%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU582^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 09:35:24 AM UTC 2026
% Result : Theorem 6.48s 2.02s
% Output : Refutation 6.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 35 unt; 0 typ; 4 def)
% Number of atoms : 1776 ( 456 equ; 0 cnn)
% Maximal formula atoms : 100 ( 31 avg)
% Number of connectives : 1095 ( 18 ~; 15 |; 299 &; 316 @)
% ( 4 <=>; 420 =>; 0 <=; 0 <~>)
% Maximal formula depth : 107 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 201 ( 197 usr; 109 con; 0-4 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 95 ( 38 ^; 48 !; 9 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_135,type,
sK4: $i > $i > $i ).
thf(func_def_136,type,
sK5: ( $i > $o ) > $i ).
thf(func_def_137,type,
sK6: ( $i > $o ) > $i > $i ).
thf(func_def_138,type,
sK7: $i > ( $i > $o ) > $i ).
thf(func_def_139,type,
sK8: $i > $i > $i ).
thf(func_def_140,type,
sK9: $i > $i ).
thf(func_def_141,type,
sK10: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_142,type,
sK11: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_143,type,
sK12: ( $i > $o ) > $i ).
thf(func_def_144,type,
sK13: $i > ( $i > $o ) > $i ).
thf(func_def_145,type,
sK14: $i > ( $i > $o ) > $i ).
thf(func_def_146,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_147,type,
sK16: $i > ( $i > $o ) > $i ).
thf(func_def_148,type,
sK17: $i > ( $i > $o ) > $i ).
thf(func_def_149,type,
sK18: $i > ( $i > $o ) > $i ).
thf(func_def_150,type,
sK19: $i > ( $i > $o ) > $i ).
thf(func_def_151,type,
sK20: ( $i > $o ) > $i ).
thf(func_def_152,type,
sK21: $i > ( $i > $o ) > $i ).
thf(func_def_153,type,
sK22: $i > ( $i > $o ) > $i ).
thf(func_def_154,type,
sK23: ( $i > $o ) > $i ).
thf(func_def_155,type,
sK24: $i > ( $i > $o ) > $i ).
thf(func_def_156,type,
sK25: $i > $i ).
thf(func_def_157,type,
sK26: $i > ( $i > $o ) > $i ).
thf(func_def_158,type,
sK27: $i > $i ).
thf(func_def_159,type,
sK28: $i > ( $i > $o ) > $i ).
thf(func_def_160,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_161,type,
sK30: $i > $i > $i ).
thf(func_def_162,type,
sK31: $i > $i ).
thf(func_def_163,type,
sK32: $i > ( $i > $o ) > $i ).
thf(func_def_164,type,
sK33: $o > $i > $i > $i ).
thf(func_def_165,type,
sK34: $i > ( $i > $i > $o ) > $i ).
thf(func_def_166,type,
sK35: $i > ( $i > $i > $o ) > $i ).
thf(func_def_167,type,
sK36: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_168,type,
sK37: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_169,type,
sK38: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_170,type,
sK39: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_171,type,
sK40: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_172,type,
sK41: $i > ( $i > $o ) > $i ).
thf(func_def_173,type,
sK42: ( $i > $o ) > $i ).
thf(func_def_174,type,
sK43: ( $i > $o ) > $i ).
thf(func_def_175,type,
sK44: ( $i > $o ) > $i ).
thf(func_def_176,type,
sK45: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_177,type,
sK46: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_178,type,
sK47: $i > $i ).
thf(func_def_179,type,
sK48: $i > $i ).
thf(func_def_180,type,
sK49: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_181,type,
sK50: ( $i > $o ) > $i > $i ).
thf(func_def_182,type,
sK51: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_183,type,
sK52: ( $i > $o ) > $i > $i ).
thf(func_def_184,type,
sK53: ( $i > $o ) > $i > $i ).
thf(func_def_185,type,
sK54: ( $i > $o ) > $i > $i ).
thf(func_def_186,type,
sK55: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_187,type,
sK56: ( $i > $o ) > $i > $i ).
thf(func_def_188,type,
sK57: ( $i > $o ) > $i > $i ).
thf(func_def_189,type,
sK58: ( $i > $o ) > $i > $i ).
thf(func_def_190,type,
sK59: $i > $i > $i ).
thf(func_def_191,type,
sK60: ( $i > $o ) > $i > $i ).
thf(func_def_192,type,
sK61: ( $i > $o ) > $i > $i ).
thf(func_def_193,type,
sK62: $i > $i > $i ).
thf(func_def_194,type,
sK63: $i > $i > $i ).
thf(func_def_195,type,
sK64: $i > $i > $i ).
thf(func_def_196,type,
sK65: $i > $i ).
thf(func_def_197,type,
sK66: $i > $i > $i > $i ).
thf(func_def_198,type,
sK67: $i > $i > $i ).
thf(func_def_199,type,
sK68: $i > $i > $i ).
thf(func_def_200,type,
sK69: $i > $i > $i ).
thf(func_def_201,type,
sK70: $i > $i > $i ).
thf(func_def_202,type,
sK71: $i > $i > $i ).
thf(func_def_203,type,
sK72: ( $i > $o ) > $i > $i ).
thf(func_def_204,type,
sK73: ( $i > $o ) > $i ).
thf(func_def_205,type,
sK74: ( $i > $o ) > $i ).
thf(func_def_206,type,
sK75: $i > $i > $i ).
thf(func_def_207,type,
sK76: ( $i > $o ) > $i ).
thf(func_def_208,type,
sK77: ( $i > $o ) > $i > $i ).
thf(func_def_209,type,
sK78: ( $i > $o ) > $i > $i ).
thf(func_def_210,type,
sK79: ( $i > $o ) > $i > $i ).
thf(func_def_211,type,
ph80:
!>[X0: $tType] : X0 ).
thf(f2845,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1880,f1893,f1898,f2842,f2843]) ).
thf(f2843,plain,
( ( ( in @ sK2 @ sK1 )
!= $true )
| ( $false
!= ( in @ sK2 @ sK1 ) )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f2842,plain,
( spl3_23
| spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f2835,f1877,f2838]) ).
thf(f2838,definition,
( spl3_23
<=> ( $false
= ( in @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_23])],[avatar_definition]) ).
thf(f1877,definition,
( spl3_5
<=> ( $true
= ( in @ sK2 @ ( setunion @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f2835,plain,
( ( $false
= ( in @ sK2 @ sK1 ) )
| spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f2831]) ).
thf(f2831,plain,
( ( $false
= ( in @ sK2 @ sK1 ) )
| ( $false = $true )
| spl3_5 ),
inference(superposition,[status(thm)],[f1790,f2045]) ).
thf(f2045,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ) )
| ( ( in @ sK2 @ X0 )
= $false ) )
| spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f2042]) ).
thf(f2042,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( in @ sK2 @ X0 )
= $false )
| ( $false
= ( in @ X0 @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ) ) )
| spl3_5 ),
inference(superposition,[status(thm)],[f1879,f1049]) ).
thf(f1049,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( setunion @ X1 ) )
= $true )
| ( $false
= ( in @ X3 @ X2 ) )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1048]) ).
thf(f1048,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( in @ X2 @ X1 )
=> ( in @ X3 @ ( setunion @ X1 ) ) )
= $true )
| ( $false
= ( in @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1047]) ).
thf(f1047,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ X2 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X3 @ ( setunion @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1046]) ).
thf(f1046,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ X2 @ X1 )
=> ( in @ Y0 @ ( setunion @ X1 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f1045]) ).
thf(f1045,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ X2 @ X1 )
=> ( in @ Y0 @ ( setunion @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1044]) ).
thf(f1044,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y1 @ ( setunion @ X1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1043]) ).
thf(f1043,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y1 @ ( setunion @ X1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1042]) ).
thf(f1042,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f598]) ).
thf(f598,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f482,f424]) ).
thf(f424,plain,
setunionI = $true,
inference(cnf_transformation,[status(thm)],[f306]) ).
thf(f306,plain,
( ( subsetI2 = $true )
& ( setadjoinIR = $true )
& ( emptyinPowerset = $true )
& ( setunionE = $true )
& ( notinsingleton = $true )
& ( powerset__Cong = $true )
& ( eqinunit = $true )
& ( quantDeMorgan2 = $true )
& ( emptyinunitempty = $true )
& ( emptyset__Cong = $true )
& ( eqimpsubset2 = $true )
& ( notinemptyset = $true )
& ( ( in @ sK2 @ ( binunion @ sK1 @ sK0 ) )
!= $true )
& ( ( in @ sK2 @ sK1 )
= $true )
& ( prop2set2propI = $true )
& ( uniqinunit = $true )
& ( sepInPowerset = $true )
& ( exuI1 = $true )
& ( setadjoinAx = $true )
& ( omegaSAx = $true )
& ( exuE2 = $true )
& ( setunion__Cong = $true )
& ( dsetconstrER = $true )
& ( noeltsimpempty = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstrI = $true )
& ( powersetE = $true )
& ( setadjoinOr = $true )
& ( emptyI = $true )
& ( upairsetIL = $true )
& ( sepSubset = $true )
& ( exuI3 = $true )
& ( subsetI1 = $true )
& ( descrp = $true )
& ( powersetI = $true )
& ( notequalI1 = $true )
& ( setunionAx = $true )
& ( upairsetE = $true )
& ( setextAx = $true )
& ( setadjoin__Cong = $true )
& ( powersetAx = $true )
& ( foundationAx = $true )
& ( setadjoinSub2 = $true )
& ( exuI2 = $true )
& ( setadjoinIL = $true )
& ( in__Cong = $true )
& ( replAx = $true )
& ( setunionI = $true )
& ( notdallE = $true )
& ( setoftrueEq = $true )
& ( setadjoinE = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( dsetconstrEL = $true )
& ( prop2setI = $true )
& ( emptysetAx = $true )
& ( nonemptyI = $true )
& ( powersetI1 = $true )
& ( prop2setE = $true )
& ( powersetE1 = $true )
& ( inCongP = $true )
& ( subsetE = $true )
& ( exuE3u = $true )
& ( nonemptyI1 = $true )
& ( subsetRefl = $true )
& ( setextsub = $true )
& ( emptysetE = $true )
& ( quantDeMorgan1 = $true )
& ( upairsetIR = $true )
& ( setext = $true )
& ( emptyInPowerset = $true )
& ( subsetE2 = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan3 = $true )
& ( nonemptyImpWitness = $true )
& ( subPowSU = $true )
& ( vacuousDall = $true )
& ( setadjoinSub = $true )
& ( subset2powerset = $true )
& ( emptyE1 = $true )
& ( eqimpsubset1 = $true )
& ( exuEu = $true )
& ( quantDeMorgan4 = $true )
& ( exu__Cong = $true )
& ( omegaIndAx = $true )
& ( omega0Ax = $true )
& ( notdexE = $true )
& ( exuE1 = $true )
& ( inPowerset = $true )
& ( singletonsswitch = $true )
& ( subsetTrans = $true )
& ( notsubsetI = $true )
& ( wellorderingAx = $true )
& ( notequalI2 = $true )
& ( powersetsubset = $true )
& ( exuE3e = $true )
& ( setbeta = $true )
& ( omega__Cong = $true )
& ( emptysetsubset = $true )
& ( nonemptyE1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f304,f305]) ).
thf(f305,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( ( in @ sK2 @ ( binunion @ sK1 @ sK0 ) )
!= $true )
& ( ( in @ sK2 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f304,plain,
( ( subsetI2 = $true )
& ( setadjoinIR = $true )
& ( emptyinPowerset = $true )
& ( setunionE = $true )
& ( notinsingleton = $true )
& ( powerset__Cong = $true )
& ( eqinunit = $true )
& ( quantDeMorgan2 = $true )
& ( emptyinunitempty = $true )
& ( emptyset__Cong = $true )
& ( eqimpsubset2 = $true )
& ( notinemptyset = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( prop2set2propI = $true )
& ( uniqinunit = $true )
& ( sepInPowerset = $true )
& ( exuI1 = $true )
& ( setadjoinAx = $true )
& ( omegaSAx = $true )
& ( exuE2 = $true )
& ( setunion__Cong = $true )
& ( dsetconstrER = $true )
& ( noeltsimpempty = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstrI = $true )
& ( powersetE = $true )
& ( setadjoinOr = $true )
& ( emptyI = $true )
& ( upairsetIL = $true )
& ( sepSubset = $true )
& ( exuI3 = $true )
& ( subsetI1 = $true )
& ( descrp = $true )
& ( powersetI = $true )
& ( notequalI1 = $true )
& ( setunionAx = $true )
& ( upairsetE = $true )
& ( setextAx = $true )
& ( setadjoin__Cong = $true )
& ( powersetAx = $true )
& ( foundationAx = $true )
& ( setadjoinSub2 = $true )
& ( exuI2 = $true )
& ( setadjoinIL = $true )
& ( in__Cong = $true )
& ( replAx = $true )
& ( setunionI = $true )
& ( notdallE = $true )
& ( setoftrueEq = $true )
& ( setadjoinE = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( dsetconstrEL = $true )
& ( prop2setI = $true )
& ( emptysetAx = $true )
& ( nonemptyI = $true )
& ( powersetI1 = $true )
& ( prop2setE = $true )
& ( powersetE1 = $true )
& ( inCongP = $true )
& ( subsetE = $true )
& ( exuE3u = $true )
& ( nonemptyI1 = $true )
& ( subsetRefl = $true )
& ( setextsub = $true )
& ( emptysetE = $true )
& ( quantDeMorgan1 = $true )
& ( upairsetIR = $true )
& ( setext = $true )
& ( emptyInPowerset = $true )
& ( subsetE2 = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan3 = $true )
& ( nonemptyImpWitness = $true )
& ( subPowSU = $true )
& ( vacuousDall = $true )
& ( setadjoinSub = $true )
& ( subset2powerset = $true )
& ( emptyE1 = $true )
& ( eqimpsubset1 = $true )
& ( exuEu = $true )
& ( quantDeMorgan4 = $true )
& ( exu__Cong = $true )
& ( omegaIndAx = $true )
& ( omega0Ax = $true )
& ( notdexE = $true )
& ( exuE1 = $true )
& ( inPowerset = $true )
& ( singletonsswitch = $true )
& ( subsetTrans = $true )
& ( notsubsetI = $true )
& ( wellorderingAx = $true )
& ( notequalI2 = $true )
& ( powersetsubset = $true )
& ( exuE3e = $true )
& ( setbeta = $true )
& ( omega__Cong = $true )
& ( emptysetsubset = $true )
& ( nonemptyE1 = $true ) ),
inference(flattening,[status(thm)],[f303]) ).
thf(f303,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f112]) ).
thf(f112,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f111]) ).
thf(f111,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f103]) ).
thf(f103,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ! [X4: $i,X3: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f102]) ).
thf(f102,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ! [X4: $i,X3: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OQI6VlFTuB/DTF2THF_23036.p',binunionIL) ).
thf(f482,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f166]) ).
thf(f166,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f165]) ).
thf(f165,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X0 @ ( setunion @ X2 ) ) ) )
= setunionI ),
inference(rectify,[status(thm)],[f41]) ).
thf(f41,axiom,
! [X1: $i,X4: $i,X3: $i] :
( ( ( in @ X1 @ X4 )
=> ( ( in @ X4 @ X3 )
=> ( in @ X1 @ ( setunion @ X3 ) ) ) )
= setunionI ),
file('/export/starexec/sandbox/tmp/tmp.OQI6VlFTuB/DTF2THF_23036.p',setunionI) ).
thf(f1879,plain,
( ( $true
!= ( in @ sK2 @ ( setunion @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ) ) )
| spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f1877]) ).
thf(f1790,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1789]) ).
thf(f1789,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1788]) ).
thf(f1788,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1787]) ).
thf(f1787,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f551]) ).
thf(f551,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f427,f334]) ).
thf(f334,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f246]) ).
thf(f246,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f245]) ).
thf(f245,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,axiom,
( setadjoinIL
= ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OQI6VlFTuB/DTF2THF_23036.p',setadjoinIL) ).
thf(f427,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f306]) ).
thf(f1898,plain,
~ spl3_9,
inference(avatar_split_clause,[status(thm)],[f104,f1895]) ).
thf(f1895,definition,
( spl3_9
<=> ( $false = $true ) ),
introduced(definition,[new_symbols(naming,[spl3_9])],[avatar_definition]) ).
thf(f104,plain,
$false != $true,
introduced(definition,[],[fool_axiom]) ).
thf(f1893,plain,
spl3_8,
inference(avatar_split_clause,[status(thm)],[f458,f1890]) ).
thf(f1890,definition,
( spl3_8
<=> ( ( in @ sK2 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition]) ).
thf(f458,plain,
( ( in @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f306]) ).
thf(f1880,plain,
~ spl3_5,
inference(avatar_split_clause,[status(thm)],[f1353,f1877]) ).
thf(f1353,plain,
( $true
!= ( in @ sK2 @ ( setunion @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f530]) ).
thf(f530,plain,
( $true
!= ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) )
@ sK1
@ sK0 ) ) ),
inference(definition_unfolding,[status(thm)],[f459,f486]) ).
thf(f486,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f282]) ).
thf(f282,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f281]) ).
thf(f281,plain,
( ( ^ [X0: $i,X1: $i] : ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) )
= binunion ),
inference(rectify,[status(thm)],[f101]) ).
thf(f101,axiom,
( ( ^ [X1: $i,X2: $i] : ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
= binunion ),
file('/export/starexec/sandbox/tmp/tmp.OQI6VlFTuB/DTF2THF_23036.p',binunion) ).
thf(f459,plain,
( ( in @ sK2 @ ( binunion @ sK1 @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f306]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU582^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n008.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 12:27:39 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.44 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SEU582^1 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.44 % Domain : Set Theory
% 0.17/0.44 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.17/0.44 % Version : Especial.
% 0.17/0.44 % English : (! A:i.! B:i.! x:i.in x A -> in x (binunion A B))
% 0.17/0.44
% 0.17/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.44 % Source : [Bro08]
% 0.17/0.44 % Names : ZFC084g [Bro08]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % 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, 0.29 v6.4.0, 0.33 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.71 v6.0.0, 0.43 v5.5.0, 0.83 v5.4.0, 0.60 v5.2.0, 0.80 v5.0.0, 1.00 v3.7.0
% 0.17/0.44 % Syntax : Number of formulae : 216 ( 101 unt; 114 typ; 101 def)
% 0.17/0.44 % Number of atoms : 541 ( 150 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 100 ( 5 avg)
% 0.17/0.44 % Number of connectives : 850 ( 29 ~; 5 |; 27 &; 532 @)
% 0.17/0.44 % ( 14 <=>; 243 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 106 ( 2 avg)
% 0.17/0.44 % Number of types : 2 ( 0 usr)
% 0.17/0.44 % Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 117 ( 114 usr; 102 con; 0-2 aty)
% 0.17/0.44 % Number of variables : 299 ( 32 ^; 239 !; 28 ?; 299 :)
% 0.17/0.44 % SPC : TH0_THM_EQU_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : http://mathgate.info/detsetitem.php?id=158
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf(in_type,type,
% 0.17/0.44 in: $i > $i > $o ).
% 0.17/0.44
% 0.17/0.44 thf(exu_type,type,
% 0.17/0.44 exu: ( $i > $o ) > $o ).
% 0.17/0.44
% 0.17/0.44 thf(exu,definition,
% 0.17/0.44 ( exu
% 0.17/0.44 = ( ^ [Xphi: $i > $o] :
% 0.17/0.44 ? [Xx: $i] :
% 0.17/0.44 ( ( Xphi @ Xx )
% 0.17/0.44 & ! [Xy: $i] :
% 0.17/0.44 ( ( Xphi @ Xy )
% 0.17/0.44 => ( Xx = Xy ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setextAx_type,type,
% 0.17/0.44 setextAx: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setextAx,definition,
% 0.17/0.44 ( setextAx
% 0.17/0.44 = ( ! [A: $i,B: $i] :
% 0.17/0.44 ( ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 <=> ( in @ Xx @ B ) )
% 0.17/0.44 => ( A = B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(emptyset_type,type,
% 0.17/0.44 emptyset: $i ).
% 0.17/0.44
% 0.17/0.44 thf(emptysetAx_type,type,
% 0.17/0.44 emptysetAx: $o ).
% 0.17/0.44
% 0.17/0.44 thf(emptysetAx,definition,
% 0.17/0.44 ( emptysetAx
% 0.17/0.44 = ( ! [Xx: $i] :
% 0.17/0.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setadjoin_type,type,
% 0.17/0.44 setadjoin: $i > $i > $i ).
% 0.17/0.44
% 0.17/0.44 thf(setadjoinAx_type,type,
% 0.17/0.44 setadjoinAx: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setadjoinAx,definition,
% 0.17/0.44 ( setadjoinAx
% 0.17/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.44 <=> ( ( Xy = Xx )
% 0.17/0.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(powerset_type,type,
% 0.17/0.44 powerset: $i > $i ).
% 0.17/0.44
% 0.17/0.44 thf(powersetAx_type,type,
% 0.17/0.44 powersetAx: $o ).
% 0.17/0.44
% 0.17/0.44 thf(powersetAx,definition,
% 0.17/0.44 ( powersetAx
% 0.17/0.44 = ( ! [A: $i,B: $i] :
% 0.17/0.44 ( ( in @ B @ ( powerset @ A ) )
% 0.17/0.44 <=> ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ B )
% 0.17/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setunion_type,type,
% 0.17/0.44 setunion: $i > $i ).
% 0.17/0.44
% 0.17/0.44 thf(setunionAx_type,type,
% 0.17/0.44 setunionAx: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setunionAx,definition,
% 0.17/0.44 ( setunionAx
% 0.17/0.44 = ( ! [A: $i,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ ( setunion @ A ) )
% 0.17/0.44 <=> ? [B: $i] :
% 0.17/0.44 ( ( in @ Xx @ B )
% 0.17/0.44 & ( in @ B @ A ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(omega_type,type,
% 0.17/0.44 omega: $i ).
% 0.17/0.44
% 0.17/0.44 thf(omega0Ax_type,type,
% 0.17/0.44 omega0Ax: $o ).
% 0.17/0.44
% 0.17/0.44 thf(omega0Ax,definition,
% 0.17/0.44 ( omega0Ax
% 0.17/0.44 = ( in @ emptyset @ omega ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(omegaSAx_type,type,
% 0.17/0.44 omegaSAx: $o ).
% 0.17/0.44
% 0.17/0.44 thf(omegaSAx,definition,
% 0.17/0.44 ( omegaSAx
% 0.17/0.44 = ( ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ omega )
% 0.17/0.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(omegaIndAx_type,type,
% 0.17/0.44 omegaIndAx: $o ).
% 0.17/0.44
% 0.17/0.44 thf(omegaIndAx,definition,
% 0.17/0.44 ( omegaIndAx
% 0.17/0.44 = ( ! [A: $i] :
% 0.17/0.44 ( ( ( in @ emptyset @ A )
% 0.17/0.44 & ! [Xx: $i] :
% 0.17/0.44 ( ( ( in @ Xx @ omega )
% 0.17/0.44 & ( in @ Xx @ A ) )
% 0.17/0.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.17/0.44 => ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ omega )
% 0.17/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(replAx_type,type,
% 0.17/0.44 replAx: $o ).
% 0.17/0.44
% 0.17/0.44 thf(replAx,definition,
% 0.17/0.44 ( replAx
% 0.17/0.44 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.17/0.44 ( ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ( exu
% 0.17/0.44 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.17/0.44 => ? [B: $i] :
% 0.17/0.44 ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ B )
% 0.17/0.44 <=> ? [Xy: $i] :
% 0.17/0.44 ( ( in @ Xy @ A )
% 0.17/0.44 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(foundationAx_type,type,
% 0.17/0.44 foundationAx: $o ).
% 0.17/0.44
% 0.17/0.44 thf(foundationAx,definition,
% 0.17/0.44 ( foundationAx
% 0.17/0.44 = ( ! [A: $i] :
% 0.17/0.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.17/0.44 => ? [B: $i] :
% 0.17/0.44 ( ( in @ B @ A )
% 0.17/0.44 & ~ ? [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ B )
% 0.17/0.44 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(wellorderingAx_type,type,
% 0.17/0.44 wellorderingAx: $o ).
% 0.17/0.44
% 0.17/0.44 thf(wellorderingAx,definition,
% 0.17/0.44 ( wellorderingAx
% 0.17/0.44 = ( ! [A: $i] :
% 0.17/0.44 ? [B: $i] :
% 0.17/0.44 ( ! [C: $i] :
% 0.17/0.44 ( ( in @ C @ B )
% 0.17/0.44 => ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ C )
% 0.17/0.44 => ( in @ Xx @ A ) ) )
% 0.17/0.44 & ! [Xx: $i,Xy: $i] :
% 0.17/0.44 ( ( ( in @ Xx @ A )
% 0.17/0.44 & ( in @ Xy @ A ) )
% 0.17/0.44 => ( ! [C: $i] :
% 0.17/0.44 ( ( in @ C @ B )
% 0.17/0.44 => ( ( in @ Xx @ C )
% 0.17/0.44 <=> ( in @ Xy @ C ) ) )
% 0.17/0.44 => ( Xx = Xy ) ) )
% 0.17/0.44 & ! [C: $i,D: $i] :
% 0.17/0.44 ( ( ( in @ C @ B )
% 0.17/0.44 & ( in @ D @ B ) )
% 0.17/0.44 => ( ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ C )
% 0.17/0.44 => ( in @ Xx @ D ) )
% 0.17/0.44 | ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ D )
% 0.17/0.44 => ( in @ Xx @ C ) ) ) )
% 0.17/0.44 & ! [C: $i] :
% 0.17/0.44 ( ( ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ C )
% 0.17/0.44 => ( in @ Xx @ A ) )
% 0.17/0.44 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.17/0.44 => ? [D: $i,Xx: $i] :
% 0.17/0.44 ( ( in @ D @ B )
% 0.17/0.44 & ( in @ Xx @ C )
% 0.17/0.44 & ~ ? [Xy: $i] :
% 0.17/0.44 ( ( in @ Xy @ D )
% 0.17/0.44 & ( in @ Xy @ C ) )
% 0.17/0.44 & ! [E: $i] :
% 0.17/0.44 ( ( in @ E @ B )
% 0.17/0.44 => ( ! [Xy: $i] :
% 0.17/0.44 ( ( in @ Xy @ E )
% 0.17/0.44 => ( in @ Xy @ D ) )
% 0.17/0.44 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(descr_type,type,
% 0.17/0.44 descr: ( $i > $o ) > $i ).
% 0.17/0.44
% 0.17/0.44 thf(descrp_type,type,
% 0.17/0.44 descrp: $o ).
% 0.17/0.44
% 0.17/0.44 thf(descrp,definition,
% 0.17/0.44 ( descrp
% 0.17/0.44 = ( ! [Xphi: $i > $o] :
% 0.17/0.44 ( ( exu
% 0.17/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.44 => ( Xphi
% 0.17/0.44 @ ( descr
% 0.17/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(dsetconstr_type,type,
% 0.17/0.44 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.17/0.44
% 0.17/0.44 thf(dsetconstrI_type,type,
% 0.17/0.44 dsetconstrI: $o ).
% 0.17/0.44
% 0.17/0.44 thf(dsetconstrI,definition,
% 0.17/0.44 ( dsetconstrI
% 0.17/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ( ( Xphi @ Xx )
% 0.17/0.44 => ( in @ Xx
% 0.17/0.44 @ ( dsetconstr @ A
% 0.17/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(dsetconstrEL_type,type,
% 0.17/0.44 dsetconstrEL: $o ).
% 0.17/0.44
% 0.17/0.44 thf(dsetconstrEL,definition,
% 0.17/0.44 ( dsetconstrEL
% 0.17/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx
% 0.17/0.44 @ ( dsetconstr @ A
% 0.17/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(dsetconstrER_type,type,
% 0.17/0.44 dsetconstrER: $o ).
% 0.17/0.44
% 0.17/0.44 thf(dsetconstrER,definition,
% 0.17/0.44 ( dsetconstrER
% 0.17/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx
% 0.17/0.44 @ ( dsetconstr @ A
% 0.17/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.44 => ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(exuE1_type,type,
% 0.17/0.44 exuE1: $o ).
% 0.17/0.44
% 0.17/0.44 thf(exuE1,definition,
% 0.17/0.44 ( exuE1
% 0.17/0.44 = ( ! [Xphi: $i > $o] :
% 0.17/0.44 ( ( exu
% 0.17/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.44 => ? [Xx: $i] :
% 0.17/0.44 ( ( Xphi @ Xx )
% 0.17/0.44 & ! [Xy: $i] :
% 0.17/0.44 ( ( Xphi @ Xy )
% 0.17/0.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(prop2set_type,type,
% 0.17/0.44 prop2set: $o > $i ).
% 0.17/0.44
% 0.17/0.44 thf(prop2setE_type,type,
% 0.17/0.44 prop2setE: $o ).
% 0.17/0.44
% 0.17/0.44 thf(prop2setE,definition,
% 0.17/0.44 ( prop2setE
% 0.17/0.44 = ( ! [Xphi: $o,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.17/0.44 => Xphi ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(emptysetE_type,type,
% 0.17/0.44 emptysetE: $o ).
% 0.17/0.44
% 0.17/0.44 thf(emptysetE,definition,
% 0.17/0.44 ( emptysetE
% 0.17/0.44 = ( ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ emptyset )
% 0.17/0.44 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(emptysetimpfalse_type,type,
% 0.17/0.44 emptysetimpfalse: $o ).
% 0.17/0.44
% 0.17/0.44 thf(emptysetimpfalse,definition,
% 0.17/0.44 ( emptysetimpfalse
% 0.17/0.44 = ( ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ emptyset )
% 0.17/0.44 => $false ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(notinemptyset_type,type,
% 0.17/0.44 notinemptyset: $o ).
% 0.17/0.44
% 0.17/0.44 thf(notinemptyset,definition,
% 0.17/0.44 ( notinemptyset
% 0.17/0.44 = ( ! [Xx: $i] :
% 0.17/0.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(exuE3e_type,type,
% 0.17/0.44 exuE3e: $o ).
% 0.17/0.44
% 0.17/0.44 thf(exuE3e,definition,
% 0.17/0.44 ( exuE3e
% 0.17/0.44 = ( ! [Xphi: $i > $o] :
% 0.17/0.44 ( ( exu
% 0.17/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.44 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setext_type,type,
% 0.17/0.44 setext: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setext,definition,
% 0.17/0.44 ( setext
% 0.17/0.44 = ( ! [A: $i,B: $i] :
% 0.17/0.44 ( ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ( in @ Xx @ B ) )
% 0.17/0.44 => ( ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ B )
% 0.17/0.44 => ( in @ Xx @ A ) )
% 0.17/0.44 => ( A = B ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(emptyI_type,type,
% 0.17/0.44 emptyI: $o ).
% 0.17/0.44
% 0.17/0.44 thf(emptyI,definition,
% 0.17/0.44 ( emptyI
% 0.17/0.44 = ( ! [A: $i] :
% 0.17/0.44 ( ! [Xx: $i] :
% 0.17/0.44 ~ ( in @ Xx @ A )
% 0.17/0.44 => ( A = emptyset ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(noeltsimpempty_type,type,
% 0.17/0.44 noeltsimpempty: $o ).
% 0.17/0.44
% 0.17/0.44 thf(noeltsimpempty,definition,
% 0.17/0.44 ( noeltsimpempty
% 0.17/0.44 = ( ! [A: $i] :
% 0.17/0.44 ( ! [Xx: $i] :
% 0.17/0.44 ~ ( in @ Xx @ A )
% 0.17/0.44 => ( A = emptyset ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setbeta_type,type,
% 0.17/0.44 setbeta: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setbeta,definition,
% 0.17/0.44 ( setbeta
% 0.17/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ( ( in @ Xx
% 0.17/0.44 @ ( dsetconstr @ A
% 0.17/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.44 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(nonempty_type,type,
% 0.17/0.44 nonempty: $i > $o ).
% 0.17/0.44
% 0.17/0.44 thf(nonempty,definition,
% 0.17/0.44 ( nonempty
% 0.17/0.44 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(nonemptyE1_type,type,
% 0.17/0.44 nonemptyE1: $o ).
% 0.17/0.44
% 0.17/0.44 thf(nonemptyE1,definition,
% 0.17/0.44 ( nonemptyE1
% 0.17/0.44 = ( ! [A: $i] :
% 0.17/0.44 ( ( nonempty @ A )
% 0.17/0.44 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(nonemptyI_type,type,
% 0.17/0.44 nonemptyI: $o ).
% 0.17/0.44
% 0.17/0.44 thf(nonemptyI,definition,
% 0.17/0.44 ( nonemptyI
% 0.17/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ( ( Xphi @ Xx )
% 0.17/0.44 => ( nonempty
% 0.17/0.44 @ ( dsetconstr @ A
% 0.17/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(nonemptyI1_type,type,
% 0.17/0.44 nonemptyI1: $o ).
% 0.17/0.44
% 0.17/0.44 thf(nonemptyI1,definition,
% 0.17/0.44 ( nonemptyI1
% 0.17/0.44 = ( ! [A: $i] :
% 0.17/0.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.17/0.44 => ( nonempty @ A ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setadjoinIL_type,type,
% 0.17/0.44 setadjoinIL: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setadjoinIL,definition,
% 0.17/0.44 ( setadjoinIL
% 0.17/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(emptyinunitempty_type,type,
% 0.17/0.44 emptyinunitempty: $o ).
% 0.17/0.44
% 0.17/0.44 thf(emptyinunitempty,definition,
% 0.17/0.44 ( emptyinunitempty
% 0.17/0.44 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setadjoinIR_type,type,
% 0.17/0.44 setadjoinIR: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setadjoinIR,definition,
% 0.17/0.44 ( setadjoinIR
% 0.17/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.44 ( ( in @ Xy @ A )
% 0.17/0.44 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setadjoinE_type,type,
% 0.17/0.44 setadjoinE: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setadjoinE,definition,
% 0.17/0.44 ( setadjoinE
% 0.17/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.44 => ! [Xphi: $o] :
% 0.17/0.44 ( ( ( Xy = Xx )
% 0.17/0.44 => Xphi )
% 0.17/0.44 => ( ( ( in @ Xy @ A )
% 0.17/0.44 => Xphi )
% 0.17/0.44 => Xphi ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setadjoinOr_type,type,
% 0.17/0.44 setadjoinOr: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setadjoinOr,definition,
% 0.17/0.44 ( setadjoinOr
% 0.17/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.44 => ( ( Xy = Xx )
% 0.17/0.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setoftrueEq_type,type,
% 0.17/0.44 setoftrueEq: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setoftrueEq,definition,
% 0.17/0.44 ( setoftrueEq
% 0.17/0.44 = ( ! [A: $i] :
% 0.17/0.44 ( ( dsetconstr @ A
% 0.17/0.44 @ ^ [Xx: $i] : $true )
% 0.17/0.44 = A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(powersetI_type,type,
% 0.17/0.44 powersetI: $o ).
% 0.17/0.44
% 0.17/0.44 thf(powersetI,definition,
% 0.17/0.44 ( powersetI
% 0.17/0.44 = ( ! [A: $i,B: $i] :
% 0.17/0.44 ( ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ B )
% 0.17/0.44 => ( in @ Xx @ A ) )
% 0.17/0.44 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(emptyinPowerset_type,type,
% 0.17/0.44 emptyinPowerset: $o ).
% 0.17/0.44
% 0.17/0.44 thf(emptyinPowerset,definition,
% 0.17/0.44 ( emptyinPowerset
% 0.17/0.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(emptyInPowerset_type,type,
% 0.17/0.44 emptyInPowerset: $o ).
% 0.17/0.44
% 0.17/0.44 thf(emptyInPowerset,definition,
% 0.17/0.44 ( emptyInPowerset
% 0.17/0.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(powersetE_type,type,
% 0.17/0.44 powersetE: $o ).
% 0.17/0.44
% 0.17/0.44 thf(powersetE,definition,
% 0.17/0.44 ( powersetE
% 0.17/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.44 ( ( in @ B @ ( powerset @ A ) )
% 0.17/0.44 => ( ( in @ Xx @ B )
% 0.17/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setunionI_type,type,
% 0.17/0.44 setunionI: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setunionI,definition,
% 0.17/0.44 ( setunionI
% 0.17/0.44 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.17/0.44 ( ( in @ Xx @ B )
% 0.17/0.44 => ( ( in @ B @ A )
% 0.17/0.44 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setunionE_type,type,
% 0.17/0.44 setunionE: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setunionE,definition,
% 0.17/0.44 ( setunionE
% 0.17/0.44 = ( ! [A: $i,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ ( setunion @ A ) )
% 0.17/0.44 => ! [Xphi: $o] :
% 0.17/0.44 ( ! [B: $i] :
% 0.17/0.44 ( ( in @ Xx @ B )
% 0.17/0.44 => ( ( in @ B @ A )
% 0.17/0.44 => Xphi ) )
% 0.17/0.44 => Xphi ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(subPowSU_type,type,
% 0.17/0.44 subPowSU: $o ).
% 0.17/0.44
% 0.17/0.44 thf(subPowSU,definition,
% 0.17/0.44 ( subPowSU
% 0.17/0.44 = ( ! [A: $i,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(exuE2_type,type,
% 0.17/0.44 exuE2: $o ).
% 0.17/0.44
% 0.17/0.44 thf(exuE2,definition,
% 0.17/0.44 ( exuE2
% 0.17/0.44 = ( ! [Xphi: $i > $o] :
% 0.17/0.44 ( ( exu
% 0.17/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.44 => ? [Xx: $i] :
% 0.17/0.44 ! [Xy: $i] :
% 0.17/0.44 ( ( Xphi @ Xy )
% 0.17/0.44 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(nonemptyImpWitness_type,type,
% 0.17/0.44 nonemptyImpWitness: $o ).
% 0.17/0.44
% 0.17/0.44 thf(nonemptyImpWitness,definition,
% 0.17/0.44 ( nonemptyImpWitness
% 0.17/0.44 = ( ! [A: $i] :
% 0.17/0.44 ( ( nonempty @ A )
% 0.17/0.44 => ? [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 & $true ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(uniqinunit_type,type,
% 0.17/0.44 uniqinunit: $o ).
% 0.17/0.44
% 0.17/0.44 thf(uniqinunit,definition,
% 0.17/0.44 ( uniqinunit
% 0.17/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.44 => ( Xx = Xy ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(notinsingleton_type,type,
% 0.17/0.44 notinsingleton: $o ).
% 0.17/0.44
% 0.17/0.44 thf(notinsingleton,definition,
% 0.17/0.44 ( notinsingleton
% 0.17/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.44 ( ( Xx != Xy )
% 0.17/0.44 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(eqinunit_type,type,
% 0.17/0.44 eqinunit: $o ).
% 0.17/0.44
% 0.17/0.44 thf(eqinunit,definition,
% 0.17/0.44 ( eqinunit
% 0.17/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.44 ( ( Xx = Xy )
% 0.17/0.44 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(singletonsswitch_type,type,
% 0.17/0.44 singletonsswitch: $o ).
% 0.17/0.44
% 0.17/0.44 thf(singletonsswitch,definition,
% 0.17/0.44 ( singletonsswitch
% 0.17/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.44 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(upairsetE_type,type,
% 0.17/0.44 upairsetE: $o ).
% 0.17/0.44
% 0.17/0.44 thf(upairsetE,definition,
% 0.17/0.44 ( upairsetE
% 0.17/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.17/0.44 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.17/0.44 => ( ( Xz = Xx )
% 0.17/0.44 | ( Xz = Xy ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(upairsetIL_type,type,
% 0.17/0.44 upairsetIL: $o ).
% 0.17/0.44
% 0.17/0.44 thf(upairsetIL,definition,
% 0.17/0.44 ( upairsetIL
% 0.17/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(upairsetIR_type,type,
% 0.17/0.44 upairsetIR: $o ).
% 0.17/0.44
% 0.17/0.44 thf(upairsetIR,definition,
% 0.17/0.44 ( upairsetIR
% 0.17/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(emptyE1_type,type,
% 0.17/0.44 emptyE1: $o ).
% 0.17/0.44
% 0.17/0.44 thf(emptyE1,definition,
% 0.17/0.44 ( emptyE1
% 0.17/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.44 ( ? [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 & ( Xphi @ Xx ) )
% 0.17/0.44 => ( ( ( dsetconstr @ A
% 0.17/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.44 = emptyset )
% 0.17/0.44 => $false ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(vacuousDall_type,type,
% 0.17/0.44 vacuousDall: $o ).
% 0.17/0.44
% 0.17/0.44 thf(vacuousDall,definition,
% 0.17/0.44 ( vacuousDall
% 0.17/0.44 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ emptyset )
% 0.17/0.44 => ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(quantDeMorgan1_type,type,
% 0.17/0.44 quantDeMorgan1: $o ).
% 0.17/0.44
% 0.17/0.44 thf(quantDeMorgan1,definition,
% 0.17/0.44 ( quantDeMorgan1
% 0.17/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.44 ( ~ ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ( Xphi @ Xx ) )
% 0.17/0.44 => ? [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(quantDeMorgan2_type,type,
% 0.17/0.44 quantDeMorgan2: $o ).
% 0.17/0.44
% 0.17/0.44 thf(quantDeMorgan2,definition,
% 0.17/0.44 ( quantDeMorgan2
% 0.17/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.44 ( ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ~ ( Xphi @ Xx ) )
% 0.17/0.44 => ~ ? [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(quantDeMorgan3_type,type,
% 0.17/0.44 quantDeMorgan3: $o ).
% 0.17/0.44
% 0.17/0.44 thf(quantDeMorgan3,definition,
% 0.17/0.44 ( quantDeMorgan3
% 0.17/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.44 ( ~ ? [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 & ( Xphi @ Xx ) )
% 0.17/0.44 => ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(quantDeMorgan4_type,type,
% 0.17/0.44 quantDeMorgan4: $o ).
% 0.17/0.44
% 0.17/0.44 thf(quantDeMorgan4,definition,
% 0.17/0.44 ( quantDeMorgan4
% 0.17/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.44 ( ? [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 & ~ ( Xphi @ Xx ) )
% 0.17/0.44 => ~ ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(prop2setI_type,type,
% 0.17/0.44 prop2setI: $o ).
% 0.17/0.44
% 0.17/0.44 thf(prop2setI,definition,
% 0.17/0.44 ( prop2setI
% 0.17/0.44 = ( ! [Xphi: $o] :
% 0.17/0.44 ( Xphi
% 0.17/0.44 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(set2prop_type,type,
% 0.17/0.44 set2prop: $i > $o ).
% 0.17/0.44
% 0.17/0.44 thf(prop2set2propI_type,type,
% 0.17/0.44 prop2set2propI: $o ).
% 0.17/0.44
% 0.17/0.44 thf(prop2set2propI,definition,
% 0.17/0.44 ( prop2set2propI
% 0.17/0.44 = ( ! [Xphi: $o] :
% 0.17/0.44 ( Xphi
% 0.17/0.44 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(notdexE_type,type,
% 0.17/0.44 notdexE: $o ).
% 0.17/0.44
% 0.17/0.44 thf(notdexE,definition,
% 0.17/0.44 ( notdexE
% 0.17/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.44 ( ~ ? [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 & ( Xphi @ Xx ) )
% 0.17/0.44 => ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(notdallE_type,type,
% 0.17/0.44 notdallE: $o ).
% 0.17/0.44
% 0.17/0.44 thf(notdallE,definition,
% 0.17/0.44 ( notdallE
% 0.17/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.44 ( ~ ! [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 => ( Xphi @ Xx ) )
% 0.17/0.44 => ? [Xx: $i] :
% 0.17/0.44 ( ( in @ Xx @ A )
% 0.17/0.44 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(exuI1_type,type,
% 0.17/0.44 exuI1: $o ).
% 0.17/0.44
% 0.17/0.44 thf(exuI1,definition,
% 0.17/0.44 ( exuI1
% 0.17/0.44 = ( ! [Xphi: $i > $o] :
% 0.17/0.44 ( ? [Xx: $i] :
% 0.17/0.44 ( ( Xphi @ Xx )
% 0.17/0.44 & ! [Xy: $i] :
% 0.17/0.44 ( ( Xphi @ Xy )
% 0.17/0.44 => ( Xx = Xy ) ) )
% 0.17/0.44 => ( exu
% 0.17/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(exuI3_type,type,
% 0.17/0.44 exuI3: $o ).
% 0.17/0.44
% 0.17/0.44 thf(exuI3,definition,
% 0.17/0.44 ( exuI3
% 0.17/0.44 = ( ! [Xphi: $i > $o] :
% 0.17/0.44 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.17/0.44 => ( ! [Xx: $i,Xy: $i] :
% 0.17/0.44 ( ( Xphi @ Xx )
% 0.17/0.44 => ( ( Xphi @ Xy )
% 0.17/0.44 => ( Xx = Xy ) ) )
% 0.17/0.44 => ( exu
% 0.17/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(exuI2_type,type,
% 0.17/0.44 exuI2: $o ).
% 0.17/0.44
% 0.17/0.44 thf(exuI2,definition,
% 0.17/0.44 ( exuI2
% 0.17/0.44 = ( ! [Xphi: $i > $o] :
% 0.17/0.44 ( ? [Xx: $i] :
% 0.17/0.44 ! [Xy: $i] :
% 0.17/0.44 ( ( Xphi @ Xy )
% 0.17/0.44 <=> ( Xy = Xx ) )
% 0.17/0.44 => ( exu
% 0.17/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(inCongP_type,type,
% 0.17/0.44 inCongP: $o ).
% 0.17/0.44
% 0.17/0.44 thf(inCongP,definition,
% 0.17/0.44 ( inCongP
% 0.17/0.44 = ( ! [A: $i,B: $i] :
% 0.17/0.44 ( ( A = B )
% 0.17/0.44 => ! [Xx: $i,Xy: $i] :
% 0.17/0.44 ( ( Xx = Xy )
% 0.17/0.44 => ( ( in @ Xx @ A )
% 0.17/0.44 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(in__Cong_type,type,
% 0.17/0.44 in__Cong: $o ).
% 0.17/0.44
% 0.17/0.44 thf(in__Cong,definition,
% 0.17/0.44 ( in__Cong
% 0.17/0.44 = ( ! [A: $i,B: $i] :
% 0.17/0.44 ( ( A = B )
% 0.17/0.44 => ! [Xx: $i,Xy: $i] :
% 0.17/0.44 ( ( Xx = Xy )
% 0.17/0.44 => ( ( in @ Xx @ A )
% 0.17/0.44 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(exuE3u_type,type,
% 0.17/0.44 exuE3u: $o ).
% 0.17/0.44
% 0.17/0.44 thf(exuE3u,definition,
% 0.17/0.44 ( exuE3u
% 0.17/0.44 = ( ! [Xphi: $i > $o] :
% 0.17/0.44 ( ( exu
% 0.17/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.44 => ! [Xx: $i,Xy: $i] :
% 0.17/0.44 ( ( Xphi @ Xx )
% 0.17/0.44 => ( ( Xphi @ Xy )
% 0.17/0.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(exu__Cong_type,type,
% 0.17/0.44 exu__Cong: $o ).
% 0.17/0.44
% 0.17/0.44 thf(exu__Cong,definition,
% 0.17/0.44 ( exu__Cong
% 0.17/0.44 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.17/0.44 ( ! [Xx: $i,Xy: $i] :
% 0.17/0.44 ( ( Xx = Xy )
% 0.17/0.44 => ( ( Xphi @ Xx )
% 0.17/0.44 <=> ( Xpsi @ Xy ) ) )
% 0.17/0.44 => ( ( exu
% 0.17/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.44 <=> ( exu
% 0.17/0.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(emptyset__Cong_type,type,
% 0.17/0.44 emptyset__Cong: $o ).
% 0.17/0.44
% 0.17/0.44 thf(emptyset__Cong,definition,
% 0.17/0.44 ( emptyset__Cong
% 0.17/0.44 = ( emptyset = emptyset ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(setadjoin__Cong_type,type,
% 0.17/0.44 setadjoin__Cong: $o ).
% 0.17/0.44
% 0.17/0.44 thf(setadjoin__Cong,definition,
% 0.17/0.44 ( setadjoin__Cong
% 0.17/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.44 ( ( Xx = Xy )
% 0.17/0.44 => ! [Xz: $i,Xu: $i] :
% 0.17/0.45 ( ( Xz = Xu )
% 0.17/0.45 => ( ( setadjoin @ Xx @ Xz )
% 0.17/0.45 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(powerset__Cong_type,type,
% 0.17/0.45 powerset__Cong: $o ).
% 0.17/0.45
% 0.17/0.45 thf(powerset__Cong,definition,
% 0.17/0.45 ( powerset__Cong
% 0.17/0.45 = ( ! [A: $i,B: $i] :
% 0.17/0.45 ( ( A = B )
% 0.17/0.45 => ( ( powerset @ A )
% 0.17/0.45 = ( powerset @ B ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(setunion__Cong_type,type,
% 0.17/0.45 setunion__Cong: $o ).
% 0.17/0.45
% 0.17/0.45 thf(setunion__Cong,definition,
% 0.17/0.45 ( setunion__Cong
% 0.17/0.45 = ( ! [A: $i,B: $i] :
% 0.17/0.45 ( ( A = B )
% 0.17/0.45 => ( ( setunion @ A )
% 0.17/0.45 = ( setunion @ B ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(omega__Cong_type,type,
% 0.17/0.45 omega__Cong: $o ).
% 0.17/0.45
% 0.17/0.45 thf(omega__Cong,definition,
% 0.17/0.45 ( omega__Cong
% 0.17/0.45 = ( omega = omega ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(exuEu_type,type,
% 0.17/0.45 exuEu: $o ).
% 0.17/0.45
% 0.17/0.45 thf(exuEu,definition,
% 0.17/0.45 ( exuEu
% 0.17/0.45 = ( ! [Xphi: $i > $o] :
% 0.17/0.45 ( ( exu
% 0.17/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.45 => ! [Xx: $i,Xy: $i] :
% 0.17/0.45 ( ( Xphi @ Xx )
% 0.17/0.45 => ( ( Xphi @ Xy )
% 0.17/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(descr__Cong_type,type,
% 0.17/0.45 descr__Cong: $o ).
% 0.17/0.45
% 0.17/0.45 thf(descr__Cong,definition,
% 0.17/0.45 ( descr__Cong
% 0.17/0.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.17/0.45 ( ! [Xx: $i,Xy: $i] :
% 0.17/0.45 ( ( Xx = Xy )
% 0.17/0.45 => ( ( Xphi @ Xx )
% 0.17/0.45 <=> ( Xpsi @ Xy ) ) )
% 0.17/0.45 => ( ( exu
% 0.17/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.45 => ( ( exu
% 0.17/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.17/0.45 => ( ( descr
% 0.17/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.45 = ( descr
% 0.17/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(dsetconstr__Cong_type,type,
% 0.17/0.45 dsetconstr__Cong: $o ).
% 0.17/0.45
% 0.17/0.45 thf(dsetconstr__Cong,definition,
% 0.17/0.45 ( dsetconstr__Cong
% 0.17/0.45 = ( ! [A: $i,B: $i] :
% 0.17/0.45 ( ( A = B )
% 0.17/0.45 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.17/0.45 ( ! [Xx: $i] :
% 0.17/0.45 ( ( in @ Xx @ A )
% 0.17/0.45 => ! [Xy: $i] :
% 0.17/0.45 ( ( in @ Xy @ B )
% 0.17/0.45 => ( ( Xx = Xy )
% 0.17/0.45 => ( ( Xphi @ Xx )
% 0.17/0.45 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.17/0.45 => ( ( dsetconstr @ A
% 0.17/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.45 = ( dsetconstr @ B
% 0.17/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(subset_type,type,
% 0.17/0.45 subset: $i > $i > $o ).
% 0.17/0.45
% 0.17/0.45 thf(disjoint_type,type,
% 0.17/0.45 disjoint: $i > $i > $o ).
% 0.17/0.45
% 0.17/0.45 thf(setsmeet_type,type,
% 0.17/0.45 setsmeet: $i > $i > $o ).
% 0.17/0.45
% 0.17/0.45 thf(subsetI1_type,type,
% 0.17/0.45 subsetI1: $o ).
% 0.17/0.45
% 0.17/0.45 thf(subsetI1,definition,
% 0.17/0.45 ( subsetI1
% 0.17/0.45 = ( ! [A: $i,B: $i] :
% 0.17/0.45 ( ! [Xx: $i] :
% 0.17/0.45 ( ( in @ Xx @ A )
% 0.17/0.45 => ( in @ Xx @ B ) )
% 0.17/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(eqimpsubset2_type,type,
% 0.17/0.45 eqimpsubset2: $o ).
% 0.17/0.45
% 0.17/0.45 thf(eqimpsubset2,definition,
% 0.17/0.45 ( eqimpsubset2
% 0.17/0.45 = ( ! [A: $i,B: $i] :
% 0.17/0.45 ( ( A = B )
% 0.17/0.45 => ( subset @ B @ A ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(eqimpsubset1_type,type,
% 0.17/0.45 eqimpsubset1: $o ).
% 0.17/0.45
% 0.17/0.45 thf(eqimpsubset1,definition,
% 0.17/0.45 ( eqimpsubset1
% 0.17/0.45 = ( ! [A: $i,B: $i] :
% 0.17/0.45 ( ( A = B )
% 0.17/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(subsetI2_type,type,
% 0.17/0.45 subsetI2: $o ).
% 0.17/0.45
% 0.17/0.45 thf(subsetI2,definition,
% 0.17/0.45 ( subsetI2
% 0.17/0.45 = ( ! [A: $i,B: $i] :
% 0.17/0.45 ( ! [Xx: $i] :
% 0.17/0.45 ( ( in @ Xx @ A )
% 0.17/0.45 => ( in @ Xx @ B ) )
% 0.17/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(emptysetsubset_type,type,
% 0.17/0.45 emptysetsubset: $o ).
% 0.17/0.45
% 0.17/0.45 thf(emptysetsubset,definition,
% 0.17/0.45 ( emptysetsubset
% 0.17/0.45 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(subsetE_type,type,
% 0.17/0.45 subsetE: $o ).
% 0.17/0.45
% 0.17/0.45 thf(subsetE,definition,
% 0.17/0.45 ( subsetE
% 0.17/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.45 ( ( subset @ A @ B )
% 0.17/0.45 => ( ( in @ Xx @ A )
% 0.17/0.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(subsetE2_type,type,
% 0.17/0.45 subsetE2: $o ).
% 0.17/0.45
% 0.17/0.45 thf(subsetE2,definition,
% 0.17/0.45 ( subsetE2
% 0.17/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.45 ( ( subset @ A @ B )
% 0.17/0.45 => ( ~ ( in @ Xx @ B )
% 0.17/0.45 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(notsubsetI_type,type,
% 0.17/0.45 notsubsetI: $o ).
% 0.17/0.45
% 0.17/0.45 thf(notsubsetI,definition,
% 0.17/0.45 ( notsubsetI
% 0.17/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.45 ( ( in @ Xx @ A )
% 0.17/0.45 => ( ~ ( in @ Xx @ B )
% 0.17/0.45 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(notequalI1_type,type,
% 0.17/0.45 notequalI1: $o ).
% 0.17/0.45
% 0.17/0.45 thf(notequalI1,definition,
% 0.17/0.45 ( notequalI1
% 0.17/0.45 = ( ! [A: $i,B: $i] :
% 0.17/0.45 ( ~ ( subset @ A @ B )
% 0.17/0.45 => ( A != B ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(notequalI2_type,type,
% 0.17/0.45 notequalI2: $o ).
% 0.17/0.45
% 0.17/0.45 thf(notequalI2,definition,
% 0.17/0.45 ( notequalI2
% 0.17/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.45 ( ( in @ Xx @ A )
% 0.17/0.45 => ( ~ ( in @ Xx @ B )
% 0.17/0.45 => ( A != B ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(subsetRefl_type,type,
% 0.17/0.45 subsetRefl: $o ).
% 0.17/0.45
% 0.17/0.45 thf(subsetRefl,definition,
% 0.17/0.45 ( subsetRefl
% 0.17/0.45 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(subsetTrans_type,type,
% 0.17/0.45 subsetTrans: $o ).
% 0.17/0.45
% 0.17/0.45 thf(subsetTrans,definition,
% 0.17/0.45 ( subsetTrans
% 0.17/0.45 = ( ! [A: $i,B: $i,C: $i] :
% 0.17/0.45 ( ( subset @ A @ B )
% 0.17/0.45 => ( ( subset @ B @ C )
% 0.17/0.45 => ( subset @ A @ C ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(setadjoinSub_type,type,
% 0.17/0.45 setadjoinSub: $o ).
% 0.17/0.45
% 0.17/0.45 thf(setadjoinSub,definition,
% 0.17/0.45 ( setadjoinSub
% 0.17/0.45 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(setadjoinSub2_type,type,
% 0.17/0.45 setadjoinSub2: $o ).
% 0.17/0.45
% 0.17/0.45 thf(setadjoinSub2,definition,
% 0.17/0.45 ( setadjoinSub2
% 0.17/0.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.17/0.45 ( ( subset @ A @ B )
% 0.17/0.45 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(subset2powerset_type,type,
% 0.17/0.45 subset2powerset: $o ).
% 0.17/0.45
% 0.17/0.45 thf(subset2powerset,definition,
% 0.17/0.45 ( subset2powerset
% 0.17/0.45 = ( ! [A: $i,B: $i] :
% 0.17/0.45 ( ( subset @ A @ B )
% 0.17/0.45 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(setextsub_type,type,
% 0.17/0.45 setextsub: $o ).
% 0.17/0.45
% 0.17/0.45 thf(setextsub,definition,
% 0.17/0.45 ( setextsub
% 0.17/0.45 = ( ! [A: $i,B: $i] :
% 0.17/0.45 ( ( subset @ A @ B )
% 0.17/0.45 => ( ( subset @ B @ A )
% 0.17/0.45 => ( A = B ) ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(subsetemptysetimpeq_type,type,
% 0.17/0.45 subsetemptysetimpeq: $o ).
% 0.17/0.45
% 0.17/0.45 thf(subsetemptysetimpeq,definition,
% 0.17/0.45 ( subsetemptysetimpeq
% 0.17/0.45 = ( ! [A: $i] :
% 0.17/0.45 ( ( subset @ A @ emptyset )
% 0.17/0.45 => ( A = emptyset ) ) ) ) ).
% 0.17/0.45
% 0.17/0.45 thf(powersetI1_type,type,
% 0.17/0.45 powersetI1: $o ).
% 0.17/0.45
% 0.17/0.45 thf(powersetI1,definition,
% 0.17/0.45 ( powersetI1
% 0.17/0.45 = ( ! [A: $i,B: $i] :
% 0.17/0.45 ( ( subset @ B @ A )
% 0.17/0.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(powersetE1_type,type,
% 0.28/0.45 powersetE1: $o ).
% 0.28/0.45
% 0.28/0.45 thf(powersetE1,definition,
% 0.28/0.45 ( powersetE1
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.45 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(inPowerset_type,type,
% 0.28/0.45 inPowerset: $o ).
% 0.28/0.45
% 0.28/0.45 thf(inPowerset,definition,
% 0.28/0.45 ( inPowerset
% 0.28/0.45 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(powersetsubset_type,type,
% 0.28/0.45 powersetsubset: $o ).
% 0.28/0.45
% 0.28/0.45 thf(powersetsubset,definition,
% 0.28/0.45 ( powersetsubset
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( subset @ A @ B )
% 0.28/0.45 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sepInPowerset_type,type,
% 0.28/0.45 sepInPowerset: $o ).
% 0.28/0.45
% 0.28/0.45 thf(sepInPowerset,definition,
% 0.28/0.45 ( sepInPowerset
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.45 ( in
% 0.28/0.45 @ ( dsetconstr @ A
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 @ ( powerset @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sepSubset_type,type,
% 0.28/0.45 sepSubset: $o ).
% 0.28/0.45
% 0.28/0.45 thf(sepSubset,definition,
% 0.28/0.45 ( sepSubset
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.45 ( subset
% 0.28/0.45 @ ( dsetconstr @ A
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(binunion_type,type,
% 0.28/0.45 binunion: $i > $i > $i ).
% 0.28/0.45
% 0.28/0.45 thf(binunion,definition,
% 0.28/0.45 ( binunion
% 0.28/0.45 = ( ^ [Xx: $i,Xy: $i] : ( setunion @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(binunionIL,conjecture,
% 0.28/0.45 ( setextAx
% 0.28/0.45 => ( emptysetAx
% 0.28/0.45 => ( setadjoinAx
% 0.28/0.45 => ( powersetAx
% 0.28/0.45 => ( setunionAx
% 0.28/0.45 => ( omega0Ax
% 0.28/0.45 => ( omegaSAx
% 0.28/0.45 => ( omegaIndAx
% 0.28/0.45 => ( replAx
% 0.28/0.45 => ( foundationAx
% 0.28/0.45 => ( wellorderingAx
% 0.28/0.45 => ( descrp
% 0.28/0.45 => ( dsetconstrI
% 0.28/0.45 => ( dsetconstrEL
% 0.28/0.45 => ( dsetconstrER
% 0.28/0.45 => ( exuE1
% 0.28/0.45 => ( prop2setE
% 0.28/0.45 => ( emptysetE
% 0.28/0.45 => ( emptysetimpfalse
% 0.28/0.45 => ( notinemptyset
% 0.28/0.45 => ( exuE3e
% 0.28/0.45 => ( setext
% 0.28/0.45 => ( emptyI
% 0.28/0.45 => ( noeltsimpempty
% 0.28/0.45 => ( setbeta
% 0.28/0.45 => ( nonemptyE1
% 0.28/0.45 => ( nonemptyI
% 0.28/0.45 => ( nonemptyI1
% 0.28/0.45 => ( setadjoinIL
% 0.28/0.45 => ( emptyinunitempty
% 0.28/0.45 => ( setadjoinIR
% 0.28/0.45 => ( setadjoinE
% 0.28/0.45 => ( setadjoinOr
% 0.28/0.45 => ( setoftrueEq
% 0.28/0.45 => ( powersetI
% 0.28/0.45 => ( emptyinPowerset
% 0.28/0.45 => ( emptyInPowerset
% 0.28/0.45 => ( powersetE
% 0.28/0.45 => ( setunionI
% 0.28/0.45 => ( setunionE
% 0.28/0.45 => ( subPowSU
% 0.28/0.45 => ( exuE2
% 0.28/0.45 => ( nonemptyImpWitness
% 0.28/0.45 => ( uniqinunit
% 0.28/0.45 => ( notinsingleton
% 0.28/0.45 => ( eqinunit
% 0.28/0.45 => ( singletonsswitch
% 0.28/0.45 => ( upairsetE
% 0.28/0.45 => ( upairsetIL
% 0.28/0.45 => ( upairsetIR
% 0.28/0.45 => ( emptyE1
% 0.28/0.45 => ( vacuousDall
% 0.28/0.45 => ( quantDeMorgan1
% 0.28/0.45 => ( quantDeMorgan2
% 0.28/0.45 => ( quantDeMorgan3
% 0.28/0.45 => ( quantDeMorgan4
% 0.28/0.45 => ( prop2setI
% 0.28/0.45 => ( prop2set2propI
% 0.28/0.45 => ( notdexE
% 0.28/0.45 => ( notdallE
% 0.28/0.45 => ( exuI1
% 0.28/0.45 => ( exuI3
% 0.28/0.45 => ( exuI2
% 0.28/0.45 => ( inCongP
% 0.28/0.45 => ( in__Cong
% 0.28/0.45 => ( exuE3u
% 0.28/0.45 => ( exu__Cong
% 0.28/0.45 => ( emptyset__Cong
% 0.28/0.45 => ( setadjoin__Cong
% 0.28/0.45 => ( powerset__Cong
% 0.28/0.45 => ( setunion__Cong
% 0.28/0.45 => ( omega__Cong
% 0.28/0.45 => ( exuEu
% 0.28/0.45 => ( descr__Cong
% 0.28/0.45 => ( dsetconstr__Cong
% 0.28/0.45 => ( subsetI1
% 0.28/0.45 => ( eqimpsubset2
% 0.28/0.45 => ( eqimpsubset1
% 0.28/0.45 => ( subsetI2
% 0.28/0.45 => ( emptysetsubset
% 0.28/0.45 => ( subsetE
% 0.28/0.45 => ( subsetE2
% 0.28/0.45 => ( notsubsetI
% 0.28/0.45 => ( notequalI1
% 0.28/0.45 => ( notequalI2
% 0.28/0.45 => ( subsetRefl
% 0.28/0.45 => ( subsetTrans
% 0.28/0.45 => ( setadjoinSub
% 0.28/0.45 => ( setadjoinSub2
% 0.28/0.45 => ( subset2powerset
% 0.28/0.45 => ( setextsub
% 0.28/0.45 => ( subsetemptysetimpeq
% 0.28/0.45 => ( powersetI1
% 0.28/0.45 => ( powersetE1
% 0.28/0.45 => ( inPowerset
% 0.28/0.45 => ( powersetsubset
% 0.28/0.45 => ( sepInPowerset
% 0.28/0.45 => ( sepSubset
% 0.28/0.45 => ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 ------------------------
% 2.06/1.36 ---- Embedded in THF ---
% 2.06/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.06/1.36 %%% Generated on Tue Feb 24 12:27:40 EST 2026
% 2.06/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 2.06/1.36 %%% Logic specification used:
% 2.06/1.36 %%% thf(spec, logic, $$dhol).
% 2.06/1.36
% 2.06/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OQI6VlFTuB/DTF2DTF23036.p
% See solution above
% 2.06/1.36 ------------------------
% 2.06/1.39 ---- Cleaned THF ---
% 2.06/1.39 thf(in_type,type,
% 2.06/1.39 in: $i > $i > $o ).
% 2.06/1.39
% 2.06/1.39 thf(exu_type,type,
% 2.06/1.39 exu: ( $i > $o ) > $o ).
% 2.06/1.39
% 2.06/1.39 thf(exu,definition,
% 2.06/1.39 ( exu
% 2.06/1.39 = ( ^ [Xphi: $i > $o] :
% 2.06/1.39 ? [Xx: $i] :
% 2.06/1.39 ( ( Xphi @ Xx )
% 2.06/1.39 & ! [Xy: $i] :
% 2.06/1.39 ( ( Xphi @ Xy )
% 2.06/1.39 => ( Xx = Xy ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setextAx_type,type,
% 2.06/1.39 setextAx: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setextAx,definition,
% 2.06/1.39 ( setextAx
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 <=> ( in @ Xx @ B ) )
% 2.06/1.39 => ( A = B ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(emptyset_type,type,
% 2.06/1.39 emptyset: $i ).
% 2.06/1.39
% 2.06/1.39 thf(emptysetAx_type,type,
% 2.06/1.39 emptysetAx: $o ).
% 2.06/1.39
% 2.06/1.39 thf(emptysetAx,definition,
% 2.06/1.39 ( emptysetAx
% 2.06/1.39 = ( ! [Xx: $i] :
% 2.06/1.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoin_type,type,
% 2.06/1.39 setadjoin: $i > $i > $i ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinAx_type,type,
% 2.06/1.39 setadjoinAx: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinAx,definition,
% 2.06/1.39 ( setadjoinAx
% 2.06/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.06/1.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.06/1.39 <=> ( ( Xy = Xx )
% 2.06/1.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(powerset_type,type,
% 2.06/1.39 powerset: $i > $i ).
% 2.06/1.39
% 2.06/1.39 thf(powersetAx_type,type,
% 2.06/1.39 powersetAx: $o ).
% 2.06/1.39
% 2.06/1.39 thf(powersetAx,definition,
% 2.06/1.39 ( powersetAx
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ( in @ B @ ( powerset @ A ) )
% 2.06/1.39 <=> ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ B )
% 2.06/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setunion_type,type,
% 2.06/1.39 setunion: $i > $i ).
% 2.06/1.39
% 2.06/1.39 thf(setunionAx_type,type,
% 2.06/1.39 setunionAx: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setunionAx,definition,
% 2.06/1.39 ( setunionAx
% 2.06/1.39 = ( ! [A: $i,Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ ( setunion @ A ) )
% 2.06/1.39 <=> ? [B: $i] :
% 2.06/1.39 ( ( in @ Xx @ B )
% 2.06/1.39 & ( in @ B @ A ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(omega_type,type,
% 2.06/1.39 omega: $i ).
% 2.06/1.39
% 2.06/1.39 thf(omega0Ax_type,type,
% 2.06/1.39 omega0Ax: $o ).
% 2.06/1.39
% 2.06/1.39 thf(omega0Ax,definition,
% 2.06/1.39 ( omega0Ax
% 2.06/1.39 = ( in @ emptyset @ omega ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(omegaSAx_type,type,
% 2.06/1.39 omegaSAx: $o ).
% 2.06/1.39
% 2.06/1.39 thf(omegaSAx,definition,
% 2.06/1.39 ( omegaSAx
% 2.06/1.39 = ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ omega )
% 2.06/1.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(omegaIndAx_type,type,
% 2.06/1.39 omegaIndAx: $o ).
% 2.06/1.39
% 2.06/1.39 thf(omegaIndAx,definition,
% 2.06/1.39 ( omegaIndAx
% 2.06/1.39 = ( ! [A: $i] :
% 2.06/1.39 ( ( ( in @ emptyset @ A )
% 2.06/1.39 & ! [Xx: $i] :
% 2.06/1.39 ( ( ( in @ Xx @ omega )
% 2.06/1.39 & ( in @ Xx @ A ) )
% 2.06/1.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.06/1.39 => ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ omega )
% 2.06/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(replAx_type,type,
% 2.06/1.39 replAx: $o ).
% 2.06/1.39
% 2.06/1.39 thf(replAx,definition,
% 2.06/1.39 ( replAx
% 2.06/1.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.06/1.39 ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( exu
% 2.06/1.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.06/1.39 => ? [B: $i] :
% 2.06/1.39 ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ B )
% 2.06/1.39 <=> ? [Xy: $i] :
% 2.06/1.39 ( ( in @ Xy @ A )
% 2.06/1.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(foundationAx_type,type,
% 2.06/1.39 foundationAx: $o ).
% 2.06/1.39
% 2.06/1.39 thf(foundationAx,definition,
% 2.06/1.39 ( foundationAx
% 2.06/1.39 = ( ! [A: $i] :
% 2.06/1.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.06/1.39 => ? [B: $i] :
% 2.06/1.39 ( ( in @ B @ A )
% 2.06/1.39 & ~ ? [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ B )
% 2.06/1.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(wellorderingAx_type,type,
% 2.06/1.39 wellorderingAx: $o ).
% 2.06/1.39
% 2.06/1.39 thf(wellorderingAx,definition,
% 2.06/1.39 ( wellorderingAx
% 2.06/1.39 = ( ! [A: $i] :
% 2.06/1.39 ? [B: $i] :
% 2.06/1.39 ( ! [C: $i] :
% 2.06/1.39 ( ( in @ C @ B )
% 2.06/1.39 => ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ C )
% 2.06/1.39 => ( in @ Xx @ A ) ) )
% 2.06/1.39 & ! [Xx: $i,Xy: $i] :
% 2.06/1.39 ( ( ( in @ Xx @ A )
% 2.06/1.39 & ( in @ Xy @ A ) )
% 2.06/1.39 => ( ! [C: $i] :
% 2.06/1.39 ( ( in @ C @ B )
% 2.06/1.39 => ( ( in @ Xx @ C )
% 2.06/1.39 <=> ( in @ Xy @ C ) ) )
% 2.06/1.39 => ( Xx = Xy ) ) )
% 2.06/1.39 & ! [C: $i,D: $i] :
% 2.06/1.39 ( ( ( in @ C @ B )
% 2.06/1.39 & ( in @ D @ B ) )
% 2.06/1.39 => ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ C )
% 2.06/1.39 => ( in @ Xx @ D ) )
% 2.06/1.39 | ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ D )
% 2.06/1.39 => ( in @ Xx @ C ) ) ) )
% 2.06/1.39 & ! [C: $i] :
% 2.06/1.39 ( ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ C )
% 2.06/1.39 => ( in @ Xx @ A ) )
% 2.06/1.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.06/1.39 => ? [D: $i,Xx: $i] :
% 2.06/1.39 ( ( in @ D @ B )
% 2.06/1.39 & ( in @ Xx @ C )
% 2.06/1.39 & ~ ? [Xy: $i] :
% 2.06/1.39 ( ( in @ Xy @ D )
% 2.06/1.39 & ( in @ Xy @ C ) )
% 2.06/1.39 & ! [E: $i] :
% 2.06/1.39 ( ( in @ E @ B )
% 2.06/1.39 => ( ! [Xy: $i] :
% 2.06/1.39 ( ( in @ Xy @ E )
% 2.06/1.39 => ( in @ Xy @ D ) )
% 2.06/1.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(descr_type,type,
% 2.06/1.39 descr: ( $i > $o ) > $i ).
% 2.06/1.39
% 2.06/1.39 thf(descrp_type,type,
% 2.06/1.39 descrp: $o ).
% 2.06/1.39
% 2.06/1.39 thf(descrp,definition,
% 2.06/1.39 ( descrp
% 2.06/1.39 = ( ! [Xphi: $i > $o] :
% 2.06/1.39 ( ( exu
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.39 => ( Xphi
% 2.06/1.39 @ ( descr
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(dsetconstr_type,type,
% 2.06/1.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.06/1.39
% 2.06/1.39 thf(dsetconstrI_type,type,
% 2.06/1.39 dsetconstrI: $o ).
% 2.06/1.39
% 2.06/1.39 thf(dsetconstrI,definition,
% 2.06/1.39 ( dsetconstrI
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( ( Xphi @ Xx )
% 2.06/1.39 => ( in @ Xx
% 2.06/1.39 @ ( dsetconstr @ A
% 2.06/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(dsetconstrEL_type,type,
% 2.06/1.39 dsetconstrEL: $o ).
% 2.06/1.39
% 2.06/1.39 thf(dsetconstrEL,definition,
% 2.06/1.39 ( dsetconstrEL
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.06/1.39 ( ( in @ Xx
% 2.06/1.39 @ ( dsetconstr @ A
% 2.06/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.06/1.39 => ( in @ Xx @ A ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(dsetconstrER_type,type,
% 2.06/1.39 dsetconstrER: $o ).
% 2.06/1.39
% 2.06/1.39 thf(dsetconstrER,definition,
% 2.06/1.39 ( dsetconstrER
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.06/1.39 ( ( in @ Xx
% 2.06/1.39 @ ( dsetconstr @ A
% 2.06/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.06/1.39 => ( Xphi @ Xx ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(exuE1_type,type,
% 2.06/1.39 exuE1: $o ).
% 2.06/1.39
% 2.06/1.39 thf(exuE1,definition,
% 2.06/1.39 ( exuE1
% 2.06/1.39 = ( ! [Xphi: $i > $o] :
% 2.06/1.39 ( ( exu
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.39 => ? [Xx: $i] :
% 2.06/1.39 ( ( Xphi @ Xx )
% 2.06/1.39 & ! [Xy: $i] :
% 2.06/1.39 ( ( Xphi @ Xy )
% 2.06/1.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(prop2set_type,type,
% 2.06/1.39 prop2set: $o > $i ).
% 2.06/1.39
% 2.06/1.39 thf(prop2setE_type,type,
% 2.06/1.39 prop2setE: $o ).
% 2.06/1.39
% 2.06/1.39 thf(prop2setE,definition,
% 2.06/1.39 ( prop2setE
% 2.06/1.39 = ( ! [Xphi: $o,Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.06/1.39 => Xphi ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(emptysetE_type,type,
% 2.06/1.39 emptysetE: $o ).
% 2.06/1.39
% 2.06/1.39 thf(emptysetE,definition,
% 2.06/1.39 ( emptysetE
% 2.06/1.39 = ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ emptyset )
% 2.06/1.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(emptysetimpfalse_type,type,
% 2.06/1.39 emptysetimpfalse: $o ).
% 2.06/1.39
% 2.06/1.39 thf(emptysetimpfalse,definition,
% 2.06/1.39 ( emptysetimpfalse
% 2.06/1.39 = ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ emptyset )
% 2.06/1.39 => $false ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(notinemptyset_type,type,
% 2.06/1.39 notinemptyset: $o ).
% 2.06/1.39
% 2.06/1.39 thf(notinemptyset,definition,
% 2.06/1.39 ( notinemptyset
% 2.06/1.39 = ( ! [Xx: $i] :
% 2.06/1.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(exuE3e_type,type,
% 2.06/1.39 exuE3e: $o ).
% 2.06/1.39
% 2.06/1.39 thf(exuE3e,definition,
% 2.06/1.39 ( exuE3e
% 2.06/1.39 = ( ! [Xphi: $i > $o] :
% 2.06/1.39 ( ( exu
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setext_type,type,
% 2.06/1.39 setext: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setext,definition,
% 2.06/1.39 ( setext
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( in @ Xx @ B ) )
% 2.06/1.39 => ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ B )
% 2.06/1.39 => ( in @ Xx @ A ) )
% 2.06/1.39 => ( A = B ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(emptyI_type,type,
% 2.06/1.39 emptyI: $o ).
% 2.06/1.39
% 2.06/1.39 thf(emptyI,definition,
% 2.06/1.39 ( emptyI
% 2.06/1.39 = ( ! [A: $i] :
% 2.06/1.39 ( ! [Xx: $i] :
% 2.06/1.39 ~ ( in @ Xx @ A )
% 2.06/1.39 => ( A = emptyset ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(noeltsimpempty_type,type,
% 2.06/1.39 noeltsimpempty: $o ).
% 2.06/1.39
% 2.06/1.39 thf(noeltsimpempty,definition,
% 2.06/1.39 ( noeltsimpempty
% 2.06/1.39 = ( ! [A: $i] :
% 2.06/1.39 ( ! [Xx: $i] :
% 2.06/1.39 ~ ( in @ Xx @ A )
% 2.06/1.39 => ( A = emptyset ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setbeta_type,type,
% 2.06/1.39 setbeta: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setbeta,definition,
% 2.06/1.39 ( setbeta
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( ( in @ Xx
% 2.06/1.39 @ ( dsetconstr @ A
% 2.06/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.06/1.39 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(nonempty_type,type,
% 2.06/1.39 nonempty: $i > $o ).
% 2.06/1.39
% 2.06/1.39 thf(nonempty,definition,
% 2.06/1.39 ( nonempty
% 2.06/1.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(nonemptyE1_type,type,
% 2.06/1.39 nonemptyE1: $o ).
% 2.06/1.39
% 2.06/1.39 thf(nonemptyE1,definition,
% 2.06/1.39 ( nonemptyE1
% 2.06/1.39 = ( ! [A: $i] :
% 2.06/1.39 ( ( nonempty @ A )
% 2.06/1.39 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(nonemptyI_type,type,
% 2.06/1.39 nonemptyI: $o ).
% 2.06/1.39
% 2.06/1.39 thf(nonemptyI,definition,
% 2.06/1.39 ( nonemptyI
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( ( Xphi @ Xx )
% 2.06/1.39 => ( nonempty
% 2.06/1.39 @ ( dsetconstr @ A
% 2.06/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(nonemptyI1_type,type,
% 2.06/1.39 nonemptyI1: $o ).
% 2.06/1.39
% 2.06/1.39 thf(nonemptyI1,definition,
% 2.06/1.39 ( nonemptyI1
% 2.06/1.39 = ( ! [A: $i] :
% 2.06/1.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.06/1.39 => ( nonempty @ A ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinIL_type,type,
% 2.06/1.39 setadjoinIL: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinIL,definition,
% 2.06/1.39 ( setadjoinIL
% 2.06/1.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(emptyinunitempty_type,type,
% 2.06/1.39 emptyinunitempty: $o ).
% 2.06/1.39
% 2.06/1.39 thf(emptyinunitempty,definition,
% 2.06/1.39 ( emptyinunitempty
% 2.06/1.39 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinIR_type,type,
% 2.06/1.39 setadjoinIR: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinIR,definition,
% 2.06/1.39 ( setadjoinIR
% 2.06/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.06/1.39 ( ( in @ Xy @ A )
% 2.06/1.39 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinE_type,type,
% 2.06/1.39 setadjoinE: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinE,definition,
% 2.06/1.39 ( setadjoinE
% 2.06/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.06/1.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.06/1.39 => ! [Xphi: $o] :
% 2.06/1.39 ( ( ( Xy = Xx )
% 2.06/1.39 => Xphi )
% 2.06/1.39 => ( ( ( in @ Xy @ A )
% 2.06/1.39 => Xphi )
% 2.06/1.39 => Xphi ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinOr_type,type,
% 2.06/1.39 setadjoinOr: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinOr,definition,
% 2.06/1.39 ( setadjoinOr
% 2.06/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.06/1.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.06/1.39 => ( ( Xy = Xx )
% 2.06/1.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setoftrueEq_type,type,
% 2.06/1.39 setoftrueEq: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setoftrueEq,definition,
% 2.06/1.39 ( setoftrueEq
% 2.06/1.39 = ( ! [A: $i] :
% 2.06/1.39 ( ( dsetconstr @ A
% 2.06/1.39 @ ^ [Xx: $i] : $true )
% 2.06/1.39 = A ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(powersetI_type,type,
% 2.06/1.39 powersetI: $o ).
% 2.06/1.39
% 2.06/1.39 thf(powersetI,definition,
% 2.06/1.39 ( powersetI
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ B )
% 2.06/1.39 => ( in @ Xx @ A ) )
% 2.06/1.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(emptyinPowerset_type,type,
% 2.06/1.39 emptyinPowerset: $o ).
% 2.06/1.39
% 2.06/1.39 thf(emptyinPowerset,definition,
% 2.06/1.39 ( emptyinPowerset
% 2.06/1.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(emptyInPowerset_type,type,
% 2.06/1.39 emptyInPowerset: $o ).
% 2.06/1.39
% 2.06/1.39 thf(emptyInPowerset,definition,
% 2.06/1.39 ( emptyInPowerset
% 2.06/1.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(powersetE_type,type,
% 2.06/1.39 powersetE: $o ).
% 2.06/1.39
% 2.06/1.39 thf(powersetE,definition,
% 2.06/1.39 ( powersetE
% 2.06/1.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.06/1.39 ( ( in @ B @ ( powerset @ A ) )
% 2.06/1.39 => ( ( in @ Xx @ B )
% 2.06/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setunionI_type,type,
% 2.06/1.39 setunionI: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setunionI,definition,
% 2.06/1.39 ( setunionI
% 2.06/1.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.06/1.39 ( ( in @ Xx @ B )
% 2.06/1.39 => ( ( in @ B @ A )
% 2.06/1.39 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setunionE_type,type,
% 2.06/1.39 setunionE: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setunionE,definition,
% 2.06/1.39 ( setunionE
% 2.06/1.39 = ( ! [A: $i,Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ ( setunion @ A ) )
% 2.06/1.39 => ! [Xphi: $o] :
% 2.06/1.39 ( ! [B: $i] :
% 2.06/1.39 ( ( in @ Xx @ B )
% 2.06/1.39 => ( ( in @ B @ A )
% 2.06/1.39 => Xphi ) )
% 2.06/1.39 => Xphi ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(subPowSU_type,type,
% 2.06/1.39 subPowSU: $o ).
% 2.06/1.39
% 2.06/1.39 thf(subPowSU,definition,
% 2.06/1.39 ( subPowSU
% 2.06/1.39 = ( ! [A: $i,Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(exuE2_type,type,
% 2.06/1.39 exuE2: $o ).
% 2.06/1.39
% 2.06/1.39 thf(exuE2,definition,
% 2.06/1.39 ( exuE2
% 2.06/1.39 = ( ! [Xphi: $i > $o] :
% 2.06/1.39 ( ( exu
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.39 => ? [Xx: $i] :
% 2.06/1.39 ! [Xy: $i] :
% 2.06/1.39 ( ( Xphi @ Xy )
% 2.06/1.39 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(nonemptyImpWitness_type,type,
% 2.06/1.39 nonemptyImpWitness: $o ).
% 2.06/1.39
% 2.06/1.39 thf(nonemptyImpWitness,definition,
% 2.06/1.39 ( nonemptyImpWitness
% 2.06/1.39 = ( ! [A: $i] :
% 2.06/1.39 ( ( nonempty @ A )
% 2.06/1.39 => ? [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 & $true ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(uniqinunit_type,type,
% 2.06/1.39 uniqinunit: $o ).
% 2.06/1.39
% 2.06/1.39 thf(uniqinunit,definition,
% 2.06/1.39 ( uniqinunit
% 2.06/1.39 = ( ! [Xx: $i,Xy: $i] :
% 2.06/1.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.06/1.39 => ( Xx = Xy ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(notinsingleton_type,type,
% 2.06/1.39 notinsingleton: $o ).
% 2.06/1.39
% 2.06/1.39 thf(notinsingleton,definition,
% 2.06/1.39 ( notinsingleton
% 2.06/1.39 = ( ! [Xx: $i,Xy: $i] :
% 2.06/1.39 ( ( Xx != Xy )
% 2.06/1.39 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(eqinunit_type,type,
% 2.06/1.39 eqinunit: $o ).
% 2.06/1.39
% 2.06/1.39 thf(eqinunit,definition,
% 2.06/1.39 ( eqinunit
% 2.06/1.39 = ( ! [Xx: $i,Xy: $i] :
% 2.06/1.39 ( ( Xx = Xy )
% 2.06/1.39 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(singletonsswitch_type,type,
% 2.06/1.39 singletonsswitch: $o ).
% 2.06/1.39
% 2.06/1.39 thf(singletonsswitch,definition,
% 2.06/1.39 ( singletonsswitch
% 2.06/1.39 = ( ! [Xx: $i,Xy: $i] :
% 2.06/1.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.06/1.39 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(upairsetE_type,type,
% 2.06/1.39 upairsetE: $o ).
% 2.06/1.39
% 2.06/1.39 thf(upairsetE,definition,
% 2.06/1.39 ( upairsetE
% 2.06/1.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.06/1.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.06/1.39 => ( ( Xz = Xx )
% 2.06/1.39 | ( Xz = Xy ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(upairsetIL_type,type,
% 2.06/1.39 upairsetIL: $o ).
% 2.06/1.39
% 2.06/1.39 thf(upairsetIL,definition,
% 2.06/1.39 ( upairsetIL
% 2.06/1.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(upairsetIR_type,type,
% 2.06/1.39 upairsetIR: $o ).
% 2.06/1.39
% 2.06/1.39 thf(upairsetIR,definition,
% 2.06/1.39 ( upairsetIR
% 2.06/1.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(emptyE1_type,type,
% 2.06/1.39 emptyE1: $o ).
% 2.06/1.39
% 2.06/1.39 thf(emptyE1,definition,
% 2.06/1.39 ( emptyE1
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 2.06/1.39 ( ? [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 & ( Xphi @ Xx ) )
% 2.06/1.39 => ( ( ( dsetconstr @ A
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.39 = emptyset )
% 2.06/1.39 => $false ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(vacuousDall_type,type,
% 2.06/1.39 vacuousDall: $o ).
% 2.06/1.39
% 2.06/1.39 thf(vacuousDall,definition,
% 2.06/1.39 ( vacuousDall
% 2.06/1.39 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ emptyset )
% 2.06/1.39 => ( Xphi @ Xx ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(quantDeMorgan1_type,type,
% 2.06/1.39 quantDeMorgan1: $o ).
% 2.06/1.39
% 2.06/1.39 thf(quantDeMorgan1,definition,
% 2.06/1.39 ( quantDeMorgan1
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 2.06/1.39 ( ~ ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( Xphi @ Xx ) )
% 2.06/1.39 => ? [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(quantDeMorgan2_type,type,
% 2.06/1.39 quantDeMorgan2: $o ).
% 2.06/1.39
% 2.06/1.39 thf(quantDeMorgan2,definition,
% 2.06/1.39 ( quantDeMorgan2
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 2.06/1.39 ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ~ ( Xphi @ Xx ) )
% 2.06/1.39 => ~ ? [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(quantDeMorgan3_type,type,
% 2.06/1.39 quantDeMorgan3: $o ).
% 2.06/1.39
% 2.06/1.39 thf(quantDeMorgan3,definition,
% 2.06/1.39 ( quantDeMorgan3
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 2.06/1.39 ( ~ ? [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 & ( Xphi @ Xx ) )
% 2.06/1.39 => ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(quantDeMorgan4_type,type,
% 2.06/1.39 quantDeMorgan4: $o ).
% 2.06/1.39
% 2.06/1.39 thf(quantDeMorgan4,definition,
% 2.06/1.39 ( quantDeMorgan4
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 2.06/1.39 ( ? [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 & ~ ( Xphi @ Xx ) )
% 2.06/1.39 => ~ ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(prop2setI_type,type,
% 2.06/1.39 prop2setI: $o ).
% 2.06/1.39
% 2.06/1.39 thf(prop2setI,definition,
% 2.06/1.39 ( prop2setI
% 2.06/1.39 = ( ! [Xphi: $o] :
% 2.06/1.39 ( Xphi
% 2.06/1.39 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(set2prop_type,type,
% 2.06/1.39 set2prop: $i > $o ).
% 2.06/1.39
% 2.06/1.39 thf(prop2set2propI_type,type,
% 2.06/1.39 prop2set2propI: $o ).
% 2.06/1.39
% 2.06/1.39 thf(prop2set2propI,definition,
% 2.06/1.39 ( prop2set2propI
% 2.06/1.39 = ( ! [Xphi: $o] :
% 2.06/1.39 ( Xphi
% 2.06/1.39 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(notdexE_type,type,
% 2.06/1.39 notdexE: $o ).
% 2.06/1.39
% 2.06/1.39 thf(notdexE,definition,
% 2.06/1.39 ( notdexE
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 2.06/1.39 ( ~ ? [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 & ( Xphi @ Xx ) )
% 2.06/1.39 => ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(notdallE_type,type,
% 2.06/1.39 notdallE: $o ).
% 2.06/1.39
% 2.06/1.39 thf(notdallE,definition,
% 2.06/1.39 ( notdallE
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 2.06/1.39 ( ~ ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( Xphi @ Xx ) )
% 2.06/1.39 => ? [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(exuI1_type,type,
% 2.06/1.39 exuI1: $o ).
% 2.06/1.39
% 2.06/1.39 thf(exuI1,definition,
% 2.06/1.39 ( exuI1
% 2.06/1.39 = ( ! [Xphi: $i > $o] :
% 2.06/1.39 ( ? [Xx: $i] :
% 2.06/1.39 ( ( Xphi @ Xx )
% 2.06/1.39 & ! [Xy: $i] :
% 2.06/1.39 ( ( Xphi @ Xy )
% 2.06/1.39 => ( Xx = Xy ) ) )
% 2.06/1.39 => ( exu
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(exuI3_type,type,
% 2.06/1.39 exuI3: $o ).
% 2.06/1.39
% 2.06/1.39 thf(exuI3,definition,
% 2.06/1.39 ( exuI3
% 2.06/1.39 = ( ! [Xphi: $i > $o] :
% 2.06/1.39 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.06/1.39 => ( ! [Xx: $i,Xy: $i] :
% 2.06/1.39 ( ( Xphi @ Xx )
% 2.06/1.39 => ( ( Xphi @ Xy )
% 2.06/1.39 => ( Xx = Xy ) ) )
% 2.06/1.39 => ( exu
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(exuI2_type,type,
% 2.06/1.39 exuI2: $o ).
% 2.06/1.39
% 2.06/1.39 thf(exuI2,definition,
% 2.06/1.39 ( exuI2
% 2.06/1.39 = ( ! [Xphi: $i > $o] :
% 2.06/1.39 ( ? [Xx: $i] :
% 2.06/1.39 ! [Xy: $i] :
% 2.06/1.39 ( ( Xphi @ Xy )
% 2.06/1.39 <=> ( Xy = Xx ) )
% 2.06/1.39 => ( exu
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(inCongP_type,type,
% 2.06/1.39 inCongP: $o ).
% 2.06/1.39
% 2.06/1.39 thf(inCongP,definition,
% 2.06/1.39 ( inCongP
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ( A = B )
% 2.06/1.39 => ! [Xx: $i,Xy: $i] :
% 2.06/1.39 ( ( Xx = Xy )
% 2.06/1.39 => ( ( in @ Xx @ A )
% 2.06/1.39 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(in__Cong_type,type,
% 2.06/1.39 in__Cong: $o ).
% 2.06/1.39
% 2.06/1.39 thf(in__Cong,definition,
% 2.06/1.39 ( in__Cong
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ( A = B )
% 2.06/1.39 => ! [Xx: $i,Xy: $i] :
% 2.06/1.39 ( ( Xx = Xy )
% 2.06/1.39 => ( ( in @ Xx @ A )
% 2.06/1.39 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(exuE3u_type,type,
% 2.06/1.39 exuE3u: $o ).
% 2.06/1.39
% 2.06/1.39 thf(exuE3u,definition,
% 2.06/1.39 ( exuE3u
% 2.06/1.39 = ( ! [Xphi: $i > $o] :
% 2.06/1.39 ( ( exu
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.39 => ! [Xx: $i,Xy: $i] :
% 2.06/1.39 ( ( Xphi @ Xx )
% 2.06/1.39 => ( ( Xphi @ Xy )
% 2.06/1.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(exu__Cong_type,type,
% 2.06/1.39 exu__Cong: $o ).
% 2.06/1.39
% 2.06/1.39 thf(exu__Cong,definition,
% 2.06/1.39 ( exu__Cong
% 2.06/1.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.06/1.39 ( ! [Xx: $i,Xy: $i] :
% 2.06/1.39 ( ( Xx = Xy )
% 2.06/1.39 => ( ( Xphi @ Xx )
% 2.06/1.39 <=> ( Xpsi @ Xy ) ) )
% 2.06/1.39 => ( ( exu
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.39 <=> ( exu
% 2.06/1.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(emptyset__Cong_type,type,
% 2.06/1.39 emptyset__Cong: $o ).
% 2.06/1.39
% 2.06/1.39 thf(emptyset__Cong,definition,
% 2.06/1.39 ( emptyset__Cong
% 2.06/1.39 = ( emptyset = emptyset ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoin__Cong_type,type,
% 2.06/1.39 setadjoin__Cong: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoin__Cong,definition,
% 2.06/1.39 ( setadjoin__Cong
% 2.06/1.39 = ( ! [Xx: $i,Xy: $i] :
% 2.06/1.39 ( ( Xx = Xy )
% 2.06/1.39 => ! [Xz: $i,Xu: $i] :
% 2.06/1.39 ( ( Xz = Xu )
% 2.06/1.39 => ( ( setadjoin @ Xx @ Xz )
% 2.06/1.39 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(powerset__Cong_type,type,
% 2.06/1.39 powerset__Cong: $o ).
% 2.06/1.39
% 2.06/1.39 thf(powerset__Cong,definition,
% 2.06/1.39 ( powerset__Cong
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ( A = B )
% 2.06/1.39 => ( ( powerset @ A )
% 2.06/1.39 = ( powerset @ B ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setunion__Cong_type,type,
% 2.06/1.39 setunion__Cong: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setunion__Cong,definition,
% 2.06/1.39 ( setunion__Cong
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ( A = B )
% 2.06/1.39 => ( ( setunion @ A )
% 2.06/1.39 = ( setunion @ B ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(omega__Cong_type,type,
% 2.06/1.39 omega__Cong: $o ).
% 2.06/1.39
% 2.06/1.39 thf(omega__Cong,definition,
% 2.06/1.39 ( omega__Cong
% 2.06/1.39 = ( omega = omega ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(exuEu_type,type,
% 2.06/1.39 exuEu: $o ).
% 2.06/1.39
% 2.06/1.39 thf(exuEu,definition,
% 2.06/1.39 ( exuEu
% 2.06/1.39 = ( ! [Xphi: $i > $o] :
% 2.06/1.39 ( ( exu
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.39 => ! [Xx: $i,Xy: $i] :
% 2.06/1.39 ( ( Xphi @ Xx )
% 2.06/1.39 => ( ( Xphi @ Xy )
% 2.06/1.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(descr__Cong_type,type,
% 2.06/1.39 descr__Cong: $o ).
% 2.06/1.39
% 2.06/1.39 thf(descr__Cong,definition,
% 2.06/1.39 ( descr__Cong
% 2.06/1.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.06/1.39 ( ! [Xx: $i,Xy: $i] :
% 2.06/1.39 ( ( Xx = Xy )
% 2.06/1.39 => ( ( Xphi @ Xx )
% 2.06/1.39 <=> ( Xpsi @ Xy ) ) )
% 2.06/1.39 => ( ( exu
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.39 => ( ( exu
% 2.06/1.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.06/1.39 => ( ( descr
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.39 = ( descr
% 2.06/1.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(dsetconstr__Cong_type,type,
% 2.06/1.39 dsetconstr__Cong: $o ).
% 2.06/1.39
% 2.06/1.39 thf(dsetconstr__Cong,definition,
% 2.06/1.39 ( dsetconstr__Cong
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ( A = B )
% 2.06/1.39 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.06/1.39 ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ! [Xy: $i] :
% 2.06/1.39 ( ( in @ Xy @ B )
% 2.06/1.39 => ( ( Xx = Xy )
% 2.06/1.39 => ( ( Xphi @ Xx )
% 2.06/1.39 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.06/1.39 => ( ( dsetconstr @ A
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.39 = ( dsetconstr @ B
% 2.06/1.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(subset_type,type,
% 2.06/1.39 subset: $i > $i > $o ).
% 2.06/1.39
% 2.06/1.39 thf(disjoint_type,type,
% 2.06/1.39 disjoint: $i > $i > $o ).
% 2.06/1.39
% 2.06/1.39 thf(setsmeet_type,type,
% 2.06/1.39 setsmeet: $i > $i > $o ).
% 2.06/1.39
% 2.06/1.39 thf(subsetI1_type,type,
% 2.06/1.39 subsetI1: $o ).
% 2.06/1.39
% 2.06/1.39 thf(subsetI1,definition,
% 2.06/1.39 ( subsetI1
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( in @ Xx @ B ) )
% 2.06/1.39 => ( subset @ A @ B ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(eqimpsubset2_type,type,
% 2.06/1.39 eqimpsubset2: $o ).
% 2.06/1.39
% 2.06/1.39 thf(eqimpsubset2,definition,
% 2.06/1.39 ( eqimpsubset2
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ( A = B )
% 2.06/1.39 => ( subset @ B @ A ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(eqimpsubset1_type,type,
% 2.06/1.39 eqimpsubset1: $o ).
% 2.06/1.39
% 2.06/1.39 thf(eqimpsubset1,definition,
% 2.06/1.39 ( eqimpsubset1
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ( A = B )
% 2.06/1.39 => ( subset @ A @ B ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(subsetI2_type,type,
% 2.06/1.39 subsetI2: $o ).
% 2.06/1.39
% 2.06/1.39 thf(subsetI2,definition,
% 2.06/1.39 ( subsetI2
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ! [Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( in @ Xx @ B ) )
% 2.06/1.39 => ( subset @ A @ B ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(emptysetsubset_type,type,
% 2.06/1.39 emptysetsubset: $o ).
% 2.06/1.39
% 2.06/1.39 thf(emptysetsubset,definition,
% 2.06/1.39 ( emptysetsubset
% 2.06/1.39 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(subsetE_type,type,
% 2.06/1.39 subsetE: $o ).
% 2.06/1.39
% 2.06/1.39 thf(subsetE,definition,
% 2.06/1.39 ( subsetE
% 2.06/1.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.06/1.39 ( ( subset @ A @ B )
% 2.06/1.39 => ( ( in @ Xx @ A )
% 2.06/1.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(subsetE2_type,type,
% 2.06/1.39 subsetE2: $o ).
% 2.06/1.39
% 2.06/1.39 thf(subsetE2,definition,
% 2.06/1.39 ( subsetE2
% 2.06/1.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.06/1.39 ( ( subset @ A @ B )
% 2.06/1.39 => ( ~ ( in @ Xx @ B )
% 2.06/1.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(notsubsetI_type,type,
% 2.06/1.39 notsubsetI: $o ).
% 2.06/1.39
% 2.06/1.39 thf(notsubsetI,definition,
% 2.06/1.39 ( notsubsetI
% 2.06/1.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( ~ ( in @ Xx @ B )
% 2.06/1.39 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(notequalI1_type,type,
% 2.06/1.39 notequalI1: $o ).
% 2.06/1.39
% 2.06/1.39 thf(notequalI1,definition,
% 2.06/1.39 ( notequalI1
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ~ ( subset @ A @ B )
% 2.06/1.39 => ( A != B ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(notequalI2_type,type,
% 2.06/1.39 notequalI2: $o ).
% 2.06/1.39
% 2.06/1.39 thf(notequalI2,definition,
% 2.06/1.39 ( notequalI2
% 2.06/1.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( ~ ( in @ Xx @ B )
% 2.06/1.39 => ( A != B ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(subsetRefl_type,type,
% 2.06/1.39 subsetRefl: $o ).
% 2.06/1.39
% 2.06/1.39 thf(subsetRefl,definition,
% 2.06/1.39 ( subsetRefl
% 2.06/1.39 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(subsetTrans_type,type,
% 2.06/1.39 subsetTrans: $o ).
% 2.06/1.39
% 2.06/1.39 thf(subsetTrans,definition,
% 2.06/1.39 ( subsetTrans
% 2.06/1.39 = ( ! [A: $i,B: $i,C: $i] :
% 2.06/1.39 ( ( subset @ A @ B )
% 2.06/1.39 => ( ( subset @ B @ C )
% 2.06/1.39 => ( subset @ A @ C ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinSub_type,type,
% 2.06/1.39 setadjoinSub: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinSub,definition,
% 2.06/1.39 ( setadjoinSub
% 2.06/1.39 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinSub2_type,type,
% 2.06/1.39 setadjoinSub2: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setadjoinSub2,definition,
% 2.06/1.39 ( setadjoinSub2
% 2.06/1.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.06/1.39 ( ( subset @ A @ B )
% 2.06/1.39 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(subset2powerset_type,type,
% 2.06/1.39 subset2powerset: $o ).
% 2.06/1.39
% 2.06/1.39 thf(subset2powerset,definition,
% 2.06/1.39 ( subset2powerset
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ( subset @ A @ B )
% 2.06/1.39 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(setextsub_type,type,
% 2.06/1.39 setextsub: $o ).
% 2.06/1.39
% 2.06/1.39 thf(setextsub,definition,
% 2.06/1.39 ( setextsub
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ( subset @ A @ B )
% 2.06/1.39 => ( ( subset @ B @ A )
% 2.06/1.39 => ( A = B ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(subsetemptysetimpeq_type,type,
% 2.06/1.39 subsetemptysetimpeq: $o ).
% 2.06/1.39
% 2.06/1.39 thf(subsetemptysetimpeq,definition,
% 2.06/1.39 ( subsetemptysetimpeq
% 2.06/1.39 = ( ! [A: $i] :
% 2.06/1.39 ( ( subset @ A @ emptyset )
% 2.06/1.39 => ( A = emptyset ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(powersetI1_type,type,
% 2.06/1.39 powersetI1: $o ).
% 2.06/1.39
% 2.06/1.39 thf(powersetI1,definition,
% 2.06/1.39 ( powersetI1
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ( subset @ B @ A )
% 2.06/1.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(powersetE1_type,type,
% 2.06/1.39 powersetE1: $o ).
% 2.06/1.39
% 2.06/1.39 thf(powersetE1,definition,
% 2.06/1.39 ( powersetE1
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ( in @ B @ ( powerset @ A ) )
% 2.06/1.39 => ( subset @ B @ A ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(inPowerset_type,type,
% 2.06/1.39 inPowerset: $o ).
% 2.06/1.39
% 2.06/1.39 thf(inPowerset,definition,
% 2.06/1.39 ( inPowerset
% 2.06/1.39 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(powersetsubset_type,type,
% 2.06/1.39 powersetsubset: $o ).
% 2.06/1.39
% 2.06/1.39 thf(powersetsubset,definition,
% 2.06/1.39 ( powersetsubset
% 2.06/1.39 = ( ! [A: $i,B: $i] :
% 2.06/1.39 ( ( subset @ A @ B )
% 2.06/1.39 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(sepInPowerset_type,type,
% 2.06/1.39 sepInPowerset: $o ).
% 2.06/1.39
% 2.06/1.39 thf(sepInPowerset,definition,
% 2.06/1.39 ( sepInPowerset
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 2.06/1.39 ( in
% 2.06/1.39 @ ( dsetconstr @ A
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.39 @ ( powerset @ A ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(sepSubset_type,type,
% 2.06/1.39 sepSubset: $o ).
% 2.06/1.39
% 2.06/1.39 thf(sepSubset,definition,
% 2.06/1.39 ( sepSubset
% 2.06/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 2.06/1.39 ( subset
% 2.06/1.39 @ ( dsetconstr @ A
% 2.06/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.39 @ A ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(binunion_type,type,
% 2.06/1.39 binunion: $i > $i > $i ).
% 2.06/1.39
% 2.06/1.39 thf(binunion,definition,
% 2.06/1.39 ( binunion
% 2.06/1.39 = ( ^ [Xx: $i,Xy: $i] : ( setunion @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.06/1.39
% 2.06/1.39 thf(binunionIL,conjecture,
% 2.06/1.39 ( setextAx
% 2.06/1.39 => ( emptysetAx
% 2.06/1.39 => ( setadjoinAx
% 2.06/1.39 => ( powersetAx
% 2.06/1.39 => ( setunionAx
% 2.06/1.39 => ( omega0Ax
% 2.06/1.39 => ( omegaSAx
% 2.06/1.39 => ( omegaIndAx
% 2.06/1.39 => ( replAx
% 2.06/1.39 => ( foundationAx
% 2.06/1.39 => ( wellorderingAx
% 2.06/1.39 => ( descrp
% 2.06/1.39 => ( dsetconstrI
% 2.06/1.39 => ( dsetconstrEL
% 2.06/1.39 => ( dsetconstrER
% 2.06/1.39 => ( exuE1
% 2.06/1.39 => ( prop2setE
% 2.06/1.39 => ( emptysetE
% 2.06/1.39 => ( emptysetimpfalse
% 2.06/1.39 => ( notinemptyset
% 2.06/1.39 => ( exuE3e
% 2.06/1.39 => ( setext
% 2.06/1.39 => ( emptyI
% 2.06/1.39 => ( noeltsimpempty
% 2.06/1.39 => ( setbeta
% 2.06/1.39 => ( nonemptyE1
% 2.06/1.39 => ( nonemptyI
% 2.06/1.39 => ( nonemptyI1
% 2.06/1.39 => ( setadjoinIL
% 2.06/1.39 => ( emptyinunitempty
% 2.06/1.39 => ( setadjoinIR
% 2.06/1.39 => ( setadjoinE
% 2.06/1.39 => ( setadjoinOr
% 2.06/1.39 => ( setoftrueEq
% 2.06/1.39 => ( powersetI
% 2.06/1.39 => ( emptyinPowerset
% 2.06/1.39 => ( emptyInPowerset
% 2.06/1.39 => ( powersetE
% 2.06/1.39 => ( setunionI
% 2.06/1.39 => ( setunionE
% 2.06/1.39 => ( subPowSU
% 2.06/1.39 => ( exuE2
% 2.06/1.39 => ( nonemptyImpWitness
% 2.06/1.39 => ( uniqinunit
% 2.06/1.39 => ( notinsingleton
% 2.06/1.39 => ( eqinunit
% 2.06/1.39 => ( singletonsswitch
% 2.06/1.39 => ( upairsetE
% 2.06/1.39 => ( upairsetIL
% 2.06/1.39 => ( upairsetIR
% 2.06/1.39 => ( emptyE1
% 2.06/1.39 => ( vacuousDall
% 2.06/1.39 => ( quantDeMorgan1
% 2.06/1.39 => ( quantDeMorgan2
% 2.06/1.39 => ( quantDeMorgan3
% 2.06/1.39 => ( quantDeMorgan4
% 2.06/1.39 => ( prop2setI
% 2.06/1.39 => ( prop2set2propI
% 2.06/1.39 => ( notdexE
% 2.06/1.39 => ( notdallE
% 2.06/1.39 => ( exuI1
% 2.06/1.39 => ( exuI3
% 2.06/1.39 => ( exuI2
% 2.06/1.39 => ( inCongP
% 2.06/1.39 => ( in__Cong
% 2.06/1.39 => ( exuE3u
% 2.06/1.39 => ( exu__Cong
% 2.06/1.39 => ( emptyset__Cong
% 2.06/1.39 => ( setadjoin__Cong
% 2.06/1.39 => ( powerset__Cong
% 2.06/1.39 => ( setunion__Cong
% 2.06/1.39 => ( omega__Cong
% 2.06/1.39 => ( exuEu
% 2.06/1.39 => ( descr__Cong
% 2.06/1.39 => ( dsetconstr__Cong
% 2.06/1.39 => ( subsetI1
% 2.06/1.39 => ( eqimpsubset2
% 2.06/1.39 => ( eqimpsubset1
% 2.06/1.39 => ( subsetI2
% 2.06/1.39 => ( emptysetsubset
% 2.06/1.39 => ( subsetE
% 2.06/1.39 => ( subsetE2
% 2.06/1.39 => ( notsubsetI
% 2.06/1.39 => ( notequalI1
% 2.06/1.39 => ( notequalI2
% 2.06/1.39 => ( subsetRefl
% 2.06/1.39 => ( subsetTrans
% 2.06/1.39 => ( setadjoinSub
% 2.06/1.39 => ( setadjoinSub2
% 2.06/1.39 => ( subset2powerset
% 2.06/1.39 => ( setextsub
% 2.06/1.39 => ( subsetemptysetimpeq
% 2.06/1.39 => ( powersetI1
% 2.06/1.39 => ( powersetE1
% 2.06/1.39 => ( inPowerset
% 2.06/1.39 => ( powersetsubset
% 2.06/1.39 => ( sepInPowerset
% 2.06/1.39 => ( sepSubset
% 2.06/1.39 => ! [A: $i,B: $i,Xx: $i] :
% 2.06/1.39 ( ( in @ Xx @ A )
% 2.06/1.39 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.06/1.39 ------------------------
% 2.25/1.41 % (23140)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/18Mi)
% 2.25/1.41 % (23137)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/2Mi)
% 2.25/1.41 % (23136)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_23036 for (2999ds/27Mi)
% 2.25/1.41 % (23137)Instruction limit reached!
% 2.25/1.41 % (23137)------------------------------
% 2.25/1.41 % (23137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.41 % (23137)Termination reason: Unknown
% 2.25/1.41 % (23137)Termination phase: shuffling
% 2.25/1.41
% 2.25/1.41 % (23137)Memory used [KB]: 1151
% 2.25/1.41 % (23137)Time elapsed: 0.002 s
% 2.25/1.41 % (23137)Instructions burned: 2 (million)
% 2.25/1.41 % (23137)------------------------------
% 2.25/1.41 % (23137)------------------------------
% 2.25/1.41 % (23135)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_23036 for (2999ds/4Mi)
% 2.25/1.41 % (23135)Instruction limit reached!
% 2.25/1.41 % (23135)------------------------------
% 2.25/1.41 % (23135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.41 % (23135)Termination reason: Unknown
% 2.25/1.41 % (23135)Termination phase: shuffling
% 2.25/1.41
% 2.25/1.41 % (23135)Memory used [KB]: 1279
% 2.25/1.41 % (23135)Time elapsed: 0.003 s
% 2.25/1.41 % (23135)Instructions burned: 4 (million)
% 2.25/1.41 % (23135)------------------------------
% 2.25/1.41 % (23135)------------------------------
% 2.25/1.41 % (23140)Instruction limit reached!
% 2.25/1.41 % (23140)------------------------------
% 2.25/1.41 % (23140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.41 % (23140)Termination reason: Unknown
% 2.25/1.41 % (23140)Termination phase: Preprocessing 3
% 2.25/1.41
% 2.25/1.41 % (23140)Memory used [KB]: 1663
% 2.25/1.41 % (23140)Time elapsed: 0.008 s
% 2.25/1.41 % (23140)Instructions burned: 20 (million)
% 2.25/1.41 % (23140)------------------------------
% 2.25/1.41 % (23140)------------------------------
% 2.25/1.42 % (23134)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/183Mi)
% 2.25/1.42 % (23138)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_23036 for (2999ds/2Mi)
% 2.25/1.42 % (23139)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_23036 for (2999ds/275Mi)
% 2.25/1.42 % (23136)Instruction limit reached!
% 2.25/1.42 % (23136)------------------------------
% 2.25/1.42 % (23136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.42 % (23136)Termination reason: Unknown
% 2.25/1.42 % (23136)Termination phase: Property scanning
% 2.25/1.42
% 2.25/1.42 % (23136)Memory used [KB]: 1535
% 2.25/1.42 % (23136)Time elapsed: 0.009 s
% 2.25/1.42 % (23136)Instructions burned: 27 (million)
% 2.25/1.42 % (23136)------------------------------
% 2.25/1.42 % (23136)------------------------------
% 2.25/1.42 % (23138)Instruction limit reached!
% 2.25/1.42 % (23138)------------------------------
% 2.25/1.42 % (23138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.42 % (23138)Termination reason: Unknown
% 2.25/1.42 % (23138)Termination phase: shuffling
% 2.25/1.42
% 2.25/1.42 % (23138)Memory used [KB]: 1151
% 2.25/1.42 % (23138)Time elapsed: 0.003 s
% 2.25/1.42 % (23138)Instructions burned: 2 (million)
% 2.25/1.42 % (23138)------------------------------
% 2.25/1.42 % (23138)------------------------------
% 2.25/1.42 % (23141)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/3Mi)
% 2.25/1.42 % (23141)Instruction limit reached!
% 2.25/1.42 % (23141)------------------------------
% 2.25/1.42 % (23141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.42 % (23141)Termination reason: Unknown
% 2.25/1.42 % (23141)Termination phase: shuffling
% 2.25/1.42
% 2.25/1.42 % (23141)Memory used [KB]: 1279
% 2.25/1.42 % (23141)Time elapsed: 0.003 s
% 2.25/1.42 % (23141)Instructions burned: 4 (million)
% 2.25/1.42 % (23141)------------------------------
% 2.25/1.42 % (23141)------------------------------
% 2.25/1.42 % (23142)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_23036 for (2999ds/37Mi)
% 2.25/1.42 % (23143)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_23036 for (2999ds/15Mi)
% 2.25/1.43 % (23144)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_23036 for (2999ds/3Mi)
% 2.25/1.43 % (23144)Instruction limit reached!
% 2.25/1.43 % (23144)------------------------------
% 2.25/1.43 % (23144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.43 % (23144)Termination reason: Unknown
% 2.25/1.43 % (23144)Termination phase: shuffling
% 2.25/1.43
% 2.25/1.43 % (23144)Memory used [KB]: 1151
% 2.25/1.43 % (23144)Time elapsed: 0.003 s
% 2.25/1.43 % (23144)Instructions burned: 4 (million)
% 2.25/1.43 % (23144)------------------------------
% 2.25/1.43 % (23144)------------------------------
% 2.25/1.43 % (23143)Instruction limit reached!
% 2.25/1.43 % (23143)------------------------------
% 2.25/1.43 % (23143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.43 % (23143)Termination reason: Unknown
% 2.25/1.43 % (23143)Termination phase: Preprocessing 3
% 2.25/1.43
% 2.25/1.43 % (23143)Memory used [KB]: 1535
% 2.25/1.43 % (23143)Time elapsed: 0.006 s
% 2.25/1.43 % (23143)Instructions burned: 16 (million)
% 2.25/1.43 % (23143)------------------------------
% 2.25/1.43 % (23143)------------------------------
% 2.25/1.43 % (23146)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/7Mi)
% 2.25/1.43 % (23146)Instruction limit reached!
% 2.25/1.43 % (23146)------------------------------
% 2.25/1.43 % (23146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.43 % (23146)Termination reason: Unknown
% 2.25/1.43 % (23146)Termination phase: shuffling
% 2.25/1.43
% 2.25/1.43 % (23146)Memory used [KB]: 1279
% 2.25/1.43 % (23146)Time elapsed: 0.004 s
% 2.25/1.43 % (23146)Instructions burned: 7 (million)
% 2.25/1.43 % (23146)------------------------------
% 2.25/1.43 % (23146)------------------------------
% 2.25/1.43 % (23142)Instruction limit reached!
% 2.25/1.43 % (23142)------------------------------
% 2.25/1.43 % (23142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.43 % (23142)Termination reason: Unknown
% 2.25/1.43 % (23142)Termination phase: Function definition elimination
% 2.25/1.43
% 2.25/1.43 % (23142)Memory used [KB]: 1535
% 2.25/1.43 % (23142)Time elapsed: 0.011 s
% 2.25/1.43 % (23142)Instructions burned: 37 (million)
% 2.25/1.43 % (23142)------------------------------
% 2.25/1.43 % (23142)------------------------------
% 2.25/1.43 % (23145)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_23036 for (2999ds/1041Mi)
% 2.25/1.44 % (23147)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/16Mi)
% 2.25/1.44 % (23148)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_23036 for (2999ds/3Mi)
% 2.25/1.44 % (23148)Instruction limit reached!
% 2.25/1.44 % (23148)------------------------------
% 2.25/1.44 % (23148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.44 % (23148)Termination reason: Unknown
% 2.25/1.44 % (23148)Termination phase: shuffling
% 2.25/1.44
% 2.25/1.44 % (23148)Memory used [KB]: 1279
% 2.25/1.44 % (23148)Time elapsed: 0.002 s
% 2.25/1.44 % (23148)Instructions burned: 4 (million)
% 2.25/1.44 % (23148)------------------------------
% 2.25/1.44 % (23148)------------------------------
% 2.25/1.44 % (23147)Instruction limit reached!
% 2.25/1.44 % (23147)------------------------------
% 2.25/1.44 % (23147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.44 % (23147)Termination reason: Unknown
% 2.25/1.44 % (23147)Termination phase: Property scanning
% 2.25/1.44
% 2.25/1.44 % (23147)Memory used [KB]: 1407
% 2.25/1.44 % (23147)Time elapsed: 0.007 s
% 2.25/1.44 % (23147)Instructions burned: 18 (million)
% 2.25/1.44 % (23147)------------------------------
% 2.25/1.44 % (23147)------------------------------
% 2.25/1.44 % (23149)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_23036 for (2999ds/3Mi)
% 2.25/1.44 % (23150)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/7Mi)
% 2.25/1.44 % (23149)Instruction limit reached!
% 2.25/1.44 % (23149)------------------------------
% 2.25/1.44 % (23149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.44 % (23149)Termination reason: Unknown
% 2.25/1.44 % (23149)Termination phase: shuffling
% 2.25/1.44
% 2.25/1.44 % (23149)Memory used [KB]: 1279
% 2.25/1.44 % (23149)Time elapsed: 0.003 s
% 2.25/1.44 % (23149)Instructions burned: 4 (million)
% 2.25/1.44 % (23149)------------------------------
% 2.25/1.44 % (23149)------------------------------
% 2.25/1.45 % (23150)Instruction limit reached!
% 2.25/1.45 % (23150)------------------------------
% 2.25/1.45 % (23150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.45 % (23150)Termination reason: Unknown
% 2.25/1.45 % (23150)Termination phase: shuffling
% 2.25/1.45
% 2.25/1.45 % (23150)Memory used [KB]: 1279
% 2.25/1.45 % (23150)Time elapsed: 0.004 s
% 2.25/1.45 % (23150)Instructions burned: 8 (million)
% 2.25/1.45 % (23150)------------------------------
% 2.25/1.45 % (23150)------------------------------
% 2.25/1.45 % (23151)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/3Mi)
% 2.25/1.45 % (23151)Instruction limit reached!
% 2.25/1.45 % (23151)------------------------------
% 2.25/1.45 % (23151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.45 % (23151)Termination reason: Unknown
% 2.25/1.45 % (23151)Termination phase: shuffling
% 2.25/1.45
% 2.25/1.45 % (23151)Memory used [KB]: 1151
% 2.25/1.45 % (23151)Time elapsed: 0.002 s
% 2.25/1.45 % (23151)Instructions burned: 4 (million)
% 2.25/1.45 % (23151)------------------------------
% 2.25/1.45 % (23151)------------------------------
% 2.25/1.45 % (23152)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/4Mi)
% 2.25/1.45 % (23152)Instruction limit reached!
% 2.25/1.45 % (23152)------------------------------
% 2.25/1.45 % (23152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.45 % (23152)Termination reason: Unknown
% 2.25/1.45 % (23152)Termination phase: shuffling
% 2.25/1.45
% 2.25/1.45 % (23152)Memory used [KB]: 1279
% 2.25/1.45 % (23152)Time elapsed: 0.003 s
% 2.25/1.45 % (23152)Instructions burned: 4 (million)
% 2.25/1.45 % (23152)------------------------------
% 2.25/1.45 % (23152)------------------------------
% 2.25/1.45 % (23153)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/18Mi)
% 2.25/1.46 % (23154)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/710Mi)
% 2.25/1.46 % (23155)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/6Mi)
% 2.25/1.46 % (23153)Instruction limit reached!
% 2.25/1.46 % (23153)------------------------------
% 2.25/1.46 % (23153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.46 % (23153)Termination reason: Unknown
% 2.25/1.46 % (23153)Termination phase: Property scanning
% 2.25/1.46
% 2.25/1.46 % (23153)Memory used [KB]: 1407
% 2.25/1.46 % (23153)Time elapsed: 0.007 s
% 2.25/1.46 % (23153)Instructions burned: 18 (million)
% 2.25/1.46 % (23153)------------------------------
% 2.25/1.46 % (23153)------------------------------
% 2.25/1.46 % (23155)Instruction limit reached!
% 2.25/1.46 % (23155)------------------------------
% 2.25/1.46 % (23155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.46 % (23155)Termination reason: Unknown
% 2.25/1.46 % (23155)Termination phase: shuffling
% 2.25/1.46
% 2.25/1.46 % (23155)Memory used [KB]: 1279
% 2.25/1.46 % (23155)Time elapsed: 0.003 s
% 2.25/1.46 % (23155)Instructions burned: 8 (million)
% 2.25/1.46 % (23155)------------------------------
% 2.25/1.46 % (23155)------------------------------
% 2.25/1.46 % (23156)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_23036 for (2999ds/902Mi)
% 2.25/1.47 % (23157)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/21Mi)
% 2.25/1.47 % (23158)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/5Mi)
% 2.25/1.47 % (23158)Instruction limit reached!
% 2.25/1.47 % (23158)------------------------------
% 2.25/1.47 % (23158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.47 % (23158)Termination reason: Unknown
% 2.25/1.47 % (23158)Termination phase: shuffling
% 2.25/1.47
% 2.25/1.47 % (23158)Memory used [KB]: 1279
% 2.25/1.47 % (23158)Time elapsed: 0.003 s
% 2.25/1.47 % (23158)Instructions burned: 8 (million)
% 2.25/1.47 % (23158)------------------------------
% 2.25/1.47 % (23158)------------------------------
% 2.25/1.48 % (23157)Instruction limit reached!
% 2.25/1.48 % (23157)------------------------------
% 2.25/1.48 % (23157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.48 % (23157)Termination reason: Unknown
% 2.25/1.48 % (23157)Termination phase: Property scanning
% 2.25/1.48
% 2.25/1.48 % (23157)Memory used [KB]: 1407
% 2.25/1.48 % (23157)Time elapsed: 0.008 s
% 2.25/1.48 % (23157)Instructions burned: 22 (million)
% 2.25/1.48 % (23157)------------------------------
% 2.25/1.48 % (23157)------------------------------
% 2.25/1.48 % (23159)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/6Mi)
% 2.25/1.48 % (23159)Instruction limit reached!
% 2.25/1.48 % (23159)------------------------------
% 2.25/1.48 % (23159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.48 % (23159)Termination reason: Unknown
% 2.25/1.48 % (23159)Termination phase: shuffling
% 2.25/1.48
% 2.25/1.48 % (23159)Memory used [KB]: 1279
% 2.25/1.48 % (23159)Time elapsed: 0.003 s
% 2.25/1.48 % (23159)Instructions burned: 6 (million)
% 2.25/1.48 % (23159)------------------------------
% 2.25/1.48 % (23159)------------------------------
% 2.25/1.49 % (23160)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/377Mi)
% 2.25/1.49 % (23161)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_23036 for (2999ds/779Mi)
% 2.25/1.52 % (23134)Instruction limit reached!
% 2.25/1.52 % (23134)------------------------------
% 2.25/1.52 % (23134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.52 % (23134)Termination reason: Unknown
% 2.25/1.52 % (23134)Termination phase: Saturation
% 2.25/1.52
% 2.25/1.52 % (23134)Memory used [KB]: 6908
% 2.25/1.52 % (23134)Time elapsed: 0.103 s
% 2.25/1.52 % (23134)Instructions burned: 184 (million)
% 2.25/1.52 % (23134)------------------------------
% 2.25/1.52 % (23134)------------------------------
% 2.25/1.53 % (23162)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_23036 for (2998ds/19Mi)
% 2.25/1.54 % (23162)Instruction limit reached!
% 2.25/1.54 % (23162)------------------------------
% 2.25/1.54 % (23162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.54 % (23162)Termination reason: Unknown
% 2.25/1.54 % (23162)Termination phase: Property scanning
% 2.25/1.54
% 2.25/1.54 % (23162)Memory used [KB]: 1407
% 2.25/1.54 % (23162)Time elapsed: 0.007 s
% 2.25/1.54 % (23162)Instructions burned: 20 (million)
% 2.25/1.54 % (23162)------------------------------
% 2.25/1.54 % (23162)------------------------------
% 2.25/1.55 % (23163)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_23036 for (2998ds/879Mi)
% 2.25/1.56 % (23139)Instruction limit reached!
% 2.25/1.56 % (23139)------------------------------
% 2.25/1.56 % (23139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.56 % (23139)Termination reason: Unknown
% 2.25/1.56 % (23139)Termination phase: Saturation
% 2.25/1.56
% 2.25/1.56 % (23139)Memory used [KB]: 7547
% 2.25/1.56 % (23139)Time elapsed: 0.148 s
% 2.25/1.56 % (23139)Instructions burned: 276 (million)
% 2.25/1.56 % (23139)------------------------------
% 2.25/1.56 % (23139)------------------------------
% 2.25/1.57 % (23164)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_23036 for (2998ds/17Mi)
% 2.25/1.58 % (23164)Instruction limit reached!
% 2.25/1.58 % (23164)------------------------------
% 2.25/1.58 % (23164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.58 % (23164)Termination reason: Unknown
% 2.25/1.58 % (23164)Termination phase: Property scanning
% 2.25/1.58
% 2.25/1.58 % (23164)Memory used [KB]: 1407
% 2.25/1.58 % (23164)Time elapsed: 0.007 s
% 2.25/1.58 % (23164)Instructions burned: 18 (million)
% 2.25/1.58 % (23164)------------------------------
% 2.25/1.58 % (23164)------------------------------
% 2.25/1.59 % (23165)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23036 for (2998ds/3Mi)
% 2.25/1.59 % (23165)Instruction limit reached!
% 2.25/1.59 % (23165)------------------------------
% 2.25/1.59 % (23165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.59 % (23165)Termination reason: Unknown
% 2.25/1.59 % (23165)Termination phase: shuffling
% 2.25/1.59
% 2.25/1.59 % (23165)Memory used [KB]: 1279
% 2.25/1.59 % (23165)Time elapsed: 0.003 s
% 2.25/1.59 % (23165)Instructions burned: 5 (million)
% 2.25/1.59 % (23165)------------------------------
% 2.25/1.59 % (23165)------------------------------
% 2.25/1.60 % (23166)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_23036 for (2998ds/30Mi)
% 2.25/1.61 % (23166)Instruction limit reached!
% 2.25/1.61 % (23166)------------------------------
% 2.25/1.61 % (23166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.61 % (23166)Termination reason: Unknown
% 2.25/1.61 % (23166)Termination phase: Property scanning
% 2.25/1.61
% 2.25/1.61 % (23166)Memory used [KB]: 1535
% 2.25/1.61 % (23166)Time elapsed: 0.010 s
% 2.25/1.61 % (23166)Instructions burned: 30 (million)
% 2.25/1.61 % (23166)------------------------------
% 2.25/1.61 % (23166)------------------------------
% 2.25/1.61 % (23160)Instruction limit reached!
% 2.25/1.61 % (23160)------------------------------
% 2.25/1.61 % (23160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.61 % (23160)Termination reason: Unknown
% 2.25/1.61 % (23160)Termination phase: Saturation
% 2.25/1.61
% 2.25/1.61 % (23160)Memory used [KB]: 7164
% 2.25/1.61 % (23160)Time elapsed: 0.124 s
% 2.25/1.61 % (23160)Instructions burned: 377 (million)
% 2.25/1.61 % (23160)------------------------------
% 2.25/1.61 % (23160)------------------------------
% 2.25/1.62 % (23167)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_23036 for (2997ds/127Mi)
% 2.25/1.62 % (23168)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_23036 for (2997ds/100Mi)
% 2.25/1.65 % (23168)Instruction limit reached!
% 2.25/1.65 % (23168)------------------------------
% 2.25/1.65 % (23168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.65 % (23168)Termination reason: Unknown
% 2.25/1.65 % (23168)Termination phase: Saturation
% 2.25/1.65
% 2.25/1.65 % (23168)Memory used [KB]: 6396
% 2.25/1.65 % (23168)Time elapsed: 0.031 s
% 2.25/1.65 % (23168)Instructions burned: 101 (million)
% 2.25/1.65 % (23168)------------------------------
% 2.25/1.65 % (23168)------------------------------
% 2.25/1.66 % (23167)Instruction limit reached!
% 2.25/1.66 % (23167)------------------------------
% 2.25/1.66 % (23167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.66 % (23167)Termination reason: Unknown
% 2.25/1.66 % (23167)Termination phase: Saturation
% 2.25/1.66
% 2.25/1.66 % (23167)Memory used [KB]: 6780
% 2.25/1.66 % (23167)Time elapsed: 0.041 s
% 2.25/1.66 % (23167)Instructions burned: 128 (million)
% 2.25/1.66 % (23167)------------------------------
% 2.25/1.66 % (23167)------------------------------
% 2.25/1.66 % (23169)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_23036 for (2997ds/3Mi)
% 2.25/1.66 % (23169)Instruction limit reached!
% 2.25/1.66 % (23169)------------------------------
% 2.25/1.66 % (23169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.66 % (23169)Termination reason: Unknown
% 2.25/1.66 % (23169)Termination phase: shuffling
% 2.25/1.66
% 2.25/1.66 % (23169)Memory used [KB]: 1151
% 2.25/1.66 % (23169)Time elapsed: 0.002 s
% 2.25/1.66 % (23169)Instructions burned: 3 (million)
% 2.25/1.66 % (23169)------------------------------
% 2.25/1.66 % (23169)------------------------------
% 2.25/1.67 % (23170)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_23036 for (2997ds/20Mi)
% 2.25/1.67 % (23171)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_23036 for (2997ds/86Mi)
% 2.25/1.67 % (23170)Instruction limit reached!
% 2.25/1.67 % (23170)------------------------------
% 2.25/1.67 % (23170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.67 % (23170)Termination reason: Unknown
% 2.25/1.67 % (23170)Termination phase: Preprocessing 3
% 2.25/1.67
% 2.25/1.67 % (23170)Memory used [KB]: 1407
% 2.25/1.67 % (23170)Time elapsed: 0.008 s
% 2.25/1.67 % (23170)Instructions burned: 20 (million)
% 2.25/1.67 % (23170)------------------------------
% 2.25/1.67 % (23170)------------------------------
% 2.25/1.68 % (23172)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_23036 for (2997ds/107Mi)
% 2.25/1.69 % (23161)Instruction limit reached!
% 2.25/1.69 % (23161)------------------------------
% 2.25/1.69 % (23161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.69 % (23161)Termination reason: Unknown
% 2.25/1.69 % (23161)Termination phase: Saturation
% 2.25/1.69
% 2.25/1.69 % (23161)Memory used [KB]: 6908
% 2.25/1.69 % (23161)Time elapsed: 0.196 s
% 2.25/1.69 % (23161)Instructions burned: 779 (million)
% 2.25/1.69 % (23161)------------------------------
% 2.25/1.69 % (23161)------------------------------
% 2.25/1.69 % (23171)Instruction limit reached!
% 2.25/1.69 % (23171)------------------------------
% 2.25/1.69 % (23171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.69 % (23171)Termination reason: Unknown
% 2.25/1.69 % (23171)Termination phase: Saturation
% 2.25/1.69
% 2.25/1.69 % (23171)Memory used [KB]: 6396
% 2.25/1.69 % (23171)Time elapsed: 0.024 s
% 2.25/1.69 % (23171)Instructions burned: 88 (million)
% 2.25/1.69 % (23171)------------------------------
% 2.25/1.69 % (23171)------------------------------
% 2.25/1.70 % (23154)Refutation not found, non-redundant clauses discarded% (23154)------------------------------
% 2.25/1.70 % (23154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.70 % (23154)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.25/1.70
% 2.25/1.70 % (23154)Memory used [KB]: 8315
% 2.25/1.70 % (23154)Time elapsed: 0.242 s
% 2.25/1.70 % (23154)Instructions burned: 708 (million)
% 2.25/1.70 % (23154)------------------------------
% 2.25/1.70 % (23154)------------------------------
% 2.25/1.70 % (23173)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_23036 for (2997ds/39Mi)
% 2.25/1.70 % (23174)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_23036 for (2997ds/448Mi)
% 2.25/1.71 % (23175)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_23036 for (2997ds/46Mi)
% 2.25/1.71 % (23173)Instruction limit reached!
% 2.25/1.71 % (23173)------------------------------
% 2.25/1.71 % (23173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.71 % (23173)Termination reason: Unknown
% 2.25/1.71 % (23173)Termination phase: Property scanning
% 2.25/1.71
% 2.25/1.71 % (23173)Memory used [KB]: 1535
% 2.25/1.71 % (23173)Time elapsed: 0.012 s
% 2.25/1.71 % (23173)Instructions burned: 42 (million)
% 2.25/1.71 % (23173)------------------------------
% 2.25/1.71 % (23173)------------------------------
% 2.25/1.71 % (23172)Instruction limit reached!
% 2.25/1.71 % (23172)------------------------------
% 2.25/1.71 % (23172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.71 % (23172)Termination reason: Unknown
% 2.25/1.71 % (23172)Termination phase: Saturation
% 2.25/1.71
% 2.25/1.71 % (23172)Memory used [KB]: 6524
% 2.25/1.71 % (23172)Time elapsed: 0.033 s
% 2.25/1.71 % (23172)Instructions burned: 107 (million)
% 2.25/1.71 % (23172)------------------------------
% 2.25/1.71 % (23172)------------------------------
% 2.25/1.72 % (23176)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_23036 for (2996ds/98Mi)
% 2.25/1.72 % (23175)Instruction limit reached!
% 2.25/1.72 % (23175)------------------------------
% 2.25/1.72 % (23175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.72 % (23175)Termination reason: Unknown
% 2.25/1.72 % (23175)Termination phase: Property scanning
% 2.25/1.72
% 2.25/1.72 % (23175)Memory used [KB]: 1535
% 2.25/1.72 % (23175)Time elapsed: 0.014 s
% 2.25/1.72 % (23175)Instructions burned: 49 (million)
% 2.25/1.72 % (23175)------------------------------
% 2.25/1.72 % (23175)------------------------------
% 2.25/1.72 % (23145)Instruction limit reached!
% 2.25/1.72 % (23145)------------------------------
% 2.25/1.72 % (23145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.72 % (23145)Termination reason: Unknown
% 2.25/1.72 % (23145)Termination phase: Saturation
% 2.25/1.72
% 2.25/1.72 % (23145)Memory used [KB]: 7803
% 2.25/1.72 % (23145)Time elapsed: 0.291 s
% 2.25/1.72 % (23145)Instructions burned: 1042 (million)
% 2.25/1.72 % (23145)------------------------------
% 2.25/1.72 % (23145)------------------------------
% 2.25/1.72 % (23177)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_23036 for (2996ds/507Mi)
% 2.25/1.73 % (23178)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_23036 for (2996ds/149Mi)
% 2.25/1.73 % (23179)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_23036 for (2996ds/39Mi)
% 2.25/1.73 % (23156)Instruction limit reached!
% 2.25/1.73 % (23156)------------------------------
% 2.25/1.73 % (23156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.73 % (23156)Termination reason: Unknown
% 2.25/1.73 % (23156)Termination phase: Saturation
% 2.25/1.73
% 2.25/1.73 % (23156)Memory used [KB]: 10362
% 2.25/1.73 % (23156)Time elapsed: 0.271 s
% 2.25/1.73 % (23156)Instructions burned: 903 (million)
% 2.25/1.73 % (23156)------------------------------
% 2.25/1.73 % (23156)------------------------------
% 2.25/1.74 % (23176)Instruction limit reached!
% 2.25/1.74 % (23176)------------------------------
% 2.25/1.74 % (23176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.74 % (23176)Termination reason: Unknown
% 2.25/1.74 % (23176)Termination phase: Saturation
% 2.25/1.74
% 2.25/1.74 % (23176)Memory used [KB]: 1663
% 2.25/1.74 % (23176)Time elapsed: 0.027 s
% 2.25/1.74 % (23176)Instructions burned: 102 (million)
% 2.25/1.74 % (23176)------------------------------
% 2.25/1.74 % (23176)------------------------------
% 2.25/1.74 % (23180)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_23036 for (2996ds/6Mi)
% 2.25/1.74 % (23179)Instruction limit reached!
% 2.25/1.74 % (23179)------------------------------
% 2.25/1.74 % (23179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.74 % (23179)Termination reason: Unknown
% 2.25/1.74 % (23179)Termination phase: Property scanning
% 2.25/1.74
% 2.25/1.74 % (23179)Memory used [KB]: 1535
% 2.25/1.74 % (23179)Time elapsed: 0.013 s
% 2.25/1.74 % (23179)Instructions burned: 41 (million)
% 2.25/1.74 % (23179)------------------------------
% 2.25/1.74 % (23179)------------------------------
% 2.25/1.75 % (23180)Instruction limit reached!
% 2.25/1.75 % (23180)------------------------------
% 2.25/1.75 % (23180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.75 % (23180)Termination reason: Unknown
% 2.25/1.75 % (23180)Termination phase: shuffling
% 2.25/1.75
% 2.25/1.75 % (23180)Memory used [KB]: 1279
% 2.25/1.75 % (23180)Time elapsed: 0.003 s
% 2.25/1.75 % (23180)Instructions burned: 6 (million)
% 2.25/1.75 % (23180)------------------------------
% 2.25/1.75 % (23180)------------------------------
% 2.25/1.75 % (23181)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_23036 for (2996ds/1087Mi)
% 2.25/1.75 % (23182)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_23036 for (2996ds/47Mi)
% 2.25/1.75 % (23183)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_23036 for (2996ds/44Mi)
% 2.25/1.77 % (23183)Instruction limit reached!
% 2.25/1.77 % (23183)------------------------------
% 2.25/1.77 % (23183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.77 % (23183)Termination reason: Unknown
% 2.25/1.77 % (23183)Termination phase: Property scanning
% 2.25/1.77
% 2.25/1.77 % (23183)Memory used [KB]: 1535
% 2.25/1.77 % (23183)Time elapsed: 0.012 s
% 2.25/1.77 % (23183)Instructions burned: 45 (million)
% 2.25/1.77 % (23183)------------------------------
% 2.25/1.77 % (23183)------------------------------
% 2.25/1.77 % (23182)Instruction limit reached!
% 2.25/1.77 % (23182)------------------------------
% 2.25/1.77 % (23182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.77 % (23182)Termination reason: Unknown
% 2.25/1.77 % (23182)Termination phase: Saturation
% 2.25/1.77
% 2.25/1.77 % (23182)Memory used [KB]: 6012
% 2.25/1.77 % (23182)Time elapsed: 0.015 s
% 2.25/1.77 % (23182)Instructions burned: 48 (million)
% 2.25/1.77 % (23182)------------------------------
% 2.25/1.77 % (23182)------------------------------
% 2.25/1.77 % (23178)Instruction limit reached!
% 2.25/1.77 % (23178)------------------------------
% 2.25/1.77 % (23178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.77 % (23178)Termination reason: Unknown
% 2.25/1.77 % (23178)Termination phase: Saturation
% 2.25/1.77
% 2.25/1.77 % (23178)Memory used [KB]: 6652
% 2.25/1.77 % (23178)Time elapsed: 0.046 s
% 2.25/1.77 % (23178)Instructions burned: 149 (million)
% 2.25/1.77 % (23178)------------------------------
% 2.25/1.77 % (23178)------------------------------
% 2.25/1.77 % (23184)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_23036 for (2996ds/432Mi)
% 2.25/1.78 % (23185)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_23036 for (2996ds/62Mi)
% 2.25/1.78 % (23186)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_23036 for (2996ds/31Mi)
% 2.25/1.79 % (23186)Instruction limit reached!
% 2.25/1.79 % (23186)------------------------------
% 2.25/1.79 % (23186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.79 % (23186)Termination reason: Unknown
% 2.25/1.79 % (23186)Termination phase: Property scanning
% 2.25/1.79
% 2.25/1.79 % (23186)Memory used [KB]: 1535
% 2.25/1.79 % (23186)Time elapsed: 0.009 s
% 2.25/1.79 % (23186)Instructions burned: 31 (million)
% 2.25/1.79 % (23186)------------------------------
% 2.25/1.79 % (23186)------------------------------
% 2.25/1.79 % (23185)Instruction limit reached!
% 2.25/1.79 % (23185)------------------------------
% 2.25/1.79 % (23185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.79 % (23185)Termination reason: Unknown
% 2.25/1.79 % (23185)Termination phase: Saturation
% 2.25/1.79
% 2.25/1.79 % (23185)Memory used [KB]: 6140
% 2.25/1.79 % (23185)Time elapsed: 0.019 s
% 2.25/1.79 % (23185)Instructions burned: 64 (million)
% 2.25/1.79 % (23185)------------------------------
% 2.25/1.79 % (23185)------------------------------
% 2.25/1.80 % (23187)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_23036 for (2996ds/96Mi)
% 2.25/1.81 % (23188)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_23036 for (2995ds/453Mi)
% 2.25/1.81 % (23174)Instruction limit reached!
% 2.25/1.81 % (23174)------------------------------
% 2.25/1.81 % (23174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.81 % (23174)Termination reason: Unknown
% 2.25/1.81 % (23174)Termination phase: Saturation
% 2.25/1.81
% 2.25/1.81 % (23174)Memory used [KB]: 6396
% 2.25/1.81 % (23174)Time elapsed: 0.107 s
% 2.25/1.81 % (23174)Instructions burned: 449 (million)
% 2.25/1.81 % (23174)------------------------------
% 2.25/1.81 % (23174)------------------------------
% 2.25/1.82 % (23189)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_23036 for (2995ds/71Mi)
% 2.25/1.83 % (23187)Instruction limit reached!
% 2.25/1.83 % (23187)------------------------------
% 2.25/1.83 % (23187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.83 % (23187)Termination reason: Unknown
% 2.25/1.83 % (23187)Termination phase: Saturation
% 2.25/1.83
% 2.25/1.83 % (23187)Memory used [KB]: 6524
% 2.25/1.83 % (23187)Time elapsed: 0.028 s
% 2.25/1.83 % (23187)Instructions burned: 98 (million)
% 2.25/1.83 % (23187)------------------------------
% 2.25/1.83 % (23187)------------------------------
% 2.25/1.84 % (23189)Instruction limit reached!
% 2.25/1.84 % (23189)------------------------------
% 2.25/1.84 % (23189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.84 % (23189)Termination reason: Unknown
% 2.25/1.84 % (23189)Termination phase: Saturation
% 2.25/1.84
% 2.25/1.84 % (23189)Memory used [KB]: 6268
% 2.25/1.84 % (23189)Time elapsed: 0.021 s
% 2.25/1.84 % (23189)Instructions burned: 72 (million)
% 2.25/1.84 % (23189)------------------------------
% 2.25/1.84 % (23189)------------------------------
% 2.25/1.84 % (23190)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_23036 for (2995ds/83Mi)
% 2.25/1.84 % (23163)Refutation not found, non-redundant clauses discarded% (23163)------------------------------
% 2.25/1.84 % (23163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.84 % (23163)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.25/1.84
% 2.25/1.84 % (23163)Memory used [KB]: 7547
% 2.25/1.84 % (23163)Time elapsed: 0.293 s
% 2.25/1.84 % (23163)Instructions burned: 871 (million)
% 2.25/1.84 % (23163)------------------------------
% 2.25/1.84 % (23163)------------------------------
% 2.25/1.84 % (23191)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_23036 for (2995ds/11Mi)
% 2.25/1.85 % (23191)Instruction limit reached!
% 2.25/1.85 % (23191)------------------------------
% 2.25/1.85 % (23191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.85 % (23191)Termination reason: Unknown
% 2.25/1.85 % (23191)Termination phase: shuffling
% 2.25/1.85
% 2.25/1.85 % (23191)Memory used [KB]: 1407
% 2.25/1.85 % (23191)Time elapsed: 0.004 s
% 2.25/1.85 % (23191)Instructions burned: 12 (million)
% 2.25/1.85 % (23191)------------------------------
% 2.25/1.85 % (23191)------------------------------
% 2.25/1.85 % (23192)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_23036 for (2995ds/41Mi)
% 2.25/1.86 % (23193)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23036 for (2995ds/6Mi)
% 2.25/1.86 % (23190)Instruction limit reached!
% 2.25/1.86 % (23190)------------------------------
% 2.25/1.86 % (23190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.86 % (23190)Termination reason: Unknown
% 2.25/1.86 % (23190)Termination phase: Saturation
% 2.25/1.86
% 2.25/1.86 % (23190)Memory used [KB]: 6268
% 2.25/1.86 % (23190)Time elapsed: 0.023 s
% 2.25/1.86 % (23190)Instructions burned: 84 (million)
% 2.25/1.86 % (23190)------------------------------
% 2.25/1.86 % (23190)------------------------------
% 2.25/1.86 % (23193)Instruction limit reached!
% 2.25/1.86 % (23193)------------------------------
% 2.25/1.86 % (23193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.86 % (23193)Termination reason: Unknown
% 2.25/1.86 % (23193)Termination phase: shuffling
% 2.25/1.86
% 2.25/1.86 % (23193)Memory used [KB]: 1279
% 2.25/1.86 % (23193)Time elapsed: 0.003 s
% 2.25/1.86 % (23193)Instructions burned: 7 (million)
% 2.25/1.86 % (23193)------------------------------
% 2.25/1.86 % (23193)------------------------------
% 2.25/1.86 % (23192)Instruction limit reached!
% 2.25/1.86 % (23192)------------------------------
% 2.25/1.86 % (23192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.86 % (23192)Termination reason: Unknown
% 2.25/1.86 % (23192)Termination phase: Property scanning
% 2.25/1.86
% 2.25/1.86 % (23192)Memory used [KB]: 1535
% 2.25/1.86 % (23192)Time elapsed: 0.013 s
% 2.25/1.86 % (23192)Instructions burned: 41 (million)
% 2.25/1.86 % (23192)------------------------------
% 2.25/1.86 % (23192)------------------------------
% 2.25/1.87 % (23194)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_23036 for (2995ds/150Mi)
% 2.25/1.87 % (23195)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_23036 for (2995ds/343Mi)
% 2.25/1.87 % (23196)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_23036 for (2995ds/109Mi)
% 2.25/1.88 % (23184)Instruction limit reached!
% 2.25/1.88 % (23184)------------------------------
% 2.25/1.88 % (23184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.88 % (23184)Termination reason: Unknown
% 2.25/1.88 % (23184)Termination phase: Saturation
% 2.25/1.88
% 2.25/1.88 % (23184)Memory used [KB]: 2558
% 2.25/1.88 % (23184)Time elapsed: 0.133 s
% 2.25/1.88 % (23184)Instructions burned: 435 (million)
% 2.25/1.88 % (23184)------------------------------
% 2.25/1.88 % (23184)------------------------------
% 2.25/1.89 % (23177)Instruction limit reached!
% 2.25/1.89 % (23177)------------------------------
% 2.25/1.89 % (23177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.89 % (23177)Termination reason: Unknown
% 2.25/1.89 % (23177)Termination phase: Saturation
% 2.25/1.89
% 2.25/1.89 % (23177)Memory used [KB]: 7036
% 2.25/1.89 % (23177)Time elapsed: 0.165 s
% 2.25/1.89 % (23177)Instructions burned: 509 (million)
% 2.25/1.89 % (23177)------------------------------
% 2.25/1.89 % (23177)------------------------------
% 2.25/1.89 % (23197)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_23036 for (2995ds/253Mi)
% 2.25/1.90 % (23198)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_23036 for (2995ds/140Mi)
% 2.25/1.90 % (23196)Instruction limit reached!
% 2.25/1.90 % (23196)------------------------------
% 2.25/1.90 % (23196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.90 % (23196)Termination reason: Unknown
% 2.25/1.90 % (23196)Termination phase: Saturation
% 2.25/1.90
% 2.25/1.90 % (23196)Memory used [KB]: 6652
% 2.25/1.90 % (23196)Time elapsed: 0.031 s
% 2.25/1.90 % (23196)Instructions burned: 109 (million)
% 2.25/1.90 % (23196)------------------------------
% 2.25/1.90 % (23196)------------------------------
% 2.25/1.91 % (23199)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_23036 for (2994ds/614Mi)
% 2.25/1.91 % (23194)Instruction limit reached!
% 2.25/1.91 % (23194)------------------------------
% 2.25/1.91 % (23194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.91 % (23194)Termination reason: Unknown
% 2.25/1.91 % (23194)Termination phase: Saturation
% 2.25/1.91
% 2.25/1.91 % (23194)Memory used [KB]: 7164
% 2.25/1.91 % (23194)Time elapsed: 0.048 s
% 2.25/1.91 % (23194)Instructions burned: 151 (million)
% 2.25/1.91 % (23194)------------------------------
% 2.25/1.91 % (23194)------------------------------
% 2.25/1.92 % (23188)Instruction limit reached!
% 2.25/1.92 % (23188)------------------------------
% 2.25/1.92 % (23188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.92 % (23188)Termination reason: Unknown
% 2.25/1.92 % (23188)Termination phase: Saturation
% 2.25/1.92
% 2.25/1.92 % (23188)Memory used [KB]: 6140
% 2.25/1.92 % (23188)Time elapsed: 0.116 s
% 2.25/1.92 % (23188)Instructions burned: 455 (million)
% 2.25/1.92 % (23188)------------------------------
% 2.25/1.92 % (23188)------------------------------
% 2.25/1.92 % (23200)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_23036 for (2994ds/202Mi)
% 2.25/1.93 % (23201)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_23036 for (2994ds/339Mi)
% 2.25/1.93 % (23198)Refutation not found, incomplete strategy
% 2.25/1.93 % (23198)------------------------------
% 2.25/1.93 % (23198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.93 % (23198)Termination reason: Refutation not found, incomplete strategy
% 2.25/1.93
% 2.25/1.93
% 2.25/1.93 % (23198)Memory used [KB]: 6140
% 2.25/1.93 % (23198)Time elapsed: 0.033 s
% 2.25/1.93 % (23198)Instructions burned: 116 (million)
% 2.25/1.93 % (23198)------------------------------
% 2.25/1.93 % (23198)------------------------------
% 2.25/1.94 % (23202)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_23036 for (2994ds/283Mi)
% 2.25/1.97 % (23197)Instruction limit reached!
% 2.25/1.97 % (23197)------------------------------
% 2.25/1.97 % (23197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.97 % (23197)Termination reason: Unknown
% 2.25/1.97 % (23197)Termination phase: Saturation
% 2.25/1.97
% 2.25/1.97 % (23197)Memory used [KB]: 7675
% 2.25/1.97 % (23197)Time elapsed: 0.078 s
% 2.25/1.97 % (23197)Instructions burned: 254 (million)
% 2.25/1.97 % (23197)------------------------------
% 2.25/1.97 % (23197)------------------------------
% 2.25/1.97 % (23195)Instruction limit reached!
% 2.25/1.97 % (23195)------------------------------
% 2.25/1.97 % (23195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.97 % (23195)Termination reason: Unknown
% 2.25/1.97 % (23195)Termination phase: Saturation
% 2.25/1.97
% 2.25/1.97 % (23195)Memory used [KB]: 7164
% 2.25/1.97 % (23195)Time elapsed: 0.105 s
% 2.25/1.97 % (23195)Instructions burned: 345 (million)
% 2.25/1.97 % (23195)------------------------------
% 2.25/1.97 % (23195)------------------------------
% 2.25/1.98 % (23203)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_23036 for (2994ds/134Mi)
% 2.25/1.98 % (23204)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_23036 for (2994ds/298Mi)
% 2.25/1.99 % (23200)Instruction limit reached!
% 2.25/1.99 % (23200)------------------------------
% 2.25/1.99 % (23200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/1.99 % (23200)Termination reason: Unknown
% 2.25/1.99 % (23200)Termination phase: Saturation
% 2.25/1.99
% 2.25/1.99 % (23200)Memory used [KB]: 7547
% 2.25/1.99 % (23200)Time elapsed: 0.063 s
% 2.25/1.99 % (23200)Instructions burned: 203 (million)
% 2.25/1.99 % (23200)------------------------------
% 2.25/1.99 % (23200)------------------------------
% 2.25/2.00 % (23205)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_23036 for (2994ds/192Mi)
% 2.25/2.01 % (23202)Instruction limit reached!
% 2.25/2.01 % (23202)------------------------------
% 2.25/2.01 % (23202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.25/2.01 % (23202)Termination reason: Unknown
% 2.25/2.01 % (23202)Termination phase: Saturation
% 2.25/2.01
% 2.25/2.01 % (23202)Memory used [KB]: 8059
% 2.25/2.01 % (23202)Time elapsed: 0.072 s
% 2.25/2.01 % (23202)Instructions burned: 285 (million)
% 2.25/2.01 % (23202)------------------------------
% 2.25/2.01 % (23202)------------------------------
% 6.48/2.01 % (23199)First to succeed.
% 6.48/2.02 % (23199)Refutation found. Thanks to Tanya!
% 6.48/2.02 % SZS status Theorem for DTF2THF_23036
% 6.48/2.02 % SZS output start Proof for DTF2THF_23036
% 6.48/2.02 thf(func_def_0, type, in: $i > $i > $o).
% 6.48/2.02 thf(func_def_1, type, exu: ($i > $o) > $o).
% 6.48/2.02 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 6.48/2.02 thf(func_def_8, type, powerset: $i > $i).
% 6.48/2.02 thf(func_def_10, type, setunion: $i > $i).
% 6.48/2.02 thf(func_def_19, type, descr: ($i > $o) > $i).
% 6.48/2.02 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_26, type, prop2set: $o > $i).
% 6.48/2.02 thf(func_def_36, type, nonempty: $i > $o).
% 6.48/2.02 thf(func_def_69, type, set2prop: $i > $o).
% 6.48/2.02 thf(func_def_88, type, subset: $i > $i > $o).
% 6.48/2.02 thf(func_def_89, type, disjoint: $i > $i > $o).
% 6.48/2.02 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 6.48/2.02 thf(func_def_114, type, binunion: $i > $i > $i).
% 6.48/2.02 thf(func_def_135, type, sK4: $i > $i > $i).
% 6.48/2.02 thf(func_def_136, type, sK5: ($i > $o) > $i).
% 6.48/2.02 thf(func_def_137, type, sK6: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_138, type, sK7: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_139, type, sK8: $i > $i > $i).
% 6.48/2.02 thf(func_def_140, type, sK9: $i > $i).
% 6.48/2.02 thf(func_def_141, type, sK10: ($i > $o) > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_142, type, sK11: ($i > $o) > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_143, type, sK12: ($i > $o) > $i).
% 6.48/2.02 thf(func_def_144, type, sK13: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_145, type, sK14: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_146, type, sK15: ($i > $o) > $i).
% 6.48/2.02 thf(func_def_147, type, sK16: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_148, type, sK17: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_149, type, sK18: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_150, type, sK19: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_151, type, sK20: ($i > $o) > $i).
% 6.48/2.02 thf(func_def_152, type, sK21: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_153, type, sK22: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_154, type, sK23: ($i > $o) > $i).
% 6.48/2.02 thf(func_def_155, type, sK24: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_156, type, sK25: $i > $i).
% 6.48/2.02 thf(func_def_157, type, sK26: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_158, type, sK27: $i > $i).
% 6.48/2.02 thf(func_def_159, type, sK28: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_160, type, sK29: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_161, type, sK30: $i > $i > $i).
% 6.48/2.02 thf(func_def_162, type, sK31: $i > $i).
% 6.48/2.02 thf(func_def_163, type, sK32: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_164, type, sK33: $o > $i > $i > $i).
% 6.48/2.02 thf(func_def_165, type, sK34: $i > ($i > $i > $o) > $i).
% 6.48/2.02 thf(func_def_166, type, sK35: $i > ($i > $i > $o) > $i).
% 6.48/2.02 thf(func_def_167, type, sK36: $i > $i > ($i > $i > $o) > $i).
% 6.48/2.02 thf(func_def_168, type, sK37: $i > $i > ($i > $i > $o) > $i).
% 6.48/2.02 thf(func_def_169, type, sK38: $i > $i > ($i > $i > $o) > $i).
% 6.48/2.02 thf(func_def_170, type, sK39: $i > $i > ($i > $i > $o) > $i).
% 6.48/2.02 thf(func_def_171, type, sK40: $i > $i > ($i > $i > $o) > $i).
% 6.48/2.02 thf(func_def_172, type, sK41: $i > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_173, type, sK42: ($i > $o) > $i).
% 6.48/2.02 thf(func_def_174, type, sK43: ($i > $o) > $i).
% 6.48/2.02 thf(func_def_175, type, sK44: ($i > $o) > $i).
% 6.48/2.02 thf(func_def_176, type, sK45: ($i > $o) > ($i > $o) > $i > $i > $i).
% 6.48/2.02 thf(func_def_177, type, sK46: $i > $i > ($i > $o) > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_178, type, sK47: $i > $i).
% 6.48/2.02 thf(func_def_179, type, sK48: $i > $i).
% 6.48/2.02 thf(func_def_180, type, sK49: ($i > $o) > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_181, type, sK50: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_182, type, sK51: ($i > $o) > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_183, type, sK52: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_184, type, sK53: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_185, type, sK54: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_186, type, sK55: ($i > $o) > ($i > $o) > $i).
% 6.48/2.02 thf(func_def_187, type, sK56: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_188, type, sK57: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_189, type, sK58: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_190, type, sK59: $i > $i > $i).
% 6.48/2.02 thf(func_def_191, type, sK60: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_192, type, sK61: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_193, type, sK62: $i > $i > $i).
% 6.48/2.02 thf(func_def_194, type, sK63: $i > $i > $i).
% 6.48/2.02 thf(func_def_195, type, sK64: $i > $i > $i).
% 6.48/2.02 thf(func_def_196, type, sK65: $i > $i).
% 6.48/2.02 thf(func_def_197, type, sK66: $i > $i > $i > $i).
% 6.48/2.02 thf(func_def_198, type, sK67: $i > $i > $i).
% 6.48/2.02 thf(func_def_199, type, sK68: $i > $i > $i).
% 6.48/2.02 thf(func_def_200, type, sK69: $i > $i > $i).
% 6.48/2.02 thf(func_def_201, type, sK70: $i > $i > $i).
% 6.48/2.02 thf(func_def_202, type, sK71: $i > $i > $i).
% 6.48/2.02 thf(func_def_203, type, sK72: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_204, type, sK73: ($i > $o) > $i).
% 6.48/2.02 thf(func_def_205, type, sK74: ($i > $o) > $i).
% 6.48/2.02 thf(func_def_206, type, sK75: $i > $i > $i).
% 6.48/2.02 thf(func_def_207, type, sK76: ($i > $o) > $i).
% 6.48/2.02 thf(func_def_208, type, sK77: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_209, type, sK78: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_210, type, sK79: ($i > $o) > $i > $i).
% 6.48/2.02 thf(func_def_211, type, ph80: !>[X0: $tType]:(X0)).
% 6.48/2.02 thf(f2845,plain,(
% 6.48/2.02 $false),
% 6.48/2.02 inference(avatar_sat_refutation,[status(thm)],[f1880,f1893,f1898,f2842,f2843])).
% 6.48/2.02 thf(f2843,plain,(
% 6.48/2.02 ((in @ sK2 @ sK1) != $true) | ($false != (in @ sK2 @ sK1)) | ($false = $true)),
% 6.48/2.02 introduced(definition,[],[theory_tautology_sat_conflict])).
% 6.48/2.02 thf(f2842,plain,(
% 6.48/2.02 spl3_23 | spl3_5),
% 6.48/2.02 inference(avatar_split_clause,[status(thm)],[f2835,f1877,f2838])).
% 6.48/2.02 thf(f2838,definition,(
% 6.48/2.02 spl3_23 <=> ($false = (in @ sK2 @ sK1))),
% 6.48/2.02 introduced(definition,[new_symbols(naming,[spl3_23])],[avatar_definition])).
% 6.48/2.02 thf(f1877,definition,(
% 6.48/2.02 spl3_5 <=> ($true = (in @ sK2 @ (setunion @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)))))),
% 6.48/2.02 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 6.48/2.02 thf(f2835,plain,(
% 6.48/2.02 ($false = (in @ sK2 @ sK1)) | spl3_5),
% 6.48/2.02 inference(trivial_inequality_removal,[status(thm)],[f2831])).
% 6.48/2.02 thf(f2831,plain,(
% 6.48/2.02 ($false = (in @ sK2 @ sK1)) | ($false = $true) | spl3_5),
% 6.48/2.02 inference(superposition,[status(thm)],[f1790,f2045])).
% 6.48/2.02 thf(f2045,plain,(
% 6.48/2.02 ( ! [X0 : $i] : (($false = (in @ X0 @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)))) | ((in @ sK2 @ X0) = $false)) ) | spl3_5),
% 6.48/2.02 inference(trivial_inequality_removal,[status(thm)],[f2042])).
% 6.48/2.02 thf(f2042,plain,(
% 6.48/2.02 ( ! [X0 : $i] : (($true != $true) | ((in @ sK2 @ X0) = $false) | ($false = (in @ X0 @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset))))) ) | spl3_5),
% 6.48/2.02 inference(superposition,[status(thm)],[f1879,f1049])).
% 6.48/2.02 thf(f1049,plain,(
% 6.48/2.02 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X3 @ (setunion @ X1)) = $true) | ($false = (in @ X3 @ X2)) | ((in @ X2 @ X1) = $false)) )),
% 6.48/2.02 inference(binary_proxy_clausification,[status(thm)],[f1048])).
% 6.48/2.02 thf(f1048,plain,(
% 6.48/2.02 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ X1) => (in @ X3 @ (setunion @ X1))) = $true) | ($false = (in @ X3 @ X2))) )),
% 6.48/2.02 inference(binary_proxy_clausification,[status(thm)],[f1047])).
% 6.48/2.02 thf(f1047,plain,(
% 6.48/2.02 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ X2) => ((in @ X2 @ X1) => (in @ X3 @ (setunion @ X1)))) = $true)) )),
% 6.48/2.02 inference(beta_eta_normalization,[status(thm)],[f1046])).
% 6.48/2.02 thf(f1046,plain,(
% 6.48/2.02 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ X2 @ X1) => (in @ Y0 @ (setunion @ X1))))) @ X3))) )),
% 6.48/2.02 inference(pi_clausification,[status(thm)],[f1045])).
% 6.48/2.02 thf(f1045,plain,(
% 6.48/2.02 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ X2 @ X1) => (in @ Y0 @ (setunion @ X1)))))))) )),
% 6.48/2.02 inference(beta_eta_normalization,[status(thm)],[f1044])).
% 6.48/2.02 thf(f1044,plain,(
% 6.48/2.02 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ X1) => (in @ Y1 @ (setunion @ X1))))))) @ X2) = $true)) )),
% 6.48/2.02 inference(pi_clausification,[status(thm)],[f1043])).
% 6.48/2.02 thf(f1043,plain,(
% 6.48/2.02 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ X1) => (in @ Y1 @ (setunion @ X1)))))))) = $true)) )),
% 6.48/2.02 inference(beta_eta_normalization,[status(thm)],[f1042])).
% 6.48/2.02 thf(f1042,plain,(
% 6.48/2.02 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0))))))))) @ X1) = $true)) )),
% 6.48/2.02 inference(pi_clausification,[status(thm)],[f598])).
% 6.48/2.02 thf(f598,plain,(
% 6.48/2.02 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) = $true)),
% 6.48/2.02 inference(definition_unfolding,[status(thm)],[f482,f424])).
% 6.48/2.02 thf(f424,plain,(
% 6.48/2.02 (setunionI = $true)),
% 6.48/2.02 inference(cnf_transformation,[status(thm)],[f306])).
% 6.48/2.02 thf(f306,plain,(
% 6.48/2.02 (subsetI2 = $true) & (setadjoinIR = $true) & (emptyinPowerset = $true) & (setunionE = $true) & (notinsingleton = $true) & (powerset__Cong = $true) & (eqinunit = $true) & (quantDeMorgan2 = $true) & (emptyinunitempty = $true) & (emptyset__Cong = $true) & (eqimpsubset2 = $true) & (notinemptyset = $true) & (((in @ sK2 @ (binunion @ sK1 @ sK0)) != $true) & ((in @ sK2 @ sK1) = $true)) & (prop2set2propI = $true) & (uniqinunit = $true) & (sepInPowerset = $true) & (exuI1 = $true) & (setadjoinAx = $true) & (omegaSAx = $true) & (exuE2 = $true) & (setunion__Cong = $true) & (dsetconstrER = $true) & (noeltsimpempty = $true) & (subsetemptysetimpeq = $true) & (dsetconstrI = $true) & (powersetE = $true) & (setadjoinOr = $true) & (emptyI = $true) & (upairsetIL = $true) & (sepSubset = $true) & (exuI3 = $true) & (subsetI1 = $true) & (descrp = $true) & (powersetI = $true) & (notequalI1 = $true) & (setunionAx = $true) & (upairsetE = $true) & (setextAx = $true) & (setadjoin__Cong = $true) & (powersetAx = $true) & (foundationAx = $true) & (setadjoinSub2 = $true) & (exuI2 = $true) & (setadjoinIL = $true) & (in__Cong = $true) & (replAx = $true) & (setunionI = $true) & (notdallE = $true) & (setoftrueEq = $true) & (setadjoinE = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (dsetconstrEL = $true) & (prop2setI = $true) & (emptysetAx = $true) & (nonemptyI = $true) & (powersetI1 = $true) & (prop2setE = $true) & (powersetE1 = $true) & (inCongP = $true) & (subsetE = $true) & (exuE3u = $true) & (nonemptyI1 = $true) & (subsetRefl = $true) & (setextsub = $true) & (emptysetE = $true) & (quantDeMorgan1 = $true) & (upairsetIR = $true) & (setext = $true) & (emptyInPowerset = $true) & (subsetE2 = $true) & (emptysetimpfalse = $true) & (quantDeMorgan3 = $true) & (nonemptyImpWitness = $true) & (subPowSU = $true) & (vacuousDall = $true) & (setadjoinSub = $true) & (subset2powerset = $true) & (emptyE1 = $true) & (eqimpsubset1 = $true) & (exuEu = $true) & (quantDeMorgan4 = $true) & (exu__Cong = $true) & (omegaIndAx = $true) & (omega0Ax = $true) & (notdexE = $true) & (exuE1 = $true) & (inPowerset = $true) & (singletonsswitch = $true) & (subsetTrans = $true) & (notsubsetI = $true) & (wellorderingAx = $true) & (notequalI2 = $true) & (powersetsubset = $true) & (exuE3e = $true) & (setbeta = $true) & (omega__Cong = $true) & (emptysetsubset = $true) & (nonemptyE1 = $true)),
% 6.48/2.02 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f304,f305])).
% 6.48/2.02 thf(f305,plain,(
% 6.48/2.02 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binunion @ X1 @ X0)) != $true) & ((in @ X2 @ X1) = $true)) => (((in @ sK2 @ (binunion @ sK1 @ sK0)) != $true) & ((in @ sK2 @ sK1) = $true))),
% 6.48/2.02 introduced(definition,[],[choice_axiom])).
% 6.48/2.02 thf(f304,plain,(
% 6.48/2.02 (subsetI2 = $true) & (setadjoinIR = $true) & (emptyinPowerset = $true) & (setunionE = $true) & (notinsingleton = $true) & (powerset__Cong = $true) & (eqinunit = $true) & (quantDeMorgan2 = $true) & (emptyinunitempty = $true) & (emptyset__Cong = $true) & (eqimpsubset2 = $true) & (notinemptyset = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binunion @ X1 @ X0)) != $true) & ((in @ X2 @ X1) = $true)) & (prop2set2propI = $true) & (uniqinunit = $true) & (sepInPowerset = $true) & (exuI1 = $true) & (setadjoinAx = $true) & (omegaSAx = $true) & (exuE2 = $true) & (setunion__Cong = $true) & (dsetconstrER = $true) & (noeltsimpempty = $true) & (subsetemptysetimpeq = $true) & (dsetconstrI = $true) & (powersetE = $true) & (setadjoinOr = $true) & (emptyI = $true) & (upairsetIL = $true) & (sepSubset = $true) & (exuI3 = $true) & (subsetI1 = $true) & (descrp = $true) & (powersetI = $true) & (notequalI1 = $true) & (setunionAx = $true) & (upairsetE = $true) & (setextAx = $true) & (setadjoin__Cong = $true) & (powersetAx = $true) & (foundationAx = $true) & (setadjoinSub2 = $true) & (exuI2 = $true) & (setadjoinIL = $true) & (in__Cong = $true) & (replAx = $true) & (setunionI = $true) & (notdallE = $true) & (setoftrueEq = $true) & (setadjoinE = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (dsetconstrEL = $true) & (prop2setI = $true) & (emptysetAx = $true) & (nonemptyI = $true) & (powersetI1 = $true) & (prop2setE = $true) & (powersetE1 = $true) & (inCongP = $true) & (subsetE = $true) & (exuE3u = $true) & (nonemptyI1 = $true) & (subsetRefl = $true) & (setextsub = $true) & (emptysetE = $true) & (quantDeMorgan1 = $true) & (upairsetIR = $true) & (setext = $true) & (emptyInPowerset = $true) & (subsetE2 = $true) & (emptysetimpfalse = $true) & (quantDeMorgan3 = $true) & (nonemptyImpWitness = $true) & (subPowSU = $true) & (vacuousDall = $true) & (setadjoinSub = $true) & (subset2powerset = $true) & (emptyE1 = $true) & (eqimpsubset1 = $true) & (exuEu = $true) & (quantDeMorgan4 = $true) & (exu__Cong = $true) & (omegaIndAx = $true) & (omega0Ax = $true) & (notdexE = $true) & (exuE1 = $true) & (inPowerset = $true) & (singletonsswitch = $true) & (subsetTrans = $true) & (notsubsetI = $true) & (wellorderingAx = $true) & (notequalI2 = $true) & (powersetsubset = $true) & (exuE3e = $true) & (setbeta = $true) & (omega__Cong = $true) & (emptysetsubset = $true) & (nonemptyE1 = $true)),
% 6.48/2.02 inference(flattening,[status(thm)],[f303])).
% 6.48/2.02 thf(f303,plain,(
% 6.48/2.02 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binunion @ X1 @ X0)) != $true) & ((in @ X2 @ X1) = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 6.48/2.02 inference(ennf_transformation,[status(thm)],[f112])).
% 6.48/2.02 thf(f112,plain,(
% 6.48/2.02 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ (binunion @ X1 @ X0)) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.48/2.02 inference(fool_elimination,[status(thm)],[f111])).
% 6.48/2.02 thf(f111,plain,(
% 6.48/2.02 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X1 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.48/2.02 inference(rectify,[status(thm)],[f103])).
% 6.48/2.02 thf(f103,negated_conjecture,(
% 6.48/2.02 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => ! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X1 @ X3) => (in @ X1 @ (binunion @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.48/2.02 inference(negated_conjecture,[status(cth)],[f102])).
% 6.48/2.02 thf(f102,conjecture,(
% 6.48/2.02 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => ! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X1 @ X3) => (in @ X1 @ (binunion @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.48/2.02 file('/export/starexec/sandbox/tmp/tmp.OQI6VlFTuB/DTF2THF_23036.p',binunionIL)).
% 6.48/2.02 thf(f482,plain,(
% 6.48/2.02 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))))),
% 6.48/2.02 inference(cnf_transformation,[status(thm)],[f166])).
% 6.48/2.02 thf(f166,plain,(
% 6.48/2.02 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))))),
% 6.48/2.02 inference(fool_elimination,[status(thm)],[f165])).
% 6.48/2.02 thf(f165,plain,(
% 6.48/2.02 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ((in @ X1 @ X2) => (in @ X0 @ (setunion @ X2)))) = setunionI)),
% 6.48/2.02 inference(rectify,[status(thm)],[f41])).
% 6.48/2.02 thf(f41,axiom,(
% 6.48/2.02 (! [X1 : $i,X4 : $i,X3 : $i] : ((in @ X1 @ X4) => ((in @ X4 @ X3) => (in @ X1 @ (setunion @ X3)))) = setunionI)),
% 6.48/2.02 file('/export/starexec/sandbox/tmp/tmp.OQI6VlFTuB/DTF2THF_23036.p',setunionI)).
% 6.48/2.02 thf(f1879,plain,(
% 6.48/2.02 ($true != (in @ sK2 @ (setunion @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset))))) | spl3_5),
% 6.48/2.02 inference(avatar_component_clause,[status(thm)],[f1877])).
% 6.48/2.02 thf(f1790,plain,(
% 6.48/2.02 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X2 @ (setadjoin @ X2 @ X1)))) )),
% 6.48/2.02 inference(beta_eta_normalization,[status(thm)],[f1789])).
% 6.48/2.02 thf(f1789,plain,(
% 6.48/2.02 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1))) @ X2) = $true)) )),
% 6.48/2.02 inference(pi_clausification,[status(thm)],[f1788])).
% 6.48/2.02 thf(f1788,plain,(
% 6.48/2.02 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1)))) = $true)) )),
% 6.48/2.02 inference(beta_eta_normalization,[status(thm)],[f1787])).
% 6.48/2.02 thf(f1787,plain,(
% 6.48/2.02 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))) @ X1) = $true)) )),
% 6.48/2.02 inference(pi_clausification,[status(thm)],[f551])).
% 6.48/2.02 thf(f551,plain,(
% 6.48/2.02 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) = $true)),
% 6.48/2.02 inference(definition_unfolding,[status(thm)],[f427,f334])).
% 6.48/2.02 thf(f334,plain,(
% 6.48/2.02 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 6.48/2.02 inference(cnf_transformation,[status(thm)],[f246])).
% 6.48/2.02 thf(f246,plain,(
% 6.48/2.02 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 6.48/2.02 inference(fool_elimination,[status(thm)],[f245])).
% 6.48/2.02 thf(f245,plain,(
% 6.48/2.02 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 6.48/2.02 inference(rectify,[status(thm)],[f31])).
% 6.48/2.02 thf(f31,axiom,(
% 6.48/2.02 (setadjoinIL = ! [X1 : $i,X2 : $i] : (in @ X1 @ (setadjoin @ X1 @ X2)))),
% 6.48/2.02 file('/export/starexec/sandbox/tmp/tmp.OQI6VlFTuB/DTF2THF_23036.p',setadjoinIL)).
% 6.48/2.02 thf(f427,plain,(
% 6.48/2.02 (setadjoinIL = $true)),
% 6.48/2.02 inference(cnf_transformation,[status(thm)],[f306])).
% 6.48/2.02 thf(f1898,plain,(
% 6.48/2.02 ~spl3_9),
% 6.48/2.02 inference(avatar_split_clause,[status(thm)],[f104,f1895])).
% 6.48/2.02 thf(f1895,definition,(
% 6.48/2.02 spl3_9 <=> ($false = $true)),
% 6.48/2.02 introduced(definition,[new_symbols(naming,[spl3_9])],[avatar_definition])).
% 6.48/2.02 thf(f104,plain,(
% 6.48/2.02 ($false != $true)),
% 6.48/2.02 introduced(definition,[],[fool_axiom])).
% 6.48/2.02 thf(f1893,plain,(
% 6.48/2.02 spl3_8),
% 6.48/2.02 inference(avatar_split_clause,[status(thm)],[f458,f1890])).
% 6.48/2.02 thf(f1890,definition,(
% 6.48/2.02 spl3_8 <=> ((in @ sK2 @ sK1) = $true)),
% 6.48/2.02 introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition])).
% 6.48/2.02 thf(f458,plain,(
% 6.48/2.02 ((in @ sK2 @ sK1) = $true)),
% 6.48/2.02 inference(cnf_transformation,[status(thm)],[f306])).
% 6.48/2.02 thf(f1880,plain,(
% 6.48/2.02 ~spl3_5),
% 6.48/2.02 inference(avatar_split_clause,[status(thm)],[f1353,f1877])).
% 6.48/2.02 thf(f1353,plain,(
% 6.48/2.02 ($true != (in @ sK2 @ (setunion @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)))))),
% 6.48/2.02 inference(beta_eta_normalization,[status(thm)],[f530])).
% 6.48/2.02 thf(f530,plain,(
% 6.48/2.02 ($true != (in @ sK2 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))) @ sK1 @ sK0)))),
% 6.48/2.02 inference(definition_unfolding,[status(thm)],[f459,f486])).
% 6.48/2.02 thf(f486,plain,(
% 6.48/2.02 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 6.48/2.02 inference(cnf_transformation,[status(thm)],[f282])).
% 6.48/2.02 thf(f282,plain,(
% 6.48/2.02 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 6.48/2.02 inference(fool_elimination,[status(thm)],[f281])).
% 6.48/2.02 thf(f281,plain,(
% 6.48/2.02 ((^[X0 : $i, X1 : $i] : (setunion @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = binunion)),
% 6.48/2.02 inference(rectify,[status(thm)],[f101])).
% 6.48/2.02 thf(f101,axiom,(
% 6.48/2.02 ((^[X1 : $i, X2 : $i] : (setunion @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) = binunion)),
% 6.48/2.02 file('/export/starexec/sandbox/tmp/tmp.OQI6VlFTuB/DTF2THF_23036.p',binunion)).
% 6.48/2.02 thf(f459,plain,(
% 6.48/2.02 ((in @ sK2 @ (binunion @ sK1 @ sK0)) != $true)),
% 6.48/2.02 inference(cnf_transformation,[status(thm)],[f306])).
% 6.48/2.02 % SZS output end Proof for DTF2THF_23036
% 6.48/2.02 % (23199)------------------------------
% 6.48/2.02 % (23199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.02 % (23199)Termination reason: Refutation
% 6.48/2.02
% 6.48/2.02 % (23199)Memory used [KB]: 7419
% 6.48/2.02 % (23199)Time elapsed: 0.107 s
% 6.48/2.02 % (23199)Instructions burned: 340 (million)
% 6.48/2.02 % (23199)------------------------------
% 6.48/2.02 % (23199)------------------------------
% 6.48/2.02 % (23133)Success in time 0.626 s
%------------------------------------------------------------------------------