%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU580^1 : 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 : n029.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 09:35:23 AM UTC 2026
% Result : Theorem 8.16s 2.49s
% Output : Refutation 8.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 83 ( 45 unt; 0 typ; 4 def)
% Number of atoms : 1883 ( 474 equ; 0 cnn)
% Maximal formula atoms : 97 ( 22 avg)
% Number of connectives : 1283 ( 34 ~; 31 |; 288 &; 450 @)
% ( 6 <=>; 427 =>; 0 <=; 0 <~>)
% Maximal formula depth : 105 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 204 ( 200 usr; 106 con; 0-4 aty)
% ( 47 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 137 ( 71 ^; 60 !; 6 ?; 137 :)
% 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_129,type,
sK1: $i > $o ).
thf(func_def_131,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_132,type,
sK4: $i > $i > $i ).
thf(func_def_133,type,
sK5: $i > $i ).
thf(func_def_134,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_135,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_136,type,
sK8: $i > ( $i > $i > $o ) > $i ).
thf(func_def_137,type,
sK9: $i > ( $i > $i > $o ) > $i ).
thf(func_def_138,type,
sK10: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_139,type,
sK11: ( $i > $o ) > $i ).
thf(func_def_140,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_141,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_142,type,
sK14: $i > $i ).
thf(func_def_143,type,
sK15: $o > $i > $i > $i ).
thf(func_def_144,type,
sK16: $i > $i > $i ).
thf(func_def_145,type,
sK17: $i > ( $i > $o ) > $i ).
thf(func_def_146,type,
sK18: $i > $i ).
thf(func_def_147,type,
sK19: $i > $i > $i ).
thf(func_def_148,type,
sK20: ( $i > $o ) > $i > $i ).
thf(func_def_149,type,
sK21: $i > $i ).
thf(func_def_150,type,
sK22: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_151,type,
sK23: $i > ( $i > $o ) > $i ).
thf(func_def_152,type,
sK24: $i > ( $i > $o ) > $i ).
thf(func_def_153,type,
sK25: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_154,type,
sK26: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_155,type,
sK27: $i > ( $i > $o ) > $i ).
thf(func_def_156,type,
sK28: $i > ( $i > $o ) > $i ).
thf(func_def_157,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_158,type,
sK30: ( $i > $o ) > $i ).
thf(func_def_159,type,
sK31: ( $i > $o ) > $i ).
thf(func_def_160,type,
sK32: ( $i > $o ) > $i ).
thf(func_def_161,type,
sK33: ( $i > $o ) > $i ).
thf(func_def_162,type,
sK34: ( $i > $o ) > $i ).
thf(func_def_163,type,
sK35: $i > $i ).
thf(func_def_164,type,
sK36: $i > $i > $i ).
thf(func_def_165,type,
sK37: $i > $i > $i ).
thf(func_def_166,type,
sK38: $i > $i > $i ).
thf(func_def_167,type,
sK39: $i > $i > $i ).
thf(func_def_168,type,
sK40: $i > $i > $i > $i ).
thf(func_def_169,type,
sK41: $i > $i ).
thf(func_def_170,type,
sK42: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_171,type,
sK43: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_172,type,
sK44: $i > ( $i > $o ) > $i ).
thf(func_def_173,type,
sK45: $i > $i > $i ).
thf(func_def_174,type,
sK46: $i > $i > $i ).
thf(func_def_175,type,
sK47: $i > $i > $i ).
thf(func_def_176,type,
sK48: $i > ( $i > $o ) > $i ).
thf(func_def_177,type,
sK49: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_178,type,
sK50: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_179,type,
sK51: ( $i > $o ) > $i ).
thf(func_def_180,type,
sK52: ( $i > $o ) > $i > $i ).
thf(func_def_181,type,
sK53: $i > $i > $i ).
thf(func_def_182,type,
sK54: ( $i > $o ) > $i ).
thf(func_def_183,type,
sK55: ( $i > $o ) > $i > $i ).
thf(func_def_184,type,
sK56: ( $i > $o ) > $i > $i ).
thf(func_def_185,type,
sK57: $i > $i ).
thf(func_def_186,type,
sK58: ( $i > $o ) > $i ).
thf(func_def_187,type,
sK59: ( $i > $o ) > $i > $i ).
thf(func_def_188,type,
sK60: $i > ( $i > $o ) > $i ).
thf(func_def_189,type,
sK61: $i > ( $i > $o ) > $i ).
thf(func_def_190,type,
sK62: ( $i > $o ) > $i > $i ).
thf(func_def_191,type,
ph63:
!>[X0: $tType] : X0 ).
thf(func_def_193,type,
sK65: $i > $i ).
thf(func_def_194,type,
sK66: $i > $i > $i ).
thf(func_def_195,type,
sK67: $i > $i > $i ).
thf(func_def_196,type,
sK68: $i > $i > $i ).
thf(func_def_197,type,
sK69: $i > $i ).
thf(func_def_198,type,
sK70: $i > $i > $i ).
thf(func_def_199,type,
sK71: $i > $i > $i ).
thf(func_def_200,type,
sK72: $i > $i > $i ).
thf(func_def_201,type,
sK73: $i > $i > $i ).
thf(func_def_202,type,
sK74: $i > $i > $i ).
thf(func_def_203,type,
sK75: $i > $i > $i ).
thf(func_def_204,type,
sK76: $i > $i ).
thf(func_def_205,type,
sK77: $i > $i ).
thf(func_def_206,type,
sK78: $i > $i > $i ).
thf(func_def_207,type,
sK79: $i > $i > $i ).
thf(func_def_208,type,
sK80: $i > $i > $i ).
thf(func_def_209,type,
sK81: $i > $i > $i ).
thf(func_def_210,type,
sK82: $i > $i > $i ).
thf(func_def_211,type,
sK83: $i > $i > $i ).
thf(func_def_212,type,
sK84: $i > $i > $i ).
thf(func_def_213,type,
sK85: $i > $i > $i ).
thf(func_def_215,type,
sK87: $i > $i > $i ).
thf(f3990,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1911,f2304,f3822,f3956,f3989]) ).
thf(f3989,plain,
( ~ spl2_12
| ~ spl2_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f3988]) ).
thf(f3988,plain,
( $false
| ~ spl2_12
| ~ spl2_13 ),
inference(trivial_inequality_removal,[status(thm)],[f3987]) ).
thf(f3987,plain,
( ( $true = $false )
| ~ spl2_12
| ~ spl2_13 ),
inference(forward_demodulation,[status(thm)],[f3975,f3821]) ).
thf(f3821,plain,
( ( $false
= ( in @ sK86 @ sK0 ) )
| ~ spl2_12 ),
inference(avatar_component_clause,[status(thm)],[f3819]) ).
thf(f3819,definition,
( spl2_12
<=> ( $false
= ( in @ sK86 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_12])],[avatar_definition]) ).
thf(f3975,plain,
( ( $true
= ( in @ sK86 @ sK0 ) )
| ~ spl2_13 ),
inference(trivial_inequality_removal,[status(thm)],[f3959]) ).
thf(f3959,plain,
( ( $true = $false )
| ( $true
= ( in @ sK86 @ sK0 ) )
| ~ spl2_13 ),
inference(superposition,[status(thm)],[f3955,f1006]) ).
thf(f1006,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) )
| ( ( in @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1005]) ).
thf(f1005,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) )
=> ( in @ X2 @ X3 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1004]) ).
thf(f1004,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( in @ X2 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f1003]) ).
thf(f1003,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( in @ X2 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1002]) ).
thf(f1002,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) )
=> ( in @ Y0 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1001]) ).
thf(f1001,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) )
=> ( in @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1000]) ).
thf(f1000,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( in @ Y1 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f999]) ).
thf(f999,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( in @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f567]) ).
thf(f567,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( in @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f431,f381]) ).
thf(f381,plain,
( dsetconstrEL
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f238]) ).
thf(f238,plain,
( dsetconstrEL
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f237]) ).
thf(f237,plain,
( dsetconstrEL
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
( dsetconstrEL
= ( ! [X3: $i,X1: $i,X0: $i > $o] :
( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( in @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qcVYf693pv/DTF2THF_5389.p',dsetconstrEL) ).
thf(f431,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f297]) ).
thf(f297,plain,
( ( nonemptyImpWitness = $true )
& ( subsetI2 = $true )
& ( subsetRefl = $true )
& ( eqimpsubset1 = $true )
& ( emptyI = $true )
& ( upairsetIL = $true )
& ( $true
!= ( in
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
@ ( powerset @ sK0 ) ) )
& ( singletonsswitch = $true )
& ( setext = $true )
& ( setadjoinIL = $true )
& ( in__Cong = $true )
& ( emptysetAx = $true )
& ( exu__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinOr = $true )
& ( exuI3 = $true )
& ( powersetI = $true )
& ( eqinunit = $true )
& ( exuE3e = $true )
& ( uniqinunit = $true )
& ( quantDeMorgan1 = $true )
& ( wellorderingAx = $true )
& ( nonemptyI = $true )
& ( subset2powerset = $true )
& ( subsetE = $true )
& ( setoftrueEq = $true )
& ( notequalI2 = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( emptyinPowerset = $true )
& ( dsetconstrI = $true )
& ( subsetI1 = $true )
& ( exuI1 = $true )
& ( emptysetE = $true )
& ( vacuousDall = $true )
& ( emptysetsubset = $true )
& ( setbeta = $true )
& ( subsetE2 = $true )
& ( emptysetimpfalse = $true )
& ( powersetE = $true )
& ( prop2set2propI = $true )
& ( powerset__Cong = $true )
& ( emptyinunitempty = $true )
& ( powersetAx = $true )
& ( quantDeMorgan3 = $true )
& ( subsetTrans = $true )
& ( subPowSU = $true )
& ( setadjoinAx = $true )
& ( emptyInPowerset = $true )
& ( dsetconstrER = $true )
& ( emptyset__Cong = $true )
& ( notdexE = $true )
& ( setunionAx = $true )
& ( foundationAx = $true )
& ( notdallE = $true )
& ( powersetE1 = $true )
& ( prop2setE = $true )
& ( setadjoin__Cong = $true )
& ( setunion__Cong = $true )
& ( dsetconstrEL = $true )
& ( descrp = $true )
& ( emptyE1 = $true )
& ( setadjoinE = $true )
& ( upairsetIR = $true )
& ( notinemptyset = $true )
& ( setunionE = $true )
& ( eqimpsubset2 = $true )
& ( nonemptyI1 = $true )
& ( setadjoinSub2 = $true )
& ( omega__Cong = $true )
& ( nonemptyE1 = $true )
& ( setextAx = $true )
& ( omega0Ax = $true )
& ( setunionI = $true )
& ( exuE2 = $true )
& ( powersetI1 = $true )
& ( prop2setI = $true )
& ( exuE3u = $true )
& ( descr__Cong = $true )
& ( notinsingleton = $true )
& ( replAx = $true )
& ( upairsetE = $true )
& ( setadjoinSub = $true )
& ( exuI2 = $true )
& ( notsubsetI = $true )
& ( noeltsimpempty = $true )
& ( inPowerset = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstr__Cong = $true )
& ( exuE1 = $true )
& ( exuEu = $true )
& ( setextsub = $true )
& ( inCongP = $true )
& ( powersetsubset = $true )
& ( notequalI1 = $true )
& ( setadjoinIR = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f295,f296]) ).
thf(f296,plain,
( ? [X0: $i,X1: $i > $o] :
( ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) )
!= $true )
=> ( $true
!= ( in
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
@ ( powerset @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f295,plain,
( ( nonemptyImpWitness = $true )
& ( subsetI2 = $true )
& ( subsetRefl = $true )
& ( eqimpsubset1 = $true )
& ( emptyI = $true )
& ( upairsetIL = $true )
& ? [X0: $i,X1: $i > $o] :
( ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) )
!= $true )
& ( singletonsswitch = $true )
& ( setext = $true )
& ( setadjoinIL = $true )
& ( in__Cong = $true )
& ( emptysetAx = $true )
& ( exu__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinOr = $true )
& ( exuI3 = $true )
& ( powersetI = $true )
& ( eqinunit = $true )
& ( exuE3e = $true )
& ( uniqinunit = $true )
& ( quantDeMorgan1 = $true )
& ( wellorderingAx = $true )
& ( nonemptyI = $true )
& ( subset2powerset = $true )
& ( subsetE = $true )
& ( setoftrueEq = $true )
& ( notequalI2 = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( emptyinPowerset = $true )
& ( dsetconstrI = $true )
& ( subsetI1 = $true )
& ( exuI1 = $true )
& ( emptysetE = $true )
& ( vacuousDall = $true )
& ( emptysetsubset = $true )
& ( setbeta = $true )
& ( subsetE2 = $true )
& ( emptysetimpfalse = $true )
& ( powersetE = $true )
& ( prop2set2propI = $true )
& ( powerset__Cong = $true )
& ( emptyinunitempty = $true )
& ( powersetAx = $true )
& ( quantDeMorgan3 = $true )
& ( subsetTrans = $true )
& ( subPowSU = $true )
& ( setadjoinAx = $true )
& ( emptyInPowerset = $true )
& ( dsetconstrER = $true )
& ( emptyset__Cong = $true )
& ( notdexE = $true )
& ( setunionAx = $true )
& ( foundationAx = $true )
& ( notdallE = $true )
& ( powersetE1 = $true )
& ( prop2setE = $true )
& ( setadjoin__Cong = $true )
& ( setunion__Cong = $true )
& ( dsetconstrEL = $true )
& ( descrp = $true )
& ( emptyE1 = $true )
& ( setadjoinE = $true )
& ( upairsetIR = $true )
& ( notinemptyset = $true )
& ( setunionE = $true )
& ( eqimpsubset2 = $true )
& ( nonemptyI1 = $true )
& ( setadjoinSub2 = $true )
& ( omega__Cong = $true )
& ( nonemptyE1 = $true )
& ( setextAx = $true )
& ( omega0Ax = $true )
& ( setunionI = $true )
& ( exuE2 = $true )
& ( powersetI1 = $true )
& ( prop2setI = $true )
& ( exuE3u = $true )
& ( descr__Cong = $true )
& ( notinsingleton = $true )
& ( replAx = $true )
& ( upairsetE = $true )
& ( setadjoinSub = $true )
& ( exuI2 = $true )
& ( notsubsetI = $true )
& ( noeltsimpempty = $true )
& ( inPowerset = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstr__Cong = $true )
& ( exuE1 = $true )
& ( exuEu = $true )
& ( setextsub = $true )
& ( inCongP = $true )
& ( powersetsubset = $true )
& ( notequalI1 = $true )
& ( setadjoinIR = $true ) ),
inference(flattening,[status(thm)],[f294]) ).
thf(f294,plain,
( ? [X0: $i,X1: $i > $o] :
( ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) )
!= $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)],[f160]) ).
thf(f160,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 )
=> ! [X0: $i,X1: $i > $o] :
( ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f159]) ).
thf(f159,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
=> ! [X0: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f100]) ).
thf(f100,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
=> ! [X3: $i,X0: $i > $o] :
( in
@ ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) )
@ ( powerset @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f99]) ).
thf(f99,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
=> ! [X3: $i,X0: $i > $o] :
( in
@ ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) )
@ ( powerset @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qcVYf693pv/DTF2THF_5389.p',sepInPowerset) ).
thf(f3955,plain,
( ( ( in @ sK86 @ ( dsetconstr @ sK0 @ sK1 ) )
= $true )
| ~ spl2_13 ),
inference(avatar_component_clause,[status(thm)],[f3953]) ).
thf(f3953,definition,
( spl2_13
<=> ( ( in @ sK86 @ ( dsetconstr @ sK0 @ sK1 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_13])],[avatar_definition]) ).
thf(f3956,plain,
( spl2_13
| ~ spl2_11 ),
inference(avatar_split_clause,[status(thm)],[f3799,f2301,f3953]) ).
thf(f2301,definition,
( spl2_11
<=> ( $false
= ( in @ ( dsetconstr @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_11])],[avatar_definition]) ).
thf(f3799,plain,
( ( ( in @ sK86 @ ( dsetconstr @ sK0 @ sK1 ) )
= $true )
| ~ spl2_11 ),
inference(binary_proxy_clausification,[status(thm)],[f3797]) ).
thf(f3797,plain,
( ( ( ( in @ sK86 @ ( dsetconstr @ sK0 @ sK1 ) )
=> ( in @ sK86 @ sK0 ) )
= $false )
| ~ spl2_11 ),
inference(beta_eta_normalization,[status(thm)],[f3796]) ).
thf(f3796,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK0 @ sK1 ) )
=> ( in @ Y0 @ sK0 ) )
@ sK86 )
= $false )
| ~ spl2_11 ),
inference(sigma_clausification,[status(thm)],[f3795]) ).
thf(f3795,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK0 @ sK1 ) )
=> ( in @ Y0 @ sK0 ) ) )
= $false )
| ~ spl2_11 ),
inference(not_proxy_clausification,[status(thm)],[f3794]) ).
thf(f3794,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK0 @ sK1 ) )
=> ( in @ Y0 @ sK0 ) ) ) ) )
| ~ spl2_11 ),
inference(boolean_simplification,[status(thm)],[f3674]) ).
thf(f3674,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK0 @ sK1 ) )
=> ( in @ Y0 @ sK0 ) ) )
= $false ) )
| ~ spl2_11 ),
inference(superposition,[status(thm)],[f1628,f2303]) ).
thf(f2303,plain,
( ( $false
= ( in @ ( dsetconstr @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) )
| ~ spl2_11 ),
inference(avatar_component_clause,[status(thm)],[f2301]) ).
thf(f1628,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= ( in @ X1 @ ( powerset @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1627]) ).
thf(f1627,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
= ( in @ X1 @ ( powerset @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1626]) ).
thf(f1626,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
= ( in @ X1 @ ( powerset @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1625]) ).
thf(f1625,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
= ( in @ Y0 @ ( powerset @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f552]) ).
thf(f552,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
= ( in @ Y0 @ ( powerset @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f447,f318]) ).
thf(f318,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
= ( in @ Y0 @ ( powerset @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
thf(f111,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
= ( in @ Y0 @ ( powerset @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f110]) ).
thf(f110,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
<=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetAx ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X3: $i,X4: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
<=> ( in @ X4 @ ( powerset @ X3 ) ) )
= powersetAx ),
file('/export/starexec/sandbox/tmp/tmp.qcVYf693pv/DTF2THF_5389.p',powersetAx) ).
thf(f447,plain,
powersetAx = $true,
inference(cnf_transformation,[status(thm)],[f297]) ).
thf(f3822,plain,
( spl2_12
| ~ spl2_11 ),
inference(avatar_split_clause,[status(thm)],[f3798,f2301,f3819]) ).
thf(f3798,plain,
( ( $false
= ( in @ sK86 @ sK0 ) )
| ~ spl2_11 ),
inference(binary_proxy_clausification,[status(thm)],[f3797]) ).
thf(f2304,plain,
( spl2_11
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f1923,f1908,f2301]) ).
thf(f1908,definition,
( spl2_4
<=> ( $true
= ( in @ ( dsetconstr @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f1923,plain,
( ( $false
= ( in @ ( dsetconstr @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) )
| spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f1921]) ).
thf(f1921,plain,
( ( $true != $true )
| ( $false
= ( in @ ( dsetconstr @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) )
| spl2_4 ),
inference(superposition,[status(thm)],[f1910,f1709]) ).
thf(f1709,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1697]) ).
thf(f1697,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f1569,f661]) ).
thf(f661,plain,
! [X1: $o] :
( ( $true
= ( in @ emptyset @ ( prop2set @ X1 ) ) )
| ( $false = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f660]) ).
thf(f660,plain,
! [X1: $o] :
( $true
= ( X1
=> ( in @ emptyset @ ( prop2set @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f659]) ).
thf(f659,plain,
! [X1: $o] :
( $true
= ( ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f584]) ).
thf(f584,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f414,f364]) ).
thf(f364,plain,
( prop2setI
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
thf(f135,plain,
( prop2setI
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f134]) ).
thf(f134,plain,
( prop2setI
= ( ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f59]) ).
thf(f59,axiom,
( prop2setI
= ( ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qcVYf693pv/DTF2THF_5389.p',prop2setI) ).
thf(f414,plain,
prop2setI = $true,
inference(cnf_transformation,[status(thm)],[f297]) ).
thf(f1569,plain,
! [X2: $o,X1: $i] :
( ( ( in @ X1 @ ( prop2set @ X2 ) )
= $false )
| ( $true = X2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f1568]) ).
thf(f1568,plain,
! [X2: $o,X1: $i] :
( $true
= ( ( in @ X1 @ ( prop2set @ X2 ) )
=> X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f1567]) ).
thf(f1567,plain,
! [X2: $o,X1: $i] :
( $true
= ( ^ [Y0: $o] :
( ( in @ X1 @ ( prop2set @ Y0 ) )
=> Y0 )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f1566]) ).
thf(f1566,plain,
! [X1: $i] :
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( in @ X1 @ ( prop2set @ Y0 ) )
=> Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1565]) ).
thf(f1565,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ ( prop2set @ Y1 ) )
=> Y1 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f564]) ).
thf(f564,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ ( prop2set @ Y1 ) )
=> Y1 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f434,f313]) ).
thf(f313,plain,
( prop2setE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ ( prop2set @ Y1 ) )
=> Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
thf(f144,plain,
( prop2setE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ Y0 @ ( prop2set @ Y1 ) )
=> Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f143]) ).
thf(f143,plain,
( prop2setE
= ( ! [X0: $o,X1: $i] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,axiom,
( prop2setE
= ( ! [X0: $o,X1: $i] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qcVYf693pv/DTF2THF_5389.p',prop2setE) ).
thf(f434,plain,
prop2setE = $true,
inference(cnf_transformation,[status(thm)],[f297]) ).
thf(f1910,plain,
( ( $true
!= ( in @ ( dsetconstr @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) )
| spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f1908]) ).
thf(f1911,plain,
~ spl2_4,
inference(avatar_split_clause,[status(thm)],[f695,f1908]) ).
thf(f695,plain,
( $true
!= ( in @ ( dsetconstr @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f485]) ).
thf(f485,plain,
( $true
!= ( in
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
@ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU580^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:27:44 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEU580^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English : (! A:i.! phi:i>o.in (dsetconstr A (^ x:i.phi x)) (powerset A))
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.45 % Source : [Bro08]
% 0.18/0.45 % Names : ZFC082g [Bro08]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v5.0.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 210 ( 98 unt; 111 typ; 98 def)
% 0.18/0.45 % Number of atoms : 531 ( 147 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 97 ( 5 avg)
% 0.18/0.45 % Number of connectives : 831 ( 29 ~; 5 |; 27 &; 516 @)
% 0.18/0.45 % ( 14 <=>; 240 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 104 ( 2 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 114 ( 111 usr; 100 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 291 ( 29 ^; 234 !; 28 ?; 291 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : http://mathgate.info/detsetitem.php?id=258
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(in_type,type,
% 0.18/0.45 in: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(exu_type,type,
% 0.18/0.45 exu: ( $i > $o ) > $o ).
% 0.18/0.45
% 0.18/0.45 thf(exu,definition,
% 0.18/0.45 ( exu
% 0.18/0.45 = ( ^ [Xphi: $i > $o] :
% 0.18/0.45 ? [Xx: $i] :
% 0.18/0.45 ( ( Xphi @ Xx )
% 0.18/0.45 & ! [Xy: $i] :
% 0.18/0.45 ( ( Xphi @ Xy )
% 0.18/0.45 => ( Xx = Xy ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setextAx_type,type,
% 0.18/0.45 setextAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setextAx,definition,
% 0.18/0.45 ( setextAx
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 <=> ( in @ Xx @ B ) )
% 0.18/0.45 => ( A = B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyset_type,type,
% 0.18/0.45 emptyset: $i ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetAx_type,type,
% 0.18/0.45 emptysetAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetAx,definition,
% 0.18/0.45 ( emptysetAx
% 0.18/0.45 = ( ! [Xx: $i] :
% 0.18/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoin_type,type,
% 0.18/0.45 setadjoin: $i > $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinAx_type,type,
% 0.18/0.45 setadjoinAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinAx,definition,
% 0.18/0.45 ( setadjoinAx
% 0.18/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.45 <=> ( ( Xy = Xx )
% 0.18/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(powerset_type,type,
% 0.18/0.45 powerset: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(powersetAx_type,type,
% 0.18/0.45 powersetAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(powersetAx,definition,
% 0.18/0.45 ( powersetAx
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.18/0.45 <=> ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setunion_type,type,
% 0.18/0.45 setunion: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(setunionAx_type,type,
% 0.18/0.45 setunionAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setunionAx,definition,
% 0.18/0.45 ( setunionAx
% 0.18/0.45 = ( ! [A: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.18/0.45 <=> ? [B: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 & ( in @ B @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(omega_type,type,
% 0.18/0.45 omega: $i ).
% 0.18/0.45
% 0.18/0.45 thf(omega0Ax_type,type,
% 0.18/0.45 omega0Ax: $o ).
% 0.18/0.45
% 0.18/0.45 thf(omega0Ax,definition,
% 0.18/0.45 ( omega0Ax
% 0.18/0.45 = ( in @ emptyset @ omega ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(omegaSAx_type,type,
% 0.18/0.45 omegaSAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(omegaSAx,definition,
% 0.18/0.45 ( omegaSAx
% 0.18/0.45 = ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ omega )
% 0.18/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(omegaIndAx_type,type,
% 0.18/0.45 omegaIndAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(omegaIndAx,definition,
% 0.18/0.45 ( omegaIndAx
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ( ( in @ emptyset @ A )
% 0.18/0.45 & ! [Xx: $i] :
% 0.18/0.45 ( ( ( in @ Xx @ omega )
% 0.18/0.45 & ( in @ Xx @ A ) )
% 0.18/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.18/0.45 => ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ omega )
% 0.18/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(replAx_type,type,
% 0.18/0.45 replAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(replAx,definition,
% 0.18/0.45 ( replAx
% 0.18/0.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( exu
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.18/0.45 => ? [B: $i] :
% 0.18/0.45 ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 <=> ? [Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ A )
% 0.18/0.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(foundationAx_type,type,
% 0.18/0.45 foundationAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(foundationAx,definition,
% 0.18/0.45 ( foundationAx
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.18/0.45 => ? [B: $i] :
% 0.18/0.45 ( ( in @ B @ A )
% 0.18/0.45 & ~ ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(wellorderingAx_type,type,
% 0.18/0.45 wellorderingAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(wellorderingAx,definition,
% 0.18/0.45 ( wellorderingAx
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ? [B: $i] :
% 0.18/0.45 ( ! [C: $i] :
% 0.18/0.45 ( ( in @ C @ B )
% 0.18/0.45 => ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ C )
% 0.18/0.45 => ( in @ Xx @ A ) ) )
% 0.18/0.45 & ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( ( in @ Xx @ A )
% 0.18/0.45 & ( in @ Xy @ A ) )
% 0.18/0.45 => ( ! [C: $i] :
% 0.18/0.45 ( ( in @ C @ B )
% 0.18/0.45 => ( ( in @ Xx @ C )
% 0.18/0.45 <=> ( in @ Xy @ C ) ) )
% 0.18/0.45 => ( Xx = Xy ) ) )
% 0.18/0.45 & ! [C: $i,D: $i] :
% 0.18/0.45 ( ( ( in @ C @ B )
% 0.18/0.45 & ( in @ D @ B ) )
% 0.18/0.45 => ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ C )
% 0.18/0.45 => ( in @ Xx @ D ) )
% 0.18/0.45 | ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ D )
% 0.18/0.45 => ( in @ Xx @ C ) ) ) )
% 0.18/0.45 & ! [C: $i] :
% 0.18/0.45 ( ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ C )
% 0.18/0.45 => ( in @ Xx @ A ) )
% 0.18/0.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.18/0.45 => ? [D: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ D @ B )
% 0.18/0.45 & ( in @ Xx @ C )
% 0.18/0.45 & ~ ? [Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ D )
% 0.18/0.45 & ( in @ Xy @ C ) )
% 0.18/0.45 & ! [E: $i] :
% 0.18/0.45 ( ( in @ E @ B )
% 0.18/0.45 => ( ! [Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ E )
% 0.18/0.45 => ( in @ Xy @ D ) )
% 0.18/0.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(descr_type,type,
% 0.18/0.45 descr: ( $i > $o ) > $i ).
% 0.18/0.45
% 0.18/0.45 thf(descrp_type,type,
% 0.18/0.45 descrp: $o ).
% 0.18/0.45
% 0.18/0.45 thf(descrp,definition,
% 0.18/0.45 ( descrp
% 0.18/0.45 = ( ! [Xphi: $i > $o] :
% 0.18/0.45 ( ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.45 => ( Xphi
% 0.18/0.45 @ ( descr
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstr_type,type,
% 0.18/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrI_type,type,
% 0.18/0.45 dsetconstrI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrI,definition,
% 0.18/0.45 ( dsetconstrI
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( ( Xphi @ Xx )
% 0.18/0.45 => ( in @ Xx
% 0.18/0.45 @ ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrEL_type,type,
% 0.18/0.45 dsetconstrEL: $o ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrEL,definition,
% 0.18/0.45 ( dsetconstrEL
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx
% 0.18/0.45 @ ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrER_type,type,
% 0.18/0.45 dsetconstrER: $o ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrER,definition,
% 0.18/0.45 ( dsetconstrER
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx
% 0.18/0.45 @ ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(exuE1_type,type,
% 0.18/0.45 exuE1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(exuE1,definition,
% 0.18/0.45 ( exuE1
% 0.18/0.45 = ( ! [Xphi: $i > $o] :
% 0.18/0.45 ( ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.45 => ? [Xx: $i] :
% 0.18/0.45 ( ( Xphi @ Xx )
% 0.18/0.45 & ! [Xy: $i] :
% 0.18/0.45 ( ( Xphi @ Xy )
% 0.18/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(prop2set_type,type,
% 0.18/0.45 prop2set: $o > $i ).
% 0.18/0.45
% 0.18/0.45 thf(prop2setE_type,type,
% 0.18/0.45 prop2setE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(prop2setE,definition,
% 0.18/0.45 ( prop2setE
% 0.18/0.45 = ( ! [Xphi: $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.18/0.45 => Xphi ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetE_type,type,
% 0.18/0.45 emptysetE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetE,definition,
% 0.18/0.45 ( emptysetE
% 0.18/0.45 = ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ emptyset )
% 0.18/0.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetimpfalse_type,type,
% 0.18/0.45 emptysetimpfalse: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetimpfalse,definition,
% 0.18/0.45 ( emptysetimpfalse
% 0.18/0.45 = ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ emptyset )
% 0.18/0.45 => $false ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(notinemptyset_type,type,
% 0.18/0.45 notinemptyset: $o ).
% 0.18/0.45
% 0.18/0.45 thf(notinemptyset,definition,
% 0.18/0.45 ( notinemptyset
% 0.18/0.45 = ( ! [Xx: $i] :
% 0.18/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(exuE3e_type,type,
% 0.18/0.45 exuE3e: $o ).
% 0.18/0.45
% 0.18/0.45 thf(exuE3e,definition,
% 0.18/0.45 ( exuE3e
% 0.18/0.45 = ( ! [Xphi: $i > $o] :
% 0.18/0.45 ( ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setext_type,type,
% 0.18/0.45 setext: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setext,definition,
% 0.18/0.45 ( setext
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( in @ Xx @ B ) )
% 0.18/0.45 => ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 => ( in @ Xx @ A ) )
% 0.18/0.45 => ( A = B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyI_type,type,
% 0.18/0.45 emptyI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyI,definition,
% 0.18/0.45 ( emptyI
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ~ ( in @ Xx @ A )
% 0.18/0.45 => ( A = emptyset ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(noeltsimpempty_type,type,
% 0.18/0.45 noeltsimpempty: $o ).
% 0.18/0.45
% 0.18/0.45 thf(noeltsimpempty,definition,
% 0.18/0.45 ( noeltsimpempty
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ~ ( in @ Xx @ A )
% 0.18/0.45 => ( A = emptyset ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setbeta_type,type,
% 0.18/0.45 setbeta: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setbeta,definition,
% 0.18/0.45 ( setbeta
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( ( in @ Xx
% 0.18/0.45 @ ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(nonempty_type,type,
% 0.18/0.45 nonempty: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(nonempty,definition,
% 0.18/0.45 ( nonempty
% 0.18/0.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyE1_type,type,
% 0.18/0.45 nonemptyE1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyE1,definition,
% 0.18/0.45 ( nonemptyE1
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ( nonempty @ A )
% 0.18/0.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyI_type,type,
% 0.18/0.45 nonemptyI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyI,definition,
% 0.18/0.45 ( nonemptyI
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( ( Xphi @ Xx )
% 0.18/0.45 => ( nonempty
% 0.18/0.45 @ ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyI1_type,type,
% 0.18/0.45 nonemptyI1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyI1,definition,
% 0.18/0.45 ( nonemptyI1
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.18/0.45 => ( nonempty @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinIL_type,type,
% 0.18/0.45 setadjoinIL: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinIL,definition,
% 0.18/0.45 ( setadjoinIL
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyinunitempty_type,type,
% 0.18/0.45 emptyinunitempty: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyinunitempty,definition,
% 0.18/0.45 ( emptyinunitempty
% 0.18/0.45 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinIR_type,type,
% 0.18/0.45 setadjoinIR: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinIR,definition,
% 0.18/0.45 ( setadjoinIR
% 0.18/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ A )
% 0.18/0.45 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinE_type,type,
% 0.18/0.45 setadjoinE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinE,definition,
% 0.18/0.45 ( setadjoinE
% 0.18/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.45 => ! [Xphi: $o] :
% 0.18/0.45 ( ( ( Xy = Xx )
% 0.18/0.45 => Xphi )
% 0.18/0.45 => ( ( ( in @ Xy @ A )
% 0.18/0.45 => Xphi )
% 0.18/0.45 => Xphi ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinOr_type,type,
% 0.18/0.45 setadjoinOr: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinOr,definition,
% 0.18/0.45 ( setadjoinOr
% 0.18/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.45 => ( ( Xy = Xx )
% 0.18/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setoftrueEq_type,type,
% 0.18/0.45 setoftrueEq: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setoftrueEq,definition,
% 0.18/0.45 ( setoftrueEq
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xx: $i] : $true )
% 0.18/0.45 = A ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(powersetI_type,type,
% 0.18/0.45 powersetI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(powersetI,definition,
% 0.18/0.45 ( powersetI
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 => ( in @ Xx @ A ) )
% 0.18/0.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyinPowerset_type,type,
% 0.18/0.45 emptyinPowerset: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyinPowerset,definition,
% 0.18/0.45 ( emptyinPowerset
% 0.18/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyInPowerset_type,type,
% 0.18/0.45 emptyInPowerset: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyInPowerset,definition,
% 0.18/0.45 ( emptyInPowerset
% 0.18/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(powersetE_type,type,
% 0.18/0.45 powersetE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(powersetE,definition,
% 0.18/0.45 ( powersetE
% 0.18/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.18/0.45 => ( ( in @ Xx @ B )
% 0.18/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setunionI_type,type,
% 0.18/0.45 setunionI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setunionI,definition,
% 0.18/0.45 ( setunionI
% 0.18/0.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 => ( ( in @ B @ A )
% 0.18/0.45 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setunionE_type,type,
% 0.18/0.45 setunionE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setunionE,definition,
% 0.18/0.45 ( setunionE
% 0.18/0.45 = ( ! [A: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.18/0.45 => ! [Xphi: $o] :
% 0.18/0.45 ( ! [B: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 => ( ( in @ B @ A )
% 0.18/0.45 => Xphi ) )
% 0.18/0.45 => Xphi ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(subPowSU_type,type,
% 0.18/0.45 subPowSU: $o ).
% 0.18/0.45
% 0.18/0.45 thf(subPowSU,definition,
% 0.18/0.45 ( subPowSU
% 0.18/0.45 = ( ! [A: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(exuE2_type,type,
% 0.18/0.45 exuE2: $o ).
% 0.18/0.45
% 0.18/0.45 thf(exuE2,definition,
% 0.18/0.45 ( exuE2
% 0.18/0.45 = ( ! [Xphi: $i > $o] :
% 0.18/0.45 ( ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.45 => ? [Xx: $i] :
% 0.18/0.45 ! [Xy: $i] :
% 0.18/0.45 ( ( Xphi @ Xy )
% 0.18/0.45 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyImpWitness_type,type,
% 0.18/0.45 nonemptyImpWitness: $o ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyImpWitness,definition,
% 0.18/0.45 ( nonemptyImpWitness
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ( nonempty @ A )
% 0.18/0.45 => ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & $true ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(uniqinunit_type,type,
% 0.18/0.45 uniqinunit: $o ).
% 0.18/0.45
% 0.18/0.45 thf(uniqinunit,definition,
% 0.18/0.45 ( uniqinunit
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.45 => ( Xx = Xy ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(notinsingleton_type,type,
% 0.18/0.45 notinsingleton: $o ).
% 0.18/0.45
% 0.18/0.45 thf(notinsingleton,definition,
% 0.18/0.45 ( notinsingleton
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( Xx != Xy )
% 0.18/0.45 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(eqinunit_type,type,
% 0.18/0.45 eqinunit: $o ).
% 0.18/0.45
% 0.18/0.45 thf(eqinunit,definition,
% 0.18/0.45 ( eqinunit
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( Xx = Xy )
% 0.18/0.45 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(singletonsswitch_type,type,
% 0.18/0.45 singletonsswitch: $o ).
% 0.18/0.45
% 0.18/0.45 thf(singletonsswitch,definition,
% 0.18/0.45 ( singletonsswitch
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.45 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(upairsetE_type,type,
% 0.18/0.45 upairsetE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(upairsetE,definition,
% 0.18/0.45 ( upairsetE
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.45 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.18/0.45 => ( ( Xz = Xx )
% 0.18/0.45 | ( Xz = Xy ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(upairsetIL_type,type,
% 0.18/0.45 upairsetIL: $o ).
% 0.18/0.45
% 0.18/0.45 thf(upairsetIL,definition,
% 0.18/0.45 ( upairsetIL
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(upairsetIR_type,type,
% 0.18/0.45 upairsetIR: $o ).
% 0.18/0.45
% 0.18/0.45 thf(upairsetIR,definition,
% 0.18/0.45 ( upairsetIR
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyE1_type,type,
% 0.18/0.45 emptyE1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyE1,definition,
% 0.18/0.45 ( emptyE1
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.45 ( ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & ( Xphi @ Xx ) )
% 0.18/0.45 => ( ( ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.45 = emptyset )
% 0.18/0.45 => $false ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(vacuousDall_type,type,
% 0.18/0.45 vacuousDall: $o ).
% 0.18/0.45
% 0.18/0.45 thf(vacuousDall,definition,
% 0.18/0.45 ( vacuousDall
% 0.18/0.45 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ emptyset )
% 0.18/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan1_type,type,
% 0.18/0.45 quantDeMorgan1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan1,definition,
% 0.18/0.45 ( quantDeMorgan1
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.45 ( ~ ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( Xphi @ Xx ) )
% 0.18/0.45 => ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan2_type,type,
% 0.18/0.45 quantDeMorgan2: $o ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan2,definition,
% 0.18/0.45 ( quantDeMorgan2
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ~ ( Xphi @ Xx ) )
% 0.18/0.45 => ~ ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan3_type,type,
% 0.18/0.45 quantDeMorgan3: $o ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan3,definition,
% 0.18/0.45 ( quantDeMorgan3
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.45 ( ~ ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & ( Xphi @ Xx ) )
% 0.18/0.45 => ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan4_type,type,
% 0.18/0.45 quantDeMorgan4: $o ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan4,definition,
% 0.18/0.45 ( quantDeMorgan4
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.45 ( ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & ~ ( Xphi @ Xx ) )
% 0.18/0.45 => ~ ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(prop2setI_type,type,
% 0.18/0.45 prop2setI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(prop2setI,definition,
% 0.18/0.45 ( prop2setI
% 0.18/0.45 = ( ! [Xphi: $o] :
% 0.18/0.45 ( Xphi
% 0.18/0.45 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(set2prop_type,type,
% 0.18/0.45 set2prop: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(prop2set2propI_type,type,
% 0.18/0.45 prop2set2propI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(prop2set2propI,definition,
% 0.18/0.45 ( prop2set2propI
% 0.18/0.45 = ( ! [Xphi: $o] :
% 0.18/0.45 ( Xphi
% 0.18/0.45 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(notdexE_type,type,
% 0.18/0.45 notdexE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(notdexE,definition,
% 0.18/0.45 ( notdexE
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.45 ( ~ ? [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 & ( Xphi @ Xx ) )
% 0.29/0.45 => ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(notdallE_type,type,
% 0.29/0.45 notdallE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(notdallE,definition,
% 0.29/0.45 ( notdallE
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.45 ( ~ ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( Xphi @ Xx ) )
% 0.29/0.45 => ? [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuI1_type,type,
% 0.29/0.45 exuI1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuI1,definition,
% 0.29/0.45 ( exuI1
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ? [Xx: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 & ! [Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) )
% 0.29/0.45 => ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuI3_type,type,
% 0.29/0.45 exuI3: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuI3,definition,
% 0.29/0.45 ( exuI3
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.29/0.45 => ( ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 => ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) )
% 0.29/0.45 => ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuI2_type,type,
% 0.29/0.45 exuI2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuI2,definition,
% 0.29/0.45 ( exuI2
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ? [Xx: $i] :
% 0.29/0.45 ! [Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xy )
% 0.29/0.45 <=> ( Xy = Xx ) )
% 0.29/0.45 => ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(inCongP_type,type,
% 0.29/0.45 inCongP: $o ).
% 0.29/0.45
% 0.29/0.45 thf(inCongP,definition,
% 0.29/0.45 ( inCongP
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xx = Xy )
% 0.29/0.45 => ( ( in @ Xx @ A )
% 0.29/0.45 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(in__Cong_type,type,
% 0.29/0.45 in__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(in__Cong,definition,
% 0.29/0.45 ( in__Cong
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xx = Xy )
% 0.29/0.45 => ( ( in @ Xx @ A )
% 0.29/0.45 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuE3u_type,type,
% 0.29/0.45 exuE3u: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuE3u,definition,
% 0.29/0.45 ( exuE3u
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 => ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 => ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exu__Cong_type,type,
% 0.29/0.45 exu__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exu__Cong,definition,
% 0.29/0.45 ( exu__Cong
% 0.29/0.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.45 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xx = Xy )
% 0.29/0.45 => ( ( Xphi @ Xx )
% 0.29/0.45 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.45 => ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 <=> ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptyset__Cong_type,type,
% 0.29/0.45 emptyset__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptyset__Cong,definition,
% 0.29/0.45 ( emptyset__Cong
% 0.29/0.45 = ( emptyset = emptyset ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoin__Cong_type,type,
% 0.29/0.45 setadjoin__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoin__Cong,definition,
% 0.29/0.45 ( setadjoin__Cong
% 0.29/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xx = Xy )
% 0.29/0.45 => ! [Xz: $i,Xu: $i] :
% 0.29/0.45 ( ( Xz = Xu )
% 0.29/0.45 => ( ( setadjoin @ Xx @ Xz )
% 0.29/0.45 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(powerset__Cong_type,type,
% 0.29/0.45 powerset__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(powerset__Cong,definition,
% 0.29/0.45 ( powerset__Cong
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ( ( powerset @ A )
% 0.29/0.45 = ( powerset @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setunion__Cong_type,type,
% 0.29/0.45 setunion__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setunion__Cong,definition,
% 0.29/0.45 ( setunion__Cong
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ( ( setunion @ A )
% 0.29/0.45 = ( setunion @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(omega__Cong_type,type,
% 0.29/0.45 omega__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(omega__Cong,definition,
% 0.29/0.45 ( omega__Cong
% 0.29/0.45 = ( omega = omega ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuEu_type,type,
% 0.29/0.45 exuEu: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuEu,definition,
% 0.29/0.45 ( exuEu
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 => ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 => ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(descr__Cong_type,type,
% 0.29/0.45 descr__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(descr__Cong,definition,
% 0.29/0.45 ( descr__Cong
% 0.29/0.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.45 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xx = Xy )
% 0.29/0.45 => ( ( Xphi @ Xx )
% 0.29/0.45 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.45 => ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 => ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.29/0.45 => ( ( descr
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 = ( descr
% 0.29/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstr__Cong_type,type,
% 0.29/0.45 dsetconstr__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstr__Cong,definition,
% 0.29/0.45 ( dsetconstr__Cong
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ! [Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ B )
% 0.29/0.45 => ( ( Xx = Xy )
% 0.29/0.45 => ( ( Xphi @ Xx )
% 0.29/0.45 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.29/0.45 => ( ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 = ( dsetconstr @ B
% 0.29/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subset_type,type,
% 0.29/0.45 subset: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(disjoint_type,type,
% 0.29/0.45 disjoint: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(setsmeet_type,type,
% 0.29/0.45 setsmeet: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetI1_type,type,
% 0.29/0.45 subsetI1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetI1,definition,
% 0.29/0.45 ( subsetI1
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( in @ Xx @ B ) )
% 0.29/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(eqimpsubset2_type,type,
% 0.29/0.45 eqimpsubset2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(eqimpsubset2,definition,
% 0.29/0.45 ( eqimpsubset2
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(eqimpsubset1_type,type,
% 0.29/0.45 eqimpsubset1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(eqimpsubset1,definition,
% 0.29/0.45 ( eqimpsubset1
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subsetI2_type,type,
% 0.29/0.45 subsetI2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetI2,definition,
% 0.29/0.45 ( subsetI2
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( in @ Xx @ B ) )
% 0.29/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetsubset_type,type,
% 0.29/0.45 emptysetsubset: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetsubset,definition,
% 0.29/0.45 ( emptysetsubset
% 0.29/0.45 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subsetE_type,type,
% 0.29/0.45 subsetE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetE,definition,
% 0.29/0.45 ( subsetE
% 0.29/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( ( in @ Xx @ A )
% 0.29/0.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subsetE2_type,type,
% 0.29/0.45 subsetE2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetE2,definition,
% 0.29/0.45 ( subsetE2
% 0.29/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( ~ ( in @ Xx @ B )
% 0.29/0.45 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(notsubsetI_type,type,
% 0.29/0.45 notsubsetI: $o ).
% 0.29/0.45
% 0.29/0.45 thf(notsubsetI,definition,
% 0.29/0.45 ( notsubsetI
% 0.29/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( ~ ( in @ Xx @ B )
% 0.29/0.45 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(notequalI1_type,type,
% 0.29/0.45 notequalI1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(notequalI1,definition,
% 0.29/0.45 ( notequalI1
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ~ ( subset @ A @ B )
% 0.29/0.45 => ( A != B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(notequalI2_type,type,
% 0.29/0.45 notequalI2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(notequalI2,definition,
% 0.29/0.45 ( notequalI2
% 0.29/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( ~ ( in @ Xx @ B )
% 0.29/0.45 => ( A != B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subsetRefl_type,type,
% 0.29/0.45 subsetRefl: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetRefl,definition,
% 0.29/0.45 ( subsetRefl
% 0.29/0.45 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subsetTrans_type,type,
% 0.29/0.45 subsetTrans: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetTrans,definition,
% 0.29/0.45 ( subsetTrans
% 0.29/0.45 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( ( subset @ B @ C )
% 0.29/0.45 => ( subset @ A @ C ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinSub_type,type,
% 0.29/0.45 setadjoinSub: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinSub,definition,
% 0.29/0.45 ( setadjoinSub
% 0.29/0.45 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinSub2_type,type,
% 0.29/0.45 setadjoinSub2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinSub2,definition,
% 0.29/0.45 ( setadjoinSub2
% 0.29/0.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subset2powerset_type,type,
% 0.29/0.45 subset2powerset: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subset2powerset,definition,
% 0.29/0.45 ( subset2powerset
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setextsub_type,type,
% 0.29/0.45 setextsub: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setextsub,definition,
% 0.29/0.45 ( setextsub
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( ( subset @ B @ A )
% 0.29/0.45 => ( A = B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subsetemptysetimpeq_type,type,
% 0.29/0.45 subsetemptysetimpeq: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetemptysetimpeq,definition,
% 0.29/0.45 ( subsetemptysetimpeq
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ( subset @ A @ emptyset )
% 0.29/0.45 => ( A = emptyset ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(powersetI1_type,type,
% 0.29/0.45 powersetI1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(powersetI1,definition,
% 0.29/0.45 ( powersetI1
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( subset @ B @ A )
% 0.29/0.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(powersetE1_type,type,
% 0.29/0.45 powersetE1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(powersetE1,definition,
% 0.29/0.45 ( powersetE1
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.45 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(inPowerset_type,type,
% 0.29/0.45 inPowerset: $o ).
% 0.29/0.45
% 0.29/0.45 thf(inPowerset,definition,
% 0.29/0.45 ( inPowerset
% 0.29/0.45 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(powersetsubset_type,type,
% 0.29/0.45 powersetsubset: $o ).
% 0.29/0.45
% 0.29/0.45 thf(powersetsubset,definition,
% 0.29/0.45 ( powersetsubset
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sepInPowerset,conjecture,
% 0.29/0.45 ( setextAx
% 0.29/0.45 => ( emptysetAx
% 0.29/0.45 => ( setadjoinAx
% 0.29/0.45 => ( powersetAx
% 0.29/0.45 => ( setunionAx
% 0.29/0.45 => ( omega0Ax
% 0.29/0.45 => ( omegaSAx
% 0.29/0.45 => ( omegaIndAx
% 0.29/0.45 => ( replAx
% 0.29/0.45 => ( foundationAx
% 0.29/0.45 => ( wellorderingAx
% 0.29/0.45 => ( descrp
% 0.29/0.45 => ( dsetconstrI
% 0.29/0.45 => ( dsetconstrEL
% 0.29/0.45 => ( dsetconstrER
% 0.29/0.45 => ( exuE1
% 0.29/0.45 => ( prop2setE
% 0.29/0.45 => ( emptysetE
% 0.29/0.45 => ( emptysetimpfalse
% 0.29/0.45 => ( notinemptyset
% 0.29/0.45 => ( exuE3e
% 0.29/0.45 => ( setext
% 0.29/0.45 => ( emptyI
% 0.29/0.45 => ( noeltsimpempty
% 0.29/0.45 => ( setbeta
% 0.29/0.45 => ( nonemptyE1
% 0.29/0.45 => ( nonemptyI
% 0.29/0.45 => ( nonemptyI1
% 0.29/0.45 => ( setadjoinIL
% 0.29/0.45 => ( emptyinunitempty
% 0.29/0.45 => ( setadjoinIR
% 0.29/0.45 => ( setadjoinE
% 0.29/0.45 => ( setadjoinOr
% 0.29/0.45 => ( setoftrueEq
% 0.29/0.45 => ( powersetI
% 0.29/0.45 => ( emptyinPowerset
% 0.29/0.45 => ( emptyInPowerset
% 0.29/0.45 => ( powersetE
% 0.29/0.45 => ( setunionI
% 0.29/0.45 => ( setunionE
% 0.29/0.45 => ( subPowSU
% 0.29/0.45 => ( exuE2
% 0.29/0.45 => ( nonemptyImpWitness
% 0.29/0.45 => ( uniqinunit
% 0.29/0.45 => ( notinsingleton
% 0.29/0.45 => ( eqinunit
% 0.29/0.45 => ( singletonsswitch
% 0.29/0.45 => ( upairsetE
% 0.29/0.45 => ( upairsetIL
% 0.29/0.45 => ( upairsetIR
% 0.29/0.45 => ( emptyE1
% 0.29/0.45 => ( vacuousDall
% 0.29/0.45 => ( quantDeMorgan1
% 0.29/0.45 => ( quantDeMorgan2
% 0.29/0.45 => ( quantDeMorgan3
% 0.29/0.45 => ( quantDeMorgan4
% 0.29/0.45 => ( prop2setI
% 0.29/0.45 => ( prop2set2propI
% 0.29/0.45 => ( notdexE
% 0.29/0.45 => ( notdallE
% 0.29/0.45 => ( exuI1
% 0.29/0.45 => ( exuI3
% 0.29/0.45 => ( exuI2
% 0.29/0.45 => ( inCongP
% 0.29/0.45 => ( in__Cong
% 0.29/0.45 => ( exuE3u
% 0.29/0.45 => ( exu__Cong
% 0.29/0.45 => ( emptyset__Cong
% 0.29/0.45 => ( setadjoin__Cong
% 0.29/0.45 => ( powerset__Cong
% 0.29/0.45 => ( setunion__Cong
% 0.29/0.45 => ( omega__Cong
% 0.29/0.45 => ( exuEu
% 0.29/0.45 => ( descr__Cong
% 0.29/0.45 => ( dsetconstr__Cong
% 0.29/0.45 => ( subsetI1
% 0.29/0.45 => ( eqimpsubset2
% 0.29/0.45 => ( eqimpsubset1
% 0.29/0.45 => ( subsetI2
% 0.29/0.45 => ( emptysetsubset
% 0.29/0.45 => ( subsetE
% 0.29/0.45 => ( subsetE2
% 0.29/0.45 => ( notsubsetI
% 0.29/0.45 => ( notequalI1
% 0.29/0.45 => ( notequalI2
% 0.29/0.45 => ( subsetRefl
% 0.29/0.45 => ( subsetTrans
% 0.29/0.45 => ( setadjoinSub
% 0.29/0.45 => ( setadjoinSub2
% 0.29/0.45 => ( subset2powerset
% 0.29/0.45 => ( setextsub
% 0.29/0.45 => ( subsetemptysetimpeq
% 0.29/0.45 => ( powersetI1
% 0.29/0.45 => ( powersetE1
% 0.29/0.45 => ( inPowerset
% 0.29/0.45 => ( powersetsubset
% 0.29/0.45 => ! [A: $i,Xphi: $i > $o] :
% 0.29/0.45 ( in
% 0.29/0.45 @ ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 2.09/1.37 ---- Embedded in THF ---
% 2.09/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.09/1.37 %%% Generated on Tue Feb 24 12:27:45 EST 2026
% 2.09/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 2.09/1.37 %%% Logic specification used:
% 2.09/1.37 %%% thf(spec, logic, $$dhol).
% 2.09/1.37
% 2.09/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qcVYf693pv/DTF2DTF5389.p
% See solution above
% 2.09/1.37 ------------------------
% 2.09/1.38 ---- Cleaned THF ---
% 2.09/1.38 thf(in_type,type,
% 2.09/1.38 in: $i > $i > $o ).
% 2.09/1.38
% 2.09/1.38 thf(exu_type,type,
% 2.09/1.38 exu: ( $i > $o ) > $o ).
% 2.09/1.38
% 2.09/1.38 thf(exu,definition,
% 2.09/1.38 ( exu
% 2.09/1.38 = ( ^ [Xphi: $i > $o] :
% 2.09/1.38 ? [Xx: $i] :
% 2.09/1.38 ( ( Xphi @ Xx )
% 2.09/1.38 & ! [Xy: $i] :
% 2.09/1.38 ( ( Xphi @ Xy )
% 2.09/1.38 => ( Xx = Xy ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(setextAx_type,type,
% 2.09/1.38 setextAx: $o ).
% 2.09/1.38
% 2.09/1.38 thf(setextAx,definition,
% 2.09/1.38 ( setextAx
% 2.09/1.38 = ( ! [A: $i,B: $i] :
% 2.09/1.38 ( ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 <=> ( in @ Xx @ B ) )
% 2.09/1.38 => ( A = B ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(emptyset_type,type,
% 2.09/1.38 emptyset: $i ).
% 2.09/1.38
% 2.09/1.38 thf(emptysetAx_type,type,
% 2.09/1.38 emptysetAx: $o ).
% 2.09/1.38
% 2.09/1.38 thf(emptysetAx,definition,
% 2.09/1.38 ( emptysetAx
% 2.09/1.38 = ( ! [Xx: $i] :
% 2.09/1.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(setadjoin_type,type,
% 2.09/1.38 setadjoin: $i > $i > $i ).
% 2.09/1.38
% 2.09/1.38 thf(setadjoinAx_type,type,
% 2.09/1.38 setadjoinAx: $o ).
% 2.09/1.38
% 2.09/1.38 thf(setadjoinAx,definition,
% 2.09/1.38 ( setadjoinAx
% 2.09/1.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.09/1.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.09/1.38 <=> ( ( Xy = Xx )
% 2.09/1.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(powerset_type,type,
% 2.09/1.38 powerset: $i > $i ).
% 2.09/1.38
% 2.09/1.38 thf(powersetAx_type,type,
% 2.09/1.38 powersetAx: $o ).
% 2.09/1.38
% 2.09/1.38 thf(powersetAx,definition,
% 2.09/1.38 ( powersetAx
% 2.09/1.38 = ( ! [A: $i,B: $i] :
% 2.09/1.38 ( ( in @ B @ ( powerset @ A ) )
% 2.09/1.38 <=> ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ B )
% 2.09/1.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(setunion_type,type,
% 2.09/1.38 setunion: $i > $i ).
% 2.09/1.38
% 2.09/1.38 thf(setunionAx_type,type,
% 2.09/1.38 setunionAx: $o ).
% 2.09/1.38
% 2.09/1.38 thf(setunionAx,definition,
% 2.09/1.38 ( setunionAx
% 2.09/1.38 = ( ! [A: $i,Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ ( setunion @ A ) )
% 2.09/1.38 <=> ? [B: $i] :
% 2.09/1.38 ( ( in @ Xx @ B )
% 2.09/1.38 & ( in @ B @ A ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(omega_type,type,
% 2.09/1.38 omega: $i ).
% 2.09/1.38
% 2.09/1.38 thf(omega0Ax_type,type,
% 2.09/1.38 omega0Ax: $o ).
% 2.09/1.38
% 2.09/1.38 thf(omega0Ax,definition,
% 2.09/1.38 ( omega0Ax
% 2.09/1.38 = ( in @ emptyset @ omega ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(omegaSAx_type,type,
% 2.09/1.38 omegaSAx: $o ).
% 2.09/1.38
% 2.09/1.38 thf(omegaSAx,definition,
% 2.09/1.38 ( omegaSAx
% 2.09/1.38 = ( ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ omega )
% 2.09/1.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(omegaIndAx_type,type,
% 2.09/1.38 omegaIndAx: $o ).
% 2.09/1.38
% 2.09/1.38 thf(omegaIndAx,definition,
% 2.09/1.38 ( omegaIndAx
% 2.09/1.38 = ( ! [A: $i] :
% 2.09/1.38 ( ( ( in @ emptyset @ A )
% 2.09/1.38 & ! [Xx: $i] :
% 2.09/1.38 ( ( ( in @ Xx @ omega )
% 2.09/1.38 & ( in @ Xx @ A ) )
% 2.09/1.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.09/1.38 => ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ omega )
% 2.09/1.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(replAx_type,type,
% 2.09/1.38 replAx: $o ).
% 2.09/1.38
% 2.09/1.38 thf(replAx,definition,
% 2.09/1.38 ( replAx
% 2.09/1.38 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.09/1.38 ( ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 => ( exu
% 2.09/1.38 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.09/1.38 => ? [B: $i] :
% 2.09/1.38 ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ B )
% 2.09/1.38 <=> ? [Xy: $i] :
% 2.09/1.38 ( ( in @ Xy @ A )
% 2.09/1.38 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(foundationAx_type,type,
% 2.09/1.38 foundationAx: $o ).
% 2.09/1.38
% 2.09/1.38 thf(foundationAx,definition,
% 2.09/1.38 ( foundationAx
% 2.09/1.38 = ( ! [A: $i] :
% 2.09/1.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.09/1.38 => ? [B: $i] :
% 2.09/1.38 ( ( in @ B @ A )
% 2.09/1.38 & ~ ? [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ B )
% 2.09/1.38 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(wellorderingAx_type,type,
% 2.09/1.38 wellorderingAx: $o ).
% 2.09/1.38
% 2.09/1.38 thf(wellorderingAx,definition,
% 2.09/1.38 ( wellorderingAx
% 2.09/1.38 = ( ! [A: $i] :
% 2.09/1.38 ? [B: $i] :
% 2.09/1.38 ( ! [C: $i] :
% 2.09/1.38 ( ( in @ C @ B )
% 2.09/1.38 => ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ C )
% 2.09/1.38 => ( in @ Xx @ A ) ) )
% 2.09/1.38 & ! [Xx: $i,Xy: $i] :
% 2.09/1.38 ( ( ( in @ Xx @ A )
% 2.09/1.38 & ( in @ Xy @ A ) )
% 2.09/1.38 => ( ! [C: $i] :
% 2.09/1.38 ( ( in @ C @ B )
% 2.09/1.38 => ( ( in @ Xx @ C )
% 2.09/1.38 <=> ( in @ Xy @ C ) ) )
% 2.09/1.38 => ( Xx = Xy ) ) )
% 2.09/1.38 & ! [C: $i,D: $i] :
% 2.09/1.38 ( ( ( in @ C @ B )
% 2.09/1.38 & ( in @ D @ B ) )
% 2.09/1.38 => ( ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ C )
% 2.09/1.38 => ( in @ Xx @ D ) )
% 2.09/1.38 | ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ D )
% 2.09/1.38 => ( in @ Xx @ C ) ) ) )
% 2.09/1.38 & ! [C: $i] :
% 2.09/1.38 ( ( ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ C )
% 2.09/1.38 => ( in @ Xx @ A ) )
% 2.09/1.38 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.09/1.38 => ? [D: $i,Xx: $i] :
% 2.09/1.38 ( ( in @ D @ B )
% 2.09/1.38 & ( in @ Xx @ C )
% 2.09/1.38 & ~ ? [Xy: $i] :
% 2.09/1.38 ( ( in @ Xy @ D )
% 2.09/1.38 & ( in @ Xy @ C ) )
% 2.09/1.38 & ! [E: $i] :
% 2.09/1.38 ( ( in @ E @ B )
% 2.09/1.38 => ( ! [Xy: $i] :
% 2.09/1.38 ( ( in @ Xy @ E )
% 2.09/1.38 => ( in @ Xy @ D ) )
% 2.09/1.38 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(descr_type,type,
% 2.09/1.38 descr: ( $i > $o ) > $i ).
% 2.09/1.38
% 2.09/1.38 thf(descrp_type,type,
% 2.09/1.38 descrp: $o ).
% 2.09/1.38
% 2.09/1.38 thf(descrp,definition,
% 2.09/1.38 ( descrp
% 2.09/1.38 = ( ! [Xphi: $i > $o] :
% 2.09/1.38 ( ( exu
% 2.09/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.38 => ( Xphi
% 2.09/1.38 @ ( descr
% 2.09/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(dsetconstr_type,type,
% 2.09/1.38 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.09/1.38
% 2.09/1.38 thf(dsetconstrI_type,type,
% 2.09/1.38 dsetconstrI: $o ).
% 2.09/1.38
% 2.09/1.38 thf(dsetconstrI,definition,
% 2.09/1.38 ( dsetconstrI
% 2.09/1.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 => ( ( Xphi @ Xx )
% 2.09/1.38 => ( in @ Xx
% 2.09/1.38 @ ( dsetconstr @ A
% 2.09/1.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(dsetconstrEL_type,type,
% 2.09/1.38 dsetconstrEL: $o ).
% 2.09/1.38
% 2.09/1.38 thf(dsetconstrEL,definition,
% 2.09/1.38 ( dsetconstrEL
% 2.09/1.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.09/1.38 ( ( in @ Xx
% 2.09/1.38 @ ( dsetconstr @ A
% 2.09/1.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.09/1.38 => ( in @ Xx @ A ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(dsetconstrER_type,type,
% 2.09/1.38 dsetconstrER: $o ).
% 2.09/1.38
% 2.09/1.38 thf(dsetconstrER,definition,
% 2.09/1.38 ( dsetconstrER
% 2.09/1.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.09/1.38 ( ( in @ Xx
% 2.09/1.38 @ ( dsetconstr @ A
% 2.09/1.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.09/1.38 => ( Xphi @ Xx ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(exuE1_type,type,
% 2.09/1.38 exuE1: $o ).
% 2.09/1.38
% 2.09/1.38 thf(exuE1,definition,
% 2.09/1.38 ( exuE1
% 2.09/1.38 = ( ! [Xphi: $i > $o] :
% 2.09/1.38 ( ( exu
% 2.09/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.38 => ? [Xx: $i] :
% 2.09/1.38 ( ( Xphi @ Xx )
% 2.09/1.38 & ! [Xy: $i] :
% 2.09/1.38 ( ( Xphi @ Xy )
% 2.09/1.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(prop2set_type,type,
% 2.09/1.38 prop2set: $o > $i ).
% 2.09/1.38
% 2.09/1.38 thf(prop2setE_type,type,
% 2.09/1.38 prop2setE: $o ).
% 2.09/1.38
% 2.09/1.38 thf(prop2setE,definition,
% 2.09/1.38 ( prop2setE
% 2.09/1.38 = ( ! [Xphi: $o,Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.09/1.38 => Xphi ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(emptysetE_type,type,
% 2.09/1.38 emptysetE: $o ).
% 2.09/1.38
% 2.09/1.38 thf(emptysetE,definition,
% 2.09/1.38 ( emptysetE
% 2.09/1.38 = ( ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ emptyset )
% 2.09/1.38 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(emptysetimpfalse_type,type,
% 2.09/1.38 emptysetimpfalse: $o ).
% 2.09/1.38
% 2.09/1.38 thf(emptysetimpfalse,definition,
% 2.09/1.38 ( emptysetimpfalse
% 2.09/1.38 = ( ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ emptyset )
% 2.09/1.38 => $false ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(notinemptyset_type,type,
% 2.09/1.38 notinemptyset: $o ).
% 2.09/1.38
% 2.09/1.38 thf(notinemptyset,definition,
% 2.09/1.38 ( notinemptyset
% 2.09/1.38 = ( ! [Xx: $i] :
% 2.09/1.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(exuE3e_type,type,
% 2.09/1.38 exuE3e: $o ).
% 2.09/1.38
% 2.09/1.38 thf(exuE3e,definition,
% 2.09/1.38 ( exuE3e
% 2.09/1.38 = ( ! [Xphi: $i > $o] :
% 2.09/1.38 ( ( exu
% 2.09/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.38 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(setext_type,type,
% 2.09/1.38 setext: $o ).
% 2.09/1.38
% 2.09/1.38 thf(setext,definition,
% 2.09/1.38 ( setext
% 2.09/1.38 = ( ! [A: $i,B: $i] :
% 2.09/1.38 ( ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 => ( in @ Xx @ B ) )
% 2.09/1.38 => ( ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ B )
% 2.09/1.38 => ( in @ Xx @ A ) )
% 2.09/1.38 => ( A = B ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(emptyI_type,type,
% 2.09/1.38 emptyI: $o ).
% 2.09/1.38
% 2.09/1.38 thf(emptyI,definition,
% 2.09/1.38 ( emptyI
% 2.09/1.38 = ( ! [A: $i] :
% 2.09/1.38 ( ! [Xx: $i] :
% 2.09/1.38 ~ ( in @ Xx @ A )
% 2.09/1.38 => ( A = emptyset ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(noeltsimpempty_type,type,
% 2.09/1.38 noeltsimpempty: $o ).
% 2.09/1.38
% 2.09/1.38 thf(noeltsimpempty,definition,
% 2.09/1.38 ( noeltsimpempty
% 2.09/1.38 = ( ! [A: $i] :
% 2.09/1.38 ( ! [Xx: $i] :
% 2.09/1.38 ~ ( in @ Xx @ A )
% 2.09/1.38 => ( A = emptyset ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(setbeta_type,type,
% 2.09/1.38 setbeta: $o ).
% 2.09/1.38
% 2.09/1.38 thf(setbeta,definition,
% 2.09/1.38 ( setbeta
% 2.09/1.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 => ( ( in @ Xx
% 2.09/1.38 @ ( dsetconstr @ A
% 2.09/1.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.09/1.38 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(nonempty_type,type,
% 2.09/1.38 nonempty: $i > $o ).
% 2.09/1.38
% 2.09/1.38 thf(nonempty,definition,
% 2.09/1.38 ( nonempty
% 2.09/1.38 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(nonemptyE1_type,type,
% 2.09/1.38 nonemptyE1: $o ).
% 2.09/1.38
% 2.09/1.38 thf(nonemptyE1,definition,
% 2.09/1.38 ( nonemptyE1
% 2.09/1.38 = ( ! [A: $i] :
% 2.09/1.38 ( ( nonempty @ A )
% 2.09/1.38 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(nonemptyI_type,type,
% 2.09/1.38 nonemptyI: $o ).
% 2.09/1.38
% 2.09/1.38 thf(nonemptyI,definition,
% 2.09/1.38 ( nonemptyI
% 2.09/1.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 => ( ( Xphi @ Xx )
% 2.09/1.38 => ( nonempty
% 2.09/1.38 @ ( dsetconstr @ A
% 2.09/1.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(nonemptyI1_type,type,
% 2.09/1.38 nonemptyI1: $o ).
% 2.09/1.38
% 2.09/1.38 thf(nonemptyI1,definition,
% 2.09/1.38 ( nonemptyI1
% 2.09/1.38 = ( ! [A: $i] :
% 2.09/1.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.09/1.38 => ( nonempty @ A ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(setadjoinIL_type,type,
% 2.09/1.38 setadjoinIL: $o ).
% 2.09/1.38
% 2.09/1.38 thf(setadjoinIL,definition,
% 2.09/1.38 ( setadjoinIL
% 2.09/1.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(emptyinunitempty_type,type,
% 2.09/1.38 emptyinunitempty: $o ).
% 2.09/1.38
% 2.09/1.38 thf(emptyinunitempty,definition,
% 2.09/1.38 ( emptyinunitempty
% 2.09/1.38 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(setadjoinIR_type,type,
% 2.09/1.38 setadjoinIR: $o ).
% 2.09/1.38
% 2.09/1.38 thf(setadjoinIR,definition,
% 2.09/1.38 ( setadjoinIR
% 2.09/1.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.09/1.38 ( ( in @ Xy @ A )
% 2.09/1.38 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(setadjoinE_type,type,
% 2.09/1.38 setadjoinE: $o ).
% 2.09/1.38
% 2.09/1.38 thf(setadjoinE,definition,
% 2.09/1.38 ( setadjoinE
% 2.09/1.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.09/1.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.09/1.38 => ! [Xphi: $o] :
% 2.09/1.38 ( ( ( Xy = Xx )
% 2.09/1.38 => Xphi )
% 2.09/1.38 => ( ( ( in @ Xy @ A )
% 2.09/1.38 => Xphi )
% 2.09/1.38 => Xphi ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(setadjoinOr_type,type,
% 2.09/1.38 setadjoinOr: $o ).
% 2.09/1.38
% 2.09/1.38 thf(setadjoinOr,definition,
% 2.09/1.38 ( setadjoinOr
% 2.09/1.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.09/1.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.09/1.38 => ( ( Xy = Xx )
% 2.09/1.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(setoftrueEq_type,type,
% 2.09/1.38 setoftrueEq: $o ).
% 2.09/1.38
% 2.09/1.38 thf(setoftrueEq,definition,
% 2.09/1.38 ( setoftrueEq
% 2.09/1.38 = ( ! [A: $i] :
% 2.09/1.38 ( ( dsetconstr @ A
% 2.09/1.38 @ ^ [Xx: $i] : $true )
% 2.09/1.38 = A ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(powersetI_type,type,
% 2.09/1.38 powersetI: $o ).
% 2.09/1.38
% 2.09/1.38 thf(powersetI,definition,
% 2.09/1.38 ( powersetI
% 2.09/1.38 = ( ! [A: $i,B: $i] :
% 2.09/1.38 ( ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ B )
% 2.09/1.38 => ( in @ Xx @ A ) )
% 2.09/1.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(emptyinPowerset_type,type,
% 2.09/1.38 emptyinPowerset: $o ).
% 2.09/1.38
% 2.09/1.38 thf(emptyinPowerset,definition,
% 2.09/1.38 ( emptyinPowerset
% 2.09/1.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(emptyInPowerset_type,type,
% 2.09/1.38 emptyInPowerset: $o ).
% 2.09/1.38
% 2.09/1.38 thf(emptyInPowerset,definition,
% 2.09/1.38 ( emptyInPowerset
% 2.09/1.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(powersetE_type,type,
% 2.09/1.38 powersetE: $o ).
% 2.09/1.38
% 2.09/1.38 thf(powersetE,definition,
% 2.09/1.38 ( powersetE
% 2.09/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.38 ( ( in @ B @ ( powerset @ A ) )
% 2.09/1.38 => ( ( in @ Xx @ B )
% 2.09/1.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(setunionI_type,type,
% 2.09/1.38 setunionI: $o ).
% 2.09/1.38
% 2.09/1.38 thf(setunionI,definition,
% 2.09/1.38 ( setunionI
% 2.09/1.38 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.09/1.38 ( ( in @ Xx @ B )
% 2.09/1.38 => ( ( in @ B @ A )
% 2.09/1.38 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(setunionE_type,type,
% 2.09/1.38 setunionE: $o ).
% 2.09/1.38
% 2.09/1.38 thf(setunionE,definition,
% 2.09/1.38 ( setunionE
% 2.09/1.38 = ( ! [A: $i,Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ ( setunion @ A ) )
% 2.09/1.38 => ! [Xphi: $o] :
% 2.09/1.38 ( ! [B: $i] :
% 2.09/1.38 ( ( in @ Xx @ B )
% 2.09/1.38 => ( ( in @ B @ A )
% 2.09/1.38 => Xphi ) )
% 2.09/1.38 => Xphi ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(subPowSU_type,type,
% 2.09/1.38 subPowSU: $o ).
% 2.09/1.38
% 2.09/1.38 thf(subPowSU,definition,
% 2.09/1.38 ( subPowSU
% 2.09/1.38 = ( ! [A: $i,Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(exuE2_type,type,
% 2.09/1.38 exuE2: $o ).
% 2.09/1.38
% 2.09/1.38 thf(exuE2,definition,
% 2.09/1.38 ( exuE2
% 2.09/1.38 = ( ! [Xphi: $i > $o] :
% 2.09/1.38 ( ( exu
% 2.09/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.38 => ? [Xx: $i] :
% 2.09/1.38 ! [Xy: $i] :
% 2.09/1.38 ( ( Xphi @ Xy )
% 2.09/1.38 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(nonemptyImpWitness_type,type,
% 2.09/1.38 nonemptyImpWitness: $o ).
% 2.09/1.38
% 2.09/1.38 thf(nonemptyImpWitness,definition,
% 2.09/1.38 ( nonemptyImpWitness
% 2.09/1.38 = ( ! [A: $i] :
% 2.09/1.38 ( ( nonempty @ A )
% 2.09/1.38 => ? [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 & $true ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(uniqinunit_type,type,
% 2.09/1.38 uniqinunit: $o ).
% 2.09/1.38
% 2.09/1.38 thf(uniqinunit,definition,
% 2.09/1.38 ( uniqinunit
% 2.09/1.38 = ( ! [Xx: $i,Xy: $i] :
% 2.09/1.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.09/1.38 => ( Xx = Xy ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(notinsingleton_type,type,
% 2.09/1.38 notinsingleton: $o ).
% 2.09/1.38
% 2.09/1.38 thf(notinsingleton,definition,
% 2.09/1.38 ( notinsingleton
% 2.09/1.38 = ( ! [Xx: $i,Xy: $i] :
% 2.09/1.38 ( ( Xx != Xy )
% 2.09/1.38 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(eqinunit_type,type,
% 2.09/1.38 eqinunit: $o ).
% 2.09/1.38
% 2.09/1.38 thf(eqinunit,definition,
% 2.09/1.38 ( eqinunit
% 2.09/1.38 = ( ! [Xx: $i,Xy: $i] :
% 2.09/1.38 ( ( Xx = Xy )
% 2.09/1.38 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(singletonsswitch_type,type,
% 2.09/1.38 singletonsswitch: $o ).
% 2.09/1.38
% 2.09/1.38 thf(singletonsswitch,definition,
% 2.09/1.38 ( singletonsswitch
% 2.09/1.38 = ( ! [Xx: $i,Xy: $i] :
% 2.09/1.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.09/1.38 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(upairsetE_type,type,
% 2.09/1.38 upairsetE: $o ).
% 2.09/1.38
% 2.09/1.38 thf(upairsetE,definition,
% 2.09/1.38 ( upairsetE
% 2.09/1.38 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.09/1.38 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.09/1.38 => ( ( Xz = Xx )
% 2.09/1.38 | ( Xz = Xy ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(upairsetIL_type,type,
% 2.09/1.38 upairsetIL: $o ).
% 2.09/1.38
% 2.09/1.38 thf(upairsetIL,definition,
% 2.09/1.38 ( upairsetIL
% 2.09/1.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(upairsetIR_type,type,
% 2.09/1.38 upairsetIR: $o ).
% 2.09/1.38
% 2.09/1.38 thf(upairsetIR,definition,
% 2.09/1.38 ( upairsetIR
% 2.09/1.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(emptyE1_type,type,
% 2.09/1.38 emptyE1: $o ).
% 2.09/1.38
% 2.09/1.38 thf(emptyE1,definition,
% 2.09/1.38 ( emptyE1
% 2.09/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.38 ( ? [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 & ( Xphi @ Xx ) )
% 2.09/1.38 => ( ( ( dsetconstr @ A
% 2.09/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.38 = emptyset )
% 2.09/1.38 => $false ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(vacuousDall_type,type,
% 2.09/1.38 vacuousDall: $o ).
% 2.09/1.38
% 2.09/1.38 thf(vacuousDall,definition,
% 2.09/1.38 ( vacuousDall
% 2.09/1.38 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ emptyset )
% 2.09/1.38 => ( Xphi @ Xx ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(quantDeMorgan1_type,type,
% 2.09/1.38 quantDeMorgan1: $o ).
% 2.09/1.38
% 2.09/1.38 thf(quantDeMorgan1,definition,
% 2.09/1.38 ( quantDeMorgan1
% 2.09/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.38 ( ~ ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 => ( Xphi @ Xx ) )
% 2.09/1.38 => ? [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(quantDeMorgan2_type,type,
% 2.09/1.38 quantDeMorgan2: $o ).
% 2.09/1.38
% 2.09/1.38 thf(quantDeMorgan2,definition,
% 2.09/1.38 ( quantDeMorgan2
% 2.09/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.38 ( ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 => ~ ( Xphi @ Xx ) )
% 2.09/1.38 => ~ ? [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(quantDeMorgan3_type,type,
% 2.09/1.38 quantDeMorgan3: $o ).
% 2.09/1.38
% 2.09/1.38 thf(quantDeMorgan3,definition,
% 2.09/1.38 ( quantDeMorgan3
% 2.09/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.38 ( ~ ? [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 & ( Xphi @ Xx ) )
% 2.09/1.38 => ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(quantDeMorgan4_type,type,
% 2.09/1.38 quantDeMorgan4: $o ).
% 2.09/1.38
% 2.09/1.38 thf(quantDeMorgan4,definition,
% 2.09/1.38 ( quantDeMorgan4
% 2.09/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.38 ( ? [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 & ~ ( Xphi @ Xx ) )
% 2.09/1.38 => ~ ! [Xx: $i] :
% 2.09/1.38 ( ( in @ Xx @ A )
% 2.09/1.38 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.38
% 2.09/1.38 thf(prop2setI_type,type,
% 2.09/1.38 prop2setI: $o ).
% 2.09/1.38
% 2.09/1.38 thf(prop2setI,definition,
% 2.09/1.39 ( prop2setI
% 2.09/1.39 = ( ! [Xphi: $o] :
% 2.09/1.39 ( Xphi
% 2.09/1.39 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(set2prop_type,type,
% 2.09/1.39 set2prop: $i > $o ).
% 2.09/1.39
% 2.09/1.39 thf(prop2set2propI_type,type,
% 2.09/1.39 prop2set2propI: $o ).
% 2.09/1.39
% 2.09/1.39 thf(prop2set2propI,definition,
% 2.09/1.39 ( prop2set2propI
% 2.09/1.39 = ( ! [Xphi: $o] :
% 2.09/1.39 ( Xphi
% 2.09/1.39 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(notdexE_type,type,
% 2.09/1.39 notdexE: $o ).
% 2.09/1.39
% 2.09/1.39 thf(notdexE,definition,
% 2.09/1.39 ( notdexE
% 2.09/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.39 ( ~ ? [Xx: $i] :
% 2.09/1.39 ( ( in @ Xx @ A )
% 2.09/1.39 & ( Xphi @ Xx ) )
% 2.09/1.39 => ! [Xx: $i] :
% 2.09/1.39 ( ( in @ Xx @ A )
% 2.09/1.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(notdallE_type,type,
% 2.09/1.39 notdallE: $o ).
% 2.09/1.39
% 2.09/1.39 thf(notdallE,definition,
% 2.09/1.39 ( notdallE
% 2.09/1.39 = ( ! [A: $i,Xphi: $i > $o] :
% 2.09/1.39 ( ~ ! [Xx: $i] :
% 2.09/1.39 ( ( in @ Xx @ A )
% 2.09/1.39 => ( Xphi @ Xx ) )
% 2.09/1.39 => ? [Xx: $i] :
% 2.09/1.39 ( ( in @ Xx @ A )
% 2.09/1.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(exuI1_type,type,
% 2.09/1.39 exuI1: $o ).
% 2.09/1.39
% 2.09/1.39 thf(exuI1,definition,
% 2.09/1.39 ( exuI1
% 2.09/1.39 = ( ! [Xphi: $i > $o] :
% 2.09/1.39 ( ? [Xx: $i] :
% 2.09/1.39 ( ( Xphi @ Xx )
% 2.09/1.39 & ! [Xy: $i] :
% 2.09/1.39 ( ( Xphi @ Xy )
% 2.09/1.39 => ( Xx = Xy ) ) )
% 2.09/1.39 => ( exu
% 2.09/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(exuI3_type,type,
% 2.09/1.39 exuI3: $o ).
% 2.09/1.39
% 2.09/1.39 thf(exuI3,definition,
% 2.09/1.39 ( exuI3
% 2.09/1.39 = ( ! [Xphi: $i > $o] :
% 2.09/1.39 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.09/1.39 => ( ! [Xx: $i,Xy: $i] :
% 2.09/1.39 ( ( Xphi @ Xx )
% 2.09/1.39 => ( ( Xphi @ Xy )
% 2.09/1.39 => ( Xx = Xy ) ) )
% 2.09/1.39 => ( exu
% 2.09/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(exuI2_type,type,
% 2.09/1.39 exuI2: $o ).
% 2.09/1.39
% 2.09/1.39 thf(exuI2,definition,
% 2.09/1.39 ( exuI2
% 2.09/1.39 = ( ! [Xphi: $i > $o] :
% 2.09/1.39 ( ? [Xx: $i] :
% 2.09/1.39 ! [Xy: $i] :
% 2.09/1.39 ( ( Xphi @ Xy )
% 2.09/1.39 <=> ( Xy = Xx ) )
% 2.09/1.39 => ( exu
% 2.09/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(inCongP_type,type,
% 2.09/1.39 inCongP: $o ).
% 2.09/1.39
% 2.09/1.39 thf(inCongP,definition,
% 2.09/1.39 ( inCongP
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ( A = B )
% 2.09/1.39 => ! [Xx: $i,Xy: $i] :
% 2.09/1.39 ( ( Xx = Xy )
% 2.09/1.39 => ( ( in @ Xx @ A )
% 2.09/1.39 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(in__Cong_type,type,
% 2.09/1.39 in__Cong: $o ).
% 2.09/1.39
% 2.09/1.39 thf(in__Cong,definition,
% 2.09/1.39 ( in__Cong
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ( A = B )
% 2.09/1.39 => ! [Xx: $i,Xy: $i] :
% 2.09/1.39 ( ( Xx = Xy )
% 2.09/1.39 => ( ( in @ Xx @ A )
% 2.09/1.39 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(exuE3u_type,type,
% 2.09/1.39 exuE3u: $o ).
% 2.09/1.39
% 2.09/1.39 thf(exuE3u,definition,
% 2.09/1.39 ( exuE3u
% 2.09/1.39 = ( ! [Xphi: $i > $o] :
% 2.09/1.39 ( ( exu
% 2.09/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.39 => ! [Xx: $i,Xy: $i] :
% 2.09/1.39 ( ( Xphi @ Xx )
% 2.09/1.39 => ( ( Xphi @ Xy )
% 2.09/1.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(exu__Cong_type,type,
% 2.09/1.39 exu__Cong: $o ).
% 2.09/1.39
% 2.09/1.39 thf(exu__Cong,definition,
% 2.09/1.39 ( exu__Cong
% 2.09/1.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.09/1.39 ( ! [Xx: $i,Xy: $i] :
% 2.09/1.39 ( ( Xx = Xy )
% 2.09/1.39 => ( ( Xphi @ Xx )
% 2.09/1.39 <=> ( Xpsi @ Xy ) ) )
% 2.09/1.39 => ( ( exu
% 2.09/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.39 <=> ( exu
% 2.09/1.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(emptyset__Cong_type,type,
% 2.09/1.39 emptyset__Cong: $o ).
% 2.09/1.39
% 2.09/1.39 thf(emptyset__Cong,definition,
% 2.09/1.39 ( emptyset__Cong
% 2.09/1.39 = ( emptyset = emptyset ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(setadjoin__Cong_type,type,
% 2.09/1.39 setadjoin__Cong: $o ).
% 2.09/1.39
% 2.09/1.39 thf(setadjoin__Cong,definition,
% 2.09/1.39 ( setadjoin__Cong
% 2.09/1.39 = ( ! [Xx: $i,Xy: $i] :
% 2.09/1.39 ( ( Xx = Xy )
% 2.09/1.39 => ! [Xz: $i,Xu: $i] :
% 2.09/1.39 ( ( Xz = Xu )
% 2.09/1.39 => ( ( setadjoin @ Xx @ Xz )
% 2.09/1.39 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(powerset__Cong_type,type,
% 2.09/1.39 powerset__Cong: $o ).
% 2.09/1.39
% 2.09/1.39 thf(powerset__Cong,definition,
% 2.09/1.39 ( powerset__Cong
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ( A = B )
% 2.09/1.39 => ( ( powerset @ A )
% 2.09/1.39 = ( powerset @ B ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(setunion__Cong_type,type,
% 2.09/1.39 setunion__Cong: $o ).
% 2.09/1.39
% 2.09/1.39 thf(setunion__Cong,definition,
% 2.09/1.39 ( setunion__Cong
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ( A = B )
% 2.09/1.39 => ( ( setunion @ A )
% 2.09/1.39 = ( setunion @ B ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(omega__Cong_type,type,
% 2.09/1.39 omega__Cong: $o ).
% 2.09/1.39
% 2.09/1.39 thf(omega__Cong,definition,
% 2.09/1.39 ( omega__Cong
% 2.09/1.39 = ( omega = omega ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(exuEu_type,type,
% 2.09/1.39 exuEu: $o ).
% 2.09/1.39
% 2.09/1.39 thf(exuEu,definition,
% 2.09/1.39 ( exuEu
% 2.09/1.39 = ( ! [Xphi: $i > $o] :
% 2.09/1.39 ( ( exu
% 2.09/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.39 => ! [Xx: $i,Xy: $i] :
% 2.09/1.39 ( ( Xphi @ Xx )
% 2.09/1.39 => ( ( Xphi @ Xy )
% 2.09/1.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(descr__Cong_type,type,
% 2.09/1.39 descr__Cong: $o ).
% 2.09/1.39
% 2.09/1.39 thf(descr__Cong,definition,
% 2.09/1.39 ( descr__Cong
% 2.09/1.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.09/1.39 ( ! [Xx: $i,Xy: $i] :
% 2.09/1.39 ( ( Xx = Xy )
% 2.09/1.39 => ( ( Xphi @ Xx )
% 2.09/1.39 <=> ( Xpsi @ Xy ) ) )
% 2.09/1.39 => ( ( exu
% 2.09/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.39 => ( ( exu
% 2.09/1.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.09/1.39 => ( ( descr
% 2.09/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.39 = ( descr
% 2.09/1.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(dsetconstr__Cong_type,type,
% 2.09/1.39 dsetconstr__Cong: $o ).
% 2.09/1.39
% 2.09/1.39 thf(dsetconstr__Cong,definition,
% 2.09/1.39 ( dsetconstr__Cong
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ( A = B )
% 2.09/1.39 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.09/1.39 ( ! [Xx: $i] :
% 2.09/1.39 ( ( in @ Xx @ A )
% 2.09/1.39 => ! [Xy: $i] :
% 2.09/1.39 ( ( in @ Xy @ B )
% 2.09/1.39 => ( ( Xx = Xy )
% 2.09/1.39 => ( ( Xphi @ Xx )
% 2.09/1.39 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.09/1.39 => ( ( dsetconstr @ A
% 2.09/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.39 = ( dsetconstr @ B
% 2.09/1.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(subset_type,type,
% 2.09/1.39 subset: $i > $i > $o ).
% 2.09/1.39
% 2.09/1.39 thf(disjoint_type,type,
% 2.09/1.39 disjoint: $i > $i > $o ).
% 2.09/1.39
% 2.09/1.39 thf(setsmeet_type,type,
% 2.09/1.39 setsmeet: $i > $i > $o ).
% 2.09/1.39
% 2.09/1.39 thf(subsetI1_type,type,
% 2.09/1.39 subsetI1: $o ).
% 2.09/1.39
% 2.09/1.39 thf(subsetI1,definition,
% 2.09/1.39 ( subsetI1
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ! [Xx: $i] :
% 2.09/1.39 ( ( in @ Xx @ A )
% 2.09/1.39 => ( in @ Xx @ B ) )
% 2.09/1.39 => ( subset @ A @ B ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(eqimpsubset2_type,type,
% 2.09/1.39 eqimpsubset2: $o ).
% 2.09/1.39
% 2.09/1.39 thf(eqimpsubset2,definition,
% 2.09/1.39 ( eqimpsubset2
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ( A = B )
% 2.09/1.39 => ( subset @ B @ A ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(eqimpsubset1_type,type,
% 2.09/1.39 eqimpsubset1: $o ).
% 2.09/1.39
% 2.09/1.39 thf(eqimpsubset1,definition,
% 2.09/1.39 ( eqimpsubset1
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ( A = B )
% 2.09/1.39 => ( subset @ A @ B ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(subsetI2_type,type,
% 2.09/1.39 subsetI2: $o ).
% 2.09/1.39
% 2.09/1.39 thf(subsetI2,definition,
% 2.09/1.39 ( subsetI2
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ! [Xx: $i] :
% 2.09/1.39 ( ( in @ Xx @ A )
% 2.09/1.39 => ( in @ Xx @ B ) )
% 2.09/1.39 => ( subset @ A @ B ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(emptysetsubset_type,type,
% 2.09/1.39 emptysetsubset: $o ).
% 2.09/1.39
% 2.09/1.39 thf(emptysetsubset,definition,
% 2.09/1.39 ( emptysetsubset
% 2.09/1.39 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(subsetE_type,type,
% 2.09/1.39 subsetE: $o ).
% 2.09/1.39
% 2.09/1.39 thf(subsetE,definition,
% 2.09/1.39 ( subsetE
% 2.09/1.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.39 ( ( subset @ A @ B )
% 2.09/1.39 => ( ( in @ Xx @ A )
% 2.09/1.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(subsetE2_type,type,
% 2.09/1.39 subsetE2: $o ).
% 2.09/1.39
% 2.09/1.39 thf(subsetE2,definition,
% 2.09/1.39 ( subsetE2
% 2.09/1.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.39 ( ( subset @ A @ B )
% 2.09/1.39 => ( ~ ( in @ Xx @ B )
% 2.09/1.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(notsubsetI_type,type,
% 2.09/1.39 notsubsetI: $o ).
% 2.09/1.39
% 2.09/1.39 thf(notsubsetI,definition,
% 2.09/1.39 ( notsubsetI
% 2.09/1.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.39 ( ( in @ Xx @ A )
% 2.09/1.39 => ( ~ ( in @ Xx @ B )
% 2.09/1.39 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(notequalI1_type,type,
% 2.09/1.39 notequalI1: $o ).
% 2.09/1.39
% 2.09/1.39 thf(notequalI1,definition,
% 2.09/1.39 ( notequalI1
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ~ ( subset @ A @ B )
% 2.09/1.39 => ( A != B ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(notequalI2_type,type,
% 2.09/1.39 notequalI2: $o ).
% 2.09/1.39
% 2.09/1.39 thf(notequalI2,definition,
% 2.09/1.39 ( notequalI2
% 2.09/1.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.09/1.39 ( ( in @ Xx @ A )
% 2.09/1.39 => ( ~ ( in @ Xx @ B )
% 2.09/1.39 => ( A != B ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(subsetRefl_type,type,
% 2.09/1.39 subsetRefl: $o ).
% 2.09/1.39
% 2.09/1.39 thf(subsetRefl,definition,
% 2.09/1.39 ( subsetRefl
% 2.09/1.39 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(subsetTrans_type,type,
% 2.09/1.39 subsetTrans: $o ).
% 2.09/1.39
% 2.09/1.39 thf(subsetTrans,definition,
% 2.09/1.39 ( subsetTrans
% 2.09/1.39 = ( ! [A: $i,B: $i,C: $i] :
% 2.09/1.39 ( ( subset @ A @ B )
% 2.09/1.39 => ( ( subset @ B @ C )
% 2.09/1.39 => ( subset @ A @ C ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(setadjoinSub_type,type,
% 2.09/1.39 setadjoinSub: $o ).
% 2.09/1.39
% 2.09/1.39 thf(setadjoinSub,definition,
% 2.09/1.39 ( setadjoinSub
% 2.09/1.39 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(setadjoinSub2_type,type,
% 2.09/1.39 setadjoinSub2: $o ).
% 2.09/1.39
% 2.09/1.39 thf(setadjoinSub2,definition,
% 2.09/1.39 ( setadjoinSub2
% 2.09/1.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.09/1.39 ( ( subset @ A @ B )
% 2.09/1.39 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(subset2powerset_type,type,
% 2.09/1.39 subset2powerset: $o ).
% 2.09/1.39
% 2.09/1.39 thf(subset2powerset,definition,
% 2.09/1.39 ( subset2powerset
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ( subset @ A @ B )
% 2.09/1.39 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(setextsub_type,type,
% 2.09/1.39 setextsub: $o ).
% 2.09/1.39
% 2.09/1.39 thf(setextsub,definition,
% 2.09/1.39 ( setextsub
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ( subset @ A @ B )
% 2.09/1.39 => ( ( subset @ B @ A )
% 2.09/1.39 => ( A = B ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(subsetemptysetimpeq_type,type,
% 2.09/1.39 subsetemptysetimpeq: $o ).
% 2.09/1.39
% 2.09/1.39 thf(subsetemptysetimpeq,definition,
% 2.09/1.39 ( subsetemptysetimpeq
% 2.09/1.39 = ( ! [A: $i] :
% 2.09/1.39 ( ( subset @ A @ emptyset )
% 2.09/1.39 => ( A = emptyset ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(powersetI1_type,type,
% 2.09/1.39 powersetI1: $o ).
% 2.09/1.39
% 2.09/1.39 thf(powersetI1,definition,
% 2.09/1.39 ( powersetI1
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ( subset @ B @ A )
% 2.09/1.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(powersetE1_type,type,
% 2.09/1.39 powersetE1: $o ).
% 2.09/1.39
% 2.09/1.39 thf(powersetE1,definition,
% 2.09/1.39 ( powersetE1
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ( in @ B @ ( powerset @ A ) )
% 2.09/1.39 => ( subset @ B @ A ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(inPowerset_type,type,
% 2.09/1.39 inPowerset: $o ).
% 2.09/1.39
% 2.09/1.39 thf(inPowerset,definition,
% 2.09/1.39 ( inPowerset
% 2.09/1.39 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(powersetsubset_type,type,
% 2.09/1.39 powersetsubset: $o ).
% 2.09/1.39
% 2.09/1.39 thf(powersetsubset,definition,
% 2.09/1.39 ( powersetsubset
% 2.09/1.39 = ( ! [A: $i,B: $i] :
% 2.09/1.39 ( ( subset @ A @ B )
% 2.09/1.39 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.09/1.39
% 2.09/1.39 thf(sepInPowerset,conjecture,
% 2.09/1.39 ( setextAx
% 2.09/1.39 => ( emptysetAx
% 2.09/1.39 => ( setadjoinAx
% 2.09/1.39 => ( powersetAx
% 2.09/1.39 => ( setunionAx
% 2.09/1.39 => ( omega0Ax
% 2.09/1.39 => ( omegaSAx
% 2.09/1.39 => ( omegaIndAx
% 2.09/1.39 => ( replAx
% 2.09/1.39 => ( foundationAx
% 2.09/1.39 => ( wellorderingAx
% 2.09/1.39 => ( descrp
% 2.09/1.39 => ( dsetconstrI
% 2.09/1.39 => ( dsetconstrEL
% 2.09/1.39 => ( dsetconstrER
% 2.09/1.39 => ( exuE1
% 2.09/1.39 => ( prop2setE
% 2.09/1.39 => ( emptysetE
% 2.09/1.39 => ( emptysetimpfalse
% 2.09/1.39 => ( notinemptyset
% 2.09/1.39 => ( exuE3e
% 2.09/1.39 => ( setext
% 2.09/1.39 => ( emptyI
% 2.09/1.39 => ( noeltsimpempty
% 2.09/1.39 => ( setbeta
% 2.09/1.39 => ( nonemptyE1
% 2.09/1.39 => ( nonemptyI
% 2.09/1.39 => ( nonemptyI1
% 2.09/1.39 => ( setadjoinIL
% 2.09/1.39 => ( emptyinunitempty
% 2.09/1.39 => ( setadjoinIR
% 2.09/1.39 => ( setadjoinE
% 2.09/1.39 => ( setadjoinOr
% 2.09/1.39 => ( setoftrueEq
% 2.09/1.39 => ( powersetI
% 2.09/1.39 => ( emptyinPowerset
% 2.09/1.39 => ( emptyInPowerset
% 2.09/1.39 => ( powersetE
% 2.09/1.39 => ( setunionI
% 2.09/1.39 => ( setunionE
% 2.09/1.39 => ( subPowSU
% 2.09/1.39 => ( exuE2
% 2.09/1.39 => ( nonemptyImpWitness
% 2.09/1.39 => ( uniqinunit
% 2.09/1.39 => ( notinsingleton
% 2.09/1.39 => ( eqinunit
% 2.09/1.39 => ( singletonsswitch
% 2.09/1.39 => ( upairsetE
% 2.09/1.39 => ( upairsetIL
% 2.09/1.39 => ( upairsetIR
% 2.09/1.39 => ( emptyE1
% 2.09/1.39 => ( vacuousDall
% 2.09/1.39 => ( quantDeMorgan1
% 2.09/1.39 => ( quantDeMorgan2
% 2.09/1.39 => ( quantDeMorgan3
% 2.09/1.39 => ( quantDeMorgan4
% 2.09/1.39 => ( prop2setI
% 2.09/1.39 => ( prop2set2propI
% 2.09/1.39 => ( notdexE
% 2.09/1.39 => ( notdallE
% 2.09/1.39 => ( exuI1
% 2.09/1.39 => ( exuI3
% 2.09/1.39 => ( exuI2
% 2.09/1.39 => ( inCongP
% 2.09/1.39 => ( in__Cong
% 2.09/1.39 => ( exuE3u
% 2.09/1.39 => ( exu__Cong
% 2.09/1.39 => ( emptyset__Cong
% 2.09/1.39 => ( setadjoin__Cong
% 2.09/1.39 => ( powerset__Cong
% 2.09/1.39 => ( setunion__Cong
% 2.09/1.39 => ( omega__Cong
% 2.09/1.39 => ( exuEu
% 2.09/1.39 => ( descr__Cong
% 2.09/1.39 => ( dsetconstr__Cong
% 2.09/1.39 => ( subsetI1
% 2.09/1.39 => ( eqimpsubset2
% 2.09/1.39 => ( eqimpsubset1
% 2.09/1.39 => ( subsetI2
% 2.09/1.39 => ( emptysetsubset
% 2.09/1.39 => ( subsetE
% 2.09/1.39 => ( subsetE2
% 2.09/1.39 => ( notsubsetI
% 2.09/1.39 => ( notequalI1
% 2.09/1.39 => ( notequalI2
% 2.09/1.39 => ( subsetRefl
% 2.09/1.39 => ( subsetTrans
% 2.09/1.39 => ( setadjoinSub
% 2.09/1.39 => ( setadjoinSub2
% 2.09/1.39 => ( subset2powerset
% 2.09/1.39 => ( setextsub
% 2.09/1.39 => ( subsetemptysetimpeq
% 2.09/1.39 => ( powersetI1
% 2.09/1.39 => ( powersetE1
% 2.09/1.39 => ( inPowerset
% 2.09/1.39 => ( powersetsubset
% 2.09/1.39 => ! [A: $i,Xphi: $i > $o] :
% 2.09/1.39 ( in
% 2.09/1.39 @ ( dsetconstr @ A
% 2.09/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.09/1.39 @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.09/1.39 ------------------------
% 2.30/1.40 % (5491)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_5389 for (2999ds/27Mi)
% 2.30/1.40 % (5490)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_5389 for (2999ds/4Mi)
% 2.30/1.40 % (5493)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_5389 for (2999ds/2Mi)
% 2.30/1.40 % (5493)Instruction limit reached!
% 2.30/1.40 % (5493)------------------------------
% 2.30/1.40 % (5493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.40 % (5493)Termination reason: Unknown
% 2.30/1.40 % (5493)Termination phase: shuffling
% 2.30/1.40
% 2.30/1.40 % (5493)Memory used [KB]: 1151
% 2.30/1.40 % (5493)Time elapsed: 0.003 s
% 2.30/1.40 % (5493)Instructions burned: 4 (million)
% 2.30/1.40 % (5493)------------------------------
% 2.30/1.40 % (5493)------------------------------
% 2.30/1.40 % (5494)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_5389 for (2999ds/275Mi)
% 2.30/1.41 % (5490)Instruction limit reached!
% 2.30/1.41 % (5490)------------------------------
% 2.30/1.41 % (5490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.41 % (5490)Termination reason: Unknown
% 2.30/1.41 % (5490)Termination phase: shuffling
% 2.30/1.41
% 2.30/1.41 % (5490)Memory used [KB]: 1279
% 2.30/1.41 % (5490)Time elapsed: 0.003 s
% 2.30/1.41 % (5490)Instructions burned: 7 (million)
% 2.30/1.41 % (5490)------------------------------
% 2.30/1.41 % (5490)------------------------------
% 2.30/1.41 % (5491)Instruction limit reached!
% 2.30/1.41 % (5491)------------------------------
% 2.30/1.41 % (5491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.41 % (5491)Termination reason: Unknown
% 2.30/1.41 % (5491)Termination phase: Property scanning
% 2.30/1.41
% 2.30/1.41 % (5491)Memory used [KB]: 1535
% 2.30/1.41 % (5491)Time elapsed: 0.009 s
% 2.30/1.41 % (5491)Instructions burned: 29 (million)
% 2.30/1.41 % (5491)------------------------------
% 2.30/1.41 % (5491)------------------------------
% 2.30/1.41 % (5492)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5389 for (2999ds/2Mi)
% 2.30/1.41 % (5495)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5389 for (2999ds/18Mi)
% 2.30/1.41 % (5492)Instruction limit reached!
% 2.30/1.41 % (5492)------------------------------
% 2.30/1.41 % (5492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.41 % (5492)Termination reason: Unknown
% 2.30/1.41 % (5492)Termination phase: shuffling
% 2.30/1.41
% 2.30/1.41 % (5492)Memory used [KB]: 1151
% 2.30/1.41 % (5492)Time elapsed: 0.003 s
% 2.30/1.41 % (5492)Instructions burned: 2 (million)
% 2.30/1.41 % (5492)------------------------------
% 2.30/1.41 % (5492)------------------------------
% 2.30/1.41 % (5489)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5389 for (2999ds/183Mi)
% 2.30/1.42 % (5496)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5389 for (2999ds/3Mi)
% 2.30/1.42 % (5497)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_5389 for (2999ds/37Mi)
% 2.30/1.42 % (5496)Instruction limit reached!
% 2.30/1.42 % (5496)------------------------------
% 2.30/1.42 % (5496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.42 % (5496)Termination reason: Unknown
% 2.30/1.42 % (5496)Termination phase: shuffling
% 2.30/1.42
% 2.30/1.42 % (5496)Memory used [KB]: 1151
% 2.30/1.42 % (5496)Time elapsed: 0.003 s
% 2.30/1.42 % (5496)Instructions burned: 4 (million)
% 2.30/1.42 % (5496)------------------------------
% 2.30/1.42 % (5496)------------------------------
% 2.30/1.42 % (5495)Instruction limit reached!
% 2.30/1.42 % (5495)------------------------------
% 2.30/1.42 % (5495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.42 % (5495)Termination reason: Unknown
% 2.30/1.42 % (5495)Termination phase: Preprocessing 3
% 2.30/1.42
% 2.30/1.42 % (5495)Memory used [KB]: 1535
% 2.30/1.42 % (5495)Time elapsed: 0.013 s
% 2.30/1.42 % (5495)Instructions burned: 19 (million)
% 2.30/1.42 % (5495)------------------------------
% 2.30/1.42 % (5495)------------------------------
% 2.30/1.43 % (5498)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_5389 for (2999ds/15Mi)
% 2.30/1.43 % (5497)Instruction limit reached!
% 2.30/1.43 % (5497)------------------------------
% 2.30/1.43 % (5497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.43 % (5497)Termination reason: Unknown
% 2.30/1.43 % (5497)Termination phase: Function definition elimination
% 2.30/1.43
% 2.30/1.43 % (5497)Memory used [KB]: 1535
% 2.30/1.43 % (5497)Time elapsed: 0.012 s
% 2.30/1.43 % (5497)Instructions burned: 37 (million)
% 2.30/1.43 % (5497)------------------------------
% 2.30/1.43 % (5497)------------------------------
% 2.30/1.43 % (5500)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_5389 for (2999ds/1041Mi)
% 2.30/1.43 % (5499)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_5389 for (2999ds/3Mi)
% 2.30/1.43 % (5499)Instruction limit reached!
% 2.30/1.43 % (5499)------------------------------
% 2.30/1.43 % (5499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.43 % (5499)Termination reason: Unknown
% 2.30/1.43 % (5499)Termination phase: shuffling
% 2.30/1.43
% 2.30/1.43 % (5499)Memory used [KB]: 1151
% 2.30/1.43 % (5499)Time elapsed: 0.004 s
% 2.30/1.43 % (5499)Instructions burned: 3 (million)
% 2.30/1.43 % (5499)------------------------------
% 2.30/1.43 % (5499)------------------------------
% 2.30/1.43 % (5498)Instruction limit reached!
% 2.30/1.43 % (5498)------------------------------
% 2.30/1.43 % (5498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.43 % (5498)Termination reason: Unknown
% 2.30/1.43 % (5498)Termination phase: Preprocessing 3
% 2.30/1.43
% 2.30/1.43 % (5498)Memory used [KB]: 1407
% 2.30/1.43 % (5498)Time elapsed: 0.009 s
% 2.30/1.43 % (5498)Instructions burned: 16 (million)
% 2.30/1.43 % (5498)------------------------------
% 2.30/1.43 % (5498)------------------------------
% 2.30/1.44 % (5502)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5389 for (2999ds/16Mi)
% 2.30/1.44 % (5501)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5389 for (2999ds/7Mi)
% 2.30/1.44 % (5502)Instruction limit reached!
% 2.30/1.44 % (5502)------------------------------
% 2.30/1.44 % (5502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.44 % (5502)Termination reason: Unknown
% 2.30/1.44 % (5502)Termination phase: Property scanning
% 2.30/1.44
% 2.30/1.44 % (5502)Memory used [KB]: 1407
% 2.30/1.44 % (5502)Time elapsed: 0.006 s
% 2.30/1.44 % (5502)Instructions burned: 17 (million)
% 2.30/1.44 % (5502)------------------------------
% 2.30/1.44 % (5502)------------------------------
% 2.30/1.44 % (5501)Instruction limit reached!
% 2.30/1.44 % (5501)------------------------------
% 2.30/1.44 % (5501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.44 % (5501)Termination reason: Unknown
% 2.30/1.44 % (5501)Termination phase: shuffling
% 2.30/1.44
% 2.30/1.44 % (5501)Memory used [KB]: 1279
% 2.30/1.44 % (5504)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_5389 for (2999ds/3Mi)
% 2.30/1.44 % (5501)Time elapsed: 0.005 s
% 2.30/1.44 % (5501)Instructions burned: 7 (million)
% 2.30/1.44 % (5501)------------------------------
% 2.30/1.44 % (5501)------------------------------
% 2.30/1.44 % (5504)Instruction limit reached!
% 2.30/1.44 % (5504)------------------------------
% 2.30/1.44 % (5504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.44 % (5504)Termination reason: Unknown
% 2.30/1.44 % (5504)Termination phase: shuffling
% 2.30/1.44
% 2.30/1.44 % (5504)Memory used [KB]: 1151
% 2.30/1.44 % (5504)Time elapsed: 0.002 s
% 2.30/1.44 % (5504)Instructions burned: 3 (million)
% 2.30/1.44 % (5504)------------------------------
% 2.30/1.44 % (5504)------------------------------
% 2.30/1.45 % (5503)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_5389 for (2999ds/3Mi)
% 2.30/1.45 % (5503)Instruction limit reached!
% 2.30/1.45 % (5503)------------------------------
% 2.30/1.45 % (5503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.45 % (5503)Termination reason: Unknown
% 2.30/1.45 % (5503)Termination phase: shuffling
% 2.30/1.45
% 2.30/1.45 % (5503)Memory used [KB]: 1151
% 2.30/1.45 % (5503)Time elapsed: 0.004 s
% 2.30/1.45 % (5503)Instructions burned: 4 (million)
% 2.30/1.45 % (5503)------------------------------
% 2.30/1.45 % (5503)------------------------------
% 2.30/1.45 % (5506)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5389 for (2999ds/7Mi)
% 2.30/1.45 % (5508)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5389 for (2999ds/4Mi)
% 2.30/1.45 % (5508)Instruction limit reached!
% 2.30/1.45 % (5508)------------------------------
% 2.30/1.45 % (5508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.45 % (5508)Termination reason: Unknown
% 2.30/1.45 % (5508)Termination phase: shuffling
% 2.30/1.45
% 2.30/1.45 % (5508)Memory used [KB]: 1151
% 2.30/1.45 % (5508)Time elapsed: 0.002 s
% 2.30/1.45 % (5508)Instructions burned: 4 (million)
% 2.30/1.45 % (5508)------------------------------
% 2.30/1.45 % (5508)------------------------------
% 2.30/1.45 % (5506)Instruction limit reached!
% 2.30/1.45 % (5506)------------------------------
% 2.30/1.45 % (5506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.45 % (5506)Termination reason: Unknown
% 2.30/1.45 % (5506)Termination phase: shuffling
% 2.30/1.45
% 2.30/1.45 % (5506)Memory used [KB]: 1279
% 2.30/1.45 % (5506)Time elapsed: 0.004 s
% 2.30/1.45 % (5506)Instructions burned: 7 (million)
% 2.30/1.45 % (5506)------------------------------
% 2.30/1.45 % (5506)------------------------------
% 2.30/1.46 % (5507)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5389 for (2999ds/3Mi)
% 2.30/1.46 % (5507)Instruction limit reached!
% 2.30/1.46 % (5507)------------------------------
% 2.30/1.46 % (5507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.46 % (5507)Termination reason: Unknown
% 2.30/1.46 % (5507)Termination phase: shuffling
% 2.30/1.46
% 2.30/1.46 % (5507)Memory used [KB]: 1151
% 2.30/1.46 % (5507)Time elapsed: 0.003 s
% 2.30/1.46 % (5507)Instructions burned: 5 (million)
% 2.30/1.46 % (5507)------------------------------
% 2.30/1.46 % (5507)------------------------------
% 2.30/1.46 % (5510)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5389 for (2999ds/710Mi)
% 2.30/1.46 % (5511)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5389 for (2999ds/6Mi)
% 2.30/1.47 % (5511)Instruction limit reached!
% 2.30/1.47 % (5511)------------------------------
% 2.30/1.47 % (5511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.47 % (5511)Termination reason: Unknown
% 2.30/1.47 % (5511)Termination phase: shuffling
% 2.30/1.47
% 2.30/1.47 % (5511)Memory used [KB]: 1279
% 2.30/1.47 % (5511)Time elapsed: 0.003 s
% 2.30/1.47 % (5511)Instructions burned: 7 (million)
% 2.30/1.47 % (5511)------------------------------
% 2.30/1.47 % (5511)------------------------------
% 2.30/1.47 % (5509)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5389 for (2999ds/18Mi)
% 2.30/1.47 % (5512)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_5389 for (2999ds/902Mi)
% 2.30/1.48 % (5513)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_5389 for (2999ds/21Mi)
% 2.30/1.48 % (5509)Instruction limit reached!
% 2.30/1.48 % (5509)------------------------------
% 2.30/1.48 % (5509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.48 % (5509)Termination reason: Unknown
% 2.30/1.48 % (5509)Termination phase: Property scanning
% 2.30/1.48
% 2.30/1.48 % (5509)Memory used [KB]: 1407
% 2.30/1.48 % (5509)Time elapsed: 0.011 s
% 2.30/1.48 % (5509)Instructions burned: 20 (million)
% 2.30/1.48 % (5509)------------------------------
% 2.30/1.48 % (5509)------------------------------
% 2.30/1.48 % (5513)Instruction limit reached!
% 2.30/1.48 % (5513)------------------------------
% 2.30/1.48 % (5513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.48 % (5513)Termination reason: Unknown
% 2.30/1.48 % (5513)Termination phase: Property scanning
% 2.30/1.48
% 2.30/1.48 % (5513)Memory used [KB]: 1407
% 2.30/1.48 % (5513)Time elapsed: 0.007 s
% 2.30/1.48 % (5513)Instructions burned: 22 (million)
% 2.30/1.48 % (5513)------------------------------
% 2.30/1.48 % (5513)------------------------------
% 2.30/1.49 % (5514)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5389 for (2999ds/5Mi)
% 2.30/1.49 % (5515)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_5389 for (2999ds/6Mi)
% 2.30/1.49 % (5514)Instruction limit reached!
% 2.30/1.49 % (5514)------------------------------
% 2.30/1.49 % (5514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.49 % (5514)Termination reason: Unknown
% 2.30/1.49 % (5514)Termination phase: shuffling
% 2.30/1.49
% 2.30/1.49 % (5514)Memory used [KB]: 1151
% 2.30/1.49 % (5514)Time elapsed: 0.003 s
% 2.30/1.49 % (5514)Instructions burned: 5 (million)
% 2.30/1.49 % (5514)------------------------------
% 2.30/1.49 % (5514)------------------------------
% 2.30/1.49 % (5515)Instruction limit reached!
% 2.30/1.49 % (5515)------------------------------
% 2.30/1.49 % (5515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.49 % (5515)Termination reason: Unknown
% 2.30/1.49 % (5515)Termination phase: shuffling
% 2.30/1.49
% 2.30/1.49 % (5515)Memory used [KB]: 1279
% 2.30/1.49 % (5515)Time elapsed: 0.003 s
% 2.30/1.49 % (5515)Instructions burned: 8 (million)
% 2.30/1.49 % (5515)------------------------------
% 2.30/1.49 % (5515)------------------------------
% 2.30/1.50 % (5494)Instruction limit reached!
% 2.30/1.50 % (5494)------------------------------
% 2.30/1.50 % (5494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.50 % (5494)Termination reason: Unknown
% 2.30/1.50 % (5494)Termination phase: Saturation
% 2.30/1.50
% 2.30/1.50 % (5494)Memory used [KB]: 7547
% 2.30/1.50 % (5494)Time elapsed: 0.094 s
% 2.30/1.50 % (5494)Instructions burned: 276 (million)
% 2.30/1.50 % (5494)------------------------------
% 2.30/1.50 % (5494)------------------------------
% 2.30/1.50 % (5489)Instruction limit reached!
% 2.30/1.50 % (5489)------------------------------
% 2.30/1.50 % (5489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.50 % (5489)Termination reason: Unknown
% 2.30/1.50 % (5489)Termination phase: Saturation
% 2.30/1.50
% 2.30/1.50 % (5489)Memory used [KB]: 6908
% 2.30/1.50 % (5489)Time elapsed: 0.085 s
% 2.30/1.50 % (5489)Instructions burned: 185 (million)
% 2.30/1.50 % (5489)------------------------------
% 2.30/1.50 % (5489)------------------------------
% 2.30/1.50 % (5516)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5389 for (2998ds/377Mi)
% 2.30/1.50 % (5517)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_5389 for (2998ds/779Mi)
% 2.30/1.51 % (5519)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_5389 for (2998ds/879Mi)
% 2.30/1.51 % (5518)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_5389 for (2998ds/19Mi)
% 2.30/1.51 % (5518)Instruction limit reached!
% 2.30/1.51 % (5518)------------------------------
% 2.30/1.51 % (5518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.51 % (5518)Termination reason: Unknown
% 2.30/1.51 % (5518)Termination phase: Property scanning
% 2.30/1.51
% 2.30/1.51 % (5518)Memory used [KB]: 1407
% 2.30/1.51 % (5518)Time elapsed: 0.007 s
% 2.30/1.51 % (5518)Instructions burned: 19 (million)
% 2.30/1.51 % (5518)------------------------------
% 2.30/1.51 % (5518)------------------------------
% 2.30/1.52 % (5520)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_5389 for (2998ds/17Mi)
% 2.30/1.53 % (5520)Instruction limit reached!
% 2.30/1.53 % (5520)------------------------------
% 2.30/1.53 % (5520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.53 % (5520)Termination reason: Unknown
% 2.30/1.53 % (5520)Termination phase: Property scanning
% 2.30/1.53
% 2.30/1.53 % (5520)Memory used [KB]: 1407
% 2.30/1.53 % (5520)Time elapsed: 0.007 s
% 2.30/1.53 % (5520)Instructions burned: 18 (million)
% 2.30/1.53 % (5520)------------------------------
% 2.30/1.53 % (5520)------------------------------
% 2.30/1.54 % (5521)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5389 for (2998ds/3Mi)
% 2.30/1.54 % (5521)Instruction limit reached!
% 2.30/1.54 % (5521)------------------------------
% 2.30/1.54 % (5521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.54 % (5521)Termination reason: Unknown
% 2.30/1.54 % (5521)Termination phase: shuffling
% 2.30/1.54
% 2.30/1.54 % (5521)Memory used [KB]: 1151
% 2.30/1.54 % (5521)Time elapsed: 0.003 s
% 2.30/1.54 % (5521)Instructions burned: 4 (million)
% 2.30/1.54 % (5521)------------------------------
% 2.30/1.54 % (5521)------------------------------
% 2.30/1.55 % (5522)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_5389 for (2998ds/30Mi)
% 2.30/1.56 % (5522)Instruction limit reached!
% 2.30/1.56 % (5522)------------------------------
% 2.30/1.56 % (5522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.56 % (5522)Termination reason: Unknown
% 2.30/1.56 % (5522)Termination phase: Function definition elimination
% 2.30/1.56
% 2.30/1.56 % (5522)Memory used [KB]: 1535
% 2.30/1.56 % (5522)Time elapsed: 0.011 s
% 2.30/1.56 % (5522)Instructions burned: 33 (million)
% 2.30/1.56 % (5522)------------------------------
% 2.30/1.56 % (5522)------------------------------
% 2.30/1.57 % (5523)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_5389 for (2998ds/127Mi)
% 2.30/1.61 % (5523)Instruction limit reached!
% 2.30/1.61 % (5523)------------------------------
% 2.30/1.61 % (5523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.61 % (5523)Termination reason: Unknown
% 2.30/1.61 % (5523)Termination phase: Saturation
% 2.30/1.61
% 2.30/1.61 % (5523)Memory used [KB]: 6780
% 2.30/1.61 % (5523)Time elapsed: 0.038 s
% 2.30/1.61 % (5523)Instructions burned: 129 (million)
% 2.30/1.61 % (5523)------------------------------
% 2.30/1.61 % (5523)------------------------------
% 2.30/1.62 % (5524)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_5389 for (2997ds/100Mi)
% 2.30/1.63 % (5516)Instruction limit reached!
% 2.30/1.63 % (5516)------------------------------
% 2.30/1.63 % (5516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.63 % (5516)Termination reason: Unknown
% 2.30/1.63 % (5516)Termination phase: Saturation
% 2.30/1.63
% 2.30/1.63 % (5516)Memory used [KB]: 7164
% 2.30/1.63 % (5516)Time elapsed: 0.126 s
% 2.30/1.63 % (5516)Instructions burned: 378 (million)
% 2.30/1.63 % (5516)------------------------------
% 2.30/1.63 % (5516)------------------------------
% 2.30/1.64 % (5525)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_5389 for (2997ds/3Mi)
% 2.30/1.64 % (5525)Instruction limit reached!
% 2.30/1.64 % (5525)------------------------------
% 2.30/1.64 % (5525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.64 % (5525)Termination reason: Unknown
% 2.30/1.64 % (5525)Termination phase: shuffling
% 2.30/1.64
% 2.30/1.64 % (5525)Memory used [KB]: 1151
% 2.30/1.64 % (5525)Time elapsed: 0.003 s
% 2.30/1.64 % (5525)Instructions burned: 4 (million)
% 2.30/1.64 % (5525)------------------------------
% 2.30/1.64 % (5525)------------------------------
% 2.30/1.64 % (5524)Instruction limit reached!
% 2.30/1.64 % (5524)------------------------------
% 2.30/1.64 % (5524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.64 % (5524)Termination reason: Unknown
% 2.30/1.64 % (5524)Termination phase: Saturation
% 2.30/1.64
% 2.30/1.64 % (5524)Memory used [KB]: 6268
% 2.30/1.64 % (5524)Time elapsed: 0.029 s
% 2.30/1.64 % (5524)Instructions burned: 101 (million)
% 2.30/1.64 % (5524)------------------------------
% 2.30/1.64 % (5524)------------------------------
% 2.30/1.65 % (5526)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_5389 for (2997ds/20Mi)
% 2.30/1.65 % (5527)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_5389 for (2997ds/86Mi)
% 2.30/1.65 % (5526)Instruction limit reached!
% 2.30/1.65 % (5526)------------------------------
% 2.30/1.65 % (5526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.65 % (5526)Termination reason: Unknown
% 2.30/1.65 % (5526)Termination phase: Preprocessing 3
% 2.30/1.65
% 2.30/1.65 % (5526)Memory used [KB]: 1407
% 2.30/1.65 % (5526)Time elapsed: 0.008 s
% 2.30/1.65 % (5526)Instructions burned: 20 (million)
% 2.30/1.65 % (5526)------------------------------
% 2.30/1.65 % (5526)------------------------------
% 2.30/1.66 % (5528)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_5389 for (2997ds/107Mi)
% 2.30/1.68 % (5527)Instruction limit reached!
% 2.30/1.68 % (5527)------------------------------
% 2.30/1.68 % (5527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.68 % (5527)Termination reason: Unknown
% 2.30/1.68 % (5527)Termination phase: Saturation
% 2.30/1.68
% 2.30/1.68 % (5527)Memory used [KB]: 6396
% 2.30/1.68 % (5527)Time elapsed: 0.024 s
% 2.30/1.68 % (5527)Instructions burned: 88 (million)
% 2.30/1.68 % (5527)------------------------------
% 2.30/1.68 % (5527)------------------------------
% 2.30/1.68 % (5510)Refutation not found, non-redundant clauses discarded% (5510)------------------------------
% 2.30/1.68 % (5510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.68 % (5510)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.30/1.68
% 2.30/1.68 % (5510)Memory used [KB]: 8187
% 2.30/1.68 % (5510)Time elapsed: 0.218 s
% 2.30/1.68 % (5510)Instructions burned: 701 (million)
% 2.30/1.68 % (5510)------------------------------
% 2.30/1.68 % (5510)------------------------------
% 2.30/1.68 % (5517)Instruction limit reached!
% 2.30/1.68 % (5517)------------------------------
% 2.30/1.68 % (5517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.68 % (5517)Termination reason: Unknown
% 2.30/1.68 % (5517)Termination phase: Saturation
% 2.30/1.68
% 2.30/1.68 % (5517)Memory used [KB]: 6652
% 2.30/1.68 % (5517)Time elapsed: 0.182 s
% 2.30/1.68 % (5517)Instructions burned: 782 (million)
% 2.30/1.68 % (5517)------------------------------
% 2.30/1.68 % (5517)------------------------------
% 2.30/1.69 % (5529)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_5389 for (2997ds/39Mi)
% 2.30/1.69 % (5500)Instruction limit reached!
% 2.30/1.69 % (5500)------------------------------
% 2.30/1.69 % (5500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.69 % (5500)Termination reason: Unknown
% 2.30/1.69 % (5500)Termination phase: Saturation
% 2.30/1.69
% 2.30/1.69 % (5500)Memory used [KB]: 7547
% 2.30/1.69 % (5500)Time elapsed: 0.261 s
% 2.30/1.69 % (5500)Instructions burned: 1044 (million)
% 2.30/1.69 % (5500)------------------------------
% 2.30/1.69 % (5500)------------------------------
% 2.30/1.69 % (5530)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_5389 for (2997ds/448Mi)
% 2.30/1.69 % (5531)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_5389 for (2997ds/46Mi)
% 2.30/1.70 % (5528)Instruction limit reached!
% 2.30/1.70 % (5528)------------------------------
% 2.30/1.70 % (5528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.70 % (5528)Termination reason: Unknown
% 2.30/1.70 % (5528)Termination phase: Saturation
% 2.30/1.70
% 2.30/1.70 % (5528)Memory used [KB]: 6524
% 2.30/1.70 % (5528)Time elapsed: 0.033 s
% 2.30/1.70 % (5528)Instructions burned: 108 (million)
% 2.30/1.70 % (5528)------------------------------
% 2.30/1.70 % (5528)------------------------------
% 2.30/1.70 % (5529)Instruction limit reached!
% 2.30/1.70 % (5529)------------------------------
% 2.30/1.70 % (5529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.70 % (5529)Termination reason: Unknown
% 2.30/1.70 % (5529)Termination phase: Property scanning
% 2.30/1.70
% 2.30/1.70 % (5529)Memory used [KB]: 1535
% 2.30/1.70 % (5529)Time elapsed: 0.011 s
% 2.30/1.70 % (5529)Instructions burned: 41 (million)
% 2.30/1.70 % (5529)------------------------------
% 2.30/1.70 % (5529)------------------------------
% 2.30/1.70 % (5532)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_5389 for (2997ds/98Mi)
% 2.30/1.70 % (5531)Instruction limit reached!
% 2.30/1.70 % (5531)------------------------------
% 2.30/1.70 % (5531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.70 % (5531)Termination reason: Unknown
% 2.30/1.70 % (5531)Termination phase: Property scanning
% 2.30/1.70
% 2.30/1.70 % (5531)Memory used [KB]: 1535
% 2.30/1.70 % (5531)Time elapsed: 0.013 s
% 2.30/1.70 % (5531)Instructions burned: 48 (million)
% 2.30/1.70 % (5531)------------------------------
% 2.30/1.70 % (5531)------------------------------
% 2.30/1.70 % (5533)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_5389 for (2996ds/507Mi)
% 2.30/1.71 % (5534)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_5389 for (2996ds/149Mi)
% 2.30/1.71 % (5535)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_5389 for (2996ds/39Mi)
% 2.30/1.72 % (5532)Instruction limit reached!
% 2.30/1.72 % (5532)------------------------------
% 2.30/1.72 % (5532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.72 % (5532)Termination reason: Unknown
% 2.30/1.72 % (5532)Termination phase: Saturation
% 2.30/1.72
% 2.30/1.72 % (5532)Memory used [KB]: 1663
% 2.30/1.72 % (5532)Time elapsed: 0.025 s
% 2.30/1.72 % (5532)Instructions burned: 98 (million)
% 2.30/1.72 % (5532)------------------------------
% 2.30/1.72 % (5532)------------------------------
% 2.30/1.72 % (5535)Instruction limit reached!
% 2.30/1.72 % (5535)------------------------------
% 2.30/1.72 % (5535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.72 % (5535)Termination reason: Unknown
% 2.30/1.72 % (5535)Termination phase: Property scanning
% 2.30/1.72
% 2.30/1.72 % (5535)Memory used [KB]: 1535
% 2.30/1.72 % (5535)Time elapsed: 0.011 s
% 2.30/1.72 % (5535)Instructions burned: 40 (million)
% 2.30/1.72 % (5535)------------------------------
% 2.30/1.72 % (5535)------------------------------
% 2.30/1.73 % (5536)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_5389 for (2996ds/6Mi)
% 2.30/1.73 % (5536)Instruction limit reached!
% 2.30/1.73 % (5536)------------------------------
% 2.30/1.73 % (5536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.73 % (5537)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_5389 for (2996ds/1087Mi)
% 2.30/1.73 % (5536)Termination reason: Unknown
% 2.30/1.73 % (5536)Termination phase: shuffling
% 2.30/1.73
% 2.30/1.73 % (5536)Memory used [KB]: 1279
% 2.30/1.73 % (5536)Time elapsed: 0.003 s
% 2.30/1.73 % (5536)Instructions burned: 8 (million)
% 2.30/1.73 % (5536)------------------------------
% 2.30/1.73 % (5536)------------------------------
% 2.30/1.74 % (5538)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_5389 for (2996ds/47Mi)
% 2.30/1.75 % (5534)Instruction limit reached!
% 2.30/1.75 % (5534)------------------------------
% 2.30/1.75 % (5534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.75 % (5534)Termination reason: Unknown
% 2.30/1.75 % (5534)Termination phase: Saturation
% 2.30/1.75
% 2.30/1.75 % (5534)Memory used [KB]: 6652
% 2.30/1.75 % (5534)Time elapsed: 0.050 s
% 2.30/1.75 % (5534)Instructions burned: 151 (million)
% 2.30/1.75 % (5534)------------------------------
% 2.30/1.75 % (5534)------------------------------
% 2.30/1.75 % (5538)Instruction limit reached!
% 2.30/1.75 % (5538)------------------------------
% 2.30/1.75 % (5538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.75 % (5538)Termination reason: Unknown
% 2.30/1.75 % (5538)Termination phase: Saturation
% 2.30/1.75
% 2.30/1.75 % (5538)Memory used [KB]: 6012
% 2.30/1.75 % (5538)Time elapsed: 0.013 s
% 2.30/1.75 % (5538)Instructions burned: 47 (million)
% 2.30/1.75 % (5538)------------------------------
% 2.30/1.75 % (5538)------------------------------
% 2.30/1.76 % (5512)Instruction limit reached!
% 2.30/1.76 % (5512)------------------------------
% 2.30/1.76 % (5512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.76 % (5512)Termination reason: Unknown
% 2.30/1.76 % (5512)Termination phase: Saturation
% 2.30/1.76
% 2.30/1.76 % (5512)Memory used [KB]: 9466
% 2.30/1.76 % (5512)Time elapsed: 0.294 s
% 2.30/1.76 % (5512)Instructions burned: 903 (million)
% 2.30/1.76 % (5512)------------------------------
% 2.30/1.76 % (5512)------------------------------
% 2.30/1.76 % (5540)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_5389 for (2996ds/432Mi)
% 2.30/1.76 % (5539)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_5389 for (2996ds/44Mi)
% 2.30/1.77 % (5541)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_5389 for (2996ds/62Mi)
% 2.30/1.78 % (5539)Instruction limit reached!
% 2.30/1.78 % (5539)------------------------------
% 2.30/1.78 % (5539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.78 % (5539)Termination reason: Unknown
% 2.30/1.78 % (5539)Termination phase: Property scanning
% 2.30/1.78
% 2.30/1.78 % (5539)Memory used [KB]: 1535
% 2.30/1.78 % (5539)Time elapsed: 0.014 s
% 2.30/1.78 % (5539)Instructions burned: 46 (million)
% 2.30/1.78 % (5539)------------------------------
% 2.30/1.78 % (5539)------------------------------
% 2.30/1.78 % (5519)Instruction limit reached!
% 2.30/1.78 % (5519)------------------------------
% 2.30/1.78 % (5519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.78 % (5519)Termination reason: Unknown
% 2.30/1.78 % (5519)Termination phase: Saturation
% 2.30/1.78
% 2.30/1.78 % (5519)Memory used [KB]: 7547
% 2.30/1.78 % (5519)Time elapsed: 0.272 s
% 2.30/1.78 % (5519)Instructions burned: 879 (million)
% 2.30/1.78 % (5519)------------------------------
% 2.30/1.78 % (5519)------------------------------
% 2.30/1.79 % (5542)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_5389 for (2996ds/31Mi)
% 2.30/1.79 % (5543)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_5389 for (2996ds/96Mi)
% 2.30/1.79 % (5541)Instruction limit reached!
% 2.30/1.79 % (5541)------------------------------
% 2.30/1.79 % (5541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.79 % (5541)Termination reason: Unknown
% 2.30/1.79 % (5541)Termination phase: Saturation
% 2.30/1.79
% 2.30/1.79 % (5541)Memory used [KB]: 6140
% 2.30/1.79 % (5541)Time elapsed: 0.018 s
% 2.30/1.79 % (5541)Instructions burned: 63 (million)
% 2.30/1.79 % (5541)------------------------------
% 2.30/1.79 % (5541)------------------------------
% 2.30/1.80 % (5542)Instruction limit reached!
% 2.30/1.80 % (5542)------------------------------
% 2.30/1.80 % (5542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.80 % (5542)Termination reason: Unknown
% 2.30/1.80 % (5542)Termination phase: Function definition elimination
% 2.30/1.80
% 2.30/1.80 % (5542)Memory used [KB]: 1535
% 2.30/1.80 % (5542)Time elapsed: 0.011 s
% 2.30/1.80 % (5542)Instructions burned: 34 (million)
% 2.30/1.80 % (5542)------------------------------
% 2.30/1.80 % (5542)------------------------------
% 2.30/1.80 % (5530)Instruction limit reached!
% 2.30/1.80 % (5530)------------------------------
% 2.30/1.80 % (5530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.80 % (5530)Termination reason: Unknown
% 2.30/1.80 % (5530)Termination phase: Saturation
% 2.30/1.80
% 2.30/1.80 % (5530)Memory used [KB]: 6140
% 2.30/1.80 % (5530)Time elapsed: 0.106 s
% 2.30/1.80 % (5530)Instructions burned: 452 (million)
% 2.30/1.80 % (5530)------------------------------
% 2.30/1.80 % (5530)------------------------------
% 2.30/1.80 % (5544)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_5389 for (2996ds/453Mi)
% 2.30/1.81 % (5545)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_5389 for (2995ds/71Mi)
% 2.30/1.81 % (5546)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_5389 for (2995ds/83Mi)
% 2.30/1.81 % (5543)Instruction limit reached!
% 2.30/1.81 % (5543)------------------------------
% 2.30/1.81 % (5543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.81 % (5543)Termination reason: Unknown
% 2.30/1.81 % (5543)Termination phase: Saturation
% 2.30/1.81
% 2.30/1.81 % (5543)Memory used [KB]: 6524
% 2.30/1.81 % (5543)Time elapsed: 0.026 s
% 2.30/1.81 % (5543)Instructions burned: 96 (million)
% 2.30/1.81 % (5543)------------------------------
% 2.30/1.81 % (5543)------------------------------
% 2.30/1.82 % (5547)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_5389 for (2995ds/11Mi)
% 2.30/1.83 % (5547)Instruction limit reached!
% 2.30/1.83 % (5547)------------------------------
% 2.30/1.83 % (5547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.83 % (5547)Termination reason: Unknown
% 2.30/1.83 % (5547)Termination phase: shuffling
% 2.30/1.83
% 2.30/1.83 % (5547)Memory used [KB]: 1407
% 2.30/1.83 % (5547)Time elapsed: 0.004 s
% 2.30/1.83 % (5547)Instructions burned: 12 (million)
% 2.30/1.83 % (5547)------------------------------
% 2.30/1.83 % (5547)------------------------------
% 2.30/1.83 % (5545)Instruction limit reached!
% 2.30/1.83 % (5545)------------------------------
% 2.30/1.83 % (5545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.83 % (5545)Termination reason: Unknown
% 2.30/1.83 % (5545)Termination phase: Saturation
% 2.30/1.83
% 2.30/1.83 % (5545)Memory used [KB]: 6140
% 2.30/1.83 % (5545)Time elapsed: 0.022 s
% 2.30/1.83 % (5545)Instructions burned: 72 (million)
% 2.30/1.83 % (5545)------------------------------
% 2.30/1.83 % (5545)------------------------------
% 2.30/1.83 % (5546)Instruction limit reached!
% 2.30/1.83 % (5546)------------------------------
% 2.30/1.83 % (5546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.83 % (5546)Termination reason: Unknown
% 2.30/1.83 % (5546)Termination phase: Saturation
% 2.30/1.83
% 2.30/1.83 % (5546)Memory used [KB]: 6268
% 2.30/1.83 % (5546)Time elapsed: 0.023 s
% 2.30/1.83 % (5546)Instructions burned: 85 (million)
% 2.30/1.83 % (5546)------------------------------
% 2.30/1.83 % (5546)------------------------------
% 2.30/1.84 % (5548)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_5389 for (2995ds/41Mi)
% 2.30/1.84 % (5549)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5389 for (2995ds/6Mi)
% 2.30/1.84 % (5550)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_5389 for (2995ds/150Mi)
% 2.30/1.84 % (5549)Instruction limit reached!
% 2.30/1.84 % (5549)------------------------------
% 2.30/1.84 % (5549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.84 % (5549)Termination reason: Unknown
% 2.30/1.84 % (5549)Termination phase: shuffling
% 2.30/1.84
% 2.30/1.84 % (5549)Memory used [KB]: 1279
% 2.30/1.84 % (5549)Time elapsed: 0.003 s
% 2.30/1.84 % (5549)Instructions burned: 8 (million)
% 2.30/1.84 % (5549)------------------------------
% 2.30/1.84 % (5549)------------------------------
% 2.30/1.85 % (5548)Instruction limit reached!
% 2.30/1.85 % (5548)------------------------------
% 2.30/1.85 % (5548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.85 % (5548)Termination reason: Unknown
% 2.30/1.85 % (5548)Termination phase: Property scanning
% 2.30/1.85
% 2.30/1.85 % (5548)Memory used [KB]: 1535
% 2.30/1.85 % (5548)Time elapsed: 0.011 s
% 2.30/1.85 % (5548)Instructions burned: 41 (million)
% 2.30/1.85 % (5548)------------------------------
% 2.30/1.85 % (5548)------------------------------
% 2.30/1.85 % (5551)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_5389 for (2995ds/343Mi)
% 2.30/1.85 % (5552)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_5389 for (2995ds/109Mi)
% 2.30/1.85 % (5533)Instruction limit reached!
% 2.30/1.85 % (5533)------------------------------
% 2.30/1.85 % (5533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.85 % (5533)Termination reason: Unknown
% 2.30/1.85 % (5533)Termination phase: Saturation
% 2.30/1.85
% 2.30/1.85 % (5533)Memory used [KB]: 7036
% 2.30/1.85 % (5533)Time elapsed: 0.151 s
% 2.30/1.85 % (5533)Instructions burned: 509 (million)
% 2.30/1.85 % (5533)------------------------------
% 2.30/1.85 % (5533)------------------------------
% 2.30/1.86 % (5553)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_5389 for (2995ds/253Mi)
% 2.30/1.87 % (5540)Instruction limit reached!
% 2.30/1.87 % (5540)------------------------------
% 2.30/1.87 % (5540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.87 % (5540)Termination reason: Unknown
% 2.30/1.87 % (5540)Termination phase: Saturation
% 2.30/1.87
% 2.30/1.87 % (5540)Memory used [KB]: 2430
% 2.30/1.87 % (5540)Time elapsed: 0.107 s
% 2.30/1.87 % (5540)Instructions burned: 435 (million)
% 2.30/1.87 % (5540)------------------------------
% 2.30/1.87 % (5540)------------------------------
% 2.30/1.88 % (5554)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_5389 for (2995ds/140Mi)
% 2.30/1.88 % (5550)Instruction limit reached!
% 2.30/1.88 % (5550)------------------------------
% 2.30/1.88 % (5550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.88 % (5550)Termination reason: Unknown
% 2.30/1.88 % (5550)Termination phase: Saturation
% 2.30/1.88
% 2.30/1.88 % (5550)Memory used [KB]: 7164
% 2.30/1.88 % (5550)Time elapsed: 0.046 s
% 2.30/1.88 % (5550)Instructions burned: 150 (million)
% 2.30/1.88 % (5550)------------------------------
% 2.30/1.88 % (5550)------------------------------
% 2.30/1.88 % (5552)Instruction limit reached!
% 2.30/1.88 % (5552)------------------------------
% 2.30/1.88 % (5552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.88 % (5552)Termination reason: Unknown
% 2.30/1.88 % (5552)Termination phase: Saturation
% 2.30/1.88
% 2.30/1.88 % (5552)Memory used [KB]: 6652
% 2.30/1.88 % (5552)Time elapsed: 0.030 s
% 2.30/1.88 % (5552)Instructions burned: 111 (million)
% 2.30/1.88 % (5552)------------------------------
% 2.30/1.88 % (5552)------------------------------
% 2.30/1.89 % (5555)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_5389 for (2995ds/614Mi)
% 2.30/1.89 % (5556)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_5389 for (2995ds/202Mi)
% 2.30/1.91 % (5554)Refutation not found, incomplete strategy
% 2.30/1.91 % (5554)------------------------------
% 2.30/1.91 % (5554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.91 % (5554)Termination reason: Refutation not found, incomplete strategy
% 2.30/1.91
% 2.30/1.91
% 2.30/1.91 % (5554)Memory used [KB]: 6140
% 2.30/1.91 % (5554)Time elapsed: 0.053 s
% 2.30/1.91 % (5554)Instructions burned: 108 (million)
% 2.30/1.91 % (5554)------------------------------
% 2.30/1.91 % (5554)------------------------------
% 2.30/1.91 % (5544)Instruction limit reached!
% 2.30/1.91 % (5544)------------------------------
% 2.30/1.91 % (5544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.91 % (5544)Termination reason: Unknown
% 2.30/1.91 % (5544)Termination phase: Saturation
% 2.30/1.91
% 2.30/1.91 % (5544)Memory used [KB]: 6140
% 2.30/1.91 % (5544)Time elapsed: 0.111 s
% 2.30/1.91 % (5544)Instructions burned: 453 (million)
% 2.30/1.91 % (5544)------------------------------
% 2.30/1.91 % (5544)------------------------------
% 2.30/1.92 % (5557)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_5389 for (2994ds/339Mi)
% 2.30/1.92 % (5558)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_5389 for (2994ds/283Mi)
% 2.30/1.94 % (5553)Instruction limit reached!
% 2.30/1.94 % (5553)------------------------------
% 2.30/1.94 % (5553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.94 % (5553)Termination reason: Unknown
% 2.30/1.94 % (5553)Termination phase: Saturation
% 2.30/1.94
% 2.30/1.94 % (5553)Memory used [KB]: 7547
% 2.30/1.94 % (5553)Time elapsed: 0.098 s
% 2.30/1.94 % (5553)Instructions burned: 254 (million)
% 2.30/1.94 % (5553)------------------------------
% 2.30/1.94 % (5553)------------------------------
% 2.30/1.95 % (5551)Instruction limit reached!
% 2.30/1.95 % (5551)------------------------------
% 2.30/1.95 % (5551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.95 % (5551)Termination reason: Unknown
% 2.30/1.95 % (5551)Termination phase: Saturation
% 2.30/1.95
% 2.30/1.95 % (5551)Memory used [KB]: 7164
% 2.30/1.95 % (5551)Time elapsed: 0.103 s
% 2.30/1.95 % (5551)Instructions burned: 344 (million)
% 2.30/1.95 % (5551)------------------------------
% 2.30/1.95 % (5551)------------------------------
% 2.30/1.95 % (5559)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_5389 for (2994ds/134Mi)
% 2.30/1.96 % (5556)Instruction limit reached!
% 2.30/1.96 % (5556)------------------------------
% 2.30/1.96 % (5556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.96 % (5556)Termination reason: Unknown
% 2.30/1.96 % (5556)Termination phase: Saturation
% 2.30/1.96
% 2.30/1.96 % (5556)Memory used [KB]: 7419
% 2.30/1.96 % (5556)Time elapsed: 0.085 s
% 2.30/1.96 % (5556)Instructions burned: 205 (million)
% 2.30/1.96 % (5556)------------------------------
% 2.30/1.96 % (5556)------------------------------
% 2.30/1.96 % (5560)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_5389 for (2994ds/298Mi)
% 2.30/1.96 % (5561)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_5389 for (2994ds/192Mi)
% 2.30/1.99 % (5559)Instruction limit reached!
% 2.30/1.99 % (5559)------------------------------
% 2.30/1.99 % (5559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.99 % (5559)Termination reason: Unknown
% 2.30/1.99 % (5559)Termination phase: Saturation
% 2.30/1.99
% 2.30/1.99 % (5559)Memory used [KB]: 6780
% 2.30/1.99 % (5559)Time elapsed: 0.039 s
% 2.30/1.99 % (5559)Instructions burned: 135 (million)
% 2.30/1.99 % (5559)------------------------------
% 2.30/1.99 % (5559)------------------------------
% 2.30/1.99 % (5558)Instruction limit reached!
% 2.30/1.99 % (5558)------------------------------
% 2.30/1.99 % (5558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.99 % (5558)Termination reason: Unknown
% 2.30/1.99 % (5558)Termination phase: Saturation
% 2.30/1.99
% 2.30/1.99 % (5558)Memory used [KB]: 7931
% 2.30/1.99 % (5558)Time elapsed: 0.071 s
% 2.30/1.99 % (5558)Instructions burned: 285 (million)
% 2.30/1.99 % (5558)------------------------------
% 2.30/1.99 % (5558)------------------------------
% 2.30/2.00 % (5562)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_5389 for (2993ds/258Mi)
% 2.30/2.00 % (5563)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_5389 for (2993ds/90Mi)
% 6.52/2.02 % (5557)Instruction limit reached!
% 6.52/2.02 % (5557)------------------------------
% 6.52/2.02 % (5557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.02 % (5557)Termination reason: Unknown
% 6.52/2.02 % (5557)Termination phase: Saturation
% 6.52/2.02
% 6.52/2.02 % (5557)Memory used [KB]: 7803
% 6.52/2.02 % (5557)Time elapsed: 0.100 s
% 6.52/2.02 % (5557)Instructions burned: 341 (million)
% 6.52/2.02 % (5557)------------------------------
% 6.52/2.02 % (5557)------------------------------
% 6.52/2.02 % (5563)Instruction limit reached!
% 6.52/2.02 % (5563)------------------------------
% 6.52/2.02 % (5563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.02 % (5563)Termination reason: Unknown
% 6.52/2.02 % (5563)Termination phase: Saturation
% 6.52/2.02
% 6.52/2.02 % (5563)Memory used [KB]: 6524
% 6.52/2.02 % (5563)Time elapsed: 0.026 s
% 6.52/2.02 % (5563)Instructions burned: 92 (million)
% 6.52/2.02 % (5563)------------------------------
% 6.52/2.02 % (5563)------------------------------
% 6.52/2.03 % (5564)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_5389 for (2993ds/231Mi)
% 6.52/2.03 % (5560)Instruction limit reached!
% 6.52/2.03 % (5560)------------------------------
% 6.52/2.03 % (5560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.03 % (5560)Termination reason: Unknown
% 6.52/2.03 % (5560)Termination phase: Saturation
% 6.52/2.03
% 6.52/2.03 % (5560)Memory used [KB]: 6268
% 6.52/2.03 % (5560)Time elapsed: 0.076 s
% 6.52/2.03 % (5560)Instructions burned: 301 (million)
% 6.52/2.03 % (5560)------------------------------
% 6.52/2.03 % (5560)------------------------------
% 6.52/2.03 % (5565)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_5389 for (2993ds/458Mi)
% 6.52/2.04 % (5566)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_5389 for (2993ds/31Mi)
% 6.52/2.04 % (5561)Instruction limit reached!
% 6.52/2.04 % (5561)------------------------------
% 6.52/2.04 % (5561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.04 % (5561)Termination reason: Unknown
% 6.52/2.04 % (5561)Termination phase: Saturation
% 6.52/2.04
% 6.52/2.04 % (5561)Memory used [KB]: 7036
% 6.52/2.04 % (5561)Time elapsed: 0.074 s
% 6.52/2.04 % (5561)Instructions burned: 193 (million)
% 6.52/2.04 % (5561)------------------------------
% 6.52/2.04 % (5561)------------------------------
% 6.52/2.05 % (5566)Instruction limit reached!
% 6.52/2.05 % (5566)------------------------------
% 6.52/2.05 % (5566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.05 % (5566)Termination reason: Unknown
% 6.52/2.05 % (5566)Termination phase: Property scanning
% 6.52/2.05
% 6.52/2.05 % (5566)Memory used [KB]: 1535
% 6.52/2.05 % (5566)Time elapsed: 0.009 s
% 6.52/2.05 % (5566)Instructions burned: 31 (million)
% 6.52/2.05 % (5566)------------------------------
% 6.52/2.05 % (5566)------------------------------
% 6.52/2.05 % (5567)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_5389 for (2993ds/297Mi)
% 6.52/2.06 % (5568)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_5389 for (2993ds/987Mi)
% 6.52/2.07 % (5537)Instruction limit reached!
% 6.52/2.07 % (5537)------------------------------
% 6.52/2.07 % (5537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.07 % (5537)Termination reason: Unknown
% 6.52/2.07 % (5537)Termination phase: Saturation
% 6.52/2.07
% 6.52/2.07 % (5537)Memory used [KB]: 9850
% 6.52/2.07 % (5537)Time elapsed: 0.337 s
% 6.52/2.07 % (5537)Instructions burned: 1089 (million)
% 6.52/2.07 % (5537)------------------------------
% 6.52/2.07 % (5537)------------------------------
% 6.52/2.07 % (5562)Instruction limit reached!
% 6.52/2.07 % (5562)------------------------------
% 6.52/2.07 % (5562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.07 % (5562)Termination reason: Unknown
% 6.52/2.07 % (5562)Termination phase: Saturation
% 6.52/2.07
% 6.52/2.07 % (5562)Memory used [KB]: 6908
% 6.52/2.07 % (5562)Time elapsed: 0.078 s
% 6.52/2.07 % (5562)Instructions burned: 259 (million)
% 6.52/2.07 % (5562)------------------------------
% 6.52/2.07 % (5562)------------------------------
% 6.52/2.08 % (5555)Instruction limit reached!
% 6.52/2.08 % (5555)------------------------------
% 6.52/2.08 % (5555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.08 % (5555)Termination reason: Unknown
% 6.52/2.08 % (5555)Termination phase: Saturation
% 6.52/2.08
% 6.52/2.08 % (5555)Memory used [KB]: 7675
% 6.52/2.08 % (5555)Time elapsed: 0.208 s
% 6.52/2.08 % (5555)Instructions burned: 614 (million)
% 6.52/2.08 % (5555)------------------------------
% 6.52/2.08 % (5555)------------------------------
% 6.52/2.08 % (5569)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_5389 for (2993ds/182Mi)
% 6.52/2.08 % (5570)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_5389 for (2993ds/182Mi)
% 6.52/2.09 % (5571)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_5389 for (2993ds/154Mi)
% 6.52/2.10 % (5564)Instruction limit reached!
% 6.52/2.10 % (5564)------------------------------
% 6.52/2.10 % (5564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.10 % (5564)Termination reason: Unknown
% 6.52/2.10 % (5564)Termination phase: Saturation
% 6.52/2.10
% 6.52/2.10 % (5564)Memory used [KB]: 9466
% 6.52/2.10 % (5564)Time elapsed: 0.069 s
% 6.52/2.10 % (5564)Instructions burned: 232 (million)
% 6.52/2.10 % (5564)------------------------------
% 6.52/2.10 % (5564)------------------------------
% 6.52/2.11 % (5572)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_5389 for (2992ds/79Mi)
% 6.95/2.12 % (5571)Instruction limit reached!
% 6.95/2.12 % (5571)------------------------------
% 6.95/2.12 % (5571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.95/2.12 % (5571)Termination reason: Unknown
% 6.95/2.12 % (5571)Termination phase: Saturation
% 6.95/2.12
% 6.95/2.12 % (5571)Memory used [KB]: 6140
% 6.95/2.12 % (5571)Time elapsed: 0.038 s
% 6.95/2.12 % (5571)Instructions burned: 155 (million)
% 6.95/2.12 % (5571)------------------------------
% 6.95/2.12 % (5571)------------------------------
% 6.95/2.13 % (5572)Instruction limit reached!
% 6.95/2.13 % (5572)------------------------------
% 6.95/2.13 % (5572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.95/2.13 % (5572)Termination reason: Unknown
% 6.95/2.13 % (5572)Termination phase: Saturation
% 6.95/2.13
% 6.95/2.13 % (5572)Memory used [KB]: 6268
% 6.95/2.13 % (5572)Time elapsed: 0.022 s
% 6.95/2.13 % (5572)Instructions burned: 79 (million)
% 6.95/2.13 % (5572)------------------------------
% 6.95/2.13 % (5572)------------------------------
% 6.95/2.13 % (5567)Instruction limit reached!
% 6.95/2.13 % (5567)------------------------------
% 6.95/2.13 % (5567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.95/2.13 % (5567)Termination reason: Unknown
% 6.95/2.13 % (5567)Termination phase: Saturation
% 6.95/2.13
% 6.95/2.13 % (5567)Memory used [KB]: 7291
% 6.95/2.13 % (5567)Time elapsed: 0.075 s
% 6.95/2.13 % (5567)Instructions burned: 299 (million)
% 6.95/2.13 % (5567)------------------------------
% 6.95/2.13 % (5567)------------------------------
% 6.95/2.13 % (5569)Instruction limit reached!
% 6.95/2.13 % (5569)------------------------------
% 6.95/2.13 % (5569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.95/2.13 % (5569)Termination reason: Unknown
% 6.95/2.13 % (5569)Termination phase: Saturation
% 6.95/2.13
% 6.95/2.13 % (5569)Memory used [KB]: 6908
% 6.95/2.13 % (5569)Time elapsed: 0.053 s
% 6.95/2.13 % (5569)Instructions burned: 183 (million)
% 6.95/2.13 % (5569)------------------------------
% 6.95/2.13 % (5569)------------------------------
% 6.95/2.13 % (5573)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_5389 for (2992ds/216Mi)
% 6.95/2.14 % (5574)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_5389 for (2992ds/114Mi)
% 6.95/2.14 % (5575)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_5389 for (2992ds/922Mi)
% 6.95/2.14 % (5576)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_5389 for (2992ds/182Mi)
% 6.95/2.14 % (5570)Instruction limit reached!
% 6.95/2.14 % (5570)------------------------------
% 6.95/2.14 % (5570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.95/2.14 % (5570)Termination reason: Unknown
% 6.95/2.14 % (5570)Termination phase: Saturation
% 6.95/2.14
% 6.95/2.14 % (5570)Memory used [KB]: 8315
% 6.95/2.14 % (5570)Time elapsed: 0.058 s
% 6.95/2.14 % (5570)Instructions burned: 184 (million)
% 6.95/2.14 % (5570)------------------------------
% 6.95/2.14 % (5570)------------------------------
% 6.95/2.15 % (5577)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_5389 for (2992ds/164Mi)
% 6.95/2.17 % (5574)Instruction limit reached!
% 6.95/2.17 % (5574)------------------------------
% 6.95/2.17 % (5574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.95/2.17 % (5574)Termination reason: Unknown
% 6.95/2.17 % (5574)Termination phase: Saturation
% 6.95/2.17
% 6.95/2.17 % (5574)Memory used [KB]: 6780
% 6.95/2.17 % (5574)Time elapsed: 0.032 s
% 6.95/2.17 % (5574)Instructions burned: 116 (million)
% 6.95/2.17 % (5574)------------------------------
% 6.95/2.17 % (5574)------------------------------
% 6.95/2.17 % (5565)Instruction limit reached!
% 6.95/2.17 % (5565)------------------------------
% 6.95/2.17 % (5565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.95/2.17 % (5565)Termination reason: Unknown
% 6.95/2.17 % (5565)Termination phase: Saturation
% 6.95/2.17
% 6.95/2.17 % (5565)Memory used [KB]: 7291
% 6.95/2.17 % (5565)Time elapsed: 0.140 s
% 6.95/2.17 % (5565)Instructions burned: 461 (million)
% 6.95/2.17 % (5565)------------------------------
% 6.95/2.17 % (5565)------------------------------
% 6.95/2.18 % (5578)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_5389 for (2992ds/50Mi)
% 6.95/2.18 % (5579)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_5389 for (2992ds/368Mi)
% 6.95/2.18 % (5576)Instruction limit reached!
% 6.95/2.18 % (5576)------------------------------
% 6.95/2.18 % (5576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.95/2.18 % (5576)Termination reason: Unknown
% 6.95/2.18 % (5576)Termination phase: Saturation
% 6.95/2.18
% 6.95/2.18 % (5576)Memory used [KB]: 6140
% 6.95/2.18 % (5576)Time elapsed: 0.045 s
% 6.95/2.18 % (5576)Instructions burned: 184 (million)
% 6.95/2.18 % (5576)------------------------------
% 6.95/2.18 % (5576)------------------------------
% 6.95/2.19 % (5573)Instruction limit reached!
% 6.95/2.19 % (5573)------------------------------
% 6.95/2.19 % (5573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.95/2.19 % (5573)Termination reason: Unknown
% 6.95/2.19 % (5573)Termination phase: Saturation
% 6.95/2.19
% 6.95/2.19 % (5573)Memory used [KB]: 7291
% 6.95/2.19 % (5573)Time elapsed: 0.053 s
% 6.95/2.19 % (5573)Instructions burned: 218 (million)
% 6.95/2.19 % (5573)------------------------------
% 6.95/2.19 % (5573)------------------------------
% 6.95/2.19 % (5578)Instruction limit reached!
% 6.95/2.19 % (5578)------------------------------
% 6.95/2.19 % (5578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.95/2.19 % (5578)Termination reason: Unknown
% 6.95/2.19 % (5578)Termination phase: Saturation
% 6.95/2.19
% 6.95/2.19 % (5578)Memory used [KB]: 10490
% 6.95/2.19 % (5578)Time elapsed: 0.014 s
% 6.95/2.19 % (5578)Instructions burned: 51 (million)
% 6.95/2.19 % (5578)------------------------------
% 6.95/2.19 % (5578)------------------------------
% 6.95/2.19 % (5580)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_5389 for (2992ds/1021Mi)
% 6.95/2.19 % (5581)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_5389 for (2992ds/267Mi)
% 7.56/2.20 % (5577)Instruction limit reached!
% 7.56/2.20 % (5577)------------------------------
% 7.56/2.20 % (5577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.56/2.20 % (5577)Termination reason: Unknown
% 7.56/2.20 % (5577)Termination phase: Saturation
% 7.56/2.20
% 7.56/2.20 % (5577)Memory used [KB]: 1918
% 7.56/2.20 % (5577)Time elapsed: 0.048 s
% 7.56/2.20 % (5577)Instructions burned: 165 (million)
% 7.56/2.20 % (5577)------------------------------
% 7.56/2.20 % (5577)------------------------------
% 7.56/2.20 % (5582)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_5389 for (2992ds/204Mi)
% 7.56/2.21 % (5583)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_5389 for (2991ds/26Mi)
% 7.56/2.21 % (5583)Instruction limit reached!
% 7.56/2.21 % (5583)------------------------------
% 7.56/2.21 % (5583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.56/2.21 % (5583)Termination reason: Unknown
% 7.56/2.21 % (5583)Termination phase: Property scanning
% 7.56/2.21
% 7.56/2.21 % (5583)Memory used [KB]: 1407
% 7.56/2.21 % (5583)Time elapsed: 0.008 s
% 7.56/2.21 % (5583)Instructions burned: 27 (million)
% 7.56/2.21 % (5583)------------------------------
% 7.56/2.21 % (5583)------------------------------
% 7.56/2.22 % (5584)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_5389 for (2991ds/53Mi)
% 7.56/2.24 % (5584)Instruction limit reached!
% 7.56/2.24 % (5584)------------------------------
% 7.56/2.24 % (5584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.56/2.24 % (5584)Termination reason: Unknown
% 7.56/2.24 % (5584)Termination phase: Saturation
% 7.56/2.24
% 7.56/2.24 % (5584)Memory used [KB]: 6012
% 7.56/2.24 % (5584)Time elapsed: 0.015 s
% 7.56/2.24 % (5584)Instructions burned: 55 (million)
% 7.56/2.24 % (5584)------------------------------
% 7.56/2.24 % (5584)------------------------------
% 7.56/2.25 % (5585)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_5389 for (2991ds/4436Mi)
% 7.56/2.26 % (5582)Instruction limit reached!
% 7.56/2.26 % (5582)------------------------------
% 7.56/2.26 % (5582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.56/2.26 % (5582)Termination reason: Unknown
% 7.56/2.26 % (5582)Termination phase: Saturation
% 7.56/2.26
% 7.56/2.26 % (5582)Memory used [KB]: 6908
% 7.56/2.26 % (5582)Time elapsed: 0.060 s
% 7.56/2.26 % (5582)Instructions burned: 204 (million)
% 7.56/2.26 % (5582)------------------------------
% 7.56/2.26 % (5582)------------------------------
% 7.56/2.26 % (5581)Instruction limit reached!
% 7.56/2.26 % (5581)------------------------------
% 7.56/2.26 % (5581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.56/2.26 % (5581)Termination reason: Unknown
% 7.56/2.26 % (5581)Termination phase: Saturation
% 7.56/2.26
% 7.56/2.26 % (5581)Memory used [KB]: 7803
% 7.56/2.26 % (5581)Time elapsed: 0.066 s
% 7.56/2.26 % (5581)Instructions burned: 267 (million)
% 7.56/2.26 % (5581)------------------------------
% 7.56/2.26 % (5581)------------------------------
% 7.56/2.27 % (5586)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_5389 for (2991ds/1539Mi)
% 7.56/2.28 % (5587)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_5389 for (2991ds/408Mi)
% 7.56/2.28 % (5579)Instruction limit reached!
% 7.56/2.28 % (5579)------------------------------
% 7.56/2.28 % (5579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.56/2.28 % (5579)Termination reason: Unknown
% 7.56/2.28 % (5579)Termination phase: Saturation
% 7.56/2.28
% 7.56/2.28 % (5579)Memory used [KB]: 6908
% 7.56/2.28 % (5579)Time elapsed: 0.096 s
% 7.56/2.28 % (5579)Instructions burned: 369 (million)
% 7.56/2.28 % (5579)------------------------------
% 7.56/2.28 % (5579)------------------------------
% 7.56/2.29 % (5588)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_5389 for (2991ds/5205Mi)
% 7.56/2.29 % (5568)Instruction limit reached!
% 7.56/2.29 % (5568)------------------------------
% 7.56/2.29 % (5568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.56/2.29 % (5568)Termination reason: Unknown
% 7.56/2.29 % (5568)Termination phase: Saturation
% 7.56/2.29
% 7.56/2.29 % (5568)Memory used [KB]: 7547
% 7.56/2.29 % (5568)Time elapsed: 0.234 s
% 7.56/2.29 % (5568)Instructions burned: 988 (million)
% 7.56/2.29 % (5568)------------------------------
% 7.56/2.29 % (5568)------------------------------
% 8.15/2.30 % (5589)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_5389 for (2991ds/1913Mi)
% 8.16/2.42 % (5587)Instruction limit reached!
% 8.16/2.42 % (5587)------------------------------
% 8.16/2.42 % (5587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.16/2.42 % (5587)Termination reason: Unknown
% 8.16/2.42 % (5587)Termination phase: Saturation
% 8.16/2.42
% 8.16/2.42 % (5587)Memory used [KB]: 8827
% 8.16/2.42 % (5587)Time elapsed: 0.146 s
% 8.16/2.42 % (5587)Instructions burned: 410 (million)
% 8.16/2.42 % (5587)------------------------------
% 8.16/2.42 % (5587)------------------------------
% 8.16/2.43 % (5590)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_5389 for (2989ds/4350Mi)
% 8.16/2.44 % (5575)Instruction limit reached!
% 8.16/2.44 % (5575)------------------------------
% 8.16/2.44 % (5575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.16/2.44 % (5575)Termination reason: Unknown
% 8.16/2.44 % (5575)Termination phase: Saturation
% 8.16/2.44
% 8.16/2.44 % (5575)Memory used [KB]: 8955
% 8.16/2.44 % (5575)Time elapsed: 0.299 s
% 8.16/2.44 % (5575)Instructions burned: 923 (million)
% 8.16/2.44 % (5575)------------------------------
% 8.16/2.44 % (5575)------------------------------
% 8.16/2.45 % (5591)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_5389 for (2989ds/68Mi)
% 8.16/2.46 % (5591)Instruction limit reached!
% 8.16/2.46 % (5591)------------------------------
% 8.16/2.46 % (5591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.16/2.46 % (5591)Termination reason: Unknown
% 8.16/2.46 % (5591)Termination phase: Saturation
% 8.16/2.46
% 8.16/2.46 % (5591)Memory used [KB]: 6268
% 8.16/2.46 % (5591)Time elapsed: 0.019 s
% 8.16/2.46 % (5591)Instructions burned: 68 (million)
% 8.16/2.46 % (5591)------------------------------
% 8.16/2.46 % (5591)------------------------------
% 8.16/2.47 % (5592)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_5389 for (2989ds/358Mi)
% 8.16/2.49 % (5586)First to succeed.
% 8.16/2.49 % (5586)Refutation found. Thanks to Tanya!
% 8.16/2.49 % SZS status Theorem for DTF2THF_5389
% 8.16/2.49 % SZS output start Proof for DTF2THF_5389
% 8.16/2.49 thf(func_def_0, type, in: $i > $i > $o).
% 8.16/2.49 thf(func_def_1, type, exu: ($i > $o) > $o).
% 8.16/2.49 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 8.16/2.49 thf(func_def_8, type, powerset: $i > $i).
% 8.16/2.49 thf(func_def_10, type, setunion: $i > $i).
% 8.16/2.49 thf(func_def_19, type, descr: ($i > $o) > $i).
% 8.16/2.49 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_26, type, prop2set: $o > $i).
% 8.16/2.49 thf(func_def_36, type, nonempty: $i > $o).
% 8.16/2.49 thf(func_def_69, type, set2prop: $i > $o).
% 8.16/2.49 thf(func_def_88, type, subset: $i > $i > $o).
% 8.16/2.49 thf(func_def_89, type, disjoint: $i > $i > $o).
% 8.16/2.49 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 8.16/2.49 thf(func_def_129, type, sK1: $i > $o).
% 8.16/2.49 thf(func_def_131, type, sK3: $i > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_132, type, sK4: $i > $i > $i).
% 8.16/2.49 thf(func_def_133, type, sK5: $i > $i).
% 8.16/2.49 thf(func_def_134, type, sK6: ($i > $o) > $i).
% 8.16/2.49 thf(func_def_135, type, sK7: ($i > $o) > $i > $i).
% 8.16/2.49 thf(func_def_136, type, sK8: $i > ($i > $i > $o) > $i).
% 8.16/2.49 thf(func_def_137, type, sK9: $i > ($i > $i > $o) > $i).
% 8.16/2.49 thf(func_def_138, type, sK10: $i > $i > ($i > $i > $o) > $i).
% 8.16/2.49 thf(func_def_139, type, sK11: ($i > $o) > $i).
% 8.16/2.49 thf(func_def_140, type, sK12: ($i > $o) > $i > $i).
% 8.16/2.49 thf(func_def_141, type, sK13: ($i > $o) > $i > $i).
% 8.16/2.49 thf(func_def_142, type, sK14: $i > $i).
% 8.16/2.49 thf(func_def_143, type, sK15: $o > $i > $i > $i).
% 8.16/2.49 thf(func_def_144, type, sK16: $i > $i > $i).
% 8.16/2.49 thf(func_def_145, type, sK17: $i > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_146, type, sK18: $i > $i).
% 8.16/2.49 thf(func_def_147, type, sK19: $i > $i > $i).
% 8.16/2.49 thf(func_def_148, type, sK20: ($i > $o) > $i > $i).
% 8.16/2.49 thf(func_def_149, type, sK21: $i > $i).
% 8.16/2.49 thf(func_def_150, type, sK22: ($i > $o) > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_151, type, sK23: $i > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_152, type, sK24: $i > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_153, type, sK25: ($i > $o) > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_154, type, sK26: ($i > $o) > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_155, type, sK27: $i > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_156, type, sK28: $i > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_157, type, sK29: ($i > $o) > $i > $i).
% 8.16/2.49 thf(func_def_158, type, sK30: ($i > $o) > $i).
% 8.16/2.49 thf(func_def_159, type, sK31: ($i > $o) > $i).
% 8.16/2.49 thf(func_def_160, type, sK32: ($i > $o) > $i).
% 8.16/2.49 thf(func_def_161, type, sK33: ($i > $o) > $i).
% 8.16/2.49 thf(func_def_162, type, sK34: ($i > $o) > $i).
% 8.16/2.49 thf(func_def_163, type, sK35: $i > $i).
% 8.16/2.49 thf(func_def_164, type, sK36: $i > $i > $i).
% 8.16/2.49 thf(func_def_165, type, sK37: $i > $i > $i).
% 8.16/2.49 thf(func_def_166, type, sK38: $i > $i > $i).
% 8.16/2.49 thf(func_def_167, type, sK39: $i > $i > $i).
% 8.16/2.49 thf(func_def_168, type, sK40: $i > $i > $i > $i).
% 8.16/2.49 thf(func_def_169, type, sK41: $i > $i).
% 8.16/2.49 thf(func_def_170, type, sK42: ($i > $o) > $i > ($i > $o) > $i > $i).
% 8.16/2.49 thf(func_def_171, type, sK43: $i > $i > ($i > $o) > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_172, type, sK44: $i > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_173, type, sK45: $i > $i > $i).
% 8.16/2.49 thf(func_def_174, type, sK46: $i > $i > $i).
% 8.16/2.49 thf(func_def_175, type, sK47: $i > $i > $i).
% 8.16/2.49 thf(func_def_176, type, sK48: $i > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_177, type, sK49: ($i > $o) > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_178, type, sK50: ($i > $o) > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_179, type, sK51: ($i > $o) > $i).
% 8.16/2.49 thf(func_def_180, type, sK52: ($i > $o) > $i > $i).
% 8.16/2.49 thf(func_def_181, type, sK53: $i > $i > $i).
% 8.16/2.49 thf(func_def_182, type, sK54: ($i > $o) > $i).
% 8.16/2.49 thf(func_def_183, type, sK55: ($i > $o) > $i > $i).
% 8.16/2.49 thf(func_def_184, type, sK56: ($i > $o) > $i > $i).
% 8.16/2.49 thf(func_def_185, type, sK57: $i > $i).
% 8.16/2.49 thf(func_def_186, type, sK58: ($i > $o) > $i).
% 8.16/2.49 thf(func_def_187, type, sK59: ($i > $o) > $i > $i).
% 8.16/2.49 thf(func_def_188, type, sK60: $i > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_189, type, sK61: $i > ($i > $o) > $i).
% 8.16/2.49 thf(func_def_190, type, sK62: ($i > $o) > $i > $i).
% 8.16/2.49 thf(func_def_191, type, ph63: !>[X0: $tType]:(X0)).
% 8.16/2.49 thf(func_def_193, type, sK65: $i > $i).
% 8.16/2.49 thf(func_def_194, type, sK66: $i > $i > $i).
% 8.16/2.49 thf(func_def_195, type, sK67: $i > $i > $i).
% 8.16/2.49 thf(func_def_196, type, sK68: $i > $i > $i).
% 8.16/2.49 thf(func_def_197, type, sK69: $i > $i).
% 8.16/2.49 thf(func_def_198, type, sK70: $i > $i > $i).
% 8.16/2.49 thf(func_def_199, type, sK71: $i > $i > $i).
% 8.16/2.49 thf(func_def_200, type, sK72: $i > $i > $i).
% 8.16/2.49 thf(func_def_201, type, sK73: $i > $i > $i).
% 8.16/2.49 thf(func_def_202, type, sK74: $i > $i > $i).
% 8.16/2.49 thf(func_def_203, type, sK75: $i > $i > $i).
% 8.16/2.49 thf(func_def_204, type, sK76: $i > $i).
% 8.16/2.49 thf(func_def_205, type, sK77: $i > $i).
% 8.16/2.49 thf(func_def_206, type, sK78: $i > $i > $i).
% 8.16/2.49 thf(func_def_207, type, sK79: $i > $i > $i).
% 8.16/2.49 thf(func_def_208, type, sK80: $i > $i > $i).
% 8.16/2.49 thf(func_def_209, type, sK81: $i > $i > $i).
% 8.16/2.49 thf(func_def_210, type, sK82: $i > $i > $i).
% 8.16/2.49 thf(func_def_211, type, sK83: $i > $i > $i).
% 8.16/2.49 thf(func_def_212, type, sK84: $i > $i > $i).
% 8.16/2.49 thf(func_def_213, type, sK85: $i > $i > $i).
% 8.16/2.49 thf(func_def_215, type, sK87: $i > $i > $i).
% 8.16/2.49 thf(f3990,plain,(
% 8.16/2.49 $false),
% 8.16/2.49 inference(avatar_sat_refutation,[status(thm)],[f1911,f2304,f3822,f3956,f3989])).
% 8.16/2.49 thf(f3989,plain,(
% 8.16/2.49 ~spl2_12 | ~spl2_13),
% 8.16/2.49 inference(avatar_contradiction_clause,[status(thm)],[f3988])).
% 8.16/2.49 thf(f3988,plain,(
% 8.16/2.49 $false | (~spl2_12 | ~spl2_13)),
% 8.16/2.49 inference(trivial_inequality_removal,[status(thm)],[f3987])).
% 8.16/2.49 thf(f3987,plain,(
% 8.16/2.49 ($true = $false) | (~spl2_12 | ~spl2_13)),
% 8.16/2.49 inference(forward_demodulation,[status(thm)],[f3975,f3821])).
% 8.16/2.49 thf(f3821,plain,(
% 8.16/2.49 ($false = (in @ sK86 @ sK0)) | ~spl2_12),
% 8.16/2.49 inference(avatar_component_clause,[status(thm)],[f3819])).
% 8.16/2.49 thf(f3819,definition,(
% 8.16/2.49 spl2_12 <=> ($false = (in @ sK86 @ sK0))),
% 8.16/2.49 introduced(definition,[new_symbols(naming,[spl2_12])],[avatar_definition])).
% 8.16/2.49 thf(f3975,plain,(
% 8.16/2.49 ($true = (in @ sK86 @ sK0)) | ~spl2_13),
% 8.16/2.49 inference(trivial_inequality_removal,[status(thm)],[f3959])).
% 8.16/2.49 thf(f3959,plain,(
% 8.16/2.49 ($true = $false) | ($true = (in @ sK86 @ sK0)) | ~spl2_13),
% 8.16/2.49 inference(superposition,[status(thm)],[f3955,f1006])).
% 8.16/2.49 thf(f1006,plain,(
% 8.16/2.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($false = (in @ X2 @ (dsetconstr @ X3 @ X1))) | ((in @ X2 @ X3) = $true)) )),
% 8.16/2.49 inference(binary_proxy_clausification,[status(thm)],[f1005])).
% 8.16/2.49 thf(f1005,plain,(
% 8.16/2.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((in @ X2 @ (dsetconstr @ X3 @ X1)) => (in @ X2 @ X3)) = $true)) )),
% 8.16/2.49 inference(beta_eta_normalization,[status(thm)],[f1004])).
% 8.16/2.49 thf(f1004,plain,(
% 8.16/2.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((in @ X2 @ (dsetconstr @ Y0 @ X1)) => (in @ X2 @ Y0))) @ X3) = $true)) )),
% 8.16/2.49 inference(pi_clausification,[status(thm)],[f1003])).
% 8.16/2.49 thf(f1003,plain,(
% 8.16/2.49 ( ! [X2 : $i,X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (dsetconstr @ Y0 @ X1)) => (in @ X2 @ Y0)))))) )),
% 8.16/2.49 inference(beta_eta_normalization,[status(thm)],[f1002])).
% 8.16/2.49 thf(f1002,plain,(
% 8.16/2.49 ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (dsetconstr @ Y1 @ X1)) => (in @ Y0 @ Y1))))) @ X2) = $true)) )),
% 8.16/2.49 inference(pi_clausification,[status(thm)],[f1001])).
% 8.16/2.49 thf(f1001,plain,(
% 8.16/2.49 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (dsetconstr @ Y1 @ X1)) => (in @ Y0 @ Y1)))))) = $true)) )),
% 8.16/2.49 inference(beta_eta_normalization,[status(thm)],[f1000])).
% 8.16/2.49 thf(f1000,plain,(
% 8.16/2.49 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (in @ Y1 @ Y2))))))) @ X1))) )),
% 8.16/2.49 inference(pi_clausification,[status(thm)],[f999])).
% 8.16/2.49 thf(f999,plain,(
% 8.16/2.49 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) = $true)),
% 8.16/2.49 inference(beta_eta_normalization,[status(thm)],[f567])).
% 8.16/2.49 thf(f567,plain,(
% 8.16/2.49 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (in @ Y1 @ Y2)))))))) = $true)),
% 8.16/2.49 inference(definition_unfolding,[status(thm)],[f431,f381])).
% 8.16/2.49 thf(f381,plain,(
% 8.16/2.49 (dsetconstrEL = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (in @ Y1 @ Y2)))))))))),
% 8.16/2.49 inference(cnf_transformation,[status(thm)],[f238])).
% 8.16/2.49 thf(f238,plain,(
% 8.16/2.49 (dsetconstrEL = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (in @ Y1 @ Y2)))))))))),
% 8.16/2.49 inference(fool_elimination,[status(thm)],[f237])).
% 8.16/2.49 thf(f237,plain,(
% 8.16/2.49 (dsetconstrEL = ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => (in @ X1 @ X0)))),
% 8.16/2.49 inference(rectify,[status(thm)],[f15])).
% 8.16/2.49 thf(f15,axiom,(
% 8.16/2.49 (dsetconstrEL = ! [X3 : $i,X1 : $i,X0 : $i > $o] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (in @ X1 @ X3)))),
% 8.16/2.49 file('/export/starexec/sandbox/tmp/tmp.qcVYf693pv/DTF2THF_5389.p',dsetconstrEL)).
% 8.16/2.49 thf(f431,plain,(
% 8.16/2.49 (dsetconstrEL = $true)),
% 8.16/2.49 inference(cnf_transformation,[status(thm)],[f297])).
% 8.16/2.49 thf(f297,plain,(
% 8.16/2.49 (nonemptyImpWitness = $true) & (subsetI2 = $true) & (subsetRefl = $true) & (eqimpsubset1 = $true) & (emptyI = $true) & (upairsetIL = $true) & ($true != (in @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0))) @ (powerset @ sK0))) & (singletonsswitch = $true) & (setext = $true) & (setadjoinIL = $true) & (in__Cong = $true) & (emptysetAx = $true) & (exu__Cong = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan2 = $true) & (setadjoinOr = $true) & (exuI3 = $true) & (powersetI = $true) & (eqinunit = $true) & (exuE3e = $true) & (uniqinunit = $true) & (quantDeMorgan1 = $true) & (wellorderingAx = $true) & (nonemptyI = $true) & (subset2powerset = $true) & (subsetE = $true) & (setoftrueEq = $true) & (notequalI2 = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (emptyinPowerset = $true) & (dsetconstrI = $true) & (subsetI1 = $true) & (exuI1 = $true) & (emptysetE = $true) & (vacuousDall = $true) & (emptysetsubset = $true) & (setbeta = $true) & (subsetE2 = $true) & (emptysetimpfalse = $true) & (powersetE = $true) & (prop2set2propI = $true) & (powerset__Cong = $true) & (emptyinunitempty = $true) & (powersetAx = $true) & (quantDeMorgan3 = $true) & (subsetTrans = $true) & (subPowSU = $true) & (setadjoinAx = $true) & (emptyInPowerset = $true) & (dsetconstrER = $true) & (emptyset__Cong = $true) & (notdexE = $true) & (setunionAx = $true) & (foundationAx = $true) & (notdallE = $true) & (powersetE1 = $true) & (prop2setE = $true) & (setadjoin__Cong = $true) & (setunion__Cong = $true) & (dsetconstrEL = $true) & (descrp = $true) & (emptyE1 = $true) & (setadjoinE = $true) & (upairsetIR = $true) & (notinemptyset = $true) & (setunionE = $true) & (eqimpsubset2 = $true) & (nonemptyI1 = $true) & (setadjoinSub2 = $true) & (omega__Cong = $true) & (nonemptyE1 = $true) & (setextAx = $true) & (omega0Ax = $true) & (setunionI = $true) & (exuE2 = $true) & (powersetI1 = $true) & (prop2setI = $true) & (exuE3u = $true) & (descr__Cong = $true) & (notinsingleton = $true) & (replAx = $true) & (upairsetE = $true) & (setadjoinSub = $true) & (exuI2 = $true) & (notsubsetI = $true) & (noeltsimpempty = $true) & (inPowerset = $true) & (subsetemptysetimpeq = $true) & (dsetconstr__Cong = $true) & (exuE1 = $true) & (exuEu = $true) & (setextsub = $true) & (inCongP = $true) & (powersetsubset = $true) & (notequalI1 = $true) & (setadjoinIR = $true)),
% 8.16/2.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f295,f296])).
% 8.16/2.49 thf(f296,plain,(
% 8.16/2.49 ? [X0 : $i,X1 : $i > $o] : ((in @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (powerset @ X0)) != $true) => ($true != (in @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0))) @ (powerset @ sK0)))),
% 8.16/2.49 introduced(definition,[],[choice_axiom])).
% 8.16/2.49 thf(f295,plain,(
% 8.16/2.49 (nonemptyImpWitness = $true) & (subsetI2 = $true) & (subsetRefl = $true) & (eqimpsubset1 = $true) & (emptyI = $true) & (upairsetIL = $true) & ? [X0 : $i,X1 : $i > $o] : ((in @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (powerset @ X0)) != $true) & (singletonsswitch = $true) & (setext = $true) & (setadjoinIL = $true) & (in__Cong = $true) & (emptysetAx = $true) & (exu__Cong = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan2 = $true) & (setadjoinOr = $true) & (exuI3 = $true) & (powersetI = $true) & (eqinunit = $true) & (exuE3e = $true) & (uniqinunit = $true) & (quantDeMorgan1 = $true) & (wellorderingAx = $true) & (nonemptyI = $true) & (subset2powerset = $true) & (subsetE = $true) & (setoftrueEq = $true) & (notequalI2 = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (emptyinPowerset = $true) & (dsetconstrI = $true) & (subsetI1 = $true) & (exuI1 = $true) & (emptysetE = $true) & (vacuousDall = $true) & (emptysetsubset = $true) & (setbeta = $true) & (subsetE2 = $true) & (emptysetimpfalse = $true) & (powersetE = $true) & (prop2set2propI = $true) & (powerset__Cong = $true) & (emptyinunitempty = $true) & (powersetAx = $true) & (quantDeMorgan3 = $true) & (subsetTrans = $true) & (subPowSU = $true) & (setadjoinAx = $true) & (emptyInPowerset = $true) & (dsetconstrER = $true) & (emptyset__Cong = $true) & (notdexE = $true) & (setunionAx = $true) & (foundationAx = $true) & (notdallE = $true) & (powersetE1 = $true) & (prop2setE = $true) & (setadjoin__Cong = $true) & (setunion__Cong = $true) & (dsetconstrEL = $true) & (descrp = $true) & (emptyE1 = $true) & (setadjoinE = $true) & (upairsetIR = $true) & (notinemptyset = $true) & (setunionE = $true) & (eqimpsubset2 = $true) & (nonemptyI1 = $true) & (setadjoinSub2 = $true) & (omega__Cong = $true) & (nonemptyE1 = $true) & (setextAx = $true) & (omega0Ax = $true) & (setunionI = $true) & (exuE2 = $true) & (powersetI1 = $true) & (prop2setI = $true) & (exuE3u = $true) & (descr__Cong = $true) & (notinsingleton = $true) & (replAx = $true) & (upairsetE = $true) & (setadjoinSub = $true) & (exuI2 = $true) & (notsubsetI = $true) & (noeltsimpempty = $true) & (inPowerset = $true) & (subsetemptysetimpeq = $true) & (dsetconstr__Cong = $true) & (exuE1 = $true) & (exuEu = $true) & (setextsub = $true) & (inCongP = $true) & (powersetsubset = $true) & (notequalI1 = $true) & (setadjoinIR = $true)),
% 8.16/2.49 inference(flattening,[status(thm)],[f294])).
% 8.16/2.49 thf(f294,plain,(
% 8.16/2.49 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i > $o] : ((in @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (powerset @ X0)) != $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)),
% 8.16/2.49 inference(ennf_transformation,[status(thm)],[f160])).
% 8.16/2.49 thf(f160,plain,(
% 8.16/2.49 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((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) => ! [X0 : $i,X1 : $i > $o] : ((in @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (powerset @ X0)) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.16/2.49 inference(fool_elimination,[status(thm)],[f159])).
% 8.16/2.49 thf(f159,plain,(
% 8.16/2.49 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (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 => ! [X0 : $i,X1 : $i > $o] : (in @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) @ (powerset @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.16/2.49 inference(rectify,[status(thm)],[f100])).
% 8.16/2.49 thf(f100,negated_conjecture,(
% 8.16/2.49 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (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 => ! [X3 : $i,X0 : $i > $o] : (in @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) @ (powerset @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.16/2.49 inference(negated_conjecture,[status(cth)],[f99])).
% 8.16/2.49 thf(f99,conjecture,(
% 8.16/2.49 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (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 => ! [X3 : $i,X0 : $i > $o] : (in @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) @ (powerset @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.16/2.49 file('/export/starexec/sandbox/tmp/tmp.qcVYf693pv/DTF2THF_5389.p',sepInPowerset)).
% 8.16/2.49 thf(f3955,plain,(
% 8.16/2.49 ((in @ sK86 @ (dsetconstr @ sK0 @ sK1)) = $true) | ~spl2_13),
% 8.16/2.49 inference(avatar_component_clause,[status(thm)],[f3953])).
% 8.16/2.49 thf(f3953,definition,(
% 8.16/2.49 spl2_13 <=> ((in @ sK86 @ (dsetconstr @ sK0 @ sK1)) = $true)),
% 8.16/2.49 introduced(definition,[new_symbols(naming,[spl2_13])],[avatar_definition])).
% 8.16/2.49 thf(f3956,plain,(
% 8.16/2.49 spl2_13 | ~spl2_11),
% 8.16/2.49 inference(avatar_split_clause,[status(thm)],[f3799,f2301,f3953])).
% 8.16/2.49 thf(f2301,definition,(
% 8.16/2.49 spl2_11 <=> ($false = (in @ (dsetconstr @ sK0 @ sK1) @ (powerset @ sK0)))),
% 8.16/2.49 introduced(definition,[new_symbols(naming,[spl2_11])],[avatar_definition])).
% 8.16/2.49 thf(f3799,plain,(
% 8.16/2.49 ((in @ sK86 @ (dsetconstr @ sK0 @ sK1)) = $true) | ~spl2_11),
% 8.16/2.49 inference(binary_proxy_clausification,[status(thm)],[f3797])).
% 8.16/2.49 thf(f3797,plain,(
% 8.16/2.49 (((in @ sK86 @ (dsetconstr @ sK0 @ sK1)) => (in @ sK86 @ sK0)) = $false) | ~spl2_11),
% 8.16/2.49 inference(beta_eta_normalization,[status(thm)],[f3796])).
% 8.16/2.49 thf(f3796,plain,(
% 8.16/2.49 (((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK0 @ sK1)) => (in @ Y0 @ sK0))) @ sK86) = $false) | ~spl2_11),
% 8.16/2.49 inference(sigma_clausification,[status(thm)],[f3795])).
% 8.16/2.49 thf(f3795,plain,(
% 8.16/2.49 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK0 @ sK1)) => (in @ Y0 @ sK0)))) = $false) | ~spl2_11),
% 8.16/2.49 inference(not_proxy_clausification,[status(thm)],[f3794])).
% 8.16/2.49 thf(f3794,plain,(
% 8.16/2.49 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK0 @ sK1)) => (in @ Y0 @ sK0)))))) | ~spl2_11),
% 8.16/2.49 inference(boolean_simplification,[status(thm)],[f3674])).
% 8.16/2.49 thf(f3674,plain,(
% 8.16/2.49 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK0 @ sK1)) => (in @ Y0 @ sK0)))) = $false)) | ~spl2_11),
% 8.16/2.49 inference(superposition,[status(thm)],[f1628,f2303])).
% 8.16/2.49 thf(f2303,plain,(
% 8.16/2.49 ($false = (in @ (dsetconstr @ sK0 @ sK1) @ (powerset @ sK0))) | ~spl2_11),
% 8.16/2.49 inference(avatar_component_clause,[status(thm)],[f2301])).
% 8.16/2.49 thf(f1628,plain,(
% 8.16/2.49 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) = (in @ X1 @ (powerset @ X2))) = $true)) )),
% 8.16/2.49 inference(beta_eta_normalization,[status(thm)],[f1627])).
% 8.16/2.49 thf(f1627,plain,(
% 8.16/2.49 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) = (in @ X1 @ (powerset @ Y0)))) @ X2) = $true)) )),
% 8.16/2.49 inference(pi_clausification,[status(thm)],[f1626])).
% 8.16/2.49 thf(f1626,plain,(
% 8.16/2.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) = (in @ X1 @ (powerset @ Y0))))) = $true)) )),
% 8.16/2.49 inference(beta_eta_normalization,[status(thm)],[f1625])).
% 8.16/2.49 thf(f1625,plain,(
% 8.16/2.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) = (in @ Y0 @ (powerset @ Y1)))))) @ X1))) )),
% 8.16/2.49 inference(pi_clausification,[status(thm)],[f552])).
% 8.16/2.49 thf(f552,plain,(
% 8.16/2.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) = (in @ Y0 @ (powerset @ Y1))))))) = $true)),
% 8.16/2.49 inference(definition_unfolding,[status(thm)],[f447,f318])).
% 8.16/2.49 thf(f318,plain,(
% 8.16/2.49 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) = (in @ Y0 @ (powerset @ Y1))))))))),
% 8.16/2.49 inference(cnf_transformation,[status(thm)],[f111])).
% 8.16/2.49 thf(f111,plain,(
% 8.16/2.49 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) = (in @ Y0 @ (powerset @ Y1))))))))),
% 8.16/2.49 inference(fool_elimination,[status(thm)],[f110])).
% 8.16/2.49 thf(f110,plain,(
% 8.16/2.49 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) <=> (in @ X1 @ (powerset @ X0))) = powersetAx)),
% 8.16/2.49 inference(rectify,[status(thm)],[f5])).
% 8.16/2.49 thf(f5,axiom,(
% 8.16/2.49 (! [X3 : $i,X4 : $i] : (! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3)) <=> (in @ X4 @ (powerset @ X3))) = powersetAx)),
% 8.16/2.49 file('/export/starexec/sandbox/tmp/tmp.qcVYf693pv/DTF2THF_5389.p',powersetAx)).
% 8.16/2.49 thf(f447,plain,(
% 8.16/2.49 (powersetAx = $true)),
% 8.16/2.49 inference(cnf_transformation,[status(thm)],[f297])).
% 8.16/2.49 thf(f3822,plain,(
% 8.16/2.49 spl2_12 | ~spl2_11),
% 8.16/2.49 inference(avatar_split_clause,[status(thm)],[f3798,f2301,f3819])).
% 8.16/2.49 thf(f3798,plain,(
% 8.16/2.49 ($false = (in @ sK86 @ sK0)) | ~spl2_11),
% 8.16/2.49 inference(binary_proxy_clausification,[status(thm)],[f3797])).
% 8.16/2.49 thf(f2304,plain,(
% 8.16/2.49 spl2_11 | spl2_4),
% 8.16/2.49 inference(avatar_split_clause,[status(thm)],[f1923,f1908,f2301])).
% 8.16/2.49 thf(f1908,definition,(
% 8.16/2.49 spl2_4 <=> ($true = (in @ (dsetconstr @ sK0 @ sK1) @ (powerset @ sK0)))),
% 8.16/2.49 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 8.16/2.49 thf(f1923,plain,(
% 8.16/2.49 ($false = (in @ (dsetconstr @ sK0 @ sK1) @ (powerset @ sK0))) | spl2_4),
% 8.16/2.49 inference(trivial_inequality_removal,[status(thm)],[f1921])).
% 8.16/2.49 thf(f1921,plain,(
% 8.16/2.49 ($true != $true) | ($false = (in @ (dsetconstr @ sK0 @ sK1) @ (powerset @ sK0))) | spl2_4),
% 8.16/2.49 inference(superposition,[status(thm)],[f1910,f1709])).
% 8.16/2.49 thf(f1709,plain,(
% 8.16/2.49 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 8.16/2.49 inference(trivial_inequality_removal,[status(thm)],[f1697])).
% 8.16/2.49 thf(f1697,plain,(
% 8.16/2.49 ( ! [X0 : $o] : (($true = X0) | ($false = X0) | ($true = $false)) )),
% 8.16/2.49 inference(superposition,[status(thm)],[f1569,f661])).
% 8.16/2.49 thf(f661,plain,(
% 8.16/2.49 ( ! [X1 : $o] : (($true = (in @ emptyset @ (prop2set @ X1))) | ($false = X1)) )),
% 8.16/2.49 inference(binary_proxy_clausification,[status(thm)],[f660])).
% 8.16/2.49 thf(f660,plain,(
% 8.16/2.49 ( ! [X1 : $o] : (($true = (X1 => (in @ emptyset @ (prop2set @ X1))))) )),
% 8.16/2.49 inference(beta_eta_normalization,[status(thm)],[f659])).
% 8.16/2.49 thf(f659,plain,(
% 8.16/2.49 ( ! [X1 : $o] : (($true = ((^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0)))) @ X1))) )),
% 8.16/2.49 inference(pi_clausification,[status(thm)],[f584])).
% 8.16/2.49 thf(f584,plain,(
% 8.16/2.49 ($true = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))),
% 8.16/2.49 inference(definition_unfolding,[status(thm)],[f414,f364])).
% 8.16/2.49 thf(f364,plain,(
% 8.16/2.49 (prop2setI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))),
% 8.16/2.49 inference(cnf_transformation,[status(thm)],[f135])).
% 8.16/2.49 thf(f135,plain,(
% 8.16/2.49 (prop2setI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))),
% 8.16/2.49 inference(fool_elimination,[status(thm)],[f134])).
% 8.16/2.49 thf(f134,plain,(
% 8.16/2.49 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 8.16/2.49 inference(rectify,[status(thm)],[f59])).
% 8.16/2.49 thf(f59,axiom,(
% 8.16/2.49 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 8.16/2.49 file('/export/starexec/sandbox/tmp/tmp.qcVYf693pv/DTF2THF_5389.p',prop2setI)).
% 8.16/2.49 thf(f414,plain,(
% 8.16/2.49 (prop2setI = $true)),
% 8.16/2.49 inference(cnf_transformation,[status(thm)],[f297])).
% 8.16/2.49 thf(f1569,plain,(
% 8.16/2.49 ( ! [X2 : $o,X1 : $i] : (((in @ X1 @ (prop2set @ X2)) = $false) | ($true = X2)) )),
% 8.16/2.49 inference(binary_proxy_clausification,[status(thm)],[f1568])).
% 8.16/2.49 thf(f1568,plain,(
% 8.16/2.49 ( ! [X2 : $o,X1 : $i] : (($true = ((in @ X1 @ (prop2set @ X2)) => X2))) )),
% 8.16/2.49 inference(beta_eta_normalization,[status(thm)],[f1567])).
% 8.16/2.49 thf(f1567,plain,(
% 8.16/2.49 ( ! [X2 : $o,X1 : $i] : (($true = ((^[Y0 : $o]: ((in @ X1 @ (prop2set @ Y0)) => Y0)) @ X2))) )),
% 8.16/2.49 inference(pi_clausification,[status(thm)],[f1566])).
% 8.16/2.49 thf(f1566,plain,(
% 8.16/2.49 ( ! [X1 : $i] : (($true = (!! @ $o @ (^[Y0 : $o]: ((in @ X1 @ (prop2set @ Y0)) => Y0))))) )),
% 8.16/2.49 inference(beta_eta_normalization,[status(thm)],[f1565])).
% 8.16/2.49 thf(f1565,plain,(
% 8.16/2.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1)))) @ X1))) )),
% 8.16/2.49 inference(pi_clausification,[status(thm)],[f564])).
% 8.16/2.49 thf(f564,plain,(
% 8.16/2.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) = $true)),
% 8.16/2.49 inference(definition_unfolding,[status(thm)],[f434,f313])).
% 8.16/2.49 thf(f313,plain,(
% 8.16/2.49 (prop2setE = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))))),
% 8.16/2.49 inference(cnf_transformation,[status(thm)],[f144])).
% 8.16/2.49 thf(f144,plain,(
% 8.16/2.49 (prop2setE = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))))),
% 8.16/2.49 inference(fool_elimination,[status(thm)],[f143])).
% 8.16/2.49 thf(f143,plain,(
% 8.16/2.49 (prop2setE = ! [X0 : $o,X1 : $i] : ((in @ X1 @ (prop2set @ X0)) => X0))),
% 8.16/2.49 inference(rectify,[status(thm)],[f18])).
% 8.16/2.49 thf(f18,axiom,(
% 8.16/2.49 (prop2setE = ! [X0 : $o,X1 : $i] : ((in @ X1 @ (prop2set @ X0)) => X0))),
% 8.16/2.49 file('/export/starexec/sandbox/tmp/tmp.qcVYf693pv/DTF2THF_5389.p',prop2setE)).
% 8.16/2.49 thf(f434,plain,(
% 8.16/2.49 (prop2setE = $true)),
% 8.16/2.49 inference(cnf_transformation,[status(thm)],[f297])).
% 8.16/2.49 thf(f1910,plain,(
% 8.16/2.49 ($true != (in @ (dsetconstr @ sK0 @ sK1) @ (powerset @ sK0))) | spl2_4),
% 8.16/2.49 inference(avatar_component_clause,[status(thm)],[f1908])).
% 8.16/2.49 thf(f1911,plain,(
% 8.16/2.49 ~spl2_4),
% 8.16/2.49 inference(avatar_split_clause,[status(thm)],[f695,f1908])).
% 8.16/2.49 thf(f695,plain,(
% 8.16/2.49 ($true != (in @ (dsetconstr @ sK0 @ sK1) @ (powerset @ sK0)))),
% 8.16/2.49 inference(beta_eta_normalization,[status(thm)],[f485])).
% 8.16/2.49 thf(f485,plain,(
% 8.16/2.49 ($true != (in @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0))) @ (powerset @ sK0)))),
% 8.16/2.49 inference(cnf_transformation,[status(thm)],[f297])).
% 8.16/2.49 % SZS output end Proof for DTF2THF_5389
% 8.16/2.49 % (5586)------------------------------
% 8.16/2.49 % (5586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.16/2.49 % (5586)Termination reason: Refutation
% 8.16/2.49
% 8.16/2.49 % (5586)Memory used [KB]: 8059
% 8.16/2.49 % (5586)Time elapsed: 0.222 s
% 8.16/2.49 % (5586)Instructions burned: 710 (million)
% 8.16/2.49 % (5586)------------------------------
% 8.16/2.49 % (5586)------------------------------
% 8.16/2.49 % (5488)Success in time 1.089 s
%------------------------------------------------------------------------------