%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU531^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 09:35:07 AM UTC 2026
% Result : Theorem 2.09s 1.47s
% Output : Refutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 12 unt; 0 typ; 3 def)
% Number of atoms : 1149 ( 330 equ; 0 cnn)
% Maximal formula atoms : 51 ( 20 avg)
% Number of connectives : 737 ( 73 ~; 63 |; 172 &; 220 @)
% ( 8 <=>; 201 =>; 0 <=; 0 <~>)
% Maximal formula depth : 57 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 128 ( 125 usr; 61 con; 0-3 aty)
% Number of variables : 79 ( 0 ^; 55 !; 24 ?; 79 :)
% 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_72,type,
sP1: $i > $i > $o ).
thf(func_def_73,type,
sP2: $i > $o ).
thf(func_def_74,type,
sP3: $i > $i > $o ).
thf(func_def_75,type,
sP4: $i > $i > $o ).
thf(func_def_77,type,
sK6: $i > $i > $o ).
thf(func_def_78,type,
sK7: $i > $i ).
thf(func_def_79,type,
sK8: $i > $i ).
thf(func_def_80,type,
sK9: ( $i > $i > $o ) > $i > $i ).
thf(func_def_81,type,
sK10: ( $i > $i > $o ) > $i > $i ).
thf(func_def_82,type,
sK11: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_89,type,
sK18: $i > $o ).
thf(func_def_94,type,
sK23: $i > $i > $i ).
thf(func_def_97,type,
sK26: $i > $i ).
thf(func_def_107,type,
sK36: ( $i > $o ) > $i ).
thf(func_def_108,type,
sK37: $i > $o ).
thf(func_def_109,type,
sK38: $i > $i ).
thf(func_def_113,type,
sK42: $i > $o ).
thf(func_def_114,type,
sK43: $i > $i ).
thf(func_def_115,type,
sK44: ( $i > $o ) > $i ).
thf(func_def_123,type,
sK52: ( $i > $o ) > $i ).
thf(func_def_124,type,
sK53: $i > $o ).
thf(func_def_127,type,
sK56: $i > $i > $i ).
thf(func_def_128,type,
sK57: $i > $i > $i ).
thf(func_def_129,type,
sK58: $i > $i > $i ).
thf(func_def_130,type,
sK59: $i > $i > $i ).
thf(func_def_131,type,
sK60: $i > $i > $i > $i ).
thf(func_def_132,type,
sK61: $i > $i ).
thf(func_def_133,type,
sK62: $i > $i ).
thf(func_def_134,type,
sK63: $i > $i ).
thf(func_def_135,type,
sK64: $i > $i ).
thf(func_def_136,type,
sK65: $i > $i > $i ).
thf(func_def_137,type,
sK66: $i > $i > $i > $i ).
thf(func_def_138,type,
sK67: $i > $i > $i > $i ).
thf(func_def_139,type,
sK68: $i > $i > $i ).
thf(func_def_140,type,
sK69: $i > $i > $i ).
thf(func_def_142,type,
sK71: $i > $i ).
thf(func_def_143,type,
sK72: $i > $i ).
thf(func_def_144,type,
sK73: $i > $i ).
thf(func_def_145,type,
sK74: $i > $i > $i ).
thf(func_def_146,type,
sK75: $i > $i ).
thf(func_def_149,type,
sK78: $i > $i ).
thf(func_def_153,type,
sK82: $i > $i ).
thf(func_def_156,type,
sK85: $i > $o ).
thf(func_def_157,type,
sK86: $o > $i > $i > $i ).
thf(func_def_167,type,
sK96: $i > $i > $i ).
thf(func_def_175,type,
sK104: $i > $o ).
thf(func_def_178,type,
sK107: $i > $o ).
thf(func_def_182,type,
sK111: $i > $i ).
thf(func_def_185,type,
sK114: $i > $o ).
thf(func_def_187,type,
sK116: $i > $i > $i ).
thf(func_def_188,type,
sK117: $i > $i > $i ).
thf(func_def_191,type,
sK120: $i > $i ).
thf(func_def_195,type,
sK124: $i > $i > $i ).
thf(func_def_199,type,
sK128: $i > $i ).
thf(func_def_205,type,
sK134: $i > $o ).
thf(func_def_207,type,
sK136: $i > $i > $i ).
thf(func_def_211,type,
ph140:
!>[X0: $tType] : X0 ).
thf(f833,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f777,f789,f826,f832]) ).
thf(f832,plain,
~ spl139_4,
inference(avatar_contradiction_clause,[status(thm)],[f831]) ).
thf(f831,plain,
( $false
| ~ spl139_4 ),
inference(trivial_inequality_removal,[status(thm)],[f830]) ).
thf(f830,plain,
( ( sK48 != sK48 )
| ~ spl139_4 ),
inference(superposition,[status(thm)],[f556,f809]) ).
thf(f809,plain,
( ( sK50 = sK48 )
| ~ spl139_4 ),
inference(avatar_component_clause,[status(thm)],[f807]) ).
thf(f807,definition,
( spl139_4
<=> ( sK50 = sK48 ) ),
introduced(definition,[new_symbols(naming,[spl139_4])],[avatar_definition]) ).
thf(f556,plain,
sK50 != sK48,
inference(cnf_transformation,[status(thm)],[f302]) ).
thf(f302,plain,
( ( setadjoinE = $true )
& ( wellorderingAx = $true )
& ( setadjoinIL = $true )
& ( notinemptyset = $true )
& ( noeltsimpempty = $true )
& ( singletonsswitch = $true )
& ( emptyInPowerset = $true )
& ( setadjoinIR = $true )
& ( nonemptyI = $true )
& ( replAx = $true )
& ( emptyinPowerset = $true )
& ( powersetAx = $true )
& ( subPowSU = $true )
& ( emptyI = $true )
& ( emptysetimpfalse = $true )
& ( setext = $true )
& ( notinsingleton = $true )
& ( emptyinunitempty = $true )
& ( dsetconstrEL = $true )
& ( setunionI = $true )
& ( nonemptyE1 = $true )
& ( omegaSAx = $true )
& ( emptysetE = $true )
& ( descrp = $true )
& ( setunionE = $true )
& ( nonemptyImpWitness = $true )
& ( ( in @ sK48 @ ( setadjoin @ sK49 @ ( setadjoin @ sK50 @ emptyset ) ) )
= $true )
& ( sK50 != sK48 )
& ( sK49 != sK48 )
& ( uniqinunit = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( exuE3e = $true )
& ( foundationAx = $true )
& ( setadjoinOr = $true )
& ( powersetE = $true )
& ( dsetconstrI = $true )
& ( setextAx = $true )
& ( powersetI = $true )
& ( eqinunit = $true )
& ( nonemptyI1 = $true )
& ( setadjoinAx = $true )
& ( dsetconstrER = $true )
& ( setbeta = $true )
& ( prop2setE = $true )
& ( emptysetAx = $true )
& ( omegaIndAx = $true )
& ( setunionAx = $true )
& ( setoftrueEq = $true )
& ( exuE2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49,sK50])],[f170,f301]) ).
thf(f301,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
& ( X0 != X2 )
& ( X0 != X1 ) )
=> ( ( ( in @ sK48 @ ( setadjoin @ sK49 @ ( setadjoin @ sK50 @ emptyset ) ) )
= $true )
& ( sK50 != sK48 )
& ( sK49 != sK48 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f170,plain,
( ( setadjoinE = $true )
& ( wellorderingAx = $true )
& ( setadjoinIL = $true )
& ( notinemptyset = $true )
& ( noeltsimpempty = $true )
& ( singletonsswitch = $true )
& ( emptyInPowerset = $true )
& ( setadjoinIR = $true )
& ( nonemptyI = $true )
& ( replAx = $true )
& ( emptyinPowerset = $true )
& ( powersetAx = $true )
& ( subPowSU = $true )
& ( emptyI = $true )
& ( emptysetimpfalse = $true )
& ( setext = $true )
& ( notinsingleton = $true )
& ( emptyinunitempty = $true )
& ( dsetconstrEL = $true )
& ( setunionI = $true )
& ( nonemptyE1 = $true )
& ( omegaSAx = $true )
& ( emptysetE = $true )
& ( descrp = $true )
& ( setunionE = $true )
& ( nonemptyImpWitness = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
& ( X0 != X2 )
& ( X0 != X1 ) )
& ( uniqinunit = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( exuE3e = $true )
& ( foundationAx = $true )
& ( setadjoinOr = $true )
& ( powersetE = $true )
& ( dsetconstrI = $true )
& ( setextAx = $true )
& ( powersetI = $true )
& ( eqinunit = $true )
& ( nonemptyI1 = $true )
& ( setadjoinAx = $true )
& ( dsetconstrER = $true )
& ( setbeta = $true )
& ( prop2setE = $true )
& ( emptysetAx = $true )
& ( omegaIndAx = $true )
& ( setunionAx = $true )
& ( setoftrueEq = $true )
& ( exuE2 = $true ) ),
inference(flattening,[status(thm)],[f169]) ).
thf(f169,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( X0 != X2 )
& ( X0 != X1 )
& ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) )
& ( 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)],[f105]) ).
thf(f105,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
=> ( ( X0 = X2 )
| ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f104]) ).
thf(f104,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X0 = X2 )
| ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f52]) ).
thf(f52,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
=> ! [X8: $i,X1: $i,X2: $i] :
( ( in @ X8 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X2 = X8 )
| ( X1 = X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
thf(f51,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
=> ! [X8: $i,X1: $i,X2: $i] :
( ( in @ X8 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X2 = X8 )
| ( X1 = X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PJlHxzAzZQ/DTF2THF_25445.p',upairsetE) ).
thf(f826,plain,
( spl139_4
| ~ spl139_1 ),
inference(avatar_split_clause,[status(thm)],[f803,f767,f807]) ).
thf(f767,definition,
( spl139_1
<=> ( ( in @ sK48 @ ( setadjoin @ sK50 @ emptyset ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl139_1])],[avatar_definition]) ).
thf(f803,plain,
( ( sK50 = sK48 )
| ~ spl139_1 ),
inference(trivial_inequality_removal,[status(thm)],[f802]) ).
thf(f802,plain,
( ( $true != $true )
| ( sK50 = sK48 )
| ~ spl139_1 ),
inference(forward_demodulation,[status(thm)],[f801,f554]) ).
thf(f554,plain,
uniqinunit = $true,
inference(cnf_transformation,[status(thm)],[f302]) ).
thf(f801,plain,
( ( uniqinunit != $true )
| ( sK50 = sK48 )
| ~ spl139_1 ),
inference(trivial_inequality_removal,[status(thm)],[f791]) ).
thf(f791,plain,
( ( uniqinunit != $true )
| ( sK50 = sK48 )
| ( $true != $true )
| ~ spl139_1 ),
inference(superposition,[status(thm)],[f634,f769]) ).
thf(f769,plain,
( ( ( in @ sK48 @ ( setadjoin @ sK50 @ emptyset ) )
= $true )
| ~ spl139_1 ),
inference(avatar_component_clause,[status(thm)],[f767]) ).
thf(f634,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
| ( uniqinunit != $true )
| ( X2 = X3 ) ),
inference(cnf_transformation,[status(thm)],[f357]) ).
thf(f357,plain,
( ( ( uniqinunit = $true )
| ( ( ( in @ sK79 @ ( setadjoin @ sK80 @ emptyset ) )
= $true )
& ( sK79 != sK80 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
| ( X2 = X3 ) )
| ( uniqinunit != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80])],[f355,f356]) ).
thf(f356,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( X0 != X1 ) )
=> ( ( ( in @ sK79 @ ( setadjoin @ sK80 @ emptyset ) )
= $true )
& ( sK79 != sK80 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f355,plain,
( ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
| ( X2 = X3 ) )
| ( uniqinunit != $true ) ) ),
inference(rectify,[status(thm)],[f354]) ).
thf(f354,plain,
( ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f182]) ).
thf(f182,plain,
( ( uniqinunit = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f57]) ).
thf(f57,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
=> ( X0 = X1 ) )
<=> ( uniqinunit = $true ) ),
inference(fool_elimination,[status(thm)],[f56]) ).
thf(f56,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
inference(rectify,[status(thm)],[f47]) ).
thf(f47,axiom,
! [X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) )
= uniqinunit ),
file('/export/starexec/sandbox2/tmp/tmp.PJlHxzAzZQ/DTF2THF_25445.p',uniqinunit) ).
thf(f789,plain,
~ spl139_2,
inference(avatar_contradiction_clause,[status(thm)],[f788]) ).
thf(f788,plain,
( $false
| ~ spl139_2 ),
inference(trivial_inequality_removal,[status(thm)],[f787]) ).
thf(f787,plain,
( ( sK48 != sK48 )
| ~ spl139_2 ),
inference(superposition,[status(thm)],[f555,f773]) ).
thf(f773,plain,
( ( sK49 = sK48 )
| ~ spl139_2 ),
inference(avatar_component_clause,[status(thm)],[f771]) ).
thf(f771,definition,
( spl139_2
<=> ( sK49 = sK48 ) ),
introduced(definition,[new_symbols(naming,[spl139_2])],[avatar_definition]) ).
thf(f555,plain,
sK49 != sK48,
inference(cnf_transformation,[status(thm)],[f302]) ).
thf(f777,plain,
( spl139_2
| spl139_1 ),
inference(avatar_split_clause,[status(thm)],[f776,f767,f771]) ).
thf(f776,plain,
( ( ( in @ sK48 @ ( setadjoin @ sK50 @ emptyset ) )
= $true )
| ( sK49 = sK48 ) ),
inference(trivial_inequality_removal,[status(thm)],[f775]) ).
thf(f775,plain,
( ( sK49 = sK48 )
| ( $true != $true )
| ( ( in @ sK48 @ ( setadjoin @ sK50 @ emptyset ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f762,f549]) ).
thf(f549,plain,
setadjoinOr = $true,
inference(cnf_transformation,[status(thm)],[f302]) ).
thf(f762,plain,
( ( ( in @ sK48 @ ( setadjoin @ sK50 @ emptyset ) )
= $true )
| ( setadjoinOr != $true )
| ( sK49 = sK48 ) ),
inference(trivial_inequality_removal,[status(thm)],[f756]) ).
thf(f756,plain,
( ( sK49 = sK48 )
| ( $true != $true )
| ( ( in @ sK48 @ ( setadjoin @ sK50 @ emptyset ) )
= $true )
| ( setadjoinOr != $true ) ),
inference(superposition,[status(thm)],[f505,f557]) ).
thf(f557,plain,
( ( in @ sK48 @ ( setadjoin @ sK49 @ ( setadjoin @ sK50 @ emptyset ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f302]) ).
thf(f505,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
| ( ( in @ X2 @ X1 )
= $true )
| ( X0 = X2 )
| ( setadjoinOr != $true ) ),
inference(cnf_transformation,[status(thm)],[f263]) ).
thf(f263,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
| ( X0 = X2 )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( setadjoinOr != $true ) )
& ( ( setadjoinOr = $true )
| ( ( ( in @ sK31 @ ( setadjoin @ sK29 @ sK30 ) )
= $true )
& ( sK29 != sK31 )
& ( $true
!= ( in @ sK31 @ sK30 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31])],[f261,f262]) ).
thf(f262,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( setadjoin @ X3 @ X4 ) )
= $true )
& ( X3 != X5 )
& ( ( in @ X5 @ X4 )
!= $true ) )
=> ( ( ( in @ sK31 @ ( setadjoin @ sK29 @ sK30 ) )
= $true )
& ( sK29 != sK31 )
& ( $true
!= ( in @ sK31 @ sK30 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f261,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
| ( X0 = X2 )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( setadjoinOr != $true ) )
& ( ( setadjoinOr = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( setadjoin @ X3 @ X4 ) )
= $true )
& ( X3 != X5 )
& ( ( in @ X5 @ X4 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f260]) ).
thf(f260,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
| ( X0 = X2 )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( setadjoinOr != $true ) )
& ( ( setadjoinOr = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
& ( X0 != X2 )
& ( ( in @ X2 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f179]) ).
thf(f179,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
| ( X0 = X2 )
| ( ( in @ X2 @ X1 )
= $true ) )
<=> ( setadjoinOr = $true ) ),
inference(flattening,[status(thm)],[f178]) ).
thf(f178,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) )
<=> ( setadjoinOr = $true ) ),
inference(ennf_transformation,[status(thm)],[f146]) ).
thf(f146,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
=> ( ( X0 = X2 )
| ( ( in @ X2 @ X1 )
= $true ) ) )
<=> ( setadjoinOr = $true ) ),
inference(fool_elimination,[status(thm)],[f145]) ).
thf(f145,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( X0 = X2 ) ) )
= setadjoinOr ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,axiom,
! [X1: $i,X3: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
=> ( ( in @ X2 @ X3 )
| ( X1 = X2 ) ) )
= setadjoinOr ),
file('/export/starexec/sandbox2/tmp/tmp.PJlHxzAzZQ/DTF2THF_25445.p',setadjoinOr) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU531^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n005.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Feb 24 12:25:44 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEU531^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.47 % Domain : Set Theory
% 0.28/0.47 % Problem : Preliminary Notions - Equality Laws
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English : (! x:i.! y:i.! z:i.in z (setadjoin x (setadjoin y emptyset)) ->
% 0.28/0.47 % z = x | z = y)
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.47 % Source : [Bro08]
% 0.28/0.47 % Names : ZFC033g [Bro08]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v3.7.0
% 0.28/0.47 % Syntax : Number of formulae : 109 ( 50 unt; 58 typ; 50 def)
% 0.28/0.47 % Number of atoms : 279 ( 68 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 50 ( 5 avg)
% 0.28/0.47 % Number of connectives : 454 ( 9 ~; 5 |; 19 &; 297 @)
% 0.28/0.47 % ( 8 <=>; 116 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 56 ( 2 avg)
% 0.28/0.47 % Number of types : 2 ( 0 usr)
% 0.28/0.47 % Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 61 ( 58 usr; 51 con; 0-2 aty)
% 0.28/0.47 % Number of variables : 149 ( 16 ^; 115 !; 18 ?; 149 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : http://mathgate.info/detsetitem.php?id=504
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(in_type,type,
% 0.28/0.47 in: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(exu_type,type,
% 0.28/0.47 exu: ( $i > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(exu,definition,
% 0.28/0.47 ( exu
% 0.28/0.47 = ( ^ [Xphi: $i > $o] :
% 0.28/0.47 ? [Xx: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 & ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setextAx_type,type,
% 0.28/0.47 setextAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setextAx,definition,
% 0.28/0.47 ( setextAx
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 <=> ( in @ Xx @ B ) )
% 0.28/0.47 => ( A = B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset_type,type,
% 0.28/0.47 emptyset: $i ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetAx_type,type,
% 0.28/0.47 emptysetAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetAx,definition,
% 0.28/0.47 ( emptysetAx
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin_type,type,
% 0.28/0.47 setadjoin: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinAx_type,type,
% 0.28/0.47 setadjoinAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinAx,definition,
% 0.28/0.47 ( setadjoinAx
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 <=> ( ( Xy = Xx )
% 0.28/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powerset_type,type,
% 0.28/0.47 powerset: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(powersetAx_type,type,
% 0.28/0.47 powersetAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetAx,definition,
% 0.28/0.47 ( powersetAx
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 <=> ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunion_type,type,
% 0.28/0.47 setunion: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setunionAx_type,type,
% 0.28/0.47 setunionAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionAx,definition,
% 0.28/0.47 ( setunionAx
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 <=> ? [B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omega_type,type,
% 0.28/0.47 omega: $i ).
% 0.28/0.47
% 0.28/0.47 thf(omega0Ax_type,type,
% 0.28/0.47 omega0Ax: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omega0Ax,definition,
% 0.28/0.47 ( omega0Ax
% 0.28/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omegaSAx_type,type,
% 0.28/0.47 omegaSAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omegaSAx,definition,
% 0.28/0.47 ( omegaSAx
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ omega )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omegaIndAx_type,type,
% 0.28/0.47 omegaIndAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omegaIndAx,definition,
% 0.28/0.47 ( omegaIndAx
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( ( in @ emptyset @ A )
% 0.28/0.47 & ! [Xx: $i] :
% 0.28/0.47 ( ( ( in @ Xx @ omega )
% 0.28/0.47 & ( in @ Xx @ A ) )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ omega )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(replAx_type,type,
% 0.28/0.47 replAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(replAx,definition,
% 0.28/0.47 ( replAx
% 0.28/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.28/0.47 => ? [B: $i] :
% 0.28/0.47 ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 <=> ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(foundationAx_type,type,
% 0.28/0.47 foundationAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(foundationAx,definition,
% 0.28/0.47 ( foundationAx
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.47 => ? [B: $i] :
% 0.28/0.47 ( ( in @ B @ A )
% 0.28/0.47 & ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(wellorderingAx_type,type,
% 0.28/0.47 wellorderingAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(wellorderingAx,definition,
% 0.28/0.47 ( wellorderingAx
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ? [B: $i] :
% 0.28/0.47 ( ! [C: $i] :
% 0.28/0.47 ( ( in @ C @ B )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ C )
% 0.28/0.47 => ( in @ Xx @ A ) ) )
% 0.28/0.47 & ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( ( in @ Xx @ A )
% 0.28/0.47 & ( in @ Xy @ A ) )
% 0.28/0.47 => ( ! [C: $i] :
% 0.28/0.47 ( ( in @ C @ B )
% 0.28/0.47 => ( ( in @ Xx @ C )
% 0.28/0.47 <=> ( in @ Xy @ C ) ) )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 & ! [C: $i,D: $i] :
% 0.28/0.47 ( ( ( in @ C @ B )
% 0.28/0.47 & ( in @ D @ B ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ C )
% 0.28/0.47 => ( in @ Xx @ D ) )
% 0.28/0.47 | ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ D )
% 0.28/0.47 => ( in @ Xx @ C ) ) ) )
% 0.28/0.47 & ! [C: $i] :
% 0.28/0.47 ( ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ C )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.28/0.47 => ? [D: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ D @ B )
% 0.28/0.47 & ( in @ Xx @ C )
% 0.28/0.47 & ~ ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ D )
% 0.28/0.47 & ( in @ Xy @ C ) )
% 0.28/0.47 & ! [E: $i] :
% 0.28/0.47 ( ( in @ E @ B )
% 0.28/0.47 => ( ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ E )
% 0.28/0.47 => ( in @ Xy @ D ) )
% 0.28/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(descr_type,type,
% 0.28/0.47 descr: ( $i > $o ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(descrp_type,type,
% 0.28/0.47 descrp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(descrp,definition,
% 0.28/0.47 ( descrp
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ( Xphi
% 0.28/0.47 @ ( descr
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr_type,type,
% 0.28/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrI_type,type,
% 0.28/0.47 dsetconstrI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrI,definition,
% 0.28/0.47 ( dsetconstrI
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrEL_type,type,
% 0.28/0.47 dsetconstrEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrEL,definition,
% 0.28/0.47 ( dsetconstrEL
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrER_type,type,
% 0.28/0.47 dsetconstrER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrER,definition,
% 0.28/0.47 ( dsetconstrER
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE1_type,type,
% 0.28/0.47 exuE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE1,definition,
% 0.28/0.47 ( exuE1
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 & ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set_type,type,
% 0.28/0.47 prop2set: $o > $i ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set,definition,
% 0.28/0.47 ( prop2set
% 0.28/0.47 = ( ^ [Xphi: $o] :
% 0.28/0.47 ( dsetconstr @ ( powerset @ emptyset )
% 0.28/0.47 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setE_type,type,
% 0.28/0.47 prop2setE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setE,definition,
% 0.28/0.47 ( prop2setE
% 0.28/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetE_type,type,
% 0.28/0.47 emptysetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetE,definition,
% 0.28/0.47 ( emptysetE
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetimpfalse_type,type,
% 0.28/0.47 emptysetimpfalse: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetimpfalse,definition,
% 0.28/0.47 ( emptysetimpfalse
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => $false ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notinemptyset_type,type,
% 0.28/0.47 notinemptyset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notinemptyset,definition,
% 0.28/0.47 ( notinemptyset
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3e_type,type,
% 0.28/0.47 exuE3e: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3e,definition,
% 0.28/0.47 ( exuE3e
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setext_type,type,
% 0.28/0.47 setext: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setext,definition,
% 0.28/0.47 ( setext
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 => ( A = B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyI_type,type,
% 0.28/0.47 emptyI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyI,definition,
% 0.28/0.47 ( emptyI
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ A )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(noeltsimpempty_type,type,
% 0.28/0.47 noeltsimpempty: $o ).
% 0.28/0.47
% 0.28/0.47 thf(noeltsimpempty,definition,
% 0.28/0.47 ( noeltsimpempty
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ A )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setbeta_type,type,
% 0.28/0.47 setbeta: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setbeta,definition,
% 0.28/0.47 ( setbeta
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonempty_type,type,
% 0.28/0.47 nonempty: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonempty,definition,
% 0.28/0.47 ( nonempty
% 0.28/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyE1_type,type,
% 0.28/0.47 nonemptyE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyE1,definition,
% 0.28/0.47 ( nonemptyE1
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( nonempty @ A )
% 0.28/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI_type,type,
% 0.28/0.47 nonemptyI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI,definition,
% 0.28/0.47 ( nonemptyI
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( nonempty
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI1_type,type,
% 0.28/0.47 nonemptyI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI1,definition,
% 0.28/0.47 ( nonemptyI1
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIL_type,type,
% 0.28/0.47 setadjoinIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIL,definition,
% 0.28/0.47 ( setadjoinIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinunitempty_type,type,
% 0.28/0.47 emptyinunitempty: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinunitempty,definition,
% 0.28/0.47 ( emptyinunitempty
% 0.28/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIR_type,type,
% 0.28/0.47 setadjoinIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIR,definition,
% 0.28/0.47 ( setadjoinIR
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinE_type,type,
% 0.28/0.47 setadjoinE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinE,definition,
% 0.28/0.47 ( setadjoinE
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ( ( Xy = Xx )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => ( ( ( in @ Xy @ A )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinOr_type,type,
% 0.28/0.47 setadjoinOr: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinOr,definition,
% 0.28/0.47 ( setadjoinOr
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 => ( ( Xy = Xx )
% 0.28/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setoftrueEq_type,type,
% 0.28/0.47 setoftrueEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setoftrueEq,definition,
% 0.28/0.47 ( setoftrueEq
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : $true )
% 0.28/0.47 = A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI_type,type,
% 0.28/0.47 powersetI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI,definition,
% 0.28/0.47 ( powersetI
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinPowerset_type,type,
% 0.28/0.47 emptyinPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinPowerset,definition,
% 0.28/0.47 ( emptyinPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyInPowerset_type,type,
% 0.28/0.47 emptyInPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyInPowerset,definition,
% 0.28/0.47 ( emptyInPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE_type,type,
% 0.28/0.47 powersetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE,definition,
% 0.28/0.47 ( powersetE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionI_type,type,
% 0.28/0.47 setunionI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionI,definition,
% 0.28/0.47 ( setunionI
% 0.28/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( ( in @ B @ A )
% 0.28/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE_type,type,
% 0.28/0.47 setunionE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE,definition,
% 0.28/0.47 ( setunionE
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ! [B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( ( in @ B @ A )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subPowSU_type,type,
% 0.28/0.47 subPowSU: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subPowSU,definition,
% 0.28/0.47 ( subPowSU
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE2_type,type,
% 0.28/0.47 exuE2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE2,definition,
% 0.28/0.47 ( exuE2
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyImpWitness_type,type,
% 0.28/0.47 nonemptyImpWitness: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyImpWitness,definition,
% 0.28/0.47 ( nonemptyImpWitness
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( nonempty @ A )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & $true ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(uniqinunit_type,type,
% 0.28/0.47 uniqinunit: $o ).
% 0.28/0.47
% 0.28/0.47 thf(uniqinunit,definition,
% 0.28/0.47 ( uniqinunit
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notinsingleton_type,type,
% 0.28/0.47 notinsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notinsingleton,definition,
% 0.28/0.47 ( notinsingleton
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx != Xy )
% 0.28/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqinunit_type,type,
% 0.28/0.47 eqinunit: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqinunit,definition,
% 0.28/0.47 ( eqinunit
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsswitch_type,type,
% 0.28/0.47 singletonsswitch: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsswitch,definition,
% 0.28/0.47 ( singletonsswitch
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetE,conjecture,
% 0.28/0.47 ( setextAx
% 0.28/0.47 => ( emptysetAx
% 0.28/0.47 => ( setadjoinAx
% 0.28/0.47 => ( powersetAx
% 0.28/0.47 => ( setunionAx
% 0.28/0.47 => ( omega0Ax
% 0.28/0.47 => ( omegaSAx
% 0.28/0.47 => ( omegaIndAx
% 0.28/0.47 => ( replAx
% 0.28/0.47 => ( foundationAx
% 0.28/0.47 => ( wellorderingAx
% 0.28/0.47 => ( descrp
% 0.28/0.47 => ( dsetconstrI
% 0.28/0.47 => ( dsetconstrEL
% 0.28/0.47 => ( dsetconstrER
% 0.28/0.47 => ( exuE1
% 0.28/0.47 => ( prop2setE
% 0.28/0.47 => ( emptysetE
% 0.28/0.47 => ( emptysetimpfalse
% 0.28/0.47 => ( notinemptyset
% 0.28/0.47 => ( exuE3e
% 0.28/0.47 => ( setext
% 0.28/0.47 => ( emptyI
% 0.28/0.47 => ( noeltsimpempty
% 0.28/0.47 => ( setbeta
% 0.28/0.47 => ( nonemptyE1
% 0.28/0.47 => ( nonemptyI
% 0.28/0.47 => ( nonemptyI1
% 0.28/0.47 => ( setadjoinIL
% 0.28/0.47 => ( emptyinunitempty
% 0.28/0.47 => ( setadjoinIR
% 0.28/0.47 => ( setadjoinE
% 0.28/0.47 => ( setadjoinOr
% 0.28/0.47 => ( setoftrueEq
% 0.28/0.47 => ( powersetI
% 0.28/0.47 => ( emptyinPowerset
% 0.28/0.47 => ( emptyInPowerset
% 0.28/0.47 => ( powersetE
% 0.28/0.47 => ( setunionI
% 0.28/0.47 => ( setunionE
% 0.28/0.47 => ( subPowSU
% 0.28/0.47 => ( exuE2
% 0.28/0.47 => ( nonemptyImpWitness
% 0.28/0.47 => ( uniqinunit
% 0.28/0.47 => ( notinsingleton
% 0.28/0.47 => ( eqinunit
% 0.28/0.47 => ( singletonsswitch
% 0.28/0.47 => ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.47 => ( ( Xz = Xx )
% 0.28/0.47 | ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.91/1.35 ---- Embedded in THF ---
% 1.91/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.91/1.35 %%% Generated on Tue Feb 24 12:25:45 EST 2026
% 1.91/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.91/1.35 %%% Logic specification used:
% 1.91/1.35 %%% thf(spec, logic, $$dhol).
% 1.91/1.35
% 1.91/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.PJlHxzAzZQ/DTF2DTF25445.p
% See solution above
% 1.91/1.35 ------------------------
% 1.91/1.36 ---- Cleaned THF ---
% 1.91/1.36 thf(in_type,type,
% 1.91/1.36 in: $i > $i > $o ).
% 1.91/1.36
% 1.91/1.36 thf(exu_type,type,
% 1.91/1.36 exu: ( $i > $o ) > $o ).
% 1.91/1.36
% 1.91/1.36 thf(exu,definition,
% 1.91/1.36 ( exu
% 1.91/1.36 = ( ^ [Xphi: $i > $o] :
% 1.91/1.36 ? [Xx: $i] :
% 1.91/1.36 ( ( Xphi @ Xx )
% 1.91/1.36 & ! [Xy: $i] :
% 1.91/1.36 ( ( Xphi @ Xy )
% 1.91/1.36 => ( Xx = Xy ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(setextAx_type,type,
% 1.91/1.36 setextAx: $o ).
% 1.91/1.36
% 1.91/1.36 thf(setextAx,definition,
% 1.91/1.36 ( setextAx
% 1.91/1.36 = ( ! [A: $i,B: $i] :
% 1.91/1.36 ( ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ A )
% 1.91/1.36 <=> ( in @ Xx @ B ) )
% 1.91/1.36 => ( A = B ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(emptyset_type,type,
% 1.91/1.36 emptyset: $i ).
% 1.91/1.36
% 1.91/1.36 thf(emptysetAx_type,type,
% 1.91/1.36 emptysetAx: $o ).
% 1.91/1.36
% 1.91/1.36 thf(emptysetAx,definition,
% 1.91/1.36 ( emptysetAx
% 1.91/1.36 = ( ! [Xx: $i] :
% 1.91/1.36 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(setadjoin_type,type,
% 1.91/1.36 setadjoin: $i > $i > $i ).
% 1.91/1.36
% 1.91/1.36 thf(setadjoinAx_type,type,
% 1.91/1.36 setadjoinAx: $o ).
% 1.91/1.36
% 1.91/1.36 thf(setadjoinAx,definition,
% 1.91/1.36 ( setadjoinAx
% 1.91/1.36 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.91/1.36 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.91/1.36 <=> ( ( Xy = Xx )
% 1.91/1.36 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(powerset_type,type,
% 1.91/1.36 powerset: $i > $i ).
% 1.91/1.36
% 1.91/1.36 thf(powersetAx_type,type,
% 1.91/1.36 powersetAx: $o ).
% 1.91/1.36
% 1.91/1.36 thf(powersetAx,definition,
% 1.91/1.36 ( powersetAx
% 1.91/1.36 = ( ! [A: $i,B: $i] :
% 1.91/1.36 ( ( in @ B @ ( powerset @ A ) )
% 1.91/1.36 <=> ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ B )
% 1.91/1.36 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(setunion_type,type,
% 1.91/1.36 setunion: $i > $i ).
% 1.91/1.36
% 1.91/1.36 thf(setunionAx_type,type,
% 1.91/1.36 setunionAx: $o ).
% 1.91/1.36
% 1.91/1.36 thf(setunionAx,definition,
% 1.91/1.36 ( setunionAx
% 1.91/1.36 = ( ! [A: $i,Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ ( setunion @ A ) )
% 1.91/1.36 <=> ? [B: $i] :
% 1.91/1.36 ( ( in @ Xx @ B )
% 1.91/1.36 & ( in @ B @ A ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(omega_type,type,
% 1.91/1.36 omega: $i ).
% 1.91/1.36
% 1.91/1.36 thf(omega0Ax_type,type,
% 1.91/1.36 omega0Ax: $o ).
% 1.91/1.36
% 1.91/1.36 thf(omega0Ax,definition,
% 1.91/1.36 ( omega0Ax
% 1.91/1.36 = ( in @ emptyset @ omega ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(omegaSAx_type,type,
% 1.91/1.36 omegaSAx: $o ).
% 1.91/1.36
% 1.91/1.36 thf(omegaSAx,definition,
% 1.91/1.36 ( omegaSAx
% 1.91/1.36 = ( ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ omega )
% 1.91/1.36 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(omegaIndAx_type,type,
% 1.91/1.36 omegaIndAx: $o ).
% 1.91/1.36
% 1.91/1.36 thf(omegaIndAx,definition,
% 1.91/1.36 ( omegaIndAx
% 1.91/1.36 = ( ! [A: $i] :
% 1.91/1.36 ( ( ( in @ emptyset @ A )
% 1.91/1.36 & ! [Xx: $i] :
% 1.91/1.36 ( ( ( in @ Xx @ omega )
% 1.91/1.36 & ( in @ Xx @ A ) )
% 1.91/1.36 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.91/1.36 => ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ omega )
% 1.91/1.36 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(replAx_type,type,
% 1.91/1.36 replAx: $o ).
% 1.91/1.36
% 1.91/1.36 thf(replAx,definition,
% 1.91/1.36 ( replAx
% 1.91/1.36 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.91/1.36 ( ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ A )
% 1.91/1.36 => ( exu
% 1.91/1.36 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.91/1.36 => ? [B: $i] :
% 1.91/1.36 ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ B )
% 1.91/1.36 <=> ? [Xy: $i] :
% 1.91/1.36 ( ( in @ Xy @ A )
% 1.91/1.36 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(foundationAx_type,type,
% 1.91/1.36 foundationAx: $o ).
% 1.91/1.36
% 1.91/1.36 thf(foundationAx,definition,
% 1.91/1.36 ( foundationAx
% 1.91/1.36 = ( ! [A: $i] :
% 1.91/1.36 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.91/1.36 => ? [B: $i] :
% 1.91/1.36 ( ( in @ B @ A )
% 1.91/1.36 & ~ ? [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ B )
% 1.91/1.36 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(wellorderingAx_type,type,
% 1.91/1.36 wellorderingAx: $o ).
% 1.91/1.36
% 1.91/1.36 thf(wellorderingAx,definition,
% 1.91/1.36 ( wellorderingAx
% 1.91/1.36 = ( ! [A: $i] :
% 1.91/1.36 ? [B: $i] :
% 1.91/1.36 ( ! [C: $i] :
% 1.91/1.36 ( ( in @ C @ B )
% 1.91/1.36 => ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ C )
% 1.91/1.36 => ( in @ Xx @ A ) ) )
% 1.91/1.36 & ! [Xx: $i,Xy: $i] :
% 1.91/1.36 ( ( ( in @ Xx @ A )
% 1.91/1.36 & ( in @ Xy @ A ) )
% 1.91/1.36 => ( ! [C: $i] :
% 1.91/1.36 ( ( in @ C @ B )
% 1.91/1.36 => ( ( in @ Xx @ C )
% 1.91/1.36 <=> ( in @ Xy @ C ) ) )
% 1.91/1.36 => ( Xx = Xy ) ) )
% 1.91/1.36 & ! [C: $i,D: $i] :
% 1.91/1.36 ( ( ( in @ C @ B )
% 1.91/1.36 & ( in @ D @ B ) )
% 1.91/1.36 => ( ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ C )
% 1.91/1.36 => ( in @ Xx @ D ) )
% 1.91/1.36 | ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ D )
% 1.91/1.36 => ( in @ Xx @ C ) ) ) )
% 1.91/1.36 & ! [C: $i] :
% 1.91/1.36 ( ( ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ C )
% 1.91/1.36 => ( in @ Xx @ A ) )
% 1.91/1.36 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.91/1.36 => ? [D: $i,Xx: $i] :
% 1.91/1.36 ( ( in @ D @ B )
% 1.91/1.36 & ( in @ Xx @ C )
% 1.91/1.36 & ~ ? [Xy: $i] :
% 1.91/1.36 ( ( in @ Xy @ D )
% 1.91/1.36 & ( in @ Xy @ C ) )
% 1.91/1.36 & ! [E: $i] :
% 1.91/1.36 ( ( in @ E @ B )
% 1.91/1.36 => ( ! [Xy: $i] :
% 1.91/1.36 ( ( in @ Xy @ E )
% 1.91/1.36 => ( in @ Xy @ D ) )
% 1.91/1.36 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(descr_type,type,
% 1.91/1.36 descr: ( $i > $o ) > $i ).
% 1.91/1.36
% 1.91/1.36 thf(descrp_type,type,
% 1.91/1.36 descrp: $o ).
% 1.91/1.36
% 1.91/1.36 thf(descrp,definition,
% 1.91/1.36 ( descrp
% 1.91/1.36 = ( ! [Xphi: $i > $o] :
% 1.91/1.36 ( ( exu
% 1.91/1.36 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.91/1.36 => ( Xphi
% 1.91/1.36 @ ( descr
% 1.91/1.36 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(dsetconstr_type,type,
% 1.91/1.36 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.91/1.36
% 1.91/1.36 thf(dsetconstrI_type,type,
% 1.91/1.36 dsetconstrI: $o ).
% 1.91/1.36
% 1.91/1.36 thf(dsetconstrI,definition,
% 1.91/1.36 ( dsetconstrI
% 1.91/1.36 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ A )
% 1.91/1.36 => ( ( Xphi @ Xx )
% 1.91/1.36 => ( in @ Xx
% 1.91/1.36 @ ( dsetconstr @ A
% 1.91/1.36 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(dsetconstrEL_type,type,
% 1.91/1.36 dsetconstrEL: $o ).
% 1.91/1.36
% 1.91/1.36 thf(dsetconstrEL,definition,
% 1.91/1.36 ( dsetconstrEL
% 1.91/1.36 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.91/1.36 ( ( in @ Xx
% 1.91/1.36 @ ( dsetconstr @ A
% 1.91/1.36 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.91/1.36 => ( in @ Xx @ A ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(dsetconstrER_type,type,
% 1.91/1.36 dsetconstrER: $o ).
% 1.91/1.36
% 1.91/1.36 thf(dsetconstrER,definition,
% 1.91/1.36 ( dsetconstrER
% 1.91/1.36 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.91/1.36 ( ( in @ Xx
% 1.91/1.36 @ ( dsetconstr @ A
% 1.91/1.36 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.91/1.36 => ( Xphi @ Xx ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(exuE1_type,type,
% 1.91/1.36 exuE1: $o ).
% 1.91/1.36
% 1.91/1.36 thf(exuE1,definition,
% 1.91/1.36 ( exuE1
% 1.91/1.36 = ( ! [Xphi: $i > $o] :
% 1.91/1.36 ( ( exu
% 1.91/1.36 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.91/1.36 => ? [Xx: $i] :
% 1.91/1.36 ( ( Xphi @ Xx )
% 1.91/1.36 & ! [Xy: $i] :
% 1.91/1.36 ( ( Xphi @ Xy )
% 1.91/1.36 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(prop2set_type,type,
% 1.91/1.36 prop2set: $o > $i ).
% 1.91/1.36
% 1.91/1.36 thf(prop2set,definition,
% 1.91/1.36 ( prop2set
% 1.91/1.36 = ( ^ [Xphi: $o] :
% 1.91/1.36 ( dsetconstr @ ( powerset @ emptyset )
% 1.91/1.36 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(prop2setE_type,type,
% 1.91/1.36 prop2setE: $o ).
% 1.91/1.36
% 1.91/1.36 thf(prop2setE,definition,
% 1.91/1.36 ( prop2setE
% 1.91/1.36 = ( ! [Xphi: $o,Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.91/1.36 => Xphi ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(emptysetE_type,type,
% 1.91/1.36 emptysetE: $o ).
% 1.91/1.36
% 1.91/1.36 thf(emptysetE,definition,
% 1.91/1.36 ( emptysetE
% 1.91/1.36 = ( ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ emptyset )
% 1.91/1.36 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(emptysetimpfalse_type,type,
% 1.91/1.36 emptysetimpfalse: $o ).
% 1.91/1.36
% 1.91/1.36 thf(emptysetimpfalse,definition,
% 1.91/1.36 ( emptysetimpfalse
% 1.91/1.36 = ( ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ emptyset )
% 1.91/1.36 => $false ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(notinemptyset_type,type,
% 1.91/1.36 notinemptyset: $o ).
% 1.91/1.36
% 1.91/1.36 thf(notinemptyset,definition,
% 1.91/1.36 ( notinemptyset
% 1.91/1.36 = ( ! [Xx: $i] :
% 1.91/1.36 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(exuE3e_type,type,
% 1.91/1.36 exuE3e: $o ).
% 1.91/1.36
% 1.91/1.36 thf(exuE3e,definition,
% 1.91/1.36 ( exuE3e
% 1.91/1.36 = ( ! [Xphi: $i > $o] :
% 1.91/1.36 ( ( exu
% 1.91/1.36 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.91/1.36 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(setext_type,type,
% 1.91/1.36 setext: $o ).
% 1.91/1.36
% 1.91/1.36 thf(setext,definition,
% 1.91/1.36 ( setext
% 1.91/1.36 = ( ! [A: $i,B: $i] :
% 1.91/1.36 ( ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ A )
% 1.91/1.36 => ( in @ Xx @ B ) )
% 1.91/1.36 => ( ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ B )
% 1.91/1.36 => ( in @ Xx @ A ) )
% 1.91/1.36 => ( A = B ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(emptyI_type,type,
% 1.91/1.36 emptyI: $o ).
% 1.91/1.36
% 1.91/1.36 thf(emptyI,definition,
% 1.91/1.36 ( emptyI
% 1.91/1.36 = ( ! [A: $i] :
% 1.91/1.36 ( ! [Xx: $i] :
% 1.91/1.36 ~ ( in @ Xx @ A )
% 1.91/1.36 => ( A = emptyset ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(noeltsimpempty_type,type,
% 1.91/1.36 noeltsimpempty: $o ).
% 1.91/1.36
% 1.91/1.36 thf(noeltsimpempty,definition,
% 1.91/1.36 ( noeltsimpempty
% 1.91/1.36 = ( ! [A: $i] :
% 1.91/1.36 ( ! [Xx: $i] :
% 1.91/1.36 ~ ( in @ Xx @ A )
% 1.91/1.36 => ( A = emptyset ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(setbeta_type,type,
% 1.91/1.36 setbeta: $o ).
% 1.91/1.36
% 1.91/1.36 thf(setbeta,definition,
% 1.91/1.36 ( setbeta
% 1.91/1.36 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ A )
% 1.91/1.36 => ( ( in @ Xx
% 1.91/1.36 @ ( dsetconstr @ A
% 1.91/1.36 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.91/1.36 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(nonempty_type,type,
% 1.91/1.36 nonempty: $i > $o ).
% 1.91/1.36
% 1.91/1.36 thf(nonempty,definition,
% 1.91/1.36 ( nonempty
% 1.91/1.36 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(nonemptyE1_type,type,
% 1.91/1.36 nonemptyE1: $o ).
% 1.91/1.36
% 1.91/1.36 thf(nonemptyE1,definition,
% 1.91/1.36 ( nonemptyE1
% 1.91/1.36 = ( ! [A: $i] :
% 1.91/1.36 ( ( nonempty @ A )
% 1.91/1.36 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(nonemptyI_type,type,
% 1.91/1.36 nonemptyI: $o ).
% 1.91/1.36
% 1.91/1.36 thf(nonemptyI,definition,
% 1.91/1.36 ( nonemptyI
% 1.91/1.36 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ A )
% 1.91/1.36 => ( ( Xphi @ Xx )
% 1.91/1.36 => ( nonempty
% 1.91/1.36 @ ( dsetconstr @ A
% 1.91/1.36 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(nonemptyI1_type,type,
% 1.91/1.36 nonemptyI1: $o ).
% 1.91/1.36
% 1.91/1.36 thf(nonemptyI1,definition,
% 1.91/1.36 ( nonemptyI1
% 1.91/1.36 = ( ! [A: $i] :
% 1.91/1.36 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.91/1.36 => ( nonempty @ A ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(setadjoinIL_type,type,
% 1.91/1.36 setadjoinIL: $o ).
% 1.91/1.36
% 1.91/1.36 thf(setadjoinIL,definition,
% 1.91/1.36 ( setadjoinIL
% 1.91/1.36 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(emptyinunitempty_type,type,
% 1.91/1.36 emptyinunitempty: $o ).
% 1.91/1.36
% 1.91/1.36 thf(emptyinunitempty,definition,
% 1.91/1.36 ( emptyinunitempty
% 1.91/1.36 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(setadjoinIR_type,type,
% 1.91/1.36 setadjoinIR: $o ).
% 1.91/1.36
% 1.91/1.36 thf(setadjoinIR,definition,
% 1.91/1.36 ( setadjoinIR
% 1.91/1.36 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.91/1.36 ( ( in @ Xy @ A )
% 1.91/1.36 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(setadjoinE_type,type,
% 1.91/1.36 setadjoinE: $o ).
% 1.91/1.36
% 1.91/1.36 thf(setadjoinE,definition,
% 1.91/1.36 ( setadjoinE
% 1.91/1.36 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.91/1.36 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.91/1.36 => ! [Xphi: $o] :
% 1.91/1.36 ( ( ( Xy = Xx )
% 1.91/1.36 => Xphi )
% 1.91/1.36 => ( ( ( in @ Xy @ A )
% 1.91/1.36 => Xphi )
% 1.91/1.36 => Xphi ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(setadjoinOr_type,type,
% 1.91/1.36 setadjoinOr: $o ).
% 1.91/1.36
% 1.91/1.36 thf(setadjoinOr,definition,
% 1.91/1.36 ( setadjoinOr
% 1.91/1.36 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.91/1.36 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.91/1.36 => ( ( Xy = Xx )
% 1.91/1.36 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(setoftrueEq_type,type,
% 1.91/1.36 setoftrueEq: $o ).
% 1.91/1.36
% 1.91/1.36 thf(setoftrueEq,definition,
% 1.91/1.36 ( setoftrueEq
% 1.91/1.36 = ( ! [A: $i] :
% 1.91/1.36 ( ( dsetconstr @ A
% 1.91/1.36 @ ^ [Xx: $i] : $true )
% 1.91/1.36 = A ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(powersetI_type,type,
% 1.91/1.36 powersetI: $o ).
% 1.91/1.36
% 1.91/1.36 thf(powersetI,definition,
% 1.91/1.36 ( powersetI
% 1.91/1.36 = ( ! [A: $i,B: $i] :
% 1.91/1.36 ( ! [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ B )
% 1.91/1.36 => ( in @ Xx @ A ) )
% 1.91/1.36 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(emptyinPowerset_type,type,
% 1.91/1.36 emptyinPowerset: $o ).
% 1.91/1.36
% 1.91/1.36 thf(emptyinPowerset,definition,
% 1.91/1.36 ( emptyinPowerset
% 1.91/1.36 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(emptyInPowerset_type,type,
% 1.91/1.36 emptyInPowerset: $o ).
% 1.91/1.36
% 1.91/1.36 thf(emptyInPowerset,definition,
% 1.91/1.36 ( emptyInPowerset
% 1.91/1.36 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(powersetE_type,type,
% 1.91/1.36 powersetE: $o ).
% 1.91/1.36
% 1.91/1.36 thf(powersetE,definition,
% 1.91/1.36 ( powersetE
% 1.91/1.36 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.91/1.36 ( ( in @ B @ ( powerset @ A ) )
% 1.91/1.36 => ( ( in @ Xx @ B )
% 1.91/1.36 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(setunionI_type,type,
% 1.91/1.36 setunionI: $o ).
% 1.91/1.36
% 1.91/1.36 thf(setunionI,definition,
% 1.91/1.36 ( setunionI
% 1.91/1.36 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.91/1.36 ( ( in @ Xx @ B )
% 1.91/1.36 => ( ( in @ B @ A )
% 1.91/1.36 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(setunionE_type,type,
% 1.91/1.36 setunionE: $o ).
% 1.91/1.36
% 1.91/1.36 thf(setunionE,definition,
% 1.91/1.36 ( setunionE
% 1.91/1.36 = ( ! [A: $i,Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ ( setunion @ A ) )
% 1.91/1.36 => ! [Xphi: $o] :
% 1.91/1.36 ( ! [B: $i] :
% 1.91/1.36 ( ( in @ Xx @ B )
% 1.91/1.36 => ( ( in @ B @ A )
% 1.91/1.36 => Xphi ) )
% 1.91/1.36 => Xphi ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(subPowSU_type,type,
% 1.91/1.36 subPowSU: $o ).
% 1.91/1.36
% 1.91/1.36 thf(subPowSU,definition,
% 1.91/1.36 ( subPowSU
% 1.91/1.36 = ( ! [A: $i,Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ A )
% 1.91/1.36 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(exuE2_type,type,
% 1.91/1.36 exuE2: $o ).
% 1.91/1.36
% 1.91/1.36 thf(exuE2,definition,
% 1.91/1.36 ( exuE2
% 1.91/1.36 = ( ! [Xphi: $i > $o] :
% 1.91/1.36 ( ( exu
% 1.91/1.36 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.91/1.36 => ? [Xx: $i] :
% 1.91/1.36 ! [Xy: $i] :
% 1.91/1.36 ( ( Xphi @ Xy )
% 1.91/1.36 <=> ( Xy = Xx ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(nonemptyImpWitness_type,type,
% 1.91/1.36 nonemptyImpWitness: $o ).
% 1.91/1.36
% 1.91/1.36 thf(nonemptyImpWitness,definition,
% 1.91/1.36 ( nonemptyImpWitness
% 1.91/1.36 = ( ! [A: $i] :
% 1.91/1.36 ( ( nonempty @ A )
% 1.91/1.36 => ? [Xx: $i] :
% 1.91/1.36 ( ( in @ Xx @ A )
% 1.91/1.36 & $true ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(uniqinunit_type,type,
% 1.91/1.36 uniqinunit: $o ).
% 1.91/1.36
% 1.91/1.36 thf(uniqinunit,definition,
% 1.91/1.36 ( uniqinunit
% 1.91/1.36 = ( ! [Xx: $i,Xy: $i] :
% 1.91/1.36 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.91/1.36 => ( Xx = Xy ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(notinsingleton_type,type,
% 1.91/1.36 notinsingleton: $o ).
% 1.91/1.36
% 1.91/1.36 thf(notinsingleton,definition,
% 1.91/1.36 ( notinsingleton
% 1.91/1.36 = ( ! [Xx: $i,Xy: $i] :
% 1.91/1.36 ( ( Xx != Xy )
% 1.91/1.36 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(eqinunit_type,type,
% 1.91/1.36 eqinunit: $o ).
% 1.91/1.36
% 1.91/1.36 thf(eqinunit,definition,
% 1.91/1.36 ( eqinunit
% 1.91/1.36 = ( ! [Xx: $i,Xy: $i] :
% 1.91/1.36 ( ( Xx = Xy )
% 1.91/1.36 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(singletonsswitch_type,type,
% 1.91/1.36 singletonsswitch: $o ).
% 1.91/1.36
% 1.91/1.36 thf(singletonsswitch,definition,
% 1.91/1.36 ( singletonsswitch
% 1.91/1.36 = ( ! [Xx: $i,Xy: $i] :
% 1.91/1.36 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.91/1.36 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.91/1.36
% 1.91/1.36 thf(upairsetE,conjecture,
% 1.91/1.36 ( setextAx
% 1.91/1.36 => ( emptysetAx
% 1.91/1.36 => ( setadjoinAx
% 1.91/1.36 => ( powersetAx
% 1.91/1.36 => ( setunionAx
% 1.91/1.36 => ( omega0Ax
% 1.91/1.36 => ( omegaSAx
% 1.91/1.36 => ( omegaIndAx
% 1.91/1.36 => ( replAx
% 1.91/1.36 => ( foundationAx
% 1.91/1.36 => ( wellorderingAx
% 1.91/1.36 => ( descrp
% 1.91/1.36 => ( dsetconstrI
% 1.91/1.36 => ( dsetconstrEL
% 1.91/1.36 => ( dsetconstrER
% 1.91/1.36 => ( exuE1
% 1.91/1.36 => ( prop2setE
% 1.91/1.36 => ( emptysetE
% 1.91/1.36 => ( emptysetimpfalse
% 1.91/1.36 => ( notinemptyset
% 1.91/1.36 => ( exuE3e
% 1.91/1.36 => ( setext
% 1.91/1.36 => ( emptyI
% 1.91/1.36 => ( noeltsimpempty
% 1.91/1.36 => ( setbeta
% 1.91/1.36 => ( nonemptyE1
% 1.91/1.36 => ( nonemptyI
% 1.91/1.36 => ( nonemptyI1
% 1.91/1.36 => ( setadjoinIL
% 1.91/1.36 => ( emptyinunitempty
% 1.91/1.36 => ( setadjoinIR
% 1.91/1.36 => ( setadjoinE
% 1.91/1.36 => ( setadjoinOr
% 1.91/1.36 => ( setoftrueEq
% 1.91/1.36 => ( powersetI
% 1.91/1.36 => ( emptyinPowerset
% 1.91/1.36 => ( emptyInPowerset
% 1.91/1.36 => ( powersetE
% 1.91/1.36 => ( setunionI
% 1.91/1.36 => ( setunionE
% 1.91/1.36 => ( subPowSU
% 1.91/1.36 => ( exuE2
% 1.91/1.36 => ( nonemptyImpWitness
% 1.91/1.36 => ( uniqinunit
% 1.91/1.36 => ( notinsingleton
% 1.91/1.36 => ( eqinunit
% 1.91/1.36 => ( singletonsswitch
% 1.91/1.36 => ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.91/1.36 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 1.91/1.36 => ( ( Xz = Xx )
% 1.91/1.36 | ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.91/1.36 ------------------------
% 1.91/1.38 % (25591)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_25445 for (2999ds/4Mi)
% 1.91/1.38 % (25592)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_25445 for (2999ds/27Mi)
% 1.91/1.38 % (25590)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/183Mi)
% 1.91/1.38 % (25594)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_25445 for (2999ds/2Mi)
% 1.91/1.38 % (25595)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_25445 for (2999ds/275Mi)
% 1.91/1.38 % (25596)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/18Mi)
% 1.91/1.38 % (25591)Instruction limit reached!
% 1.91/1.38 % (25591)------------------------------
% 1.91/1.38 % (25591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.38 % (25591)Termination reason: Unknown
% 1.91/1.38 % (25591)Termination phase: shuffling
% 1.91/1.38
% 1.91/1.38 % (25591)Memory used [KB]: 1151
% 1.91/1.38 % (25591)Time elapsed: 0.003 s
% 1.91/1.38 % (25591)Instructions burned: 5 (million)
% 1.91/1.38 % (25591)------------------------------
% 1.91/1.38 % (25591)------------------------------
% 1.91/1.38 % (25594)Instruction limit reached!
% 1.91/1.38 % (25594)------------------------------
% 1.91/1.38 % (25594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.38 % (25594)Termination reason: Unknown
% 1.91/1.38 % (25594)Termination phase: shuffling
% 1.91/1.38
% 1.91/1.38 % (25594)Memory used [KB]: 1023
% 1.91/1.38 % (25594)Time elapsed: 0.002 s
% 1.91/1.38 % (25594)Instructions burned: 3 (million)
% 1.91/1.38 % (25594)------------------------------
% 1.91/1.38 % (25594)------------------------------
% 1.91/1.39 % (25596)Instruction limit reached!
% 1.91/1.39 % (25596)------------------------------
% 1.91/1.39 % (25596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.39 % (25596)Termination reason: Unknown
% 1.91/1.39 % (25596)Termination phase: Preprocessing 3
% 1.91/1.39
% 1.91/1.39 % (25596)Memory used [KB]: 1535
% 1.91/1.39 % (25596)Time elapsed: 0.007 s
% 1.91/1.39 % (25596)Instructions burned: 18 (million)
% 1.91/1.39 % (25596)------------------------------
% 1.91/1.39 % (25596)------------------------------
% 1.91/1.39 % (25592)Instruction limit reached!
% 1.91/1.39 % (25592)------------------------------
% 1.91/1.39 % (25592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.39 % (25592)Termination reason: Unknown
% 1.91/1.39 % (25592)Termination phase: Saturation
% 1.91/1.39
% 1.91/1.39 % (25592)Memory used [KB]: 5756
% 1.91/1.39 % (25592)Time elapsed: 0.009 s
% 1.91/1.39 % (25592)Instructions burned: 27 (million)
% 1.91/1.39 % (25592)------------------------------
% 1.91/1.39 % (25592)------------------------------
% 1.91/1.39 % (25597)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/3Mi)
% 1.91/1.39 % (25593)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/2Mi)
% 1.91/1.39 % (25597)Instruction limit reached!
% 1.91/1.39 % (25597)------------------------------
% 1.91/1.39 % (25597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.39 % (25597)Termination reason: Unknown
% 1.91/1.39 % (25597)Termination phase: shuffling
% 1.91/1.39
% 1.91/1.39 % (25597)Memory used [KB]: 1023
% 1.91/1.39 % (25597)Time elapsed: 0.002 s
% 1.91/1.39 % (25597)Instructions burned: 3 (million)
% 1.91/1.39 % (25597)------------------------------
% 1.91/1.39 % (25597)------------------------------
% 1.91/1.39 % (25598)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_25445 for (2999ds/37Mi)
% 1.91/1.39 % (25593)Instruction limit reached!
% 1.91/1.39 % (25593)------------------------------
% 1.91/1.39 % (25593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.39 % (25593)Termination reason: Unknown
% 1.91/1.39 % (25593)Termination phase: shuffling
% 1.91/1.39
% 1.91/1.39 % (25593)Memory used [KB]: 1023
% 1.91/1.39 % (25593)Time elapsed: 0.005 s
% 1.91/1.39 % (25593)Instructions burned: 3 (million)
% 1.91/1.39 % (25593)------------------------------
% 1.91/1.39 % (25593)------------------------------
% 1.91/1.40 % (25599)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_25445 for (2999ds/15Mi)
% 1.91/1.40 % (25600)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_25445 for (2999ds/3Mi)
% 2.09/1.40 % (25600)Instruction limit reached!
% 2.09/1.40 % (25600)------------------------------
% 2.09/1.40 % (25600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.40 % (25600)Termination reason: Unknown
% 2.09/1.40 % (25600)Termination phase: shuffling
% 2.09/1.40
% 2.09/1.40 % (25600)Memory used [KB]: 1151
% 2.09/1.40 % (25600)Time elapsed: 0.003 s
% 2.09/1.40 % (25600)Instructions burned: 6 (million)
% 2.09/1.40 % (25600)------------------------------
% 2.09/1.40 % (25600)------------------------------
% 2.09/1.40 % (25601)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_25445 for (2999ds/1041Mi)
% 2.09/1.40 % (25599)Instruction limit reached!
% 2.09/1.40 % (25599)------------------------------
% 2.09/1.40 % (25599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.40 % (25599)Termination reason: Unknown
% 2.09/1.40 % (25599)Termination phase: Preprocessing 3
% 2.09/1.40
% 2.09/1.40 % (25599)Memory used [KB]: 1407
% 2.09/1.40 % (25599)Time elapsed: 0.006 s
% 2.09/1.40 % (25599)Instructions burned: 16 (million)
% 2.09/1.40 % (25599)------------------------------
% 2.09/1.40 % (25599)------------------------------
% 2.09/1.40 % (25598)Instruction limit reached!
% 2.09/1.40 % (25598)------------------------------
% 2.09/1.40 % (25598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.40 % (25598)Termination reason: Unknown
% 2.09/1.40 % (25598)Termination phase: Saturation
% 2.09/1.40
% 2.09/1.40 % (25598)Memory used [KB]: 5756
% 2.09/1.40 % (25598)Time elapsed: 0.012 s
% 2.09/1.40 % (25598)Instructions burned: 38 (million)
% 2.09/1.40 % (25598)------------------------------
% 2.09/1.40 % (25598)------------------------------
% 2.09/1.41 % (25602)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/7Mi)
% 2.09/1.41 % (25609)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/3Mi)
% 2.09/1.41 % (25610)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_25445 for (2999ds/3Mi)
% 2.09/1.41 % (25606)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/16Mi)
% 2.09/1.41 % (25609)Instruction limit reached!
% 2.09/1.41 % (25609)------------------------------
% 2.09/1.41 % (25609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.41 % (25609)Termination reason: Unknown
% 2.09/1.41 % (25609)Termination phase: shuffling
% 2.09/1.41
% 2.09/1.41 % (25609)Memory used [KB]: 1151
% 2.09/1.41 % (25609)Time elapsed: 0.003 s
% 2.09/1.41 % (25609)Instructions burned: 4 (million)
% 2.09/1.41 % (25609)------------------------------
% 2.09/1.41 % (25609)------------------------------
% 2.09/1.41 % (25610)Instruction limit reached!
% 2.09/1.41 % (25610)------------------------------
% 2.09/1.41 % (25610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.41 % (25610)Termination reason: Unknown
% 2.09/1.41 % (25610)Termination phase: shuffling
% 2.09/1.41
% 2.09/1.41 % (25610)Memory used [KB]: 1151
% 2.09/1.41 % (25610)Time elapsed: 0.003 s
% 2.09/1.41 % (25610)Instructions burned: 4 (million)
% 2.09/1.41 % (25610)------------------------------
% 2.09/1.41 % (25610)------------------------------
% 2.09/1.41 % (25602)Instruction limit reached!
% 2.09/1.41 % (25602)------------------------------
% 2.09/1.41 % (25602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.41 % (25602)Termination reason: Unknown
% 2.09/1.41 % (25602)Termination phase: shuffling
% 2.09/1.41
% 2.09/1.41 % (25602)Memory used [KB]: 1151
% 2.09/1.41 % (25602)Time elapsed: 0.006 s
% 2.09/1.41 % (25602)Instructions burned: 8 (million)
% 2.09/1.41 % (25602)------------------------------
% 2.09/1.41 % (25602)------------------------------
% 2.09/1.42 % (25606)Instruction limit reached!
% 2.09/1.42 % (25606)------------------------------
% 2.09/1.42 % (25606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.42 % (25606)Termination reason: Unknown
% 2.09/1.42 % (25606)Termination phase: Twee Goal Transformation
% 2.09/1.42
% 2.09/1.42 % (25606)Memory used [KB]: 1279
% 2.09/1.42 % (25606)Time elapsed: 0.006 s
% 2.09/1.42 % (25606)Instructions burned: 19 (million)
% 2.09/1.42 % (25606)------------------------------
% 2.09/1.42 % (25606)------------------------------
% 2.09/1.42 % (25612)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/7Mi)
% 2.09/1.43 % (25614)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/3Mi)
% 2.09/1.43 % (25616)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/18Mi)
% 2.09/1.43 % (25614)Instruction limit reached!
% 2.09/1.43 % (25614)------------------------------
% 2.09/1.43 % (25614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.43 % (25614)Termination reason: Unknown
% 2.09/1.43 % (25614)Termination phase: shuffling
% 2.09/1.43
% 2.09/1.43 % (25614)Memory used [KB]: 1023
% 2.09/1.43 % (25614)Time elapsed: 0.003 s
% 2.09/1.43 % (25614)Instructions burned: 3 (million)
% 2.09/1.43 % (25614)------------------------------
% 2.09/1.43 % (25614)------------------------------
% 2.09/1.43 % (25612)Instruction limit reached!
% 2.09/1.43 % (25612)------------------------------
% 2.09/1.43 % (25612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.43 % (25612)Termination reason: Unknown
% 2.09/1.43 % (25612)Termination phase: Property scanning
% 2.09/1.43
% 2.09/1.43 % (25612)Memory used [KB]: 1151
% 2.09/1.43 % (25612)Time elapsed: 0.006 s
% 2.09/1.43 % (25612)Instructions burned: 8 (million)
% 2.09/1.43 % (25612)------------------------------
% 2.09/1.43 % (25612)------------------------------
% 2.09/1.43 % (25616)Instruction limit reached!
% 2.09/1.43 % (25616)------------------------------
% 2.09/1.43 % (25616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.43 % (25616)Termination reason: Unknown
% 2.09/1.43 % (25616)Termination phase: Saturation
% 2.09/1.43
% 2.09/1.43 % (25616)Memory used [KB]: 5756
% 2.09/1.43 % (25616)Time elapsed: 0.006 s
% 2.09/1.43 % (25616)Instructions burned: 19 (million)
% 2.09/1.43 % (25616)------------------------------
% 2.09/1.43 % (25616)------------------------------
% 2.09/1.44 % (25615)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/4Mi)
% 2.09/1.44 % (25626)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/902Mi)
% 2.09/1.44 % (25615)Instruction limit reached!
% 2.09/1.44 % (25615)------------------------------
% 2.09/1.44 % (25615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.44 % (25615)Termination reason: Unknown
% 2.09/1.44 % (25615)Termination phase: shuffling
% 2.09/1.44
% 2.09/1.44 % (25615)Memory used [KB]: 1151
% 2.09/1.44 % (25615)Time elapsed: 0.005 s
% 2.09/1.44 % (25615)Instructions burned: 4 (million)
% 2.09/1.44 % (25615)------------------------------
% 2.09/1.44 % (25615)------------------------------
% 2.09/1.44 % (25625)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/6Mi)
% 2.09/1.44 % (25625)Instruction limit reached!
% 2.09/1.44 % (25625)------------------------------
% 2.09/1.44 % (25625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.44 % (25625)Termination reason: Unknown
% 2.09/1.44 % (25625)Termination phase: Property scanning
% 2.09/1.44
% 2.09/1.44 % (25625)Memory used [KB]: 1151
% 2.09/1.44 % (25625)Time elapsed: 0.004 s
% 2.09/1.44 % (25625)Instructions burned: 8 (million)
% 2.09/1.44 % (25625)------------------------------
% 2.09/1.44 % (25625)------------------------------
% 2.09/1.45 % (25624)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/710Mi)
% 2.09/1.45 % (25590)Instruction limit reached!
% 2.09/1.45 % (25590)------------------------------
% 2.09/1.45 % (25590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.45 % (25590)Termination reason: Unknown
% 2.09/1.45 % (25590)Termination phase: Saturation
% 2.09/1.45
% 2.09/1.45 % (25590)Memory used [KB]: 6908
% 2.09/1.45 % (25590)Time elapsed: 0.072 s
% 2.09/1.45 % (25590)Instructions burned: 184 (million)
% 2.09/1.45 % (25590)------------------------------
% 2.09/1.45 % (25590)------------------------------
% 2.09/1.46 % (25630)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_25445 for (2999ds/5Mi)
% 2.09/1.46 % (25630)Instruction limit reached!
% 2.09/1.46 % (25630)------------------------------
% 2.09/1.46 % (25630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.46 % (25630)Termination reason: Unknown
% 2.09/1.46 % (25630)Termination phase: shuffling
% 2.09/1.46
% 2.09/1.46 % (25630)Memory used [KB]: 1151
% 2.09/1.46 % (25630)Time elapsed: 0.004 s
% 2.09/1.46 % (25630)Instructions burned: 5 (million)
% 2.09/1.46 % (25630)------------------------------
% 2.09/1.46 % (25630)------------------------------
% 2.09/1.46 % (25626)First to succeed.
% 2.09/1.47 % (25626)Refutation found. Thanks to Tanya!
% 2.09/1.47 % SZS status Theorem for DTF2THF_25445
% 2.09/1.47 % SZS output start Proof for DTF2THF_25445
% 2.09/1.47 thf(func_def_0, type, in: $i > $i > $o).
% 2.09/1.47 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.09/1.47 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.09/1.47 thf(func_def_8, type, powerset: $i > $i).
% 2.09/1.47 thf(func_def_10, type, setunion: $i > $i).
% 2.09/1.47 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.09/1.47 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.09/1.47 thf(func_def_26, type, prop2set: $o > $i).
% 2.09/1.47 thf(func_def_36, type, nonempty: $i > $o).
% 2.09/1.47 thf(func_def_72, type, sP1: $i > $i > $o).
% 2.09/1.47 thf(func_def_73, type, sP2: $i > $o).
% 2.09/1.47 thf(func_def_74, type, sP3: $i > $i > $o).
% 2.09/1.47 thf(func_def_75, type, sP4: $i > $i > $o).
% 2.09/1.47 thf(func_def_77, type, sK6: $i > $i > $o).
% 2.09/1.47 thf(func_def_78, type, sK7: $i > $i).
% 2.09/1.47 thf(func_def_79, type, sK8: $i > $i).
% 2.09/1.47 thf(func_def_80, type, sK9: ($i > $i > $o) > $i > $i).
% 2.09/1.47 thf(func_def_81, type, sK10: ($i > $i > $o) > $i > $i).
% 2.09/1.47 thf(func_def_82, type, sK11: $i > ($i > $i > $o) > $i > $i).
% 2.09/1.47 thf(func_def_89, type, sK18: $i > $o).
% 2.09/1.47 thf(func_def_94, type, sK23: $i > $i > $i).
% 2.09/1.47 thf(func_def_97, type, sK26: $i > $i).
% 2.09/1.47 thf(func_def_107, type, sK36: ($i > $o) > $i).
% 2.09/1.47 thf(func_def_108, type, sK37: $i > $o).
% 2.09/1.47 thf(func_def_109, type, sK38: $i > $i).
% 2.09/1.47 thf(func_def_113, type, sK42: $i > $o).
% 2.09/1.47 thf(func_def_114, type, sK43: $i > $i).
% 2.09/1.47 thf(func_def_115, type, sK44: ($i > $o) > $i).
% 2.09/1.47 thf(func_def_123, type, sK52: ($i > $o) > $i).
% 2.09/1.47 thf(func_def_124, type, sK53: $i > $o).
% 2.09/1.47 thf(func_def_127, type, sK56: $i > $i > $i).
% 2.09/1.47 thf(func_def_128, type, sK57: $i > $i > $i).
% 2.09/1.47 thf(func_def_129, type, sK58: $i > $i > $i).
% 2.09/1.47 thf(func_def_130, type, sK59: $i > $i > $i).
% 2.09/1.47 thf(func_def_131, type, sK60: $i > $i > $i > $i).
% 2.09/1.47 thf(func_def_132, type, sK61: $i > $i).
% 2.09/1.47 thf(func_def_133, type, sK62: $i > $i).
% 2.09/1.47 thf(func_def_134, type, sK63: $i > $i).
% 2.09/1.47 thf(func_def_135, type, sK64: $i > $i).
% 2.09/1.47 thf(func_def_136, type, sK65: $i > $i > $i).
% 2.09/1.47 thf(func_def_137, type, sK66: $i > $i > $i > $i).
% 2.09/1.47 thf(func_def_138, type, sK67: $i > $i > $i > $i).
% 2.09/1.47 thf(func_def_139, type, sK68: $i > $i > $i).
% 2.09/1.47 thf(func_def_140, type, sK69: $i > $i > $i).
% 2.09/1.47 thf(func_def_142, type, sK71: $i > $i).
% 2.09/1.47 thf(func_def_143, type, sK72: $i > $i).
% 2.09/1.47 thf(func_def_144, type, sK73: $i > $i).
% 2.09/1.47 thf(func_def_145, type, sK74: $i > $i > $i).
% 2.09/1.47 thf(func_def_146, type, sK75: $i > $i).
% 2.09/1.47 thf(func_def_149, type, sK78: $i > $i).
% 2.09/1.47 thf(func_def_153, type, sK82: $i > $i).
% 2.09/1.47 thf(func_def_156, type, sK85: $i > $o).
% 2.09/1.47 thf(func_def_157, type, sK86: $o > $i > $i > $i).
% 2.09/1.47 thf(func_def_167, type, sK96: $i > $i > $i).
% 2.09/1.47 thf(func_def_175, type, sK104: $i > $o).
% 2.09/1.47 thf(func_def_178, type, sK107: $i > $o).
% 2.09/1.47 thf(func_def_182, type, sK111: $i > $i).
% 2.09/1.47 thf(func_def_185, type, sK114: $i > $o).
% 2.09/1.47 thf(func_def_187, type, sK116: $i > $i > $i).
% 2.09/1.47 thf(func_def_188, type, sK117: $i > $i > $i).
% 2.09/1.47 thf(func_def_191, type, sK120: $i > $i).
% 2.09/1.47 thf(func_def_195, type, sK124: $i > $i > $i).
% 2.09/1.47 thf(func_def_199, type, sK128: $i > $i).
% 2.09/1.47 thf(func_def_205, type, sK134: $i > $o).
% 2.09/1.47 thf(func_def_207, type, sK136: $i > $i > $i).
% 2.09/1.47 thf(func_def_211, type, ph140: !>[X0: $tType]:(X0)).
% 2.09/1.47 thf(f833,plain,(
% 2.09/1.47 $false),
% 2.09/1.47 inference(avatar_sat_refutation,[status(thm)],[f777,f789,f826,f832])).
% 2.09/1.47 thf(f832,plain,(
% 2.09/1.47 ~spl139_4),
% 2.09/1.47 inference(avatar_contradiction_clause,[status(thm)],[f831])).
% 2.09/1.47 thf(f831,plain,(
% 2.09/1.47 $false | ~spl139_4),
% 2.09/1.47 inference(trivial_inequality_removal,[status(thm)],[f830])).
% 2.09/1.47 thf(f830,plain,(
% 2.09/1.47 (sK48 != sK48) | ~spl139_4),
% 2.09/1.47 inference(superposition,[status(thm)],[f556,f809])).
% 2.09/1.47 thf(f809,plain,(
% 2.09/1.47 (sK50 = sK48) | ~spl139_4),
% 2.09/1.47 inference(avatar_component_clause,[status(thm)],[f807])).
% 2.09/1.47 thf(f807,definition,(
% 2.09/1.47 spl139_4 <=> (sK50 = sK48)),
% 2.09/1.47 introduced(definition,[new_symbols(naming,[spl139_4])],[avatar_definition])).
% 2.09/1.47 thf(f556,plain,(
% 2.09/1.47 (sK50 != sK48)),
% 2.09/1.47 inference(cnf_transformation,[status(thm)],[f302])).
% 2.09/1.47 thf(f302,plain,(
% 2.09/1.47 (setadjoinE = $true) & (wellorderingAx = $true) & (setadjoinIL = $true) & (notinemptyset = $true) & (noeltsimpempty = $true) & (singletonsswitch = $true) & (emptyInPowerset = $true) & (setadjoinIR = $true) & (nonemptyI = $true) & (replAx = $true) & (emptyinPowerset = $true) & (powersetAx = $true) & (subPowSU = $true) & (emptyI = $true) & (emptysetimpfalse = $true) & (setext = $true) & (notinsingleton = $true) & (emptyinunitempty = $true) & (dsetconstrEL = $true) & (setunionI = $true) & (nonemptyE1 = $true) & (omegaSAx = $true) & (emptysetE = $true) & (descrp = $true) & (setunionE = $true) & (nonemptyImpWitness = $true) & (((in @ sK48 @ (setadjoin @ sK49 @ (setadjoin @ sK50 @ emptyset))) = $true) & (sK50 != sK48) & (sK49 != sK48)) & (uniqinunit = $true) & (omega0Ax = $true) & (exuE1 = $true) & (exuE3e = $true) & (foundationAx = $true) & (setadjoinOr = $true) & (powersetE = $true) & (dsetconstrI = $true) & (setextAx = $true) & (powersetI = $true) & (eqinunit = $true) & (nonemptyI1 = $true) & (setadjoinAx = $true) & (dsetconstrER = $true) & (setbeta = $true) & (prop2setE = $true) & (emptysetAx = $true) & (omegaIndAx = $true) & (setunionAx = $true) & (setoftrueEq = $true) & (exuE2 = $true)),
% 2.09/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49,sK50])],[f170,f301])).
% 2.09/1.47 thf(f301,plain,(
% 2.09/1.47 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) & (X0 != X2) & (X0 != X1)) => (((in @ sK48 @ (setadjoin @ sK49 @ (setadjoin @ sK50 @ emptyset))) = $true) & (sK50 != sK48) & (sK49 != sK48))),
% 2.09/1.47 introduced(definition,[],[choice_axiom])).
% 2.09/1.47 thf(f170,plain,(
% 2.09/1.47 (setadjoinE = $true) & (wellorderingAx = $true) & (setadjoinIL = $true) & (notinemptyset = $true) & (noeltsimpempty = $true) & (singletonsswitch = $true) & (emptyInPowerset = $true) & (setadjoinIR = $true) & (nonemptyI = $true) & (replAx = $true) & (emptyinPowerset = $true) & (powersetAx = $true) & (subPowSU = $true) & (emptyI = $true) & (emptysetimpfalse = $true) & (setext = $true) & (notinsingleton = $true) & (emptyinunitempty = $true) & (dsetconstrEL = $true) & (setunionI = $true) & (nonemptyE1 = $true) & (omegaSAx = $true) & (emptysetE = $true) & (descrp = $true) & (setunionE = $true) & (nonemptyImpWitness = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) & (X0 != X2) & (X0 != X1)) & (uniqinunit = $true) & (omega0Ax = $true) & (exuE1 = $true) & (exuE3e = $true) & (foundationAx = $true) & (setadjoinOr = $true) & (powersetE = $true) & (dsetconstrI = $true) & (setextAx = $true) & (powersetI = $true) & (eqinunit = $true) & (nonemptyI1 = $true) & (setadjoinAx = $true) & (dsetconstrER = $true) & (setbeta = $true) & (prop2setE = $true) & (emptysetAx = $true) & (omegaIndAx = $true) & (setunionAx = $true) & (setoftrueEq = $true) & (exuE2 = $true)),
% 2.09/1.47 inference(flattening,[status(thm)],[f169])).
% 2.09/1.47 thf(f169,plain,(
% 2.09/1.47 ((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (((X0 != X2) & (X0 != X1)) & ($true = (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.09/1.47 inference(ennf_transformation,[status(thm)],[f105])).
% 2.09/1.47 thf(f105,plain,(
% 2.09/1.47 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) => ((X0 = X2) | (X0 = X1))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.09/1.47 inference(fool_elimination,[status(thm)],[f104])).
% 2.09/1.47 thf(f104,plain,(
% 2.09/1.47 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) => ((X0 = X2) | (X0 = X1))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.09/1.47 inference(rectify,[status(thm)],[f52])).
% 2.09/1.47 thf(f52,negated_conjecture,(
% 2.09/1.47 ~(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 => ! [X8 : $i,X1 : $i,X2 : $i] : ((in @ X8 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) => ((X2 = X8) | (X1 = X8))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.09/1.47 inference(negated_conjecture,[status(cth)],[f51])).
% 2.09/1.47 thf(f51,conjecture,(
% 2.09/1.47 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 => ! [X8 : $i,X1 : $i,X2 : $i] : ((in @ X8 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) => ((X2 = X8) | (X1 = X8)))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.09/1.47 file('/export/starexec/sandbox2/tmp/tmp.PJlHxzAzZQ/DTF2THF_25445.p',upairsetE)).
% 2.09/1.47 thf(f826,plain,(
% 2.09/1.47 spl139_4 | ~spl139_1),
% 2.09/1.47 inference(avatar_split_clause,[status(thm)],[f803,f767,f807])).
% 2.09/1.47 thf(f767,definition,(
% 2.09/1.47 spl139_1 <=> ((in @ sK48 @ (setadjoin @ sK50 @ emptyset)) = $true)),
% 2.09/1.47 introduced(definition,[new_symbols(naming,[spl139_1])],[avatar_definition])).
% 2.09/1.47 thf(f803,plain,(
% 2.09/1.47 (sK50 = sK48) | ~spl139_1),
% 2.09/1.47 inference(trivial_inequality_removal,[status(thm)],[f802])).
% 2.09/1.47 thf(f802,plain,(
% 2.09/1.47 ($true != $true) | (sK50 = sK48) | ~spl139_1),
% 2.09/1.47 inference(forward_demodulation,[status(thm)],[f801,f554])).
% 2.09/1.47 thf(f554,plain,(
% 2.09/1.47 (uniqinunit = $true)),
% 2.09/1.47 inference(cnf_transformation,[status(thm)],[f302])).
% 2.09/1.47 thf(f801,plain,(
% 2.09/1.47 (uniqinunit != $true) | (sK50 = sK48) | ~spl139_1),
% 2.09/1.47 inference(trivial_inequality_removal,[status(thm)],[f791])).
% 2.09/1.47 thf(f791,plain,(
% 2.09/1.47 (uniqinunit != $true) | (sK50 = sK48) | ($true != $true) | ~spl139_1),
% 2.09/1.47 inference(superposition,[status(thm)],[f634,f769])).
% 2.09/1.47 thf(f769,plain,(
% 2.09/1.47 ((in @ sK48 @ (setadjoin @ sK50 @ emptyset)) = $true) | ~spl139_1),
% 2.09/1.47 inference(avatar_component_clause,[status(thm)],[f767])).
% 2.09/1.47 thf(f634,plain,(
% 2.09/1.47 ( ! [X2 : $i,X3 : $i] : (($true != (in @ X2 @ (setadjoin @ X3 @ emptyset))) | (uniqinunit != $true) | (X2 = X3)) )),
% 2.09/1.47 inference(cnf_transformation,[status(thm)],[f357])).
% 2.09/1.47 thf(f357,plain,(
% 2.09/1.47 ((uniqinunit = $true) | (((in @ sK79 @ (setadjoin @ sK80 @ emptyset)) = $true) & (sK79 != sK80))) & (! [X2 : $i,X3 : $i] : (($true != (in @ X2 @ (setadjoin @ X3 @ emptyset))) | (X2 = X3)) | (uniqinunit != $true))),
% 2.09/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80])],[f355,f356])).
% 2.09/1.47 thf(f356,plain,(
% 2.09/1.47 ? [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) & (X0 != X1)) => (((in @ sK79 @ (setadjoin @ sK80 @ emptyset)) = $true) & (sK79 != sK80))),
% 2.09/1.47 introduced(definition,[],[choice_axiom])).
% 2.09/1.47 thf(f355,plain,(
% 2.09/1.47 ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) & (X0 != X1))) & (! [X2 : $i,X3 : $i] : (($true != (in @ X2 @ (setadjoin @ X3 @ emptyset))) | (X2 = X3)) | (uniqinunit != $true))),
% 2.09/1.47 inference(rectify,[status(thm)],[f354])).
% 2.09/1.47 thf(f354,plain,(
% 2.09/1.47 ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) & (X0 != X1))) & (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) | (uniqinunit != $true))),
% 2.09/1.47 inference(nnf_transformation,[status(thm)],[f182])).
% 2.09/1.47 thf(f182,plain,(
% 2.09/1.47 (uniqinunit = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1))),
% 2.09/1.47 inference(ennf_transformation,[status(thm)],[f57])).
% 2.09/1.47 thf(f57,plain,(
% 2.09/1.47 ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) => (X0 = X1)) <=> (uniqinunit = $true)),
% 2.09/1.47 inference(fool_elimination,[status(thm)],[f56])).
% 2.09/1.47 thf(f56,plain,(
% 2.09/1.47 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 2.09/1.47 inference(rectify,[status(thm)],[f47])).
% 2.09/1.47 thf(f47,axiom,(
% 2.09/1.47 (! [X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X2 @ emptyset)) => (X1 = X2)) = uniqinunit)),
% 2.09/1.47 file('/export/starexec/sandbox2/tmp/tmp.PJlHxzAzZQ/DTF2THF_25445.p',uniqinunit)).
% 2.09/1.47 thf(f789,plain,(
% 2.09/1.47 ~spl139_2),
% 2.09/1.47 inference(avatar_contradiction_clause,[status(thm)],[f788])).
% 2.09/1.47 thf(f788,plain,(
% 2.09/1.47 $false | ~spl139_2),
% 2.09/1.47 inference(trivial_inequality_removal,[status(thm)],[f787])).
% 2.09/1.47 thf(f787,plain,(
% 2.09/1.47 (sK48 != sK48) | ~spl139_2),
% 2.09/1.47 inference(superposition,[status(thm)],[f555,f773])).
% 2.09/1.47 thf(f773,plain,(
% 2.09/1.47 (sK49 = sK48) | ~spl139_2),
% 2.09/1.47 inference(avatar_component_clause,[status(thm)],[f771])).
% 2.09/1.47 thf(f771,definition,(
% 2.09/1.47 spl139_2 <=> (sK49 = sK48)),
% 2.09/1.47 introduced(definition,[new_symbols(naming,[spl139_2])],[avatar_definition])).
% 2.09/1.47 thf(f555,plain,(
% 2.09/1.47 (sK49 != sK48)),
% 2.09/1.47 inference(cnf_transformation,[status(thm)],[f302])).
% 2.09/1.47 thf(f777,plain,(
% 2.09/1.47 spl139_2 | spl139_1),
% 2.09/1.47 inference(avatar_split_clause,[status(thm)],[f776,f767,f771])).
% 2.09/1.47 thf(f776,plain,(
% 2.09/1.47 ((in @ sK48 @ (setadjoin @ sK50 @ emptyset)) = $true) | (sK49 = sK48)),
% 2.09/1.47 inference(trivial_inequality_removal,[status(thm)],[f775])).
% 2.09/1.47 thf(f775,plain,(
% 2.09/1.47 (sK49 = sK48) | ($true != $true) | ((in @ sK48 @ (setadjoin @ sK50 @ emptyset)) = $true)),
% 2.09/1.47 inference(forward_demodulation,[status(thm)],[f762,f549])).
% 2.09/1.47 thf(f549,plain,(
% 2.09/1.47 (setadjoinOr = $true)),
% 2.09/1.47 inference(cnf_transformation,[status(thm)],[f302])).
% 2.09/1.47 thf(f762,plain,(
% 2.09/1.47 ((in @ sK48 @ (setadjoin @ sK50 @ emptyset)) = $true) | (setadjoinOr != $true) | (sK49 = sK48)),
% 2.09/1.47 inference(trivial_inequality_removal,[status(thm)],[f756])).
% 2.09/1.47 thf(f756,plain,(
% 2.09/1.47 (sK49 = sK48) | ($true != $true) | ((in @ sK48 @ (setadjoin @ sK50 @ emptyset)) = $true) | (setadjoinOr != $true)),
% 2.09/1.47 inference(superposition,[status(thm)],[f505,f557])).
% 2.09/1.47 thf(f557,plain,(
% 2.09/1.47 ((in @ sK48 @ (setadjoin @ sK49 @ (setadjoin @ sK50 @ emptyset))) = $true)),
% 2.09/1.47 inference(cnf_transformation,[status(thm)],[f302])).
% 2.09/1.47 thf(f505,plain,(
% 2.09/1.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (setadjoin @ X0 @ X1))) | ((in @ X2 @ X1) = $true) | (X0 = X2) | (setadjoinOr != $true)) )),
% 2.09/1.47 inference(cnf_transformation,[status(thm)],[f263])).
% 2.09/1.47 thf(f263,plain,(
% 2.09/1.47 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (setadjoin @ X0 @ X1))) | (X0 = X2) | ((in @ X2 @ X1) = $true)) | (setadjoinOr != $true)) & ((setadjoinOr = $true) | (((in @ sK31 @ (setadjoin @ sK29 @ sK30)) = $true) & (sK29 != sK31) & ($true != (in @ sK31 @ sK30))))),
% 2.09/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31])],[f261,f262])).
% 2.09/1.47 thf(f262,plain,(
% 2.09/1.47 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (setadjoin @ X3 @ X4)) = $true) & (X3 != X5) & ((in @ X5 @ X4) != $true)) => (((in @ sK31 @ (setadjoin @ sK29 @ sK30)) = $true) & (sK29 != sK31) & ($true != (in @ sK31 @ sK30)))),
% 2.09/1.47 introduced(definition,[],[choice_axiom])).
% 2.09/1.47 thf(f261,plain,(
% 2.09/1.47 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (setadjoin @ X0 @ X1))) | (X0 = X2) | ((in @ X2 @ X1) = $true)) | (setadjoinOr != $true)) & ((setadjoinOr = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (setadjoin @ X3 @ X4)) = $true) & (X3 != X5) & ((in @ X5 @ X4) != $true)))),
% 2.09/1.47 inference(rectify,[status(thm)],[f260])).
% 2.09/1.47 thf(f260,plain,(
% 2.09/1.47 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (setadjoin @ X0 @ X1))) | (X0 = X2) | ((in @ X2 @ X1) = $true)) | (setadjoinOr != $true)) & ((setadjoinOr = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setadjoin @ X0 @ X1))) & (X0 != X2) & ((in @ X2 @ X1) != $true)))),
% 2.09/1.47 inference(nnf_transformation,[status(thm)],[f179])).
% 2.09/1.47 thf(f179,plain,(
% 2.09/1.47 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (setadjoin @ X0 @ X1))) | (X0 = X2) | ((in @ X2 @ X1) = $true)) <=> (setadjoinOr = $true)),
% 2.09/1.47 inference(flattening,[status(thm)],[f178])).
% 2.09/1.47 thf(f178,plain,(
% 2.09/1.47 ! [X0 : $i,X1 : $i,X2 : $i] : (((X0 = X2) | ((in @ X2 @ X1) = $true)) | ($true != (in @ X2 @ (setadjoin @ X0 @ X1)))) <=> (setadjoinOr = $true)),
% 2.09/1.47 inference(ennf_transformation,[status(thm)],[f146])).
% 2.09/1.47 thf(f146,plain,(
% 2.09/1.47 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setadjoin @ X0 @ X1))) => ((X0 = X2) | ((in @ X2 @ X1) = $true))) <=> (setadjoinOr = $true)),
% 2.09/1.47 inference(fool_elimination,[status(thm)],[f145])).
% 2.09/1.47 thf(f145,plain,(
% 2.09/1.47 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X0 @ X1)) => ((in @ X2 @ X1) | (X0 = X2))) = setadjoinOr)),
% 2.09/1.47 inference(rectify,[status(thm)],[f36])).
% 2.09/1.47 thf(f36,axiom,(
% 2.09/1.47 (! [X1 : $i,X3 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X1 @ X3)) => ((in @ X2 @ X3) | (X1 = X2))) = setadjoinOr)),
% 2.09/1.47 file('/export/starexec/sandbox2/tmp/tmp.PJlHxzAzZQ/DTF2THF_25445.p',setadjoinOr)).
% 2.09/1.47 % SZS output end Proof for DTF2THF_25445
% 2.09/1.47 % (25626)------------------------------
% 2.09/1.47 % (25626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.09/1.47 % (25626)Termination reason: Refutation
% 2.09/1.47
% 2.09/1.47 % (25626)Memory used [KB]: 6396
% 2.09/1.47 % (25626)Time elapsed: 0.025 s
% 2.09/1.47 % (25626)Instructions burned: 55 (million)
% 2.09/1.47 % (25626)------------------------------
% 2.09/1.47 % (25626)------------------------------
% 2.09/1.47 % (25589)Success in time 0.088 s
%------------------------------------------------------------------------------