%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PLA054^4 : 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 : n025.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 09:27:55 AM UTC 2026
% Result : Theorem 1.85s 1.44s
% Output : Refutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 15
% Syntax : Number of formulae : 127 ( 67 unt; 0 typ; 4 def)
% Number of atoms : 1201 ( 206 equ; 0 cnn)
% Maximal formula atoms : 26 ( 9 avg)
% Number of connectives : 1918 ( 41 ~; 118 |; 83 &;1420 @)
% ( 4 <=>; 135 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 84 ( 84 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 25 usr; 13 con; 0-3 aty)
% ( 94 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 400 ( 277 ^; 121 !; 2 ?; 400 :)
% 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,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_17,type,
h: $i > mworld > $o ).
thf(func_def_18,type,
closed: $i > mworld > $o ).
thf(func_def_19,type,
combo: $i > $i > mworld > $o ).
thf(func_def_20,type,
open: $i > mworld > $o ).
thf(func_def_38,type,
sK1: $i > mworld > $i > $i ).
thf(func_def_39,type,
sK2: mworld ).
thf(func_def_40,type,
sK3: mworld ).
thf(f372,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f293,f307,f343,f361,f370]) ).
thf(f370,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[status(thm)],[f369]) ).
thf(f369,plain,
( $false
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f364]) ).
thf(f364,plain,
( ( $true = $false )
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f138,f340]) ).
thf(f340,plain,
( ( $false
= ( mrel @ sK2 @ sK3 ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f338]) ).
thf(f338,definition,
( spl0_12
<=> ( $false
= ( mrel @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f138,plain,
( $true
= ( mrel @ sK2 @ sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
( $false
= ( ( mrel @ sK2 @ sK3 )
=> ( open @ d @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f135]) ).
thf(f135,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( open @ d @ Y0 ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( open @ d @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f127]) ).
thf(f127,plain,
! [X2: $i,X1: $i] :
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( ( combo @ d @ X1 @ Y0 )
& ( h @ X2 @ Y0 ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( open @ d @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f126]) ).
thf(f126,plain,
! [X2: $i,X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( ( combo @ d @ X1 @ Y1 )
& ( h @ Y0 @ Y1 ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( open @ d @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f125]) ).
thf(f125,plain,
! [X1: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( ( combo @ d @ X1 @ Y1 )
& ( h @ Y0 @ Y1 ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( open @ d @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f124]) ).
thf(f124,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK2 @ Y2 )
=> ( ( combo @ d @ Y0 @ Y2 )
& ( h @ Y1 @ Y2 ) ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK2 @ Y2 )
=> ( open @ d @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK2 @ Y2 )
=> ( ( combo @ d @ Y0 @ Y2 )
& ( h @ Y1 @ Y2 ) ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK2 @ Y2 )
=> ( open @ d @ Y2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK2 @ Y2 )
=> ( ( combo @ d @ Y0 @ Y2 )
& ( h @ Y1 @ Y2 ) ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK2 @ Y2 )
=> ( open @ d @ Y2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f120]) ).
thf(f120,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( ( combo @ d @ Y1 @ Y3 )
& ( h @ Y2 @ Y3 ) ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( open @ d @ Y3 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( ( combo @ d @ Y1 @ Y3 )
& ( h @ Y2 @ Y3 ) ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( open @ d @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ ( combo @ d @ Y0 )
@ ( h @ Y1 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( open @ d ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f73,f63,f71,f59,f59,f70,f71,f60,f71]) ).
thf(f60,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f33]) ).
thf(f33,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( mand
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',mand_def) ).
thf(f70,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f48]) ).
thf(f48,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.Ib8TI9icsv/DTF2THF_10722.p',mimplies_def) ).
thf(f59,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f41]) ).
thf(f41,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X6: $i] : ( X1 @ X6 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',mexists_di_def) ).
thf(f71,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,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.Ib8TI9icsv/DTF2THF_10722.p',mbox_def) ).
thf(f63,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f45,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.Ib8TI9icsv/DTF2THF_10722.p',mlocal_def) ).
thf(f73,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ Y0 ) @ ( h @ Y1 ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
thf(f56,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ Y0 ) @ ( h @ Y1 ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f47]) ).
thf(f47,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ Y0 ) @ ( h @ Y1 ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f46]) ).
thf(f46,plain,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ X0 ) @ ( h @ X1 ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X4: $i] :
( mexists_di
@ ^ [X8: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ X4 ) @ ( h @ X8 ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
thf(f18,conjecture,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X4: $i] :
( mexists_di
@ ^ [X8: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ X4 ) @ ( h @ X8 ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',con) ).
thf(f361,plain,
( spl0_9
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f360]) ).
thf(f360,plain,
( $false
| spl0_9
| ~ spl0_11 ),
inference(subsumption_resolution,[status(thm)],[f351,f275]) ).
thf(f275,plain,
( ( ( mrel @ mactual @ sK2 )
!= $false )
| spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f274]) ).
thf(f274,definition,
( spl0_9
<=> ( ( mrel @ mactual @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f351,plain,
( ( ( mrel @ mactual @ sK2 )
= $false )
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f345]) ).
thf(f345,plain,
( ( $true = $false )
| ( ( mrel @ mactual @ sK2 )
= $false )
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f284,f61]) ).
thf(f61,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,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.Ib8TI9icsv/DTF2THF_10722.p',mrel_reflexive) ).
thf(f284,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ X0 @ sK2 ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f283]) ).
thf(f283,definition,
( spl0_11
<=> ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK2 ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f343,plain,
( spl0_12
| spl0_11
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f342,f223,f283,f338]) ).
thf(f223,definition,
( spl0_4
<=> ( $false
= ( closed @ d @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f342,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ X0 @ sK2 ) )
| ( $false
= ( mrel @ sK2 @ sK3 ) ) )
| spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f328,f224]) ).
thf(f224,plain,
( ( $false
!= ( closed @ d @ sK2 ) )
| spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f223]) ).
thf(f328,plain,
! [X0: mworld] :
( ( $false
= ( closed @ d @ sK2 ) )
| ( $false
= ( mrel @ X0 @ sK2 ) )
| ( $false
= ( mrel @ sK2 @ sK3 ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f322]) ).
thf(f322,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK2 ) )
| ( $true = $false )
| ( $false
= ( closed @ d @ sK2 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ sK2 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f218,f61]) ).
thf(f218,plain,
! [X0: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK2 @ X0 ) )
| ( $false
= ( closed @ d @ X0 ) )
| ( $false
= ( mrel @ X1 @ X0 ) )
| ( ( mrel @ X0 @ sK3 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f207]) ).
thf(f207,plain,
! [X0: mworld,X1: mworld] :
( ( $false
= ( mrel @ X1 @ X0 ) )
| ( $false
= ( closed @ d @ X0 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true = $false )
| ( ( mrel @ X0 @ sK3 )
= $false )
| ( $false
= ( mrel @ sK2 @ X0 ) ) ),
inference(superposition,[status(thm)],[f137,f202]) ).
thf(f202,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( open @ d @ X2 ) )
| ( $false
= ( mrel @ X1 @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $false
= ( mrel @ X3 @ X1 ) )
| ( $false
= ( closed @ d @ X1 ) )
| ( $false
= ( mrel @ mactual @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f201]) ).
thf(f201,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X3 ) )
| ( $true
= ( open @ d @ X2 ) )
| ( $false
= ( mrel @ X1 @ X2 ) )
| ( $false
= ( mrel @ X3 @ X1 ) )
| ( $false
= ( closed @ d @ X1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f187]) ).
thf(f187,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X3 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( open @ d @ X2 ) )
| ( $true = $false )
| ( $false
= ( mrel @ X3 @ X1 ) )
| ( $false
= ( closed @ d @ X1 ) ) ),
inference(superposition,[status(thm)],[f186,f134]) ).
thf(f134,plain,
! [X3: mworld,X1: $i] :
( ( $true
= ( combo @ d @ X1 @ X3 ) )
| ( $false
= ( mrel @ sK2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
! [X2: $i,X3: mworld,X1: $i] :
( ( $false
= ( mrel @ sK2 @ X3 ) )
| ( $true
= ( ( combo @ d @ X1 @ X3 )
& ( h @ X2 @ X3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
! [X2: $i,X3: mworld,X1: $i] :
( $true
= ( ( mrel @ sK2 @ X3 )
=> ( ( combo @ d @ X1 @ X3 )
& ( h @ X2 @ X3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f130]) ).
thf(f130,plain,
! [X2: $i,X3: mworld,X1: $i] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( ( combo @ d @ X1 @ Y0 )
& ( h @ X2 @ Y0 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f129]) ).
thf(f129,plain,
! [X2: $i,X1: $i] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( ( combo @ d @ X1 @ Y0 )
& ( h @ X2 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f127]) ).
thf(f186,plain,
! [X2: $i,X3: mworld,X0: $i,X1: mworld,X4: mworld] :
( ( $false
= ( combo @ X2 @ X0 @ X3 ) )
| ( ( mrel @ X3 @ X4 )
= $false )
| ( $true
= ( open @ X2 @ X4 ) )
| ( $false
= ( mrel @ sK2 @ X3 ) )
| ( $false
= ( closed @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X1 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f183]) ).
thf(f183,plain,
! [X2: $i,X3: mworld,X0: $i,X1: mworld,X4: mworld] :
( ( $true
= ( open @ X2 @ X4 ) )
| ( $false
= ( mrel @ sK2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X3 @ X4 )
= $false )
| ( $false
= ( closed @ X2 @ X3 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true = $false )
| ( $false
= ( combo @ X2 @ X0 @ X3 ) ) ),
inference(superposition,[status(thm)],[f103,f133]) ).
thf(f133,plain,
! [X2: $i,X3: mworld] :
( ( $true
= ( h @ X2 @ X3 ) )
| ( $false
= ( mrel @ sK2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f132]) ).
thf(f103,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld,X5: mworld] :
( ( ( h @ ( sK1 @ X3 @ X1 @ X2 ) @ X4 )
= $false )
| ( ( open @ X2 @ X5 )
= $true )
| ( $false
= ( closed @ X2 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( ( mrel @ X4 @ X5 )
= $false )
| ( $false
= ( combo @ X2 @ X3 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( open @ X2 @ X5 ) ) )
| ( ( h @ ( sK1 @ X3 @ X1 @ X2 ) @ X4 )
= $false )
| ( $false
= ( combo @ X2 @ X3 @ X4 ) )
| ( $false
= ( closed @ X2 @ X4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f101]) ).
thf(f101,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( mrel @ X1 @ X4 ) )
| ( ( h @ ( sK1 @ X3 @ X1 @ X2 ) @ X4 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( combo @ X2 @ X3 @ X4 ) )
| ( $false
= ( closed @ X2 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( open @ X2 @ Y0 ) )
@ X5 ) ) ),
inference(pi_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld] :
( ( $false
= ( closed @ X2 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( open @ X2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( combo @ X2 @ X3 @ X4 ) )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( ( h @ ( sK1 @ X3 @ X1 @ X2 ) @ X4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X1 @ X4 ) )
| ( $false
= ( closed @ X2 @ X4 ) )
| ( ( ( combo @ X2 @ X3 @ X4 )
& ( h @ ( sK1 @ X3 @ X1 @ X2 ) @ X4 ) )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( open @ X2 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( closed @ X2 @ X4 )
& ( combo @ X2 @ X3 @ X4 )
& ( h @ ( sK1 @ X3 @ X1 @ X2 ) @ X4 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( open @ X2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ X1 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld] :
( ( $true
= ( ( ( closed @ X2 @ X4 )
& ( combo @ X2 @ X3 @ X4 )
& ( h @ ( sK1 @ X3 @ X1 @ X2 ) @ X4 ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( open @ X2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X1 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X4 )
=> ( ( ( closed @ X2 @ X4 )
& ( combo @ X2 @ X3 @ X4 )
& ( h @ ( sK1 @ X3 @ X1 @ X2 ) @ X4 ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( open @ X2 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( closed @ X2 @ Y0 )
& ( combo @ X2 @ X3 @ Y0 )
& ( h @ ( sK1 @ X3 @ X1 @ X2 ) @ Y0 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( open @ X2 @ Y1 ) ) ) ) )
@ X4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( closed @ X2 @ Y0 )
& ( combo @ X2 @ X3 @ Y0 )
& ( h @ ( sK1 @ X3 @ X1 @ X2 ) @ Y0 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( open @ X2 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( closed @ X2 @ Y0 )
& ( combo @ X2 @ X3 @ Y0 )
& ( h @ ( sK1 @ X3 @ X1 @ X2 ) @ Y0 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( open @ X2 @ Y1 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( closed @ X2 @ Y0 )
& ~ ( combo @ X2 @ X3 @ Y0 )
& ( h @ o @ Y0 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( closed @ X2 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( closed @ X2 @ Y1 )
& ( combo @ X2 @ X3 @ Y1 )
& ( h @ Y0 @ Y1 ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( open @ X2 @ Y2 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( closed @ X2 @ Y1 )
& ~ ( combo @ X2 @ X3 @ Y1 )
& ( h @ o @ Y1 ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( closed @ X2 @ Y2 ) ) ) ) ) ) )
@ ( sK1 @ X3 @ X1 @ X2 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( closed @ X2 @ Y1 )
& ( combo @ X2 @ X3 @ Y1 )
& ( h @ Y0 @ Y1 ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( open @ X2 @ Y2 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( closed @ X2 @ Y1 )
& ~ ( combo @ X2 @ X3 @ Y1 )
& ( h @ o @ Y1 ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( closed @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( closed @ X2 @ Y2 )
& ( combo @ X2 @ Y0 @ Y2 )
& ( h @ Y1 @ Y2 ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( open @ X2 @ Y3 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( closed @ X2 @ Y2 )
& ~ ( combo @ X2 @ Y0 @ Y2 )
& ( h @ o @ Y2 ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( closed @ X2 @ Y3 ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( closed @ X2 @ Y2 )
& ( combo @ X2 @ Y0 @ Y2 )
& ( h @ Y1 @ Y2 ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( open @ X2 @ Y3 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( closed @ X2 @ Y2 )
& ~ ( combo @ X2 @ Y0 @ Y2 )
& ( h @ o @ Y2 ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( closed @ X2 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f87]) ).
thf(f87,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( ( ( closed @ Y0 @ Y3 )
& ( combo @ Y0 @ Y1 @ Y3 )
& ( h @ Y2 @ Y3 ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( open @ Y0 @ Y4 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( ( ( closed @ Y0 @ Y3 )
& ~ ( combo @ Y0 @ Y1 @ Y3 )
& ( h @ o @ Y3 ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( closed @ Y0 @ Y4 ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: mworld] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( ( ( closed @ Y0 @ Y3 )
& ( combo @ Y0 @ Y1 @ Y3 )
& ( h @ Y2 @ Y3 ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( open @ Y0 @ Y4 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( ( ( closed @ Y0 @ Y3 )
& ~ ( combo @ Y0 @ Y1 @ Y3 )
& ( h @ o @ Y3 ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( closed @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( ( ( closed @ Y0 @ Y3 )
& ( combo @ Y0 @ Y1 @ Y3 )
& ( h @ Y2 @ Y3 ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( open @ Y0 @ Y4 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( ( ( closed @ Y0 @ Y3 )
& ~ ( combo @ Y0 @ Y1 @ Y3 )
& ( h @ o @ Y3 ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( closed @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y0 @ Y4 )
=> ( ( ( closed @ Y1 @ Y4 )
& ( combo @ Y1 @ Y2 @ Y4 )
& ( h @ Y3 @ Y4 ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( open @ Y1 @ Y5 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y0 @ Y4 )
=> ( ( ( closed @ Y1 @ Y4 )
& ~ ( combo @ Y1 @ Y2 @ Y4 )
& ( h @ o @ Y4 ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( closed @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y0 @ Y4 )
=> ( ( ( closed @ Y1 @ Y4 )
& ( combo @ Y1 @ Y2 @ Y4 )
& ( h @ Y3 @ Y4 ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( open @ Y1 @ Y5 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y0 @ Y4 )
=> ( ( ( closed @ Y1 @ Y4 )
& ~ ( combo @ Y1 @ Y2 @ Y4 )
& ( h @ o @ Y4 ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( closed @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( closed @ Y0 )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( combo @ Y0 @ Y1 )
@ ( h @ Y2 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( open @ Y0 ) ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( closed @ Y0 )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
~ ( Y3 @ Y4 )
@ ( combo @ Y0 @ Y1 ) )
@ ( h @ o ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( closed @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f64,f63,f71,f72,f72,f59,f60,f71,f70,f60,f60,f71,f71,f70,f60,f60,f65,f71]) ).
thf(f65,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) )
= mnot ),
file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',mnot_def) ).
thf(f72,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f53,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f52]) ).
thf(f52,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X6: $i] : ( X1 @ X6 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',mforall_di_def) ).
thf(f64,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mexists_di
@ ^ [Y2: $i] : ( mand @ ( mbox @ ( mimplies @ ( mand @ ( closed @ Y0 ) @ ( mand @ ( combo @ Y0 @ Y1 ) @ ( h @ Y2 ) ) ) @ ( mbox @ ( open @ Y0 ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( closed @ Y0 ) @ ( mand @ ( mnot @ ( combo @ Y0 @ Y1 ) ) @ ( h @ o ) ) ) @ ( mbox @ ( closed @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mexists_di
@ ^ [Y2: $i] : ( mand @ ( mbox @ ( mimplies @ ( mand @ ( closed @ Y0 ) @ ( mand @ ( combo @ Y0 @ Y1 ) @ ( h @ Y2 ) ) ) @ ( mbox @ ( open @ Y0 ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( closed @ Y0 ) @ ( mand @ ( mnot @ ( combo @ Y0 @ Y1 ) ) @ ( h @ o ) ) ) @ ( mbox @ ( closed @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X2: $i] : ( mand @ ( mbox @ ( mimplies @ ( mand @ ( closed @ X0 ) @ ( mand @ ( combo @ X0 @ X1 ) @ ( h @ X2 ) ) ) @ ( mbox @ ( open @ X0 ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( closed @ X0 ) @ ( mand @ ( mnot @ ( combo @ X0 @ X1 ) ) @ ( h @ o ) ) ) @ ( mbox @ ( closed @ X0 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X7: $i] :
( mforall_di
@ ^ [X4: $i] :
( mexists_di
@ ^ [X8: $i] : ( mand @ ( mbox @ ( mimplies @ ( mand @ ( closed @ X7 ) @ ( mand @ ( combo @ X7 @ X4 ) @ ( h @ X8 ) ) ) @ ( mbox @ ( open @ X7 ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( closed @ X7 ) @ ( mand @ ( mnot @ ( combo @ X7 @ X4 ) ) @ ( h @ o ) ) ) @ ( mbox @ ( closed @ X7 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',ax1) ).
thf(f137,plain,
( $false
= ( open @ d @ sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f307,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[status(thm)],[f306]) ).
thf(f306,plain,
( $false
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f298]) ).
thf(f298,plain,
( ( $true = $false )
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f276,f123]) ).
thf(f123,plain,
( ( mrel @ mactual @ sK2 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f121]) ).
thf(f276,plain,
( ( ( mrel @ mactual @ sK2 )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f274]) ).
thf(f293,plain,
( spl0_9
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f290,f223,f274]) ).
thf(f290,plain,
( ( ( mrel @ mactual @ sK2 )
= $false )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f288]) ).
thf(f288,plain,
( ( ( mrel @ mactual @ sK2 )
= $false )
| ( $true = $false )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f225,f156]) ).
thf(f156,plain,
! [X1: mworld] :
( ( $true
= ( closed @ d @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f155]) ).
thf(f155,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( closed @ d @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f154]) ).
thf(f154,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( closed @ d @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f153]) ).
thf(f153,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( closed @ d @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( closed @ d ) ) ) ),
inference(definition_unfolding,[status(thm)],[f75,f63,f71]) ).
thf(f75,plain,
( ( mlocal @ ( mbox @ ( closed @ d ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( ( mlocal @ ( mbox @ ( closed @ d ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f39]) ).
thf(f39,plain,
mlocal @ ( mbox @ ( closed @ d ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
mlocal @ ( mbox @ ( closed @ d ) ),
file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',ax2) ).
thf(f225,plain,
( ( $false
= ( closed @ d @ sK2 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PLA054^4 : TPTP v9.2.1. Released v8.1.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n025.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 11:28:27 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
% 0.30/0.48 ---- Original DTF file ---
% 0.30/0.48 thf(spec,logic,$$dhol).
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 % File : PLA054^4 : TPTP v9.2.1. Released v8.1.0.
% 0.30/0.48 % Domain : Planning
% 0.30/0.48 % Problem : Abductive planning: Safe problem
% 0.30/0.48 % Version : [BP13] axioms.
% 0.30/0.48 % English :
% 0.30/0.48
% 0.30/0.48 % Refs : [Sto98] Stone (1998), Abductive Planning with Sensing
% 0.30/0.48 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.30/0.48 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.30/0.48 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.30/0.48 % Source : [TPTP]
% 0.30/0.48 % Names : APM005+1 [QMLTP]
% 0.30/0.48
% 0.30/0.48 % Status : Theorem
% 0.30/0.48 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.30/0.48 % Syntax : Number of formulae : 38 ( 11 unt; 20 typ; 10 def)
% 0.30/0.48 % Number of atoms : 82 ( 10 equ; 0 cnn)
% 0.30/0.48 % Maximal formula atoms : 25 ( 4 avg)
% 0.30/0.48 % Number of connectives : 110 ( 1 ~; 1 |; 3 &; 101 @)
% 0.30/0.48 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.48 % Maximal formula depth : 19 ( 5 avg)
% 0.30/0.48 % Number of types : 3 ( 1 usr)
% 0.30/0.48 % Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% 0.30/0.48 % Number of symbols : 20 ( 19 usr; 4 con; 0-3 aty)
% 0.30/0.48 % Number of variables : 38 ( 30 ^; 6 !; 2 ?; 38 :)
% 0.30/0.48 % SPC : TH0_THM_EQU_NAR
% 0.30/0.48
% 0.30/0.48 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.30/0.48 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.30/0.48 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.30/0.48 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.30/0.48 % $modalities == $modal_system_S4].
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 thf(mworld,type,
% 0.30/0.48 mworld: $tType ).
% 0.30/0.48
% 0.30/0.48 thf(mrel_type,type,
% 0.30/0.48 mrel: mworld > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(mactual_type,type,
% 0.30/0.48 mactual: mworld ).
% 0.30/0.48
% 0.30/0.48 thf(mlocal_type,type,
% 0.30/0.48 mlocal: ( mworld > $o ) > $o ).
% 0.30/0.48
% 0.30/0.48 thf(mlocal_def,definition,
% 0.30/0.48 ( mlocal
% 0.30/0.48 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(mnot_type,type,
% 0.30/0.48 mnot: ( mworld > $o ) > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(mand_type,type,
% 0.30/0.48 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(mor_type,type,
% 0.30/0.48 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(mimplies_type,type,
% 0.30/0.48 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(mequiv_type,type,
% 0.30/0.48 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(mnot_def,definition,
% 0.30/0.48 ( mnot
% 0.30/0.48 = ( ^ [A: mworld > $o,W: mworld] :
% 0.30/0.48 ~ ( A @ W ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(mand_def,definition,
% 0.30/0.48 ( mand
% 0.30/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.48 ( ( A @ W )
% 0.30/0.48 & ( B @ W ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(mor_def,definition,
% 0.30/0.48 ( mor
% 0.30/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.48 ( ( A @ W )
% 0.30/0.48 | ( B @ W ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(mimplies_def,definition,
% 0.30/0.48 ( mimplies
% 0.30/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.48 ( ( A @ W )
% 0.30/0.48 => ( B @ W ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(mequiv_def,definition,
% 0.30/0.48 ( mequiv
% 0.30/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.48 ( ( A @ W )
% 0.30/0.48 <=> ( B @ W ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(mbox_type,type,
% 0.30/0.48 mbox: ( mworld > $o ) > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(mbox_def,definition,
% 0.30/0.48 ( mbox
% 0.30/0.48 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.48 ! [V: mworld] :
% 0.30/0.48 ( ( mrel @ W @ V )
% 0.30/0.48 => ( Phi @ V ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(mdia_type,type,
% 0.30/0.48 mdia: ( mworld > $o ) > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(mdia_def,definition,
% 0.30/0.48 ( mdia
% 0.30/0.48 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.48 ? [V: mworld] :
% 0.30/0.48 ( ( mrel @ W @ V )
% 0.30/0.48 & ( Phi @ V ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(mrel_reflexive,axiom,
% 0.30/0.48 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.30/0.48
% 0.30/0.48 thf(mrel_transitive,axiom,
% 0.30/0.48 ! [W: mworld,V: mworld,U: mworld] :
% 0.30/0.48 ( ( ( mrel @ W @ V )
% 0.30/0.48 & ( mrel @ V @ U ) )
% 0.30/0.48 => ( mrel @ W @ U ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(mforall_di_type,type,
% 0.30/0.48 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(mforall_di_def,definition,
% 0.30/0.48 ( mforall_di
% 0.30/0.48 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.30/0.48 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(mexists_di_type,type,
% 0.30/0.48 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(mexists_di_def,definition,
% 0.30/0.48 ( mexists_di
% 0.30/0.48 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.30/0.48 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(d_decl,type,
% 0.30/0.48 d: $i ).
% 0.30/0.48
% 0.30/0.48 thf(n_decl,type,
% 0.30/0.48 n: $i ).
% 0.30/0.48
% 0.30/0.48 thf(o_decl,type,
% 0.30/0.48 o: $i ).
% 0.30/0.48
% 0.30/0.48 thf(h_decl,type,
% 0.30/0.48 h: $i > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(closed_decl,type,
% 0.30/0.48 closed: $i > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(combo_decl,type,
% 0.30/0.48 combo: $i > $i > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(open_decl,type,
% 0.30/0.48 open: $i > mworld > $o ).
% 0.30/0.48
% 0.30/0.48 thf(ax1,axiom,
% 0.30/0.48 ( mlocal
% 0.30/0.48 @ ( mbox
% 0.30/0.48 @ ( mforall_di
% 0.30/0.48 @ ^ [S: $i] :
% 0.30/0.48 ( mforall_di
% 0.30/0.48 @ ^ [V: $i] :
% 0.30/0.48 ( mexists_di
% 0.30/0.48 @ ^ [O: $i] : ( mand @ ( mbox @ ( mimplies @ ( mand @ ( closed @ S ) @ ( mand @ ( combo @ S @ V ) @ ( h @ O ) ) ) @ ( mbox @ ( open @ S ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( closed @ S ) @ ( mand @ ( mnot @ ( combo @ S @ V ) ) @ ( h @ o ) ) ) @ ( mbox @ ( closed @ S ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(ax2,axiom,
% 0.30/0.48 mlocal @ ( mbox @ ( closed @ d ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(ax3,axiom,
% 0.30/0.48 mlocal @ ( mbox @ ( mor @ ( combo @ d @ n ) @ ( mnot @ ( combo @ d @ n ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(ax4,axiom,
% 0.30/0.48 ( mlocal
% 0.30/0.48 @ ( mbox
% 0.30/0.48 @ ( mforall_di
% 0.30/0.48 @ ^ [S: $i] : ( mnot @ ( mand @ ( open @ S ) @ ( closed @ S ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(ax5,axiom,
% 0.30/0.48 ( mlocal
% 0.30/0.48 @ ( mexists_di
% 0.30/0.48 @ ^ [V: $i] : ( mbox @ ( combo @ d @ V ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(con,conjecture,
% 0.30/0.48 ( mlocal
% 0.30/0.48 @ ( mbox
% 0.30/0.48 @ ( mexists_di
% 0.30/0.48 @ ^ [V: $i] :
% 0.30/0.48 ( mexists_di
% 0.30/0.48 @ ^ [O: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ V ) @ ( h @ O ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 ------------------------
% 1.69/1.36 ---- Embedded in THF ---
% 1.69/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.69/1.36 %%% Generated on Tue Feb 24 11:28:28 EST 2026
% 1.69/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.69/1.36 %%% Logic specification used:
% 1.69/1.36 %%% thf(spec, logic, $$dhol).
% 1.69/1.36
% 1.69/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2DTF10722.p
% See solution above
% 1.69/1.36 ------------------------
% 1.69/1.37 ---- Cleaned THF ---
% 1.69/1.37 thf(mworld,type,
% 1.69/1.37 mworld: $tType ).
% 1.69/1.37
% 1.69/1.37 thf(mrel_type,type,
% 1.69/1.37 mrel: mworld > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(mactual_type,type,
% 1.69/1.37 mactual: mworld ).
% 1.69/1.37
% 1.69/1.37 thf(mlocal_type,type,
% 1.69/1.37 mlocal: ( mworld > $o ) > $o ).
% 1.69/1.37
% 1.69/1.37 thf(mlocal_def,definition,
% 1.69/1.37 ( mlocal
% 1.69/1.37 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(mnot_type,type,
% 1.69/1.37 mnot: ( mworld > $o ) > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(mand_type,type,
% 1.69/1.37 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(mor_type,type,
% 1.69/1.37 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(mimplies_type,type,
% 1.69/1.37 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(mequiv_type,type,
% 1.69/1.37 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(mnot_def,definition,
% 1.69/1.37 ( mnot
% 1.69/1.37 = ( ^ [A: mworld > $o,W: mworld] :
% 1.69/1.37 ~ ( A @ W ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(mand_def,definition,
% 1.69/1.37 ( mand
% 1.69/1.37 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.69/1.37 ( ( A @ W )
% 1.69/1.37 & ( B @ W ) ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(mor_def,definition,
% 1.69/1.37 ( mor
% 1.69/1.37 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.69/1.37 ( ( A @ W )
% 1.69/1.37 | ( B @ W ) ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(mimplies_def,definition,
% 1.69/1.37 ( mimplies
% 1.69/1.37 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.69/1.37 ( ( A @ W )
% 1.69/1.37 => ( B @ W ) ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(mequiv_def,definition,
% 1.69/1.37 ( mequiv
% 1.69/1.37 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.69/1.37 ( ( A @ W )
% 1.69/1.37 <=> ( B @ W ) ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(mbox_type,type,
% 1.69/1.37 mbox: ( mworld > $o ) > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(mbox_def,definition,
% 1.69/1.37 ( mbox
% 1.69/1.37 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.69/1.37 ! [V: mworld] :
% 1.69/1.37 ( ( mrel @ W @ V )
% 1.69/1.37 => ( Phi @ V ) ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(mdia_type,type,
% 1.69/1.37 mdia: ( mworld > $o ) > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(mdia_def,definition,
% 1.69/1.37 ( mdia
% 1.69/1.37 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.69/1.37 ? [V: mworld] :
% 1.69/1.37 ( ( mrel @ W @ V )
% 1.69/1.37 & ( Phi @ V ) ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(mrel_reflexive,axiom,
% 1.69/1.37 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.69/1.37
% 1.69/1.37 thf(mrel_transitive,axiom,
% 1.69/1.37 ! [W: mworld,V: mworld,U: mworld] :
% 1.69/1.37 ( ( ( mrel @ W @ V )
% 1.69/1.37 & ( mrel @ V @ U ) )
% 1.69/1.37 => ( mrel @ W @ U ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(mforall_di_type,type,
% 1.69/1.37 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(mforall_di_def,definition,
% 1.69/1.37 ( mforall_di
% 1.69/1.37 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.69/1.37 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(mexists_di_type,type,
% 1.69/1.37 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(mexists_di_def,definition,
% 1.69/1.37 ( mexists_di
% 1.69/1.37 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.69/1.37 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(d_decl,type,
% 1.69/1.37 d: $i ).
% 1.69/1.37
% 1.69/1.37 thf(n_decl,type,
% 1.69/1.37 n: $i ).
% 1.69/1.37
% 1.69/1.37 thf(o_decl,type,
% 1.69/1.37 o: $i ).
% 1.69/1.37
% 1.69/1.37 thf(h_decl,type,
% 1.69/1.37 h: $i > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(closed_decl,type,
% 1.69/1.37 closed: $i > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(combo_decl,type,
% 1.69/1.37 combo: $i > $i > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(open_decl,type,
% 1.69/1.37 open: $i > mworld > $o ).
% 1.69/1.37
% 1.69/1.37 thf(ax1,axiom,
% 1.69/1.37 ( mlocal
% 1.69/1.37 @ ( mbox
% 1.69/1.37 @ ( mforall_di
% 1.69/1.37 @ ^ [S: $i] :
% 1.69/1.37 ( mforall_di
% 1.69/1.37 @ ^ [V: $i] :
% 1.69/1.37 ( mexists_di
% 1.69/1.37 @ ^ [O: $i] : ( mand @ ( mbox @ ( mimplies @ ( mand @ ( closed @ S ) @ ( mand @ ( combo @ S @ V ) @ ( h @ O ) ) ) @ ( mbox @ ( open @ S ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( closed @ S ) @ ( mand @ ( mnot @ ( combo @ S @ V ) ) @ ( h @ o ) ) ) @ ( mbox @ ( closed @ S ) ) ) ) ) ) ) ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(ax2,axiom,
% 1.69/1.37 mlocal @ ( mbox @ ( closed @ d ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(ax3,axiom,
% 1.69/1.37 mlocal @ ( mbox @ ( mor @ ( combo @ d @ n ) @ ( mnot @ ( combo @ d @ n ) ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(ax4,axiom,
% 1.69/1.37 ( mlocal
% 1.69/1.37 @ ( mbox
% 1.69/1.37 @ ( mforall_di
% 1.69/1.37 @ ^ [S: $i] : ( mnot @ ( mand @ ( open @ S ) @ ( closed @ S ) ) ) ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(ax5,axiom,
% 1.69/1.37 ( mlocal
% 1.69/1.37 @ ( mexists_di
% 1.69/1.37 @ ^ [V: $i] : ( mbox @ ( combo @ d @ V ) ) ) ) ).
% 1.69/1.37
% 1.69/1.37 thf(con,conjecture,
% 1.69/1.37 ( mlocal
% 1.69/1.37 @ ( mbox
% 1.69/1.37 @ ( mexists_di
% 1.69/1.37 @ ^ [V: $i] :
% 1.69/1.37 ( mexists_di
% 1.69/1.37 @ ^ [O: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ V ) @ ( h @ O ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ) ).
% 1.69/1.37 ------------------------
% 1.69/1.39 % (11050)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_10722 for (2999ds/4Mi)
% 1.69/1.39 % (11050)Instruction limit reached!
% 1.69/1.39 % (11050)------------------------------
% 1.69/1.39 % (11050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (11050)Termination reason: Unknown
% 1.69/1.39 % (11050)Termination phase: Saturation
% 1.69/1.39
% 1.69/1.39 % (11050)Memory used [KB]: 5500
% 1.69/1.39 % (11050)Time elapsed: 0.003 s
% 1.69/1.39 % (11050)Instructions burned: 7 (million)
% 1.69/1.39 % (11050)------------------------------
% 1.69/1.39 % (11050)------------------------------
% 1.69/1.39 % (11051)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_10722 for (2999ds/27Mi)
% 1.69/1.40 % (11049)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10722 for (2999ds/183Mi)
% 1.85/1.40 % (11052)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10722 for (2999ds/2Mi)
% 1.85/1.40 % (11053)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_10722 for (2999ds/2Mi)
% 1.85/1.40 % (11054)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_10722 for (2999ds/275Mi)
% 1.85/1.40 % (11055)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10722 for (2999ds/18Mi)
% 1.85/1.40 % (11052)Instruction limit reached!
% 1.85/1.40 % (11052)------------------------------
% 1.85/1.40 % (11052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.85/1.40 % (11052)Termination reason: Unknown
% 1.85/1.40 % (11052)Termination phase: shuffling
% 1.85/1.40
% 1.85/1.40 % (11052)Memory used [KB]: 1023
% 1.85/1.40 % (11052)Time elapsed: 0.003 s
% 1.85/1.40 % (11052)Instructions burned: 2 (million)
% 1.85/1.40 % (11052)------------------------------
% 1.85/1.40 % (11052)------------------------------
% 1.85/1.40 % (11053)Instruction limit reached!
% 1.85/1.40 % (11053)------------------------------
% 1.85/1.40 % (11053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.85/1.40 % (11053)Termination reason: Unknown
% 1.85/1.40 % (11053)Termination phase: shuffling
% 1.85/1.40
% 1.85/1.40 % (11053)Memory used [KB]: 1023
% 1.85/1.40 % (11053)Time elapsed: 0.003 s
% 1.85/1.40 % (11053)Instructions burned: 2 (million)
% 1.85/1.40 % (11053)------------------------------
% 1.85/1.40 % (11053)------------------------------
% 1.85/1.40 % (11054)Refutation not found, incomplete strategy
% 1.85/1.40 % (11054)------------------------------
% 1.85/1.40 % (11054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.85/1.40 % (11054)Termination reason: Refutation not found, incomplete strategy
% 1.85/1.40
% 1.85/1.40
% 1.85/1.40 % (11054)Memory used [KB]: 5500
% 1.85/1.40 % (11054)Time elapsed: 0.005 s
% 1.85/1.40 % (11054)Instructions burned: 5 (million)
% 1.85/1.40 % (11054)------------------------------
% 1.85/1.40 % (11054)------------------------------
% 1.85/1.40 % (11056)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10722 for (2999ds/3Mi)
% 1.85/1.40 % (11056)Instruction limit reached!
% 1.85/1.40 % (11056)------------------------------
% 1.85/1.40 % (11056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.85/1.40 % (11056)Termination reason: Unknown
% 1.85/1.40 % (11056)Termination phase: Function definition elimination
% 1.85/1.40
% 1.85/1.40 % (11056)Memory used [KB]: 1023
% 1.85/1.40 % (11056)Time elapsed: 0.003 s
% 1.85/1.40 % (11056)Instructions burned: 5 (million)
% 1.85/1.40 % (11056)------------------------------
% 1.85/1.40 % (11056)------------------------------
% 1.85/1.40 % (11051)Instruction limit reached!
% 1.85/1.40 % (11051)------------------------------
% 1.85/1.40 % (11051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.85/1.40 % (11051)Termination reason: Unknown
% 1.85/1.40 % (11051)Termination phase: Saturation
% 1.85/1.40
% 1.85/1.40 % (11051)Memory used [KB]: 5756
% 1.85/1.40 % (11051)Time elapsed: 0.014 s
% 1.85/1.40 % (11051)Instructions burned: 27 (million)
% 1.85/1.40 % (11051)------------------------------
% 1.85/1.40 % (11051)------------------------------
% 1.85/1.41 % (11055)Instruction limit reached!
% 1.85/1.41 % (11055)------------------------------
% 1.85/1.41 % (11055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.85/1.41 % (11055)Termination reason: Unknown
% 1.85/1.41 % (11055)Termination phase: Saturation
% 1.85/1.41
% 1.85/1.41 % (11055)Memory used [KB]: 5628
% 1.85/1.41 % (11055)Time elapsed: 0.012 s
% 1.85/1.41 % (11055)Instructions burned: 18 (million)
% 1.85/1.41 % (11055)------------------------------
% 1.85/1.41 % (11055)------------------------------
% 1.85/1.41 % (11060)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_10722 for (2999ds/1041Mi)
% 1.85/1.41 % (11061)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10722 for (2999ds/7Mi)
% 1.85/1.41 % (11057)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_10722 for (2999ds/37Mi)
% 1.85/1.42 % (11058)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_10722 for (2999ds/15Mi)
% 1.85/1.42 % (11061)Instruction limit reached!
% 1.85/1.42 % (11061)------------------------------
% 1.85/1.42 % (11061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.85/1.42 % (11061)Termination reason: Unknown
% 1.85/1.42 % (11061)Termination phase: Saturation
% 1.85/1.42
% 1.85/1.42 % (11061)Memory used [KB]: 1023
% 1.85/1.42 % (11061)Time elapsed: 0.004 s
% 1.85/1.42 % (11061)Instructions burned: 8 (million)
% 1.85/1.42 % (11061)------------------------------
% 1.85/1.42 % (11061)------------------------------
% 1.85/1.42 % (11059)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_10722 for (2999ds/3Mi)
% 1.85/1.42 % (11059)Instruction limit reached!
% 1.85/1.42 % (11059)------------------------------
% 1.85/1.42 % (11059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.85/1.42 % (11059)Termination reason: Unknown
% 1.85/1.42 % (11059)Termination phase: Property scanning
% 1.85/1.42
% 1.85/1.42 % (11059)Memory used [KB]: 1023
% 1.85/1.42 % (11059)Time elapsed: 0.004 s
% 1.85/1.42 % (11059)Instructions burned: 4 (million)
% 1.85/1.42 % (11059)------------------------------
% 1.85/1.42 % (11059)------------------------------
% 1.85/1.42 % (11058)Instruction limit reached!
% 1.85/1.42 % (11058)------------------------------
% 1.85/1.42 % (11058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.85/1.42 % (11058)Termination reason: Unknown
% 1.85/1.42 % (11058)Termination phase: Saturation
% 1.85/1.42
% 1.85/1.42 % (11058)Memory used [KB]: 5756
% 1.85/1.42 % (11058)Time elapsed: 0.010 s
% 1.85/1.42 % (11058)Instructions burned: 15 (million)
% 1.85/1.42 % (11058)------------------------------
% 1.85/1.42 % (11058)------------------------------
% 1.85/1.42 % (11062)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10722 for (2999ds/16Mi)
% 1.85/1.43 % (11063)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_10722 for (2999ds/3Mi)
% 1.85/1.43 % (11063)Instruction limit reached!
% 1.85/1.43 % (11063)------------------------------
% 1.85/1.43 % (11063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.85/1.43 % (11063)Termination reason: Unknown
% 1.85/1.43 % (11063)Termination phase: Property scanning
% 1.85/1.43
% 1.85/1.43 % (11063)Memory used [KB]: 1023
% 1.85/1.43 % (11063)Time elapsed: 0.003 s
% 1.85/1.43 % (11063)Instructions burned: 4 (million)
% 1.85/1.43 % (11063)------------------------------
% 1.85/1.43 % (11063)------------------------------
% 1.85/1.43 % (11049)First to succeed.
% 1.85/1.43 % (11062)Instruction limit reached!
% 1.85/1.43 % (11062)------------------------------
% 1.85/1.43 % (11062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.85/1.43 % (11062)Termination reason: Unknown
% 1.85/1.43 % (11062)Termination phase: Saturation
% 1.85/1.43
% 1.85/1.43 % (11062)Memory used [KB]: 5628
% 1.85/1.43 % (11062)Time elapsed: 0.010 s
% 1.85/1.43 % (11062)Instructions burned: 16 (million)
% 1.85/1.43 % (11062)------------------------------
% 1.85/1.43 % (11062)------------------------------
% 1.85/1.43 % (11057)Instruction limit reached!
% 1.85/1.43 % (11057)------------------------------
% 1.85/1.43 % (11057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.85/1.43 % (11057)Termination reason: Unknown
% 1.85/1.43 % (11057)Termination phase: Saturation
% 1.85/1.43
% 1.85/1.43 % (11057)Memory used [KB]: 5756
% 1.85/1.43 % (11057)Time elapsed: 0.020 s
% 1.85/1.43 % (11057)Instructions burned: 39 (million)
% 1.85/1.43 % (11057)------------------------------
% 1.85/1.43 % (11057)------------------------------
% 1.85/1.44 % (11049)Refutation found. Thanks to Tanya!
% 1.85/1.44 % SZS status Theorem for DTF2THF_10722
% 1.85/1.44 % SZS output start Proof for DTF2THF_10722
% 1.85/1.44 thf(type_def_5, type, mworld: $tType).
% 1.85/1.44 thf(func_def_0, type, mworld: $tType).
% 1.85/1.44 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.85/1.44 thf(func_def_2, type, mactual: mworld).
% 1.85/1.44 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.85/1.44 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.85/1.44 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.85/1.44 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.85/1.44 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.85/1.44 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.85/1.44 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.85/1.44 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.85/1.44 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.85/1.44 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.85/1.44 thf(func_def_17, type, h: $i > mworld > $o).
% 1.85/1.44 thf(func_def_18, type, closed: $i > mworld > $o).
% 1.85/1.44 thf(func_def_19, type, combo: $i > $i > mworld > $o).
% 1.85/1.44 thf(func_def_20, type, open: $i > mworld > $o).
% 1.85/1.44 thf(func_def_38, type, sK1: $i > mworld > $i > $i).
% 1.85/1.44 thf(func_def_39, type, sK2: mworld).
% 1.85/1.44 thf(func_def_40, type, sK3: mworld).
% 1.85/1.44 thf(f372,plain,(
% 1.85/1.44 $false),
% 1.85/1.44 inference(avatar_sat_refutation,[status(thm)],[f293,f307,f343,f361,f370])).
% 1.85/1.44 thf(f370,plain,(
% 1.85/1.44 ~spl0_12),
% 1.85/1.44 inference(avatar_contradiction_clause,[status(thm)],[f369])).
% 1.85/1.44 thf(f369,plain,(
% 1.85/1.44 $false | ~spl0_12),
% 1.85/1.44 inference(trivial_inequality_removal,[status(thm)],[f364])).
% 1.85/1.44 thf(f364,plain,(
% 1.85/1.44 ($true = $false) | ~spl0_12),
% 1.85/1.44 inference(superposition,[status(thm)],[f138,f340])).
% 1.85/1.44 thf(f340,plain,(
% 1.85/1.44 ($false = (mrel @ sK2 @ sK3)) | ~spl0_12),
% 1.85/1.44 inference(avatar_component_clause,[status(thm)],[f338])).
% 1.85/1.44 thf(f338,definition,(
% 1.85/1.44 spl0_12 <=> ($false = (mrel @ sK2 @ sK3))),
% 1.85/1.44 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.85/1.44 thf(f138,plain,(
% 1.85/1.44 ($true = (mrel @ sK2 @ sK3))),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.85/1.44 thf(f136,plain,(
% 1.85/1.44 ($false = ((mrel @ sK2 @ sK3) => (open @ d @ sK3)))),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f135])).
% 1.85/1.44 thf(f135,plain,(
% 1.85/1.44 (((^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (open @ d @ Y0))) @ sK3) = $false)),
% 1.85/1.44 inference(sigma_clausification,[status(thm)],[f128])).
% 1.85/1.44 thf(f128,plain,(
% 1.85/1.44 ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (open @ d @ Y0)))))),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f127])).
% 1.85/1.44 thf(f127,plain,(
% 1.85/1.44 ( ! [X2 : $i,X1 : $i] : (($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => ((combo @ d @ X1 @ Y0) & (h @ X2 @ Y0))))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (open @ d @ Y0))))))) )),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f126])).
% 1.85/1.44 thf(f126,plain,(
% 1.85/1.44 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => ((combo @ d @ X1 @ Y1) & (h @ Y0 @ Y1))))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (open @ d @ Y1)))))) @ X2))) )),
% 1.85/1.44 inference(pi_clausification,[status(thm)],[f125])).
% 1.85/1.44 thf(f125,plain,(
% 1.85/1.44 ( ! [X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => ((combo @ d @ X1 @ Y1) & (h @ Y0 @ Y1))))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (open @ d @ Y1))))))))) )),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f124])).
% 1.85/1.44 thf(f124,plain,(
% 1.85/1.44 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK2 @ Y2) => ((combo @ d @ Y0 @ Y2) & (h @ Y1 @ Y2))))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK2 @ Y2) => (open @ d @ Y2)))))))) @ X1))) )),
% 1.85/1.44 inference(pi_clausification,[status(thm)],[f122])).
% 1.85/1.44 thf(f122,plain,(
% 1.85/1.44 ($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK2 @ Y2) => ((combo @ d @ Y0 @ Y2) & (h @ Y1 @ Y2))))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK2 @ Y2) => (open @ d @ Y2))))))))))),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f121])).
% 1.85/1.44 thf(f121,plain,(
% 1.85/1.44 ($false = ((mrel @ mactual @ sK2) => (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK2 @ Y2) => ((combo @ d @ Y0 @ Y2) & (h @ Y1 @ Y2))))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK2 @ Y2) => (open @ d @ Y2)))))))))))),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f120])).
% 1.85/1.44 thf(f120,plain,(
% 1.85/1.44 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => ((combo @ d @ Y1 @ Y3) & (h @ Y2 @ Y3))))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (open @ d @ Y3))))))))))) @ sK2))),
% 1.85/1.44 inference(sigma_clausification,[status(thm)],[f119])).
% 1.85/1.44 thf(f119,plain,(
% 1.85/1.44 ($true != (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => ((combo @ d @ Y1 @ Y3) & (h @ Y2 @ Y3))))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (open @ d @ Y3)))))))))))))),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f80])).
% 1.85/1.44 thf(f80,plain,(
% 1.85/1.44 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (?? @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (combo @ d @ Y0) @ (h @ Y1))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ (open @ d))))))))))),
% 1.85/1.44 inference(definition_unfolding,[status(thm)],[f73,f63,f71,f59,f59,f70,f71,f60,f71])).
% 1.85/1.44 thf(f60,plain,(
% 1.85/1.44 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.85/1.44 inference(cnf_transformation,[status(thm)],[f34])).
% 1.85/1.44 thf(f34,plain,(
% 1.85/1.44 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.85/1.44 inference(fool_elimination,[status(thm)],[f33])).
% 1.85/1.44 thf(f33,plain,(
% 1.85/1.44 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 1.85/1.44 inference(rectify,[status(thm)],[f3])).
% 1.85/1.44 thf(f3,axiom,(
% 1.85/1.44 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))))),
% 1.85/1.44 file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',mand_def)).
% 1.85/1.44 thf(f70,plain,(
% 1.85/1.44 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.85/1.44 inference(cnf_transformation,[status(thm)],[f49])).
% 1.85/1.44 thf(f49,plain,(
% 1.85/1.44 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.85/1.44 inference(fool_elimination,[status(thm)],[f48])).
% 1.85/1.44 thf(f48,plain,(
% 1.85/1.44 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.85/1.44 inference(rectify,[status(thm)],[f5])).
% 1.85/1.44 thf(f5,axiom,(
% 1.85/1.44 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.85/1.44 file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',mimplies_def)).
% 1.85/1.44 thf(f59,plain,(
% 1.85/1.44 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.85/1.44 inference(cnf_transformation,[status(thm)],[f42])).
% 1.85/1.44 thf(f42,plain,(
% 1.85/1.44 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.85/1.44 inference(fool_elimination,[status(thm)],[f41])).
% 1.85/1.44 thf(f41,plain,(
% 1.85/1.44 (mexists_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : (X0 @ X2 @ X1))))),
% 1.85/1.44 inference(rectify,[status(thm)],[f12])).
% 1.85/1.44 thf(f12,axiom,(
% 1.85/1.44 (mexists_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (? [X6 : $i] : (X1 @ X6 @ X2))))),
% 1.85/1.44 file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',mexists_di_def)).
% 1.85/1.44 thf(f71,plain,(
% 1.85/1.44 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.85/1.44 inference(cnf_transformation,[status(thm)],[f22])).
% 1.85/1.44 thf(f22,plain,(
% 1.85/1.44 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.85/1.44 inference(fool_elimination,[status(thm)],[f21])).
% 1.85/1.44 thf(f21,plain,(
% 1.85/1.44 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 1.85/1.44 inference(rectify,[status(thm)],[f7])).
% 1.85/1.44 thf(f7,axiom,(
% 1.85/1.44 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 1.85/1.44 file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',mbox_def)).
% 1.85/1.44 thf(f63,plain,(
% 1.85/1.44 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.85/1.44 inference(cnf_transformation,[status(thm)],[f45])).
% 1.85/1.44 thf(f45,plain,(
% 1.85/1.44 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.85/1.44 inference(fool_elimination,[status(thm)],[f1])).
% 1.85/1.44 thf(f1,axiom,(
% 1.85/1.44 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.85/1.44 file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',mlocal_def)).
% 1.85/1.44 thf(f73,plain,(
% 1.85/1.44 ($true != (mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mbox @ (mand @ (combo @ d @ Y0) @ (h @ Y1))) @ (mbox @ (open @ d))))))))))),
% 1.85/1.44 inference(cnf_transformation,[status(thm)],[f56])).
% 1.85/1.44 thf(f56,plain,(
% 1.85/1.44 ($true != (mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mbox @ (mand @ (combo @ d @ Y0) @ (h @ Y1))) @ (mbox @ (open @ d))))))))))),
% 1.85/1.44 inference(flattening,[status(thm)],[f47])).
% 1.85/1.44 thf(f47,plain,(
% 1.85/1.44 ~($true = (mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mbox @ (mand @ (combo @ d @ Y0) @ (h @ Y1))) @ (mbox @ (open @ d))))))))))),
% 1.85/1.44 inference(fool_elimination,[status(thm)],[f46])).
% 1.85/1.44 thf(f46,plain,(
% 1.85/1.44 ~(mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : (mexists_di @ (^[X1 : $i] : (mimplies @ (mbox @ (mand @ (combo @ d @ X0) @ (h @ X1))) @ (mbox @ (open @ d)))))))))),
% 1.85/1.44 inference(rectify,[status(thm)],[f19])).
% 1.85/1.44 thf(f19,negated_conjecture,(
% 1.85/1.44 ~(mlocal @ (mbox @ (mexists_di @ (^[X4 : $i] : (mexists_di @ (^[X8 : $i] : (mimplies @ (mbox @ (mand @ (combo @ d @ X4) @ (h @ X8))) @ (mbox @ (open @ d)))))))))),
% 1.85/1.44 inference(negated_conjecture,[status(cth)],[f18])).
% 1.85/1.44 thf(f18,conjecture,(
% 1.85/1.44 (mlocal @ (mbox @ (mexists_di @ (^[X4 : $i] : (mexists_di @ (^[X8 : $i] : (mimplies @ (mbox @ (mand @ (combo @ d @ X4) @ (h @ X8))) @ (mbox @ (open @ d)))))))))),
% 1.85/1.44 file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',con)).
% 1.85/1.44 thf(f361,plain,(
% 1.85/1.44 spl0_9 | ~spl0_11),
% 1.85/1.44 inference(avatar_contradiction_clause,[status(thm)],[f360])).
% 1.85/1.44 thf(f360,plain,(
% 1.85/1.44 $false | (spl0_9 | ~spl0_11)),
% 1.85/1.44 inference(subsumption_resolution,[status(thm)],[f351,f275])).
% 1.85/1.44 thf(f275,plain,(
% 1.85/1.44 ((mrel @ mactual @ sK2) != $false) | spl0_9),
% 1.85/1.44 inference(avatar_component_clause,[status(thm)],[f274])).
% 1.85/1.44 thf(f274,definition,(
% 1.85/1.44 spl0_9 <=> ((mrel @ mactual @ sK2) = $false)),
% 1.85/1.44 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.85/1.44 thf(f351,plain,(
% 1.85/1.44 ((mrel @ mactual @ sK2) = $false) | ~spl0_11),
% 1.85/1.44 inference(trivial_inequality_removal,[status(thm)],[f345])).
% 1.85/1.44 thf(f345,plain,(
% 1.85/1.44 ($true = $false) | ((mrel @ mactual @ sK2) = $false) | ~spl0_11),
% 1.85/1.44 inference(superposition,[status(thm)],[f284,f61])).
% 1.85/1.44 thf(f61,plain,(
% 1.85/1.44 ( ! [X0 : mworld] : (($true = (mrel @ X0 @ X0))) )),
% 1.85/1.44 inference(cnf_transformation,[status(thm)],[f26])).
% 1.85/1.44 thf(f26,plain,(
% 1.85/1.44 ! [X0 : mworld] : ($true = (mrel @ X0 @ X0))),
% 1.85/1.44 inference(fool_elimination,[status(thm)],[f25])).
% 1.85/1.44 thf(f25,plain,(
% 1.85/1.44 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 1.85/1.44 inference(rectify,[status(thm)],[f9])).
% 1.85/1.44 thf(f9,axiom,(
% 1.85/1.44 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 1.85/1.44 file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',mrel_reflexive)).
% 1.85/1.44 thf(f284,plain,(
% 1.85/1.44 ( ! [X0 : mworld] : (($false = (mrel @ mactual @ X0)) | ($false = (mrel @ X0 @ sK2))) ) | ~spl0_11),
% 1.85/1.44 inference(avatar_component_clause,[status(thm)],[f283])).
% 1.85/1.44 thf(f283,definition,(
% 1.85/1.44 spl0_11 <=> ! [X0 : mworld] : (($false = (mrel @ X0 @ sK2)) | ($false = (mrel @ mactual @ X0)))),
% 1.85/1.44 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.85/1.44 thf(f343,plain,(
% 1.85/1.44 spl0_12 | spl0_11 | spl0_4),
% 1.85/1.44 inference(avatar_split_clause,[status(thm)],[f342,f223,f283,f338])).
% 1.85/1.44 thf(f223,definition,(
% 1.85/1.44 spl0_4 <=> ($false = (closed @ d @ sK2))),
% 1.85/1.44 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.85/1.44 thf(f342,plain,(
% 1.85/1.44 ( ! [X0 : mworld] : (($false = (mrel @ mactual @ X0)) | ($false = (mrel @ X0 @ sK2)) | ($false = (mrel @ sK2 @ sK3))) ) | spl0_4),
% 1.85/1.44 inference(subsumption_resolution,[status(thm)],[f328,f224])).
% 1.85/1.44 thf(f224,plain,(
% 1.85/1.44 ($false != (closed @ d @ sK2)) | spl0_4),
% 1.85/1.44 inference(avatar_component_clause,[status(thm)],[f223])).
% 1.85/1.44 thf(f328,plain,(
% 1.85/1.44 ( ! [X0 : mworld] : (($false = (closed @ d @ sK2)) | ($false = (mrel @ X0 @ sK2)) | ($false = (mrel @ sK2 @ sK3)) | ($false = (mrel @ mactual @ X0))) )),
% 1.85/1.44 inference(trivial_inequality_removal,[status(thm)],[f322])).
% 1.85/1.44 thf(f322,plain,(
% 1.85/1.44 ( ! [X0 : mworld] : (($false = (mrel @ X0 @ sK2)) | ($true = $false) | ($false = (closed @ d @ sK2)) | ($false = (mrel @ mactual @ X0)) | ($false = (mrel @ sK2 @ sK3))) )),
% 1.85/1.44 inference(superposition,[status(thm)],[f218,f61])).
% 1.85/1.44 thf(f218,plain,(
% 1.85/1.44 ( ! [X0 : mworld,X1 : mworld] : (($false = (mrel @ sK2 @ X0)) | ($false = (closed @ d @ X0)) | ($false = (mrel @ X1 @ X0)) | ((mrel @ X0 @ sK3) = $false) | ($false = (mrel @ mactual @ X1))) )),
% 1.85/1.44 inference(trivial_inequality_removal,[status(thm)],[f207])).
% 1.85/1.44 thf(f207,plain,(
% 1.85/1.44 ( ! [X0 : mworld,X1 : mworld] : (($false = (mrel @ X1 @ X0)) | ($false = (closed @ d @ X0)) | ($false = (mrel @ mactual @ X1)) | ($true = $false) | ((mrel @ X0 @ sK3) = $false) | ($false = (mrel @ sK2 @ X0))) )),
% 1.85/1.44 inference(superposition,[status(thm)],[f137,f202])).
% 1.85/1.44 thf(f202,plain,(
% 1.85/1.44 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (open @ d @ X2)) | ($false = (mrel @ X1 @ X2)) | ($false = (mrel @ sK2 @ X1)) | ($false = (mrel @ X3 @ X1)) | ($false = (closed @ d @ X1)) | ($false = (mrel @ mactual @ X3))) )),
% 1.85/1.44 inference(trivial_inequality_removal,[status(thm)],[f201])).
% 1.85/1.44 thf(f201,plain,(
% 1.85/1.44 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = $false) | ($false = (mrel @ sK2 @ X1)) | ($false = (mrel @ mactual @ X3)) | ($true = (open @ d @ X2)) | ($false = (mrel @ X1 @ X2)) | ($false = (mrel @ X3 @ X1)) | ($false = (closed @ d @ X1))) )),
% 1.85/1.44 inference(duplicate_literal_removal,[status(thm)],[f187])).
% 1.85/1.44 thf(f187,plain,(
% 1.85/1.44 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X3)) | ($false = (mrel @ sK2 @ X1)) | ($false = (mrel @ X1 @ X2)) | ($false = (mrel @ sK2 @ X1)) | ($true = (open @ d @ X2)) | ($true = $false) | ($false = (mrel @ X3 @ X1)) | ($false = (closed @ d @ X1))) )),
% 1.85/1.44 inference(superposition,[status(thm)],[f186,f134])).
% 1.85/1.44 thf(f134,plain,(
% 1.85/1.44 ( ! [X3 : mworld,X1 : $i] : (($true = (combo @ d @ X1 @ X3)) | ($false = (mrel @ sK2 @ X3))) )),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f132])).
% 1.85/1.44 thf(f132,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : mworld,X1 : $i] : (($false = (mrel @ sK2 @ X3)) | ($true = ((combo @ d @ X1 @ X3) & (h @ X2 @ X3)))) )),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.85/1.44 thf(f131,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : mworld,X1 : $i] : (($true = ((mrel @ sK2 @ X3) => ((combo @ d @ X1 @ X3) & (h @ X2 @ X3))))) )),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f130])).
% 1.85/1.44 thf(f130,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : mworld,X1 : $i] : (($true = ((^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => ((combo @ d @ X1 @ Y0) & (h @ X2 @ Y0)))) @ X3))) )),
% 1.85/1.44 inference(pi_clausification,[status(thm)],[f129])).
% 1.85/1.44 thf(f129,plain,(
% 1.85/1.44 ( ! [X2 : $i,X1 : $i] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => ((combo @ d @ X1 @ Y0) & (h @ X2 @ Y0))))) = $true)) )),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f127])).
% 1.85/1.44 thf(f186,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : mworld,X0 : $i,X1 : mworld,X4 : mworld] : (($false = (combo @ X2 @ X0 @ X3)) | ((mrel @ X3 @ X4) = $false) | ($true = (open @ X2 @ X4)) | ($false = (mrel @ sK2 @ X3)) | ($false = (closed @ X2 @ X3)) | ($false = (mrel @ mactual @ X1)) | ($false = (mrel @ X1 @ X3))) )),
% 1.85/1.44 inference(trivial_inequality_removal,[status(thm)],[f183])).
% 1.85/1.44 thf(f183,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : mworld,X0 : $i,X1 : mworld,X4 : mworld] : (($true = (open @ X2 @ X4)) | ($false = (mrel @ sK2 @ X3)) | ($false = (mrel @ mactual @ X1)) | ((mrel @ X3 @ X4) = $false) | ($false = (closed @ X2 @ X3)) | ($false = (mrel @ X1 @ X3)) | ($true = $false) | ($false = (combo @ X2 @ X0 @ X3))) )),
% 1.85/1.44 inference(superposition,[status(thm)],[f103,f133])).
% 1.85/1.44 thf(f133,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : mworld] : (($true = (h @ X2 @ X3)) | ($false = (mrel @ sK2 @ X3))) )),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f132])).
% 1.85/1.44 thf(f103,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld,X5 : mworld] : (((h @ (sK1 @ X3 @ X1 @ X2) @ X4) = $false) | ((open @ X2 @ X5) = $true) | ($false = (closed @ X2 @ X4)) | ($false = (mrel @ mactual @ X1)) | ($false = (mrel @ X1 @ X4)) | ((mrel @ X4 @ X5) = $false) | ($false = (combo @ X2 @ X3 @ X4))) )),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f102])).
% 1.85/1.44 thf(f102,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (mrel @ X1 @ X4)) | ($true = ((mrel @ X4 @ X5) => (open @ X2 @ X5))) | ((h @ (sK1 @ X3 @ X1 @ X2) @ X4) = $false) | ($false = (combo @ X2 @ X3 @ X4)) | ($false = (closed @ X2 @ X4))) )),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f101])).
% 1.85/1.44 thf(f101,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld,X5 : mworld] : (($false = (mrel @ X1 @ X4)) | ((h @ (sK1 @ X3 @ X1 @ X2) @ X4) = $false) | ($false = (mrel @ mactual @ X1)) | ($false = (combo @ X2 @ X3 @ X4)) | ($false = (closed @ X2 @ X4)) | ($true = ((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0))) @ X5))) )),
% 1.85/1.44 inference(pi_clausification,[status(thm)],[f100])).
% 1.85/1.44 thf(f100,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (($false = (closed @ X2 @ X4)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0))))) | ($false = (mrel @ mactual @ X1)) | ($false = (combo @ X2 @ X3 @ X4)) | ($false = (mrel @ X1 @ X4)) | ((h @ (sK1 @ X3 @ X1 @ X2) @ X4) = $false)) )),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.85/1.44 thf(f99,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (($false = (mrel @ X1 @ X4)) | ($false = (closed @ X2 @ X4)) | (((combo @ X2 @ X3 @ X4) & (h @ (sK1 @ X3 @ X1 @ X2) @ X4)) = $false) | ($false = (mrel @ mactual @ X1)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0)))))) )),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.85/1.44 thf(f98,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = ((closed @ X2 @ X4) & ((combo @ X2 @ X3 @ X4) & (h @ (sK1 @ X3 @ X1 @ X2) @ X4)))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0))))) | ($false = (mrel @ X1 @ X4))) )),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.85/1.44 thf(f97,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (($true = (((closed @ X2 @ X4) & ((combo @ X2 @ X3 @ X4) & (h @ (sK1 @ X3 @ X1 @ X2) @ X4))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0)))))) | ($false = (mrel @ mactual @ X1)) | ($false = (mrel @ X1 @ X4))) )),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f96])).
% 1.85/1.44 thf(f96,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((mrel @ X1 @ X4) => (((closed @ X2 @ X4) & ((combo @ X2 @ X3 @ X4) & (h @ (sK1 @ X3 @ X1 @ X2) @ X4))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (open @ X2 @ Y0)))))))) )),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f95])).
% 1.85/1.44 thf(f95,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : mworld] : (($false = (mrel @ mactual @ X1)) | (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((closed @ X2 @ Y0) & ((combo @ X2 @ X3 @ Y0) & (h @ (sK1 @ X3 @ X1 @ X2) @ Y0))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (open @ X2 @ Y1))))))) @ X4) = $true)) )),
% 1.85/1.44 inference(pi_clausification,[status(thm)],[f94])).
% 1.85/1.44 thf(f94,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((closed @ X2 @ Y0) & ((combo @ X2 @ X3 @ Y0) & (h @ (sK1 @ X3 @ X1 @ X2) @ Y0))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (open @ X2 @ Y1))))))))) | ($false = (mrel @ mactual @ X1))) )),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.85/1.44 thf(f92,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((closed @ X2 @ Y0) & ((combo @ X2 @ X3 @ Y0) & (h @ (sK1 @ X3 @ X1 @ X2) @ Y0))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (open @ X2 @ Y1)))))))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((closed @ X2 @ Y0) & ((~ (combo @ X2 @ X3 @ Y0)) & (h @ o @ Y0))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (closed @ X2 @ Y1)))))))))) | ($false = (mrel @ mactual @ X1))) )),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.85/1.44 thf(f91,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((closed @ X2 @ Y1) & ((combo @ X2 @ X3 @ Y1) & (h @ Y0 @ Y1))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (open @ X2 @ Y2)))))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((closed @ X2 @ Y1) & ((~ (combo @ X2 @ X3 @ Y1)) & (h @ o @ Y1))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (closed @ X2 @ Y2)))))))))) @ (sK1 @ X3 @ X1 @ X2)))) )),
% 1.85/1.44 inference(sigma_clausification,[status(thm)],[f90])).
% 1.85/1.44 thf(f90,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (?? @ $i @ (^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((closed @ X2 @ Y1) & ((combo @ X2 @ X3 @ Y1) & (h @ Y0 @ Y1))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (open @ X2 @ Y2)))))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((closed @ X2 @ Y1) & ((~ (combo @ X2 @ X3 @ Y1)) & (h @ o @ Y1))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (closed @ X2 @ Y2))))))))))))) )),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f89])).
% 1.85/1.44 thf(f89,plain,(
% 1.85/1.44 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((closed @ X2 @ Y2) & ((combo @ X2 @ Y0 @ Y2) & (h @ Y1 @ Y2))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (open @ X2 @ Y3)))))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((closed @ X2 @ Y2) & ((~ (combo @ X2 @ Y0 @ Y2)) & (h @ o @ Y2))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (closed @ X2 @ Y3)))))))))))) @ X3))) )),
% 1.85/1.44 inference(pi_clausification,[status(thm)],[f88])).
% 1.85/1.44 thf(f88,plain,(
% 1.85/1.44 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((closed @ X2 @ Y2) & ((combo @ X2 @ Y0 @ Y2) & (h @ Y1 @ Y2))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (open @ X2 @ Y3)))))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((closed @ X2 @ Y2) & ((~ (combo @ X2 @ Y0 @ Y2)) & (h @ o @ Y2))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (closed @ X2 @ Y3))))))))))))))) )),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f87])).
% 1.85/1.44 thf(f87,plain,(
% 1.85/1.44 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((combo @ Y0 @ Y1 @ Y3) & (h @ Y2 @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (open @ Y0 @ Y4)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((~ (combo @ Y0 @ Y1 @ Y3)) & (h @ o @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (closed @ Y0 @ Y4)))))))))))))) @ X2))) )),
% 1.85/1.44 inference(pi_clausification,[status(thm)],[f86])).
% 1.85/1.44 thf(f86,plain,(
% 1.85/1.44 ( ! [X1 : mworld] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((combo @ Y0 @ Y1 @ Y3) & (h @ Y2 @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (open @ Y0 @ Y4)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((~ (combo @ Y0 @ Y1 @ Y3)) & (h @ o @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (closed @ Y0 @ Y4)))))))))))))))) | ($false = (mrel @ mactual @ X1))) )),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 1.85/1.44 thf(f85,plain,(
% 1.85/1.44 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((combo @ Y0 @ Y1 @ Y3) & (h @ Y2 @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (open @ Y0 @ Y4)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (((closed @ Y0 @ Y3) & ((~ (combo @ Y0 @ Y1 @ Y3)) & (h @ o @ Y3))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (closed @ Y0 @ Y4)))))))))))))))))) )),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f84])).
% 1.85/1.44 thf(f84,plain,(
% 1.85/1.44 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y0 @ Y4) => (((closed @ Y1 @ Y4) & ((combo @ Y1 @ Y2 @ Y4) & (h @ Y3 @ Y4))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (open @ Y1 @ Y5)))))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y0 @ Y4) => (((closed @ Y1 @ Y4) & ((~ (combo @ Y1 @ Y2 @ Y4)) & (h @ o @ Y4))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (closed @ Y1 @ Y5))))))))))))))))) @ X1))) )),
% 1.85/1.44 inference(pi_clausification,[status(thm)],[f83])).
% 1.85/1.44 thf(f83,plain,(
% 1.85/1.44 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y0 @ Y4) => (((closed @ Y1 @ Y4) & ((combo @ Y1 @ Y2 @ Y4) & (h @ Y3 @ Y4))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (open @ Y1 @ Y5)))))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y0 @ Y4) => (((closed @ Y1 @ Y4) & ((~ (combo @ Y1 @ Y2 @ Y4)) & (h @ o @ Y4))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (closed @ Y1 @ Y5)))))))))))))))))))),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.85/1.44 thf(f77,plain,(
% 1.85/1.44 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (?? @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (Y3 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ (closed @ Y0) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ (combo @ Y0 @ Y1) @ (h @ Y2))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (Y3 @ Y5))))))) @ (open @ Y0)))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (Y3 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ (closed @ Y0) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (~ (Y3 @ Y4))))) @ (combo @ Y0 @ Y1)) @ (h @ o))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (Y3 @ Y5))))))) @ (closed @ Y0))))))))))))))),
% 1.85/1.44 inference(definition_unfolding,[status(thm)],[f64,f63,f71,f72,f72,f59,f60,f71,f70,f60,f60,f71,f71,f70,f60,f60,f65,f71])).
% 1.85/1.44 thf(f65,plain,(
% 1.85/1.44 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.85/1.44 inference(cnf_transformation,[status(thm)],[f28])).
% 1.85/1.44 thf(f28,plain,(
% 1.85/1.44 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.85/1.44 inference(fool_elimination,[status(thm)],[f27])).
% 1.85/1.44 thf(f27,plain,(
% 1.85/1.44 ((^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))) = mnot)),
% 1.85/1.44 inference(rectify,[status(thm)],[f2])).
% 1.85/1.44 thf(f2,axiom,(
% 1.85/1.44 ((^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))) = mnot)),
% 1.85/1.44 file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',mnot_def)).
% 1.85/1.44 thf(f72,plain,(
% 1.85/1.44 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.85/1.44 inference(cnf_transformation,[status(thm)],[f53])).
% 1.85/1.44 thf(f53,plain,(
% 1.85/1.44 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.85/1.44 inference(fool_elimination,[status(thm)],[f52])).
% 1.85/1.44 thf(f52,plain,(
% 1.85/1.44 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))))),
% 1.85/1.44 inference(rectify,[status(thm)],[f11])).
% 1.85/1.44 thf(f11,axiom,(
% 1.85/1.44 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X6 : $i] : (X1 @ X6 @ X2))))),
% 1.85/1.44 file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',mforall_di_def)).
% 1.85/1.44 thf(f64,plain,(
% 1.85/1.44 ($true = (mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mexists_di @ (^[Y2 : $i]: (mand @ (mbox @ (mimplies @ (mand @ (closed @ Y0) @ (mand @ (combo @ Y0 @ Y1) @ (h @ Y2))) @ (mbox @ (open @ Y0)))) @ (mbox @ (mimplies @ (mand @ (closed @ Y0) @ (mand @ (mnot @ (combo @ Y0 @ Y1)) @ (h @ o))) @ (mbox @ (closed @ Y0))))))))))))))),
% 1.85/1.44 inference(cnf_transformation,[status(thm)],[f24])).
% 1.85/1.44 thf(f24,plain,(
% 1.85/1.44 ($true = (mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mexists_di @ (^[Y2 : $i]: (mand @ (mbox @ (mimplies @ (mand @ (closed @ Y0) @ (mand @ (combo @ Y0 @ Y1) @ (h @ Y2))) @ (mbox @ (open @ Y0)))) @ (mbox @ (mimplies @ (mand @ (closed @ Y0) @ (mand @ (mnot @ (combo @ Y0 @ Y1)) @ (h @ o))) @ (mbox @ (closed @ Y0))))))))))))))),
% 1.85/1.44 inference(fool_elimination,[status(thm)],[f23])).
% 1.85/1.44 thf(f23,plain,(
% 1.85/1.44 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mexists_di @ (^[X2 : $i] : (mand @ (mbox @ (mimplies @ (mand @ (closed @ X0) @ (mand @ (combo @ X0 @ X1) @ (h @ X2))) @ (mbox @ (open @ X0)))) @ (mbox @ (mimplies @ (mand @ (closed @ X0) @ (mand @ (mnot @ (combo @ X0 @ X1)) @ (h @ o))) @ (mbox @ (closed @ X0)))))))))))))),
% 1.85/1.44 inference(rectify,[status(thm)],[f13])).
% 1.85/1.44 thf(f13,axiom,(
% 1.85/1.44 (mlocal @ (mbox @ (mforall_di @ (^[X7 : $i] : (mforall_di @ (^[X4 : $i] : (mexists_di @ (^[X8 : $i] : (mand @ (mbox @ (mimplies @ (mand @ (closed @ X7) @ (mand @ (combo @ X7 @ X4) @ (h @ X8))) @ (mbox @ (open @ X7)))) @ (mbox @ (mimplies @ (mand @ (closed @ X7) @ (mand @ (mnot @ (combo @ X7 @ X4)) @ (h @ o))) @ (mbox @ (closed @ X7)))))))))))))),
% 1.85/1.44 file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',ax1)).
% 1.85/1.44 thf(f137,plain,(
% 1.85/1.44 ($false = (open @ d @ sK3))),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.85/1.44 thf(f307,plain,(
% 1.85/1.44 ~spl0_9),
% 1.85/1.44 inference(avatar_contradiction_clause,[status(thm)],[f306])).
% 1.85/1.44 thf(f306,plain,(
% 1.85/1.44 $false | ~spl0_9),
% 1.85/1.44 inference(trivial_inequality_removal,[status(thm)],[f298])).
% 1.85/1.44 thf(f298,plain,(
% 1.85/1.44 ($true = $false) | ~spl0_9),
% 1.85/1.44 inference(superposition,[status(thm)],[f276,f123])).
% 1.85/1.44 thf(f123,plain,(
% 1.85/1.44 ((mrel @ mactual @ sK2) = $true)),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f121])).
% 1.85/1.44 thf(f276,plain,(
% 1.85/1.44 ((mrel @ mactual @ sK2) = $false) | ~spl0_9),
% 1.85/1.44 inference(avatar_component_clause,[status(thm)],[f274])).
% 1.85/1.44 thf(f293,plain,(
% 1.85/1.44 spl0_9 | ~spl0_4),
% 1.85/1.44 inference(avatar_split_clause,[status(thm)],[f290,f223,f274])).
% 1.85/1.44 thf(f290,plain,(
% 1.85/1.44 ((mrel @ mactual @ sK2) = $false) | ~spl0_4),
% 1.85/1.44 inference(trivial_inequality_removal,[status(thm)],[f288])).
% 1.85/1.44 thf(f288,plain,(
% 1.85/1.44 ((mrel @ mactual @ sK2) = $false) | ($true = $false) | ~spl0_4),
% 1.85/1.44 inference(superposition,[status(thm)],[f225,f156])).
% 1.85/1.44 thf(f156,plain,(
% 1.85/1.44 ( ! [X1 : mworld] : (($true = (closed @ d @ X1)) | ($false = (mrel @ mactual @ X1))) )),
% 1.85/1.44 inference(binary_proxy_clausification,[status(thm)],[f155])).
% 1.85/1.44 thf(f155,plain,(
% 1.85/1.44 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (closed @ d @ X1)))) )),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f154])).
% 1.85/1.44 thf(f154,plain,(
% 1.85/1.44 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (closed @ d @ Y0))) @ X1))) )),
% 1.85/1.44 inference(pi_clausification,[status(thm)],[f153])).
% 1.85/1.44 thf(f153,plain,(
% 1.85/1.44 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (closed @ d @ Y0)))))),
% 1.85/1.44 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.85/1.44 thf(f82,plain,(
% 1.85/1.44 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (closed @ d))))),
% 1.85/1.44 inference(definition_unfolding,[status(thm)],[f75,f63,f71])).
% 1.85/1.44 thf(f75,plain,(
% 1.85/1.44 ((mlocal @ (mbox @ (closed @ d))) = $true)),
% 1.85/1.44 inference(cnf_transformation,[status(thm)],[f40])).
% 1.85/1.44 thf(f40,plain,(
% 1.85/1.44 ((mlocal @ (mbox @ (closed @ d))) = $true)),
% 1.85/1.44 inference(fool_elimination,[status(thm)],[f39])).
% 1.85/1.44 thf(f39,plain,(
% 1.85/1.44 (mlocal @ (mbox @ (closed @ d)))),
% 1.85/1.44 inference(rectify,[status(thm)],[f14])).
% 1.85/1.44 thf(f14,axiom,(
% 1.85/1.44 (mlocal @ (mbox @ (closed @ d)))),
% 1.85/1.44 file('/export/starexec/sandbox/tmp/tmp.Ib8TI9icsv/DTF2THF_10722.p',ax2)).
% 1.85/1.44 thf(f225,plain,(
% 1.85/1.44 ($false = (closed @ d @ sK2)) | ~spl0_4),
% 1.85/1.44 inference(avatar_component_clause,[status(thm)],[f223])).
% 1.85/1.44 % SZS output end Proof for DTF2THF_10722
% 1.85/1.44 % (11049)------------------------------
% 1.85/1.44 % (11049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.85/1.44 % (11049)Termination reason: Refutation
% 1.85/1.44
% 1.85/1.44 % (11049)Memory used [KB]: 6012
% 1.85/1.44 % (11049)Time elapsed: 0.040 s
% 1.85/1.44 % (11049)Instructions burned: 56 (million)
% 1.85/1.44 % (11049)------------------------------
% 1.85/1.44 % (11049)------------------------------
% 1.85/1.44 % (11048)Success in time 0.052 s
%------------------------------------------------------------------------------