%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO903^10 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 09:55:10 AM UTC 2026
% Result : Theorem 2.05s 1.65s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 45
% Syntax : Number of formulae : 515 ( 88 unt; 0 typ; 24 def)
% Number of atoms : 7497 (1608 equ; 0 cnn)
% Maximal formula atoms : 17 ( 14 avg)
% Number of connectives : 9840 ( 494 ~;1510 |; 6 &;6309 @)
% ( 24 <=>; 844 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 211 ( 211 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 39 usr; 30 con; 0-3 aty)
% ( 647 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 1726 (1075 ^; 649 !; 2 ?;1726 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mrel: mworld > mworld > $o ).
thf(func_def_2,type,
mactual: mworld ).
thf(func_def_3,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_5,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
v1: mworld > $o ).
thf(func_def_13,type,
v2: mworld > $o ).
thf(func_def_14,type,
v3: mworld > $o ).
thf(func_def_15,type,
v4: mworld > $o ).
thf(func_def_30,type,
sK1: mworld ).
thf(f1662,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1213,f1229,f1258,f1272,f1274,f1275,f1277,f1280,f1282,f1286,f1289,f1291,f1299,f1302,f1313,f1319,f1348,f1350,f1363,f1374,f1375,f1401,f1402,f1425,f1433,f1439,f1445,f1452,f1461,f1468,f1498,f1504,f1515,f1583,f1617,f1620,f1660]) ).
thf(f1660,plain,
( spl0_5
| ~ spl0_19
| spl0_26 ),
inference(avatar_contradiction_clause,[status(thm)],[f1659]) ).
thf(f1659,plain,
( $false
| spl0_5
| ~ spl0_19
| spl0_26 ),
inference(subsumption_resolution,[status(thm)],[f1658,f1191]) ).
thf(f1191,plain,
( ( ( v1 @ mactual )
!= $true )
| spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f1190]) ).
thf(f1190,definition,
( spl0_5
<=> ( ( v1 @ mactual )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f1658,plain,
( ( ( v1 @ mactual )
= $true )
| ~ spl0_19
| spl0_26 ),
inference(subsumption_resolution,[status(thm)],[f1648,f1345]) ).
thf(f1345,plain,
( ( $false
!= ( mrel @ mactual @ mactual ) )
| spl0_26 ),
inference(avatar_component_clause,[status(thm)],[f1344]) ).
thf(f1344,definition,
( spl0_26
<=> ( $false
= ( mrel @ mactual @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_26])],[avatar_definition]) ).
thf(f1648,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( ( v1 @ mactual )
= $true )
| ~ spl0_19
| spl0_26 ),
inference(trivial_inequality_removal,[status(thm)],[f1644]) ).
thf(f1644,plain,
( ( $false != $false )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ( ( v1 @ mactual )
= $true )
| ~ spl0_19
| spl0_26 ),
inference(superposition,[status(thm)],[f1345,f1246]) ).
thf(f1246,plain,
( ! [X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( v1 @ X3 )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) )
| ~ spl0_19 ),
inference(avatar_component_clause,[status(thm)],[f1245]) ).
thf(f1245,definition,
( spl0_19
<=> ! [X1: mworld,X3: mworld] :
( ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v1 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition]) ).
thf(f1620,plain,
( spl0_2
| ~ spl0_7
| spl0_26 ),
inference(avatar_contradiction_clause,[status(thm)],[f1619]) ).
thf(f1619,plain,
( $false
| spl0_2
| ~ spl0_7
| spl0_26 ),
inference(subsumption_resolution,[status(thm)],[f1618,f1180]) ).
thf(f1180,plain,
( ( $false
!= ( v3 @ mactual ) )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f1179]) ).
thf(f1179,definition,
( spl0_2
<=> ( $false
= ( v3 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f1618,plain,
( ( $false
= ( v3 @ mactual ) )
| ~ spl0_7
| spl0_26 ),
inference(subsumption_resolution,[status(thm)],[f1606,f1345]) ).
thf(f1606,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false
= ( v3 @ mactual ) )
| ~ spl0_7
| spl0_26 ),
inference(trivial_inequality_removal,[status(thm)],[f1603]) ).
thf(f1603,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false != $false )
| ( $false
= ( v3 @ mactual ) )
| ~ spl0_7
| spl0_26 ),
inference(superposition,[status(thm)],[f1345,f1198]) ).
thf(f1198,plain,
( ! [X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X1 @ X4 ) )
| ( $false
= ( v3 @ X4 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f1197]) ).
thf(f1197,definition,
( spl0_7
<=> ! [X4: mworld,X1: mworld] :
( ( $false
= ( mrel @ X1 @ X4 ) )
| ( $false
= ( v3 @ X4 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f1617,plain,
( spl0_23
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f1608,f1197,f1266]) ).
thf(f1266,definition,
( spl0_23
<=> ! [X2: mworld] :
( ( $false
= ( v3 @ X2 ) )
| ( ( mrel @ mactual @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition]) ).
thf(f1608,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( v3 @ X0 )
= $false ) )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1602]) ).
thf(f1602,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( ( v3 @ X0 )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) ) )
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f229,f1198]) ).
thf(f229,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f183]) ).
thf(f183,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f182]) ).
thf(f182,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X2: mworld] : ( mrel @ X2 @ X2 ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',mrel_reflexive) ).
thf(f1583,plain,
( spl0_2
| ~ spl0_23
| spl0_26 ),
inference(avatar_contradiction_clause,[status(thm)],[f1582]) ).
thf(f1582,plain,
( $false
| spl0_2
| ~ spl0_23
| spl0_26 ),
inference(subsumption_resolution,[status(thm)],[f1574,f1180]) ).
thf(f1574,plain,
( ( $false
= ( v3 @ mactual ) )
| ~ spl0_23
| spl0_26 ),
inference(trivial_inequality_removal,[status(thm)],[f1571]) ).
thf(f1571,plain,
( ( $false != $false )
| ( $false
= ( v3 @ mactual ) )
| ~ spl0_23
| spl0_26 ),
inference(superposition,[status(thm)],[f1345,f1267]) ).
thf(f1267,plain,
( ! [X2: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( v3 @ X2 ) ) )
| ~ spl0_23 ),
inference(avatar_component_clause,[status(thm)],[f1266]) ).
thf(f1515,plain,
( ~ spl0_4
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[status(thm)],[f1514]) ).
thf(f1514,plain,
( $false
| ~ spl0_4
| ~ spl0_25 ),
inference(trivial_inequality_removal,[status(thm)],[f1510]) ).
thf(f1510,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_25 ),
inference(superposition,[status(thm)],[f1484,f1342]) ).
thf(f1342,plain,
( ( ( v4 @ sK1 )
= $true )
| ~ spl0_25 ),
inference(avatar_component_clause,[status(thm)],[f1340]) ).
thf(f1340,definition,
( spl0_25
<=> ( ( v4 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition]) ).
thf(f1484,plain,
( ( ( v4 @ sK1 )
= $false )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f1476]) ).
thf(f1476,plain,
( ( $true = $false )
| ( ( v4 @ sK1 )
= $false )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f1187,f891]) ).
thf(f891,plain,
( $true
= ( mrel @ mactual @ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f890]) ).
thf(f890,plain,
( ( ?? @ mworld @ ( mrel @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f889]) ).
thf(f889,plain,
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] : ( mrel @ mactual @ Y0 ) ) ),
inference(boolean_simplification,[status(thm)],[f888]) ).
thf(f888,plain,
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ mactual @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f298]) ).
thf(f298,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f246,f192,f205]) ).
thf(f205,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
thf(f84,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f83]) ).
thf(f83,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X2: mworld] :
? [X4: mworld] :
( ( mrel @ X2 @ X4 )
& ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',mdia_def) ).
thf(f192,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
thf(f125,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',mlocal_def) ).
thf(f246,plain,
( $true
= ( mlocal
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
thf(f108,plain,
( $true
= ( mlocal
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) ),
inference(fool_elimination,[status(thm)],[f107]) ).
thf(f107,plain,
( mlocal
@ ( mdia
@ ^ [X0: mworld] : $true ) ),
inference(rectify,[status(thm)],[f61]) ).
thf(f61,axiom,
( mlocal
@ ( mdia
@ ^ [X2: mworld] : $true ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',deontic1) ).
thf(f1187,plain,
( ! [X2: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( v4 @ X2 ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f1186]) ).
thf(f1186,definition,
( spl0_4
<=> ! [X2: mworld] :
( ( $false
= ( v4 @ X2 ) )
| ( ( mrel @ mactual @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f1504,plain,
( spl0_10
| ~ spl0_13 ),
inference(avatar_split_clause,[status(thm)],[f1411,f1219,f1208]) ).
thf(f1208,definition,
( spl0_10
<=> ! [X2: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v2 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f1219,definition,
( spl0_13
<=> ! [X2: mworld,X4: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v2 @ X4 )
= $true )
| ( ( mrel @ X2 @ X4 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f1411,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) )
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f1405]) ).
thf(f1405,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true = $false )
| ( $true
= ( v2 @ X0 ) ) )
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f1220,f229]) ).
thf(f1220,plain,
( ! [X2: mworld,X4: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v2 @ X4 )
= $true )
| ( ( mrel @ X2 @ X4 )
= $false ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f1219]) ).
thf(f1498,plain,
( ~ spl0_10
| spl0_18 ),
inference(avatar_contradiction_clause,[status(thm)],[f1497]) ).
thf(f1497,plain,
( $false
| ~ spl0_10
| spl0_18 ),
inference(subsumption_resolution,[status(thm)],[f1325,f1241]) ).
thf(f1241,plain,
( ( $true
!= ( v2 @ mactual ) )
| spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f1240]) ).
thf(f1240,definition,
( spl0_18
<=> ( $true
= ( v2 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition]) ).
thf(f1325,plain,
( ( $true
= ( v2 @ mactual ) )
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f1323]) ).
thf(f1323,plain,
( ( $true = $false )
| ( $true
= ( v2 @ mactual ) )
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f229,f1209]) ).
thf(f1209,plain,
( ! [X2: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v2 @ X2 )
= $true ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f1208]) ).
thf(f1468,plain,
( ~ spl0_10
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[status(thm)],[f1467]) ).
thf(f1467,plain,
( $false
| ~ spl0_10
| ~ spl0_27 ),
inference(trivial_inequality_removal,[status(thm)],[f1463]) ).
thf(f1463,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_27 ),
inference(superposition,[status(thm)],[f1399,f1328]) ).
thf(f1328,plain,
( ( $true
= ( v2 @ sK1 ) )
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f1322]) ).
thf(f1322,plain,
( ( $true = $false )
| ( $true
= ( v2 @ sK1 ) )
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f1209,f891]) ).
thf(f1399,plain,
( ( $false
= ( v2 @ sK1 ) )
| ~ spl0_27 ),
inference(avatar_component_clause,[status(thm)],[f1397]) ).
thf(f1397,definition,
( spl0_27
<=> ( $false
= ( v2 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_27])],[avatar_definition]) ).
thf(f1461,plain,
( ~ spl0_18
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[status(thm)],[f1460]) ).
thf(f1460,plain,
( $false
| ~ spl0_18
| ~ spl0_21 ),
inference(trivial_inequality_removal,[status(thm)],[f1457]) ).
thf(f1457,plain,
( ( $true = $false )
| ~ spl0_18
| ~ spl0_21 ),
inference(superposition,[status(thm)],[f1242,f1255]) ).
thf(f1255,plain,
( ( $false
= ( v2 @ mactual ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[status(thm)],[f1253]) ).
thf(f1253,definition,
( spl0_21
<=> ( $false
= ( v2 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition]) ).
thf(f1242,plain,
( ( $true
= ( v2 @ mactual ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f1240]) ).
thf(f1452,plain,
( ~ spl0_1
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f1451]) ).
thf(f1451,plain,
( $false
| ~ spl0_1
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1448]) ).
thf(f1448,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f1177,f1224]) ).
thf(f1224,plain,
( ( $true
= ( v4 @ mactual ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f1222]) ).
thf(f1222,definition,
( spl0_14
<=> ( $true
= ( v4 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f1177,plain,
( ( $false
= ( v4 @ mactual ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f1175]) ).
thf(f1175,definition,
( spl0_1
<=> ( $false
= ( v4 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f1445,plain,
( ~ spl0_8
| spl0_17
| spl0_26 ),
inference(avatar_contradiction_clause,[status(thm)],[f1444]) ).
thf(f1444,plain,
( $false
| ~ spl0_8
| spl0_17
| spl0_26 ),
inference(subsumption_resolution,[status(thm)],[f1443,f1236]) ).
thf(f1236,plain,
( ( ( v1 @ mactual )
!= $false )
| spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f1235]) ).
thf(f1235,definition,
( spl0_17
<=> ( ( v1 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f1443,plain,
( ( ( v1 @ mactual )
= $false )
| ~ spl0_8
| spl0_26 ),
inference(subsumption_resolution,[status(thm)],[f1384,f1345]) ).
thf(f1384,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( ( v1 @ mactual )
= $false )
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f1380]) ).
thf(f1380,plain,
( ( ( v1 @ mactual )
= $false )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false != $false )
| ~ spl0_8 ),
inference(equality_factoring,[status(thm)],[f1202]) ).
thf(f1202,plain,
( ! [X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( v1 @ X3 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f1201]) ).
thf(f1201,definition,
( spl0_8
<=> ! [X1: mworld,X3: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( v1 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f1439,plain,
( ~ spl0_2
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f1438]) ).
thf(f1438,plain,
( $false
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f1434]) ).
thf(f1434,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f1217,f1181]) ).
thf(f1181,plain,
( ( $false
= ( v3 @ mactual ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f1179]) ).
thf(f1217,plain,
( ( $true
= ( v3 @ mactual ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f1215]) ).
thf(f1215,definition,
( spl0_12
<=> ( $true
= ( v3 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f1433,plain,
~ spl0_26,
inference(avatar_contradiction_clause,[status(thm)],[f1432]) ).
thf(f1432,plain,
( $false
| ~ spl0_26 ),
inference(trivial_inequality_removal,[status(thm)],[f1429]) ).
thf(f1429,plain,
( ( $true = $false )
| ~ spl0_26 ),
inference(superposition,[status(thm)],[f229,f1346]) ).
thf(f1346,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl0_26 ),
inference(avatar_component_clause,[status(thm)],[f1344]) ).
thf(f1425,plain,
( spl0_26
| spl0_12
| ~ spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f1424,f1227,f1215,f1344]) ).
thf(f1227,definition,
( spl0_15
<=> ! [X4: mworld,X2: mworld] :
( ( $true
= ( v3 @ X4 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ X2 @ X4 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f1424,plain,
( ( $true
= ( v3 @ mactual ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f1419]) ).
thf(f1419,plain,
( ( $true
= ( v3 @ mactual ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false != $false )
| ~ spl0_15 ),
inference(equality_factoring,[status(thm)],[f1228]) ).
thf(f1228,plain,
( ! [X2: mworld,X4: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v3 @ X4 ) )
| ( ( mrel @ X2 @ X4 )
= $false ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f1227]) ).
thf(f1402,plain,
( spl0_26
| spl0_27
| ~ spl0_11 ),
inference(avatar_split_clause,[status(thm)],[f1393,f1211,f1397,f1344]) ).
thf(f1211,definition,
( spl0_11
<=> ! [X5: mworld,X1: mworld] :
( ( ( v2 @ X5 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f1393,plain,
( ( $false
= ( v2 @ sK1 ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f1387]) ).
thf(f1387,plain,
( ( $false
= ( v2 @ sK1 ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ( $true = $false )
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f1212,f891]) ).
thf(f1212,plain,
( ! [X1: mworld,X5: mworld] :
( ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( v2 @ X5 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f1211]) ).
thf(f1401,plain,
( spl0_26
| spl0_21
| ~ spl0_11 ),
inference(avatar_split_clause,[status(thm)],[f1394,f1211,f1253,f1344]) ).
thf(f1394,plain,
( ( $false
= ( v2 @ mactual ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f1390]) ).
thf(f1390,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false != $false )
| ( $false
= ( v2 @ mactual ) )
| ~ spl0_11 ),
inference(equality_factoring,[status(thm)],[f1212]) ).
thf(f1375,plain,
( spl0_25
| ~ spl0_24 ),
inference(avatar_split_clause,[status(thm)],[f1368,f1270,f1340]) ).
thf(f1270,definition,
( spl0_24
<=> ! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v4 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition]) ).
thf(f1368,plain,
( ( ( v4 @ sK1 )
= $true )
| ~ spl0_24 ),
inference(trivial_inequality_removal,[status(thm)],[f1365]) ).
thf(f1365,plain,
( ( $true = $false )
| ( ( v4 @ sK1 )
= $true )
| ~ spl0_24 ),
inference(superposition,[status(thm)],[f1271,f891]) ).
thf(f1271,plain,
( ! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v4 @ X1 )
= $true ) )
| ~ spl0_24 ),
inference(avatar_component_clause,[status(thm)],[f1270]) ).
thf(f1374,plain,
( spl0_14
| ~ spl0_24 ),
inference(avatar_split_clause,[status(thm)],[f1369,f1270,f1222]) ).
thf(f1369,plain,
( ( $true
= ( v4 @ mactual ) )
| ~ spl0_24 ),
inference(trivial_inequality_removal,[status(thm)],[f1366]) ).
thf(f1366,plain,
( ( $true
= ( v4 @ mactual ) )
| ( $true = $false )
| ~ spl0_24 ),
inference(superposition,[status(thm)],[f229,f1271]) ).
thf(f1363,plain,
( spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f1357,f1194,f1186]) ).
thf(f1194,definition,
( spl0_6
<=> ! [X2: mworld,X3: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v4 @ X3 )
= $false )
| ( ( mrel @ X2 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f1357,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( v4 @ X0 )
= $false ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f1354]) ).
thf(f1354,plain,
( ! [X0: mworld] :
( ( ( v4 @ X0 )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true = $false ) )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f229,f1195]) ).
thf(f1195,plain,
( ! [X2: mworld,X3: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ X2 @ X3 )
= $false )
| ( ( v4 @ X3 )
= $false ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f1194]) ).
thf(f1350,plain,
( spl0_26
| spl0_14
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f1335,f1183,f1222,f1344]) ).
thf(f1183,definition,
( spl0_3
<=> ! [X1: mworld,X3: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( v4 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f1335,plain,
( ( $true
= ( v4 @ mactual ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f1333]) ).
thf(f1333,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false != $false )
| ( $true
= ( v4 @ mactual ) )
| ~ spl0_3 ),
inference(equality_factoring,[status(thm)],[f1184]) ).
thf(f1184,plain,
( ! [X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( v4 @ X3 )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f1183]) ).
thf(f1348,plain,
( spl0_25
| spl0_26
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f1337,f1183,f1344,f1340]) ).
thf(f1337,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( ( v4 @ sK1 )
= $true )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f1330]) ).
thf(f1330,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( ( v4 @ sK1 )
= $true )
| ( $true = $false )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f1184,f891]) ).
thf(f1319,plain,
( ~ spl0_5
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f1318]) ).
thf(f1318,plain,
( $false
| ~ spl0_5
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f1314]) ).
thf(f1314,plain,
( ( $true = $false )
| ~ spl0_5
| ~ spl0_17 ),
inference(superposition,[status(thm)],[f1237,f1192]) ).
thf(f1192,plain,
( ( ( v1 @ mactual )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f1190]) ).
thf(f1237,plain,
( ( ( v1 @ mactual )
= $false )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f1235]) ).
thf(f1313,plain,
( spl0_17
| ~ spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f1308,f1204,f1235]) ).
thf(f1204,definition,
( spl0_9
<=> ! [X2: mworld] :
( ( $false
= ( v1 @ X2 ) )
| ( ( mrel @ mactual @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f1308,plain,
( ( ( v1 @ mactual )
= $false )
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f1306]) ).
thf(f1306,plain,
( ( ( v1 @ mactual )
= $false )
| ( $true = $false )
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f229,f1205]) ).
thf(f1205,plain,
( ! [X2: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( v1 @ X2 ) ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f1204]) ).
thf(f1302,plain,
( spl0_6
| spl0_4
| spl0_11
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f340,f1179,f1211,f1186,f1194]) ).
thf(f340,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v4 @ X5 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( ( v2 @ X4 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( v4 @ X3 )
= $false )
| ( ( mrel @ X2 @ X5 )
= $false )
| ( $false
= ( v3 @ mactual ) ) ),
inference(not_proxy_clausification,[status(thm)],[f339]) ).
thf(f339,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( mrel @ X2 @ X5 )
= $false )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( ( ~ ( v4 @ X5 ) )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v4 @ X3 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v2 @ X4 )
= $false )
| ( $false
= ( v3 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f338]) ).
thf(f338,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v3 @ mactual ) )
| ( ( v2 @ X4 )
= $false )
| ( ( ( mrel @ X2 @ X5 )
=> ~ ( v4 @ X5 ) )
= $true )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( ( v4 @ X3 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f337]) ).
thf(f337,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v4 @ X3 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v4 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v3 @ mactual ) )
| ( ( v2 @ X4 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f336]) ).
thf(f336,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v4 @ X3 )
= $false )
| ( $false
= ( v3 @ mactual ) )
| ( ( v2 @ X4 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f335]) ).
thf(f335,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( v4 @ X3 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( ~ ( v2 @ X4 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f334]) ).
thf(f334,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( v3 @ mactual ) )
| ( ( v4 @ X3 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $true
= ( ( mrel @ X1 @ X4 )
=> ~ ( v2 @ X4 ) ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f333]) ).
thf(f333,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X3 ) )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) )
@ X4 ) )
| ( ( v4 @ X3 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f332]) ).
thf(f332,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( v4 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f331]) ).
thf(f331,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
| ( ( v4 @ X3 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f330]) ).
thf(f330,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( ( v4 @ X3 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f329]) ).
thf(f329,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ~ ( v4 @ X3 ) )
= $true )
| ( ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f328]) ).
thf(f328,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ mactual @ X3 )
=> ~ ( v4 @ X3 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f327]) ).
thf(f327,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v4 @ Y0 ) )
@ X3 ) )
| ( ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ~ ( v3 @ mactual ) ) ) ),
inference(pi_clausification,[status(thm)],[f326]) ).
thf(f326,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
| ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f325]) ).
thf(f325,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) )
| ( ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
| ( $true
= ( ~ ( v3 @ mactual ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f324]) ).
thf(f324,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f323]) ).
thf(f323,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( v3 @ mactual ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f322]) ).
thf(f322,plain,
! [X1: mworld] :
( ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f321]) ).
thf(f321,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f320]) ).
thf(f320,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f319]) ).
thf(f319,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( v3 @ mactual ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f318]) ).
thf(f318,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v4 @ Y0 ) ) )
| ~ ( v3 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f292]) ).
thf(f292,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v3 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v4 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v4 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f240,f192,f203,f194,f203,f213,f194,f203,f213,f213,f194,f213,f213,f194]) ).
thf(f213,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
thf(f90,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) )
= mbox ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',mbox_def) ).
thf(f194,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
thf(f147,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f146]) ).
thf(f146,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',mnot_def) ).
thf(f203,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f181]) ).
thf(f181,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f180]) ).
thf(f180,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X3 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',mor_def) ).
thf(f240,plain,
( ( mlocal @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f98]) ).
thf(f98,plain,
( ( mlocal @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f97]) ).
thf(f97,plain,
mlocal @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f56]) ).
thf(f56,axiom,
mlocal @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat46) ).
thf(f1299,plain,
( spl0_2
| spl0_3
| spl0_17
| spl0_23 ),
inference(avatar_split_clause,[status(thm)],[f395,f1266,f1235,f1183,f1179]) ).
thf(f395,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v4 @ X3 )
= $true )
| ( ( v1 @ mactual )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( v3 @ X1 ) )
| ( ( mrel @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f394]) ).
thf(f394,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v1 @ mactual )
= $false )
| ( $false
= ( v3 @ X1 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( v4 @ X3 ) ) )
| ( $false
= ( v3 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f393]) ).
thf(f393,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v1 @ mactual )
= $false )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v4 @ Y0 ) )
@ X3 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f392]) ).
thf(f392,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v4 @ Y0 ) ) ) )
| ( ( v1 @ mactual )
= $false )
| ( $false
= ( v3 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f391]) ).
thf(f391,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v1 @ mactual )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v4 @ Y0 ) ) ) )
| ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f390]) ).
thf(f390,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v1 @ mactual )
= $false )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( $false
= ( v3 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f389]) ).
thf(f389,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( ( v1 @ mactual )
= $false )
| ( $false
= ( v3 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f388]) ).
thf(f388,plain,
! [X1: mworld] :
( ( $false
= ( v3 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( ( v1 @ mactual )
= $false )
| ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f387]) ).
thf(f387,plain,
! [X1: mworld] :
( ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( ( v1 @ mactual )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f386]) ).
thf(f386,plain,
! [X1: mworld] :
( ( ( ( mrel @ mactual @ X1 )
=> ~ ( v3 @ X1 ) )
= $true )
| ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( ( v1 @ mactual )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f385]) ).
thf(f385,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v3 @ Y0 ) )
@ X1 )
= $true )
| ( ( v1 @ mactual )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( v3 @ mactual ) ) ) ),
inference(pi_clausification,[status(thm)],[f384]) ).
thf(f384,plain,
( ( ( v1 @ mactual )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( v3 @ mactual ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f383]) ).
thf(f383,plain,
( ( ( ~ ( v1 @ mactual ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f382]) ).
thf(f382,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
= $true )
| ( ( ~ ( v1 @ mactual ) )
= $true )
| ( $true
= ( ~ ( v3 @ mactual ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f381]) ).
thf(f381,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
| ~ ( v3 @ mactual ) ) )
| ( ( ~ ( v1 @ mactual ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f380]) ).
thf(f380,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
| ~ ( v3 @ mactual )
| ~ ( v1 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f266]) ).
thf(f266,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v3 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v4 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f210,f192,f203,f194,f203,f194,f203,f213,f194,f213,f213]) ).
thf(f210,plain,
( ( mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f171]) ).
thf(f171,plain,
( ( mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f170]) ).
thf(f170,plain,
mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ),
inference(rectify,[status(thm)],[f45]) ).
thf(f45,axiom,
mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat35) ).
thf(f1291,plain,
( spl0_6
| spl0_18
| spl0_7
| spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f540,f1227,f1197,f1240,f1194]) ).
thf(f540,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( v3 @ X5 )
= $false )
| ( $true
= ( v3 @ X4 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v4 @ X6 )
= $false )
| ( ( mrel @ X2 @ X4 )
= $false )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ X3 @ X6 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f539]) ).
thf(f539,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X2 @ X4 )
= $false )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( v3 @ X5 )
= $false )
| ( $true
= ( v2 @ mactual ) )
| ( $true
= ( v3 @ X4 ) )
| ( ( mrel @ X3 @ X6 )
= $false )
| ( ( ~ ( v4 @ X6 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f538]) ).
thf(f538,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( ( mrel @ X3 @ X6 )
=> ~ ( v4 @ X6 ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v3 @ X4 ) )
| ( ( v3 @ X5 )
= $false )
| ( ( mrel @ X2 @ X4 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f537]) ).
thf(f537,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( v3 @ X5 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v4 @ Y0 ) )
@ X6 ) )
| ( ( mrel @ X2 @ X4 )
= $false )
| ( $true
= ( v3 @ X4 ) )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f536]) ).
thf(f536,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v3 @ X5 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( $true
= ( v3 @ X4 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v4 @ Y0 ) ) )
= $true )
| ( ( mrel @ X2 @ X4 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $true
= ( v2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f535]) ).
thf(f535,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ X2 @ X4 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v3 @ X4 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( v3 @ X5 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f534]) ).
thf(f534,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( ( mrel @ X2 @ X4 )
=> ( v3 @ X4 ) )
= $true )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( ( v3 @ X5 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f533]) ).
thf(f533,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( ~ ( v3 @ X5 ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( ( mrel @ X2 @ X4 )
=> ( v3 @ X4 ) )
= $true )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f532]) ).
thf(f532,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( ( mrel @ X1 @ X5 )
=> ~ ( v3 @ X5 ) ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( ( mrel @ X2 @ X4 )
=> ( v3 @ X4 ) )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f531]) ).
thf(f531,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) )
@ X5 )
= $true )
| ( ( ( mrel @ X2 @ X4 )
=> ( v3 @ X4 ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f530]) ).
thf(f530,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ X2 @ X4 )
=> ( v3 @ X4 ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f529]) ).
thf(f529,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) )
@ X4 ) )
| ( ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f528]) ).
thf(f528,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f527]) ).
thf(f527,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f526]) ).
thf(f526,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) ) ) )
| ( $true
= ( v2 @ mactual ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) )
@ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f525]) ).
thf(f525,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f524]) ).
thf(f524,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f523]) ).
thf(f523,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f522]) ).
thf(f522,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
= $true )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f521]) ).
thf(f521,plain,
! [X1: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) )
@ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f520]) ).
thf(f520,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f519]) ).
thf(f519,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f518]) ).
thf(f518,plain,
( ( $true
= ( v2 @ mactual ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f517]) ).
thf(f517,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( v2 @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f286]) ).
thf(f286,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v2
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v3 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v4 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f234,f192,f203,f203,f213,f213,f203,f213,f213,f194,f213,f213,f194]) ).
thf(f234,plain,
( ( mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f137]) ).
thf(f137,plain,
( ( mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f136]) ).
thf(f136,plain,
mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,axiom,
mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat21) ).
thf(f1289,plain,
( spl0_21
| spl0_5
| spl0_23
| spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f570,f1227,f1266,f1190,f1253]) ).
thf(f570,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( v2 @ mactual ) )
| ( ( mrel @ X2 @ X3 )
= $false )
| ( $false
= ( v3 @ X1 ) )
| ( ( v1 @ mactual )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v3 @ X3 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f569]) ).
thf(f569,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v2 @ mactual ) )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( v3 @ X3 ) ) )
| ( $false
= ( v3 @ X1 ) )
| ( ( v1 @ mactual )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f568]) ).
thf(f568,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( v1 @ mactual )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( $false
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ( v3 @ X3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f567]) ).
thf(f567,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v1 @ mactual )
= $true )
| ( $false
= ( v2 @ mactual ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( v3 @ X1 ) ) ) ),
inference(pi_clausification,[status(thm)],[f566]) ).
thf(f566,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( v2 @ mactual ) )
| ( ( v1 @ mactual )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f565]) ).
thf(f565,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v2 @ mactual ) )
| ( ( v1 @ mactual )
= $true )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( v3 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f564]) ).
thf(f564,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( v2 @ mactual ) )
| ( ( ( mrel @ mactual @ X1 )
=> ~ ( v3 @ X1 ) )
= $true )
| ( ( v1 @ mactual )
= $true )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f563]) ).
thf(f563,plain,
! [X2: mworld,X1: mworld] :
( ( ( v1 @ mactual )
= $true )
| ( ( ( mrel @ mactual @ X1 )
=> ~ ( v3 @ X1 ) )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( $false
= ( v2 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f562]) ).
thf(f562,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( ( ( mrel @ mactual @ X1 )
=> ~ ( v3 @ X1 ) )
= $true )
| ( ( v1 @ mactual )
= $true )
| ( $false
= ( v2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f561]) ).
thf(f561,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v3 @ Y0 ) )
@ X1 )
= $true )
| ( ( v1 @ mactual )
= $true )
| ( $false
= ( v2 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f560]) ).
thf(f560,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
| ( $false
= ( v2 @ mactual ) )
| ( ( v1 @ mactual )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f559]) ).
thf(f559,plain,
( ( ( v1 @ mactual )
= $true )
| ( ( ~ ( v2 @ mactual ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f558]) ).
thf(f558,plain,
( ( ( v1 @ mactual )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
= $true )
| ( ( ~ ( v2 @ mactual ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f557]) ).
thf(f557,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
| ~ ( v2 @ mactual ) ) )
| ( ( v1 @ mactual )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f556]) ).
thf(f556,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
| ~ ( v2 @ mactual )
| ( v1 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f287]) ).
thf(f287,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v1
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v2 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v3 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f235,f192,f203,f203,f194,f203,f213,f194,f213,f213]) ).
thf(f235,plain,
( ( mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f68]) ).
thf(f68,plain,
( ( mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f67]) ).
thf(f67,plain,
mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,axiom,
mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat8) ).
thf(f1286,plain,
( spl0_18
| spl0_9
| spl0_11
| spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f618,f1227,f1211,f1204,f1240]) ).
thf(f618,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X3 @ X4 )
= $false )
| ( ( v2 @ X5 )
= $false )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ X2 @ X5 )
= $false )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( v3 @ X4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f617]) ).
thf(f617,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( ~ ( v2 @ X5 ) )
= $true )
| ( ( mrel @ X3 @ X4 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ X2 @ X5 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( v3 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f616]) ).
thf(f616,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X3 @ X4 )
= $false )
| ( $true
= ( v3 @ X4 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( mrel @ X2 @ X5 )
=> ~ ( v2 @ X5 ) ) )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f615]) ).
thf(f615,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( ( mrel @ X3 @ X4 )
=> ( v3 @ X4 ) )
= $true )
| ( $true
= ( ( mrel @ X2 @ X5 )
=> ~ ( v2 @ X5 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f614]) ).
thf(f614,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( ( mrel @ X3 @ X4 )
=> ( v3 @ X4 ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v2 @ mactual ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v2 @ Y0 ) )
@ X5 ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $false
= ( v1 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f613]) ).
thf(f613,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v2 @ Y0 ) ) )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( v1 @ X1 ) )
| ( ( ( mrel @ X3 @ X4 )
=> ( v3 @ X4 ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f612]) ).
thf(f612,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v2 @ Y0 ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f611]) ).
thf(f611,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v3 @ Y0 ) ) ) )
| ( $true
= ( v2 @ mactual ) )
| ( $false
= ( v1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v2 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f610]) ).
thf(f610,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( v1 @ X1 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v3 @ Y0 ) ) ) ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v2 @ Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f609]) ).
thf(f609,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) )
@ X3 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v2 @ Y0 ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f608]) ).
thf(f608,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v2 @ Y0 ) ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( $false
= ( v1 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f607]) ).
thf(f607,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v2 @ mactual ) )
| ( $false
= ( v1 @ X1 ) )
| ( ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f606]) ).
thf(f606,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v2 @ mactual ) )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) )
@ X2 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f605]) ).
thf(f605,plain,
! [X1: mworld] :
( ( $false
= ( v1 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f604]) ).
thf(f604,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ~ ( v1 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( v2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f603]) ).
thf(f603,plain,
! [X1: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ~ ( v1 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f602]) ).
thf(f602,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ mactual @ X1 )
=> ~ ( v1 @ X1 ) ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f601]) ).
thf(f601,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v1 @ Y0 ) )
@ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( v2 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f600]) ).
thf(f600,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v1 @ Y0 ) ) ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f599]) ).
thf(f599,plain,
( ( $true
= ( v2 @ mactual ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f598]) ).
thf(f598,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( v1 @ Y0 ) ) )
| ( v2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f284]) ).
thf(f284,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v2
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v1 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f232,f192,f203,f203,f213,f194,f203,f213,f213,f213,f213,f194]) ).
thf(f232,plain,
( ( mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f116]) ).
thf(f116,plain,
( ( mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f115]) ).
thf(f115,plain,
mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,axiom,
mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat20) ).
thf(f1282,plain,
( spl0_3
| spl0_7
| spl0_17
| spl0_18 ),
inference(avatar_split_clause,[status(thm)],[f695,f1240,f1235,f1197,f1183]) ).
thf(f695,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( mrel @ X2 @ X4 )
= $false )
| ( $false
= ( v3 @ X3 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v1 @ mactual )
= $false )
| ( $true
= ( v4 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f694]) ).
thf(f694,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( ( mrel @ X2 @ X4 )
=> ( v4 @ X4 ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( $false
= ( v3 @ X3 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v1 @ mactual )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f693]) ).
thf(f693,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v1 @ mactual )
= $false )
| ( $false
= ( v3 @ X3 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v4 @ Y0 ) )
@ X4 ) ) ),
inference(pi_clausification,[status(thm)],[f692]) ).
thf(f692,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v4 @ Y0 ) ) ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v3 @ X3 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( v1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f691]) ).
thf(f691,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( v3 @ X3 ) )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v4 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v1 @ mactual )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f690]) ).
thf(f690,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v1 @ mactual )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( ~ ( v3 @ X3 ) ) )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v4 @ Y0 ) ) ) ) )
| ( $true
= ( v2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f689]) ).
thf(f689,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ X1 @ X3 )
=> ~ ( v3 @ X3 ) )
= $true )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v4 @ Y0 ) ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v1 @ mactual )
= $false )
| ( $true
= ( v2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f688]) ).
thf(f688,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v4 @ Y0 ) ) ) ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v1 @ mactual )
= $false ) ),
inference(pi_clausification,[status(thm)],[f687]) ).
thf(f687,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v4 @ Y0 ) ) ) ) )
| ( ( v1 @ mactual )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f686]) ).
thf(f686,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( ( v1 @ mactual )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f685]) ).
thf(f685,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( v1 @ mactual )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f684]) ).
thf(f684,plain,
! [X1: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ~ ( v1 @ mactual ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f683]) ).
thf(f683,plain,
! [X1: mworld] :
( ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
= $true )
| ( ( ~ ( v1 @ mactual ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( $true
= ( v2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f682]) ).
thf(f682,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) )
@ X1 )
= $true )
| ( ( ~ ( v1 @ mactual ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( $true
= ( v2 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f681]) ).
thf(f681,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) ) )
| ( ( ~ ( v1 @ mactual ) )
= $true )
| ( $true
= ( v2 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f680]) ).
thf(f680,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( ~ ( v1 @ mactual ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f679]) ).
thf(f679,plain,
( ( $true
= ( v2 @ mactual ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ~ ( v1 @ mactual ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f678]) ).
thf(f678,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ~ ( v1 @ mactual )
| ( v2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f253]) ).
thf(f253,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v2
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v4 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v3 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f191,f192,f203,f203,f194,f203,f213,f213,f213,f213,f194]) ).
thf(f191,plain,
( ( mlocal @ ( mor @ v2 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f122]) ).
thf(f122,plain,
( ( mlocal @ ( mor @ v2 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f121]) ).
thf(f121,plain,
mlocal @ ( mor @ v2 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,axiom,
mlocal @ ( mor @ v2 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat17) ).
thf(f1280,plain,
( spl0_19
| spl0_21
| spl0_3
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f726,f1179,f1183,f1253,f1245]) ).
thf(f726,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X3 ) )
| ( $true
= ( v1 @ X2 ) )
| ( ( mrel @ X3 @ X4 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v2 @ mactual ) )
| ( $true
= ( v4 @ X4 ) )
| ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f725]) ).
thf(f725,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v1 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $false
= ( v2 @ mactual ) )
| ( ( ( mrel @ X3 @ X4 )
=> ( v4 @ X4 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f724]) ).
thf(f724,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v4 @ Y0 ) )
@ X4 ) )
| ( $false
= ( v2 @ mactual ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( v1 @ X2 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f723]) ).
thf(f723,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v1 @ X2 ) )
| ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v4 @ Y0 ) ) ) )
| ( $false
= ( v2 @ mactual ) )
| ( $false
= ( mrel @ mactual @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f722]) ).
thf(f722,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v1 @ X2 ) )
| ( $false
= ( v2 @ mactual ) )
| ( $true
= ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v4 @ Y0 ) ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v3 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f721]) ).
thf(f721,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( v2 @ mactual ) )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) )
@ X3 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v1 @ X2 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f720]) ).
thf(f720,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( v2 @ mactual ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v1 @ X2 ) )
| ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f719]) ).
thf(f719,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ X1 @ X2 )
=> ( v1 @ X2 ) ) )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f718]) ).
thf(f718,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( v1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f717]) ).
thf(f717,plain,
! [X1: mworld] :
( ( $false
= ( v2 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( v1 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f716]) ).
thf(f716,plain,
! [X1: mworld] :
( ( $false
= ( v2 @ mactual ) )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( v1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f715]) ).
thf(f715,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( $false
= ( v2 @ mactual ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v1 @ Y1 ) ) ) )
@ X1 )
= $true )
| ( $false
= ( v3 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f714]) ).
thf(f714,plain,
( ( $false
= ( v2 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v1 @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( $false
= ( v3 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f713]) ).
thf(f713,plain,
( ( $false
= ( v2 @ mactual ) )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v1 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f712]) ).
thf(f712,plain,
( ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( $false
= ( v2 @ mactual ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v1 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f711]) ).
thf(f711,plain,
( ( ( ~ ( v2 @ mactual ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v1 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( v3 @ mactual ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f710]) ).
thf(f710,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v1 @ Y1 ) ) ) ) )
| ~ ( v3 @ mactual ) ) )
| ( ( ~ ( v2 @ mactual ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f709]) ).
thf(f709,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v1 @ Y1 ) ) ) ) )
| ~ ( v3 @ mactual )
| ~ ( v2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f264]) ).
thf(f264,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v2 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v3 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v1 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v4 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f208,f192,f203,f194,f203,f194,f203,f213,f213,f213,f213]) ).
thf(f208,plain,
( ( mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f179]) ).
thf(f179,plain,
( ( mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f178]) ).
thf(f178,plain,
mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ),
inference(rectify,[status(thm)],[f50]) ).
thf(f50,axiom,
mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat40) ).
thf(f1277,plain,
( spl0_7
| spl0_5
| spl0_2
| spl0_18 ),
inference(avatar_split_clause,[status(thm)],[f767,f1240,f1179,f1190,f1197]) ).
thf(f767,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( v3 @ X2 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v3 @ mactual ) )
| ( ( v1 @ mactual )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f766]) ).
thf(f766,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v2 @ mactual ) )
| ( $true
= ( ~ ( v3 @ X2 ) ) )
| ( ( v1 @ mactual )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f765]) ).
thf(f765,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( v3 @ mactual ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( v1 @ mactual )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ~ ( v3 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f764]) ).
thf(f764,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( v1 @ mactual )
= $true )
| ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f763]) ).
thf(f763,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v1 @ mactual )
= $true )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( v2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f762]) ).
thf(f762,plain,
! [X1: mworld] :
( ( ( v1 @ mactual )
= $true )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
= $true )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( v2 @ mactual ) ) ),
inference(not_proxy_clausification,[status(thm)],[f761]) ).
thf(f761,plain,
! [X1: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
= $true )
| ( ( v1 @ mactual )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f760]) ).
thf(f760,plain,
! [X1: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) )
@ X1 )
= $true )
| ( ( v1 @ mactual )
= $true )
| ( $true
= ( ~ ( v3 @ mactual ) ) ) ),
inference(pi_clausification,[status(thm)],[f759]) ).
thf(f759,plain,
( ( ( v1 @ mactual )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) ) )
| ( $true
= ( v2 @ mactual ) )
| ( $true
= ( ~ ( v3 @ mactual ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f758]) ).
thf(f758,plain,
( ( ( v1 @ mactual )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) )
| ~ ( v3 @ mactual ) ) )
| ( $true
= ( v2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f757]) ).
thf(f757,plain,
( ( ( v1 @ mactual )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) )
| ~ ( v3 @ mactual )
| ( v2 @ mactual ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f756]) ).
thf(f756,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) )
| ~ ( v3 @ mactual )
| ( v2 @ mactual )
| ( v1 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f272]) ).
thf(f272,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v1
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v2
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v3 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f219,f192,f203,f203,f203,f194,f213,f213,f194]) ).
thf(f219,plain,
( ( mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f76,plain,
( ( mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f75]) ).
thf(f75,plain,
mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat2) ).
thf(f1275,plain,
( spl0_12
| spl0_5
| spl0_3
| spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f795,f1227,f1183,f1190,f1215]) ).
thf(f795,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( v1 @ mactual )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v3 @ mactual ) )
| ( $true
= ( v3 @ X4 ) )
| ( ( mrel @ X2 @ X4 )
= $false )
| ( ( v4 @ X3 )
= $true )
| ( $false
= ( mrel @ X1 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f794]) ).
thf(f794,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( v4 @ X3 )
= $true )
| ( $true
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v1 @ mactual )
= $true )
| ( ( ( mrel @ X2 @ X4 )
=> ( v3 @ X4 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f793]) ).
thf(f793,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ X1 @ X3 )
=> ( v4 @ X3 ) ) )
| ( $true
= ( v3 @ mactual ) )
| ( ( ( mrel @ X2 @ X4 )
=> ( v3 @ X4 ) )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v1 @ mactual )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f792]) ).
thf(f792,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( mrel @ X1 @ X3 )
=> ( v4 @ X3 ) ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) )
@ X4 ) )
| ( ( v1 @ mactual )
= $true ) ),
inference(pi_clausification,[status(thm)],[f791]) ).
thf(f791,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v1 @ mactual )
= $true )
| ( $true
= ( v3 @ mactual ) )
| ( $true
= ( ( mrel @ X1 @ X3 )
=> ( v4 @ X3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f790]) ).
thf(f790,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v1 @ mactual )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( v4 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( v3 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f789]) ).
thf(f789,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( v4 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) )
= $true )
| ( $true
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v1 @ mactual )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f788]) ).
thf(f788,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v3 @ mactual ) )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( v4 @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) )
= $true )
| ( ( v1 @ mactual )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f787]) ).
thf(f787,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) ) ) )
| ( ( v1 @ mactual )
= $true )
| ( $true
= ( v3 @ mactual ) )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( v4 @ Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f786]) ).
thf(f786,plain,
! [X2: mworld,X1: mworld] :
( ( ( v1 @ mactual )
= $true )
| ( $true
= ( v3 @ mactual ) )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( v4 @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f785]) ).
thf(f785,plain,
! [X1: mworld] :
( ( $true
= ( v3 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( v4 @ Y0 ) ) ) )
= $true )
| ( ( v1 @ mactual )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f784]) ).
thf(f784,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) )
@ X1 )
= $true )
| ( ( v1 @ mactual )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( v3 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f783]) ).
thf(f783,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( ( v1 @ mactual )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( v3 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f782]) ).
thf(f782,plain,
( ( $true
= ( v3 @ mactual ) )
| ( ( v1 @ mactual )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f781]) ).
thf(f781,plain,
( ( ( v1 @ mactual )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( v3 @ mactual ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f780]) ).
thf(f780,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( v3 @ mactual )
| ( v1 @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f281]) ).
thf(f281,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v1
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v3
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v4 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f228,f192,f203,f203,f203,f213,f213,f213,f213]) ).
thf(f228,plain,
( ( mlocal @ ( mor @ v1 @ ( mor @ v3 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f112]) ).
thf(f112,plain,
( ( mlocal @ ( mor @ v1 @ ( mor @ v3 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f111]) ).
thf(f111,plain,
mlocal @ ( mor @ v1 @ ( mor @ v3 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
mlocal @ ( mor @ v1 @ ( mor @ v3 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat5) ).
thf(f1274,plain,
( spl0_7
| spl0_17
| spl0_8
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f815,f1179,f1201,f1235,f1197]) ).
thf(f815,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( v3 @ mactual ) )
| ( ( v1 @ mactual )
= $false )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( ( mrel @ X2 @ X3 )
= $false )
| ( $false
= ( v1 @ X4 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v3 @ X3 ) )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f814]) ).
thf(f814,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( v1 @ mactual )
= $false )
| ( ( mrel @ X2 @ X3 )
= $false )
| ( $true
= ( ~ ( v1 @ X4 ) ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( $false
= ( v3 @ X3 ) )
| ( $false
= ( v3 @ mactual ) ) ),
inference(not_proxy_clausification,[status(thm)],[f813]) ).
thf(f813,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X1 @ X4 ) )
| ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( ~ ( v3 @ X3 ) ) )
| ( ( v1 @ mactual )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ~ ( v1 @ X4 ) ) )
| ( ( mrel @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f812]) ).
thf(f812,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( mrel @ X1 @ X4 )
=> ~ ( v1 @ X4 ) ) )
| ( ( v1 @ mactual )
= $false )
| ( ( mrel @ X2 @ X3 )
= $false )
| ( $true
= ( ~ ( v3 @ X3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f811]) ).
thf(f811,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( v3 @ mactual ) )
| ( ( v1 @ mactual )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ X2 @ X3 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( ~ ( v3 @ X3 ) ) ) ),
inference(pi_clausification,[status(thm)],[f810]) ).
thf(f810,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v1 @ mactual )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ X2 @ X3 )
= $false )
| ( $true
= ( ~ ( v3 @ X3 ) ) )
| ( $false
= ( v3 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f809]) ).
thf(f809,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ X2 @ X3 )
= $false )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v1 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ~ ( v3 @ X3 ) ) )
| ( ( v1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f808]) ).
thf(f808,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( v3 @ mactual ) )
| ( $true
= ( ( mrel @ X2 @ X3 )
=> ~ ( v3 @ X3 ) ) )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v1 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v1 @ mactual )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f807]) ).
thf(f807,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v1 @ Y0 ) ) ) )
= $true )
| ( ( v1 @ mactual )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f806]) ).
thf(f806,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( v3 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v1 @ mactual )
= $false )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v1 @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f805]) ).
thf(f805,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( v3 @ mactual ) )
| ( ( v1 @ mactual )
= $false )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v3 @ Y0 ) ) ) ) )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v1 @ Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f804]) ).
thf(f804,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( $false
= ( v3 @ mactual ) )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v1 @ Y0 ) ) ) )
= $true )
| ( ( v1 @ mactual )
= $false ) ),
inference(pi_clausification,[status(thm)],[f803]) ).
thf(f803,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) ) )
| ( $false
= ( v3 @ mactual ) )
| ( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v1 @ Y0 ) ) ) )
= $true )
| ( ( v1 @ mactual )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f802]) ).
thf(f802,plain,
! [X1: mworld] :
( ( ( v1 @ mactual )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) ) )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f801]) ).
thf(f801,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) ) )
| ( ( v1 @ mactual )
= $false )
| ( $false
= ( v3 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f800]) ).
thf(f800,plain,
( ( $true
= ( ~ ( v3 @ mactual ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) ) )
| ( ( v1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f799]) ).
thf(f799,plain,
( ( ( v1 @ mactual )
= $false )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( v3 @ mactual ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f798]) ).
thf(f798,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) )
| ~ ( v3 @ mactual ) ) )
| ( ( v1 @ mactual )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f797]) ).
thf(f797,plain,
( ( ( ~ ( v1 @ mactual ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) )
| ~ ( v3 @ mactual ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f796]) ).
thf(f796,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) )
| ~ ( v3 @ mactual )
| ~ ( v1 @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f268]) ).
thf(f268,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v3 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v1 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v3 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f212,f192,f203,f194,f203,f194,f203,f213,f213,f194,f213,f213,f194]) ).
thf(f212,plain,
( ( mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f80]) ).
thf(f80,plain,
( ( mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f79]) ).
thf(f79,plain,
mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f46]) ).
thf(f46,axiom,
mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat36) ).
thf(f1272,plain,
( spl0_24
| spl0_13
| spl0_18
| spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f852,f1227,f1240,f1219,f1270]) ).
thf(f852,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ X2 @ X4 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( v3 @ X5 )
= $true )
| ( ( v2 @ X4 )
= $true )
| ( ( v4 @ X1 )
= $true )
| ( ( mrel @ X3 @ X5 )
= $false )
| ( $true
= ( v2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f851]) ).
thf(f851,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( v4 @ X1 )
= $true )
| ( $true
= ( ( mrel @ X3 @ X5 )
=> ( v3 @ X5 ) ) )
| ( ( v2 @ X4 )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ X2 @ X4 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f850]) ).
thf(f850,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( v4 @ X1 )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v2 @ X4 )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ X2 @ X4 )
= $false )
| ( $true
= ( v2 @ mactual ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v3 @ Y0 ) )
@ X5 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f849]) ).
thf(f849,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( v2 @ X4 )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( v4 @ X1 )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( mrel @ X2 @ X4 )
= $false )
| ( $true
= ( v2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f848]) ).
thf(f848,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v2 @ mactual ) )
| ( $true
= ( ( mrel @ X2 @ X4 )
=> ( v2 @ X4 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v3 @ Y0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( v4 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f847]) ).
thf(f847,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( v4 @ X1 )
= $true )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v3 @ Y0 ) ) ) )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f846]) ).
thf(f846,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v3 @ Y0 ) ) ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v2 @ mactual ) )
| ( ( v4 @ X1 )
= $true )
| ( $false
= ( mrel @ mactual @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f845]) ).
thf(f845,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v3 @ Y0 ) ) ) ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( v4 @ X1 )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v2 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f844]) ).
thf(f844,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v2 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) )
@ X3 ) )
| ( ( v4 @ X1 )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v2 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f843]) ).
thf(f843,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v2 @ Y0 ) ) ) )
| ( ( v4 @ X1 )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f842]) ).
thf(f842,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v2 @ Y0 ) ) ) ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v4 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f841]) ).
thf(f841,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v2 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v2 @ mactual ) )
| ( ( v4 @ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f840]) ).
thf(f840,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v2 @ Y1 ) ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v4 @ X1 )
= $true )
| ( $true
= ( v2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f839]) ).
thf(f839,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v2 @ Y1 ) ) ) ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v4 @ X1 )
= $true )
| ( $true
= ( v2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f838]) ).
thf(f838,plain,
! [X1: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( v4 @ X1 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f837]) ).
thf(f837,plain,
! [X1: mworld] :
( ( $true
= ( v2 @ mactual ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( v4 @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v2 @ Y1 ) ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f836]) ).
thf(f836,plain,
( ( $true
= ( v2 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( v4 @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v2 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f835]) ).
thf(f835,plain,
( ( $true
= ( v2 @ mactual ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v2 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( v4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f834]) ).
thf(f834,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v2 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( v4 @ Y0 ) ) )
| ( v2 @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f278]) ).
thf(f278,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v2
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v4 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v3 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f225,f192,f203,f203,f213,f203,f213,f213,f213,f213]) ).
thf(f225,plain,
( ( mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f141]) ).
thf(f141,plain,
( ( mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f140]) ).
thf(f140,plain,
mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,axiom,
mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat19) ).
thf(f1258,plain,
( spl0_21
| spl0_15
| spl0_3
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f955,f1201,f1183,f1227,f1253]) ).
thf(f955,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( v4 @ X5 )
= $true )
| ( ( mrel @ mactual @ X4 )
= $false )
| ( $false
= ( v2 @ mactual ) )
| ( $false
= ( v1 @ X6 ) )
| ( ( mrel @ X4 @ X5 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ X3 @ X6 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $true
= ( v3 @ X2 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f954]) ).
thf(f954,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ~ ( v1 @ X6 ) )
= $true )
| ( $true
= ( v3 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( mrel @ mactual @ X4 )
= $false )
| ( ( mrel @ X4 @ X5 )
= $false )
| ( ( mrel @ X3 @ X6 )
= $false )
| ( $false
= ( v2 @ mactual ) )
| ( ( v4 @ X5 )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f953]) ).
thf(f953,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X4 @ X5 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $true
= ( ( mrel @ X3 @ X6 )
=> ~ ( v1 @ X6 ) ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( v2 @ mactual ) )
| ( ( v4 @ X5 )
= $true )
| ( $true
= ( v3 @ X2 ) )
| ( ( mrel @ mactual @ X4 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f952]) ).
thf(f952,plain,
! [X2: mworld,X3: mworld,X1: mworld,X6: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X4 @ X5 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( v4 @ X5 )
= $true )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v1 @ Y0 ) )
@ X6 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v3 @ X2 ) )
| ( ( mrel @ mactual @ X4 )
= $false )
| ( $false
= ( v2 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f951]) ).
thf(f951,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( v2 @ mactual ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( mrel @ mactual @ X4 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v3 @ X2 ) )
| ( ( v4 @ X5 )
= $true )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( mrel @ X4 @ X5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f950]) ).
thf(f950,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( ( mrel @ mactual @ X4 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v3 @ X2 ) )
| ( $false
= ( v2 @ mactual ) )
| ( ( ( mrel @ X4 @ X5 )
=> ( v4 @ X5 ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v1 @ Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f949]) ).
thf(f949,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ mactual @ X4 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v2 @ mactual ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( v4 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v3 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f948]) ).
thf(f948,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( mrel @ mactual @ X4 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( v4 @ Y0 ) ) ) )
| ( $false
= ( v2 @ mactual ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v1 @ Y0 ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( v3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f947]) ).
thf(f947,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ mactual @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( v4 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v1 @ Y0 ) ) )
= $true )
| ( $false
= ( v2 @ mactual ) )
| ( $true
= ( v3 @ X2 ) )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f946]) ).
thf(f946,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( v2 @ mactual ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( v3 @ X2 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v1 @ Y0 ) ) )
= $true )
| ( $true
= ( ( mrel @ mactual @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( v4 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f945]) ).
thf(f945,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( v2 @ mactual ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( v3 @ X2 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( mrel @ mactual @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( v4 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f944]) ).
thf(f944,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( v2 @ mactual ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( v3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) )
@ X4 ) )
| ( ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v1 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f943]) ).
thf(f943,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( v3 @ X2 ) ) )
| ( ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ~ ( v1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( v2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f942]) ).
thf(f942,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( $false
= ( v2 @ mactual ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( v3 @ X2 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f941]) ).
thf(f941,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) ) )
| ( $false
= ( v2 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( v3 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f940]) ).
thf(f940,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) ) )
| ( $false
= ( v2 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( v3 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f939]) ).
thf(f939,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( v3 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v2 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f938]) ).
thf(f938,plain,
! [X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( v3 @ Y0 ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f937]) ).
thf(f937,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( v3 @ Y0 ) ) ) ) )
| ( $false
= ( v2 @ mactual ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f936]) ).
thf(f936,plain,
! [X1: mworld] :
( ( $false
= ( v2 @ mactual ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f935]) ).
thf(f935,plain,
( ( $false
= ( v2 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f934]) ).
thf(f934,plain,
( ( ( ~ ( v2 @ mactual ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f933]) ).
thf(f933,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) ) ) )
| ( ( ~ ( v2 @ mactual ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f932]) ).
thf(f932,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v1 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ~ ( v2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f262]) ).
thf(f262,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v2 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v4 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f206,f192,f203,f194,f203,f213,f213,f203,f213,f213,f213,f213,f194]) ).
thf(f206,plain,
( ( mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f82]) ).
thf(f82,plain,
( ( mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f81]) ).
thf(f81,plain,
mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f53]) ).
thf(f53,axiom,
mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat43) ).
thf(f1229,plain,
( spl0_6
| spl0_1
| spl0_12
| spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f1086,f1227,f1215,f1175,f1194]) ).
thf(f1086,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( v3 @ X4 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ X2 @ X4 )
= $false )
| ( $false
= ( v4 @ mactual ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v3 @ mactual ) )
| ( ( v4 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f1085]) ).
thf(f1085,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v3 @ X4 ) )
| ( ( ~ ( v4 @ X3 ) )
= $true )
| ( $false
= ( v4 @ mactual ) )
| ( ( mrel @ X2 @ X4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1084]) ).
thf(f1084,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ X2 @ X4 )
=> ( v3 @ X4 ) )
= $true )
| ( ( ~ ( v4 @ X3 ) )
= $true )
| ( $false
= ( v4 @ mactual ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v3 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1083]) ).
thf(f1083,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ~ ( v4 @ X3 ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v3 @ mactual ) )
| ( $false
= ( v4 @ mactual ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_clausification,[status(thm)],[f1082]) ).
thf(f1082,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( v3 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) )
= $true )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( ~ ( v4 @ X3 ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( v4 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1081]) ).
thf(f1081,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( v4 @ mactual ) )
| ( $true
= ( ( mrel @ X1 @ X3 )
=> ~ ( v4 @ X3 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( v3 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1080]) ).
thf(f1080,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v3 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) )
= $true )
| ( $false
= ( v4 @ mactual ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v4 @ Y0 ) )
@ X3 )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f1079]) ).
thf(f1079,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( v3 @ mactual ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( v4 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1078]) ).
thf(f1078,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( v4 @ mactual ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
| ( $true
= ( v3 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1077]) ).
thf(f1077,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( v4 @ mactual ) )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) ) )
| ( $true
= ( v3 @ mactual ) )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( v3 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1076]) ).
thf(f1076,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( v3 @ mactual ) )
| ( $false
= ( v4 @ mactual ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f1075]) ).
thf(f1075,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) ) )
| ( $true
= ( v3 @ mactual ) )
| ( $false
= ( v4 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1074]) ).
thf(f1074,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( v4 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( v3 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f1073]) ).
thf(f1073,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( v4 @ mactual ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( v3 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1072]) ).
thf(f1072,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v3 @ mactual ) )
| ( $false
= ( v4 @ mactual ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1071]) ).
thf(f1071,plain,
( ( ( ~ ( v4 @ mactual ) )
= $true )
| ( $true
= ( v3 @ mactual ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1070]) ).
thf(f1070,plain,
( ( $true
= ( v3 @ mactual ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ~ ( v4 @ mactual ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1069]) ).
thf(f1069,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v3 @ Y1 ) ) ) ) )
| ~ ( v4 @ mactual )
| ( v3 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f303]) ).
thf(f303,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v3
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v4 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v4 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f251,f192,f203,f203,f194,f203,f213,f213,f213,f213,f194]) ).
thf(f251,plain,
( ( mlocal @ ( mor @ v3 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f86]) ).
thf(f86,plain,
( ( mlocal @ ( mor @ v3 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f85]) ).
thf(f85,plain,
mlocal @ ( mor @ v3 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,axiom,
mlocal @ ( mor @ v3 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat26) ).
thf(f1213,plain,
( spl0_10
| spl0_5
| spl0_11
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f1122,f1183,f1211,f1190,f1208]) ).
thf(f1122,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( v2 @ X2 )
= $true )
| ( ( v2 @ X5 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v1 @ mactual )
= $true )
| ( ( mrel @ X3 @ X4 )
= $false )
| ( $true
= ( v4 @ X4 ) )
| ( $false
= ( mrel @ X1 @ X5 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1121]) ).
thf(f1121,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( v2 @ X2 )
= $true )
| ( ( mrel @ X3 @ X4 )
= $false )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v4 @ X4 ) )
| ( ( v1 @ mactual )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( ~ ( v2 @ X5 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1120]) ).
thf(f1120,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( v2 @ X2 )
= $true )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( mrel @ X3 @ X4 )
= $false )
| ( $true
= ( ( mrel @ X1 @ X5 )
=> ~ ( v2 @ X5 ) ) )
| ( $true
= ( v4 @ X4 ) )
| ( ( v1 @ mactual )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1119]) ).
thf(f1119,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld,X5: mworld] :
( ( $true
= ( v4 @ X4 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( v2 @ X2 )
= $true )
| ( ( v1 @ mactual )
= $true )
| ( ( mrel @ X3 @ X4 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) )
@ X5 )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f1118]) ).
thf(f1118,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( v1 @ mactual )
= $true )
| ( ( v2 @ X2 )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) )
| ( ( mrel @ X3 @ X4 )
= $false )
| ( $true
= ( v4 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1117]) ).
thf(f1117,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true
= ( v4 @ X4 ) )
| ( ( mrel @ X3 @ X4 )
= $false )
| ( ( v2 @ X2 )
= $true )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( v1 @ mactual )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1116]) ).
thf(f1116,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( ( ( mrel @ X3 @ X4 )
=> ( v4 @ X4 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( v2 @ X2 )
= $true )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) )
| ( ( v1 @ mactual )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1115]) ).
thf(f1115,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ mactual @ X2 )
=> ( v2 @ X2 ) ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( ( v1 @ mactual )
= $true )
| ( ( ( mrel @ X3 @ X4 )
=> ( v4 @ X4 ) )
= $true )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1114]) ).
thf(f1114,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) )
| ( ( v1 @ mactual )
= $true )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( v2 @ X2 ) ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v4 @ Y0 ) )
@ X4 ) ) ),
inference(pi_clausification,[status(thm)],[f1113]) ).
thf(f1113,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v4 @ Y0 ) ) ) )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) )
| ( ( v1 @ mactual )
= $true )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( v2 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1112]) ).
thf(f1112,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ mactual @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v4 @ Y0 ) ) ) ) )
| ( ( v1 @ mactual )
= $true )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( v2 @ X2 ) ) )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1111]) ).
thf(f1111,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ mactual @ X2 )
=> ( v2 @ X2 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) )
@ X3 ) )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) )
| ( ( v1 @ mactual )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1110]) ).
thf(f1110,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( ( v1 @ mactual )
= $true )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( v2 @ X2 ) ) )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1109]) ).
thf(f1109,plain,
! [X2: mworld,X1: mworld] :
( ( ( v1 @ mactual )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( v2 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1108]) ).
thf(f1108,plain,
! [X1: mworld] :
( ( ( v1 @ mactual )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( v2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ~ ( v2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1107]) ).
thf(f1107,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) )
@ X1 ) )
| ( ( v1 @ mactual )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( v2 @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f1106]) ).
thf(f1106,plain,
( ( ( v1 @ mactual )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( v2 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1105]) ).
thf(f1105,plain,
( ( ( v1 @ mactual )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( v2 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1104]) ).
thf(f1104,plain,
( ( ( v1 @ mactual )
= $true )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( v2 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1103]) ).
thf(f1103,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( v2 @ Y0 ) ) )
| ( v1 @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f270]) ).
thf(f270,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v1
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v2 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v4 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f215,f192,f203,f203,f213,f203,f213,f213,f213,f213,f194]) ).
thf(f215,plain,
( ( mlocal @ ( mor @ v1 @ ( mor @ ( mbox @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f165]) ).
thf(f165,plain,
( ( mlocal @ ( mor @ v1 @ ( mor @ ( mbox @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f164]) ).
thf(f164,plain,
mlocal @ ( mor @ v1 @ ( mor @ ( mbox @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,axiom,
mlocal @ ( mor @ v1 @ ( mor @ ( mbox @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat13) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO903^10 : TPTP v9.2.1. Released v8.1.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n026.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:53:55 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SYO903^10 : TPTP v9.2.1. Released v8.1.0.
% 0.20/0.47 % Domain : Syntactic
% 0.20/0.47 % Problem : PSAT - CNF - K=4 C=50 V=4 D=2.8
% 0.20/0.47 % Version : [BP13] axioms.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.20/0.47 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.20/0.47 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.20/0.47 % Source : [TPTP]
% 0.20/0.47 % Names : SYM329+1 [QMLTP]
% 0.20/0.47
% 0.20/0.47 % Status : ContradictoryAxioms
% 0.20/0.47 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0
% 0.20/0.47 % Syntax : Number of formulae : 77 ( 9 unt; 15 typ; 8 def)
% 0.20/0.47 % Number of atoms : 713 ( 8 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 17 ( 11 avg)
% 0.20/0.47 % Number of connectives : 672 ( 1 ~; 1 |; 3 &; 663 @)
% 0.20/0.47 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 9 ( 7 avg)
% 0.20/0.47 % Number of types : 2 ( 1 usr)
% 0.20/0.47 % Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 17 ( 14 usr; 3 con; 0-3 aty)
% 0.20/0.47 % Number of variables : 27 ( 21 ^; 5 !; 1 ?; 27 :)
% 0.20/0.47 % SPC : TH0_CAX_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.20/0.47 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.20/0.47 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.20/0.47 % $modal == [$constants == $rigid,$quantification == $varying,
% 0.20/0.47 % $modalities == $modal_system_S4].
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(mworld,type,
% 0.20/0.47 mworld: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(mrel_type,type,
% 0.20/0.47 mrel: mworld > mworld > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mactual_type,type,
% 0.20/0.47 mactual: mworld ).
% 0.20/0.47
% 0.20/0.47 thf(mlocal_type,type,
% 0.20/0.47 mlocal: ( mworld > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mlocal_def,definition,
% 0.20/0.47 ( mlocal
% 0.20/0.47 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(mnot_type,type,
% 0.20/0.47 mnot: ( mworld > $o ) > mworld > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mand_type,type,
% 0.20/0.47 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mor_type,type,
% 0.20/0.47 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mimplies_type,type,
% 0.20/0.47 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mequiv_type,type,
% 0.20/0.47 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mnot_def,definition,
% 0.20/0.47 ( mnot
% 0.20/0.47 = ( ^ [A: mworld > $o,W: mworld] :
% 0.20/0.47 ~ ( A @ W ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(mand_def,definition,
% 0.20/0.47 ( mand
% 0.20/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.47 ( ( A @ W )
% 0.20/0.47 & ( B @ W ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(mor_def,definition,
% 0.20/0.47 ( mor
% 0.20/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.47 ( ( A @ W )
% 0.20/0.47 | ( B @ W ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(mimplies_def,definition,
% 0.20/0.47 ( mimplies
% 0.20/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.47 ( ( A @ W )
% 0.20/0.47 => ( B @ W ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(mequiv_def,definition,
% 0.20/0.47 ( mequiv
% 0.20/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.47 ( ( A @ W )
% 0.20/0.47 <=> ( B @ W ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(mbox_type,type,
% 0.20/0.47 mbox: ( mworld > $o ) > mworld > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mbox_def,definition,
% 0.20/0.47 ( mbox
% 0.20/0.47 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.47 ! [V: mworld] :
% 0.20/0.47 ( ( mrel @ W @ V )
% 0.20/0.47 => ( Phi @ V ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(mdia_type,type,
% 0.20/0.47 mdia: ( mworld > $o ) > mworld > $o ).
% 0.20/0.47
% 0.20/0.47 thf(mdia_def,definition,
% 0.20/0.47 ( mdia
% 0.20/0.47 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.47 ? [V: mworld] :
% 0.20/0.47 ( ( mrel @ W @ V )
% 0.20/0.47 & ( Phi @ V ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(mrel_reflexive,axiom,
% 0.20/0.47 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.20/0.47
% 0.20/0.47 thf(mrel_transitive,axiom,
% 0.20/0.47 ! [W: mworld,V: mworld,U: mworld] :
% 0.20/0.47 ( ( ( mrel @ W @ V )
% 0.20/0.47 & ( mrel @ V @ U ) )
% 0.20/0.47 => ( mrel @ W @ U ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(v1_decl,type,
% 0.20/0.47 v1: mworld > $o ).
% 0.20/0.47
% 0.20/0.47 thf(v2_decl,type,
% 0.20/0.47 v2: mworld > $o ).
% 0.20/0.47
% 0.20/0.47 thf(v3_decl,type,
% 0.20/0.47 v3: mworld > $o ).
% 0.20/0.47
% 0.20/0.47 thf(v4_decl,type,
% 0.20/0.47 v4: mworld > $o ).
% 0.20/0.47
% 0.20/0.47 thf(persat1,axiom,
% 0.20/0.47 mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ v3 @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat2,axiom,
% 0.20/0.47 mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat3,axiom,
% 0.20/0.47 mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat4,axiom,
% 0.20/0.47 mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat5,axiom,
% 0.20/0.47 mlocal @ ( mor @ v1 @ ( mor @ v3 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat6,axiom,
% 0.20/0.47 mlocal @ ( mor @ v1 @ ( mor @ v4 @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat7,axiom,
% 0.20/0.47 mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mnot @ v4 ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat8,axiom,
% 0.20/0.47 mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat9,axiom,
% 0.20/0.47 mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ v4 ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat10,axiom,
% 0.20/0.47 mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat11,axiom,
% 0.20/0.47 mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat12,axiom,
% 0.20/0.47 mlocal @ ( mor @ v1 @ ( mor @ ( mbox @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat13,axiom,
% 0.20/0.47 mlocal @ ( mor @ v1 @ ( mor @ ( mbox @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat14,axiom,
% 0.20/0.47 mlocal @ ( mor @ v2 @ ( mor @ v3 @ ( mor @ v4 @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat15,axiom,
% 0.20/0.47 mlocal @ ( mor @ v2 @ ( mor @ v4 @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat16,axiom,
% 0.20/0.47 mlocal @ ( mor @ v2 @ ( mor @ v4 @ ( mor @ ( mbox @ ( mnot @ v2 ) ) @ ( mbox @ ( mbox @ v2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat17,axiom,
% 0.20/0.47 mlocal @ ( mor @ v2 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat18,axiom,
% 0.20/0.47 mlocal @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat19,axiom,
% 0.20/0.47 mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat20,axiom,
% 0.20/0.47 mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat21,axiom,
% 0.20/0.47 mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat22,axiom,
% 0.20/0.47 mlocal @ ( mor @ v3 @ ( mor @ v4 @ ( mor @ ( mbox @ v2 ) @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat23,axiom,
% 0.20/0.47 mlocal @ ( mor @ v3 @ ( mor @ v4 @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat24,axiom,
% 0.20/0.47 mlocal @ ( mor @ v3 @ ( mor @ v4 @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat25,axiom,
% 0.20/0.47 mlocal @ ( mor @ v3 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat26,axiom,
% 0.20/0.47 mlocal @ ( mor @ v3 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat27,axiom,
% 0.20/0.47 mlocal @ ( mor @ v3 @ ( mor @ ( mbox @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat28,axiom,
% 0.20/0.47 mlocal @ ( mor @ v4 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ v1 ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat29,axiom,
% 0.20/0.47 mlocal @ ( mor @ v4 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat30,axiom,
% 0.20/0.47 mlocal @ ( mor @ v4 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ v1 ) @ ( mbox @ ( mbox @ v2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat31,axiom,
% 0.20/0.47 mlocal @ ( mor @ v4 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat32,axiom,
% 0.20/0.47 mlocal @ ( mor @ v4 @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat33,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat34,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat35,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat36,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat37,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat38,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat39,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat40,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat41,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mnot @ v2 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat42,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat43,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat44,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat45,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat46,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat47,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat48,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ v3 ) @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat49,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ v4 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(persat50,axiom,
% 0.20/0.47 mlocal @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mnot @ v2 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(deontic1,axiom,
% 0.20/0.47 ( mlocal
% 0.20/0.47 @ ( mdia
% 0.20/0.47 @ ^ [W: mworld] : $true ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(result1,conjecture,
% 0.20/0.47 ( mlocal
% 0.20/0.47 @ ^ [W: mworld] : $false ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 2.02/1.52 ---- Embedded in THF ---
% 2.02/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.02/1.52 %%% Generated on Tue Feb 24 14:53:56 EST 2026
% 2.02/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.02/1.52 %%% Logic specification used:
% 2.02/1.52 %%% thf(spec, logic, $$dhol).
% 2.02/1.52
% 2.02/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2DTF7992.p
% See solution above
% 2.02/1.52 ------------------------
% 2.02/1.53 ---- Cleaned THF ---
% 2.02/1.53 thf(mworld,type,
% 2.02/1.53 mworld: $tType ).
% 2.02/1.53
% 2.02/1.53 thf(mrel_type,type,
% 2.02/1.53 mrel: mworld > mworld > $o ).
% 2.02/1.53
% 2.02/1.53 thf(mactual_type,type,
% 2.02/1.53 mactual: mworld ).
% 2.02/1.53
% 2.02/1.53 thf(mlocal_type,type,
% 2.02/1.53 mlocal: ( mworld > $o ) > $o ).
% 2.02/1.53
% 2.02/1.53 thf(mlocal_def,definition,
% 2.02/1.53 ( mlocal
% 2.02/1.53 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(mnot_type,type,
% 2.02/1.53 mnot: ( mworld > $o ) > mworld > $o ).
% 2.02/1.53
% 2.02/1.53 thf(mand_type,type,
% 2.02/1.53 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.02/1.53
% 2.02/1.53 thf(mor_type,type,
% 2.02/1.53 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.02/1.53
% 2.02/1.53 thf(mimplies_type,type,
% 2.02/1.53 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.02/1.53
% 2.02/1.53 thf(mequiv_type,type,
% 2.02/1.53 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.02/1.53
% 2.02/1.53 thf(mnot_def,definition,
% 2.02/1.53 ( mnot
% 2.02/1.53 = ( ^ [A: mworld > $o,W: mworld] :
% 2.02/1.53 ~ ( A @ W ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(mand_def,definition,
% 2.02/1.53 ( mand
% 2.02/1.53 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.02/1.53 ( ( A @ W )
% 2.02/1.53 & ( B @ W ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(mor_def,definition,
% 2.02/1.53 ( mor
% 2.02/1.53 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.02/1.53 ( ( A @ W )
% 2.02/1.53 | ( B @ W ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(mimplies_def,definition,
% 2.02/1.53 ( mimplies
% 2.02/1.53 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.02/1.53 ( ( A @ W )
% 2.02/1.53 => ( B @ W ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(mequiv_def,definition,
% 2.02/1.53 ( mequiv
% 2.02/1.53 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.02/1.53 ( ( A @ W )
% 2.02/1.53 <=> ( B @ W ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(mbox_type,type,
% 2.02/1.53 mbox: ( mworld > $o ) > mworld > $o ).
% 2.02/1.53
% 2.02/1.53 thf(mbox_def,definition,
% 2.02/1.53 ( mbox
% 2.02/1.53 = ( ^ [Phi: mworld > $o,W: mworld] :
% 2.02/1.53 ! [V: mworld] :
% 2.02/1.53 ( ( mrel @ W @ V )
% 2.02/1.53 => ( Phi @ V ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(mdia_type,type,
% 2.02/1.53 mdia: ( mworld > $o ) > mworld > $o ).
% 2.02/1.53
% 2.02/1.53 thf(mdia_def,definition,
% 2.02/1.53 ( mdia
% 2.02/1.53 = ( ^ [Phi: mworld > $o,W: mworld] :
% 2.02/1.53 ? [V: mworld] :
% 2.02/1.53 ( ( mrel @ W @ V )
% 2.02/1.53 & ( Phi @ V ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(mrel_reflexive,axiom,
% 2.02/1.53 ! [W: mworld] : ( mrel @ W @ W ) ).
% 2.02/1.53
% 2.02/1.53 thf(mrel_transitive,axiom,
% 2.02/1.53 ! [W: mworld,V: mworld,U: mworld] :
% 2.02/1.53 ( ( ( mrel @ W @ V )
% 2.02/1.53 & ( mrel @ V @ U ) )
% 2.02/1.53 => ( mrel @ W @ U ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(v1_decl,type,
% 2.02/1.53 v1: mworld > $o ).
% 2.02/1.53
% 2.02/1.53 thf(v2_decl,type,
% 2.02/1.53 v2: mworld > $o ).
% 2.02/1.53
% 2.02/1.53 thf(v3_decl,type,
% 2.02/1.53 v3: mworld > $o ).
% 2.02/1.53
% 2.02/1.53 thf(v4_decl,type,
% 2.02/1.53 v4: mworld > $o ).
% 2.02/1.53
% 2.02/1.53 thf(persat1,axiom,
% 2.02/1.53 mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ v3 @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat2,axiom,
% 2.02/1.53 mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat3,axiom,
% 2.02/1.53 mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat4,axiom,
% 2.02/1.53 mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat5,axiom,
% 2.02/1.53 mlocal @ ( mor @ v1 @ ( mor @ v3 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat6,axiom,
% 2.02/1.53 mlocal @ ( mor @ v1 @ ( mor @ v4 @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat7,axiom,
% 2.02/1.53 mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mnot @ v4 ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat8,axiom,
% 2.02/1.53 mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat9,axiom,
% 2.02/1.53 mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ v4 ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat10,axiom,
% 2.02/1.53 mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat11,axiom,
% 2.02/1.53 mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat12,axiom,
% 2.02/1.53 mlocal @ ( mor @ v1 @ ( mor @ ( mbox @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat13,axiom,
% 2.02/1.53 mlocal @ ( mor @ v1 @ ( mor @ ( mbox @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat14,axiom,
% 2.02/1.53 mlocal @ ( mor @ v2 @ ( mor @ v3 @ ( mor @ v4 @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat15,axiom,
% 2.02/1.53 mlocal @ ( mor @ v2 @ ( mor @ v4 @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat16,axiom,
% 2.02/1.53 mlocal @ ( mor @ v2 @ ( mor @ v4 @ ( mor @ ( mbox @ ( mnot @ v2 ) ) @ ( mbox @ ( mbox @ v2 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat17,axiom,
% 2.02/1.53 mlocal @ ( mor @ v2 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat18,axiom,
% 2.02/1.53 mlocal @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat19,axiom,
% 2.02/1.53 mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat20,axiom,
% 2.02/1.53 mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat21,axiom,
% 2.02/1.53 mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat22,axiom,
% 2.02/1.53 mlocal @ ( mor @ v3 @ ( mor @ v4 @ ( mor @ ( mbox @ v2 ) @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat23,axiom,
% 2.02/1.53 mlocal @ ( mor @ v3 @ ( mor @ v4 @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat24,axiom,
% 2.02/1.53 mlocal @ ( mor @ v3 @ ( mor @ v4 @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat25,axiom,
% 2.02/1.53 mlocal @ ( mor @ v3 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v2 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat26,axiom,
% 2.02/1.53 mlocal @ ( mor @ v3 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat27,axiom,
% 2.02/1.53 mlocal @ ( mor @ v3 @ ( mor @ ( mbox @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat28,axiom,
% 2.02/1.53 mlocal @ ( mor @ v4 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ v1 ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat29,axiom,
% 2.02/1.53 mlocal @ ( mor @ v4 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat30,axiom,
% 2.02/1.53 mlocal @ ( mor @ v4 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ v1 ) @ ( mbox @ ( mbox @ v2 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat31,axiom,
% 2.02/1.53 mlocal @ ( mor @ v4 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat32,axiom,
% 2.02/1.53 mlocal @ ( mor @ v4 @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat33,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat34,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat35,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat36,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat37,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat38,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat39,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat40,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat41,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mnot @ v2 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat42,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat43,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat44,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat45,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat46,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat47,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat48,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ v3 ) @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat49,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ v4 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(persat50,axiom,
% 2.02/1.53 mlocal @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mnot @ v2 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(deontic1,axiom,
% 2.02/1.53 ( mlocal
% 2.02/1.53 @ ( mdia
% 2.02/1.53 @ ^ [W: mworld] : $true ) ) ).
% 2.02/1.53
% 2.02/1.53 thf(result1,conjecture,
% 2.02/1.53 ( mlocal
% 2.02/1.53 @ ^ [W: mworld] : $false ) ).
% 2.02/1.53 ------------------------
% 2.02/1.56 % (8092)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_7992 for (2999ds/4Mi)
% 2.02/1.56 % (8096)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_7992 for (2999ds/275Mi)
% 2.02/1.56 % (8093)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_7992 for (2999ds/27Mi)
% 2.02/1.56 % (8091)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/183Mi)
% 2.02/1.56 % (8094)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/2Mi)
% 2.02/1.56 % (8095)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_7992 for (2999ds/2Mi)
% 2.02/1.56 % (8097)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/18Mi)
% 2.02/1.56 % (8094)Instruction limit reached!
% 2.02/1.56 % (8094)------------------------------
% 2.02/1.56 % (8094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.02/1.56 % (8094)Termination reason: Unknown
% 2.02/1.56 % (8094)Termination phase: shuffling
% 2.02/1.56 % (8095)Instruction limit reached!
% 2.02/1.56 % (8095)------------------------------
% 2.02/1.56 % (8095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.02/1.56
% 2.02/1.56 % (8094)Memory used [KB]: 1023
% 2.02/1.56 % (8094)Time elapsed: 0.003 s
% 2.02/1.56 % (8094)Instructions burned: 3 (million)
% 2.02/1.56 % (8094)------------------------------
% 2.02/1.56 % (8094)------------------------------
% 2.02/1.56 % (8095)Termination reason: Unknown
% 2.02/1.56 % (8095)Termination phase: shuffling
% 2.02/1.56
% 2.02/1.56 % (8095)Memory used [KB]: 1023
% 2.02/1.56 % (8095)Time elapsed: 0.003 s
% 2.02/1.56 % (8095)Instructions burned: 3 (million)
% 2.02/1.56 % (8095)------------------------------
% 2.02/1.56 % (8095)------------------------------
% 2.02/1.56 % (8092)Instruction limit reached!
% 2.02/1.56 % (8092)------------------------------
% 2.02/1.56 % (8092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.02/1.56 % (8092)Termination reason: Unknown
% 2.02/1.56 % (8092)Termination phase: Property scanning
% 2.02/1.56
% 2.02/1.56 % (8092)Memory used [KB]: 1023
% 2.02/1.56 % (8092)Time elapsed: 0.004 s
% 2.02/1.56 % (8092)Instructions burned: 5 (million)
% 2.02/1.56 % (8092)------------------------------
% 2.02/1.56 % (8092)------------------------------
% 2.02/1.56 % (8096)Refutation not found, incomplete strategy
% 2.02/1.56 % (8096)------------------------------
% 2.02/1.56 % (8096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.02/1.56 % (8096)Termination reason: Refutation not found, incomplete strategy
% 2.02/1.56
% 2.02/1.56
% 2.02/1.56 % (8096)Memory used [KB]: 5500
% 2.02/1.56 % (8096)Time elapsed: 0.009 s
% 2.02/1.56 % (8096)Instructions burned: 16 (million)
% 2.02/1.56 % (8096)------------------------------
% 2.02/1.56 % (8096)------------------------------
% 2.02/1.56 % (8097)Instruction limit reached!
% 2.02/1.56 % (8097)------------------------------
% 2.02/1.56 % (8097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.02/1.56 % (8097)Termination reason: Unknown
% 2.02/1.56 % (8097)Termination phase: Function definition elimination
% 2.02/1.56
% 2.02/1.56 % (8097)Memory used [KB]: 1023
% 2.02/1.56 % (8097)Time elapsed: 0.010 s
% 2.02/1.56 % (8097)Instructions burned: 19 (million)
% 2.02/1.56 % (8097)------------------------------
% 2.02/1.56 % (8097)------------------------------
% 2.02/1.57 % (8093)Instruction limit reached!
% 2.02/1.57 % (8093)------------------------------
% 2.02/1.57 % (8093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.02/1.57 % (8093)Termination reason: Unknown
% 2.02/1.57 % (8093)Termination phase: Property scanning
% 2.02/1.57
% 2.02/1.57 % (8093)Memory used [KB]: 1151
% 2.02/1.57 % (8093)Time elapsed: 0.014 s
% 2.02/1.57 % (8093)Instructions burned: 28 (million)
% 2.02/1.57 % (8093)------------------------------
% 2.02/1.57 % (8093)------------------------------
% 2.02/1.57 % (8098)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/3Mi)
% 2.02/1.57 % (8099)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_7992 for (2999ds/37Mi)
% 2.02/1.57 % (8100)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_7992 for (2999ds/15Mi)
% 2.02/1.57 % (8098)Instruction limit reached!
% 2.02/1.57 % (8098)------------------------------
% 2.02/1.57 % (8098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.02/1.57 % (8098)Termination reason: Unknown
% 2.02/1.57 % (8098)Termination phase: shuffling
% 2.02/1.57
% 2.02/1.57 % (8098)Memory used [KB]: 1023
% 2.02/1.57 % (8098)Time elapsed: 0.003 s
% 2.02/1.57 % (8098)Instructions burned: 4 (million)
% 2.02/1.57 % (8098)------------------------------
% 2.02/1.57 % (8098)------------------------------
% 2.02/1.58 % (8101)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_7992 for (2999ds/3Mi)
% 2.02/1.58 % (8100)Instruction limit reached!
% 2.02/1.58 % (8100)------------------------------
% 2.02/1.58 % (8100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.02/1.58 % (8102)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_7992 for (2999ds/1041Mi)
% 2.02/1.58 % (8100)Termination reason: Unknown
% 2.02/1.58 % (8100)Termination phase: Property scanning
% 2.02/1.58
% 2.02/1.58 % (8100)Memory used [KB]: 1023
% 2.02/1.58 % (8100)Time elapsed: 0.008 s
% 2.02/1.58 % (8100)Instructions burned: 15 (million)
% 2.02/1.58 % (8100)------------------------------
% 2.02/1.58 % (8100)------------------------------
% 2.02/1.58 % (8101)Instruction limit reached!
% 2.02/1.58 % (8101)------------------------------
% 2.02/1.58 % (8101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.02/1.58 % (8101)Termination reason: Unknown
% 2.02/1.58 % (8101)Termination phase: shuffling
% 2.02/1.58
% 2.02/1.58 % (8101)Memory used [KB]: 1023
% 2.02/1.58 % (8101)Time elapsed: 0.003 s
% 2.02/1.58 % (8101)Instructions burned: 4 (million)
% 2.02/1.58 % (8101)------------------------------
% 2.02/1.58 % (8101)------------------------------
% 2.02/1.58 % (8103)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/7Mi)
% 2.02/1.59 % (8103)Instruction limit reached!
% 2.02/1.59 % (8103)------------------------------
% 2.02/1.59 % (8103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.02/1.59 % (8103)Termination reason: Unknown
% 2.02/1.59 % (8103)Termination phase: shuffling
% 2.02/1.59
% 2.02/1.59 % (8103)Memory used [KB]: 1023
% 2.02/1.59 % (8103)Time elapsed: 0.005 s
% 2.02/1.59 % (8103)Instructions burned: 8 (million)
% 2.02/1.59 % (8103)------------------------------
% 2.02/1.59 % (8103)------------------------------
% 2.02/1.59 % (8099)Instruction limit reached!
% 2.02/1.59 % (8099)------------------------------
% 2.02/1.59 % (8099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.02/1.59 % (8099)Termination reason: Unknown
% 2.02/1.59 % (8099)Termination phase: Saturation
% 2.02/1.59
% 2.02/1.59 % (8099)Memory used [KB]: 5628
% 2.02/1.59 % (8099)Time elapsed: 0.017 s
% 2.02/1.59 % (8099)Instructions burned: 37 (million)
% 2.02/1.59 % (8099)------------------------------
% 2.02/1.59 % (8099)------------------------------
% 2.02/1.59 % (8104)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/16Mi)
% 2.05/1.60 % (8105)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_7992 for (2999ds/3Mi)
% 2.05/1.60 % (8106)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_7992 for (2999ds/3Mi)
% 2.05/1.60 % (8105)Instruction limit reached!
% 2.05/1.60 % (8105)------------------------------
% 2.05/1.60 % (8105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.60 % (8105)Termination reason: Unknown
% 2.05/1.60 % (8105)Termination phase: shuffling
% 2.05/1.60
% 2.05/1.60 % (8105)Memory used [KB]: 1023
% 2.05/1.60 % (8105)Time elapsed: 0.003 s
% 2.05/1.60 % (8105)Instructions burned: 4 (million)
% 2.05/1.60 % (8105)------------------------------
% 2.05/1.60 % (8105)------------------------------
% 2.05/1.60 % (8104)Instruction limit reached!
% 2.05/1.60 % (8104)------------------------------
% 2.05/1.60 % (8104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.60 % (8104)Termination reason: Unknown
% 2.05/1.60 % (8104)Termination phase: Property scanning
% 2.05/1.60
% 2.05/1.60 % (8104)Memory used [KB]: 1023
% 2.05/1.60 % (8104)Time elapsed: 0.009 s
% 2.05/1.60 % (8104)Instructions burned: 17 (million)
% 2.05/1.60 % (8104)------------------------------
% 2.05/1.60 % (8104)------------------------------
% 2.05/1.60 % (8106)Instruction limit reached!
% 2.05/1.60 % (8106)------------------------------
% 2.05/1.60 % (8106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.60 % (8106)Termination reason: Unknown
% 2.05/1.60 % (8106)Termination phase: shuffling
% 2.05/1.60
% 2.05/1.60 % (8106)Memory used [KB]: 1023
% 2.05/1.60 % (8106)Time elapsed: 0.003 s
% 2.05/1.60 % (8106)Instructions burned: 4 (million)
% 2.05/1.60 % (8106)------------------------------
% 2.05/1.60 % (8106)------------------------------
% 2.05/1.60 % (8107)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/7Mi)
% 2.05/1.60 % (8108)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/3Mi)
% 2.05/1.61 % (8108)Instruction limit reached!
% 2.05/1.61 % (8108)------------------------------
% 2.05/1.61 % (8108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.61 % (8108)Termination reason: Unknown
% 2.05/1.61 % (8108)Termination phase: shuffling
% 2.05/1.61
% 2.05/1.61 % (8108)Memory used [KB]: 1023
% 2.05/1.61 % (8108)Time elapsed: 0.003 s
% 2.05/1.61 % (8108)Instructions burned: 4 (million)
% 2.05/1.61 % (8108)------------------------------
% 2.05/1.61 % (8108)------------------------------
% 2.05/1.61 % (8107)Instruction limit reached!
% 2.05/1.61 % (8107)------------------------------
% 2.05/1.61 % (8107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.61 % (8107)Termination reason: Unknown
% 2.05/1.61 % (8107)Termination phase: shuffling
% 2.05/1.61
% 2.05/1.61 % (8107)Memory used [KB]: 1023
% 2.05/1.61 % (8107)Time elapsed: 0.005 s
% 2.05/1.61 % (8107)Instructions burned: 8 (million)
% 2.05/1.61 % (8107)------------------------------
% 2.05/1.61 % (8107)------------------------------
% 2.05/1.61 % (8109)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/4Mi)
% 2.05/1.61 % (8110)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/18Mi)
% 2.05/1.61 % (8111)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/710Mi)
% 2.05/1.62 % (8109)Instruction limit reached!
% 2.05/1.62 % (8109)------------------------------
% 2.05/1.62 % (8109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.62 % (8109)Termination reason: Unknown
% 2.05/1.62 % (8109)Termination phase: shuffling
% 2.05/1.62
% 2.05/1.62 % (8109)Memory used [KB]: 1023
% 2.05/1.62 % (8109)Time elapsed: 0.003 s
% 2.05/1.62 % (8109)Instructions burned: 4 (million)
% 2.05/1.62 % (8109)------------------------------
% 2.05/1.62 % (8109)------------------------------
% 2.05/1.62 % (8111)Refutation not found, incomplete strategy
% 2.05/1.62 % (8111)------------------------------
% 2.05/1.62 % (8111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.62 % (8111)Termination reason: Refutation not found, incomplete strategy
% 2.05/1.62
% 2.05/1.62
% 2.05/1.62 % (8111)Memory used [KB]: 5500
% 2.05/1.62 % (8111)Time elapsed: 0.008 s
% 2.05/1.62 % (8111)Instructions burned: 15 (million)
% 2.05/1.62 % (8111)------------------------------
% 2.05/1.62 % (8111)------------------------------
% 2.05/1.62 % (8112)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/6Mi)
% 2.05/1.62 % (8110)Instruction limit reached!
% 2.05/1.62 % (8110)------------------------------
% 2.05/1.62 % (8110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.62 % (8110)Termination reason: Unknown
% 2.05/1.62 % (8110)Termination phase: Property scanning
% 2.05/1.62
% 2.05/1.62 % (8110)Memory used [KB]: 1023
% 2.05/1.62 % (8110)Time elapsed: 0.010 s
% 2.05/1.62 % (8110)Instructions burned: 20 (million)
% 2.05/1.62 % (8110)------------------------------
% 2.05/1.62 % (8110)------------------------------
% 2.05/1.62 % (8091)First to succeed.
% 2.05/1.62 % (8113)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_7992 for (2999ds/902Mi)
% 2.05/1.62 % (8112)Instruction limit reached!
% 2.05/1.62 % (8112)------------------------------
% 2.05/1.62 % (8112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.62 % (8112)Termination reason: Unknown
% 2.05/1.62 % (8112)Termination phase: shuffling
% 2.05/1.62
% 2.05/1.62 % (8112)Memory used [KB]: 1023
% 2.05/1.62 % (8112)Time elapsed: 0.004 s
% 2.05/1.62 % (8112)Instructions burned: 6 (million)
% 2.05/1.62 % (8112)------------------------------
% 2.05/1.62 % (8112)------------------------------
% 2.05/1.63 % (8114)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_7992 for (2999ds/21Mi)
% 2.05/1.63 % (8113)Refutation not found, incomplete strategy
% 2.05/1.63 % (8113)------------------------------
% 2.05/1.63 % (8113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.63 % (8113)Termination reason: Refutation not found, incomplete strategy
% 2.05/1.63
% 2.05/1.63
% 2.05/1.63 % (8113)Memory used [KB]: 5628
% 2.05/1.63 % (8113)Time elapsed: 0.013 s
% 2.05/1.63 % (8113)Instructions burned: 24 (million)
% 2.05/1.63 % (8113)------------------------------
% 2.05/1.63 % (8113)------------------------------
% 2.05/1.64 % (8115)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/5Mi)
% 2.05/1.64 % (8116)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_7992 for (2999ds/6Mi)
% 2.05/1.64 % (8114)Instruction limit reached!
% 2.05/1.64 % (8114)------------------------------
% 2.05/1.64 % (8114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.64 % (8117)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/377Mi)
% 2.05/1.64 % (8114)Termination reason: Unknown
% 2.05/1.64 % (8114)Termination phase: Property scanning
% 2.05/1.64
% 2.05/1.64 % (8114)Memory used [KB]: 1023
% 2.05/1.64 % (8114)Time elapsed: 0.011 s
% 2.05/1.64 % (8114)Instructions burned: 22 (million)
% 2.05/1.64 % (8114)------------------------------
% 2.05/1.64 % (8114)------------------------------
% 2.05/1.64 % (8115)Instruction limit reached!
% 2.05/1.64 % (8115)------------------------------
% 2.05/1.64 % (8115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.64 % (8115)Termination reason: Unknown
% 2.05/1.64 % (8115)Termination phase: Property scanning
% 2.05/1.64
% 2.05/1.64 % (8115)Memory used [KB]: 1023
% 2.05/1.64 % (8115)Time elapsed: 0.004 s
% 2.05/1.64 % (8115)Instructions burned: 6 (million)
% 2.05/1.64 % (8115)------------------------------
% 2.05/1.64 % (8115)------------------------------
% 2.05/1.64 % (8116)Instruction limit reached!
% 2.05/1.64 % (8116)------------------------------
% 2.05/1.64 % (8116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.64 % (8116)Termination reason: Unknown
% 2.05/1.64 % (8116)Termination phase: Property scanning
% 2.05/1.64
% 2.05/1.64 % (8116)Memory used [KB]: 1023
% 2.05/1.64 % (8116)Time elapsed: 0.004 s
% 2.05/1.64 % (8116)Instructions burned: 6 (million)
% 2.05/1.64 % (8116)------------------------------
% 2.05/1.64 % (8116)------------------------------
% 2.05/1.65 % (8091)Refutation found. Thanks to Tanya!
% 2.05/1.65 % SZS status Theorem for DTF2THF_7992
% 2.05/1.65 % SZS output start Proof for DTF2THF_7992
% 2.05/1.65 thf(type_def_5, type, mworld: $tType).
% 2.05/1.65 thf(func_def_0, type, mworld: $tType).
% 2.05/1.65 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 2.05/1.65 thf(func_def_2, type, mactual: mworld).
% 2.05/1.65 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 2.05/1.65 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 2.05/1.65 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.05/1.65 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.05/1.65 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.05/1.65 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.05/1.65 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 2.05/1.65 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 2.05/1.65 thf(func_def_12, type, v1: mworld > $o).
% 2.05/1.65 thf(func_def_13, type, v2: mworld > $o).
% 2.05/1.65 thf(func_def_14, type, v3: mworld > $o).
% 2.05/1.65 thf(func_def_15, type, v4: mworld > $o).
% 2.05/1.65 thf(func_def_30, type, sK1: mworld).
% 2.05/1.65 thf(f1662,plain,(
% 2.05/1.65 $false),
% 2.05/1.65 inference(avatar_sat_refutation,[status(thm)],[f1213,f1229,f1258,f1272,f1274,f1275,f1277,f1280,f1282,f1286,f1289,f1291,f1299,f1302,f1313,f1319,f1348,f1350,f1363,f1374,f1375,f1401,f1402,f1425,f1433,f1439,f1445,f1452,f1461,f1468,f1498,f1504,f1515,f1583,f1617,f1620,f1660])).
% 2.05/1.65 thf(f1660,plain,(
% 2.05/1.65 spl0_5 | ~spl0_19 | spl0_26),
% 2.05/1.65 inference(avatar_contradiction_clause,[status(thm)],[f1659])).
% 2.05/1.65 thf(f1659,plain,(
% 2.05/1.65 $false | (spl0_5 | ~spl0_19 | spl0_26)),
% 2.05/1.65 inference(subsumption_resolution,[status(thm)],[f1658,f1191])).
% 2.05/1.65 thf(f1191,plain,(
% 2.05/1.65 ((v1 @ mactual) != $true) | spl0_5),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1190])).
% 2.05/1.65 thf(f1190,definition,(
% 2.05/1.65 spl0_5 <=> ((v1 @ mactual) = $true)),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 2.05/1.65 thf(f1658,plain,(
% 2.05/1.65 ((v1 @ mactual) = $true) | (~spl0_19 | spl0_26)),
% 2.05/1.65 inference(subsumption_resolution,[status(thm)],[f1648,f1345])).
% 2.05/1.65 thf(f1345,plain,(
% 2.05/1.65 ($false != (mrel @ mactual @ mactual)) | spl0_26),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1344])).
% 2.05/1.65 thf(f1344,definition,(
% 2.05/1.65 spl0_26 <=> ($false = (mrel @ mactual @ mactual))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_26])],[avatar_definition])).
% 2.05/1.65 thf(f1648,plain,(
% 2.05/1.65 ($false = (mrel @ mactual @ mactual)) | ((v1 @ mactual) = $true) | (~spl0_19 | spl0_26)),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1644])).
% 2.05/1.65 thf(f1644,plain,(
% 2.05/1.65 ($false != $false) | ($false = (mrel @ mactual @ mactual)) | ((v1 @ mactual) = $true) | (~spl0_19 | spl0_26)),
% 2.05/1.65 inference(superposition,[status(thm)],[f1345,f1246])).
% 2.05/1.65 thf(f1246,plain,(
% 2.05/1.65 ( ! [X3 : mworld,X1 : mworld] : (($false = (mrel @ X1 @ X3)) | ((v1 @ X3) = $true) | ((mrel @ mactual @ X1) = $false)) ) | ~spl0_19),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1245])).
% 2.05/1.65 thf(f1245,definition,(
% 2.05/1.65 spl0_19 <=> ! [X1 : mworld,X3 : mworld] : (($false = (mrel @ X1 @ X3)) | ((mrel @ mactual @ X1) = $false) | ((v1 @ X3) = $true))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition])).
% 2.05/1.65 thf(f1620,plain,(
% 2.05/1.65 spl0_2 | ~spl0_7 | spl0_26),
% 2.05/1.65 inference(avatar_contradiction_clause,[status(thm)],[f1619])).
% 2.05/1.65 thf(f1619,plain,(
% 2.05/1.65 $false | (spl0_2 | ~spl0_7 | spl0_26)),
% 2.05/1.65 inference(subsumption_resolution,[status(thm)],[f1618,f1180])).
% 2.05/1.65 thf(f1180,plain,(
% 2.05/1.65 ($false != (v3 @ mactual)) | spl0_2),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1179])).
% 2.05/1.65 thf(f1179,definition,(
% 2.05/1.65 spl0_2 <=> ($false = (v3 @ mactual))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 2.05/1.65 thf(f1618,plain,(
% 2.05/1.65 ($false = (v3 @ mactual)) | (~spl0_7 | spl0_26)),
% 2.05/1.65 inference(subsumption_resolution,[status(thm)],[f1606,f1345])).
% 2.05/1.65 thf(f1606,plain,(
% 2.05/1.65 ($false = (mrel @ mactual @ mactual)) | ($false = (v3 @ mactual)) | (~spl0_7 | spl0_26)),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1603])).
% 2.05/1.65 thf(f1603,plain,(
% 2.05/1.65 ($false = (mrel @ mactual @ mactual)) | ($false != $false) | ($false = (v3 @ mactual)) | (~spl0_7 | spl0_26)),
% 2.05/1.65 inference(superposition,[status(thm)],[f1345,f1198])).
% 2.05/1.65 thf(f1198,plain,(
% 2.05/1.65 ( ! [X1 : mworld,X4 : mworld] : (($false = (mrel @ X1 @ X4)) | ($false = (v3 @ X4)) | ((mrel @ mactual @ X1) = $false)) ) | ~spl0_7),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1197])).
% 2.05/1.65 thf(f1197,definition,(
% 2.05/1.65 spl0_7 <=> ! [X4 : mworld,X1 : mworld] : (($false = (mrel @ X1 @ X4)) | ($false = (v3 @ X4)) | ((mrel @ mactual @ X1) = $false))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 2.05/1.65 thf(f1617,plain,(
% 2.05/1.65 spl0_23 | ~spl0_7),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f1608,f1197,f1266])).
% 2.05/1.65 thf(f1266,definition,(
% 2.05/1.65 spl0_23 <=> ! [X2 : mworld] : (($false = (v3 @ X2)) | ((mrel @ mactual @ X2) = $false))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition])).
% 2.05/1.65 thf(f1608,plain,(
% 2.05/1.65 ( ! [X0 : mworld] : (($false = (mrel @ mactual @ X0)) | ((v3 @ X0) = $false)) ) | ~spl0_7),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1602])).
% 2.05/1.65 thf(f1602,plain,(
% 2.05/1.65 ( ! [X0 : mworld] : (($true = $false) | ((v3 @ X0) = $false) | ($false = (mrel @ mactual @ X0))) ) | ~spl0_7),
% 2.05/1.65 inference(superposition,[status(thm)],[f229,f1198])).
% 2.05/1.65 thf(f229,plain,(
% 2.05/1.65 ( ! [X0 : mworld] : (($true = (mrel @ X0 @ X0))) )),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f183])).
% 2.05/1.65 thf(f183,plain,(
% 2.05/1.65 ! [X0 : mworld] : ($true = (mrel @ X0 @ X0))),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f182])).
% 2.05/1.65 thf(f182,plain,(
% 2.05/1.65 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 2.05/1.65 inference(rectify,[status(thm)],[f9])).
% 2.05/1.65 thf(f9,axiom,(
% 2.05/1.65 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',mrel_reflexive)).
% 2.05/1.65 thf(f1583,plain,(
% 2.05/1.65 spl0_2 | ~spl0_23 | spl0_26),
% 2.05/1.65 inference(avatar_contradiction_clause,[status(thm)],[f1582])).
% 2.05/1.65 thf(f1582,plain,(
% 2.05/1.65 $false | (spl0_2 | ~spl0_23 | spl0_26)),
% 2.05/1.65 inference(subsumption_resolution,[status(thm)],[f1574,f1180])).
% 2.05/1.65 thf(f1574,plain,(
% 2.05/1.65 ($false = (v3 @ mactual)) | (~spl0_23 | spl0_26)),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1571])).
% 2.05/1.65 thf(f1571,plain,(
% 2.05/1.65 ($false != $false) | ($false = (v3 @ mactual)) | (~spl0_23 | spl0_26)),
% 2.05/1.65 inference(superposition,[status(thm)],[f1345,f1267])).
% 2.05/1.65 thf(f1267,plain,(
% 2.05/1.65 ( ! [X2 : mworld] : (((mrel @ mactual @ X2) = $false) | ($false = (v3 @ X2))) ) | ~spl0_23),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1266])).
% 2.05/1.65 thf(f1515,plain,(
% 2.05/1.65 ~spl0_4 | ~spl0_25),
% 2.05/1.65 inference(avatar_contradiction_clause,[status(thm)],[f1514])).
% 2.05/1.65 thf(f1514,plain,(
% 2.05/1.65 $false | (~spl0_4 | ~spl0_25)),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1510])).
% 2.05/1.65 thf(f1510,plain,(
% 2.05/1.65 ($true = $false) | (~spl0_4 | ~spl0_25)),
% 2.05/1.65 inference(superposition,[status(thm)],[f1484,f1342])).
% 2.05/1.65 thf(f1342,plain,(
% 2.05/1.65 ((v4 @ sK1) = $true) | ~spl0_25),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1340])).
% 2.05/1.65 thf(f1340,definition,(
% 2.05/1.65 spl0_25 <=> ((v4 @ sK1) = $true)),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition])).
% 2.05/1.65 thf(f1484,plain,(
% 2.05/1.65 ((v4 @ sK1) = $false) | ~spl0_4),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1476])).
% 2.05/1.65 thf(f1476,plain,(
% 2.05/1.65 ($true = $false) | ((v4 @ sK1) = $false) | ~spl0_4),
% 2.05/1.65 inference(superposition,[status(thm)],[f1187,f891])).
% 2.05/1.65 thf(f891,plain,(
% 2.05/1.65 ($true = (mrel @ mactual @ sK1))),
% 2.05/1.65 inference(sigma_clausification,[status(thm)],[f890])).
% 2.05/1.65 thf(f890,plain,(
% 2.05/1.65 ((?? @ mworld @ (mrel @ mactual)) = $true)),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f889])).
% 2.05/1.65 thf(f889,plain,(
% 2.05/1.65 ($true = (?? @ mworld @ (^[Y0 : mworld]: (mrel @ mactual @ Y0))))),
% 2.05/1.65 inference(boolean_simplification,[status(thm)],[f888])).
% 2.05/1.65 thf(f888,plain,(
% 2.05/1.65 ($true = (?? @ mworld @ (^[Y0 : mworld]: ($true & (mrel @ mactual @ Y0)))))),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f298])).
% 2.05/1.65 thf(f298,plain,(
% 2.05/1.65 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true)))) = $true)),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f246,f192,f205])).
% 2.05/1.65 thf(f205,plain,(
% 2.05/1.65 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f84])).
% 2.05/1.65 thf(f84,plain,(
% 2.05/1.65 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f83])).
% 2.05/1.65 thf(f83,plain,(
% 2.05/1.65 (mdia = (^[X0 : mworld > $o, X1 : mworld] : (? [X2 : mworld] : ((mrel @ X1 @ X2) & (X0 @ X2)))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f8])).
% 2.05/1.65 thf(f8,axiom,(
% 2.05/1.65 (mdia = (^[X0 : mworld > $o, X2 : mworld] : (? [X4 : mworld] : ((mrel @ X2 @ X4) & (X0 @ X4)))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',mdia_def)).
% 2.05/1.65 thf(f192,plain,(
% 2.05/1.65 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f125])).
% 2.05/1.65 thf(f125,plain,(
% 2.05/1.65 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f1])).
% 2.05/1.65 thf(f1,axiom,(
% 2.05/1.65 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',mlocal_def)).
% 2.05/1.65 thf(f246,plain,(
% 2.05/1.65 ($true = (mlocal @ (mdia @ (^[Y0 : mworld]: ($true)))))),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f108])).
% 2.05/1.65 thf(f108,plain,(
% 2.05/1.65 ($true = (mlocal @ (mdia @ (^[Y0 : mworld]: ($true)))))),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f107])).
% 2.05/1.65 thf(f107,plain,(
% 2.05/1.65 (mlocal @ (mdia @ (^[X0 : mworld] : ($true))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f61])).
% 2.05/1.65 thf(f61,axiom,(
% 2.05/1.65 (mlocal @ (mdia @ (^[X2 : mworld] : ($true))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',deontic1)).
% 2.05/1.65 thf(f1187,plain,(
% 2.05/1.65 ( ! [X2 : mworld] : (((mrel @ mactual @ X2) = $false) | ($false = (v4 @ X2))) ) | ~spl0_4),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1186])).
% 2.05/1.65 thf(f1186,definition,(
% 2.05/1.65 spl0_4 <=> ! [X2 : mworld] : (($false = (v4 @ X2)) | ((mrel @ mactual @ X2) = $false))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 2.05/1.65 thf(f1504,plain,(
% 2.05/1.65 spl0_10 | ~spl0_13),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f1411,f1219,f1208])).
% 2.05/1.65 thf(f1208,definition,(
% 2.05/1.65 spl0_10 <=> ! [X2 : mworld] : (((mrel @ mactual @ X2) = $false) | ((v2 @ X2) = $true))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 2.05/1.65 thf(f1219,definition,(
% 2.05/1.65 spl0_13 <=> ! [X2 : mworld,X4 : mworld] : (((mrel @ mactual @ X2) = $false) | ((v2 @ X4) = $true) | ((mrel @ X2 @ X4) = $false))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 2.05/1.65 thf(f1411,plain,(
% 2.05/1.65 ( ! [X0 : mworld] : (($false = (mrel @ mactual @ X0)) | ($true = (v2 @ X0))) ) | ~spl0_13),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1405])).
% 2.05/1.65 thf(f1405,plain,(
% 2.05/1.65 ( ! [X0 : mworld] : (($false = (mrel @ mactual @ X0)) | ($true = $false) | ($true = (v2 @ X0))) ) | ~spl0_13),
% 2.05/1.65 inference(superposition,[status(thm)],[f1220,f229])).
% 2.05/1.65 thf(f1220,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X4 : mworld] : (((mrel @ mactual @ X2) = $false) | ((v2 @ X4) = $true) | ((mrel @ X2 @ X4) = $false)) ) | ~spl0_13),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1219])).
% 2.05/1.65 thf(f1498,plain,(
% 2.05/1.65 ~spl0_10 | spl0_18),
% 2.05/1.65 inference(avatar_contradiction_clause,[status(thm)],[f1497])).
% 2.05/1.65 thf(f1497,plain,(
% 2.05/1.65 $false | (~spl0_10 | spl0_18)),
% 2.05/1.65 inference(subsumption_resolution,[status(thm)],[f1325,f1241])).
% 2.05/1.65 thf(f1241,plain,(
% 2.05/1.65 ($true != (v2 @ mactual)) | spl0_18),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1240])).
% 2.05/1.65 thf(f1240,definition,(
% 2.05/1.65 spl0_18 <=> ($true = (v2 @ mactual))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition])).
% 2.05/1.65 thf(f1325,plain,(
% 2.05/1.65 ($true = (v2 @ mactual)) | ~spl0_10),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1323])).
% 2.05/1.65 thf(f1323,plain,(
% 2.05/1.65 ($true = $false) | ($true = (v2 @ mactual)) | ~spl0_10),
% 2.05/1.65 inference(superposition,[status(thm)],[f229,f1209])).
% 2.05/1.65 thf(f1209,plain,(
% 2.05/1.65 ( ! [X2 : mworld] : (((mrel @ mactual @ X2) = $false) | ((v2 @ X2) = $true)) ) | ~spl0_10),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1208])).
% 2.05/1.65 thf(f1468,plain,(
% 2.05/1.65 ~spl0_10 | ~spl0_27),
% 2.05/1.65 inference(avatar_contradiction_clause,[status(thm)],[f1467])).
% 2.05/1.65 thf(f1467,plain,(
% 2.05/1.65 $false | (~spl0_10 | ~spl0_27)),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1463])).
% 2.05/1.65 thf(f1463,plain,(
% 2.05/1.65 ($true = $false) | (~spl0_10 | ~spl0_27)),
% 2.05/1.65 inference(superposition,[status(thm)],[f1399,f1328])).
% 2.05/1.65 thf(f1328,plain,(
% 2.05/1.65 ($true = (v2 @ sK1)) | ~spl0_10),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1322])).
% 2.05/1.65 thf(f1322,plain,(
% 2.05/1.65 ($true = $false) | ($true = (v2 @ sK1)) | ~spl0_10),
% 2.05/1.65 inference(superposition,[status(thm)],[f1209,f891])).
% 2.05/1.65 thf(f1399,plain,(
% 2.05/1.65 ($false = (v2 @ sK1)) | ~spl0_27),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1397])).
% 2.05/1.65 thf(f1397,definition,(
% 2.05/1.65 spl0_27 <=> ($false = (v2 @ sK1))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_27])],[avatar_definition])).
% 2.05/1.65 thf(f1461,plain,(
% 2.05/1.65 ~spl0_18 | ~spl0_21),
% 2.05/1.65 inference(avatar_contradiction_clause,[status(thm)],[f1460])).
% 2.05/1.65 thf(f1460,plain,(
% 2.05/1.65 $false | (~spl0_18 | ~spl0_21)),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1457])).
% 2.05/1.65 thf(f1457,plain,(
% 2.05/1.65 ($true = $false) | (~spl0_18 | ~spl0_21)),
% 2.05/1.65 inference(superposition,[status(thm)],[f1242,f1255])).
% 2.05/1.65 thf(f1255,plain,(
% 2.05/1.65 ($false = (v2 @ mactual)) | ~spl0_21),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1253])).
% 2.05/1.65 thf(f1253,definition,(
% 2.05/1.65 spl0_21 <=> ($false = (v2 @ mactual))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition])).
% 2.05/1.65 thf(f1242,plain,(
% 2.05/1.65 ($true = (v2 @ mactual)) | ~spl0_18),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1240])).
% 2.05/1.65 thf(f1452,plain,(
% 2.05/1.65 ~spl0_1 | ~spl0_14),
% 2.05/1.65 inference(avatar_contradiction_clause,[status(thm)],[f1451])).
% 2.05/1.65 thf(f1451,plain,(
% 2.05/1.65 $false | (~spl0_1 | ~spl0_14)),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1448])).
% 2.05/1.65 thf(f1448,plain,(
% 2.05/1.65 ($true = $false) | (~spl0_1 | ~spl0_14)),
% 2.05/1.65 inference(superposition,[status(thm)],[f1177,f1224])).
% 2.05/1.65 thf(f1224,plain,(
% 2.05/1.65 ($true = (v4 @ mactual)) | ~spl0_14),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1222])).
% 2.05/1.65 thf(f1222,definition,(
% 2.05/1.65 spl0_14 <=> ($true = (v4 @ mactual))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 2.05/1.65 thf(f1177,plain,(
% 2.05/1.65 ($false = (v4 @ mactual)) | ~spl0_1),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1175])).
% 2.05/1.65 thf(f1175,definition,(
% 2.05/1.65 spl0_1 <=> ($false = (v4 @ mactual))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 2.05/1.65 thf(f1445,plain,(
% 2.05/1.65 ~spl0_8 | spl0_17 | spl0_26),
% 2.05/1.65 inference(avatar_contradiction_clause,[status(thm)],[f1444])).
% 2.05/1.65 thf(f1444,plain,(
% 2.05/1.65 $false | (~spl0_8 | spl0_17 | spl0_26)),
% 2.05/1.65 inference(subsumption_resolution,[status(thm)],[f1443,f1236])).
% 2.05/1.65 thf(f1236,plain,(
% 2.05/1.65 ((v1 @ mactual) != $false) | spl0_17),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1235])).
% 2.05/1.65 thf(f1235,definition,(
% 2.05/1.65 spl0_17 <=> ((v1 @ mactual) = $false)),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 2.05/1.65 thf(f1443,plain,(
% 2.05/1.65 ((v1 @ mactual) = $false) | (~spl0_8 | spl0_26)),
% 2.05/1.65 inference(subsumption_resolution,[status(thm)],[f1384,f1345])).
% 2.05/1.65 thf(f1384,plain,(
% 2.05/1.65 ($false = (mrel @ mactual @ mactual)) | ((v1 @ mactual) = $false) | ~spl0_8),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1380])).
% 2.05/1.65 thf(f1380,plain,(
% 2.05/1.65 ((v1 @ mactual) = $false) | ($false = (mrel @ mactual @ mactual)) | ($false != $false) | ~spl0_8),
% 2.05/1.65 inference(equality_factoring,[status(thm)],[f1202])).
% 2.05/1.65 thf(f1202,plain,(
% 2.05/1.65 ( ! [X3 : mworld,X1 : mworld] : (($false = (mrel @ X1 @ X3)) | ((v1 @ X3) = $false) | ((mrel @ mactual @ X1) = $false)) ) | ~spl0_8),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1201])).
% 2.05/1.65 thf(f1201,definition,(
% 2.05/1.65 spl0_8 <=> ! [X1 : mworld,X3 : mworld] : (((mrel @ mactual @ X1) = $false) | ($false = (mrel @ X1 @ X3)) | ((v1 @ X3) = $false))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 2.05/1.65 thf(f1439,plain,(
% 2.05/1.65 ~spl0_2 | ~spl0_12),
% 2.05/1.65 inference(avatar_contradiction_clause,[status(thm)],[f1438])).
% 2.05/1.65 thf(f1438,plain,(
% 2.05/1.65 $false | (~spl0_2 | ~spl0_12)),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1434])).
% 2.05/1.65 thf(f1434,plain,(
% 2.05/1.65 ($true = $false) | (~spl0_2 | ~spl0_12)),
% 2.05/1.65 inference(superposition,[status(thm)],[f1217,f1181])).
% 2.05/1.65 thf(f1181,plain,(
% 2.05/1.65 ($false = (v3 @ mactual)) | ~spl0_2),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1179])).
% 2.05/1.65 thf(f1217,plain,(
% 2.05/1.65 ($true = (v3 @ mactual)) | ~spl0_12),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1215])).
% 2.05/1.65 thf(f1215,definition,(
% 2.05/1.65 spl0_12 <=> ($true = (v3 @ mactual))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 2.05/1.65 thf(f1433,plain,(
% 2.05/1.65 ~spl0_26),
% 2.05/1.65 inference(avatar_contradiction_clause,[status(thm)],[f1432])).
% 2.05/1.65 thf(f1432,plain,(
% 2.05/1.65 $false | ~spl0_26),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1429])).
% 2.05/1.65 thf(f1429,plain,(
% 2.05/1.65 ($true = $false) | ~spl0_26),
% 2.05/1.65 inference(superposition,[status(thm)],[f229,f1346])).
% 2.05/1.65 thf(f1346,plain,(
% 2.05/1.65 ($false = (mrel @ mactual @ mactual)) | ~spl0_26),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1344])).
% 2.05/1.65 thf(f1425,plain,(
% 2.05/1.65 spl0_26 | spl0_12 | ~spl0_15),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f1424,f1227,f1215,f1344])).
% 2.05/1.65 thf(f1227,definition,(
% 2.05/1.65 spl0_15 <=> ! [X4 : mworld,X2 : mworld] : (($true = (v3 @ X4)) | ((mrel @ mactual @ X2) = $false) | ((mrel @ X2 @ X4) = $false))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 2.05/1.65 thf(f1424,plain,(
% 2.05/1.65 ($true = (v3 @ mactual)) | ($false = (mrel @ mactual @ mactual)) | ~spl0_15),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1419])).
% 2.05/1.65 thf(f1419,plain,(
% 2.05/1.65 ($true = (v3 @ mactual)) | ($false = (mrel @ mactual @ mactual)) | ($false != $false) | ~spl0_15),
% 2.05/1.65 inference(equality_factoring,[status(thm)],[f1228])).
% 2.05/1.65 thf(f1228,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X4 : mworld] : (((mrel @ mactual @ X2) = $false) | ($true = (v3 @ X4)) | ((mrel @ X2 @ X4) = $false)) ) | ~spl0_15),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1227])).
% 2.05/1.65 thf(f1402,plain,(
% 2.05/1.65 spl0_26 | spl0_27 | ~spl0_11),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f1393,f1211,f1397,f1344])).
% 2.05/1.65 thf(f1211,definition,(
% 2.05/1.65 spl0_11 <=> ! [X5 : mworld,X1 : mworld] : (((v2 @ X5) = $false) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ X1 @ X5)))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 2.05/1.65 thf(f1393,plain,(
% 2.05/1.65 ($false = (v2 @ sK1)) | ($false = (mrel @ mactual @ mactual)) | ~spl0_11),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1387])).
% 2.05/1.65 thf(f1387,plain,(
% 2.05/1.65 ($false = (v2 @ sK1)) | ($false = (mrel @ mactual @ mactual)) | ($true = $false) | ~spl0_11),
% 2.05/1.65 inference(superposition,[status(thm)],[f1212,f891])).
% 2.05/1.65 thf(f1212,plain,(
% 2.05/1.65 ( ! [X1 : mworld,X5 : mworld] : (($false = (mrel @ X1 @ X5)) | ((v2 @ X5) = $false) | ((mrel @ mactual @ X1) = $false)) ) | ~spl0_11),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1211])).
% 2.05/1.65 thf(f1401,plain,(
% 2.05/1.65 spl0_26 | spl0_21 | ~spl0_11),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f1394,f1211,f1253,f1344])).
% 2.05/1.65 thf(f1394,plain,(
% 2.05/1.65 ($false = (v2 @ mactual)) | ($false = (mrel @ mactual @ mactual)) | ~spl0_11),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1390])).
% 2.05/1.65 thf(f1390,plain,(
% 2.05/1.65 ($false = (mrel @ mactual @ mactual)) | ($false != $false) | ($false = (v2 @ mactual)) | ~spl0_11),
% 2.05/1.65 inference(equality_factoring,[status(thm)],[f1212])).
% 2.05/1.65 thf(f1375,plain,(
% 2.05/1.65 spl0_25 | ~spl0_24),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f1368,f1270,f1340])).
% 2.05/1.65 thf(f1270,definition,(
% 2.05/1.65 spl0_24 <=> ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((v4 @ X1) = $true))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition])).
% 2.05/1.65 thf(f1368,plain,(
% 2.05/1.65 ((v4 @ sK1) = $true) | ~spl0_24),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1365])).
% 2.05/1.65 thf(f1365,plain,(
% 2.05/1.65 ($true = $false) | ((v4 @ sK1) = $true) | ~spl0_24),
% 2.05/1.65 inference(superposition,[status(thm)],[f1271,f891])).
% 2.05/1.65 thf(f1271,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((v4 @ X1) = $true)) ) | ~spl0_24),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1270])).
% 2.05/1.65 thf(f1374,plain,(
% 2.05/1.65 spl0_14 | ~spl0_24),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f1369,f1270,f1222])).
% 2.05/1.65 thf(f1369,plain,(
% 2.05/1.65 ($true = (v4 @ mactual)) | ~spl0_24),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1366])).
% 2.05/1.65 thf(f1366,plain,(
% 2.05/1.65 ($true = (v4 @ mactual)) | ($true = $false) | ~spl0_24),
% 2.05/1.65 inference(superposition,[status(thm)],[f229,f1271])).
% 2.05/1.65 thf(f1363,plain,(
% 2.05/1.65 spl0_4 | ~spl0_6),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f1357,f1194,f1186])).
% 2.05/1.65 thf(f1194,definition,(
% 2.05/1.65 spl0_6 <=> ! [X2 : mworld,X3 : mworld] : (((mrel @ mactual @ X2) = $false) | ((v4 @ X3) = $false) | ((mrel @ X2 @ X3) = $false))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 2.05/1.65 thf(f1357,plain,(
% 2.05/1.65 ( ! [X0 : mworld] : (($false = (mrel @ mactual @ X0)) | ((v4 @ X0) = $false)) ) | ~spl0_6),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1354])).
% 2.05/1.65 thf(f1354,plain,(
% 2.05/1.65 ( ! [X0 : mworld] : (((v4 @ X0) = $false) | ($false = (mrel @ mactual @ X0)) | ($true = $false)) ) | ~spl0_6),
% 2.05/1.65 inference(superposition,[status(thm)],[f229,f1195])).
% 2.05/1.65 thf(f1195,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld] : (((mrel @ mactual @ X2) = $false) | ((mrel @ X2 @ X3) = $false) | ((v4 @ X3) = $false)) ) | ~spl0_6),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1194])).
% 2.05/1.65 thf(f1350,plain,(
% 2.05/1.65 spl0_26 | spl0_14 | ~spl0_3),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f1335,f1183,f1222,f1344])).
% 2.05/1.65 thf(f1183,definition,(
% 2.05/1.65 spl0_3 <=> ! [X1 : mworld,X3 : mworld] : (((mrel @ mactual @ X1) = $false) | ($false = (mrel @ X1 @ X3)) | ((v4 @ X3) = $true))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 2.05/1.65 thf(f1335,plain,(
% 2.05/1.65 ($true = (v4 @ mactual)) | ($false = (mrel @ mactual @ mactual)) | ~spl0_3),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1333])).
% 2.05/1.65 thf(f1333,plain,(
% 2.05/1.65 ($false = (mrel @ mactual @ mactual)) | ($false != $false) | ($true = (v4 @ mactual)) | ~spl0_3),
% 2.05/1.65 inference(equality_factoring,[status(thm)],[f1184])).
% 2.05/1.65 thf(f1184,plain,(
% 2.05/1.65 ( ! [X3 : mworld,X1 : mworld] : (($false = (mrel @ X1 @ X3)) | ((v4 @ X3) = $true) | ((mrel @ mactual @ X1) = $false)) ) | ~spl0_3),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1183])).
% 2.05/1.65 thf(f1348,plain,(
% 2.05/1.65 spl0_25 | spl0_26 | ~spl0_3),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f1337,f1183,f1344,f1340])).
% 2.05/1.65 thf(f1337,plain,(
% 2.05/1.65 ($false = (mrel @ mactual @ mactual)) | ((v4 @ sK1) = $true) | ~spl0_3),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1330])).
% 2.05/1.65 thf(f1330,plain,(
% 2.05/1.65 ($false = (mrel @ mactual @ mactual)) | ((v4 @ sK1) = $true) | ($true = $false) | ~spl0_3),
% 2.05/1.65 inference(superposition,[status(thm)],[f1184,f891])).
% 2.05/1.65 thf(f1319,plain,(
% 2.05/1.65 ~spl0_5 | ~spl0_17),
% 2.05/1.65 inference(avatar_contradiction_clause,[status(thm)],[f1318])).
% 2.05/1.65 thf(f1318,plain,(
% 2.05/1.65 $false | (~spl0_5 | ~spl0_17)),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1314])).
% 2.05/1.65 thf(f1314,plain,(
% 2.05/1.65 ($true = $false) | (~spl0_5 | ~spl0_17)),
% 2.05/1.65 inference(superposition,[status(thm)],[f1237,f1192])).
% 2.05/1.65 thf(f1192,plain,(
% 2.05/1.65 ((v1 @ mactual) = $true) | ~spl0_5),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1190])).
% 2.05/1.65 thf(f1237,plain,(
% 2.05/1.65 ((v1 @ mactual) = $false) | ~spl0_17),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1235])).
% 2.05/1.65 thf(f1313,plain,(
% 2.05/1.65 spl0_17 | ~spl0_9),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f1308,f1204,f1235])).
% 2.05/1.65 thf(f1204,definition,(
% 2.05/1.65 spl0_9 <=> ! [X2 : mworld] : (($false = (v1 @ X2)) | ((mrel @ mactual @ X2) = $false))),
% 2.05/1.65 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 2.05/1.65 thf(f1308,plain,(
% 2.05/1.65 ((v1 @ mactual) = $false) | ~spl0_9),
% 2.05/1.65 inference(trivial_inequality_removal,[status(thm)],[f1306])).
% 2.05/1.65 thf(f1306,plain,(
% 2.05/1.65 ((v1 @ mactual) = $false) | ($true = $false) | ~spl0_9),
% 2.05/1.65 inference(superposition,[status(thm)],[f229,f1205])).
% 2.05/1.65 thf(f1205,plain,(
% 2.05/1.65 ( ! [X2 : mworld] : (((mrel @ mactual @ X2) = $false) | ($false = (v1 @ X2))) ) | ~spl0_9),
% 2.05/1.65 inference(avatar_component_clause,[status(thm)],[f1204])).
% 2.05/1.65 thf(f1302,plain,(
% 2.05/1.65 spl0_6 | spl0_4 | spl0_11 | spl0_2),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f340,f1179,f1211,f1186,f1194])).
% 2.05/1.65 thf(f340,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ mactual @ X1) = $false) | ((v4 @ X5) = $false) | ((mrel @ mactual @ X2) = $false) | ($false = (mrel @ X1 @ X4)) | ((v2 @ X4) = $false) | ($false = (mrel @ mactual @ X3)) | ((v4 @ X3) = $false) | ((mrel @ X2 @ X5) = $false) | ($false = (v3 @ mactual))) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f339])).
% 2.05/1.65 thf(f339,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = (mrel @ mactual @ X3)) | ((mrel @ X2 @ X5) = $false) | ($false = (mrel @ X1 @ X4)) | ((~ (v4 @ X5)) = $true) | ((mrel @ mactual @ X2) = $false) | ((v4 @ X3) = $false) | ((mrel @ mactual @ X1) = $false) | ((v2 @ X4) = $false) | ($false = (v3 @ mactual))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f338])).
% 2.05/1.65 thf(f338,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = (v3 @ mactual)) | ((v2 @ X4) = $false) | (((mrel @ X2 @ X5) => (~ (v4 @ X5))) = $true) | ($false = (mrel @ X1 @ X4)) | ((v4 @ X3) = $false) | ((mrel @ mactual @ X2) = $false) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ mactual @ X3))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f337])).
% 2.05/1.65 thf(f337,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ mactual @ X2) = $false) | ($false = (mrel @ mactual @ X3)) | ($false = (mrel @ X1 @ X4)) | ((mrel @ mactual @ X1) = $false) | ((v4 @ X3) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v4 @ Y0)))) @ X5)) | ($false = (v3 @ mactual)) | ((v2 @ X4) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f336])).
% 2.05/1.65 thf(f336,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((mrel @ mactual @ X2) = $false) | ((v4 @ X3) = $false) | ($false = (v3 @ mactual)) | ((v2 @ X4) = $false) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ X1 @ X4)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v4 @ Y0)))))) | ($false = (mrel @ mactual @ X3))) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f335])).
% 2.05/1.65 thf(f335,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((v4 @ X3) = $false) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ mactual @ X3)) | ($false = (mrel @ X1 @ X4)) | ((mrel @ mactual @ X2) = $false) | ($false = (v3 @ mactual)) | ($true = (~ (v2 @ X4))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v4 @ Y0))))))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f334])).
% 2.05/1.65 thf(f334,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = (v3 @ mactual)) | ((v4 @ X3) = $false) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ mactual @ X3)) | ($true = ((mrel @ X1 @ X4) => (~ (v2 @ X4)))) | ((mrel @ mactual @ X2) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v4 @ Y0))))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f333])).
% 2.05/1.65 thf(f333,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = (mrel @ mactual @ X3)) | ($false = (v3 @ mactual)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v4 @ Y0)))))) | ((mrel @ mactual @ X1) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0)))) @ X4)) | ((v4 @ X3) = $false) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f332])).
% 2.05/1.65 thf(f332,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X2) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0)))))) | ((mrel @ mactual @ X1) = $false) | ($false = (v3 @ mactual)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v4 @ Y0)))))) | ($false = (mrel @ mactual @ X3)) | ((v4 @ X3) = $false)) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f331])).
% 2.05/1.65 thf(f331,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X2) = $false) | ($true = (~ (v3 @ mactual))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v4 @ Y0)))))) | ((v4 @ X3) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0)))))) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ mactual @ X3))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f330])).
% 2.05/1.65 thf(f330,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v4 @ Y0)))))) = $true) | ($true = (~ (v3 @ mactual))) | ((v4 @ X3) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0)))))) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ mactual @ X3))) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f329])).
% 2.05/1.65 thf(f329,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((~ (v4 @ X3)) = $true) | (((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v4 @ Y0)))))) = $true) | ((mrel @ mactual @ X1) = $false) | ($true = (~ (v3 @ mactual))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0)))))) | ($false = (mrel @ mactual @ X3))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f328])).
% 2.05/1.65 thf(f328,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((mrel @ mactual @ X3) => (~ (v4 @ X3)))) | ((mrel @ mactual @ X1) = $false) | (((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v4 @ Y0)))))) = $true) | ($true = (~ (v3 @ mactual))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0))))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f327])).
% 2.05/1.65 thf(f327,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0)))))) | ($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0)))) @ X3)) | (((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v4 @ Y0)))))) = $true) | ((mrel @ mactual @ X1) = $false) | ($true = (~ (v3 @ mactual)))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f326])).
% 2.05/1.65 thf(f326,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0)))))) | ($true = (~ (v3 @ mactual))) | (((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v4 @ Y0)))))) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0))))))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f325])).
% 2.05/1.65 thf(f325,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0))))))) | (((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v4 @ Y0)))))) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0)))))) | ($true = (~ (v3 @ mactual)))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f324])).
% 2.05/1.65 thf(f324,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (~ (v3 @ mactual))) | ($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0))))))) | ($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))) @ X2)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0))))))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f323])).
% 2.05/1.65 thf(f323,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0)))))) | ($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0))))))) | ($true = (~ (v3 @ mactual)))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f322])).
% 2.05/1.65 thf(f322,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (~ (v3 @ mactual))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) = $true) | ($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1))))))) @ X1)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0))))))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f321])).
% 2.05/1.65 thf(f321,plain,(
% 2.05/1.65 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) = $true) | ($true = (~ (v3 @ mactual))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0))))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f320])).
% 2.05/1.65 thf(f320,plain,(
% 2.05/1.65 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))))) | ($true = (~ (v3 @ mactual))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0))))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f319])).
% 2.05/1.65 thf(f319,plain,(
% 2.05/1.65 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1))))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0))))))) | ($true = (~ (v3 @ mactual)))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f318])).
% 2.05/1.65 thf(f318,plain,(
% 2.05/1.65 ($true = ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1))))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v4 @ Y0)))))) | (~ (v3 @ mactual))))),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f292])).
% 2.05/1.65 thf(f292,plain,(
% 2.05/1.65 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v4)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v2))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v4))))))) = $true)),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f240,f192,f203,f194,f203,f213,f194,f203,f213,f213,f194,f213,f213,f194])).
% 2.05/1.65 thf(f213,plain,(
% 2.05/1.65 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f90])).
% 2.05/1.65 thf(f90,plain,(
% 2.05/1.65 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f89])).
% 2.05/1.65 thf(f89,plain,(
% 2.05/1.65 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 2.05/1.65 inference(rectify,[status(thm)],[f7])).
% 2.05/1.65 thf(f7,axiom,(
% 2.05/1.65 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',mbox_def)).
% 2.05/1.65 thf(f194,plain,(
% 2.05/1.65 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f147])).
% 2.05/1.65 thf(f147,plain,(
% 2.05/1.65 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f146])).
% 2.05/1.65 thf(f146,plain,(
% 2.05/1.65 (mnot = (^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f2])).
% 2.05/1.65 thf(f2,axiom,(
% 2.05/1.65 (mnot = (^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',mnot_def)).
% 2.05/1.65 thf(f203,plain,(
% 2.05/1.65 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f181])).
% 2.05/1.65 thf(f181,plain,(
% 2.05/1.65 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f180])).
% 2.05/1.65 thf(f180,plain,(
% 2.05/1.65 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 2.05/1.65 inference(rectify,[status(thm)],[f4])).
% 2.05/1.65 thf(f4,axiom,(
% 2.05/1.65 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) | (X3 @ X2))) = mor)),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',mor_def)).
% 2.05/1.65 thf(f240,plain,(
% 2.05/1.65 ((mlocal @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v4)) @ (mor @ (mbox @ (mbox @ (mnot @ v2))) @ (mbox @ (mbox @ (mnot @ v4))))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f98])).
% 2.05/1.65 thf(f98,plain,(
% 2.05/1.65 ((mlocal @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v4)) @ (mor @ (mbox @ (mbox @ (mnot @ v2))) @ (mbox @ (mbox @ (mnot @ v4))))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f97])).
% 2.05/1.65 thf(f97,plain,(
% 2.05/1.65 (mlocal @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v4)) @ (mor @ (mbox @ (mbox @ (mnot @ v2))) @ (mbox @ (mbox @ (mnot @ v4)))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f56])).
% 2.05/1.65 thf(f56,axiom,(
% 2.05/1.65 (mlocal @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v4)) @ (mor @ (mbox @ (mbox @ (mnot @ v2))) @ (mbox @ (mbox @ (mnot @ v4)))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat46)).
% 2.05/1.65 thf(f1299,plain,(
% 2.05/1.65 spl0_2 | spl0_3 | spl0_17 | spl0_23),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f395,f1266,f1235,f1183,f1179])).
% 2.05/1.65 thf(f395,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = (v3 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ((v4 @ X3) = $true) | ((v1 @ mactual) = $false) | ((mrel @ mactual @ X2) = $false) | ($false = (v3 @ X1)) | ((mrel @ X2 @ X3) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f394])).
% 2.05/1.65 thf(f394,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((v1 @ mactual) = $false) | ($false = (v3 @ X1)) | ((mrel @ mactual @ X2) = $false) | ($true = ((mrel @ X2 @ X3) => (v4 @ X3))) | ($false = (v3 @ mactual))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f393])).
% 2.05/1.65 thf(f393,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X2) = $false) | ((v1 @ mactual) = $false) | ($false = (v3 @ X1)) | ($false = (v3 @ mactual)) | ($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v4 @ Y0))) @ X3)) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f392])).
% 2.05/1.65 thf(f392,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($false = (v3 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ((mrel @ mactual @ X2) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v4 @ Y0))))) | ((v1 @ mactual) = $false) | ($false = (v3 @ X1))) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f391])).
% 2.05/1.65 thf(f391,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (~ (v3 @ X1))) | ((mrel @ mactual @ X2) = $false) | ((v1 @ mactual) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v4 @ Y0))))) | ($false = (v3 @ mactual)) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f390])).
% 2.05/1.65 thf(f390,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((v1 @ mactual) = $false) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v4 @ Y0)))))) | ($true = (~ (v3 @ X1))) | ($false = (v3 @ mactual))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f389])).
% 2.05/1.65 thf(f389,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = (~ (v3 @ X1))) | (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X2) = $true) | ((v1 @ mactual) = $false) | ($false = (v3 @ mactual))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f388])).
% 2.05/1.65 thf(f388,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($false = (v3 @ mactual)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ((v1 @ mactual) = $false) | ($true = (~ (v3 @ X1))) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f387])).
% 2.05/1.65 thf(f387,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (~ (v3 @ mactual))) | ($true = (~ (v3 @ X1))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ((v1 @ mactual) = $false) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f386])).
% 2.05/1.65 thf(f386,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (~ (v3 @ X1))) = $true) | ($true = (~ (v3 @ mactual))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ((v1 @ mactual) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f385])).
% 2.05/1.65 thf(f385,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v3 @ Y0)))) @ X1) = $true) | ((v1 @ mactual) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ($true = (~ (v3 @ mactual)))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f384])).
% 2.05/1.65 thf(f384,plain,(
% 2.05/1.65 ((v1 @ mactual) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v3 @ Y0)))))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ($true = (~ (v3 @ mactual)))),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f383])).
% 2.05/1.65 thf(f383,plain,(
% 2.05/1.65 ((~ (v1 @ mactual)) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ($true = (~ (v3 @ mactual))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v3 @ Y0))))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f382])).
% 2.05/1.65 thf(f382,plain,(
% 2.05/1.65 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v3 @ Y0)))))) = $true) | ((~ (v1 @ mactual)) = $true) | ($true = (~ (v3 @ mactual)))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f381])).
% 2.05/1.65 thf(f381,plain,(
% 2.05/1.65 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v3 @ Y0)))))) | (~ (v3 @ mactual)))) | ((~ (v1 @ mactual)) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f380])).
% 2.05/1.65 thf(f380,plain,(
% 2.05/1.65 ($true = ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v3 @ Y0)))))) | (~ (v3 @ mactual))) | (~ (v1 @ mactual))))),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f266])).
% 2.05/1.65 thf(f266,plain,(
% 2.05/1.65 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v1) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v4)))))) = $true)),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f210,f192,f203,f194,f203,f194,f203,f213,f194,f213,f213])).
% 2.05/1.65 thf(f210,plain,(
% 2.05/1.65 ((mlocal @ (mor @ (mnot @ v1) @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v3)) @ (mbox @ (mbox @ v4)))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f171])).
% 2.05/1.65 thf(f171,plain,(
% 2.05/1.65 ((mlocal @ (mor @ (mnot @ v1) @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v3)) @ (mbox @ (mbox @ v4)))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f170])).
% 2.05/1.65 thf(f170,plain,(
% 2.05/1.65 (mlocal @ (mor @ (mnot @ v1) @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v3)) @ (mbox @ (mbox @ v4))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f45])).
% 2.05/1.65 thf(f45,axiom,(
% 2.05/1.65 (mlocal @ (mor @ (mnot @ v1) @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mnot @ v3)) @ (mbox @ (mbox @ v4))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat35)).
% 2.05/1.65 thf(f1291,plain,(
% 2.05/1.65 spl0_6 | spl0_18 | spl0_7 | spl0_15),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f540,f1227,f1197,f1240,f1194])).
% 2.05/1.65 thf(f540,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X6 : mworld,X4 : mworld,X5 : mworld] : (($false = (mrel @ X1 @ X5)) | ((v3 @ X5) = $false) | ($true = (v3 @ X4)) | ((mrel @ mactual @ X2) = $false) | ((v4 @ X6) = $false) | ((mrel @ X2 @ X4) = $false) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ((mrel @ X3 @ X6) = $false) | ($false = (mrel @ mactual @ X3))) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f539])).
% 2.05/1.65 thf(f539,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X6 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ X2 @ X4) = $false) | ($false = (mrel @ X1 @ X5)) | ((mrel @ mactual @ X2) = $false) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ mactual @ X3)) | ((v3 @ X5) = $false) | ($true = (v2 @ mactual)) | ($true = (v3 @ X4)) | ((mrel @ X3 @ X6) = $false) | ((~ (v4 @ X6)) = $true)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f538])).
% 2.05/1.65 thf(f538,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X6 : mworld,X4 : mworld,X5 : mworld] : ((((mrel @ X3 @ X6) => (~ (v4 @ X6))) = $true) | ($true = (v2 @ mactual)) | ($false = (mrel @ mactual @ X3)) | ((mrel @ mactual @ X2) = $false) | ($false = (mrel @ X1 @ X5)) | ((mrel @ mactual @ X1) = $false) | ($true = (v3 @ X4)) | ((v3 @ X5) = $false) | ((mrel @ X2 @ X4) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f537])).
% 2.05/1.65 thf(f537,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X6 : mworld,X4 : mworld,X5 : mworld] : (($true = (v2 @ mactual)) | ($false = (mrel @ X1 @ X5)) | ($false = (mrel @ mactual @ X3)) | ((v3 @ X5) = $false) | ((mrel @ mactual @ X1) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v4 @ Y0)))) @ X6)) | ((mrel @ X2 @ X4) = $false) | ($true = (v3 @ X4)) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f536])).
% 2.05/1.65 thf(f536,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ mactual @ X1) = $false) | ((v3 @ X5) = $false) | ((mrel @ mactual @ X2) = $false) | ($false = (mrel @ X1 @ X5)) | ($true = (v3 @ X4)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v4 @ Y0))))) = $true) | ((mrel @ X2 @ X4) = $false) | ($false = (mrel @ mactual @ X3)) | ($true = (v2 @ mactual))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f535])).
% 2.05/1.65 thf(f535,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = (mrel @ X1 @ X5)) | (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v4 @ Y0)))))) = $true) | ((mrel @ X2 @ X4) = $false) | ((mrel @ mactual @ X1) = $false) | ($true = (v3 @ X4)) | ($true = (v2 @ mactual)) | ((v3 @ X5) = $false) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f534])).
% 2.05/1.65 thf(f534,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : ((((mrel @ X2 @ X4) => (v3 @ X4)) = $true) | ($false = (mrel @ X1 @ X5)) | (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v4 @ Y0)))))) = $true) | ((v3 @ X5) = $false) | ((mrel @ mactual @ X1) = $false) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f533])).
% 2.05/1.65 thf(f533,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((~ (v3 @ X5)) = $true) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X2) = $false) | (((mrel @ X2 @ X4) => (v3 @ X4)) = $true) | ($false = (mrel @ X1 @ X5)) | ((mrel @ mactual @ X1) = $false) | (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v4 @ Y0)))))) = $true)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f532])).
% 2.05/1.65 thf(f532,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($true = ((mrel @ X1 @ X5) => (~ (v3 @ X5)))) | ($true = (v2 @ mactual)) | (((mrel @ X2 @ X4) => (v3 @ X4)) = $true) | ((mrel @ mactual @ X2) = $false) | (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v4 @ Y0)))))) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f531])).
% 2.05/1.65 thf(f531,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ mactual @ X2) = $false) | ((mrel @ mactual @ X1) = $false) | (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v4 @ Y0)))))) = $true) | ($true = (v2 @ mactual)) | (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0)))) @ X5) = $true) | (((mrel @ X2 @ X4) => (v3 @ X4)) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f530])).
% 2.05/1.65 thf(f530,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0))))) = $true) | ($true = (v2 @ mactual)) | (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v4 @ Y0)))))) = $true) | (((mrel @ X2 @ X4) => (v3 @ X4)) = $true) | ((mrel @ mactual @ X1) = $false) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f529])).
% 2.05/1.65 thf(f529,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))) @ X4)) | (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v4 @ Y0)))))) = $true) | ((mrel @ mactual @ X2) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0))))) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f528])).
% 2.05/1.65 thf(f528,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0))))) = $true) | ($true = (v2 @ mactual)) | (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v4 @ Y0)))))) = $true) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f527])).
% 2.05/1.65 thf(f527,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (v2 @ mactual)) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0))))) = $true) | (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v4 @ Y0)))))) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f526])).
% 2.05/1.65 thf(f526,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))))) | ($true = (v2 @ mactual)) | ($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))) @ X3)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0))))) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f525])).
% 2.05/1.65 thf(f525,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (v2 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) = $true) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))))) | ((mrel @ mactual @ X1) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0))))) = $true)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f524])).
% 2.05/1.65 thf(f524,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (v2 @ mactual)) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0)))))) = $true) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) = $true)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f523])).
% 2.05/1.65 thf(f523,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))) @ X2) = $true) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0)))))) = $true) | ($true = (v2 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f522])).
% 2.05/1.65 thf(f522,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ($true = (v2 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) = $true) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0)))))) = $true)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f521])).
% 2.05/1.65 thf(f521,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (v2 @ mactual)) | (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))) @ X1) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f520])).
% 2.05/1.65 thf(f520,plain,(
% 2.05/1.65 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ($true = (v2 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f519])).
% 2.05/1.65 thf(f519,plain,(
% 2.05/1.65 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))))) = $true) | ($true = (v2 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f518])).
% 2.05/1.65 thf(f518,plain,(
% 2.05/1.65 ($true = (v2 @ mactual)) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f517])).
% 2.05/1.65 thf(f517,plain,(
% 2.05/1.65 (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))) | (v2 @ mactual)) = $true)),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f286])).
% 2.05/1.65 thf(f286,plain,(
% 2.05/1.65 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v2 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v4))))))) = $true)),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f234,f192,f203,f203,f213,f213,f203,f213,f213,f194,f213,f213,f194])).
% 2.05/1.65 thf(f234,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v2 @ (mor @ (mbox @ (mbox @ v3)) @ (mor @ (mbox @ (mbox @ (mnot @ v3))) @ (mbox @ (mbox @ (mnot @ v4))))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f137])).
% 2.05/1.65 thf(f137,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v2 @ (mor @ (mbox @ (mbox @ v3)) @ (mor @ (mbox @ (mbox @ (mnot @ v3))) @ (mbox @ (mbox @ (mnot @ v4))))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f136])).
% 2.05/1.65 thf(f136,plain,(
% 2.05/1.65 (mlocal @ (mor @ v2 @ (mor @ (mbox @ (mbox @ v3)) @ (mor @ (mbox @ (mbox @ (mnot @ v3))) @ (mbox @ (mbox @ (mnot @ v4)))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f31])).
% 2.05/1.65 thf(f31,axiom,(
% 2.05/1.65 (mlocal @ (mor @ v2 @ (mor @ (mbox @ (mbox @ v3)) @ (mor @ (mbox @ (mbox @ (mnot @ v3))) @ (mbox @ (mbox @ (mnot @ v4)))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat21)).
% 2.05/1.65 thf(f1289,plain,(
% 2.05/1.65 spl0_21 | spl0_5 | spl0_23 | spl0_15),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f570,f1227,f1266,f1190,f1253])).
% 2.05/1.65 thf(f570,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = (v2 @ mactual)) | ((mrel @ X2 @ X3) = $false) | ($false = (v3 @ X1)) | ((v1 @ mactual) = $true) | ((mrel @ mactual @ X2) = $false) | ($true = (v3 @ X3)) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f569])).
% 2.05/1.65 thf(f569,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X2) = $false) | ((mrel @ mactual @ X1) = $false) | ($false = (v2 @ mactual)) | ($true = ((mrel @ X2 @ X3) => (v3 @ X3))) | ($false = (v3 @ X1)) | ((v1 @ mactual) = $true)) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f568])).
% 2.05/1.65 thf(f568,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((v1 @ mactual) = $true) | ((mrel @ mactual @ X2) = $false) | ($true = (~ (v3 @ X1))) | ($false = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ($true = ((mrel @ X2 @ X3) => (v3 @ X3)))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f567])).
% 2.05/1.65 thf(f567,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((mrel @ mactual @ X2) = $false) | ((v1 @ mactual) = $true) | ($false = (v2 @ mactual)) | ($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))) @ X3)) | ($true = (~ (v3 @ X1)))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f566])).
% 2.05/1.65 thf(f566,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($false = (v2 @ mactual)) | ((v1 @ mactual) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))) = $true) | ($true = (~ (v3 @ X1))) | ((mrel @ mactual @ X1) = $false) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f565])).
% 2.05/1.65 thf(f565,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($false = (v2 @ mactual)) | ((v1 @ mactual) = $true) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))))) | ($true = (~ (v3 @ X1)))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f564])).
% 2.05/1.65 thf(f564,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($false = (v2 @ mactual)) | (((mrel @ mactual @ X1) => (~ (v3 @ X1))) = $true) | ((v1 @ mactual) = $true) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f563])).
% 2.05/1.65 thf(f563,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((v1 @ mactual) = $true) | (((mrel @ mactual @ X1) => (~ (v3 @ X1))) = $true) | (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))) @ X2) = $true) | ($false = (v2 @ mactual))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f562])).
% 2.05/1.65 thf(f562,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | (((mrel @ mactual @ X1) => (~ (v3 @ X1))) = $true) | ((v1 @ mactual) = $true) | ($false = (v2 @ mactual))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f561])).
% 2.05/1.65 thf(f561,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v3 @ Y0)))) @ X1) = $true) | ((v1 @ mactual) = $true) | ($false = (v2 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f560])).
% 2.05/1.65 thf(f560,plain,(
% 2.05/1.65 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v3 @ Y0)))))) | ($false = (v2 @ mactual)) | ((v1 @ mactual) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true)),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f559])).
% 2.05/1.65 thf(f559,plain,(
% 2.05/1.65 ((v1 @ mactual) = $true) | ((~ (v2 @ mactual)) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v3 @ Y0)))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f558])).
% 2.05/1.65 thf(f558,plain,(
% 2.05/1.65 ((v1 @ mactual) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v3 @ Y0)))))) = $true) | ((~ (v2 @ mactual)) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f557])).
% 2.05/1.65 thf(f557,plain,(
% 2.05/1.65 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v3 @ Y0)))))) | (~ (v2 @ mactual)))) | ((v1 @ mactual) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f556])).
% 2.05/1.65 thf(f556,plain,(
% 2.05/1.65 ($true = ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v3 @ Y0)))))) | (~ (v2 @ mactual))) | (v1 @ mactual)))),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f287])).
% 2.05/1.65 thf(f287,plain,(
% 2.05/1.65 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v1 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v2) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v3)))))) = $true)),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f235,f192,f203,f203,f194,f203,f213,f194,f213,f213])).
% 2.05/1.65 thf(f235,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v1 @ (mor @ (mnot @ v2) @ (mor @ (mbox @ (mnot @ v3)) @ (mbox @ (mbox @ v3)))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f68])).
% 2.05/1.65 thf(f68,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v1 @ (mor @ (mnot @ v2) @ (mor @ (mbox @ (mnot @ v3)) @ (mbox @ (mbox @ v3)))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f67])).
% 2.05/1.65 thf(f67,plain,(
% 2.05/1.65 (mlocal @ (mor @ v1 @ (mor @ (mnot @ v2) @ (mor @ (mbox @ (mnot @ v3)) @ (mbox @ (mbox @ v3))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f18])).
% 2.05/1.65 thf(f18,axiom,(
% 2.05/1.65 (mlocal @ (mor @ v1 @ (mor @ (mnot @ v2) @ (mor @ (mbox @ (mnot @ v3)) @ (mbox @ (mbox @ v3))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat8)).
% 2.05/1.65 thf(f1286,plain,(
% 2.05/1.65 spl0_18 | spl0_9 | spl0_11 | spl0_15),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f618,f1227,f1211,f1204,f1240])).
% 2.05/1.65 thf(f618,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ X3 @ X4) = $false) | ((v2 @ X5) = $false) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ mactual @ X3)) | ((mrel @ mactual @ X2) = $false) | ((mrel @ X2 @ X5) = $false) | ($false = (v1 @ X1)) | ($true = (v3 @ X4))) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f617])).
% 2.05/1.65 thf(f617,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((~ (v2 @ X5)) = $true) | ((mrel @ X3 @ X4) = $false) | ((mrel @ mactual @ X2) = $false) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ((mrel @ X2 @ X5) = $false) | ($false = (mrel @ mactual @ X3)) | ($false = (v1 @ X1)) | ($true = (v3 @ X4))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f616])).
% 2.05/1.65 thf(f616,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ X3 @ X4) = $false) | ($true = (v3 @ X4)) | ((mrel @ mactual @ X1) = $false) | ($true = ((mrel @ X2 @ X5) => (~ (v2 @ X5)))) | ($false = (v1 @ X1)) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X2) = $false) | ($false = (mrel @ mactual @ X3))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f615])).
% 2.05/1.65 thf(f615,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ mactual @ X2) = $false) | ($false = (mrel @ mactual @ X3)) | ($false = (v1 @ X1)) | ($true = (v2 @ mactual)) | (((mrel @ X3 @ X4) => (v3 @ X4)) = $true) | ($true = ((mrel @ X2 @ X5) => (~ (v2 @ X5)))) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f614])).
% 2.05/1.65 thf(f614,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : ((((mrel @ X3 @ X4) => (v3 @ X4)) = $true) | ((mrel @ mactual @ X1) = $false) | ((mrel @ mactual @ X2) = $false) | ($true = (v2 @ mactual)) | ($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v2 @ Y0)))) @ X5)) | ($false = (mrel @ mactual @ X3)) | ($false = (v1 @ X1))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f613])).
% 2.05/1.65 thf(f613,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = (mrel @ mactual @ X3)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v2 @ Y0))))) = $true) | ((mrel @ mactual @ X2) = $false) | ($false = (v1 @ X1)) | (((mrel @ X3 @ X4) => (v3 @ X4)) = $true) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f612])).
% 2.05/1.65 thf(f612,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((mrel @ mactual @ X1) = $false) | ($false = (v1 @ X1)) | ($true = ((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v3 @ Y0))) @ X4)) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X2) = $false) | ($false = (mrel @ mactual @ X3)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v2 @ Y0))))) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f611])).
% 2.05/1.65 thf(f611,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X2) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v3 @ Y0))))) | ($true = (v2 @ mactual)) | ($false = (v1 @ X1)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v2 @ Y0))))) = $true) | ($false = (mrel @ mactual @ X3)) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f610])).
% 2.05/1.65 thf(f610,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = (v1 @ X1)) | ((mrel @ mactual @ X2) = $false) | ((mrel @ mactual @ X1) = $false) | ($true = ((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v3 @ Y0)))))) | ($true = (v2 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v2 @ Y0))))) = $true)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f609])).
% 2.05/1.65 thf(f609,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))) @ X3)) | ($false = (v1 @ X1)) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X2) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v2 @ Y0))))) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f608])).
% 2.05/1.65 thf(f608,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ((mrel @ mactual @ X2) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v2 @ Y0))))) = $true) | ($true = (v2 @ mactual)) | ($false = (v1 @ X1))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f607])).
% 2.05/1.65 thf(f607,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = (v2 @ mactual)) | ($false = (v1 @ X1)) | (((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v2 @ Y0)))))) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f606])).
% 2.05/1.65 thf(f606,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = (v2 @ mactual)) | ($false = (v1 @ X1)) | ($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1))))))) @ X2)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f605])).
% 2.05/1.65 thf(f605,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($false = (v1 @ X1)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) = $true) | ($true = (v2 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f604])).
% 2.05/1.65 thf(f604,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = (~ (v1 @ X1))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) = $true) | ($true = (v2 @ mactual))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f603])).
% 2.05/1.65 thf(f603,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (v2 @ mactual)) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))) = $true) | ((mrel @ mactual @ X1) = $false) | ($true = (~ (v1 @ X1)))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f602])).
% 2.05/1.65 thf(f602,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (~ (v1 @ X1)))) | ($true = (v2 @ mactual)) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))) = $true)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f601])).
% 2.05/1.65 thf(f601,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0)))) @ X1)) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))) = $true) | ($true = (v2 @ mactual))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f600])).
% 2.05/1.65 thf(f600,plain,(
% 2.05/1.65 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0)))))) | ($true = (v2 @ mactual)) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f599])).
% 2.05/1.65 thf(f599,plain,(
% 2.05/1.65 ($true = (v2 @ mactual)) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0)))))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f598])).
% 2.05/1.65 thf(f598,plain,(
% 2.05/1.65 ($true = ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (v1 @ Y0)))))) | (v2 @ mactual)))),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f284])).
% 2.05/1.65 thf(f284,plain,(
% 2.05/1.65 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v2 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v1)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v2))))))) = $true)),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f232,f192,f203,f203,f213,f194,f203,f213,f213,f213,f213,f194])).
% 2.05/1.65 thf(f232,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v2 @ (mor @ (mbox @ (mnot @ v1)) @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ (mnot @ v2))))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f116])).
% 2.05/1.65 thf(f116,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v2 @ (mor @ (mbox @ (mnot @ v1)) @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ (mnot @ v2))))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f115])).
% 2.05/1.65 thf(f115,plain,(
% 2.05/1.65 (mlocal @ (mor @ v2 @ (mor @ (mbox @ (mnot @ v1)) @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ (mnot @ v2)))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f30])).
% 2.05/1.65 thf(f30,axiom,(
% 2.05/1.65 (mlocal @ (mor @ v2 @ (mor @ (mbox @ (mnot @ v1)) @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ (mnot @ v2)))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat20)).
% 2.05/1.65 thf(f1282,plain,(
% 2.05/1.65 spl0_3 | spl0_7 | spl0_17 | spl0_18),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f695,f1240,f1235,f1197,f1183])).
% 2.05/1.65 thf(f695,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((mrel @ mactual @ X2) = $false) | ($false = (mrel @ X1 @ X3)) | ((mrel @ X2 @ X4) = $false) | ($false = (v3 @ X3)) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ((v1 @ mactual) = $false) | ($true = (v4 @ X4))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f694])).
% 2.05/1.65 thf(f694,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = (mrel @ X1 @ X3)) | ((mrel @ mactual @ X2) = $false) | (((mrel @ X2 @ X4) => (v4 @ X4)) = $true) | ($true = (v2 @ mactual)) | ($false = (v3 @ X3)) | ((mrel @ mactual @ X1) = $false) | ((v1 @ mactual) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f693])).
% 2.05/1.65 thf(f693,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((mrel @ mactual @ X2) = $false) | ((v1 @ mactual) = $false) | ($false = (v3 @ X3)) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ X1 @ X3)) | ($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v4 @ Y0))) @ X4))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f692])).
% 2.05/1.65 thf(f692,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v4 @ Y0))))) | ($false = (mrel @ X1 @ X3)) | ((mrel @ mactual @ X2) = $false) | ((mrel @ mactual @ X1) = $false) | ($false = (v3 @ X3)) | ($true = (v2 @ mactual)) | ((v1 @ mactual) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f691])).
% 2.05/1.65 thf(f691,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = (v3 @ X3)) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v4 @ Y0)))))) | ($false = (mrel @ X1 @ X3)) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ((v1 @ mactual) = $false)) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f690])).
% 2.05/1.65 thf(f690,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((v1 @ mactual) = $false) | ($false = (mrel @ X1 @ X3)) | ($true = (~ (v3 @ X3))) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v4 @ Y0)))))) | ($true = (v2 @ mactual))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f689])).
% 2.05/1.65 thf(f689,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((mrel @ X1 @ X3) => (~ (v3 @ X3))) = $true) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v4 @ Y0)))))) | ((mrel @ mactual @ X1) = $false) | ((v1 @ mactual) = $false) | ($true = (v2 @ mactual))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f688])).
% 2.05/1.65 thf(f688,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0)))) @ X3)) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v4 @ Y0)))))) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ((v1 @ mactual) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f687])).
% 2.05/1.65 thf(f687,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0))))) = $true) | ($true = (v2 @ mactual)) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v4 @ Y0)))))) | ((v1 @ mactual) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f686])).
% 2.05/1.65 thf(f686,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (v2 @ mactual)) | ((v1 @ mactual) = $false) | ((mrel @ mactual @ X1) = $false) | (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X2) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0))))) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f685])).
% 2.05/1.65 thf(f685,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0))))) = $true) | ((v1 @ mactual) = $false)) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f684])).
% 2.05/1.65 thf(f684,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ((~ (v1 @ mactual)) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0))))) = $true)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f683])).
% 2.05/1.65 thf(f683,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0)))))) = $true) | ((~ (v1 @ mactual)) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ($true = (v2 @ mactual))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f682])).
% 2.05/1.65 thf(f682,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))) @ X1) = $true) | ((~ (v1 @ mactual)) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ($true = (v2 @ mactual))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f681])).
% 2.05/1.65 thf(f681,plain,(
% 2.05/1.65 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))))) | ((~ (v1 @ mactual)) = $true) | ($true = (v2 @ mactual)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f680])).
% 2.05/1.65 thf(f680,plain,(
% 2.05/1.65 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))) | ($true = (v2 @ mactual)) | ((~ (v1 @ mactual)) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f679])).
% 2.05/1.65 thf(f679,plain,(
% 2.05/1.65 ($true = (v2 @ mactual)) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | (~ (v1 @ mactual))) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f678])).
% 2.05/1.65 thf(f678,plain,(
% 2.05/1.65 ($true = ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | (~ (v1 @ mactual))) | (v2 @ mactual)))),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f253])).
% 2.05/1.65 thf(f253,plain,(
% 2.05/1.65 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v2 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v1) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v4)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3))))))) = $true)),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f191,f192,f203,f203,f194,f203,f213,f213,f213,f213,f194])).
% 2.05/1.65 thf(f191,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v2 @ (mor @ (mnot @ v1) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v3))))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f122])).
% 2.05/1.65 thf(f122,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v2 @ (mor @ (mnot @ v1) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v3))))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f121])).
% 2.05/1.65 thf(f121,plain,(
% 2.05/1.65 (mlocal @ (mor @ v2 @ (mor @ (mnot @ v1) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v3)))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f27])).
% 2.05/1.65 thf(f27,axiom,(
% 2.05/1.65 (mlocal @ (mor @ v2 @ (mor @ (mnot @ v1) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v3)))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat17)).
% 2.05/1.65 thf(f1280,plain,(
% 2.05/1.65 spl0_19 | spl0_21 | spl0_3 | spl0_2),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f726,f1179,f1183,f1253,f1245])).
% 2.05/1.65 thf(f726,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = (mrel @ mactual @ X3)) | ($true = (v1 @ X2)) | ((mrel @ X3 @ X4) = $false) | ((mrel @ mactual @ X1) = $false) | ($false = (v2 @ mactual)) | ($true = (v4 @ X4)) | ($false = (v3 @ mactual)) | ((mrel @ X1 @ X2) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f725])).
% 2.05/1.65 thf(f725,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((mrel @ X1 @ X2) = $false) | ($false = (v3 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ($true = (v1 @ X2)) | ($false = (mrel @ mactual @ X3)) | ($false = (v2 @ mactual)) | (((mrel @ X3 @ X4) => (v4 @ X4)) = $true)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f724])).
% 2.05/1.65 thf(f724,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v4 @ Y0))) @ X4)) | ($false = (v2 @ mactual)) | ((mrel @ X1 @ X2) = $false) | ($false = (mrel @ mactual @ X3)) | ($false = (v3 @ mactual)) | ($true = (v1 @ X2)) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f723])).
% 2.05/1.65 thf(f723,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = (v1 @ X2)) | ($false = (v3 @ mactual)) | ((mrel @ X1 @ X2) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v4 @ Y0))))) | ($false = (v2 @ mactual)) | ($false = (mrel @ mactual @ X3))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f722])).
% 2.05/1.65 thf(f722,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ X1 @ X2) = $false) | ($true = (v1 @ X2)) | ($false = (v2 @ mactual)) | ($true = ((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v4 @ Y0)))))) | ((mrel @ mactual @ X1) = $false) | ($false = (v3 @ mactual))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f721])).
% 2.05/1.65 thf(f721,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = (v2 @ mactual)) | ($false = (v3 @ mactual)) | ($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X3)) | ((mrel @ mactual @ X1) = $false) | ($true = (v1 @ X2)) | ((mrel @ X1 @ X2) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f720])).
% 2.05/1.65 thf(f720,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($false = (v2 @ mactual)) | ((mrel @ X1 @ X2) = $false) | ($true = (v1 @ X2)) | ($false = (v3 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f719])).
% 2.05/1.65 thf(f719,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ X1 @ X2) => (v1 @ X2))) | ($false = (v3 @ mactual)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ((mrel @ mactual @ X1) = $false) | ($false = (v2 @ mactual))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f718])).
% 2.05/1.65 thf(f718,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($false = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ($false = (v3 @ mactual)) | ($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v1 @ Y0))) @ X2)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f717])).
% 2.05/1.65 thf(f717,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($false = (v2 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v1 @ Y0)))) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ($false = (v3 @ mactual)) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f716])).
% 2.05/1.65 thf(f716,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($false = (v2 @ mactual)) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v1 @ Y0))))) = $true) | ($false = (v3 @ mactual)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f715])).
% 2.05/1.65 thf(f715,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ($false = (v2 @ mactual)) | (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1)))))) @ X1) = $true) | ($false = (v3 @ mactual))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f714])).
% 2.05/1.65 thf(f714,plain,(
% 2.05/1.65 ($false = (v2 @ mactual)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1)))))))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ($false = (v3 @ mactual))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f713])).
% 2.05/1.65 thf(f713,plain,(
% 2.05/1.65 ($false = (v2 @ mactual)) | ($false = (v3 @ mactual)) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1)))))))))),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f712])).
% 2.05/1.65 thf(f712,plain,(
% 2.05/1.65 ($true = (~ (v3 @ mactual))) | ($false = (v2 @ mactual)) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1)))))))))),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f711])).
% 2.05/1.65 thf(f711,plain,(
% 2.05/1.65 ((~ (v2 @ mactual)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1))))))))) | ($true = (~ (v3 @ mactual)))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f710])).
% 2.05/1.65 thf(f710,plain,(
% 2.05/1.65 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1)))))))) | (~ (v3 @ mactual)))) | ((~ (v2 @ mactual)) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f709])).
% 2.05/1.65 thf(f709,plain,(
% 2.05/1.65 ($true = ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v1 @ Y1)))))))) | (~ (v3 @ mactual))) | (~ (v2 @ mactual))))),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f264])).
% 2.05/1.65 thf(f264,plain,(
% 2.05/1.65 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v2) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v1)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v4)))))))),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f208,f192,f203,f194,f203,f194,f203,f213,f213,f213,f213])).
% 2.05/1.65 thf(f208,plain,(
% 2.05/1.65 ((mlocal @ (mor @ (mnot @ v2) @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mbox @ v1)) @ (mbox @ (mbox @ v4)))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f179])).
% 2.05/1.65 thf(f179,plain,(
% 2.05/1.65 ((mlocal @ (mor @ (mnot @ v2) @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mbox @ v1)) @ (mbox @ (mbox @ v4)))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f178])).
% 2.05/1.65 thf(f178,plain,(
% 2.05/1.65 (mlocal @ (mor @ (mnot @ v2) @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mbox @ v1)) @ (mbox @ (mbox @ v4))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f50])).
% 2.05/1.65 thf(f50,axiom,(
% 2.05/1.65 (mlocal @ (mor @ (mnot @ v2) @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mbox @ v1)) @ (mbox @ (mbox @ v4))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat40)).
% 2.05/1.65 thf(f1277,plain,(
% 2.05/1.65 spl0_7 | spl0_5 | spl0_2 | spl0_18),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f767,f1240,f1179,f1190,f1197])).
% 2.05/1.65 thf(f767,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($false = (v3 @ X2)) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ($false = (v3 @ mactual)) | ((v1 @ mactual) = $true) | ((mrel @ X1 @ X2) = $false)) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f766])).
% 2.05/1.65 thf(f766,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($false = (v3 @ mactual)) | ((mrel @ X1 @ X2) = $false) | ($true = (v2 @ mactual)) | ($true = (~ (v3 @ X2))) | ((v1 @ mactual) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f765])).
% 2.05/1.65 thf(f765,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($false = (v3 @ mactual)) | ($true = (v2 @ mactual)) | ((v1 @ mactual) = $true) | ((mrel @ mactual @ X1) = $false) | ($true = ((mrel @ X1 @ X2) => (~ (v3 @ X2))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f764])).
% 2.05/1.65 thf(f764,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0)))) @ X2)) | ($true = (v2 @ mactual)) | ((v1 @ mactual) = $true) | ($false = (v3 @ mactual)) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f763])).
% 2.05/1.65 thf(f763,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0))))) = $true) | ((mrel @ mactual @ X1) = $false) | ((v1 @ mactual) = $true) | ($false = (v3 @ mactual)) | ($true = (v2 @ mactual))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f762])).
% 2.05/1.65 thf(f762,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (((v1 @ mactual) = $true) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0)))))) = $true) | ($false = (v3 @ mactual)) | ($true = (v2 @ mactual))) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f761])).
% 2.05/1.65 thf(f761,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (v2 @ mactual)) | ($true = (~ (v3 @ mactual))) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v3 @ Y0)))))) = $true) | ((v1 @ mactual) = $true)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f760])).
% 2.05/1.65 thf(f760,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (v2 @ mactual)) | (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))) @ X1) = $true) | ((v1 @ mactual) = $true) | ($true = (~ (v3 @ mactual)))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f759])).
% 2.05/1.65 thf(f759,plain,(
% 2.05/1.65 ((v1 @ mactual) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))))) | ($true = (v2 @ mactual)) | ($true = (~ (v3 @ mactual)))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f758])).
% 2.05/1.65 thf(f758,plain,(
% 2.05/1.65 ((v1 @ mactual) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))) | (~ (v3 @ mactual)))) | ($true = (v2 @ mactual))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f757])).
% 2.05/1.65 thf(f757,plain,(
% 2.05/1.65 ((v1 @ mactual) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))) | (~ (v3 @ mactual))) | (v2 @ mactual)) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f756])).
% 2.05/1.65 thf(f756,plain,(
% 2.05/1.65 ($true = ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))) | (~ (v3 @ mactual))) | (v2 @ mactual)) | (v1 @ mactual)))),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f272])).
% 2.05/1.65 thf(f272,plain,(
% 2.05/1.65 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v1 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v2 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3))))))))),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f219,f192,f203,f203,f203,f194,f213,f213,f194])).
% 2.05/1.65 thf(f219,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v1 @ (mor @ v2 @ (mor @ (mnot @ v3) @ (mbox @ (mbox @ (mnot @ v3))))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f76])).
% 2.05/1.65 thf(f76,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v1 @ (mor @ v2 @ (mor @ (mnot @ v3) @ (mbox @ (mbox @ (mnot @ v3))))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f75])).
% 2.05/1.65 thf(f75,plain,(
% 2.05/1.65 (mlocal @ (mor @ v1 @ (mor @ v2 @ (mor @ (mnot @ v3) @ (mbox @ (mbox @ (mnot @ v3)))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f12])).
% 2.05/1.65 thf(f12,axiom,(
% 2.05/1.65 (mlocal @ (mor @ v1 @ (mor @ v2 @ (mor @ (mnot @ v3) @ (mbox @ (mbox @ (mnot @ v3)))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat2)).
% 2.05/1.65 thf(f1275,plain,(
% 2.05/1.65 spl0_12 | spl0_5 | spl0_3 | spl0_15),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f795,f1227,f1183,f1190,f1215])).
% 2.05/1.65 thf(f795,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((v1 @ mactual) = $true) | ((mrel @ mactual @ X1) = $false) | ((mrel @ mactual @ X2) = $false) | ($true = (v3 @ mactual)) | ($true = (v3 @ X4)) | ((mrel @ X2 @ X4) = $false) | ((v4 @ X3) = $true) | ($false = (mrel @ X1 @ X3))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f794])).
% 2.05/1.65 thf(f794,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((v4 @ X3) = $true) | ($true = (v3 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ X1 @ X3)) | ((mrel @ mactual @ X2) = $false) | ((v1 @ mactual) = $true) | (((mrel @ X2 @ X4) => (v3 @ X4)) = $true)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f793])).
% 2.05/1.65 thf(f793,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((mrel @ X1 @ X3) => (v4 @ X3))) | ($true = (v3 @ mactual)) | (((mrel @ X2 @ X4) => (v3 @ X4)) = $true) | ((mrel @ mactual @ X2) = $false) | ((v1 @ mactual) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f792])).
% 2.05/1.65 thf(f792,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (v3 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ($true = ((mrel @ X1 @ X3) => (v4 @ X3))) | ((mrel @ mactual @ X2) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))) @ X4)) | ((v1 @ mactual) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f791])).
% 2.05/1.65 thf(f791,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))) = $true) | ((mrel @ mactual @ X1) = $false) | ((mrel @ mactual @ X2) = $false) | ((v1 @ mactual) = $true) | ($true = (v3 @ mactual)) | ($true = ((mrel @ X1 @ X3) => (v4 @ X3)))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f790])).
% 2.05/1.65 thf(f790,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X2) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))) = $true) | ((mrel @ mactual @ X1) = $false) | ((v1 @ mactual) = $true) | (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))) @ X3) = $true) | ($true = (v3 @ mactual))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f789])).
% 2.05/1.65 thf(f789,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))) = $true) | ($true = (v3 @ mactual)) | ((mrel @ mactual @ X2) = $false) | ((mrel @ mactual @ X1) = $false) | ((v1 @ mactual) = $true)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f788])).
% 2.05/1.65 thf(f788,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X2) = $false) | ($true = (v3 @ mactual)) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))))) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))) = $true) | ((v1 @ mactual) = $true)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f787])).
% 2.05/1.65 thf(f787,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))))) | ((v1 @ mactual) = $true) | ($true = (v3 @ mactual)) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))))) = $true)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f786])).
% 2.05/1.65 thf(f786,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((v1 @ mactual) = $true) | ($true = (v3 @ mactual)) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))))) = $true) | (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))) @ X2) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f785])).
% 2.05/1.65 thf(f785,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (v3 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v4 @ Y0))))) = $true) | ((v1 @ mactual) = $true)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f784])).
% 2.05/1.65 thf(f784,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X1) = $true) | ((v1 @ mactual) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ($true = (v3 @ mactual))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f783])).
% 2.05/1.65 thf(f783,plain,(
% 2.05/1.65 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ((v1 @ mactual) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ($true = (v3 @ mactual))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f782])).
% 2.05/1.65 thf(f782,plain,(
% 2.05/1.65 ($true = (v3 @ mactual)) | ((v1 @ mactual) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f781])).
% 2.05/1.65 thf(f781,plain,(
% 2.05/1.65 ((v1 @ mactual) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))) | (v3 @ mactual)) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f780])).
% 2.05/1.65 thf(f780,plain,(
% 2.05/1.65 (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))) | (v3 @ mactual)) | (v1 @ mactual)) = $true)),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f281])).
% 2.05/1.65 thf(f281,plain,(
% 2.05/1.65 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v1 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v3 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v4)))))))),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f228,f192,f203,f203,f203,f213,f213,f213,f213])).
% 2.05/1.65 thf(f228,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v1 @ (mor @ v3 @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ v4)))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f112])).
% 2.05/1.65 thf(f112,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v1 @ (mor @ v3 @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ v4)))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f111])).
% 2.05/1.65 thf(f111,plain,(
% 2.05/1.65 (mlocal @ (mor @ v1 @ (mor @ v3 @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ v4))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f15])).
% 2.05/1.65 thf(f15,axiom,(
% 2.05/1.65 (mlocal @ (mor @ v1 @ (mor @ v3 @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ v4))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat5)).
% 2.05/1.65 thf(f1274,plain,(
% 2.05/1.65 spl0_7 | spl0_17 | spl0_8 | spl0_2),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f815,f1179,f1201,f1235,f1197])).
% 2.05/1.65 thf(f815,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = (v3 @ mactual)) | ((v1 @ mactual) = $false) | ($false = (mrel @ X1 @ X4)) | ((mrel @ X2 @ X3) = $false) | ($false = (v1 @ X4)) | ((mrel @ mactual @ X1) = $false) | ($false = (v3 @ X3)) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f814])).
% 2.05/1.65 thf(f814,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((v1 @ mactual) = $false) | ((mrel @ X2 @ X3) = $false) | ($true = (~ (v1 @ X4))) | ((mrel @ mactual @ X2) = $false) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ X1 @ X4)) | ($false = (v3 @ X3)) | ($false = (v3 @ mactual))) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f813])).
% 2.05/1.65 thf(f813,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = (mrel @ X1 @ X4)) | ($false = (v3 @ mactual)) | ((mrel @ mactual @ X2) = $false) | ($true = (~ (v3 @ X3))) | ((v1 @ mactual) = $false) | ((mrel @ mactual @ X1) = $false) | ($true = (~ (v1 @ X4))) | ((mrel @ X2 @ X3) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f812])).
% 2.05/1.65 thf(f812,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = (v3 @ mactual)) | ((mrel @ mactual @ X2) = $false) | ((mrel @ mactual @ X1) = $false) | ($true = ((mrel @ X1 @ X4) => (~ (v1 @ X4)))) | ((v1 @ mactual) = $false) | ((mrel @ X2 @ X3) = $false) | ($true = (~ (v3 @ X3)))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f811])).
% 2.05/1.65 thf(f811,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))) @ X4)) | ($false = (v3 @ mactual)) | ((v1 @ mactual) = $false) | ((mrel @ mactual @ X1) = $false) | ((mrel @ X2 @ X3) = $false) | ((mrel @ mactual @ X2) = $false) | ($true = (~ (v3 @ X3)))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f810])).
% 2.05/1.65 thf(f810,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X2) = $false) | ((v1 @ mactual) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0))))) = $true) | ((mrel @ mactual @ X1) = $false) | ((mrel @ X2 @ X3) = $false) | ($true = (~ (v3 @ X3))) | ($false = (v3 @ mactual))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f809])).
% 2.05/1.65 thf(f809,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = (v3 @ mactual)) | ((mrel @ mactual @ X2) = $false) | ((mrel @ X2 @ X3) = $false) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))))) = $true) | ($true = (~ (v3 @ X3))) | ((v1 @ mactual) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f808])).
% 2.05/1.65 thf(f808,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = (v3 @ mactual)) | ($true = ((mrel @ X2 @ X3) => (~ (v3 @ X3)))) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))))) = $true) | ((mrel @ mactual @ X2) = $false) | ((v1 @ mactual) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f807])).
% 2.05/1.65 thf(f807,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))))) = $true) | ((v1 @ mactual) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v3 @ Y0)))) @ X3)) | ($false = (v3 @ mactual)) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f806])).
% 2.05/1.65 thf(f806,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($false = (v3 @ mactual)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v3 @ Y0)))))) | ((mrel @ mactual @ X2) = $false) | ((v1 @ mactual) = $false) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))))) = $true)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f805])).
% 2.05/1.65 thf(f805,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($false = (v3 @ mactual)) | ((v1 @ mactual) = $false) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v3 @ Y0))))))) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))))) = $true)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f804])).
% 2.05/1.65 thf(f804,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))) @ X2) = $true) | ($false = (v3 @ mactual)) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))))) = $true) | ((v1 @ mactual) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f803])).
% 2.05/1.65 thf(f803,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))))) | ($false = (v3 @ mactual)) | (((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v1 @ Y0)))))) = $true) | ((v1 @ mactual) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f802])).
% 2.05/1.65 thf(f802,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (((v1 @ mactual) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))))) | ($false = (v3 @ mactual)) | ($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))) @ X1))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f801])).
% 2.05/1.65 thf(f801,plain,(
% 2.05/1.65 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))))) | ((v1 @ mactual) = $false) | ($false = (v3 @ mactual)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))))),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f800])).
% 2.05/1.65 thf(f800,plain,(
% 2.05/1.65 ($true = (~ (v3 @ mactual))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1))))))))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))))) | ((v1 @ mactual) = $false)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f799])).
% 2.05/1.65 thf(f799,plain,(
% 2.05/1.65 ((v1 @ mactual) = $false) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))))) = $true) | ($true = (~ (v3 @ mactual)))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f798])).
% 2.05/1.65 thf(f798,plain,(
% 2.05/1.65 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))))) | (~ (v3 @ mactual)))) | ((v1 @ mactual) = $false)),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f797])).
% 2.05/1.65 thf(f797,plain,(
% 2.05/1.65 ((~ (v1 @ mactual)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))))) | (~ (v3 @ mactual))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f796])).
% 2.05/1.65 thf(f796,plain,(
% 2.05/1.65 (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v3 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))))) | (~ (v3 @ mactual))) | (~ (v1 @ mactual))) = $true)),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f268])).
% 2.05/1.65 thf(f268,plain,(
% 2.05/1.65 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v1) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v1))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v3))))))) = $true)),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f212,f192,f203,f194,f203,f194,f203,f213,f213,f194,f213,f213,f194])).
% 2.05/1.65 thf(f212,plain,(
% 2.05/1.65 ((mlocal @ (mor @ (mnot @ v1) @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mbox @ (mnot @ v1))) @ (mbox @ (mbox @ (mnot @ v3))))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f80])).
% 2.05/1.65 thf(f80,plain,(
% 2.05/1.65 ((mlocal @ (mor @ (mnot @ v1) @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mbox @ (mnot @ v1))) @ (mbox @ (mbox @ (mnot @ v3))))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f79])).
% 2.05/1.65 thf(f79,plain,(
% 2.05/1.65 (mlocal @ (mor @ (mnot @ v1) @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mbox @ (mnot @ v1))) @ (mbox @ (mbox @ (mnot @ v3)))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f46])).
% 2.05/1.65 thf(f46,axiom,(
% 2.05/1.65 (mlocal @ (mor @ (mnot @ v1) @ (mor @ (mnot @ v3) @ (mor @ (mbox @ (mbox @ (mnot @ v1))) @ (mbox @ (mbox @ (mnot @ v3)))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat36)).
% 2.05/1.65 thf(f1272,plain,(
% 2.05/1.65 spl0_24 | spl0_13 | spl0_18 | spl0_15),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f852,f1227,f1240,f1219,f1270])).
% 2.05/1.65 thf(f852,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ mactual @ X1) = $false) | ((mrel @ mactual @ X2) = $false) | ((mrel @ X2 @ X4) = $false) | ($false = (mrel @ mactual @ X3)) | ((v3 @ X5) = $true) | ((v2 @ X4) = $true) | ((v4 @ X1) = $true) | ((mrel @ X3 @ X5) = $false) | ($true = (v2 @ mactual))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f851])).
% 2.05/1.65 thf(f851,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((v4 @ X1) = $true) | ($true = ((mrel @ X3 @ X5) => (v3 @ X5))) | ((v2 @ X4) = $true) | ((mrel @ mactual @ X2) = $false) | ($false = (mrel @ mactual @ X3)) | ($true = (v2 @ mactual)) | ((mrel @ X2 @ X4) = $false) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f850])).
% 2.05/1.65 thf(f850,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = (mrel @ mactual @ X3)) | ((v4 @ X1) = $true) | ((mrel @ mactual @ X2) = $false) | ((v2 @ X4) = $true) | ((mrel @ mactual @ X1) = $false) | ((mrel @ X2 @ X4) = $false) | ($true = (v2 @ mactual)) | (((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v3 @ Y0))) @ X5) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f849])).
% 2.05/1.65 thf(f849,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((v2 @ X4) = $true) | ((mrel @ mactual @ X2) = $false) | ((v4 @ X1) = $true) | ((mrel @ mactual @ X1) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v3 @ Y0))))) | ($false = (mrel @ mactual @ X3)) | ((mrel @ X2 @ X4) = $false) | ($true = (v2 @ mactual))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f848])).
% 2.05/1.65 thf(f848,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((mrel @ mactual @ X2) = $false) | ((mrel @ mactual @ X1) = $false) | ($true = (v2 @ mactual)) | ($true = ((mrel @ X2 @ X4) => (v2 @ X4))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v3 @ Y0))))) | ($false = (mrel @ mactual @ X3)) | ((v4 @ X1) = $true)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f847])).
% 2.05/1.65 thf(f847,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((v4 @ X1) = $true) | ($false = (mrel @ mactual @ X3)) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v2 @ Y0))) @ X4)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v3 @ Y0))))) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f846])).
% 2.05/1.65 thf(f846,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v2 @ Y0))))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v3 @ Y0))))) | ((mrel @ mactual @ X2) = $false) | ($true = (v2 @ mactual)) | ((v4 @ X1) = $true) | ($false = (mrel @ mactual @ X3))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f845])).
% 2.05/1.65 thf(f845,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X2) = $false) | ($true = ((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v3 @ Y0)))))) | ($true = (v2 @ mactual)) | ((v4 @ X1) = $true) | ((mrel @ mactual @ X1) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v2 @ Y0)))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f844])).
% 2.05/1.65 thf(f844,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v2 @ Y0))))) | ($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))) @ X3)) | ((v4 @ X1) = $true) | ((mrel @ mactual @ X2) = $false) | ($true = (v2 @ mactual)) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f843])).
% 2.05/1.65 thf(f843,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (v2 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ((mrel @ mactual @ X1) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v2 @ Y0))))) | ((v4 @ X1) = $true) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f842])).
% 2.05/1.65 thf(f842,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v2 @ Y0)))))) | ($true = (v2 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ((mrel @ mactual @ X1) = $false) | ((v4 @ X1) = $true)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f841])).
% 2.05/1.65 thf(f841,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v2 @ Y1)))))) @ X2)) | ($true = (v2 @ mactual)) | ((v4 @ X1) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f840])).
% 2.05/1.65 thf(f840,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v2 @ Y1)))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ((mrel @ mactual @ X1) = $false) | ((v4 @ X1) = $true) | ($true = (v2 @ mactual))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f839])).
% 2.05/1.65 thf(f839,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v2 @ Y1))))))))) | ((mrel @ mactual @ X1) = $false) | ((v4 @ X1) = $true) | ($true = (v2 @ mactual))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f838])).
% 2.05/1.65 thf(f838,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (v2 @ mactual)) | ($true = ((mrel @ mactual @ X1) => (v4 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v2 @ Y1)))))))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f837])).
% 2.05/1.65 thf(f837,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (v2 @ mactual)) | (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (v4 @ Y0))) @ X1) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v2 @ Y1)))))))))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f836])).
% 2.05/1.65 thf(f836,plain,(
% 2.05/1.65 ($true = (v2 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (v4 @ Y0)))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v2 @ Y1)))))))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f835])).
% 2.05/1.65 thf(f835,plain,(
% 2.05/1.65 ($true = (v2 @ mactual)) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (v4 @ Y0))))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f834])).
% 2.05/1.65 thf(f834,plain,(
% 2.05/1.65 (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (v4 @ Y0))))) | (v2 @ mactual)) = $true)),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f278])).
% 2.05/1.65 thf(f278,plain,(
% 2.05/1.65 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v2 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v4) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v2)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v3)))))))),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f225,f192,f203,f203,f213,f203,f213,f213,f213,f213])).
% 2.05/1.65 thf(f225,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v2 @ (mor @ (mbox @ v4) @ (mor @ (mbox @ (mbox @ v2)) @ (mbox @ (mbox @ v3)))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f141])).
% 2.05/1.65 thf(f141,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v2 @ (mor @ (mbox @ v4) @ (mor @ (mbox @ (mbox @ v2)) @ (mbox @ (mbox @ v3)))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f140])).
% 2.05/1.65 thf(f140,plain,(
% 2.05/1.65 (mlocal @ (mor @ v2 @ (mor @ (mbox @ v4) @ (mor @ (mbox @ (mbox @ v2)) @ (mbox @ (mbox @ v3))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f29])).
% 2.05/1.65 thf(f29,axiom,(
% 2.05/1.65 (mlocal @ (mor @ v2 @ (mor @ (mbox @ v4) @ (mor @ (mbox @ (mbox @ v2)) @ (mbox @ (mbox @ v3))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat19)).
% 2.05/1.65 thf(f1258,plain,(
% 2.05/1.65 spl0_21 | spl0_15 | spl0_3 | spl0_8),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f955,f1201,f1183,f1227,f1253])).
% 2.05/1.65 thf(f955,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X6 : mworld,X4 : mworld,X5 : mworld] : (((v4 @ X5) = $true) | ((mrel @ mactual @ X4) = $false) | ($false = (v2 @ mactual)) | ($false = (v1 @ X6)) | ((mrel @ X4 @ X5) = $false) | ((mrel @ X1 @ X2) = $false) | ((mrel @ X3 @ X6) = $false) | ($false = (mrel @ mactual @ X3)) | ($true = (v3 @ X2)) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f954])).
% 2.05/1.65 thf(f954,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X6 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ mactual @ X1) = $false) | ((~ (v1 @ X6)) = $true) | ($true = (v3 @ X2)) | ($false = (mrel @ mactual @ X3)) | ((mrel @ mactual @ X4) = $false) | ((mrel @ X4 @ X5) = $false) | ((mrel @ X3 @ X6) = $false) | ($false = (v2 @ mactual)) | ((v4 @ X5) = $true) | ((mrel @ X1 @ X2) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f953])).
% 2.05/1.65 thf(f953,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X6 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ X4 @ X5) = $false) | ($false = (mrel @ mactual @ X3)) | ($true = ((mrel @ X3 @ X6) => (~ (v1 @ X6)))) | ((mrel @ X1 @ X2) = $false) | ($false = (v2 @ mactual)) | ((v4 @ X5) = $true) | ($true = (v3 @ X2)) | ((mrel @ mactual @ X4) = $false) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f952])).
% 2.05/1.65 thf(f952,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X6 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ X4 @ X5) = $false) | ($false = (mrel @ mactual @ X3)) | ((mrel @ X1 @ X2) = $false) | ((v4 @ X5) = $true) | ($true = ((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v1 @ Y0)))) @ X6)) | ((mrel @ mactual @ X1) = $false) | ($true = (v3 @ X2)) | ((mrel @ mactual @ X4) = $false) | ($false = (v2 @ mactual))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f951])).
% 2.05/1.65 thf(f951,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = (v2 @ mactual)) | ((mrel @ X1 @ X2) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v1 @ Y0))))) = $true) | ((mrel @ mactual @ X4) = $false) | ((mrel @ mactual @ X1) = $false) | ($true = (v3 @ X2)) | ((v4 @ X5) = $true) | ($false = (mrel @ mactual @ X3)) | ((mrel @ X4 @ X5) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f950])).
% 2.05/1.65 thf(f950,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ X1 @ X2) = $false) | ((mrel @ mactual @ X4) = $false) | ($false = (mrel @ mactual @ X3)) | ((mrel @ mactual @ X1) = $false) | ($true = (v3 @ X2)) | ($false = (v2 @ mactual)) | (((mrel @ X4 @ X5) => (v4 @ X5)) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v1 @ Y0))))) = $true)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f949])).
% 2.05/1.65 thf(f949,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ mactual @ X4) = $false) | ($false = (mrel @ mactual @ X3)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v1 @ Y0))))) = $true) | ((mrel @ mactual @ X1) = $false) | ($false = (v2 @ mactual)) | ((mrel @ X1 @ X2) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (v4 @ Y0))) @ X5)) | ($true = (v3 @ X2))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f948])).
% 2.05/1.65 thf(f948,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((mrel @ mactual @ X4) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (v4 @ Y0))))) | ($false = (v2 @ mactual)) | ($false = (mrel @ mactual @ X3)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v1 @ Y0))))) = $true) | ((mrel @ mactual @ X1) = $false) | ((mrel @ X1 @ X2) = $false) | ($true = (v3 @ X2))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f947])).
% 2.05/1.65 thf(f947,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((mrel @ mactual @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (v4 @ Y0)))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v1 @ Y0))))) = $true) | ($false = (v2 @ mactual)) | ($true = (v3 @ X2)) | ((mrel @ X1 @ X2) = $false) | ($false = (mrel @ mactual @ X3)) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f946])).
% 2.05/1.65 thf(f946,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = (v2 @ mactual)) | ($false = (mrel @ mactual @ X3)) | ((mrel @ mactual @ X1) = $false) | ($true = ((mrel @ X1 @ X2) => (v3 @ X2))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v1 @ Y0))))) = $true) | ($true = ((mrel @ mactual @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (v4 @ Y0))))))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f945])).
% 2.05/1.65 thf(f945,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v1 @ Y0)))))) = $true) | ($false = (v2 @ mactual)) | ($true = ((mrel @ X1 @ X2) => (v3 @ X2))) | ((mrel @ mactual @ X1) = $false) | ($true = ((mrel @ mactual @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (v4 @ Y0))))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f944])).
% 2.05/1.65 thf(f944,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = (v2 @ mactual)) | ($true = ((mrel @ X1 @ X2) => (v3 @ X2))) | ($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X4)) | (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v1 @ Y0)))))) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f943])).
% 2.05/1.65 thf(f943,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ((mrel @ mactual @ X1) = $false) | ($true = ((mrel @ X1 @ X2) => (v3 @ X2))) | (((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (~ (v1 @ Y0)))))) = $true) | ($false = (v2 @ mactual))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f942])).
% 2.05/1.65 thf(f942,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))) @ X3) = $true) | ($false = (v2 @ mactual)) | ($true = ((mrel @ X1 @ X2) => (v3 @ X2))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f941])).
% 2.05/1.65 thf(f941,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))))) | ($false = (v2 @ mactual)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ($true = ((mrel @ X1 @ X2) => (v3 @ X2)))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f940])).
% 2.05/1.65 thf(f940,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1))))))))) | ($false = (v2 @ mactual)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v3 @ Y0))) @ X2) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f939])).
% 2.05/1.65 thf(f939,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v3 @ Y0))))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ((mrel @ mactual @ X1) = $false) | ($false = (v2 @ mactual)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f938])).
% 2.05/1.65 thf(f938,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v3 @ Y0))))) | ((mrel @ mactual @ X1) = $false) | ($false = (v2 @ mactual))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f937])).
% 2.05/1.65 thf(f937,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (v3 @ Y0)))))) | ($false = (v2 @ mactual)) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f936])).
% 2.05/1.65 thf(f936,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($false = (v2 @ mactual)) | ($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))) @ X1)) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f935])).
% 2.05/1.65 thf(f935,plain,(
% 2.05/1.65 ($false = (v2 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))))),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f934])).
% 2.05/1.65 thf(f934,plain,(
% 2.05/1.65 ((~ (v2 @ mactual)) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f933])).
% 2.05/1.65 thf(f933,plain,(
% 2.05/1.65 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))))) | ((~ (v2 @ mactual)) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f932])).
% 2.05/1.65 thf(f932,plain,(
% 2.05/1.65 ($true = ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v1 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))) | (~ (v2 @ mactual))))),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f262])).
% 2.05/1.65 thf(f262,plain,(
% 2.05/1.65 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v2) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v4)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v1))))))))),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f206,f192,f203,f194,f203,f213,f213,f203,f213,f213,f213,f213,f194])).
% 2.05/1.65 thf(f206,plain,(
% 2.05/1.65 ((mlocal @ (mor @ (mnot @ v2) @ (mor @ (mbox @ (mbox @ v3)) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v1))))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f82])).
% 2.05/1.65 thf(f82,plain,(
% 2.05/1.65 ((mlocal @ (mor @ (mnot @ v2) @ (mor @ (mbox @ (mbox @ v3)) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v1))))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f81])).
% 2.05/1.65 thf(f81,plain,(
% 2.05/1.65 (mlocal @ (mor @ (mnot @ v2) @ (mor @ (mbox @ (mbox @ v3)) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v1)))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f53])).
% 2.05/1.65 thf(f53,axiom,(
% 2.05/1.65 (mlocal @ (mor @ (mnot @ v2) @ (mor @ (mbox @ (mbox @ v3)) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v1)))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat43)).
% 2.05/1.65 thf(f1229,plain,(
% 2.05/1.65 spl0_6 | spl0_1 | spl0_12 | spl0_15),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f1086,f1227,f1215,f1175,f1194])).
% 2.05/1.65 thf(f1086,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (v3 @ X4)) | ((mrel @ mactual @ X1) = $false) | ((mrel @ X2 @ X4) = $false) | ($false = (v4 @ mactual)) | ($false = (mrel @ X1 @ X3)) | ((mrel @ mactual @ X2) = $false) | ($true = (v3 @ mactual)) | ((v4 @ X3) = $false)) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f1085])).
% 2.05/1.65 thf(f1085,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (v3 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ X1 @ X3)) | ((mrel @ mactual @ X2) = $false) | ($true = (v3 @ X4)) | ((~ (v4 @ X3)) = $true) | ($false = (v4 @ mactual)) | ((mrel @ X2 @ X4) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1084])).
% 2.05/1.65 thf(f1084,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((mrel @ X2 @ X4) => (v3 @ X4)) = $true) | ((~ (v4 @ X3)) = $true) | ($false = (v4 @ mactual)) | ((mrel @ mactual @ X2) = $false) | ($false = (mrel @ X1 @ X3)) | ((mrel @ mactual @ X1) = $false) | ($true = (v3 @ mactual))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f1083])).
% 2.05/1.65 thf(f1083,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((~ (v4 @ X3)) = $true) | ((mrel @ mactual @ X1) = $false) | ((mrel @ mactual @ X2) = $false) | ($true = (v3 @ mactual)) | ($false = (v4 @ mactual)) | ($false = (mrel @ X1 @ X3)) | ($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))) @ X4))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f1082])).
% 2.05/1.65 thf(f1082,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (v3 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))) = $true) | ($false = (mrel @ X1 @ X3)) | ((~ (v4 @ X3)) = $true) | ((mrel @ mactual @ X1) = $false) | ((mrel @ mactual @ X2) = $false) | ($false = (v4 @ mactual))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1081])).
% 2.05/1.65 thf(f1081,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = (v4 @ mactual)) | ($true = ((mrel @ X1 @ X3) => (~ (v4 @ X3)))) | ((mrel @ mactual @ X1) = $false) | ($true = (v3 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))) = $true) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f1080])).
% 2.05/1.65 thf(f1080,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((mrel @ mactual @ X2) = $false) | ($true = (v3 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))) = $true) | ($false = (v4 @ mactual)) | (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))) @ X3) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f1079])).
% 2.05/1.65 thf(f1079,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (v3 @ mactual)) | ((mrel @ mactual @ X2) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))))) | ((mrel @ mactual @ X1) = $false) | ($false = (v4 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))) = $true)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1078])).
% 2.05/1.65 thf(f1078,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($false = (v4 @ mactual)) | ((mrel @ mactual @ X1) = $false) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0)))))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))))) | ($true = (v3 @ mactual))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1077])).
% 2.05/1.65 thf(f1077,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($false = (v4 @ mactual)) | ($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0))))))) | ($true = (v3 @ mactual)) | ($true = ((mrel @ mactual @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (v3 @ Y0))))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f1076])).
% 2.05/1.65 thf(f1076,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (v3 @ mactual)) | ($false = (v4 @ mactual)) | (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))) @ X2) = $true) | ($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0)))))))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f1075])).
% 2.05/1.65 thf(f1075,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v4 @ Y0))))))) | ($true = (v3 @ mactual)) | ($false = (v4 @ mactual))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f1074])).
% 2.05/1.65 thf(f1074,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))))) @ X1)) | ($false = (v4 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ($true = (v3 @ mactual))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f1073])).
% 2.05/1.65 thf(f1073,plain,(
% 2.05/1.65 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) = $true) | ($false = (v4 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))) = $true) | ($true = (v3 @ mactual))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1072])).
% 2.05/1.65 thf(f1072,plain,(
% 2.05/1.65 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1))))))))) | ($true = (v3 @ mactual)) | ($false = (v4 @ mactual))),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f1071])).
% 2.05/1.65 thf(f1071,plain,(
% 2.05/1.65 ((~ (v4 @ mactual)) = $true) | ($true = (v3 @ mactual)) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1070])).
% 2.05/1.65 thf(f1070,plain,(
% 2.05/1.65 ($true = (v3 @ mactual)) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))) | (~ (v4 @ mactual))) = $true)),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1069])).
% 2.05/1.65 thf(f1069,plain,(
% 2.05/1.65 ($true = ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v3 @ Y1)))))))) | (~ (v4 @ mactual))) | (v3 @ mactual)))),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f303])).
% 2.05/1.65 thf(f303,plain,(
% 2.05/1.65 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v3 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v4) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v4))))))) = $true)),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f251,f192,f203,f203,f194,f203,f213,f213,f213,f213,f194])).
% 2.05/1.65 thf(f251,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v3 @ (mor @ (mnot @ v4) @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ (mnot @ v4))))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f86])).
% 2.05/1.65 thf(f86,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v3 @ (mor @ (mnot @ v4) @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ (mnot @ v4))))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f85])).
% 2.05/1.65 thf(f85,plain,(
% 2.05/1.65 (mlocal @ (mor @ v3 @ (mor @ (mnot @ v4) @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ (mnot @ v4)))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f36])).
% 2.05/1.65 thf(f36,axiom,(
% 2.05/1.65 (mlocal @ (mor @ v3 @ (mor @ (mnot @ v4) @ (mor @ (mbox @ (mbox @ v3)) @ (mbox @ (mbox @ (mnot @ v4)))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat26)).
% 2.05/1.65 thf(f1213,plain,(
% 2.05/1.65 spl0_10 | spl0_5 | spl0_11 | spl0_3),
% 2.05/1.65 inference(avatar_split_clause,[status(thm)],[f1122,f1183,f1211,f1190,f1208])).
% 2.05/1.65 thf(f1122,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ mactual @ X2) = $false) | ($false = (mrel @ mactual @ X3)) | ((v2 @ X2) = $true) | ((v2 @ X5) = $false) | ((mrel @ mactual @ X1) = $false) | ((v1 @ mactual) = $true) | ((mrel @ X3 @ X4) = $false) | ($true = (v4 @ X4)) | ($false = (mrel @ X1 @ X5))) )),
% 2.05/1.65 inference(not_proxy_clausification,[status(thm)],[f1121])).
% 2.05/1.65 thf(f1121,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((v2 @ X2) = $true) | ((mrel @ X3 @ X4) = $false) | ($false = (mrel @ X1 @ X5)) | ((mrel @ mactual @ X2) = $false) | ($true = (v4 @ X4)) | ((v1 @ mactual) = $true) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ mactual @ X3)) | ((~ (v2 @ X5)) = $true)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1120])).
% 2.05/1.65 thf(f1120,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ mactual @ X1) = $false) | ((v2 @ X2) = $true) | ($false = (mrel @ mactual @ X3)) | ((mrel @ X3 @ X4) = $false) | ($true = ((mrel @ X1 @ X5) => (~ (v2 @ X5)))) | ($true = (v4 @ X4)) | ((v1 @ mactual) = $true) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f1119])).
% 2.05/1.65 thf(f1119,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld,X5 : mworld] : (($true = (v4 @ X4)) | ((mrel @ mactual @ X1) = $false) | ($false = (mrel @ mactual @ X3)) | ((v2 @ X2) = $true) | ((v1 @ mactual) = $true) | ((mrel @ X3 @ X4) = $false) | (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0)))) @ X5) = $true) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f1118])).
% 2.05/1.65 thf(f1118,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((v1 @ mactual) = $true) | ((v2 @ X2) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0)))))) | ((mrel @ X3 @ X4) = $false) | ($true = (v4 @ X4)) | ($false = (mrel @ mactual @ X3)) | ((mrel @ mactual @ X2) = $false) | ((mrel @ mactual @ X1) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1117])).
% 2.05/1.65 thf(f1117,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0))))))) | ((mrel @ mactual @ X2) = $false) | ($true = (v4 @ X4)) | ((mrel @ X3 @ X4) = $false) | ((v2 @ X2) = $true) | ($false = (mrel @ mactual @ X3)) | ((v1 @ mactual) = $true)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1116])).
% 2.05/1.65 thf(f1116,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((mrel @ X3 @ X4) => (v4 @ X4)) = $true) | ($false = (mrel @ mactual @ X3)) | ((v2 @ X2) = $true) | ($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0))))))) | ((v1 @ mactual) = $true) | ((mrel @ mactual @ X2) = $false)) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1115])).
% 2.05/1.65 thf(f1115,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((mrel @ mactual @ X2) => (v2 @ X2))) | ($false = (mrel @ mactual @ X3)) | ((v1 @ mactual) = $true) | (((mrel @ X3 @ X4) => (v4 @ X4)) = $true) | ($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0)))))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f1114])).
% 2.05/1.65 thf(f1114,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0))))))) | ((v1 @ mactual) = $true) | ($true = ((mrel @ mactual @ X2) => (v2 @ X2))) | ($false = (mrel @ mactual @ X3)) | ($true = ((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v4 @ Y0))) @ X4))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f1113])).
% 2.05/1.65 thf(f1113,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X3)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v4 @ Y0))))) | ($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0))))))) | ((v1 @ mactual) = $true) | ($true = ((mrel @ mactual @ X2) => (v2 @ X2)))) )),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1112])).
% 2.05/1.65 thf(f1112,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((mrel @ mactual @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v4 @ Y0)))))) | ((v1 @ mactual) = $true) | ($true = ((mrel @ mactual @ X2) => (v2 @ X2))) | ($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0)))))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f1111])).
% 2.05/1.65 thf(f1111,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((mrel @ mactual @ X2) => (v2 @ X2))) | ($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X3)) | ($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0))))))) | ((v1 @ mactual) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f1110])).
% 2.05/1.65 thf(f1110,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ((v1 @ mactual) = $true) | ($true = ((mrel @ mactual @ X2) => (v2 @ X2))) | ($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0)))))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f1109])).
% 2.05/1.65 thf(f1109,plain,(
% 2.05/1.65 ( ! [X2 : mworld,X1 : mworld] : (((v1 @ mactual) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0))))))) | (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (v2 @ Y0))) @ X2) = $true)) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f1108])).
% 2.05/1.65 thf(f1108,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (((v1 @ mactual) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (v2 @ Y0))))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (~ (v2 @ Y0)))))))) )),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f1107])).
% 2.05/1.65 thf(f1107,plain,(
% 2.05/1.65 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1))))))) @ X1)) | ((v1 @ mactual) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (v2 @ Y0))))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))))) )),
% 2.05/1.65 inference(pi_clausification,[status(thm)],[f1106])).
% 2.05/1.65 thf(f1106,plain,(
% 2.05/1.65 ((v1 @ mactual) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (v2 @ Y0)))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1105])).
% 2.05/1.65 thf(f1105,plain,(
% 2.05/1.65 ((v1 @ mactual) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) = $true) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (v2 @ Y0)))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1104])).
% 2.05/1.65 thf(f1104,plain,(
% 2.05/1.65 ((v1 @ mactual) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (v2 @ Y0))))))),
% 2.05/1.65 inference(binary_proxy_clausification,[status(thm)],[f1103])).
% 2.05/1.65 thf(f1103,plain,(
% 2.05/1.65 (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v2 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (v2 @ Y0))))) | (v1 @ mactual)) = $true)),
% 2.05/1.65 inference(beta_eta_normalization,[status(thm)],[f270])).
% 2.05/1.65 thf(f270,plain,(
% 2.05/1.65 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v1 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v2) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v4)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v2))))))))),
% 2.05/1.65 inference(definition_unfolding,[status(thm)],[f215,f192,f203,f203,f213,f203,f213,f213,f213,f213,f194])).
% 2.05/1.65 thf(f215,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v1 @ (mor @ (mbox @ v2) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v2))))))) = $true)),
% 2.05/1.65 inference(cnf_transformation,[status(thm)],[f165])).
% 2.05/1.65 thf(f165,plain,(
% 2.05/1.65 ((mlocal @ (mor @ v1 @ (mor @ (mbox @ v2) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v2))))))) = $true)),
% 2.05/1.65 inference(fool_elimination,[status(thm)],[f164])).
% 2.05/1.65 thf(f164,plain,(
% 2.05/1.65 (mlocal @ (mor @ v1 @ (mor @ (mbox @ v2) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v2)))))))),
% 2.05/1.65 inference(rectify,[status(thm)],[f23])).
% 2.05/1.65 thf(f23,axiom,(
% 2.05/1.65 (mlocal @ (mor @ v1 @ (mor @ (mbox @ v2) @ (mor @ (mbox @ (mbox @ v4)) @ (mbox @ (mbox @ (mnot @ v2)))))))),
% 2.05/1.65 file('/export/starexec/sandbox/tmp/tmp.NcTxorUQi1/DTF2THF_7992.p',persat13)).
% 2.05/1.65 % SZS output end Proof for DTF2THF_7992
% 2.05/1.65 % (8091)------------------------------
% 2.05/1.65 % (8091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.65 % (8091)Termination reason: Refutation
% 2.05/1.65
% 2.05/1.65 % (8091)Memory used [KB]: 6524
% 2.05/1.65 % (8091)Time elapsed: 0.091 s
% 2.05/1.65 % (8091)Instructions burned: 165 (million)
% 2.05/1.65 % (8091)------------------------------
% 2.05/1.65 % (8091)------------------------------
% 2.05/1.65 % (8090)Success in time 0.093 s
%------------------------------------------------------------------------------