%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO901^11 : 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 : n027.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 09:55:09 AM UTC 2026
% Result : Theorem 2.00s 1.60s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 24
% Syntax : Number of formulae : 177 ( 35 unt; 0 typ; 17 def)
% Number of atoms : 1083 ( 253 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 1123 ( 188 ~; 244 |; 3 &; 578 @)
% ( 19 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 33 usr; 25 con; 0-3 aty)
% ( 33 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 158 ( 93 ^; 65 !; 0 ?; 158 :)
% 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,
p: mworld > $o ).
thf(func_def_13,type,
q: mworld > $o ).
thf(func_def_28,type,
sK1: mworld ).
thf(func_def_29,type,
sK2: mworld ).
thf(func_def_30,type,
sK3: mworld ).
thf(func_def_31,type,
sK4: mworld ).
thf(f644,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f90,f99,f104,f113,f118,f246,f359,f373,f391,f425,f431,f465,f581,f590,f597,f603,f613,f614,f637,f643]) ).
thf(f643,plain,
( ~ spl0_7
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[status(thm)],[f642]) ).
thf(f642,plain,
( $false
| ~ spl0_7
| ~ spl0_23 ),
inference(trivial_inequality_removal,[status(thm)],[f639]) ).
thf(f639,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_23 ),
inference(superposition,[status(thm)],[f112,f585]) ).
thf(f585,plain,
( ( $true
= ( q @ sK3 ) )
| ~ spl0_23 ),
inference(avatar_component_clause,[status(thm)],[f583]) ).
thf(f583,definition,
( spl0_23
<=> ( $true
= ( q @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition]) ).
thf(f112,plain,
( ( $false
= ( q @ sK3 ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f110]) ).
thf(f110,definition,
( spl0_7
<=> ( $false
= ( q @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f637,plain,
( ~ spl0_24
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[status(thm)],[f636]) ).
thf(f636,plain,
( $false
| ~ spl0_24
| ~ spl0_25 ),
inference(trivial_inequality_removal,[status(thm)],[f632]) ).
thf(f632,plain,
( ( $true = $false )
| ~ spl0_24
| ~ spl0_25 ),
inference(superposition,[status(thm)],[f589,f607]) ).
thf(f607,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl0_25 ),
inference(avatar_component_clause,[status(thm)],[f605]) ).
thf(f605,definition,
( spl0_25
<=> ( $true
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition]) ).
thf(f589,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl0_24 ),
inference(avatar_component_clause,[status(thm)],[f587]) ).
thf(f587,definition,
( spl0_24
<=> ( $false
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition]) ).
thf(f614,plain,
( spl0_25
| ~ spl0_1
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f499,f115,f85,f605]) ).
thf(f85,definition,
( spl0_1
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ sK1 @ X2 ) )
| ( $true
= ( p @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f115,definition,
( spl0_8
<=> ( ( mrel @ sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f499,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl0_1
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f481]) ).
thf(f481,plain,
( ( $true
= ( p @ sK3 ) )
| ( $true = $false )
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f86,f117]) ).
thf(f117,plain,
( ( ( mrel @ sK1 @ sK3 )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f115]) ).
thf(f86,plain,
( ! [X2: mworld] :
( ( $false
= ( mrel @ sK1 @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f85]) ).
thf(f613,plain,
( ~ spl0_17
| spl0_19
| spl0_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f612]) ).
thf(f612,plain,
( $false
| ~ spl0_17
| spl0_19
| spl0_20 ),
inference(subsumption_resolution,[status(thm)],[f611,f417]) ).
thf(f417,plain,
( ( $false
!= ( q @ sK2 ) )
| spl0_20 ),
inference(avatar_component_clause,[status(thm)],[f416]) ).
thf(f416,definition,
( spl0_20
<=> ( $false
= ( q @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition]) ).
thf(f611,plain,
( ( $false
= ( q @ sK2 ) )
| ~ spl0_17
| spl0_19 ),
inference(subsumption_resolution,[status(thm)],[f518,f413]) ).
thf(f413,plain,
( ( $true
!= ( p @ sK2 ) )
| spl0_19 ),
inference(avatar_component_clause,[status(thm)],[f412]) ).
thf(f412,definition,
( spl0_19
<=> ( $true
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition]) ).
thf(f518,plain,
( ( $true
= ( p @ sK2 ) )
| ( $false
= ( q @ sK2 ) )
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f516]) ).
thf(f516,plain,
( ( $false
= ( q @ sK2 ) )
| ( $true != $true )
| ( $true
= ( p @ sK2 ) )
| ~ spl0_17 ),
inference(superposition,[status(thm)],[f354,f47]) ).
thf(f47,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f31]) ).
thf(f31,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.LZ8lv80Rf8/DTF2THF_13393.p',mrel_reflexive) ).
thf(f354,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ sK2 @ X0 ) )
| ( ( p @ X0 )
= $true )
| ( $false
= ( q @ X0 ) ) )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f353]) ).
thf(f353,definition,
( spl0_17
<=> ! [X0: mworld] :
( ( ( p @ X0 )
= $true )
| ( $false
= ( q @ X0 ) )
| ( $true
!= ( mrel @ sK2 @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f603,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[status(thm)],[f602]) ).
thf(f602,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_21 ),
inference(trivial_inequality_removal,[status(thm)],[f599]) ).
thf(f599,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_21 ),
inference(superposition,[status(thm)],[f506,f576]) ).
thf(f576,plain,
( ( $false
= ( p @ sK4 ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[status(thm)],[f574]) ).
thf(f574,definition,
( spl0_21
<=> ( $false
= ( p @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition]) ).
thf(f506,plain,
( ( $true
= ( p @ sK4 ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f493]) ).
thf(f493,plain,
( ( $true = $false )
| ( $true
= ( p @ sK4 ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f103,f86]) ).
thf(f103,plain,
( ( $true
= ( mrel @ sK1 @ sK4 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f101,definition,
( spl0_5
<=> ( $true
= ( mrel @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f597,plain,
( ~ spl0_4
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f596]) ).
thf(f596,plain,
( $false
| ~ spl0_4
| ~ spl0_22 ),
inference(trivial_inequality_removal,[status(thm)],[f593]) ).
thf(f593,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_22 ),
inference(superposition,[status(thm)],[f98,f580]) ).
thf(f580,plain,
( ( $true
= ( q @ sK4 ) )
| ~ spl0_22 ),
inference(avatar_component_clause,[status(thm)],[f578]) ).
thf(f578,definition,
( spl0_22
<=> ( $true
= ( q @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition]) ).
thf(f98,plain,
( ( $false
= ( q @ sK4 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f96]) ).
thf(f96,definition,
( spl0_4
<=> ( $false
= ( q @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f590,plain,
( spl0_23
| spl0_24
| ~ spl0_8
| ~ spl0_18 ),
inference(avatar_split_clause,[status(thm)],[f568,f356,f115,f587,f583]) ).
thf(f356,definition,
( spl0_18
<=> ( $true
= ( mrel @ sK1 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition]) ).
thf(f568,plain,
( ( $true
= ( q @ sK3 ) )
| ( $false
= ( p @ sK3 ) )
| ~ spl0_8
| ~ spl0_18 ),
inference(trivial_inequality_removal,[status(thm)],[f565]) ).
thf(f565,plain,
( ( $false
= ( p @ sK3 ) )
| ( $true != $true )
| ( $true
= ( q @ sK3 ) )
| ~ spl0_8
| ~ spl0_18 ),
inference(superposition,[status(thm)],[f475,f117]) ).
thf(f475,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ sK1 @ X0 ) )
| ( $true
= ( q @ X0 ) )
| ( ( p @ X0 )
= $false ) )
| ~ spl0_18 ),
inference(trivial_inequality_removal,[status(thm)],[f466]) ).
thf(f466,plain,
( ! [X0: mworld] :
( ( $true
= ( q @ X0 ) )
| ( $true != $true )
| ( $true
!= ( mrel @ sK1 @ X0 ) )
| ( ( p @ X0 )
= $false ) )
| ~ spl0_18 ),
inference(superposition,[status(thm)],[f174,f357]) ).
thf(f357,plain,
( ( $true
= ( mrel @ sK1 @ mactual ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f356]) ).
thf(f174,plain,
! [X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X1 @ mactual ) )
| ( $true
!= ( mrel @ X1 @ X0 ) )
| ( ( p @ X0 )
= $false )
| ( $true
= ( q @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f164]) ).
thf(f164,plain,
! [X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X1 @ X0 ) )
| ( $true
!= ( mrel @ X1 @ mactual ) )
| ( ( p @ X0 )
= $false )
| ( $true
= ( q @ X0 ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f58,f48]) ).
thf(f48,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( $true
= ( mrel @ X2 @ X1 ) )
| ( $true
!= ( mrel @ X0 @ X1 ) )
| ( $true
!= ( mrel @ X0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( $true
!= ( mrel @ X0 @ X1 ) )
| ( $true
!= ( mrel @ X0 @ X2 ) )
| ( $true
= ( mrel @ X2 @ X1 ) ) ),
inference(flattening,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( $true
= ( mrel @ X2 @ X1 ) )
| ( $true
!= ( mrel @ X0 @ X1 ) )
| ( $true
!= ( mrel @ X0 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( $true
= ( mrel @ X0 @ X1 ) )
& ( $true
= ( mrel @ X0 @ X2 ) ) )
=> ( $true
= ( mrel @ X2 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X2 )
& ( mrel @ X0 @ X1 ) )
=> ( mrel @ X2 @ X1 ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
! [X2: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X2 @ X5 )
& ( mrel @ X2 @ X4 ) )
=> ( mrel @ X5 @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2THF_13393.p',mrel_euclidean) ).
thf(f58,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( p @ X1 )
= $false )
| ( $true
= ( q @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: mworld] :
( ( ( p @ X1 )
= ( q @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( p @ X1 )
= ( q @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( p @ X1 )
= ( q @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
= ( q @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
= ( q @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( $true
!= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
= ( q @ Y0 ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
= ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) )
@ p
@ q ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f41,f38,f44,f45,f46,f45,f46,f45,f45]) ).
thf(f46,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X3 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2THF_13393.p',mequiv_def) ).
thf(f45,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2THF_13393.p',mbox_def) ).
thf(f44,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f29]) ).
thf(f29,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( mimplies
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2THF_13393.p',mimplies_def) ).
thf(f38,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2THF_13393.p',mlocal_def) ).
thf(f41,plain,
( ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
( ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
~ ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f11,conjecture,
mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2THF_13393.p',con) ).
thf(f581,plain,
( spl0_21
| spl0_22
| ~ spl0_5
| ~ spl0_18 ),
inference(avatar_split_clause,[status(thm)],[f572,f356,f101,f578,f574]) ).
thf(f572,plain,
( ( $false
= ( p @ sK4 ) )
| ( $true
= ( q @ sK4 ) )
| ~ spl0_5
| ~ spl0_18 ),
inference(trivial_inequality_removal,[status(thm)],[f566]) ).
thf(f566,plain,
( ( $false
= ( p @ sK4 ) )
| ( $true != $true )
| ( $true
= ( q @ sK4 ) )
| ~ spl0_5
| ~ spl0_18 ),
inference(superposition,[status(thm)],[f475,f103]) ).
thf(f465,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f464]) ).
thf(f464,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f461]) ).
thf(f461,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f98,f442]) ).
thf(f442,plain,
( ( $true
= ( q @ sK4 ) )
| ~ spl0_2
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f437]) ).
thf(f437,plain,
( ( $true
= ( q @ sK4 ) )
| ( $true = $false )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f89,f103]) ).
thf(f89,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f88]) ).
thf(f88,definition,
( spl0_2
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( q @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f431,plain,
( ~ spl0_3
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[status(thm)],[f430]) ).
thf(f430,plain,
( $false
| ~ spl0_3
| ~ spl0_19 ),
inference(trivial_inequality_removal,[status(thm)],[f427]) ).
thf(f427,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_19 ),
inference(superposition,[status(thm)],[f94,f414]) ).
thf(f414,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl0_19 ),
inference(avatar_component_clause,[status(thm)],[f412]) ).
thf(f94,plain,
( ( ( p @ sK2 )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f92,definition,
( spl0_3
<=> ( ( p @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f425,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f424]) ).
thf(f424,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_20 ),
inference(trivial_inequality_removal,[status(thm)],[f420]) ).
thf(f420,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_20 ),
inference(superposition,[status(thm)],[f418,f399]) ).
thf(f399,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f393]) ).
thf(f393,plain,
( ( $true = $false )
| ( $true
= ( q @ sK2 ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f108,f89]) ).
thf(f108,plain,
( ( $true
= ( mrel @ sK1 @ sK2 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f106]) ).
thf(f106,definition,
( spl0_6
<=> ( $true
= ( mrel @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f418,plain,
( ( $false
= ( q @ sK2 ) )
| ~ spl0_20 ),
inference(avatar_component_clause,[status(thm)],[f416]) ).
thf(f391,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f390]) ).
thf(f390,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f387]) ).
thf(f387,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f112,f383]) ).
thf(f383,plain,
( ( $true
= ( q @ sK3 ) )
| ~ spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f379]) ).
thf(f379,plain,
( ( $true
= ( q @ sK3 ) )
| ( $true = $false )
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f89,f117]) ).
thf(f373,plain,
spl0_18,
inference(avatar_contradiction_clause,[status(thm)],[f372]) ).
thf(f372,plain,
( $false
| spl0_18 ),
inference(subsumption_resolution,[status(thm)],[f371,f47]) ).
thf(f371,plain,
( ( $true
!= ( mrel @ mactual @ mactual ) )
| spl0_18 ),
inference(trivial_inequality_removal,[status(thm)],[f363]) ).
thf(f363,plain,
( ( $true != $true )
| ( $true
!= ( mrel @ mactual @ mactual ) )
| spl0_18 ),
inference(superposition,[status(thm)],[f362,f62]) ).
thf(f62,plain,
( $true
= ( mrel @ mactual @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( mrel @ mactual @ sK1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
= ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
= ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f362,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ X0 @ sK1 ) )
| ( $true
!= ( mrel @ X0 @ mactual ) ) )
| spl0_18 ),
inference(trivial_inequality_removal,[status(thm)],[f361]) ).
thf(f361,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ X0 @ mactual ) )
| ( $true
!= ( mrel @ X0 @ sK1 ) )
| ( $true != $true ) )
| spl0_18 ),
inference(superposition,[status(thm)],[f358,f48]) ).
thf(f358,plain,
( ( $true
!= ( mrel @ sK1 @ mactual ) )
| spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f356]) ).
thf(f359,plain,
( spl0_17
| ~ spl0_18
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f348,f106,f356,f353]) ).
thf(f348,plain,
( ! [X0: mworld] :
( ( ( p @ X0 )
= $true )
| ( $true
!= ( mrel @ sK1 @ mactual ) )
| ( $true
!= ( mrel @ sK2 @ X0 ) )
| ( $false
= ( q @ X0 ) ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f346]) ).
thf(f346,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ sK1 @ mactual ) )
| ( $true != $true )
| ( $true
!= ( mrel @ sK2 @ X0 ) )
| ( $false
= ( q @ X0 ) )
| ( ( p @ X0 )
= $true ) )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f273,f108]) ).
thf(f273,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X2 @ X0 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( q @ X1 ) )
| ( ( mrel @ X2 @ mactual )
!= $true )
| ( $true
!= ( mrel @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f271]) ).
thf(f271,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( $true != $true )
| ( $true
!= ( mrel @ X0 @ X1 ) )
| ( ( mrel @ X2 @ mactual )
!= $true )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( q @ X1 ) )
| ( $true
!= ( mrel @ X2 @ X0 ) ) ),
inference(superposition,[status(thm)],[f161,f48]) ).
thf(f161,plain,
! [X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X1 @ mactual ) )
| ( $false
= ( q @ X0 ) )
| ( ( p @ X0 )
= $true )
| ( $true
!= ( mrel @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f156]) ).
thf(f156,plain,
! [X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X1 @ X0 ) )
| ( $false
= ( q @ X0 ) )
| ( $true
!= ( mrel @ X1 @ mactual ) )
| ( ( p @ X0 )
= $true )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f48,f57]) ).
thf(f57,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( q @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f246,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f245]) ).
thf(f245,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f242]) ).
thf(f242,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f94,f239]) ).
thf(f239,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f234]) ).
thf(f234,plain,
( ( $true
= ( p @ sK2 ) )
| ( $true = $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f108,f86]) ).
thf(f118,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f73,f106,f115]) ).
thf(f73,plain,
( ( ( mrel @ sK1 @ sK3 )
= $true )
| ( $true
= ( mrel @ sK1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $false
= ( ( mrel @ sK1 @ sK3 )
=> ( q @ sK3 ) ) )
| ( $true
= ( mrel @ sK1 @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) )
@ sK3 ) )
| ( $true
= ( mrel @ sK1 @ sK2 ) ) ),
inference(sigma_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( $true
= ( mrel @ sK1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( ( $false
= ( ( mrel @ sK1 @ sK2 )
=> ( p @ sK2 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ sK2 ) ) ),
inference(sigma_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) )
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f113,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f72,f110,f106]) ).
thf(f72,plain,
( ( $false
= ( q @ sK3 ) )
| ( $true
= ( mrel @ sK1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f104,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f77,f101,f92]) ).
thf(f77,plain,
( ( ( p @ sK2 )
= $false )
| ( $true
= ( mrel @ sK1 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ( p @ sK2 )
= $false )
| ( $false
= ( ( mrel @ sK1 @ sK4 )
=> ( q @ sK4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( p @ sK2 )
= $false )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) )
@ sK4 ) ) ),
inference(sigma_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( ( p @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f99,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f76,f96,f92]) ).
thf(f76,plain,
( ( $false
= ( q @ sK4 ) )
| ( ( p @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f90,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f83,f88,f85]) ).
thf(f83,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X2 ) )
| ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ( mrel @ sK1 @ X2 )
=> ( p @ X2 ) ) )
| ( $false
= ( mrel @ sK1 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ X2 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( mrel @ sK1 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ sK1 @ X1 )
=> ( q @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO901^11 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n027.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 14:53:52 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.48 thf(spec,logic,$$dhol).
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % File : SYO901^11 : TPTP v9.2.1. Released v8.1.0.
% 0.19/0.48 % Domain : Syntactic
% 0.19/0.48 % Problem : Mixed modal propositional logic WFFs. problem 14
% 0.19/0.48 % Version : [BP13] axioms.
% 0.19/0.48 % English :
% 0.19/0.48
% 0.19/0.48 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.19/0.48 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.19/0.48 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.19/0.48 % Source : [TPTP]
% 0.19/0.48 % Names : SYM168+1 [QMLTP]
% 0.19/0.48
% 0.19/0.48 % Status : Theorem
% 0.19/0.48 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.19/0.48 % Syntax : Number of formulae : 24 ( 9 unt; 13 typ; 8 def)
% 0.19/0.48 % Number of atoms : 34 ( 8 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 12 ( 3 avg)
% 0.19/0.48 % Number of connectives : 44 ( 1 ~; 1 |; 3 &; 35 @)
% 0.19/0.48 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 8 ( 2 avg)
% 0.19/0.48 % Number of types : 2 ( 1 usr)
% 0.19/0.48 % Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 13 ( 12 usr; 1 con; 0-3 aty)
% 0.19/0.48 % Number of variables : 25 ( 19 ^; 5 !; 1 ?; 25 :)
% 0.19/0.48 % SPC : TH0_THM_EQU_NAR
% 0.19/0.48
% 0.19/0.48 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.19/0.48 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.19/0.48 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.19/0.48 % $modal == [$constants == $rigid,$quantification == $varying,
% 0.19/0.48 % $modalities == $modal_system_S5].
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf(mworld,type,
% 0.19/0.48 mworld: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(mrel_type,type,
% 0.19/0.48 mrel: mworld > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mactual_type,type,
% 0.19/0.48 mactual: mworld ).
% 0.19/0.48
% 0.19/0.48 thf(mlocal_type,type,
% 0.19/0.48 mlocal: ( mworld > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mlocal_def,definition,
% 0.19/0.48 ( mlocal
% 0.19/0.48 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mnot_type,type,
% 0.19/0.48 mnot: ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mand_type,type,
% 0.19/0.48 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mor_type,type,
% 0.19/0.48 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mimplies_type,type,
% 0.19/0.48 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mequiv_type,type,
% 0.19/0.48 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mnot_def,definition,
% 0.19/0.48 ( mnot
% 0.19/0.48 = ( ^ [A: mworld > $o,W: mworld] :
% 0.19/0.48 ~ ( A @ W ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mand_def,definition,
% 0.19/0.48 ( mand
% 0.19/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.48 ( ( A @ W )
% 0.19/0.48 & ( B @ W ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mor_def,definition,
% 0.19/0.48 ( mor
% 0.19/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.48 ( ( A @ W )
% 0.19/0.48 | ( B @ W ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mimplies_def,definition,
% 0.19/0.48 ( mimplies
% 0.19/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.48 ( ( A @ W )
% 0.19/0.48 => ( B @ W ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mequiv_def,definition,
% 0.19/0.48 ( mequiv
% 0.19/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.48 ( ( A @ W )
% 0.19/0.48 <=> ( B @ W ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mbox_type,type,
% 0.19/0.48 mbox: ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mbox_def,definition,
% 0.19/0.48 ( mbox
% 0.19/0.48 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.19/0.48 ! [V: mworld] :
% 0.19/0.48 ( ( mrel @ W @ V )
% 0.19/0.48 => ( Phi @ V ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mdia_type,type,
% 0.19/0.48 mdia: ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mdia_def,definition,
% 0.19/0.48 ( mdia
% 0.19/0.48 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.19/0.48 ? [V: mworld] :
% 0.19/0.48 ( ( mrel @ W @ V )
% 0.19/0.48 & ( Phi @ V ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mrel_reflexive,axiom,
% 0.19/0.48 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.19/0.48
% 0.19/0.48 thf(mrel_euclidean,axiom,
% 0.19/0.48 ! [W: mworld,V: mworld,U: mworld] :
% 0.19/0.48 ( ( ( mrel @ W @ U )
% 0.19/0.48 & ( mrel @ W @ V ) )
% 0.19/0.48 => ( mrel @ U @ V ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(p_decl,type,
% 0.19/0.48 p: mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(q_decl,type,
% 0.19/0.48 q: mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(con,conjecture,
% 0.19/0.48 mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 ------------------------
% 1.89/1.54 ---- Embedded in THF ---
% 1.89/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.89/1.54 %%% Generated on Tue Feb 24 14:53:53 EST 2026
% 1.89/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 1.89/1.54 %%% Logic specification used:
% 1.89/1.54 %%% thf(spec, logic, $$dhol).
% 1.89/1.54
% 1.89/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2DTF13393.p
% See solution above
% 1.89/1.54 ------------------------
% 1.89/1.55 ---- Cleaned THF ---
% 1.89/1.55 thf(mworld,type,
% 1.89/1.55 mworld: $tType ).
% 1.89/1.55
% 1.89/1.55 thf(mrel_type,type,
% 1.89/1.55 mrel: mworld > mworld > $o ).
% 1.89/1.55
% 1.89/1.55 thf(mactual_type,type,
% 1.89/1.55 mactual: mworld ).
% 1.89/1.55
% 1.89/1.55 thf(mlocal_type,type,
% 1.89/1.55 mlocal: ( mworld > $o ) > $o ).
% 1.89/1.55
% 1.89/1.55 thf(mlocal_def,definition,
% 1.89/1.55 ( mlocal
% 1.89/1.55 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.89/1.55
% 1.89/1.55 thf(mnot_type,type,
% 1.89/1.55 mnot: ( mworld > $o ) > mworld > $o ).
% 1.89/1.55
% 1.89/1.55 thf(mand_type,type,
% 1.89/1.55 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.89/1.55
% 1.89/1.55 thf(mor_type,type,
% 1.89/1.55 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.89/1.55
% 1.89/1.55 thf(mimplies_type,type,
% 1.89/1.55 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.89/1.55
% 1.89/1.55 thf(mequiv_type,type,
% 1.89/1.55 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.89/1.55
% 1.89/1.55 thf(mnot_def,definition,
% 1.89/1.55 ( mnot
% 1.89/1.55 = ( ^ [A: mworld > $o,W: mworld] :
% 1.89/1.55 ~ ( A @ W ) ) ) ).
% 1.89/1.55
% 1.89/1.55 thf(mand_def,definition,
% 1.89/1.55 ( mand
% 1.89/1.55 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.89/1.55 ( ( A @ W )
% 1.89/1.55 & ( B @ W ) ) ) ) ).
% 1.89/1.55
% 1.89/1.55 thf(mor_def,definition,
% 1.89/1.55 ( mor
% 1.89/1.55 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.89/1.55 ( ( A @ W )
% 1.89/1.55 | ( B @ W ) ) ) ) ).
% 1.89/1.55
% 1.89/1.55 thf(mimplies_def,definition,
% 1.89/1.55 ( mimplies
% 1.89/1.55 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.89/1.55 ( ( A @ W )
% 1.89/1.55 => ( B @ W ) ) ) ) ).
% 1.89/1.55
% 1.89/1.55 thf(mequiv_def,definition,
% 1.89/1.55 ( mequiv
% 1.89/1.55 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.89/1.55 ( ( A @ W )
% 1.89/1.55 <=> ( B @ W ) ) ) ) ).
% 1.89/1.55
% 1.89/1.55 thf(mbox_type,type,
% 1.89/1.55 mbox: ( mworld > $o ) > mworld > $o ).
% 1.89/1.55
% 1.89/1.55 thf(mbox_def,definition,
% 1.89/1.55 ( mbox
% 1.89/1.55 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.89/1.55 ! [V: mworld] :
% 1.89/1.55 ( ( mrel @ W @ V )
% 1.89/1.55 => ( Phi @ V ) ) ) ) ).
% 1.89/1.55
% 1.89/1.55 thf(mdia_type,type,
% 1.89/1.55 mdia: ( mworld > $o ) > mworld > $o ).
% 1.89/1.55
% 1.89/1.55 thf(mdia_def,definition,
% 1.89/1.55 ( mdia
% 1.89/1.55 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.89/1.55 ? [V: mworld] :
% 1.89/1.55 ( ( mrel @ W @ V )
% 1.89/1.55 & ( Phi @ V ) ) ) ) ).
% 1.89/1.55
% 1.89/1.55 thf(mrel_reflexive,axiom,
% 1.89/1.55 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.89/1.55
% 1.89/1.55 thf(mrel_euclidean,axiom,
% 1.89/1.55 ! [W: mworld,V: mworld,U: mworld] :
% 1.89/1.55 ( ( ( mrel @ W @ U )
% 1.89/1.55 & ( mrel @ W @ V ) )
% 1.89/1.55 => ( mrel @ U @ V ) ) ).
% 1.89/1.55
% 1.89/1.55 thf(p_decl,type,
% 1.89/1.55 p: mworld > $o ).
% 1.89/1.55
% 1.89/1.55 thf(q_decl,type,
% 1.89/1.55 q: mworld > $o ).
% 1.89/1.55
% 1.89/1.55 thf(con,conjecture,
% 1.89/1.55 mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) ).
% 1.89/1.55 ------------------------
% 1.89/1.57 % (13496)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_13393 for (2999ds/2Mi)
% 1.89/1.57 % (13494)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_13393 for (2999ds/27Mi)
% 1.89/1.57 % (13492)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13393 for (2999ds/183Mi)
% 1.89/1.57 % (13493)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_13393 for (2999ds/4Mi)
% 1.89/1.57 % (13498)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13393 for (2999ds/18Mi)
% 1.89/1.57 % (13495)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13393 for (2999ds/2Mi)
% 1.89/1.57 % (13496)Instruction limit reached!
% 1.89/1.57 % (13496)------------------------------
% 1.89/1.57 % (13496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.57 % (13496)Termination reason: Unknown
% 1.89/1.57 % (13496)Termination phase: Property scanning
% 1.89/1.57
% 1.89/1.57 % (13496)Memory used [KB]: 1023
% 1.89/1.57 % (13496)Time elapsed: 0.003 s
% 1.89/1.57 % (13496)Instructions burned: 3 (million)
% 1.89/1.57 % (13497)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_13393 for (2999ds/275Mi)
% 1.89/1.57 % (13496)------------------------------
% 1.89/1.57 % (13496)------------------------------
% 1.89/1.57 % (13493)Instruction limit reached!
% 1.89/1.57 % (13493)------------------------------
% 1.89/1.57 % (13493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.57 % (13493)Termination reason: Unknown
% 1.89/1.57 % (13493)Termination phase: Saturation
% 1.89/1.57
% 1.89/1.57 % (13493)Memory used [KB]: 5500
% 1.89/1.57 % (13493)Time elapsed: 0.004 s
% 1.89/1.57 % (13493)Instructions burned: 5 (million)
% 1.89/1.57 % (13493)------------------------------
% 1.89/1.57 % (13493)------------------------------
% 1.89/1.57 % (13495)Instruction limit reached!
% 1.89/1.57 % (13495)------------------------------
% 1.89/1.57 % (13495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.57 % (13495)Termination reason: Unknown
% 1.89/1.57 % (13495)Termination phase: Saturation
% 1.89/1.57
% 1.89/1.57 % (13495)Memory used [KB]: 1023
% 1.89/1.57 % (13495)Time elapsed: 0.003 s
% 1.89/1.57 % (13495)Instructions burned: 3 (million)
% 1.89/1.57 % (13495)------------------------------
% 1.89/1.57 % (13495)------------------------------
% 1.89/1.57 % (13497)Refutation not found, incomplete strategy
% 1.89/1.57 % (13497)------------------------------
% 1.89/1.57 % (13497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.57 % (13497)Termination reason: Refutation not found, incomplete strategy
% 1.89/1.57
% 1.89/1.57
% 1.89/1.57 % (13497)Memory used [KB]: 5500
% 1.89/1.57 % (13497)Time elapsed: 0.003 s
% 1.89/1.57 % (13497)Instructions burned: 2 (million)
% 1.89/1.57 % (13497)------------------------------
% 1.89/1.57 % (13497)------------------------------
% 1.89/1.58 % (13498)Instruction limit reached!
% 1.89/1.58 % (13498)------------------------------
% 1.89/1.58 % (13498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.58 % (13498)Termination reason: Unknown
% 1.89/1.58 % (13498)Termination phase: Saturation
% 1.89/1.58
% 1.89/1.58 % (13498)Memory used [KB]: 5628
% 1.89/1.58 % (13498)Time elapsed: 0.013 s
% 1.89/1.58 % (13498)Instructions burned: 19 (million)
% 1.89/1.58 % (13498)------------------------------
% 1.89/1.58 % (13498)------------------------------
% 1.89/1.59 % (13494)Instruction limit reached!
% 1.89/1.59 % (13494)------------------------------
% 1.89/1.59 % (13494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.59 % (13494)Termination reason: Unknown
% 1.89/1.59 % (13494)Termination phase: Saturation
% 1.89/1.59
% 1.89/1.59 % (13494)Memory used [KB]: 5628
% 1.89/1.59 % (13494)Time elapsed: 0.018 s
% 1.89/1.59 % (13494)Instructions burned: 28 (million)
% 1.89/1.59 % (13494)------------------------------
% 1.89/1.59 % (13494)------------------------------
% 1.89/1.59 % (13500)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_13393 for (2999ds/37Mi)
% 1.89/1.59 % (13499)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13393 for (2999ds/3Mi)
% 1.89/1.59 % (13502)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_13393 for (2999ds/3Mi)
% 1.89/1.59 % (13501)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_13393 for (2999ds/15Mi)
% 1.89/1.59 % (13499)Instruction limit reached!
% 1.89/1.59 % (13499)------------------------------
% 1.89/1.59 % (13499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.59 % (13499)Termination reason: Unknown
% 1.89/1.59 % (13499)Termination phase: Function definition elimination
% 1.89/1.59
% 1.89/1.59 % (13499)Memory used [KB]: 1023
% 1.89/1.59 % (13499)Time elapsed: 0.003 s
% 1.89/1.59 % (13499)Instructions burned: 3 (million)
% 1.89/1.59 % (13499)------------------------------
% 1.89/1.59 % (13499)------------------------------
% 1.89/1.59 % (13502)Instruction limit reached!
% 1.89/1.59 % (13502)------------------------------
% 1.89/1.59 % (13502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.59 % (13502)Termination reason: Unknown
% 1.89/1.59 % (13502)Termination phase: Property scanning
% 1.89/1.59
% 1.89/1.59 % (13502)Memory used [KB]: 1023
% 1.89/1.59 % (13502)Time elapsed: 0.003 s
% 1.89/1.59 % (13502)Instructions burned: 3 (million)
% 1.89/1.59 % (13502)------------------------------
% 1.89/1.59 % (13502)------------------------------
% 2.00/1.60 % (13501)Instruction limit reached!
% 2.00/1.60 % (13501)------------------------------
% 2.00/1.60 % (13501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.00/1.60 % (13501)Termination reason: Unknown
% 2.00/1.60 % (13501)Termination phase: Saturation
% 2.00/1.60
% 2.00/1.60 % (13501)Memory used [KB]: 5628
% 2.00/1.60 % (13501)Time elapsed: 0.011 s
% 2.00/1.60 % (13501)Instructions burned: 16 (million)
% 2.00/1.60 % (13501)------------------------------
% 2.00/1.60 % (13501)------------------------------
% 2.00/1.60 % (13503)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_13393 for (2999ds/1041Mi)
% 2.00/1.60 % (13492)First to succeed.
% 2.00/1.60 % (13504)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13393 for (2999ds/7Mi)
% 2.00/1.60 % (13492)Refutation found. Thanks to Tanya!
% 2.00/1.60 % SZS status Theorem for DTF2THF_13393
% 2.00/1.60 % SZS output start Proof for DTF2THF_13393
% 2.00/1.60 thf(type_def_5, type, mworld: $tType).
% 2.00/1.60 thf(func_def_0, type, mworld: $tType).
% 2.00/1.60 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 2.00/1.60 thf(func_def_2, type, mactual: mworld).
% 2.00/1.60 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 2.00/1.60 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 2.00/1.60 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.00/1.60 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.00/1.60 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.00/1.60 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.00/1.60 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 2.00/1.60 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 2.00/1.60 thf(func_def_12, type, p: mworld > $o).
% 2.00/1.60 thf(func_def_13, type, q: mworld > $o).
% 2.00/1.60 thf(func_def_28, type, sK1: mworld).
% 2.00/1.60 thf(func_def_29, type, sK2: mworld).
% 2.00/1.60 thf(func_def_30, type, sK3: mworld).
% 2.00/1.60 thf(func_def_31, type, sK4: mworld).
% 2.00/1.60 thf(f644,plain,(
% 2.00/1.60 $false),
% 2.00/1.60 inference(avatar_sat_refutation,[status(thm)],[f90,f99,f104,f113,f118,f246,f359,f373,f391,f425,f431,f465,f581,f590,f597,f603,f613,f614,f637,f643])).
% 2.00/1.60 thf(f643,plain,(
% 2.00/1.60 ~spl0_7 | ~spl0_23),
% 2.00/1.60 inference(avatar_contradiction_clause,[status(thm)],[f642])).
% 2.00/1.60 thf(f642,plain,(
% 2.00/1.60 $false | (~spl0_7 | ~spl0_23)),
% 2.00/1.60 inference(trivial_inequality_removal,[status(thm)],[f639])).
% 2.00/1.60 thf(f639,plain,(
% 2.00/1.60 ($true = $false) | (~spl0_7 | ~spl0_23)),
% 2.00/1.60 inference(superposition,[status(thm)],[f112,f585])).
% 2.00/1.60 thf(f585,plain,(
% 2.00/1.60 ($true = (q @ sK3)) | ~spl0_23),
% 2.00/1.60 inference(avatar_component_clause,[status(thm)],[f583])).
% 2.00/1.60 thf(f583,definition,(
% 2.00/1.60 spl0_23 <=> ($true = (q @ sK3))),
% 2.00/1.60 introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition])).
% 2.00/1.60 thf(f112,plain,(
% 2.00/1.60 ($false = (q @ sK3)) | ~spl0_7),
% 2.00/1.60 inference(avatar_component_clause,[status(thm)],[f110])).
% 2.00/1.60 thf(f110,definition,(
% 2.00/1.60 spl0_7 <=> ($false = (q @ sK3))),
% 2.00/1.60 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 2.00/1.60 thf(f637,plain,(
% 2.00/1.60 ~spl0_24 | ~spl0_25),
% 2.00/1.60 inference(avatar_contradiction_clause,[status(thm)],[f636])).
% 2.00/1.60 thf(f636,plain,(
% 2.00/1.60 $false | (~spl0_24 | ~spl0_25)),
% 2.00/1.60 inference(trivial_inequality_removal,[status(thm)],[f632])).
% 2.00/1.60 thf(f632,plain,(
% 2.00/1.60 ($true = $false) | (~spl0_24 | ~spl0_25)),
% 2.00/1.60 inference(superposition,[status(thm)],[f589,f607])).
% 2.00/1.60 thf(f607,plain,(
% 2.00/1.60 ($true = (p @ sK3)) | ~spl0_25),
% 2.00/1.60 inference(avatar_component_clause,[status(thm)],[f605])).
% 2.00/1.60 thf(f605,definition,(
% 2.00/1.60 spl0_25 <=> ($true = (p @ sK3))),
% 2.00/1.60 introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition])).
% 2.00/1.60 thf(f589,plain,(
% 2.00/1.60 ($false = (p @ sK3)) | ~spl0_24),
% 2.00/1.60 inference(avatar_component_clause,[status(thm)],[f587])).
% 2.00/1.60 thf(f587,definition,(
% 2.00/1.60 spl0_24 <=> ($false = (p @ sK3))),
% 2.00/1.60 introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition])).
% 2.00/1.60 thf(f614,plain,(
% 2.00/1.60 spl0_25 | ~spl0_1 | ~spl0_8),
% 2.00/1.60 inference(avatar_split_clause,[status(thm)],[f499,f115,f85,f605])).
% 2.00/1.60 thf(f85,definition,(
% 2.00/1.60 spl0_1 <=> ! [X2 : mworld] : (($false = (mrel @ sK1 @ X2)) | ($true = (p @ X2)))),
% 2.00/1.60 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 2.00/1.60 thf(f115,definition,(
% 2.00/1.60 spl0_8 <=> ((mrel @ sK1 @ sK3) = $true)),
% 2.00/1.60 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 2.00/1.60 thf(f499,plain,(
% 2.00/1.60 ($true = (p @ sK3)) | (~spl0_1 | ~spl0_8)),
% 2.00/1.60 inference(trivial_inequality_removal,[status(thm)],[f481])).
% 2.00/1.60 thf(f481,plain,(
% 2.00/1.60 ($true = (p @ sK3)) | ($true = $false) | (~spl0_1 | ~spl0_8)),
% 2.00/1.60 inference(superposition,[status(thm)],[f86,f117])).
% 2.00/1.60 thf(f117,plain,(
% 2.00/1.60 ((mrel @ sK1 @ sK3) = $true) | ~spl0_8),
% 2.00/1.60 inference(avatar_component_clause,[status(thm)],[f115])).
% 2.00/1.60 thf(f86,plain,(
% 2.00/1.60 ( ! [X2 : mworld] : (($false = (mrel @ sK1 @ X2)) | ($true = (p @ X2))) ) | ~spl0_1),
% 2.00/1.60 inference(avatar_component_clause,[status(thm)],[f85])).
% 2.00/1.60 thf(f613,plain,(
% 2.00/1.60 ~spl0_17 | spl0_19 | spl0_20),
% 2.00/1.60 inference(avatar_contradiction_clause,[status(thm)],[f612])).
% 2.00/1.60 thf(f612,plain,(
% 2.00/1.60 $false | (~spl0_17 | spl0_19 | spl0_20)),
% 2.00/1.60 inference(subsumption_resolution,[status(thm)],[f611,f417])).
% 2.00/1.60 thf(f417,plain,(
% 2.00/1.60 ($false != (q @ sK2)) | spl0_20),
% 2.00/1.60 inference(avatar_component_clause,[status(thm)],[f416])).
% 2.00/1.60 thf(f416,definition,(
% 2.00/1.60 spl0_20 <=> ($false = (q @ sK2))),
% 2.00/1.60 introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition])).
% 2.00/1.60 thf(f611,plain,(
% 2.00/1.60 ($false = (q @ sK2)) | (~spl0_17 | spl0_19)),
% 2.00/1.60 inference(subsumption_resolution,[status(thm)],[f518,f413])).
% 2.00/1.60 thf(f413,plain,(
% 2.00/1.60 ($true != (p @ sK2)) | spl0_19),
% 2.00/1.60 inference(avatar_component_clause,[status(thm)],[f412])).
% 2.00/1.60 thf(f412,definition,(
% 2.00/1.60 spl0_19 <=> ($true = (p @ sK2))),
% 2.00/1.60 introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition])).
% 2.00/1.60 thf(f518,plain,(
% 2.00/1.60 ($true = (p @ sK2)) | ($false = (q @ sK2)) | ~spl0_17),
% 2.00/1.60 inference(trivial_inequality_removal,[status(thm)],[f516])).
% 2.00/1.60 thf(f516,plain,(
% 2.00/1.60 ($false = (q @ sK2)) | ($true != $true) | ($true = (p @ sK2)) | ~spl0_17),
% 2.00/1.60 inference(superposition,[status(thm)],[f354,f47])).
% 2.00/1.60 thf(f47,plain,(
% 2.00/1.60 ( ! [X0 : mworld] : (($true = (mrel @ X0 @ X0))) )),
% 2.00/1.60 inference(cnf_transformation,[status(thm)],[f32])).
% 2.00/1.60 thf(f32,plain,(
% 2.00/1.60 ! [X0 : mworld] : ($true = (mrel @ X0 @ X0))),
% 2.00/1.60 inference(fool_elimination,[status(thm)],[f31])).
% 2.00/1.60 thf(f31,plain,(
% 2.00/1.60 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 2.00/1.60 inference(rectify,[status(thm)],[f9])).
% 2.00/1.60 thf(f9,axiom,(
% 2.00/1.60 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 2.00/1.60 file('/export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2THF_13393.p',mrel_reflexive)).
% 2.00/1.60 thf(f354,plain,(
% 2.00/1.60 ( ! [X0 : mworld] : (($true != (mrel @ sK2 @ X0)) | ((p @ X0) = $true) | ($false = (q @ X0))) ) | ~spl0_17),
% 2.00/1.60 inference(avatar_component_clause,[status(thm)],[f353])).
% 2.00/1.60 thf(f353,definition,(
% 2.00/1.60 spl0_17 <=> ! [X0 : mworld] : (((p @ X0) = $true) | ($false = (q @ X0)) | ($true != (mrel @ sK2 @ X0)))),
% 2.00/1.60 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 2.00/1.60 thf(f603,plain,(
% 2.00/1.60 ~spl0_1 | ~spl0_5 | ~spl0_21),
% 2.00/1.60 inference(avatar_contradiction_clause,[status(thm)],[f602])).
% 2.00/1.60 thf(f602,plain,(
% 2.00/1.60 $false | (~spl0_1 | ~spl0_5 | ~spl0_21)),
% 2.00/1.60 inference(trivial_inequality_removal,[status(thm)],[f599])).
% 2.00/1.60 thf(f599,plain,(
% 2.00/1.60 ($true = $false) | (~spl0_1 | ~spl0_5 | ~spl0_21)),
% 2.00/1.60 inference(superposition,[status(thm)],[f506,f576])).
% 2.00/1.60 thf(f576,plain,(
% 2.00/1.60 ($false = (p @ sK4)) | ~spl0_21),
% 2.00/1.60 inference(avatar_component_clause,[status(thm)],[f574])).
% 2.00/1.60 thf(f574,definition,(
% 2.00/1.60 spl0_21 <=> ($false = (p @ sK4))),
% 2.00/1.60 introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition])).
% 2.00/1.60 thf(f506,plain,(
% 2.00/1.60 ($true = (p @ sK4)) | (~spl0_1 | ~spl0_5)),
% 2.00/1.60 inference(trivial_inequality_removal,[status(thm)],[f493])).
% 2.00/1.60 thf(f493,plain,(
% 2.00/1.60 ($true = $false) | ($true = (p @ sK4)) | (~spl0_1 | ~spl0_5)),
% 2.00/1.60 inference(superposition,[status(thm)],[f103,f86])).
% 2.00/1.60 thf(f103,plain,(
% 2.00/1.60 ($true = (mrel @ sK1 @ sK4)) | ~spl0_5),
% 2.00/1.60 inference(avatar_component_clause,[status(thm)],[f101])).
% 2.00/1.60 thf(f101,definition,(
% 2.00/1.60 spl0_5 <=> ($true = (mrel @ sK1 @ sK4))),
% 2.00/1.60 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 2.00/1.60 thf(f597,plain,(
% 2.00/1.60 ~spl0_4 | ~spl0_22),
% 2.00/1.60 inference(avatar_contradiction_clause,[status(thm)],[f596])).
% 2.00/1.60 thf(f596,plain,(
% 2.00/1.61 $false | (~spl0_4 | ~spl0_22)),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f593])).
% 2.00/1.61 thf(f593,plain,(
% 2.00/1.61 ($true = $false) | (~spl0_4 | ~spl0_22)),
% 2.00/1.61 inference(superposition,[status(thm)],[f98,f580])).
% 2.00/1.61 thf(f580,plain,(
% 2.00/1.61 ($true = (q @ sK4)) | ~spl0_22),
% 2.00/1.61 inference(avatar_component_clause,[status(thm)],[f578])).
% 2.00/1.61 thf(f578,definition,(
% 2.00/1.61 spl0_22 <=> ($true = (q @ sK4))),
% 2.00/1.61 introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition])).
% 2.00/1.61 thf(f98,plain,(
% 2.00/1.61 ($false = (q @ sK4)) | ~spl0_4),
% 2.00/1.61 inference(avatar_component_clause,[status(thm)],[f96])).
% 2.00/1.61 thf(f96,definition,(
% 2.00/1.61 spl0_4 <=> ($false = (q @ sK4))),
% 2.00/1.61 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 2.00/1.61 thf(f590,plain,(
% 2.00/1.61 spl0_23 | spl0_24 | ~spl0_8 | ~spl0_18),
% 2.00/1.61 inference(avatar_split_clause,[status(thm)],[f568,f356,f115,f587,f583])).
% 2.00/1.61 thf(f356,definition,(
% 2.00/1.61 spl0_18 <=> ($true = (mrel @ sK1 @ mactual))),
% 2.00/1.61 introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition])).
% 2.00/1.61 thf(f568,plain,(
% 2.00/1.61 ($true = (q @ sK3)) | ($false = (p @ sK3)) | (~spl0_8 | ~spl0_18)),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f565])).
% 2.00/1.61 thf(f565,plain,(
% 2.00/1.61 ($false = (p @ sK3)) | ($true != $true) | ($true = (q @ sK3)) | (~spl0_8 | ~spl0_18)),
% 2.00/1.61 inference(superposition,[status(thm)],[f475,f117])).
% 2.00/1.61 thf(f475,plain,(
% 2.00/1.61 ( ! [X0 : mworld] : (($true != (mrel @ sK1 @ X0)) | ($true = (q @ X0)) | ((p @ X0) = $false)) ) | ~spl0_18),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f466])).
% 2.00/1.61 thf(f466,plain,(
% 2.00/1.61 ( ! [X0 : mworld] : (($true = (q @ X0)) | ($true != $true) | ($true != (mrel @ sK1 @ X0)) | ((p @ X0) = $false)) ) | ~spl0_18),
% 2.00/1.61 inference(superposition,[status(thm)],[f174,f357])).
% 2.00/1.61 thf(f357,plain,(
% 2.00/1.61 ($true = (mrel @ sK1 @ mactual)) | ~spl0_18),
% 2.00/1.61 inference(avatar_component_clause,[status(thm)],[f356])).
% 2.00/1.61 thf(f174,plain,(
% 2.00/1.61 ( ! [X0 : mworld,X1 : mworld] : (($true != (mrel @ X1 @ mactual)) | ($true != (mrel @ X1 @ X0)) | ((p @ X0) = $false) | ($true = (q @ X0))) )),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f164])).
% 2.00/1.61 thf(f164,plain,(
% 2.00/1.61 ( ! [X0 : mworld,X1 : mworld] : (($true != (mrel @ X1 @ X0)) | ($true != (mrel @ X1 @ mactual)) | ((p @ X0) = $false) | ($true = (q @ X0)) | ($true = $false)) )),
% 2.00/1.61 inference(superposition,[status(thm)],[f58,f48])).
% 2.00/1.61 thf(f48,plain,(
% 2.00/1.61 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : (($true = (mrel @ X2 @ X1)) | ($true != (mrel @ X0 @ X1)) | ($true != (mrel @ X0 @ X2))) )),
% 2.00/1.61 inference(cnf_transformation,[status(thm)],[f37])).
% 2.00/1.61 thf(f37,plain,(
% 2.00/1.61 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (($true != (mrel @ X0 @ X1)) | ($true != (mrel @ X0 @ X2)) | ($true = (mrel @ X2 @ X1)))),
% 2.00/1.61 inference(flattening,[status(thm)],[f36])).
% 2.00/1.61 thf(f36,plain,(
% 2.00/1.61 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (($true = (mrel @ X2 @ X1)) | (($true != (mrel @ X0 @ X1)) | ($true != (mrel @ X0 @ X2))))),
% 2.00/1.61 inference(ennf_transformation,[status(thm)],[f28])).
% 2.00/1.61 thf(f28,plain,(
% 2.00/1.61 ! [X0 : mworld,X1 : mworld,X2 : mworld] : ((($true = (mrel @ X0 @ X1)) & ($true = (mrel @ X0 @ X2))) => ($true = (mrel @ X2 @ X1)))),
% 2.00/1.61 inference(fool_elimination,[status(thm)],[f27])).
% 2.00/1.61 thf(f27,plain,(
% 2.00/1.61 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X0 @ X2) & (mrel @ X0 @ X1)) => (mrel @ X2 @ X1))),
% 2.00/1.61 inference(rectify,[status(thm)],[f10])).
% 2.00/1.61 thf(f10,axiom,(
% 2.00/1.61 ! [X2 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ X2 @ X5) & (mrel @ X2 @ X4)) => (mrel @ X5 @ X4))),
% 2.00/1.61 file('/export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2THF_13393.p',mrel_euclidean)).
% 2.00/1.61 thf(f58,plain,(
% 2.00/1.61 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((p @ X1) = $false) | ($true = (q @ X1))) )),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 2.00/1.61 thf(f56,plain,(
% 2.00/1.61 ( ! [X1 : mworld] : (((p @ X1) = (q @ X1)) | ($false = (mrel @ mactual @ X1))) )),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 2.00/1.61 thf(f55,plain,(
% 2.00/1.61 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((p @ X1) = (q @ X1)))) )),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 2.00/1.61 thf(f54,plain,(
% 2.00/1.61 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => ((p @ X1) = (q @ X1))))) )),
% 2.00/1.61 inference(beta_eta_normalization,[status(thm)],[f53])).
% 2.00/1.61 thf(f53,plain,(
% 2.00/1.61 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) = (q @ Y0)))) @ X1))) )),
% 2.00/1.61 inference(pi_clausification,[status(thm)],[f52])).
% 2.00/1.61 thf(f52,plain,(
% 2.00/1.61 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) = (q @ Y0))))))),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 2.00/1.61 thf(f50,plain,(
% 2.00/1.61 ($true != ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) = (q @ Y0))))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))) = (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1))))))))))),
% 2.00/1.61 inference(beta_eta_normalization,[status(thm)],[f49])).
% 2.00/1.61 thf(f49,plain,(
% 2.00/1.61 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))) @ p @ q)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ p) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ q))))))),
% 2.00/1.61 inference(definition_unfolding,[status(thm)],[f41,f38,f44,f45,f46,f45,f46,f45,f45])).
% 2.00/1.61 thf(f46,plain,(
% 2.00/1.61 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 2.00/1.61 inference(cnf_transformation,[status(thm)],[f20])).
% 2.00/1.61 thf(f20,plain,(
% 2.00/1.61 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 2.00/1.61 inference(fool_elimination,[status(thm)],[f19])).
% 2.00/1.61 thf(f19,plain,(
% 2.00/1.61 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) <=> (X1 @ X2))) = mequiv)),
% 2.00/1.61 inference(rectify,[status(thm)],[f6])).
% 2.00/1.61 thf(f6,axiom,(
% 2.00/1.61 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X3 @ X2))) = mequiv)),
% 2.00/1.61 file('/export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2THF_13393.p',mequiv_def)).
% 2.00/1.61 thf(f45,plain,(
% 2.00/1.61 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 2.00/1.61 inference(cnf_transformation,[status(thm)],[f24])).
% 2.00/1.61 thf(f24,plain,(
% 2.00/1.61 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 2.00/1.61 inference(fool_elimination,[status(thm)],[f23])).
% 2.00/1.61 thf(f23,plain,(
% 2.00/1.61 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 2.00/1.61 inference(rectify,[status(thm)],[f7])).
% 2.00/1.61 thf(f7,axiom,(
% 2.00/1.61 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 2.00/1.61 file('/export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2THF_13393.p',mbox_def)).
% 2.00/1.61 thf(f44,plain,(
% 2.00/1.61 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 2.00/1.61 inference(cnf_transformation,[status(thm)],[f30])).
% 2.00/1.61 thf(f30,plain,(
% 2.00/1.61 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 2.00/1.61 inference(fool_elimination,[status(thm)],[f29])).
% 2.00/1.61 thf(f29,plain,(
% 2.00/1.61 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 2.00/1.61 inference(rectify,[status(thm)],[f5])).
% 2.00/1.61 thf(f5,axiom,(
% 2.00/1.61 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 2.00/1.61 file('/export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2THF_13393.p',mimplies_def)).
% 2.00/1.61 thf(f38,plain,(
% 2.00/1.61 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 2.00/1.61 inference(cnf_transformation,[status(thm)],[f18])).
% 2.00/1.61 thf(f18,plain,(
% 2.00/1.61 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 2.00/1.61 inference(fool_elimination,[status(thm)],[f1])).
% 2.00/1.61 thf(f1,axiom,(
% 2.00/1.61 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 2.00/1.61 file('/export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2THF_13393.p',mlocal_def)).
% 2.00/1.61 thf(f41,plain,(
% 2.00/1.61 ((mlocal @ (mimplies @ (mbox @ (mequiv @ p @ q)) @ (mbox @ (mequiv @ (mbox @ p) @ (mbox @ q))))) != $true)),
% 2.00/1.61 inference(cnf_transformation,[status(thm)],[f35])).
% 2.00/1.61 thf(f35,plain,(
% 2.00/1.61 ((mlocal @ (mimplies @ (mbox @ (mequiv @ p @ q)) @ (mbox @ (mequiv @ (mbox @ p) @ (mbox @ q))))) != $true)),
% 2.00/1.61 inference(flattening,[status(thm)],[f22])).
% 2.00/1.61 thf(f22,plain,(
% 2.00/1.61 ~((mlocal @ (mimplies @ (mbox @ (mequiv @ p @ q)) @ (mbox @ (mequiv @ (mbox @ p) @ (mbox @ q))))) = $true)),
% 2.00/1.61 inference(fool_elimination,[status(thm)],[f21])).
% 2.00/1.61 thf(f21,plain,(
% 2.00/1.61 ~(mlocal @ (mimplies @ (mbox @ (mequiv @ p @ q)) @ (mbox @ (mequiv @ (mbox @ p) @ (mbox @ q)))))),
% 2.00/1.61 inference(rectify,[status(thm)],[f12])).
% 2.00/1.61 thf(f12,negated_conjecture,(
% 2.00/1.61 ~(mlocal @ (mimplies @ (mbox @ (mequiv @ p @ q)) @ (mbox @ (mequiv @ (mbox @ p) @ (mbox @ q)))))),
% 2.00/1.61 inference(negated_conjecture,[status(cth)],[f11])).
% 2.00/1.61 thf(f11,conjecture,(
% 2.00/1.61 (mlocal @ (mimplies @ (mbox @ (mequiv @ p @ q)) @ (mbox @ (mequiv @ (mbox @ p) @ (mbox @ q)))))),
% 2.00/1.61 file('/export/starexec/sandbox/tmp/tmp.LZ8lv80Rf8/DTF2THF_13393.p',con)).
% 2.00/1.61 thf(f581,plain,(
% 2.00/1.61 spl0_21 | spl0_22 | ~spl0_5 | ~spl0_18),
% 2.00/1.61 inference(avatar_split_clause,[status(thm)],[f572,f356,f101,f578,f574])).
% 2.00/1.61 thf(f572,plain,(
% 2.00/1.61 ($false = (p @ sK4)) | ($true = (q @ sK4)) | (~spl0_5 | ~spl0_18)),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f566])).
% 2.00/1.61 thf(f566,plain,(
% 2.00/1.61 ($false = (p @ sK4)) | ($true != $true) | ($true = (q @ sK4)) | (~spl0_5 | ~spl0_18)),
% 2.00/1.61 inference(superposition,[status(thm)],[f475,f103])).
% 2.00/1.61 thf(f465,plain,(
% 2.00/1.61 ~spl0_2 | ~spl0_4 | ~spl0_5),
% 2.00/1.61 inference(avatar_contradiction_clause,[status(thm)],[f464])).
% 2.00/1.61 thf(f464,plain,(
% 2.00/1.61 $false | (~spl0_2 | ~spl0_4 | ~spl0_5)),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f461])).
% 2.00/1.61 thf(f461,plain,(
% 2.00/1.61 ($true = $false) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
% 2.00/1.61 inference(superposition,[status(thm)],[f98,f442])).
% 2.00/1.61 thf(f442,plain,(
% 2.00/1.61 ($true = (q @ sK4)) | (~spl0_2 | ~spl0_5)),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f437])).
% 2.00/1.61 thf(f437,plain,(
% 2.00/1.61 ($true = (q @ sK4)) | ($true = $false) | (~spl0_2 | ~spl0_5)),
% 2.00/1.61 inference(superposition,[status(thm)],[f89,f103])).
% 2.00/1.61 thf(f89,plain,(
% 2.00/1.61 ( ! [X1 : mworld] : (($false = (mrel @ sK1 @ X1)) | ($true = (q @ X1))) ) | ~spl0_2),
% 2.00/1.61 inference(avatar_component_clause,[status(thm)],[f88])).
% 2.00/1.61 thf(f88,definition,(
% 2.00/1.61 spl0_2 <=> ! [X1 : mworld] : (($false = (mrel @ sK1 @ X1)) | ($true = (q @ X1)))),
% 2.00/1.61 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 2.00/1.61 thf(f431,plain,(
% 2.00/1.61 ~spl0_3 | ~spl0_19),
% 2.00/1.61 inference(avatar_contradiction_clause,[status(thm)],[f430])).
% 2.00/1.61 thf(f430,plain,(
% 2.00/1.61 $false | (~spl0_3 | ~spl0_19)),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f427])).
% 2.00/1.61 thf(f427,plain,(
% 2.00/1.61 ($true = $false) | (~spl0_3 | ~spl0_19)),
% 2.00/1.61 inference(superposition,[status(thm)],[f94,f414])).
% 2.00/1.61 thf(f414,plain,(
% 2.00/1.61 ($true = (p @ sK2)) | ~spl0_19),
% 2.00/1.61 inference(avatar_component_clause,[status(thm)],[f412])).
% 2.00/1.61 thf(f94,plain,(
% 2.00/1.61 ((p @ sK2) = $false) | ~spl0_3),
% 2.00/1.61 inference(avatar_component_clause,[status(thm)],[f92])).
% 2.00/1.61 thf(f92,definition,(
% 2.00/1.61 spl0_3 <=> ((p @ sK2) = $false)),
% 2.00/1.61 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 2.00/1.61 thf(f425,plain,(
% 2.00/1.61 ~spl0_2 | ~spl0_6 | ~spl0_20),
% 2.00/1.61 inference(avatar_contradiction_clause,[status(thm)],[f424])).
% 2.00/1.61 thf(f424,plain,(
% 2.00/1.61 $false | (~spl0_2 | ~spl0_6 | ~spl0_20)),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f420])).
% 2.00/1.61 thf(f420,plain,(
% 2.00/1.61 ($true = $false) | (~spl0_2 | ~spl0_6 | ~spl0_20)),
% 2.00/1.61 inference(superposition,[status(thm)],[f418,f399])).
% 2.00/1.61 thf(f399,plain,(
% 2.00/1.61 ($true = (q @ sK2)) | (~spl0_2 | ~spl0_6)),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f393])).
% 2.00/1.61 thf(f393,plain,(
% 2.00/1.61 ($true = $false) | ($true = (q @ sK2)) | (~spl0_2 | ~spl0_6)),
% 2.00/1.61 inference(superposition,[status(thm)],[f108,f89])).
% 2.00/1.61 thf(f108,plain,(
% 2.00/1.61 ($true = (mrel @ sK1 @ sK2)) | ~spl0_6),
% 2.00/1.61 inference(avatar_component_clause,[status(thm)],[f106])).
% 2.00/1.61 thf(f106,definition,(
% 2.00/1.61 spl0_6 <=> ($true = (mrel @ sK1 @ sK2))),
% 2.00/1.61 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 2.00/1.61 thf(f418,plain,(
% 2.00/1.61 ($false = (q @ sK2)) | ~spl0_20),
% 2.00/1.61 inference(avatar_component_clause,[status(thm)],[f416])).
% 2.00/1.61 thf(f391,plain,(
% 2.00/1.61 ~spl0_2 | ~spl0_7 | ~spl0_8),
% 2.00/1.61 inference(avatar_contradiction_clause,[status(thm)],[f390])).
% 2.00/1.61 thf(f390,plain,(
% 2.00/1.61 $false | (~spl0_2 | ~spl0_7 | ~spl0_8)),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f387])).
% 2.00/1.61 thf(f387,plain,(
% 2.00/1.61 ($true = $false) | (~spl0_2 | ~spl0_7 | ~spl0_8)),
% 2.00/1.61 inference(superposition,[status(thm)],[f112,f383])).
% 2.00/1.61 thf(f383,plain,(
% 2.00/1.61 ($true = (q @ sK3)) | (~spl0_2 | ~spl0_8)),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f379])).
% 2.00/1.61 thf(f379,plain,(
% 2.00/1.61 ($true = (q @ sK3)) | ($true = $false) | (~spl0_2 | ~spl0_8)),
% 2.00/1.61 inference(superposition,[status(thm)],[f89,f117])).
% 2.00/1.61 thf(f373,plain,(
% 2.00/1.61 spl0_18),
% 2.00/1.61 inference(avatar_contradiction_clause,[status(thm)],[f372])).
% 2.00/1.61 thf(f372,plain,(
% 2.00/1.61 $false | spl0_18),
% 2.00/1.61 inference(subsumption_resolution,[status(thm)],[f371,f47])).
% 2.00/1.61 thf(f371,plain,(
% 2.00/1.61 ($true != (mrel @ mactual @ mactual)) | spl0_18),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f363])).
% 2.00/1.61 thf(f363,plain,(
% 2.00/1.61 ($true != $true) | ($true != (mrel @ mactual @ mactual)) | spl0_18),
% 2.00/1.61 inference(superposition,[status(thm)],[f362,f62])).
% 2.00/1.61 thf(f62,plain,(
% 2.00/1.61 ($true = (mrel @ mactual @ sK1))),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 2.00/1.61 thf(f60,plain,(
% 2.00/1.61 (((mrel @ mactual @ sK1) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0)))) = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0)))))) = $false)),
% 2.00/1.61 inference(beta_eta_normalization,[status(thm)],[f59])).
% 2.00/1.61 thf(f59,plain,(
% 2.00/1.61 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))) = (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1))))))) @ sK1))),
% 2.00/1.61 inference(sigma_clausification,[status(thm)],[f51])).
% 2.00/1.61 thf(f51,plain,(
% 2.00/1.61 ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))) = (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1)))))))))),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 2.00/1.61 thf(f362,plain,(
% 2.00/1.61 ( ! [X0 : mworld] : (($true != (mrel @ X0 @ sK1)) | ($true != (mrel @ X0 @ mactual))) ) | spl0_18),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f361])).
% 2.00/1.61 thf(f361,plain,(
% 2.00/1.61 ( ! [X0 : mworld] : (($true != (mrel @ X0 @ mactual)) | ($true != (mrel @ X0 @ sK1)) | ($true != $true)) ) | spl0_18),
% 2.00/1.61 inference(superposition,[status(thm)],[f358,f48])).
% 2.00/1.61 thf(f358,plain,(
% 2.00/1.61 ($true != (mrel @ sK1 @ mactual)) | spl0_18),
% 2.00/1.61 inference(avatar_component_clause,[status(thm)],[f356])).
% 2.00/1.61 thf(f359,plain,(
% 2.00/1.61 spl0_17 | ~spl0_18 | ~spl0_6),
% 2.00/1.61 inference(avatar_split_clause,[status(thm)],[f348,f106,f356,f353])).
% 2.00/1.61 thf(f348,plain,(
% 2.00/1.61 ( ! [X0 : mworld] : (((p @ X0) = $true) | ($true != (mrel @ sK1 @ mactual)) | ($true != (mrel @ sK2 @ X0)) | ($false = (q @ X0))) ) | ~spl0_6),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f346])).
% 2.00/1.61 thf(f346,plain,(
% 2.00/1.61 ( ! [X0 : mworld] : (($true != (mrel @ sK1 @ mactual)) | ($true != $true) | ($true != (mrel @ sK2 @ X0)) | ($false = (q @ X0)) | ((p @ X0) = $true)) ) | ~spl0_6),
% 2.00/1.61 inference(superposition,[status(thm)],[f273,f108])).
% 2.00/1.61 thf(f273,plain,(
% 2.00/1.61 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : (($true != (mrel @ X2 @ X0)) | ($true = (p @ X1)) | ($false = (q @ X1)) | ((mrel @ X2 @ mactual) != $true) | ($true != (mrel @ X0 @ X1))) )),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f271])).
% 2.00/1.61 thf(f271,plain,(
% 2.00/1.61 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : (($true != $true) | ($true != (mrel @ X0 @ X1)) | ((mrel @ X2 @ mactual) != $true) | ($true = (p @ X1)) | ($false = (q @ X1)) | ($true != (mrel @ X2 @ X0))) )),
% 2.00/1.61 inference(superposition,[status(thm)],[f161,f48])).
% 2.00/1.61 thf(f161,plain,(
% 2.00/1.61 ( ! [X0 : mworld,X1 : mworld] : (($true != (mrel @ X1 @ mactual)) | ($false = (q @ X0)) | ((p @ X0) = $true) | ($true != (mrel @ X1 @ X0))) )),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f156])).
% 2.00/1.61 thf(f156,plain,(
% 2.00/1.61 ( ! [X0 : mworld,X1 : mworld] : (($true != (mrel @ X1 @ X0)) | ($false = (q @ X0)) | ($true != (mrel @ X1 @ mactual)) | ((p @ X0) = $true) | ($true = $false)) )),
% 2.00/1.61 inference(superposition,[status(thm)],[f48,f57])).
% 2.00/1.61 thf(f57,plain,(
% 2.00/1.61 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (q @ X1)) | ($true = (p @ X1))) )),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 2.00/1.61 thf(f246,plain,(
% 2.00/1.61 ~spl0_1 | ~spl0_3 | ~spl0_6),
% 2.00/1.61 inference(avatar_contradiction_clause,[status(thm)],[f245])).
% 2.00/1.61 thf(f245,plain,(
% 2.00/1.61 $false | (~spl0_1 | ~spl0_3 | ~spl0_6)),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f242])).
% 2.00/1.61 thf(f242,plain,(
% 2.00/1.61 ($true = $false) | (~spl0_1 | ~spl0_3 | ~spl0_6)),
% 2.00/1.61 inference(superposition,[status(thm)],[f94,f239])).
% 2.00/1.61 thf(f239,plain,(
% 2.00/1.61 ($true = (p @ sK2)) | (~spl0_1 | ~spl0_6)),
% 2.00/1.61 inference(trivial_inequality_removal,[status(thm)],[f234])).
% 2.00/1.61 thf(f234,plain,(
% 2.00/1.61 ($true = (p @ sK2)) | ($true = $false) | (~spl0_1 | ~spl0_6)),
% 2.00/1.61 inference(superposition,[status(thm)],[f108,f86])).
% 2.00/1.61 thf(f118,plain,(
% 2.00/1.61 spl0_8 | spl0_6),
% 2.00/1.61 inference(avatar_split_clause,[status(thm)],[f73,f106,f115])).
% 2.00/1.61 thf(f73,plain,(
% 2.00/1.61 ((mrel @ sK1 @ sK3) = $true) | ($true = (mrel @ sK1 @ sK2))),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 2.00/1.61 thf(f71,plain,(
% 2.00/1.61 ($false = ((mrel @ sK1 @ sK3) => (q @ sK3))) | ($true = (mrel @ sK1 @ sK2))),
% 2.00/1.61 inference(beta_eta_normalization,[status(thm)],[f70])).
% 2.00/1.61 thf(f70,plain,(
% 2.00/1.61 ($false = ((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0))) @ sK3)) | ($true = (mrel @ sK1 @ sK2))),
% 2.00/1.61 inference(sigma_clausification,[status(thm)],[f69])).
% 2.00/1.61 thf(f69,plain,(
% 2.00/1.61 ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0))))) | ($true = (mrel @ sK1 @ sK2))),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 2.00/1.61 thf(f67,plain,(
% 2.00/1.61 ($false = ((mrel @ sK1 @ sK2) => (p @ sK2))) | ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0)))))),
% 2.00/1.61 inference(beta_eta_normalization,[status(thm)],[f66])).
% 2.00/1.61 thf(f66,plain,(
% 2.00/1.61 ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0))))) | ($false = ((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0))) @ sK2))),
% 2.00/1.61 inference(sigma_clausification,[status(thm)],[f65])).
% 2.00/1.61 thf(f65,plain,(
% 2.00/1.61 ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0))))) | ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0)))))),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 2.00/1.61 thf(f63,plain,(
% 2.00/1.61 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0)))) != (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0)))))),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 2.00/1.61 thf(f61,plain,(
% 2.00/1.61 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0)))) = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0))))))),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 2.00/1.61 thf(f113,plain,(
% 2.00/1.61 spl0_6 | spl0_7),
% 2.00/1.61 inference(avatar_split_clause,[status(thm)],[f72,f110,f106])).
% 2.00/1.61 thf(f72,plain,(
% 2.00/1.61 ($false = (q @ sK3)) | ($true = (mrel @ sK1 @ sK2))),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 2.00/1.61 thf(f104,plain,(
% 2.00/1.61 spl0_3 | spl0_5),
% 2.00/1.61 inference(avatar_split_clause,[status(thm)],[f77,f101,f92])).
% 2.00/1.61 thf(f77,plain,(
% 2.00/1.61 ((p @ sK2) = $false) | ($true = (mrel @ sK1 @ sK4))),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 2.00/1.61 thf(f75,plain,(
% 2.00/1.61 ((p @ sK2) = $false) | ($false = ((mrel @ sK1 @ sK4) => (q @ sK4)))),
% 2.00/1.61 inference(beta_eta_normalization,[status(thm)],[f74])).
% 2.00/1.61 thf(f74,plain,(
% 2.00/1.61 ((p @ sK2) = $false) | ($false = ((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0))) @ sK4))),
% 2.00/1.61 inference(sigma_clausification,[status(thm)],[f68])).
% 2.00/1.61 thf(f68,plain,(
% 2.00/1.61 ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0))))) | ((p @ sK2) = $false)),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 2.00/1.61 thf(f99,plain,(
% 2.00/1.61 spl0_3 | spl0_4),
% 2.00/1.61 inference(avatar_split_clause,[status(thm)],[f76,f96,f92])).
% 2.00/1.61 thf(f76,plain,(
% 2.00/1.61 ($false = (q @ sK4)) | ((p @ sK2) = $false)),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 2.00/1.61 thf(f90,plain,(
% 2.00/1.61 spl0_1 | spl0_2),
% 2.00/1.61 inference(avatar_split_clause,[status(thm)],[f83,f88,f85])).
% 2.00/1.61 thf(f83,plain,(
% 2.00/1.61 ( ! [X2 : mworld,X1 : mworld] : (($false = (mrel @ sK1 @ X2)) | ($false = (mrel @ sK1 @ X1)) | ($true = (q @ X1)) | ($true = (p @ X2))) )),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 2.00/1.61 thf(f82,plain,(
% 2.00/1.61 ( ! [X2 : mworld,X1 : mworld] : (($true = (q @ X1)) | ($true = ((mrel @ sK1 @ X2) => (p @ X2))) | ($false = (mrel @ sK1 @ X1))) )),
% 2.00/1.61 inference(beta_eta_normalization,[status(thm)],[f81])).
% 2.00/1.61 thf(f81,plain,(
% 2.00/1.61 ( ! [X2 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0))) @ X2)) | ($true = (q @ X1)) | ($false = (mrel @ sK1 @ X1))) )),
% 2.00/1.61 inference(pi_clausification,[status(thm)],[f80])).
% 2.00/1.61 thf(f80,plain,(
% 2.00/1.61 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0))))) | ($false = (mrel @ sK1 @ X1)) | ($true = (q @ X1))) )),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 2.00/1.61 thf(f79,plain,(
% 2.00/1.61 ( ! [X1 : mworld] : (($true = ((mrel @ sK1 @ X1) => (q @ X1))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0)))))) )),
% 2.00/1.61 inference(beta_eta_normalization,[status(thm)],[f78])).
% 2.00/1.61 thf(f78,plain,(
% 2.00/1.61 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0))) @ X1)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0)))))) )),
% 2.00/1.61 inference(pi_clausification,[status(thm)],[f64])).
% 2.00/1.61 thf(f64,plain,(
% 2.00/1.61 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0))))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0)))))),
% 2.00/1.61 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 2.00/1.61 % SZS output end Proof for DTF2THF_13393
% 2.00/1.61 % (13492)------------------------------
% 2.00/1.61 % (13492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.00/1.61 % (13492)Termination reason: Refutation
% 2.00/1.61
% 2.00/1.61 % (13492)Memory used [KB]: 5884
% 2.00/1.61 % (13492)Time elapsed: 0.035 s
% 2.00/1.61 % (13492)Instructions burned: 55 (million)
% 2.00/1.61 % (13492)------------------------------
% 2.00/1.61 % (13492)------------------------------
% 2.00/1.61 % (13491)Success in time 0.045 s
%------------------------------------------------------------------------------