > $i).
% 0.32/1.49 thf(func_def_142, type, sK47: ($i > $o) > $i > $i).
% 0.32/1.49 thf(func_def_143, type, sK48: $i > $i > $i).
% 0.32/1.49 thf(func_def_144, type, sK49: $i > $i).
% 0.32/1.49 thf(func_def_145, type, sK50: $i > $i).
% 0.32/1.49 thf(func_def_146, type, sK51: $o > $i > $i > $i).
% 0.32/1.49 thf(func_def_147, type, sK52: ($i > $o) > $i).
% 0.32/1.49 thf(func_def_148, type, sK53: ($i > $o) > $i).
% 0.32/1.49 thf(func_def_149, type, sK54: ($i > $o) > $i).
% 0.32/1.49 thf(func_def_150, type, sK55: ($i > $o) > $i).
% 0.32/1.49 thf(func_def_151, type, sK56: ($i > $o) > $i).
% 0.32/1.49 thf(func_def_152, type, sK57: $i > ($i > $o) > $i).
% 0.32/1.49 thf(f1583,plain,(
% 0.32/1.49 $false),
% 0.32/1.49 inference(avatar_sat_refutation,[status(thm)],[f1326,f1330,f1334,f1335,f1342,f1346,f1350,f1351,f1423,f1459,f1485,f1539,f1582])).
% 0.32/1.49 thf(f1582,plain,(
% 0.32/1.49 ~spl2_9 | ~spl2_11 | ~spl2_13 | ~spl2_15),
% 0.32/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1581])).
% 0.32/1.49 thf(f1581,plain,(
% 0.32/1.49 $false | (~spl2_9 | ~spl2_11 | ~spl2_13 | ~spl2_15)),
% 0.32/1.49 inference(subsumption_resolution,[status(thm)],[f1572,f1555])).
% 0.32/1.49 thf(f1555,plain,(
% 0.32/1.49 (sK22 != (sK19 @ sK22)) | (~spl2_9 | ~spl2_13)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1550])).
% 0.32/1.49 thf(f1550,plain,(
% 0.32/1.49 (sK22 != (sK19 @ sK22)) | ($false = $true) | (~spl2_9 | ~spl2_13)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1341,f1546])).
% 0.32/1.49 thf(f1546,plain,(
% 0.32/1.49 ((sK1 @ sK22) = $true) | ~spl2_9),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1542])).
% 0.32/1.49 thf(f1542,plain,(
% 0.32/1.49 ($false = $true) | ((sK1 @ sK22) = $true) | ~spl2_9),
% 0.32/1.49 inference(superposition,[status(thm)],[f1325,f798])).
% 0.32/1.49 thf(f798,plain,(
% 0.32/1.49 ( ! [X3 : $i] : (($false = (sK0 @ X3)) | ((sK1 @ X3) = $true)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f414])).
% 0.32/1.49 thf(f414,plain,(
% 0.32/1.49 ( ! [X3 : $i] : (((sK1 @ X3) = (sK0 @ X3))) )),
% 0.32/1.49 inference(equality_resolution,[status(thm)],[f277])).
% 0.32/1.49 thf(f277,plain,(
% 0.32/1.49 ( ! [X2 : $i,X3 : $i] : (((sK1 @ X2) = (sK0 @ X3)) | (X2 != X3)) )),
% 0.32/1.49 inference(cnf_transformation,[status(thm)],[f209])).
% 0.32/1.49 thf(f209,plain,(
% 0.32/1.49 (emptysetE = $true) & (foundationAx = $true) & (descrp = $true) & (setoftrueEq = $true) & (quantDeMorgan1 = $true) & (subPowSU = $true) & (nonemptyE1 = $true) & (! [X2 : $i,X3 : $i] : (((sK1 @ X2) = (sK0 @ X3)) | (X2 != X3)) & ((exu @ (^[Y0 : $i]: (sK1 @ Y0))) != (exu @ (^[Y0 : $i]: (sK0 @ Y0))))) & (prop2set2propI = $true) & (exuE3e = $true) & (in__Cong = $true) & (omegaIndAx = $true) & (upairsetE = $true) & (emptyinunitempty = $true) & (powersetE = $true) & (nonemptyImpWitness = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (emptysetimpfalse = $true) & (replAx = $true) & (powersetAx = $true) & (singletonsswitch = $true) & (emptyE1 = $true) & (setadjoinAx = $true) & (setunionE = $true) & (powersetI = $true) & (emptyinPowerset = $true) & (notdallE = $true) & (exuE3u = $true) & (exuI2 = $true) & (quantDeMorgan2 = $true) & (notdexE = $true) & (emptysetAx = $true) & (quantDeMorgan3 = $true) & (dsetconstrI = $true) & (nonemptyI = $true) & (exuE2 = $true) & (nonemptyI1 = $true) & (setunionI = $true) & (eqinunit = $true) & (notinsingleton = $true) & (noeltsimpempty = $true) & (vacuousDall = $true) & (upairsetIL = $true) & (exuE1 = $true) & (setext = $true) & (uniqinunit = $true) & (wellorderingAx = $true) & (setunionAx = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (emptyInPowerset = $true) & (prop2setE = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setadjoinIL = $true) & (emptyI = $true) & (exuI1 = $true) & (setbeta = $true) & (setadjoinIR = $true) & (quantDeMorgan4 = $true) & (exuI3 = $true) & (prop2setI = $true) & (notinemptyset = $true) & (inCongP = $true) & (setextAx = $true) & (upairsetIR = $true)),
% 0.32/1.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f207,f208])).
% 0.32/1.49 thf(f208,plain,(
% 0.32/1.49 ? [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i,X3 : $i] : (((X1 @ X2) = (X0 @ X3)) | (X2 != X3)) & ((exu @ (^[Y0 : $i]: (X0 @ Y0))) != (exu @ (^[Y0 : $i]: (X1 @ Y0))))) => (! [X3 : $i,X2 : $i] : (((sK1 @ X2) = (sK0 @ X3)) | (X2 != X3)) & ((exu @ (^[Y0 : $i]: (sK1 @ Y0))) != (exu @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 0.32/1.49 introduced(definition,[],[choice_axiom])).
% 0.32/1.49 thf(f207,plain,(
% 0.32/1.49 (emptysetE = $true) & (foundationAx = $true) & (descrp = $true) & (setoftrueEq = $true) & (quantDeMorgan1 = $true) & (subPowSU = $true) & (nonemptyE1 = $true) & ? [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i,X3 : $i] : (((X1 @ X2) = (X0 @ X3)) | (X2 != X3)) & ((exu @ (^[Y0 : $i]: (X0 @ Y0))) != (exu @ (^[Y0 : $i]: (X1 @ Y0))))) & (prop2set2propI = $true) & (exuE3e = $true) & (in__Cong = $true) & (omegaIndAx = $true) & (upairsetE = $true) & (emptyinunitempty = $true) & (powersetE = $true) & (nonemptyImpWitness = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (emptysetimpfalse = $true) & (replAx = $true) & (powersetAx = $true) & (singletonsswitch = $true) & (emptyE1 = $true) & (setadjoinAx = $true) & (setunionE = $true) & (powersetI = $true) & (emptyinPowerset = $true) & (notdallE = $true) & (exuE3u = $true) & (exuI2 = $true) & (quantDeMorgan2 = $true) & (notdexE = $true) & (emptysetAx = $true) & (quantDeMorgan3 = $true) & (dsetconstrI = $true) & (nonemptyI = $true) & (exuE2 = $true) & (nonemptyI1 = $true) & (setunionI = $true) & (eqinunit = $true) & (notinsingleton = $true) & (noeltsimpempty = $true) & (vacuousDall = $true) & (upairsetIL = $true) & (exuE1 = $true) & (setext = $true) & (uniqinunit = $true) & (wellorderingAx = $true) & (setunionAx = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (emptyInPowerset = $true) & (prop2setE = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setadjoinIL = $true) & (emptyI = $true) & (exuI1 = $true) & (setbeta = $true) & (setadjoinIR = $true) & (quantDeMorgan4 = $true) & (exuI3 = $true) & (prop2setI = $true) & (notinemptyset = $true) & (inCongP = $true) & (setextAx = $true) & (upairsetIR = $true)),
% 0.32/1.49 inference(flattening,[status(thm)],[f206])).
% 0.32/1.49 thf(f206,plain,(
% 0.32/1.49 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i,X3 : $i] : (((X1 @ X2) = (X0 @ X3)) | (X2 != X3)) & ((exu @ (^[Y0 : $i]: (X0 @ Y0))) != (exu @ (^[Y0 : $i]: (X1 @ Y0))))) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 0.32/1.49 inference(ennf_transformation,[status(thm)],[f85])).
% 0.32/1.49 thf(f85,plain,(
% 0.32/1.49 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ! [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i,X3 : $i] : ((X2 = X3) => ((X1 @ X2) = (X0 @ X3))) => ((exu @ (^[Y0 : $i]: (X0 @ Y0))) = (exu @ (^[Y0 : $i]: (X1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.32/1.49 inference(fool_elimination,[status(thm)],[f84])).
% 0.32/1.49 thf(f84,plain,(
% 0.32/1.49 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => ! [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i,X3 : $i] : ((X2 = X3) => ((X1 @ X2) <=> (X0 @ X3))) => ((exu @ (^[X4 : $i] : (X0 @ X4))) <=> (exu @ (^[X5 : $i] : (X1 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.32/1.49 inference(rectify,[status(thm)],[f70])).
% 0.32/1.49 thf(f70,negated_conjecture,(
% 0.32/1.49 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => ! [X9 : $i > $o,X0 : $i > $o] : (! [X1 : $i,X2 : $i] : ((X1 = X2) => ((X0 @ X1) <=> (X9 @ X2))) => ((exu @ (^[X1 : $i] : (X9 @ X1))) <=> (exu @ (^[X1 : $i] : (X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.32/1.49 inference(negated_conjecture,[status(cth)],[f69])).
% 0.32/1.49 thf(f69,conjecture,(
% 0.32/1.49 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => ! [X9 : $i > $o,X0 : $i > $o] : (! [X1 : $i,X2 : $i] : ((X1 = X2) => ((X0 @ X1) <=> (X9 @ X2))) => ((exu @ (^[X1 : $i] : (X9 @ X1))) <=> (exu @ (^[X1 : $i] : (X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.32/1.49 file('/export/starexec/sandbox/tmp/tmp.wcL8QCezj3/DTF2THF_7859.p',exu__Cong)).
% 0.32/1.49 thf(f1325,plain,(
% 0.32/1.49 ((sK0 @ sK22) = $true) | ~spl2_9),
% 0.32/1.49 inference(avatar_component_clause,[status(thm)],[f1323])).
% 0.32/1.49 thf(f1323,definition,(
% 0.32/1.49 spl2_9 <=> ((sK0 @ sK22) = $true)),
% 0.32/1.49 introduced(definition,[new_symbols(naming,[spl2_9])],[avatar_definition])).
% 0.32/1.49 thf(f1341,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (((sK1 @ X1) = $false) | ((sK19 @ X1) != X1)) ) | ~spl2_13),
% 0.32/1.49 inference(avatar_component_clause,[status(thm)],[f1340])).
% 0.32/1.49 thf(f1340,definition,(
% 0.32/1.49 spl2_13 <=> ! [X1 : $i] : (((sK1 @ X1) = $false) | ((sK19 @ X1) != X1))),
% 0.32/1.49 introduced(definition,[new_symbols(naming,[spl2_13])],[avatar_definition])).
% 0.32/1.49 thf(f1572,plain,(
% 0.32/1.49 (sK22 = (sK19 @ sK22)) | (~spl2_9 | ~spl2_11 | ~spl2_15)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1571])).
% 0.32/1.49 thf(f1571,plain,(
% 0.32/1.49 ($false = $true) | (sK22 = (sK19 @ sK22)) | (~spl2_9 | ~spl2_11 | ~spl2_15)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1546,f1564])).
% 0.32/1.49 thf(f1564,plain,(
% 0.32/1.49 ( ! [X0 : $i] : (((sK1 @ X0) = $false) | ((sK19 @ X0) = sK22)) ) | (~spl2_11 | ~spl2_15)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1557])).
% 0.32/1.49 thf(f1557,plain,(
% 0.32/1.49 ( ! [X0 : $i] : (((sK19 @ X0) = sK22) | ($false = $true) | ((sK1 @ X0) = $false)) ) | (~spl2_11 | ~spl2_15)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1526,f1333])).
% 0.32/1.49 thf(f1333,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (((sK0 @ X1) = $false) | (sK22 = X1)) ) | ~spl2_11),
% 0.32/1.49 inference(avatar_component_clause,[status(thm)],[f1332])).
% 0.32/1.49 thf(f1332,definition,(
% 0.32/1.49 spl2_11 <=> ! [X1 : $i] : ((sK22 = X1) | ((sK0 @ X1) = $false))),
% 0.32/1.49 introduced(definition,[new_symbols(naming,[spl2_11])],[avatar_definition])).
% 0.32/1.49 thf(f1526,plain,(
% 0.32/1.49 ( ! [X0 : $i] : (((sK0 @ (sK19 @ X0)) = $true) | ((sK1 @ X0) = $false)) ) | ~spl2_15),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1521])).
% 0.32/1.49 thf(f1521,plain,(
% 0.32/1.49 ( ! [X0 : $i] : (((sK0 @ (sK19 @ X0)) = $true) | ($false = $true) | ((sK1 @ X0) = $false)) ) | ~spl2_15),
% 0.32/1.49 inference(superposition,[status(thm)],[f799,f1349])).
% 0.32/1.49 thf(f1349,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (((sK1 @ (sK19 @ X1)) = $true) | ((sK1 @ X1) = $false)) ) | ~spl2_15),
% 0.32/1.49 inference(avatar_component_clause,[status(thm)],[f1348])).
% 0.32/1.49 thf(f1348,definition,(
% 0.32/1.49 spl2_15 <=> ! [X1 : $i] : (((sK1 @ X1) = $false) | ((sK1 @ (sK19 @ X1)) = $true))),
% 0.32/1.49 introduced(definition,[new_symbols(naming,[spl2_15])],[avatar_definition])).
% 0.32/1.49 thf(f799,plain,(
% 0.32/1.49 ( ! [X3 : $i] : (((sK1 @ X3) = $false) | ((sK0 @ X3) = $true)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f414])).
% 0.32/1.49 thf(f1539,plain,(
% 0.32/1.49 ~spl2_8 | ~spl2_10 | ~spl2_13 | ~spl2_15),
% 0.32/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1538])).
% 0.32/1.49 thf(f1538,plain,(
% 0.32/1.49 $false | (~spl2_8 | ~spl2_10 | ~spl2_13 | ~spl2_15)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1534])).
% 0.32/1.49 thf(f1534,plain,(
% 0.32/1.49 ($false = $true) | (~spl2_8 | ~spl2_10 | ~spl2_13 | ~spl2_15)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1321,f1531])).
% 0.32/1.49 thf(f1531,plain,(
% 0.32/1.49 ((sK1 @ sK21) = $false) | (~spl2_8 | ~spl2_10 | ~spl2_13 | ~spl2_15)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1528])).
% 0.32/1.49 thf(f1528,plain,(
% 0.32/1.49 ((sK1 @ sK21) = $false) | (sK21 != sK21) | (~spl2_8 | ~spl2_10 | ~spl2_13 | ~spl2_15)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1511,f1527])).
% 0.32/1.49 thf(f1527,plain,(
% 0.32/1.49 ( ! [X0 : $i] : ((sK21 = (sK19 @ X0)) | ((sK1 @ X0) = $false)) ) | (~spl2_10 | ~spl2_15)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1517])).
% 0.32/1.49 thf(f1517,plain,(
% 0.32/1.49 ( ! [X0 : $i] : ((sK21 = (sK19 @ X0)) | ((sK1 @ X0) = $false) | ($false = $true)) ) | (~spl2_10 | ~spl2_15)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1349,f1329])).
% 0.32/1.49 thf(f1329,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (((sK1 @ X1) = $false) | (sK21 = X1)) ) | ~spl2_10),
% 0.32/1.49 inference(avatar_component_clause,[status(thm)],[f1328])).
% 0.32/1.49 thf(f1328,definition,(
% 0.32/1.49 spl2_10 <=> ! [X1 : $i] : ((sK21 = X1) | ((sK1 @ X1) = $false))),
% 0.32/1.49 introduced(definition,[new_symbols(naming,[spl2_10])],[avatar_definition])).
% 0.32/1.49 thf(f1511,plain,(
% 0.32/1.49 ((sK19 @ sK21) != sK21) | (~spl2_8 | ~spl2_13)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1508])).
% 0.32/1.49 thf(f1508,plain,(
% 0.32/1.49 ($false = $true) | ((sK19 @ sK21) != sK21) | (~spl2_8 | ~spl2_13)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1321,f1341])).
% 0.32/1.49 thf(f1321,plain,(
% 0.32/1.49 ((sK1 @ sK21) = $true) | ~spl2_8),
% 0.32/1.49 inference(avatar_component_clause,[status(thm)],[f1319])).
% 0.32/1.49 thf(f1319,definition,(
% 0.32/1.49 spl2_8 <=> ((sK1 @ sK21) = $true)),
% 0.32/1.49 introduced(definition,[new_symbols(naming,[spl2_8])],[avatar_definition])).
% 0.32/1.49 thf(f1485,plain,(
% 0.32/1.49 ~spl2_9 | ~spl2_11 | ~spl2_12 | ~spl2_14),
% 0.32/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1484])).
% 0.32/1.49 thf(f1484,plain,(
% 0.32/1.49 $false | (~spl2_9 | ~spl2_11 | ~spl2_12 | ~spl2_14)),
% 0.32/1.49 inference(subsumption_resolution,[status(thm)],[f1478,f1442])).
% 0.32/1.49 thf(f1442,plain,(
% 0.32/1.49 ((sK20 @ sK22) != sK22) | (~spl2_9 | ~spl2_12)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1436])).
% 0.32/1.49 thf(f1436,plain,(
% 0.32/1.49 ($false = $true) | ((sK20 @ sK22) != sK22) | (~spl2_9 | ~spl2_12)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1338,f1325])).
% 0.32/1.49 thf(f1338,plain,(
% 0.32/1.49 ( ! [X2 : $i] : (((sK0 @ X2) = $false) | ((sK20 @ X2) != X2)) ) | ~spl2_12),
% 0.32/1.49 inference(avatar_component_clause,[status(thm)],[f1337])).
% 0.32/1.49 thf(f1337,definition,(
% 0.32/1.49 spl2_12 <=> ! [X2 : $i] : (((sK20 @ X2) != X2) | ((sK0 @ X2) = $false))),
% 0.32/1.49 introduced(definition,[new_symbols(naming,[spl2_12])],[avatar_definition])).
% 0.32/1.49 thf(f1478,plain,(
% 0.32/1.49 ((sK20 @ sK22) = sK22) | (~spl2_9 | ~spl2_11 | ~spl2_14)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1473])).
% 0.32/1.49 thf(f1473,plain,(
% 0.32/1.49 ((sK20 @ sK22) = sK22) | ($false = $true) | (~spl2_9 | ~spl2_11 | ~spl2_14)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1467,f1325])).
% 0.32/1.49 thf(f1467,plain,(
% 0.32/1.49 ( ! [X0 : $i] : (((sK0 @ X0) = $false) | ((sK20 @ X0) = sK22)) ) | (~spl2_11 | ~spl2_14)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1463])).
% 0.32/1.49 thf(f1463,plain,(
% 0.32/1.49 ( ! [X0 : $i] : (((sK20 @ X0) = sK22) | ((sK0 @ X0) = $false) | ($false = $true)) ) | (~spl2_11 | ~spl2_14)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1345,f1333])).
% 0.32/1.49 thf(f1345,plain,(
% 0.32/1.49 ( ! [X2 : $i] : (((sK0 @ (sK20 @ X2)) = $true) | ((sK0 @ X2) = $false)) ) | ~spl2_14),
% 0.32/1.49 inference(avatar_component_clause,[status(thm)],[f1344])).
% 0.32/1.49 thf(f1344,definition,(
% 0.32/1.49 spl2_14 <=> ! [X2 : $i] : (((sK0 @ X2) = $false) | ((sK0 @ (sK20 @ X2)) = $true))),
% 0.32/1.49 introduced(definition,[new_symbols(naming,[spl2_14])],[avatar_definition])).
% 0.32/1.49 thf(f1459,plain,(
% 0.32/1.49 spl2_8 | ~spl2_9 | ~spl2_10),
% 0.32/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1458])).
% 0.32/1.49 thf(f1458,plain,(
% 0.32/1.49 $false | (spl2_8 | ~spl2_9 | ~spl2_10)),
% 0.32/1.49 inference(subsumption_resolution,[status(thm)],[f1455,f1320])).
% 0.32/1.49 thf(f1320,plain,(
% 0.32/1.49 ((sK1 @ sK21) != $true) | spl2_8),
% 0.32/1.49 inference(avatar_component_clause,[status(thm)],[f1319])).
% 0.32/1.49 thf(f1455,plain,(
% 0.32/1.49 ((sK1 @ sK21) = $true) | (~spl2_9 | ~spl2_10)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1443,f1454])).
% 0.32/1.49 thf(f1454,plain,(
% 0.32/1.49 (sK21 = sK22) | (~spl2_9 | ~spl2_10)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1448])).
% 0.32/1.49 thf(f1448,plain,(
% 0.32/1.49 ($false = $true) | (sK21 = sK22) | (~spl2_9 | ~spl2_10)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1443,f1329])).
% 0.32/1.49 thf(f1443,plain,(
% 0.32/1.49 ((sK1 @ sK22) = $true) | ~spl2_9),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1434])).
% 0.32/1.49 thf(f1434,plain,(
% 0.32/1.49 ((sK1 @ sK22) = $true) | ($false = $true) | ~spl2_9),
% 0.32/1.49 inference(superposition,[status(thm)],[f1325,f798])).
% 0.32/1.49 thf(f1423,plain,(
% 0.32/1.49 ~spl2_8 | ~spl2_10 | ~spl2_12 | ~spl2_14),
% 0.32/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1422])).
% 0.32/1.49 thf(f1422,plain,(
% 0.32/1.49 $false | (~spl2_8 | ~spl2_10 | ~spl2_12 | ~spl2_14)),
% 0.32/1.49 inference(subsumption_resolution,[status(thm)],[f1417,f1388])).
% 0.32/1.49 thf(f1388,plain,(
% 0.32/1.49 ((sK20 @ sK21) != sK21) | (~spl2_8 | ~spl2_12)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1386])).
% 0.32/1.49 thf(f1386,plain,(
% 0.32/1.49 ($false = $true) | ((sK20 @ sK21) != sK21) | (~spl2_8 | ~spl2_12)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1372,f1338])).
% 0.32/1.49 thf(f1372,plain,(
% 0.32/1.49 ((sK0 @ sK21) = $true) | ~spl2_8),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1368])).
% 0.32/1.49 thf(f1368,plain,(
% 0.32/1.49 ((sK0 @ sK21) = $true) | ($false = $true) | ~spl2_8),
% 0.32/1.49 inference(superposition,[status(thm)],[f799,f1321])).
% 0.32/1.49 thf(f1417,plain,(
% 0.32/1.49 ((sK20 @ sK21) = sK21) | (~spl2_8 | ~spl2_10 | ~spl2_14)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1410])).
% 0.32/1.49 thf(f1410,plain,(
% 0.32/1.49 ((sK20 @ sK21) = sK21) | ($false = $true) | (~spl2_8 | ~spl2_10 | ~spl2_14)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1408,f1372])).
% 0.32/1.49 thf(f1408,plain,(
% 0.32/1.49 ( ! [X0 : $i] : (((sK0 @ X0) = $false) | ((sK20 @ X0) = sK21)) ) | (~spl2_10 | ~spl2_14)),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1405])).
% 0.32/1.49 thf(f1405,plain,(
% 0.32/1.49 ( ! [X0 : $i] : (($false = $true) | ((sK0 @ X0) = $false) | ((sK20 @ X0) = sK21)) ) | (~spl2_10 | ~spl2_14)),
% 0.32/1.49 inference(superposition,[status(thm)],[f1329,f1401])).
% 0.32/1.49 thf(f1401,plain,(
% 0.32/1.49 ( ! [X0 : $i] : (((sK1 @ (sK20 @ X0)) = $true) | ((sK0 @ X0) = $false)) ) | ~spl2_14),
% 0.32/1.49 inference(trivial_inequality_removal,[status(thm)],[f1397])).
% 0.32/1.49 thf(f1397,plain,(
% 0.32/1.49 ( ! [X0 : $i] : (((sK0 @ X0) = $false) | ((sK1 @ (sK20 @ X0)) = $true) | ($false = $true)) ) | ~spl2_14),
% 0.32/1.49 inference(superposition,[status(thm)],[f798,f1345])).
% 0.32/1.49 thf(f1351,plain,(
% 0.32/1.49 spl2_15 | spl2_14),
% 0.32/1.49 inference(avatar_split_clause,[status(thm)],[f684,f1344,f1348])).
% 0.32/1.49 thf(f684,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | ((sK0 @ X2) = $false) | ((sK1 @ (sK19 @ X1)) = $true) | ((sK0 @ (sK20 @ X2)) = $true)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f682])).
% 0.32/1.49 thf(f682,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : ((((sK0 @ (sK20 @ X2)) => (X2 = (sK20 @ X2))) = $false) | ((sK0 @ X2) = $false) | ((sK1 @ (sK19 @ X1)) = $true) | ((sK1 @ X1) = $false)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f680])).
% 0.32/1.49 thf(f680,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X2) = $false) | (((sK1 @ (sK19 @ X1)) => (X1 = (sK19 @ X1))) = $false) | ((sK1 @ X1) = $false) | (((sK0 @ (sK20 @ X2)) => (X2 = (sK20 @ X2))) = $false)) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f679])).
% 0.32/1.49 thf(f679,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X2) = $false) | ((sK1 @ X1) = $false) | (((^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0))) @ (sK20 @ X2)) = $false) | (((sK1 @ (sK19 @ X1)) => (X1 = (sK19 @ X1))) = $false)) )),
% 0.32/1.49 inference(sigma_clausification,[status(thm)],[f678])).
% 0.32/1.49 thf(f678,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0)))) = $false) | (((sK1 @ (sK19 @ X1)) => (X1 = (sK19 @ X1))) = $false) | ((sK1 @ X1) = $false) | ((sK0 @ X2) = $false)) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f677])).
% 0.32/1.49 thf(f677,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0)))) = $false) | (((^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0))) @ (sK19 @ X1)) = $false) | ((sK1 @ X1) = $false) | ((sK0 @ X2) = $false)) )),
% 0.32/1.49 inference(sigma_clausification,[status(thm)],[f676])).
% 0.32/1.49 thf(f676,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | ((sK0 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0)))) = $false)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f675])).
% 0.32/1.49 thf(f675,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0)))) & (sK0 @ X2))) | ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0)))) = $false) | ((sK1 @ X1) = $false)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f674])).
% 0.32/1.49 thf(f674,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0)))) & (sK1 @ X1)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0)))) & (sK0 @ X2)))) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f673])).
% 0.32/1.49 thf(f673,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0)))) & (sK1 @ X1)) = $false) | ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0))) @ X2))) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f672])).
% 0.32/1.49 thf(f672,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0)))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0)))) & (sK1 @ X1)) = $false)) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f671])).
% 0.32/1.49 thf(f671,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))) & (sK1 @ Y0))) @ X1)) | ((?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0)))) = $false)) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f670])).
% 0.32/1.49 thf(f670,plain,(
% 0.32/1.49 ($false = (?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))) & (sK1 @ Y0))))) | ((?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0)))) = $false)),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f668])).
% 0.32/1.49 thf(f668,plain,(
% 0.32/1.49 ((?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0)))) != (?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))) & (sK1 @ Y0)))))),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f347])).
% 0.32/1.49 thf(f347,plain,(
% 0.32/1.49 (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))) @ (^[Y0 : $i]: (sK1 @ Y0))) != ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))) @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 0.32/1.49 inference(definition_unfolding,[status(thm)],[f276,f286,f286])).
% 0.32/1.49 thf(f286,plain,(
% 0.32/1.49 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 0.32/1.49 inference(cnf_transformation,[status(thm)],[f179])).
% 0.32/1.49 thf(f179,plain,(
% 0.32/1.49 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 0.32/1.49 inference(fool_elimination,[status(thm)],[f178])).
% 0.32/1.49 thf(f178,plain,(
% 0.32/1.49 ((^[X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))) = exu)),
% 0.32/1.49 inference(rectify,[status(thm)],[f1])).
% 0.32/1.49 thf(f1,axiom,(
% 0.32/1.49 ((^[X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))) = exu)),
% 0.32/1.49 file('/export/starexec/sandbox/tmp/tmp.wcL8QCezj3/DTF2THF_7859.p',exu)).
% 0.32/1.49 thf(f276,plain,(
% 0.32/1.49 ((exu @ (^[Y0 : $i]: (sK1 @ Y0))) != (exu @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 0.32/1.49 inference(cnf_transformation,[status(thm)],[f209])).
% 0.32/1.49 thf(f1350,plain,(
% 0.32/1.49 spl2_12 | spl2_15),
% 0.32/1.49 inference(avatar_split_clause,[status(thm)],[f685,f1348,f1337])).
% 0.32/1.49 thf(f685,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | ((sK20 @ X2) != X2) | ((sK0 @ X2) = $false) | ((sK1 @ (sK19 @ X1)) = $true)) )),
% 0.32/1.49 inference(equality_proxy_clausification,[status(thm)],[f683])).
% 0.32/1.49 thf(f683,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK1 @ (sK19 @ X1)) = $true) | ((sK1 @ X1) = $false) | ((sK0 @ X2) = $false) | ((X2 = (sK20 @ X2)) = $false)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f682])).
% 0.32/1.49 thf(f1346,plain,(
% 0.32/1.49 spl2_14 | spl2_13),
% 0.32/1.49 inference(avatar_split_clause,[status(thm)],[f688,f1340,f1344])).
% 0.32/1.49 thf(f688,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK19 @ X1) != X1) | ((sK0 @ X2) = $false) | ((sK1 @ X1) = $false) | ((sK0 @ (sK20 @ X2)) = $true)) )),
% 0.32/1.49 inference(equality_proxy_clausification,[status(thm)],[f687])).
% 0.32/1.49 thf(f687,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | ((sK0 @ (sK20 @ X2)) = $true) | ((X1 = (sK19 @ X1)) = $false) | ((sK0 @ X2) = $false)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f681])).
% 0.32/1.49 thf(f681,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X2) = $false) | (((sK0 @ (sK20 @ X2)) => (X2 = (sK20 @ X2))) = $false) | ((X1 = (sK19 @ X1)) = $false) | ((sK1 @ X1) = $false)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f680])).
% 0.32/1.49 thf(f1342,plain,(
% 0.32/1.49 spl2_12 | spl2_13),
% 0.32/1.49 inference(avatar_split_clause,[status(thm)],[f690,f1340,f1337])).
% 0.32/1.49 thf(f690,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | ((sK20 @ X2) != X2) | ((sK19 @ X1) != X1) | ((sK0 @ X2) = $false)) )),
% 0.32/1.49 inference(equality_proxy_clausification,[status(thm)],[f689])).
% 0.32/1.49 thf(f689,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | ((sK0 @ X2) = $false) | ((sK20 @ X2) != X2) | ((X1 = (sK19 @ X1)) = $false)) )),
% 0.32/1.49 inference(equality_proxy_clausification,[status(thm)],[f686])).
% 0.32/1.49 thf(f686,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | ((X2 = (sK20 @ X2)) = $false) | ((X1 = (sK19 @ X1)) = $false) | ((sK0 @ X2) = $false)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f681])).
% 0.32/1.49 thf(f1335,plain,(
% 0.32/1.49 spl2_11 | spl2_10),
% 0.32/1.49 inference(avatar_split_clause,[status(thm)],[f706,f1328,f1332])).
% 0.32/1.49 thf(f706,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : ((sK22 = X1) | ((sK1 @ X2) = $false) | ((sK0 @ X1) = $false) | (sK21 = X2)) )),
% 0.32/1.49 inference(equality_proxy_clausification,[status(thm)],[f705])).
% 0.32/1.49 thf(f705,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X2) = $false) | ((sK22 = X1) = $true) | ((sK0 @ X1) = $false) | (sK21 = X2)) )),
% 0.32/1.49 inference(equality_proxy_clausification,[status(thm)],[f704])).
% 0.32/1.49 thf(f704,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : (((sK21 = X2) = $true) | ((sK1 @ X2) = $false) | ((sK0 @ X1) = $false) | ((sK22 = X1) = $true)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f703])).
% 0.32/1.49 thf(f703,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X2) => (sK21 = X2)) = $true) | ((sK0 @ X1) = $false) | ((sK22 = X1) = $true)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f702])).
% 0.32/1.49 thf(f702,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : ((((sK0 @ X1) => (sK22 = X1)) = $true) | (((sK1 @ X2) => (sK21 = X2)) = $true)) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f701])).
% 0.32/1.49 thf(f701,plain,(
% 0.32/1.49 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((sK1 @ Y0) => (sK21 = Y0))) @ X2) = $true) | (((sK0 @ X1) => (sK22 = X1)) = $true)) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f700])).
% 0.32/1.49 thf(f700,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK21 = Y0)))) = $true) | (((sK0 @ X1) => (sK22 = X1)) = $true)) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f699])).
% 0.32/1.49 thf(f699,plain,(
% 0.32/1.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ Y0) => (sK22 = Y0))) @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK21 = Y0)))) = $true)) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f698])).
% 0.32/1.49 thf(f698,plain,(
% 0.32/1.49 ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK22 = Y0)))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK21 = Y0)))) = $true)),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f696])).
% 0.32/1.49 thf(f696,plain,(
% 0.32/1.49 (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK21 = Y0)))) & (sK1 @ sK21)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK22 = Y0)))) = $true)),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f694])).
% 0.32/1.49 thf(f694,plain,(
% 0.32/1.49 (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK22 = Y0)))) & (sK0 @ sK22)) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK21 = Y0)))) & (sK1 @ sK21)) = $true)),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f693])).
% 0.32/1.49 thf(f693,plain,(
% 0.32/1.49 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0))) @ sK22) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK21 = Y0)))) & (sK1 @ sK21)) = $true)),
% 0.32/1.49 inference(sigma_clausification,[status(thm)],[f692])).
% 0.32/1.49 thf(f692,plain,(
% 0.32/1.49 ((?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0)))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK21 = Y0)))) & (sK1 @ sK21)) = $true)),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f691])).
% 0.32/1.49 thf(f691,plain,(
% 0.32/1.49 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))) & (sK1 @ Y0))) @ sK21) = $true) | ((?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0)))) = $true)),
% 0.32/1.49 inference(sigma_clausification,[status(thm)],[f669])).
% 0.32/1.49 thf(f669,plain,(
% 0.32/1.49 ((?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))) & (sK1 @ Y0)))) = $true) | ((?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0)))) = $true)),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f668])).
% 0.32/1.49 thf(f1334,plain,(
% 0.32/1.49 spl2_8 | spl2_11),
% 0.32/1.49 inference(avatar_split_clause,[status(thm)],[f710,f1332,f1319])).
% 0.32/1.49 thf(f710,plain,(
% 0.32/1.49 ( ! [X1 : $i] : ((sK22 = X1) | ((sK0 @ X1) = $false) | ((sK1 @ sK21) = $true)) )),
% 0.32/1.49 inference(equality_proxy_clausification,[status(thm)],[f709])).
% 0.32/1.49 thf(f709,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (((sK22 = X1) = $true) | ((sK0 @ X1) = $false) | ((sK1 @ sK21) = $true)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f708])).
% 0.32/1.49 thf(f708,plain,(
% 0.32/1.49 ( ! [X1 : $i] : ((((sK0 @ X1) => (sK22 = X1)) = $true) | ((sK1 @ sK21) = $true)) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f707])).
% 0.32/1.49 thf(f707,plain,(
% 0.32/1.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ Y0) => (sK22 = Y0))) @ X1) = $true) | ((sK1 @ sK21) = $true)) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f697])).
% 0.32/1.49 thf(f697,plain,(
% 0.32/1.49 ((sK1 @ sK21) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK22 = Y0)))) = $true)),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f696])).
% 0.32/1.49 thf(f1330,plain,(
% 0.32/1.49 spl2_10 | spl2_9),
% 0.32/1.49 inference(avatar_split_clause,[status(thm)],[f716,f1323,f1328])).
% 0.32/1.49 thf(f716,plain,(
% 0.32/1.49 ( ! [X1 : $i] : ((sK21 = X1) | ((sK0 @ sK22) = $true) | ((sK1 @ X1) = $false)) )),
% 0.32/1.49 inference(equality_proxy_clausification,[status(thm)],[f715])).
% 0.32/1.49 thf(f715,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (((sK1 @ X1) = $false) | ((sK21 = X1) = $true) | ((sK0 @ sK22) = $true)) )),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f714])).
% 0.32/1.49 thf(f714,plain,(
% 0.32/1.49 ( ! [X1 : $i] : (((sK0 @ sK22) = $true) | (((sK1 @ X1) => (sK21 = X1)) = $true)) )),
% 0.32/1.49 inference(beta_eta_normalization,[status(thm)],[f713])).
% 0.32/1.49 thf(f713,plain,(
% 0.32/1.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK1 @ Y0) => (sK21 = Y0))) @ X1) = $true) | ((sK0 @ sK22) = $true)) )),
% 0.32/1.49 inference(pi_clausification,[status(thm)],[f712])).
% 0.32/1.49 thf(f712,plain,(
% 0.32/1.49 ((sK0 @ sK22) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK21 = Y0)))) = $true)),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f695])).
% 0.32/1.49 thf(f695,plain,(
% 0.32/1.49 (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK21 = Y0)))) & (sK1 @ sK21)) = $true) | ((sK0 @ sK22) = $true)),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f694])).
% 0.32/1.49 thf(f1326,plain,(
% 0.32/1.49 spl2_8 | spl2_9),
% 0.32/1.49 inference(avatar_split_clause,[status(thm)],[f711,f1323,f1319])).
% 0.32/1.49 thf(f711,plain,(
% 0.32/1.49 ((sK0 @ sK22) = $true) | ((sK1 @ sK21) = $true)),
% 0.32/1.49 inference(binary_proxy_clausification,[status(thm)],[f695])).
% 0.32/1.49 % SZS output end Proof for DTF2THF_7859
% 0.32/1.49 % (7976)------------------------------
% 0.32/1.49 % (7976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.49 % (7976)Termination reason: Refutation
% 0.32/1.49
% 0.32/1.49 % (7976)Memory used [KB]: 6652
% 0.32/1.49 % (7976)Time elapsed: 0.045 s
% 0.32/1.49 % (7976)Instructions burned: 129 (million)
% 0.32/1.49 % (7976)------------------------------
% 0.32/1.49 % (7976)------------------------------
% 0.32/1.49 % (7975)Success in time 0.044 s
%------------------------------------------------------------------------------