%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NLP266^4 : 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 : n001.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 09:22:25 AM UTC 2026
% Result : Theorem 1.87s 2.07s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 20
% Syntax : Number of formulae : 203 ( 67 unt; 0 typ; 8 def)
% Number of atoms : 2160 ( 428 equ; 0 cnn)
% Maximal formula atoms : 20 ( 10 avg)
% Number of connectives : 3908 ( 67 ~; 312 |; 102 &;3088 @)
% ( 8 <=>; 150 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 93 ( 93 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 36 usr; 17 con; 0-4 aty)
% ( 127 !!; 54 ??; 0 @@+; 0 @@-)
% Number of variables : 708 ( 394 ^; 312 !; 2 ?; 708 :)
% 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_16,type,
number: $i > $i > mworld > $o ).
thf(func_def_17,type,
string: $i > mworld > $o ).
thf(func_def_18,type,
in: $i > $i > $i > mworld > $o ).
thf(func_def_19,type,
do: $i > $i > $i > mworld > $o ).
thf(func_def_20,type,
entry_box: $i > mworld > $o ).
thf(func_def_21,type,
userid: $i > $i > mworld > $o ).
thf(func_def_38,type,
sK1: mworld > $i ).
thf(func_def_42,type,
sK2: $i > mworld > $i > $i > $i ).
thf(func_def_44,type,
sK4: mworld ).
thf(func_def_45,type,
sK5: $i > $i > $i > $i > mworld ).
thf(func_def_46,type,
sK6: $i > $i > mworld ).
thf(func_def_47,type,
sK7: $i > $i > $i > $i > $i ).
thf(func_def_48,type,
sK8: $i > $i > $i > $i > $i ).
thf(f393,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f186,f200,f295,f303,f327,f335,f345,f367,f391]) ).
thf(f391,plain,
( ~ spl0_1
| spl0_5
| spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f390]) ).
thf(f390,plain,
( $false
| ~ spl0_1
| spl0_5
| spl0_7
| ~ spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f389,f292]) ).
thf(f292,plain,
( ( ( entry_box @ sK3 @ sK4 )
!= $false )
| spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f291]) ).
thf(f291,definition,
( spl0_5
<=> ( ( entry_box @ sK3 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f389,plain,
( ( ( entry_box @ sK3 @ sK4 )
= $false )
| ~ spl0_1
| spl0_7
| ~ spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f388,f116]) ).
thf(f116,plain,
( ( mrel @ mactual @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
( ( ( mrel @ mactual @ sK4 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK4 @ Y4 )
=> ( ( userid @ u @ Y0 @ Y4 )
& ( entry_box @ Y1 @ Y4 )
& ( number @ Y1 @ one @ Y4 ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK4 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y3 @ Y2 @ Y5 @ Y4 )
=> ( in @ Y0 @ Y1 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f113]) ).
thf(f113,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( ( userid @ u @ Y1 @ Y5 )
& ( entry_box @ Y2 @ Y5 )
& ( number @ Y2 @ one @ Y5 ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( do @ Y4 @ Y3 @ Y6 @ Y5 )
=> ( in @ Y1 @ Y2 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( ( userid @ u @ Y1 @ Y5 )
& ( entry_box @ Y2 @ Y5 )
& ( number @ Y2 @ one @ Y5 ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( do @ Y4 @ Y3 @ Y6 @ Y5 )
=> ( in @ Y1 @ Y2 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,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: $i > mworld > $o,Y4: mworld] :
( ?? @ $i
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) )
@ ^ [Y3: $i] :
( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ ( ^ [Y4: mworld > $o,Y5: mworld] :
( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ ( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ ( userid @ u @ Y0 )
@ ( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ ( entry_box @ Y1 )
@ ( number @ Y1 @ one ) ) ) )
@ ( ^ [Y4: mworld > $o,Y5: mworld] :
( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ ( ^ [Y4: $i > mworld > $o,Y5: mworld] :
( !! @ $i
@ ^ [Y6: $i] : ( Y4 @ Y6 @ Y5 ) )
@ ^ [Y4: $i] :
( ^ [Y5: mworld > $o,Y6: mworld > $o,Y7: mworld] :
( ( Y5 @ Y7 )
=> ( Y6 @ Y7 ) )
@ ( do @ Y3 @ Y2 @ Y4 )
@ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f60,f65,f54,f55,f55,f55,f55,f61,f54,f61,f61,f54,f66,f64]) ).
thf(f64,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',mimplies_def) ).
thf(f66,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,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.l3lOMfjeXj/DTF2THF_4164.p',mforall_di_def) ).
thf(f61,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',mand_def) ).
thf(f55,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) )
= mexists_di ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X6: $i] : ( X1 @ X6 @ X2 ) )
= mexists_di ),
file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',mexists_di_def) ).
thf(f54,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',mbox_def) ).
thf(f65,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,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.l3lOMfjeXj/DTF2THF_4164.p',mlocal_def) ).
thf(f60,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mexists_di
@ ^ [Y2: $i] :
( mexists_di
@ ^ [Y3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( mand @ ( entry_box @ Y1 ) @ ( number @ Y1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y3 @ Y2 @ Y4 ) @ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f50,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mexists_di
@ ^ [Y2: $i] :
( mexists_di
@ ^ [Y3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( mand @ ( entry_box @ Y1 ) @ ( number @ Y1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y3 @ Y2 @ Y4 ) @ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f45]) ).
thf(f45,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mexists_di
@ ^ [Y2: $i] :
( mexists_di
@ ^ [Y3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( mand @ ( entry_box @ Y1 ) @ ( number @ Y1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y3 @ Y2 @ Y4 ) @ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f44]) ).
thf(f44,plain,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X2: $i] :
( mexists_di
@ ^ [X3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ X0 ) @ ( mand @ ( entry_box @ X1 ) @ ( number @ X1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mimplies @ ( do @ X3 @ X2 @ X4 ) @ ( in @ X0 @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X7: $i] :
( mexists_di
@ ^ [X3: $i] :
( mexists_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X8: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ X7 ) @ ( mand @ ( entry_box @ X3 ) @ ( number @ X3 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X9: $i] : ( mimplies @ ( do @ X8 @ X1 @ X9 ) @ ( in @ X7 @ X3 @ X9 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f16,conjecture,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X7: $i] :
( mexists_di
@ ^ [X3: $i] :
( mexists_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X8: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ X7 ) @ ( mand @ ( entry_box @ X3 ) @ ( number @ X3 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X9: $i] : ( mimplies @ ( do @ X8 @ X1 @ X9 ) @ ( in @ X7 @ X3 @ X9 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',con) ).
thf(f388,plain,
( ( ( mrel @ mactual @ sK4 )
!= $true )
| ( ( entry_box @ sK3 @ sK4 )
= $false )
| ~ spl0_1
| spl0_7
| ~ spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f381,f317]) ).
thf(f317,plain,
( ( ( string @ ( sK1 @ mactual ) @ sK4 )
!= $false )
| spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f316]) ).
thf(f316,definition,
( spl0_7
<=> ( ( string @ ( sK1 @ mactual ) @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f381,plain,
( ( ( string @ ( sK1 @ mactual ) @ sK4 )
= $false )
| ( ( entry_box @ sK3 @ sK4 )
= $false )
| ( ( mrel @ mactual @ sK4 )
!= $true )
| ~ spl0_1
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f379]) ).
thf(f379,plain,
( ( ( entry_box @ sK3 @ sK4 )
= $false )
| ( ( mrel @ mactual @ sK4 )
!= $true )
| ( $true != $true )
| ( ( string @ ( sK1 @ mactual ) @ sK4 )
= $false )
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f371,f180]) ).
thf(f180,plain,
( ! [X0: $i,X1: $i] :
( ( ( mrel @ sK4 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( ( entry_box @ X1 @ sK4 )
= $false )
| ( ( string @ X0 @ sK4 )
= $false ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f179]) ).
thf(f179,definition,
( spl0_1
<=> ! [X0: $i,X1: $i] :
( ( ( string @ X0 @ sK4 )
= $false )
| ( ( mrel @ sK4 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( ( entry_box @ X1 @ sK4 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f371,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ X0 @ ( sK6 @ ( sK1 @ mactual ) @ sK3 ) ) )
| ( $true
!= ( mrel @ mactual @ X0 ) ) )
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f368]) ).
thf(f368,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ mactual @ X0 ) )
| ( $true
!= ( mrel @ X0 @ ( sK6 @ ( sK1 @ mactual ) @ sK3 ) ) )
| ( $true = $false ) )
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f322,f63]) ).
thf(f63,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( $true
= ( mrel @ X0 @ X2 ) )
| ( ( mrel @ X1 @ X2 )
!= $true )
| ( $true
!= ( mrel @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
thf(f52,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X1 @ X2 )
!= $true )
| ( $true
!= ( mrel @ X0 @ X1 ) )
| ( $true
= ( mrel @ X0 @ X2 ) ) ),
inference(flattening,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( $true
= ( mrel @ X0 @ X2 ) )
| ( $true
!= ( mrel @ X0 @ X1 ) )
| ( ( mrel @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( $true
= ( mrel @ X0 @ X1 ) )
& ( ( mrel @ X1 @ X2 )
= $true ) )
=> ( $true
= ( mrel @ X0 @ X2 ) ) ),
inference(fool_elimination,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X1 @ X2 )
& ( mrel @ X0 @ X1 ) )
=> ( mrel @ X0 @ X2 ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
! [X2: mworld,X4: mworld,X5: mworld] :
( ( ( mrel @ X4 @ X5 )
& ( mrel @ X2 @ X4 ) )
=> ( mrel @ X2 @ X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',mrel_transitive) ).
thf(f322,plain,
( ( ( mrel @ mactual @ ( sK6 @ ( sK1 @ mactual ) @ sK3 ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f320]) ).
thf(f320,definition,
( spl0_8
<=> ( ( mrel @ mactual @ ( sK6 @ ( sK1 @ mactual ) @ sK3 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f367,plain,
( spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f364,f324,f320]) ).
thf(f324,definition,
( spl0_9
<=> ( ( entry_box @ sK3 @ ( sK6 @ ( sK1 @ mactual ) @ sK3 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f364,plain,
( ( ( mrel @ mactual @ ( sK6 @ ( sK1 @ mactual ) @ sK3 ) )
= $false )
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f363]) ).
thf(f363,plain,
( ( ( mrel @ mactual @ ( sK6 @ ( sK1 @ mactual ) @ sK3 ) )
= $false )
| ( $true = $false )
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f111,f326]) ).
thf(f326,plain,
( ( ( entry_box @ sK3 @ ( sK6 @ ( sK1 @ mactual ) @ sK3 ) )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f324]) ).
thf(f111,plain,
! [X1: mworld] :
( ( $true
= ( entry_box @ sK3 @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X1: mworld] :
( ( ( ( entry_box @ sK3 @ X1 )
& ( number @ sK3 @ one @ X1 ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( entry_box @ sK3 @ X1 )
& ( number @ sK3 @ one @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f107]) ).
thf(f107,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( entry_box @ sK3 @ Y0 )
& ( number @ sK3 @ one @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( entry_box @ sK3 @ Y0 )
& ( number @ sK3 @ one @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f105]) ).
thf(f105,plain,
( $true
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( ( entry_box @ Y0 @ Y1 )
& ( number @ Y0 @ one @ Y1 ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( ( entry_box @ Y0 @ Y1 )
& ( number @ Y0 @ one @ Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) )
@ ( entry_box @ Y0 )
@ ( number @ Y0 @ one ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f57,f65,f55,f54,f61]) ).
thf(f57,plain,
( $true
= ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( entry_box @ Y0 ) @ ( number @ Y0 @ one ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( entry_box @ Y0 ) @ ( number @ Y0 @ one ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( mlocal
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( mand @ ( entry_box @ X0 ) @ ( number @ X0 @ one ) ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
( mlocal
@ ( mexists_di
@ ^ [X3: $i] : ( mbox @ ( mand @ ( entry_box @ X3 ) @ ( number @ X3 @ one ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',ax2) ).
thf(f345,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[status(thm)],[f344]) ).
thf(f344,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f338]) ).
thf(f338,plain,
( ( $true = $false )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f59,f314]) ).
thf(f314,plain,
( ( ( mrel @ mactual @ mactual )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f312]) ).
thf(f312,definition,
( spl0_6
<=> ( ( mrel @ mactual @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f59,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f36]) ).
thf(f36,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.l3lOMfjeXj/DTF2THF_4164.p',mrel_reflexive) ).
thf(f335,plain,
( spl0_6
| spl0_2
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f334,f316,f182,f312]) ).
thf(f182,definition,
( spl0_2
<=> ( ( mrel @ mactual @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f334,plain,
( ( ( mrel @ mactual @ mactual )
= $false )
| spl0_2
| ~ spl0_7 ),
inference(subsumption_resolution,[status(thm)],[f330,f183]) ).
thf(f183,plain,
( ( ( mrel @ mactual @ sK4 )
!= $false )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f182]) ).
thf(f330,plain,
( ( ( mrel @ mactual @ mactual )
= $false )
| ( ( mrel @ mactual @ sK4 )
= $false )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f328]) ).
thf(f328,plain,
( ( $true = $false )
| ( ( mrel @ mactual @ mactual )
= $false )
| ( ( mrel @ mactual @ sK4 )
= $false )
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f318,f82]) ).
thf(f82,plain,
! [X2: mworld,X1: mworld] :
( ( ( string @ ( sK1 @ X1 ) @ X2 )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $false )
| ( $true
= ( ( userid @ u @ ( sK1 @ X1 ) @ X2 )
& ( string @ ( sK1 @ X1 ) @ X2 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ( mrel @ X1 @ X2 )
=> ( ( userid @ u @ ( sK1 @ X1 ) @ X2 )
& ( string @ ( sK1 @ X1 ) @ X2 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( userid @ u @ ( sK1 @ X1 ) @ Y0 )
& ( string @ ( sK1 @ X1 ) @ Y0 ) ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( userid @ u @ ( sK1 @ X1 ) @ Y0 )
& ( string @ ( sK1 @ X1 ) @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( userid @ u @ Y0 @ Y1 )
& ( string @ Y0 @ Y1 ) ) ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( userid @ u @ Y0 @ Y1 )
& ( string @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( userid @ u @ Y0 @ Y1 )
& ( string @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( userid @ u @ Y1 @ Y2 )
& ( string @ Y1 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( userid @ u @ Y1 @ Y2 )
& ( string @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,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: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) )
@ ( userid @ u @ Y0 )
@ ( string @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f68,f65,f54,f55,f54,f61]) ).
thf(f68,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( string @ Y0 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( string @ Y0 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f48]) ).
thf(f48,plain,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( mand @ ( userid @ u @ X0 ) @ ( string @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X7: $i] : ( mbox @ ( mand @ ( userid @ u @ X7 ) @ ( string @ X7 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',ax1) ).
thf(f318,plain,
( ( ( string @ ( sK1 @ mactual ) @ sK4 )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f316]) ).
thf(f327,plain,
( spl0_6
| spl0_7
| spl0_8
| spl0_9
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f308,f288,f324,f320,f316,f312]) ).
thf(f288,definition,
( spl0_4
<=> ! [X0: mworld] :
( ( $false
= ( string @ ( sK1 @ X0 ) @ sK4 ) )
| ( ( entry_box @ sK3 @ ( sK6 @ ( sK1 @ X0 ) @ sK3 ) )
= $false )
| ( ( mrel @ X0 @ ( sK6 @ ( sK1 @ X0 ) @ sK3 ) )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ mactual @ ( sK6 @ ( sK1 @ X0 ) @ sK3 ) )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f308,plain,
( ( ( entry_box @ sK3 @ ( sK6 @ ( sK1 @ mactual ) @ sK3 ) )
= $false )
| ( ( mrel @ mactual @ mactual )
= $false )
| ( ( mrel @ mactual @ ( sK6 @ ( sK1 @ mactual ) @ sK3 ) )
= $false )
| ( ( string @ ( sK1 @ mactual ) @ sK4 )
= $false )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f307]) ).
thf(f307,plain,
( ( $false != $false )
| ( ( mrel @ mactual @ ( sK6 @ ( sK1 @ mactual ) @ sK3 ) )
= $false )
| ( ( mrel @ mactual @ mactual )
= $false )
| ( ( string @ ( sK1 @ mactual ) @ sK4 )
= $false )
| ( ( entry_box @ sK3 @ ( sK6 @ ( sK1 @ mactual ) @ sK3 ) )
= $false )
| ~ spl0_4 ),
inference(equality_factoring,[status(thm)],[f289]) ).
thf(f289,plain,
( ! [X0: mworld] :
( ( ( mrel @ mactual @ ( sK6 @ ( sK1 @ X0 ) @ sK3 ) )
= $false )
| ( $false
= ( string @ ( sK1 @ X0 ) @ sK4 ) )
| ( ( mrel @ X0 @ ( sK6 @ ( sK1 @ X0 ) @ sK3 ) )
= $false )
| ( ( entry_box @ sK3 @ ( sK6 @ ( sK1 @ X0 ) @ sK3 ) )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f288]) ).
thf(f303,plain,
( spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f302]) ).
thf(f302,plain,
( $false
| spl0_2
| ~ spl0_5 ),
inference(subsumption_resolution,[status(thm)],[f298,f183]) ).
thf(f298,plain,
( ( ( mrel @ mactual @ sK4 )
= $false )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f296]) ).
thf(f296,plain,
( ( $true = $false )
| ( ( mrel @ mactual @ sK4 )
= $false )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f293,f111]) ).
thf(f293,plain,
( ( ( entry_box @ sK3 @ sK4 )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f291]) ).
thf(f295,plain,
( spl0_5
| spl0_4
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f285,f182,f288,f291]) ).
thf(f285,plain,
( ! [X0: mworld] :
( ( ( mrel @ X0 @ ( sK6 @ ( sK1 @ X0 ) @ sK3 ) )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ mactual @ ( sK6 @ ( sK1 @ X0 ) @ sK3 ) )
= $false )
| ( $false
= ( string @ ( sK1 @ X0 ) @ sK4 ) )
| ( ( entry_box @ sK3 @ sK4 )
= $false )
| ( ( entry_box @ sK3 @ ( sK6 @ ( sK1 @ X0 ) @ sK3 ) )
= $false ) )
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f284]) ).
thf(f284,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( ( mrel @ mactual @ ( sK6 @ ( sK1 @ X0 ) @ sK3 ) )
= $false )
| ( ( mrel @ X0 @ ( sK6 @ ( sK1 @ X0 ) @ sK3 ) )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( string @ ( sK1 @ X0 ) @ sK4 ) )
| ( ( entry_box @ sK3 @ ( sK6 @ ( sK1 @ X0 ) @ sK3 ) )
= $false )
| ( ( entry_box @ sK3 @ sK4 )
= $false ) )
| spl0_2 ),
inference(superposition,[status(thm)],[f110,f282]) ).
thf(f282,plain,
( ! [X0: mworld,X1: $i] :
( ( ( number @ X1 @ one @ ( sK6 @ ( sK1 @ X0 ) @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ sK4 )
= $false )
| ( ( entry_box @ X1 @ ( sK6 @ ( sK1 @ X0 ) @ X1 ) )
= $false )
| ( ( mrel @ X0 @ ( sK6 @ ( sK1 @ X0 ) @ X1 ) )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( string @ ( sK1 @ X0 ) @ sK4 ) ) )
| spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f279]) ).
thf(f279,plain,
( ! [X0: mworld,X1: $i] :
( ( ( entry_box @ X1 @ ( sK6 @ ( sK1 @ X0 ) @ X1 ) )
= $false )
| ( $true = $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ X0 @ ( sK6 @ ( sK1 @ X0 ) @ X1 ) )
= $false )
| ( $false
= ( string @ ( sK1 @ X0 ) @ sK4 ) )
| ( ( number @ X1 @ one @ ( sK6 @ ( sK1 @ X0 ) @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ sK4 )
= $false ) )
| spl0_2 ),
inference(superposition,[status(thm)],[f278,f83]) ).
thf(f83,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( userid @ u @ ( sK1 @ X1 ) @ X2 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f81]) ).
thf(f278,plain,
( ! [X0: $i,X1: $i] :
( ( ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( string @ X0 @ sK4 )
= $false )
| ( ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ sK4 )
= $false ) )
| spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f277,f183]) ).
thf(f277,plain,
! [X0: $i,X1: $i] :
( ( ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( mrel @ mactual @ sK4 )
= $false )
| ( ( entry_box @ X1 @ sK4 )
= $false )
| ( ( string @ X0 @ sK4 )
= $false )
| ( ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f276]) ).
thf(f276,plain,
! [X0: $i,X1: $i] :
( ( ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( mrel @ mactual @ sK4 )
= $false )
| ( ( entry_box @ X1 @ sK4 )
= $false )
| ( $true = $false )
| ( ( string @ X0 @ sK4 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f264]) ).
thf(f264,plain,
! [X0: $i,X1: $i] :
( ( ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( string @ X0 @ sK4 )
= $false )
| ( ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ sK4 )
= $false )
| ( ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( mrel @ mactual @ sK4 )
= $false )
| ( ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f141,f209]) ).
thf(f209,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( ( mrel @ X2 @ ( sK5 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( string @ X0 @ X2 )
= $false )
| ( ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f208]) ).
thf(f208,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( ( entry_box @ X1 @ X2 )
= $false )
| ( ( string @ X0 @ X2 )
= $false )
| ( ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( mrel @ X2 @ ( sK5 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( $true = $false )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f204]) ).
thf(f204,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( ( mrel @ mactual @ X2 )
= $false )
| ( ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( mrel @ X2 @ ( sK5 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ X2 )
= $false )
| ( $true = $false )
| ( ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) )
= $false )
| ( ( string @ X0 @ X2 )
= $false ) ),
inference(superposition,[status(thm)],[f157,f149]) ).
thf(f149,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X2 @ ( sK8 @ X1 @ X3 @ X4 @ X2 ) @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
= $false )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
| ( ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f148]) ).
thf(f148,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X2 @ ( sK8 @ X1 @ X3 @ X4 @ X2 ) @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( ( ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
= $false )
| ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
= $false )
| ( $false
= ( in @ X1 @ X2 @ ( sK8 @ X1 @ X3 @ X4 @ X2 ) @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( do @ X4 @ X3 @ ( sK8 @ X1 @ X3 @ X4 @ X2 ) @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ ( sK8 @ X1 @ X3 @ X4 @ X2 ) @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) ) )
| ( ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f142]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) )
@ ( sK8 @ X1 @ X3 @ X4 @ X2 ) )
= $false )
| ( ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) ) )
= $false )
| ( ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( mrel @ sK4 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) ) ) )
= $false )
| ( ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f129]) ).
thf(f129,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( mrel @ sK4 @ ( sK6 @ X1 @ X2 ) )
=> ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) ) )
= $false )
| ( ( ( mrel @ sK4 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f128]) ).
thf(f128,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( mrel @ sK4 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) ) ) )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( ( userid @ u @ X1 @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( number @ X2 @ one @ Y0 ) ) )
@ ( sK6 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f127]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( ( userid @ u @ X1 @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( number @ X2 @ one @ Y0 ) ) ) )
= $false )
| ( ( ( mrel @ sK4 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f126]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( ( userid @ u @ X1 @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( number @ X2 @ one @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) )
@ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f125]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( ( userid @ u @ X1 @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( number @ X2 @ one @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( ( userid @ u @ X1 @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( number @ X2 @ one @ Y0 ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f123]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK4 @ Y1 )
=> ( ( userid @ u @ X1 @ Y1 )
& ( entry_box @ X2 @ Y1 )
& ( number @ X2 @ one @ Y1 ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK4 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ Y0 @ X3 @ Y2 @ Y1 )
=> ( in @ X1 @ X2 @ Y2 @ Y1 ) ) ) ) ) )
@ X4 )
= $false ),
inference(pi_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK4 @ Y1 )
=> ( ( userid @ u @ X1 @ Y1 )
& ( entry_box @ X2 @ Y1 )
& ( number @ X2 @ one @ Y1 ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK4 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ Y0 @ X3 @ Y2 @ Y1 )
=> ( in @ X1 @ X2 @ Y2 @ Y1 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f121]) ).
thf(f121,plain,
! [X2: $i,X3: $i,X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK4 @ Y2 )
=> ( ( userid @ u @ X1 @ Y2 )
& ( entry_box @ X2 @ Y2 )
& ( number @ X2 @ one @ Y2 ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK4 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( do @ Y1 @ Y0 @ Y3 @ Y2 )
=> ( in @ X1 @ X2 @ Y3 @ Y2 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
! [X2: $i,X1: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK4 @ Y2 )
=> ( ( userid @ u @ X1 @ Y2 )
& ( entry_box @ X2 @ Y2 )
& ( number @ X2 @ one @ Y2 ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK4 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( do @ Y1 @ Y0 @ Y3 @ Y2 )
=> ( in @ X1 @ X2 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f119]) ).
thf(f119,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK4 @ Y3 )
=> ( ( userid @ u @ X1 @ Y3 )
& ( entry_box @ Y0 @ Y3 )
& ( number @ Y0 @ one @ Y3 ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK4 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( do @ Y2 @ Y1 @ Y4 @ Y3 )
=> ( in @ X1 @ Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) )
@ X2 )
= $false ),
inference(pi_clausification,[status(thm)],[f118]) ).
thf(f118,plain,
! [X1: $i] :
( ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK4 @ Y3 )
=> ( ( userid @ u @ X1 @ Y3 )
& ( entry_box @ Y0 @ Y3 )
& ( number @ Y0 @ one @ Y3 ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK4 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( do @ Y2 @ Y1 @ Y4 @ Y3 )
=> ( in @ X1 @ Y0 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f117]) ).
thf(f117,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK4 @ Y4 )
=> ( ( userid @ u @ Y0 @ Y4 )
& ( entry_box @ Y1 @ Y4 )
& ( number @ Y1 @ one @ Y4 ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK4 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y3 @ Y2 @ Y5 @ Y4 )
=> ( in @ Y0 @ Y1 @ Y5 @ Y4 ) ) ) ) ) ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK4 @ Y4 )
=> ( ( userid @ u @ Y0 @ Y4 )
& ( entry_box @ Y1 @ Y4 )
& ( number @ Y1 @ one @ Y4 ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK4 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y3 @ Y2 @ Y5 @ Y4 )
=> ( in @ Y0 @ Y1 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f114]) ).
thf(f157,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X1 @ X3 @ ( sK8 @ X4 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X0 @ X5 ) @ ( sK5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( ( userid @ u @ X4 @ ( sK6 @ X4 @ X5 ) )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( entry_box @ X3 @ X2 )
= $false )
| ( ( mrel @ X2 @ ( sK5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) )
= $false )
| ( ( string @ X1 @ X2 )
= $false )
| ( ( number @ X5 @ one @ ( sK6 @ X4 @ X5 ) )
= $false )
| ( ( entry_box @ X5 @ ( sK6 @ X4 @ X5 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f155]) ).
thf(f155,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( entry_box @ X3 @ X2 )
= $false )
| ( ( string @ X1 @ X2 )
= $false )
| ( ( entry_box @ X5 @ ( sK6 @ X4 @ X5 ) )
= $false )
| ( ( userid @ u @ X4 @ ( sK6 @ X4 @ X5 ) )
= $false )
| ( ( mrel @ X2 @ ( sK5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) )
= $false )
| ( $true = $false )
| ( ( number @ X5 @ one @ ( sK6 @ X4 @ X5 ) )
= $false )
| ( $true
= ( in @ X1 @ X3 @ ( sK8 @ X4 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X0 @ X5 ) @ ( sK5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(superposition,[status(thm)],[f103,f147]) ).
thf(f147,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( do @ X4 @ X3 @ ( sK8 @ X1 @ X3 @ X4 @ X2 ) @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
| ( ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
= $false )
| ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f146]) ).
thf(f146,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
= $false )
| ( ( ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
= $false )
| ( $true
= ( do @ X4 @ X3 @ ( sK8 @ X1 @ X3 @ X4 @ X2 ) @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f145]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( do @ X4 @ X3 @ ( sK8 @ X1 @ X3 @ X4 @ X2 ) @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f103,plain,
! [X2: $i,X3: $i,X1: mworld,X6: $i,X4: $i,X5: mworld] :
( ( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ X6 @ X5 )
= $false )
| ( $false
= ( string @ X3 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( in @ X3 @ X4 @ X6 @ X5 )
= $true )
| ( ( entry_box @ X4 @ X1 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X1: mworld,X6: $i,X4: $i,X5: mworld] :
( ( $true
= ( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ X6 @ X5 )
=> ( in @ X3 @ X4 @ X6 @ X5 ) ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( entry_box @ X4 @ X1 )
= $false )
| ( $false
= ( string @ X3 @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f101]) ).
thf(f101,plain,
! [X2: $i,X3: $i,X1: mworld,X6: $i,X4: $i,X5: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( string @ X3 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( entry_box @ X4 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ Y0 @ X5 )
=> ( in @ X3 @ X4 @ Y0 @ X5 ) )
@ X6 ) ) ),
inference(pi_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( string @ X3 @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( entry_box @ X4 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ Y0 @ X5 )
=> ( in @ X3 @ X4 @ Y0 @ X5 ) ) )
= $true )
| ( $false
= ( mrel @ X1 @ X5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i,X5: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( string @ X3 @ X1 ) )
| ( ( entry_box @ X4 @ X1 )
= $false )
| ( ( ( mrel @ X1 @ X5 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ Y0 @ X5 )
=> ( in @ X3 @ X4 @ Y0 @ X5 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f98]) ).
thf(f98,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i,X5: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ Y1 @ Y0 )
=> ( in @ X3 @ X4 @ Y1 @ Y0 ) ) ) )
@ X5 )
= $true )
| ( ( entry_box @ X4 @ X1 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( string @ X3 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ Y1 @ Y0 )
=> ( in @ X3 @ X4 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( string @ X3 @ X1 ) )
| ( ( entry_box @ X4 @ X1 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( ( entry_box @ X4 @ X1 )
= $false )
| ( $false
= ( string @ X3 @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) )
@ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( ( entry_box @ X4 @ X1 )
= $false )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( string @ X3 @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( ( string @ X3 @ X1 )
& ( entry_box @ X4 @ X1 ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ( ( string @ X3 @ X1 )
& ( entry_box @ X4 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( ( string @ X3 @ X1 )
& ( entry_box @ Y0 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( do @ X2 @ Y1 @ Y3 @ Y2 )
=> ( in @ X3 @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
@ X4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( string @ X3 @ X1 )
& ( entry_box @ Y0 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( do @ X2 @ Y1 @ Y3 @ Y2 )
=> ( in @ X3 @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( string @ Y0 @ X1 )
& ( entry_box @ Y1 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( do @ X2 @ Y2 @ Y4 @ Y3 )
=> ( in @ Y0 @ Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) )
@ X3 )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( string @ Y0 @ X1 )
& ( entry_box @ Y1 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( do @ X2 @ Y2 @ Y4 @ Y3 )
=> ( in @ Y0 @ Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: $i,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( string @ Y1 @ X1 )
& ( entry_box @ Y2 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ X1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y0 @ Y3 @ Y5 @ Y4 )
=> ( in @ Y1 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: mworld] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( string @ Y1 @ X1 )
& ( entry_box @ Y2 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ X1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y0 @ Y3 @ Y5 @ Y4 )
=> ( in @ Y1 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( string @ Y1 @ X1 )
& ( entry_box @ Y2 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ X1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y0 @ Y3 @ Y5 @ Y4 )
=> ( in @ Y1 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( string @ Y2 @ Y0 )
& ( entry_box @ Y3 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( do @ Y1 @ Y4 @ Y6 @ Y5 )
=> ( in @ Y2 @ Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( string @ Y2 @ Y0 )
& ( entry_box @ Y3 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( do @ Y1 @ Y4 @ Y6 @ Y5 )
=> ( in @ Y2 @ Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,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 > $o,Y5: mworld] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( string @ Y1 )
@ ( entry_box @ Y2 ) )
@ ( ^ [Y3: $i > mworld > $o,Y4: mworld] :
( ?? @ $i
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) )
@ ^ [Y3: $i] :
( ^ [Y4: mworld > $o,Y5: mworld] :
( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ ( ^ [Y4: $i > mworld > $o,Y5: mworld] :
( !! @ $i
@ ^ [Y6: $i] : ( Y4 @ Y6 @ Y5 ) )
@ ^ [Y4: $i] :
( ^ [Y5: mworld > $o,Y6: mworld > $o,Y7: mworld] :
( ( Y5 @ Y7 )
=> ( Y6 @ Y7 ) )
@ ( do @ Y0 @ Y3 @ Y4 )
@ ( in @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f58,f65,f54,f66,f66,f66,f64,f61,f55,f54,f66,f64]) ).
thf(f58,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] :
( mimplies @ ( mand @ ( string @ Y1 ) @ ( entry_box @ Y2 ) )
@ ( mexists_di
@ ^ [Y3: $i] :
( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y0 @ Y3 @ Y4 ) @ ( in @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] :
( mimplies @ ( mand @ ( string @ Y1 ) @ ( entry_box @ Y2 ) )
@ ( mexists_di
@ ^ [Y3: $i] :
( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y0 @ Y3 @ Y4 ) @ ( in @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] :
( mimplies @ ( mand @ ( string @ X1 ) @ ( entry_box @ X2 ) )
@ ( mexists_di
@ ^ [X3: $i] :
( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mimplies @ ( do @ X0 @ X3 @ X4 ) @ ( in @ X1 @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X8: $i] :
( mforall_di
@ ^ [X7: $i] :
( mforall_di
@ ^ [X3: $i] :
( mimplies @ ( mand @ ( string @ X7 ) @ ( entry_box @ X3 ) )
@ ( mexists_di
@ ^ [X1: $i] :
( mbox
@ ( mforall_di
@ ^ [X9: $i] : ( mimplies @ ( do @ X8 @ X1 @ X9 ) @ ( in @ X7 @ X3 @ X9 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',ax3) ).
thf(f141,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( mrel @ sK4 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
| ( ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
= $false )
| ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
= $false )
| ( ( ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
= $false )
| ( $true
= ( mrel @ sK4 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
= $false )
| ( $true
= ( mrel @ sK4 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f110,plain,
! [X1: mworld] :
( ( $true
= ( number @ sK3 @ one @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f200,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f199]) ).
thf(f199,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f192]) ).
thf(f192,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f184,f116]) ).
thf(f184,plain,
( ( ( mrel @ mactual @ sK4 )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f182]) ).
thf(f186,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f174,f179,f182]) ).
thf(f174,plain,
! [X0: $i,X1: $i] :
( ( ( mrel @ mactual @ sK4 )
= $false )
| ( ( entry_box @ X1 @ sK4 )
= $false )
| ( ( string @ X0 @ sK4 )
= $false )
| ( ( mrel @ sK4 @ ( sK6 @ X0 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f173]) ).
thf(f173,plain,
! [X0: $i,X1: $i] :
( ( ( string @ X0 @ sK4 )
= $false )
| ( ( mrel @ sK4 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $true = $false )
| ( ( entry_box @ X1 @ sK4 )
= $false )
| ( ( mrel @ mactual @ sK4 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f169]) ).
thf(f169,plain,
! [X0: $i,X1: $i] :
( ( ( entry_box @ X1 @ sK4 )
= $false )
| ( $true = $false )
| ( ( mrel @ sK4 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( ( mrel @ mactual @ sK4 )
= $false )
| ( ( string @ X0 @ sK4 )
= $false )
| ( ( mrel @ sK4 @ ( sK6 @ X0 @ X1 ) )
= $true ) ),
inference(superposition,[status(thm)],[f133,f163]) ).
thf(f163,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( ( mrel @ X2 @ ( sK5 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) )
= $false )
| ( ( mrel @ sK4 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( ( entry_box @ X1 @ X2 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( string @ X0 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f162]) ).
thf(f162,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( ( entry_box @ X1 @ X2 )
= $false )
| ( ( mrel @ sK4 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( ( mrel @ X2 @ ( sK5 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) )
= $false )
| ( $true = $false )
| ( ( string @ X0 @ X2 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f159]) ).
thf(f159,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( ( mrel @ sK4 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $true = $false )
| ( ( mrel @ sK4 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( ( mrel @ X2 @ ( sK5 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) )
= $false )
| ( ( string @ X0 @ X2 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( entry_box @ X1 @ X2 )
= $false ) ),
inference(superposition,[status(thm)],[f136,f153]) ).
thf(f153,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ X1 @ X3 @ ( sK7 @ X4 @ X5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) )
= $true )
| ( ( mrel @ X2 @ ( sK5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) )
= $false )
| ( ( entry_box @ X3 @ X2 )
= $false )
| ( ( mrel @ sK4 @ ( sK6 @ X4 @ X5 ) )
= $true )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( ( string @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( mrel @ X2 @ ( sK5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) )
= $false )
| ( ( string @ X1 @ X2 )
= $false )
| ( ( mrel @ sK4 @ ( sK6 @ X4 @ X5 ) )
= $true )
| ( ( entry_box @ X3 @ X2 )
= $false )
| ( ( mrel @ mactual @ X2 )
= $false )
| ( $true = $false )
| ( ( in @ X1 @ X3 @ ( sK7 @ X4 @ X5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) )
= $true ) ),
inference(superposition,[status(thm)],[f137,f103]) ).
thf(f137,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( do @ X4 @ X3 @ ( sK7 @ X1 @ X2 @ X3 @ X4 ) @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
= $true )
| ( $true
= ( mrel @ sK4 @ ( sK6 @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( do @ X4 @ X3 @ ( sK7 @ X1 @ X2 @ X3 @ X4 ) @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ ( sK7 @ X1 @ X2 @ X3 @ X4 ) @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) )
= $false )
| ( $true
= ( mrel @ sK4 @ ( sK6 @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f134]) ).
thf(f134,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) )
@ ( sK7 @ X1 @ X2 @ X3 @ X4 ) )
= $false )
| ( $true
= ( mrel @ sK4 @ ( sK6 @ X1 @ X2 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) ) )
= $false )
| ( $true
= ( mrel @ sK4 @ ( sK6 @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( mrel @ sK4 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) ) ) )
= $false )
| ( $true
= ( mrel @ sK4 @ ( sK6 @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f129]) ).
thf(f136,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X2 @ ( sK7 @ X1 @ X2 @ X3 @ X4 ) @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $true
= ( mrel @ sK4 @ ( sK6 @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f133,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( mrel @ sK4 @ ( sK5 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $true
= ( mrel @ sK4 @ ( sK6 @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.24 % Problem : NLP266^4 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.25 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.52 % Computer : n001.cluster.edu
% 0.16/0.52 % Model : x86_64 x86_64
% 0.16/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.52 % Memory : 8042.1875MB
% 0.16/0.52 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.52 % CPULimit : 300
% 0.16/0.52 % WCLimit : 300
% 0.16/0.52 % DateTime : Tue Feb 24 10:55:07 EST 2026
% 0.16/0.52 % CPUTime :
% 0.16/0.52 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.81 ---- Original DTF file ---
% 0.21/0.81 thf(spec,logic,$$dhol).
% 0.21/0.81 %------------------------------------------------------------------------------
% 0.21/0.81 % File : NLP266^4 : TPTP v9.2.1. Released v8.1.0.
% 0.21/0.81 % Domain : Natural Language Processing
% 0.21/0.81 % Problem : Generation of abstract instructions: enter a number in a box
% 0.21/0.81 % Version : [BP13] axioms.
% 0.21/0.81 % English :
% 0.21/0.81
% 0.21/0.81 % Refs : [Sto00] Stone (2000), Towards a Computational Account of Knowl
% 0.21/0.81 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.21/0.81 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.21/0.81 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.21/0.81 % Source : [TPTP]
% 0.21/0.81 % Names : APM003+1 [QMLTP]
% 0.21/0.81
% 0.21/0.81 % Status : Theorem
% 0.21/0.81 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0
% 0.21/0.81 % Syntax : Number of formulae : 37 ( 11 unt; 21 typ; 10 def)
% 0.21/0.81 % Number of atoms : 72 ( 10 equ; 0 cnn)
% 0.21/0.81 % Maximal formula atoms : 18 ( 4 avg)
% 0.21/0.81 % Number of connectives : 104 ( 1 ~; 1 |; 3 &; 95 @)
% 0.21/0.81 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.21/0.81 % Maximal formula depth : 20 ( 5 avg)
% 0.21/0.81 % Number of types : 3 ( 1 usr)
% 0.21/0.81 % Number of type conns : 75 ( 75 >; 0 *; 0 +; 0 <<)
% 0.21/0.81 % Number of symbols : 21 ( 20 usr; 3 con; 0-4 aty)
% 0.21/0.81 % Number of variables : 43 ( 35 ^; 6 !; 2 ?; 43 :)
% 0.21/0.81 % SPC : TH0_THM_EQU_NAR
% 0.21/0.81
% 0.21/0.81 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.21/0.81 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.21/0.81 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.21/0.81 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.21/0.81 % $modalities == $modal_system_S4].
% 0.21/0.81 %------------------------------------------------------------------------------
% 0.21/0.81 thf(mworld,type,
% 0.21/0.81 mworld: $tType ).
% 0.21/0.81
% 0.21/0.81 thf(mrel_type,type,
% 0.21/0.81 mrel: mworld > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(mactual_type,type,
% 0.21/0.81 mactual: mworld ).
% 0.21/0.81
% 0.21/0.81 thf(mlocal_type,type,
% 0.21/0.81 mlocal: ( mworld > $o ) > $o ).
% 0.21/0.81
% 0.21/0.81 thf(mlocal_def,definition,
% 0.21/0.81 ( mlocal
% 0.21/0.81 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(mnot_type,type,
% 0.21/0.81 mnot: ( mworld > $o ) > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(mand_type,type,
% 0.21/0.81 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(mor_type,type,
% 0.21/0.81 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(mimplies_type,type,
% 0.21/0.81 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(mequiv_type,type,
% 0.21/0.81 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(mnot_def,definition,
% 0.21/0.81 ( mnot
% 0.21/0.81 = ( ^ [A: mworld > $o,W: mworld] :
% 0.21/0.81 ~ ( A @ W ) ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(mand_def,definition,
% 0.21/0.81 ( mand
% 0.21/0.81 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.21/0.81 ( ( A @ W )
% 0.21/0.81 & ( B @ W ) ) ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(mor_def,definition,
% 0.21/0.81 ( mor
% 0.21/0.81 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.21/0.81 ( ( A @ W )
% 0.21/0.81 | ( B @ W ) ) ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(mimplies_def,definition,
% 0.21/0.81 ( mimplies
% 0.21/0.81 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.21/0.81 ( ( A @ W )
% 0.21/0.81 => ( B @ W ) ) ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(mequiv_def,definition,
% 0.21/0.81 ( mequiv
% 0.21/0.81 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.21/0.81 ( ( A @ W )
% 0.21/0.81 <=> ( B @ W ) ) ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(mbox_type,type,
% 0.21/0.81 mbox: ( mworld > $o ) > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(mbox_def,definition,
% 0.21/0.81 ( mbox
% 0.21/0.81 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.21/0.81 ! [V: mworld] :
% 0.21/0.81 ( ( mrel @ W @ V )
% 0.21/0.81 => ( Phi @ V ) ) ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(mdia_type,type,
% 0.21/0.81 mdia: ( mworld > $o ) > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(mdia_def,definition,
% 0.21/0.81 ( mdia
% 0.21/0.81 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.21/0.81 ? [V: mworld] :
% 0.21/0.81 ( ( mrel @ W @ V )
% 0.21/0.81 & ( Phi @ V ) ) ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(mrel_reflexive,axiom,
% 0.21/0.81 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.21/0.81
% 0.21/0.81 thf(mrel_transitive,axiom,
% 0.21/0.81 ! [W: mworld,V: mworld,U: mworld] :
% 0.21/0.81 ( ( ( mrel @ W @ V )
% 0.21/0.81 & ( mrel @ V @ U ) )
% 0.21/0.81 => ( mrel @ W @ U ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(mforall_di_type,type,
% 0.21/0.81 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(mforall_di_def,definition,
% 0.21/0.81 ( mforall_di
% 0.21/0.81 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.21/0.81 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(mexists_di_type,type,
% 0.21/0.81 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(mexists_di_def,definition,
% 0.21/0.81 ( mexists_di
% 0.21/0.81 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.21/0.81 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(u_decl,type,
% 0.21/0.81 u: $i ).
% 0.21/0.81
% 0.21/0.81 thf(one_decl,type,
% 0.21/0.81 one: $i ).
% 0.21/0.81
% 0.21/0.81 thf(number_decl,type,
% 0.21/0.81 number: $i > $i > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(string_decl,type,
% 0.21/0.81 string: $i > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(in_decl,type,
% 0.21/0.81 in: $i > $i > $i > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(do_decl,type,
% 0.21/0.81 do: $i > $i > $i > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(entry_box_decl,type,
% 0.21/0.81 entry_box: $i > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(userid_decl,type,
% 0.21/0.81 userid: $i > $i > mworld > $o ).
% 0.21/0.81
% 0.21/0.81 thf(ax1,axiom,
% 0.21/0.81 ( mlocal
% 0.21/0.81 @ ( mbox
% 0.21/0.81 @ ( mexists_di
% 0.21/0.81 @ ^ [I: $i] : ( mbox @ ( mand @ ( userid @ u @ I ) @ ( string @ I ) ) ) ) ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(ax2,axiom,
% 0.21/0.81 ( mlocal
% 0.21/0.81 @ ( mexists_di
% 0.21/0.81 @ ^ [B: $i] : ( mbox @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(ax3,axiom,
% 0.21/0.81 ( mlocal
% 0.21/0.81 @ ( mbox
% 0.21/0.81 @ ( mforall_di
% 0.21/0.81 @ ^ [S: $i] :
% 0.21/0.81 ( mforall_di
% 0.21/0.81 @ ^ [I: $i] :
% 0.21/0.81 ( mforall_di
% 0.21/0.81 @ ^ [B: $i] :
% 0.21/0.81 ( mimplies @ ( mand @ ( string @ I ) @ ( entry_box @ B ) )
% 0.21/0.81 @ ( mexists_di
% 0.21/0.81 @ ^ [A: $i] :
% 0.21/0.81 ( mbox
% 0.21/0.81 @ ( mforall_di
% 0.21/0.81 @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.81
% 0.21/0.81 thf(con,conjecture,
% 0.21/0.81 ( mlocal
% 0.21/0.81 @ ( mbox
% 0.21/0.81 @ ( mexists_di
% 0.21/0.81 @ ^ [I: $i] :
% 0.21/0.81 ( mexists_di
% 0.21/0.81 @ ^ [B: $i] :
% 0.21/0.81 ( mexists_di
% 0.21/0.81 @ ^ [A: $i] :
% 0.21/0.81 ( mexists_di
% 0.21/0.81 @ ^ [S: $i] :
% 0.21/0.81 ( mand @ ( mbox @ ( mand @ ( userid @ u @ I ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
% 0.21/0.81 @ ( mbox
% 0.21/0.81 @ ( mforall_di
% 0.21/0.81 @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.82
% 0.21/0.82 %------------------------------------------------------------------------------
% 0.21/0.82 ------------------------
% 1.66/1.98 ---- Embedded in THF ---
% 1.66/1.99 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.99 %%% Generated on Tue Feb 24 10:55:08 EST 2026
% 1.66/1.99 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.99 %%% Logic specification used:
% 1.66/1.99 %%% thf(spec, logic, $$dhol).
% 1.66/1.99
% 1.66/1.99 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2DTF4164.p
% See solution above
% 1.66/1.99 ------------------------
% 1.66/2.00 ---- Cleaned THF ---
% 1.66/2.00 thf(mworld,type,
% 1.66/2.00 mworld: $tType ).
% 1.66/2.00
% 1.66/2.00 thf(mrel_type,type,
% 1.66/2.00 mrel: mworld > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(mactual_type,type,
% 1.66/2.00 mactual: mworld ).
% 1.66/2.00
% 1.66/2.00 thf(mlocal_type,type,
% 1.66/2.00 mlocal: ( mworld > $o ) > $o ).
% 1.66/2.00
% 1.66/2.00 thf(mlocal_def,definition,
% 1.66/2.00 ( mlocal
% 1.66/2.00 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(mnot_type,type,
% 1.66/2.00 mnot: ( mworld > $o ) > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(mand_type,type,
% 1.66/2.00 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(mor_type,type,
% 1.66/2.00 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(mimplies_type,type,
% 1.66/2.00 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(mequiv_type,type,
% 1.66/2.00 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(mnot_def,definition,
% 1.66/2.00 ( mnot
% 1.66/2.00 = ( ^ [A: mworld > $o,W: mworld] :
% 1.66/2.00 ~ ( A @ W ) ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(mand_def,definition,
% 1.66/2.00 ( mand
% 1.66/2.00 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.66/2.00 ( ( A @ W )
% 1.66/2.00 & ( B @ W ) ) ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(mor_def,definition,
% 1.66/2.00 ( mor
% 1.66/2.00 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.66/2.00 ( ( A @ W )
% 1.66/2.00 | ( B @ W ) ) ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(mimplies_def,definition,
% 1.66/2.00 ( mimplies
% 1.66/2.00 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.66/2.00 ( ( A @ W )
% 1.66/2.00 => ( B @ W ) ) ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(mequiv_def,definition,
% 1.66/2.00 ( mequiv
% 1.66/2.00 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.66/2.00 ( ( A @ W )
% 1.66/2.00 <=> ( B @ W ) ) ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(mbox_type,type,
% 1.66/2.00 mbox: ( mworld > $o ) > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(mbox_def,definition,
% 1.66/2.00 ( mbox
% 1.66/2.00 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.66/2.00 ! [V: mworld] :
% 1.66/2.00 ( ( mrel @ W @ V )
% 1.66/2.00 => ( Phi @ V ) ) ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(mdia_type,type,
% 1.66/2.00 mdia: ( mworld > $o ) > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(mdia_def,definition,
% 1.66/2.00 ( mdia
% 1.66/2.00 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.66/2.00 ? [V: mworld] :
% 1.66/2.00 ( ( mrel @ W @ V )
% 1.66/2.00 & ( Phi @ V ) ) ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(mrel_reflexive,axiom,
% 1.66/2.00 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.66/2.00
% 1.66/2.00 thf(mrel_transitive,axiom,
% 1.66/2.00 ! [W: mworld,V: mworld,U: mworld] :
% 1.66/2.00 ( ( ( mrel @ W @ V )
% 1.66/2.00 & ( mrel @ V @ U ) )
% 1.66/2.00 => ( mrel @ W @ U ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(mforall_di_type,type,
% 1.66/2.00 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(mforall_di_def,definition,
% 1.66/2.00 ( mforall_di
% 1.66/2.00 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.66/2.00 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(mexists_di_type,type,
% 1.66/2.00 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(mexists_di_def,definition,
% 1.66/2.00 ( mexists_di
% 1.66/2.00 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.66/2.00 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(u_decl,type,
% 1.66/2.00 u: $i ).
% 1.66/2.00
% 1.66/2.00 thf(one_decl,type,
% 1.66/2.00 one: $i ).
% 1.66/2.00
% 1.66/2.00 thf(number_decl,type,
% 1.66/2.00 number: $i > $i > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(string_decl,type,
% 1.66/2.00 string: $i > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(in_decl,type,
% 1.66/2.00 in: $i > $i > $i > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(do_decl,type,
% 1.66/2.00 do: $i > $i > $i > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(entry_box_decl,type,
% 1.66/2.00 entry_box: $i > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(userid_decl,type,
% 1.66/2.00 userid: $i > $i > mworld > $o ).
% 1.66/2.00
% 1.66/2.00 thf(ax1,axiom,
% 1.66/2.00 ( mlocal
% 1.66/2.00 @ ( mbox
% 1.66/2.00 @ ( mexists_di
% 1.66/2.00 @ ^ [I: $i] : ( mbox @ ( mand @ ( userid @ u @ I ) @ ( string @ I ) ) ) ) ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(ax2,axiom,
% 1.66/2.00 ( mlocal
% 1.66/2.00 @ ( mexists_di
% 1.66/2.00 @ ^ [B: $i] : ( mbox @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(ax3,axiom,
% 1.66/2.00 ( mlocal
% 1.66/2.00 @ ( mbox
% 1.66/2.00 @ ( mforall_di
% 1.66/2.00 @ ^ [S: $i] :
% 1.66/2.00 ( mforall_di
% 1.66/2.00 @ ^ [I: $i] :
% 1.66/2.00 ( mforall_di
% 1.66/2.00 @ ^ [B: $i] :
% 1.66/2.00 ( mimplies @ ( mand @ ( string @ I ) @ ( entry_box @ B ) )
% 1.66/2.00 @ ( mexists_di
% 1.66/2.00 @ ^ [A: $i] :
% 1.66/2.00 ( mbox
% 1.66/2.00 @ ( mforall_di
% 1.66/2.00 @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ).
% 1.66/2.00
% 1.66/2.00 thf(con,conjecture,
% 1.66/2.00 ( mlocal
% 1.66/2.00 @ ( mbox
% 1.66/2.00 @ ( mexists_di
% 1.66/2.00 @ ^ [I: $i] :
% 1.66/2.00 ( mexists_di
% 1.66/2.00 @ ^ [B: $i] :
% 1.66/2.00 ( mexists_di
% 1.66/2.00 @ ^ [A: $i] :
% 1.66/2.00 ( mexists_di
% 1.66/2.00 @ ^ [S: $i] :
% 1.66/2.00 ( mand @ ( mbox @ ( mand @ ( userid @ u @ I ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
% 1.66/2.00 @ ( mbox
% 1.66/2.00 @ ( mforall_di
% 1.66/2.00 @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ).
% 1.66/2.00 ------------------------
% 1.66/2.01 % (4480)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4164 for (2999ds/18Mi)
% 1.87/2.02 % (4480)Instruction limit reached!
% 1.87/2.02 % (4480)------------------------------
% 1.87/2.02 % (4480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.02 % (4480)Termination reason: Unknown
% 1.87/2.02 % (4480)Termination phase: Saturation
% 1.87/2.02
% 1.87/2.02 % (4480)Memory used [KB]: 5628
% 1.87/2.02 % (4480)Time elapsed: 0.007 s
% 1.87/2.02 % (4480)Instructions burned: 20 (million)
% 1.87/2.02 % (4480)------------------------------
% 1.87/2.02 % (4480)------------------------------
% 1.87/2.02 % (4474)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4164 for (2999ds/183Mi)
% 1.87/2.02 % (4475)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_4164 for (2999ds/4Mi)
% 1.87/2.02 % (4476)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_4164 for (2999ds/27Mi)
% 1.87/2.02 % (4477)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4164 for (2999ds/2Mi)
% 1.87/2.02 % (4478)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_4164 for (2999ds/2Mi)
% 1.87/2.02 % (4479)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_4164 for (2999ds/275Mi)
% 1.87/2.02 % (4477)Instruction limit reached!
% 1.87/2.02 % (4477)------------------------------
% 1.87/2.02 % (4477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.02 % (4477)Termination reason: Unknown
% 1.87/2.02 % (4477)Termination phase: shuffling
% 1.87/2.02
% 1.87/2.02 % (4477)Memory used [KB]: 1023
% 1.87/2.02 % (4477)Time elapsed: 0.003 s
% 1.87/2.02 % (4477)Instructions burned: 2 (million)
% 1.87/2.02 % (4477)------------------------------
% 1.87/2.02 % (4477)------------------------------
% 1.87/2.02 % (4478)Instruction limit reached!
% 1.87/2.02 % (4478)------------------------------
% 1.87/2.02 % (4478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.02 % (4478)Termination reason: Unknown
% 1.87/2.02 % (4478)Termination phase: shuffling
% 1.87/2.02
% 1.87/2.02 % (4478)Memory used [KB]: 1023
% 1.87/2.02 % (4478)Time elapsed: 0.003 s
% 1.87/2.02 % (4478)Instructions burned: 2 (million)
% 1.87/2.02 % (4478)------------------------------
% 1.87/2.02 % (4478)------------------------------
% 1.87/2.02 % (4475)Instruction limit reached!
% 1.87/2.02 % (4475)------------------------------
% 1.87/2.02 % (4475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.02 % (4475)Termination reason: Unknown
% 1.87/2.02 % (4475)Termination phase: Preprocessing 1
% 1.87/2.02
% 1.87/2.02 % (4475)Memory used [KB]: 1023
% 1.87/2.02 % (4475)Time elapsed: 0.004 s
% 1.87/2.02 % (4475)Instructions burned: 4 (million)
% 1.87/2.02 % (4475)------------------------------
% 1.87/2.02 % (4475)------------------------------
% 1.87/2.02 % (4479)Refutation not found, incomplete strategy
% 1.87/2.02 % (4479)------------------------------
% 1.87/2.02 % (4479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.02 % (4479)Termination reason: Refutation not found, incomplete strategy
% 1.87/2.02
% 1.87/2.02
% 1.87/2.02 % (4479)Memory used [KB]: 5500
% 1.87/2.02 % (4479)Time elapsed: 0.005 s
% 1.87/2.02 % (4479)Instructions burned: 5 (million)
% 1.87/2.02 % (4479)------------------------------
% 1.87/2.02 % (4479)------------------------------
% 1.87/2.03 % (4481)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4164 for (2999ds/3Mi)
% 1.87/2.03 % (4481)Instruction limit reached!
% 1.87/2.03 % (4481)------------------------------
% 1.87/2.03 % (4481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.03 % (4481)Termination reason: Unknown
% 1.87/2.03 % (4481)Termination phase: Property scanning
% 1.87/2.03
% 1.87/2.03 % (4481)Memory used [KB]: 1023
% 1.87/2.03 % (4481)Time elapsed: 0.002 s
% 1.87/2.03 % (4481)Instructions burned: 4 (million)
% 1.87/2.03 % (4481)------------------------------
% 1.87/2.03 % (4481)------------------------------
% 1.87/2.04 % (4476)Instruction limit reached!
% 1.87/2.04 % (4476)------------------------------
% 1.87/2.04 % (4476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.04 % (4476)Termination reason: Unknown
% 1.87/2.04 % (4476)Termination phase: Saturation
% 1.87/2.04
% 1.87/2.04 % (4476)Memory used [KB]: 5756
% 1.87/2.04 % (4476)Time elapsed: 0.018 s
% 1.87/2.04 % (4476)Instructions burned: 28 (million)
% 1.87/2.04 % (4476)------------------------------
% 1.87/2.04 % (4476)------------------------------
% 1.87/2.04 % (4486)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4164 for (2999ds/7Mi)
% 1.87/2.04 % (4482)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_4164 for (2999ds/37Mi)
% 1.87/2.04 % (4483)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_4164 for (2999ds/15Mi)
% 1.87/2.04 % (4484)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_4164 for (2999ds/3Mi)
% 1.87/2.04 % (4486)Instruction limit reached!
% 1.87/2.04 % (4486)------------------------------
% 1.87/2.04 % (4486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.04 % (4486)Termination reason: Unknown
% 1.87/2.04 % (4486)Termination phase: Property scanning
% 1.87/2.04
% 1.87/2.04 % (4486)Memory used [KB]: 1023
% 1.87/2.04 % (4486)Time elapsed: 0.003 s
% 1.87/2.04 % (4486)Instructions burned: 7 (million)
% 1.87/2.04 % (4486)------------------------------
% 1.87/2.04 % (4486)------------------------------
% 1.87/2.04 % (4484)Instruction limit reached!
% 1.87/2.04 % (4484)------------------------------
% 1.87/2.04 % (4484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.04 % (4484)Termination reason: Unknown
% 1.87/2.04 % (4484)Termination phase: Property scanning
% 1.87/2.04
% 1.87/2.04 % (4484)Memory used [KB]: 1023
% 1.87/2.04 % (4484)Time elapsed: 0.004 s
% 1.87/2.04 % (4484)Instructions burned: 4 (million)
% 1.87/2.04 % (4484)------------------------------
% 1.87/2.04 % (4484)------------------------------
% 1.87/2.04 % (4485)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_4164 for (2999ds/1041Mi)
% 1.87/2.05 % (4483)Instruction limit reached!
% 1.87/2.05 % (4483)------------------------------
% 1.87/2.05 % (4483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.05 % (4483)Termination reason: Unknown
% 1.87/2.05 % (4483)Termination phase: Saturation
% 1.87/2.05
% 1.87/2.05 % (4483)Memory used [KB]: 5628
% 1.87/2.05 % (4483)Time elapsed: 0.010 s
% 1.87/2.05 % (4483)Instructions burned: 15 (million)
% 1.87/2.05 % (4483)------------------------------
% 1.87/2.05 % (4483)------------------------------
% 1.87/2.05 % (4488)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_4164 for (2999ds/3Mi)
% 1.87/2.05 % (4488)Instruction limit reached!
% 1.87/2.05 % (4488)------------------------------
% 1.87/2.05 % (4488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.05 % (4488)Termination reason: Unknown
% 1.87/2.05 % (4488)Termination phase: Property scanning
% 1.87/2.05
% 1.87/2.05 % (4488)Memory used [KB]: 1023
% 1.87/2.05 % (4488)Time elapsed: 0.002 s
% 1.87/2.05 % (4488)Instructions burned: 3 (million)
% 1.87/2.05 % (4488)------------------------------
% 1.87/2.05 % (4488)------------------------------
% 1.87/2.05 % (4487)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4164 for (2999ds/16Mi)
% 1.87/2.06 % (4489)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4164 for (2999ds/3Mi)
% 1.87/2.06 % (4491)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4164 for (2999ds/3Mi)
% 1.87/2.06 % (4482)Instruction limit reached!
% 1.87/2.06 % (4482)------------------------------
% 1.87/2.06 % (4482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.06 % (4482)Termination reason: Unknown
% 1.87/2.06 % (4482)Termination phase: Saturation
% 1.87/2.06
% 1.87/2.06 % (4482)Memory used [KB]: 5756
% 1.87/2.06 % (4482)Time elapsed: 0.023 s
% 1.87/2.06 % (4482)Instructions burned: 38 (million)
% 1.87/2.06 % (4482)------------------------------
% 1.87/2.06 % (4482)------------------------------
% 1.87/2.06 % (4491)Instruction limit reached!
% 1.87/2.06 % (4491)------------------------------
% 1.87/2.06 % (4491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.06 % (4491)Termination reason: Unknown
% 1.87/2.06 % (4491)Termination phase: Property scanning
% 1.87/2.06
% 1.87/2.06 % (4491)Memory used [KB]: 1023
% 1.87/2.06 % (4491)Time elapsed: 0.002 s
% 1.87/2.06 % (4491)Instructions burned: 4 (million)
% 1.87/2.06 % (4491)------------------------------
% 1.87/2.06 % (4491)------------------------------
% 1.87/2.06 % (4489)Instruction limit reached!
% 1.87/2.06 % (4489)------------------------------
% 1.87/2.06 % (4489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.06 % (4489)Termination reason: Unknown
% 1.87/2.06 % (4489)Termination phase: Property scanning
% 1.87/2.06
% 1.87/2.06 % (4489)Memory used [KB]: 1023
% 1.87/2.06 % (4489)Time elapsed: 0.004 s
% 1.87/2.06 % (4489)Instructions burned: 4 (million)
% 1.87/2.06 % (4489)------------------------------
% 1.87/2.06 % (4489)------------------------------
% 1.87/2.06 % (4474)First to succeed.
% 1.87/2.06 % (4487)Instruction limit reached!
% 1.87/2.06 % (4487)------------------------------
% 1.87/2.06 % (4487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.06 % (4487)Termination reason: Unknown
% 1.87/2.06 % (4487)Termination phase: Saturation
% 1.87/2.06
% 1.87/2.06 % (4487)Memory used [KB]: 5628
% 1.87/2.06 % (4487)Time elapsed: 0.011 s
% 1.87/2.06 % (4487)Instructions burned: 17 (million)
% 1.87/2.06 % (4487)------------------------------
% 1.87/2.06 % (4487)------------------------------
% 1.87/2.06 % (4490)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4164 for (2999ds/7Mi)
% 1.87/2.07 % (4474)Refutation found. Thanks to Tanya!
% 1.87/2.07 % SZS status Theorem for DTF2THF_4164
% 1.87/2.07 % SZS output start Proof for DTF2THF_4164
% 1.87/2.07 thf(type_def_5, type, mworld: $tType).
% 1.87/2.07 thf(func_def_0, type, mworld: $tType).
% 1.87/2.07 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.87/2.07 thf(func_def_2, type, mactual: mworld).
% 1.87/2.07 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.87/2.07 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.87/2.07 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.87/2.07 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.87/2.07 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.87/2.07 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.87/2.07 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.87/2.07 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.87/2.07 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.87/2.07 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.87/2.07 thf(func_def_16, type, number: $i > $i > mworld > $o).
% 1.87/2.07 thf(func_def_17, type, string: $i > mworld > $o).
% 1.87/2.07 thf(func_def_18, type, in: $i > $i > $i > mworld > $o).
% 1.87/2.07 thf(func_def_19, type, do: $i > $i > $i > mworld > $o).
% 1.87/2.07 thf(func_def_20, type, entry_box: $i > mworld > $o).
% 1.87/2.07 thf(func_def_21, type, userid: $i > $i > mworld > $o).
% 1.87/2.07 thf(func_def_38, type, sK1: mworld > $i).
% 1.87/2.07 thf(func_def_42, type, sK2: $i > mworld > $i > $i > $i).
% 1.87/2.07 thf(func_def_44, type, sK4: mworld).
% 1.87/2.07 thf(func_def_45, type, sK5: $i > $i > $i > $i > mworld).
% 1.87/2.07 thf(func_def_46, type, sK6: $i > $i > mworld).
% 1.87/2.07 thf(func_def_47, type, sK7: $i > $i > $i > $i > $i).
% 1.87/2.07 thf(func_def_48, type, sK8: $i > $i > $i > $i > $i).
% 1.87/2.07 thf(f393,plain,(
% 1.87/2.07 $false),
% 1.87/2.07 inference(avatar_sat_refutation,[status(thm)],[f186,f200,f295,f303,f327,f335,f345,f367,f391])).
% 1.87/2.07 thf(f391,plain,(
% 1.87/2.07 ~spl0_1 | spl0_5 | spl0_7 | ~spl0_8),
% 1.87/2.07 inference(avatar_contradiction_clause,[status(thm)],[f390])).
% 1.87/2.07 thf(f390,plain,(
% 1.87/2.07 $false | (~spl0_1 | spl0_5 | spl0_7 | ~spl0_8)),
% 1.87/2.07 inference(subsumption_resolution,[status(thm)],[f389,f292])).
% 1.87/2.07 thf(f292,plain,(
% 1.87/2.07 ((entry_box @ sK3 @ sK4) != $false) | spl0_5),
% 1.87/2.07 inference(avatar_component_clause,[status(thm)],[f291])).
% 1.87/2.07 thf(f291,definition,(
% 1.87/2.07 spl0_5 <=> ((entry_box @ sK3 @ sK4) = $false)),
% 1.87/2.07 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.87/2.07 thf(f389,plain,(
% 1.87/2.07 ((entry_box @ sK3 @ sK4) = $false) | (~spl0_1 | spl0_7 | ~spl0_8)),
% 1.87/2.07 inference(subsumption_resolution,[status(thm)],[f388,f116])).
% 1.87/2.07 thf(f116,plain,(
% 1.87/2.07 ((mrel @ mactual @ sK4) = $true)),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f114])).
% 1.87/2.07 thf(f114,plain,(
% 1.87/2.07 (((mrel @ mactual @ sK4) => (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK4 @ Y4) => ((userid @ u @ Y0 @ Y4) & ((entry_box @ Y1 @ Y4) & (number @ Y1 @ one @ Y4)))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK4 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((do @ Y3 @ Y2 @ Y5 @ Y4) => (in @ Y0 @ Y1 @ Y5 @ Y4))))))))))))))))) = $false)),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f113])).
% 1.87/2.07 thf(f113,plain,(
% 1.87/2.07 (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => ((userid @ u @ Y1 @ Y5) & ((entry_box @ Y2 @ Y5) & (number @ Y2 @ one @ Y5)))))) & (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (!! @ $i @ (^[Y6 : $i]: ((do @ Y4 @ Y3 @ Y6 @ Y5) => (in @ Y1 @ Y2 @ Y6 @ Y5)))))))))))))))))) @ sK4) = $false)),
% 1.87/2.07 inference(sigma_clausification,[status(thm)],[f112])).
% 1.87/2.07 thf(f112,plain,(
% 1.87/2.07 ($true != (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => ((userid @ u @ Y1 @ Y5) & ((entry_box @ Y2 @ Y5) & (number @ Y2 @ one @ Y5)))))) & (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (!! @ $i @ (^[Y6 : $i]: ((do @ Y4 @ Y3 @ Y6 @ Y5) => (in @ Y1 @ Y2 @ Y6 @ Y5))))))))))))))))))))),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.87/2.07 thf(f71,plain,(
% 1.87/2.07 ($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 : $i > mworld > $o]: ((^[Y4 : mworld]: (?? @ $i @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))) @ (^[Y3 : $i]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld]: ((Y4 @ Y6) & (Y5 @ Y6))))))) @ ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ ((^[Y4 : mworld > $o]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld]: ((Y4 @ Y6) & (Y5 @ Y6))))))) @ (userid @ u @ Y0) @ ((^[Y4 : mworld > $o]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld]: ((Y4 @ Y6) & (Y5 @ Y6))))))) @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ ((^[Y4 : $i > mworld > $o]: ((^[Y5 : mworld]: (!! @ $i @ (^[Y6 : $i]: (Y4 @ Y6 @ Y5)))))) @ (^[Y4 : $i]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld > $o]: ((^[Y7 : mworld]: ((Y5 @ Y7) => (Y6 @ Y7))))))) @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))))),
% 1.87/2.07 inference(definition_unfolding,[status(thm)],[f60,f65,f54,f55,f55,f55,f55,f61,f54,f61,f61,f54,f66,f64])).
% 1.87/2.07 thf(f64,plain,(
% 1.87/2.07 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.87/2.07 inference(cnf_transformation,[status(thm)],[f33])).
% 1.87/2.07 thf(f33,plain,(
% 1.87/2.07 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.87/2.07 inference(fool_elimination,[status(thm)],[f32])).
% 1.87/2.07 thf(f32,plain,(
% 1.87/2.07 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 1.87/2.07 inference(rectify,[status(thm)],[f5])).
% 1.87/2.07 thf(f5,axiom,(
% 1.87/2.07 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 1.87/2.07 file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',mimplies_def)).
% 1.87/2.07 thf(f66,plain,(
% 1.87/2.07 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.87/2.07 inference(cnf_transformation,[status(thm)],[f22])).
% 1.87/2.07 thf(f22,plain,(
% 1.87/2.07 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.87/2.07 inference(fool_elimination,[status(thm)],[f21])).
% 1.87/2.07 thf(f21,plain,(
% 1.87/2.07 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))))),
% 1.87/2.07 inference(rectify,[status(thm)],[f11])).
% 1.87/2.07 thf(f11,axiom,(
% 1.87/2.07 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X6 : $i] : (X1 @ X6 @ X2))))),
% 1.87/2.07 file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',mforall_di_def)).
% 1.87/2.07 thf(f61,plain,(
% 1.87/2.07 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.87/2.07 inference(cnf_transformation,[status(thm)],[f47])).
% 1.87/2.07 thf(f47,plain,(
% 1.87/2.07 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.87/2.07 inference(fool_elimination,[status(thm)],[f46])).
% 1.87/2.07 thf(f46,plain,(
% 1.87/2.07 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))) = mand)),
% 1.87/2.07 inference(rectify,[status(thm)],[f3])).
% 1.87/2.07 thf(f3,axiom,(
% 1.87/2.07 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))) = mand)),
% 1.87/2.07 file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',mand_def)).
% 1.87/2.07 thf(f55,plain,(
% 1.87/2.07 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.87/2.07 inference(cnf_transformation,[status(thm)],[f35])).
% 1.87/2.07 thf(f35,plain,(
% 1.87/2.07 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.87/2.07 inference(fool_elimination,[status(thm)],[f34])).
% 1.87/2.07 thf(f34,plain,(
% 1.87/2.07 ((^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : (X0 @ X2 @ X1))) = mexists_di)),
% 1.87/2.07 inference(rectify,[status(thm)],[f12])).
% 1.87/2.07 thf(f12,axiom,(
% 1.87/2.07 ((^[X1 : $i > mworld > $o, X2 : mworld] : (? [X6 : $i] : (X1 @ X6 @ X2))) = mexists_di)),
% 1.87/2.07 file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',mexists_di_def)).
% 1.87/2.07 thf(f54,plain,(
% 1.87/2.07 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.87/2.07 inference(cnf_transformation,[status(thm)],[f24])).
% 1.87/2.07 thf(f24,plain,(
% 1.87/2.07 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.87/2.07 inference(fool_elimination,[status(thm)],[f23])).
% 1.87/2.07 thf(f23,plain,(
% 1.87/2.07 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 1.87/2.07 inference(rectify,[status(thm)],[f7])).
% 1.87/2.07 thf(f7,axiom,(
% 1.87/2.07 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 1.87/2.07 file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',mbox_def)).
% 1.87/2.07 thf(f65,plain,(
% 1.87/2.07 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.87/2.07 inference(cnf_transformation,[status(thm)],[f27])).
% 1.87/2.07 thf(f27,plain,(
% 1.87/2.07 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.87/2.07 inference(fool_elimination,[status(thm)],[f1])).
% 1.87/2.07 thf(f1,axiom,(
% 1.87/2.07 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.87/2.07 file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',mlocal_def)).
% 1.87/2.07 thf(f60,plain,(
% 1.87/2.07 ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mexists_di @ (^[Y2 : $i]: (mexists_di @ (^[Y3 : $i]: (mand @ (mbox @ (mand @ (userid @ u @ Y0) @ (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ (mbox @ (mforall_di @ (^[Y4 : $i]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))) != $true)),
% 1.87/2.07 inference(cnf_transformation,[status(thm)],[f50])).
% 1.87/2.07 thf(f50,plain,(
% 1.87/2.07 ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mexists_di @ (^[Y2 : $i]: (mexists_di @ (^[Y3 : $i]: (mand @ (mbox @ (mand @ (userid @ u @ Y0) @ (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ (mbox @ (mforall_di @ (^[Y4 : $i]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))) != $true)),
% 1.87/2.07 inference(flattening,[status(thm)],[f45])).
% 1.87/2.07 thf(f45,plain,(
% 1.87/2.07 ~((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mexists_di @ (^[Y2 : $i]: (mexists_di @ (^[Y3 : $i]: (mand @ (mbox @ (mand @ (userid @ u @ Y0) @ (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ (mbox @ (mforall_di @ (^[Y4 : $i]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))) = $true)),
% 1.87/2.07 inference(fool_elimination,[status(thm)],[f44])).
% 1.87/2.07 thf(f44,plain,(
% 1.87/2.07 ~(mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : (mexists_di @ (^[X1 : $i] : (mexists_di @ (^[X2 : $i] : (mexists_di @ (^[X3 : $i] : (mand @ (mbox @ (mand @ (userid @ u @ X0) @ (mand @ (entry_box @ X1) @ (number @ X1 @ one)))) @ (mbox @ (mforall_di @ (^[X4 : $i] : (mimplies @ (do @ X3 @ X2 @ X4) @ (in @ X0 @ X1 @ X4))))))))))))))))),
% 1.87/2.07 inference(rectify,[status(thm)],[f17])).
% 1.87/2.07 thf(f17,negated_conjecture,(
% 1.87/2.07 ~(mlocal @ (mbox @ (mexists_di @ (^[X7 : $i] : (mexists_di @ (^[X3 : $i] : (mexists_di @ (^[X1 : $i] : (mexists_di @ (^[X8 : $i] : (mand @ (mbox @ (mand @ (userid @ u @ X7) @ (mand @ (entry_box @ X3) @ (number @ X3 @ one)))) @ (mbox @ (mforall_di @ (^[X9 : $i] : (mimplies @ (do @ X8 @ X1 @ X9) @ (in @ X7 @ X3 @ X9))))))))))))))))),
% 1.87/2.07 inference(negated_conjecture,[status(cth)],[f16])).
% 1.87/2.07 thf(f16,conjecture,(
% 1.87/2.07 (mlocal @ (mbox @ (mexists_di @ (^[X7 : $i] : (mexists_di @ (^[X3 : $i] : (mexists_di @ (^[X1 : $i] : (mexists_di @ (^[X8 : $i] : (mand @ (mbox @ (mand @ (userid @ u @ X7) @ (mand @ (entry_box @ X3) @ (number @ X3 @ one)))) @ (mbox @ (mforall_di @ (^[X9 : $i] : (mimplies @ (do @ X8 @ X1 @ X9) @ (in @ X7 @ X3 @ X9))))))))))))))))),
% 1.87/2.07 file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',con)).
% 1.87/2.07 thf(f388,plain,(
% 1.87/2.07 ((mrel @ mactual @ sK4) != $true) | ((entry_box @ sK3 @ sK4) = $false) | (~spl0_1 | spl0_7 | ~spl0_8)),
% 1.87/2.07 inference(subsumption_resolution,[status(thm)],[f381,f317])).
% 1.87/2.07 thf(f317,plain,(
% 1.87/2.07 ((string @ (sK1 @ mactual) @ sK4) != $false) | spl0_7),
% 1.87/2.07 inference(avatar_component_clause,[status(thm)],[f316])).
% 1.87/2.07 thf(f316,definition,(
% 1.87/2.07 spl0_7 <=> ((string @ (sK1 @ mactual) @ sK4) = $false)),
% 1.87/2.07 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.87/2.07 thf(f381,plain,(
% 1.87/2.07 ((string @ (sK1 @ mactual) @ sK4) = $false) | ((entry_box @ sK3 @ sK4) = $false) | ((mrel @ mactual @ sK4) != $true) | (~spl0_1 | ~spl0_8)),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f379])).
% 1.87/2.07 thf(f379,plain,(
% 1.87/2.07 ((entry_box @ sK3 @ sK4) = $false) | ((mrel @ mactual @ sK4) != $true) | ($true != $true) | ((string @ (sK1 @ mactual) @ sK4) = $false) | (~spl0_1 | ~spl0_8)),
% 1.87/2.07 inference(superposition,[status(thm)],[f371,f180])).
% 1.87/2.07 thf(f180,plain,(
% 1.87/2.07 ( ! [X0 : $i,X1 : $i] : (((mrel @ sK4 @ (sK6 @ X0 @ X1)) = $true) | ((entry_box @ X1 @ sK4) = $false) | ((string @ X0 @ sK4) = $false)) ) | ~spl0_1),
% 1.87/2.07 inference(avatar_component_clause,[status(thm)],[f179])).
% 1.87/2.07 thf(f179,definition,(
% 1.87/2.07 spl0_1 <=> ! [X0 : $i,X1 : $i] : (((string @ X0 @ sK4) = $false) | ((mrel @ sK4 @ (sK6 @ X0 @ X1)) = $true) | ((entry_box @ X1 @ sK4) = $false))),
% 1.87/2.07 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.87/2.07 thf(f371,plain,(
% 1.87/2.07 ( ! [X0 : mworld] : (($true != (mrel @ X0 @ (sK6 @ (sK1 @ mactual) @ sK3))) | ($true != (mrel @ mactual @ X0))) ) | ~spl0_8),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f368])).
% 1.87/2.07 thf(f368,plain,(
% 1.87/2.07 ( ! [X0 : mworld] : (($true != (mrel @ mactual @ X0)) | ($true != (mrel @ X0 @ (sK6 @ (sK1 @ mactual) @ sK3))) | ($true = $false)) ) | ~spl0_8),
% 1.87/2.07 inference(superposition,[status(thm)],[f322,f63])).
% 1.87/2.07 thf(f63,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : (($true = (mrel @ X0 @ X2)) | ((mrel @ X1 @ X2) != $true) | ($true != (mrel @ X0 @ X1))) )),
% 1.87/2.07 inference(cnf_transformation,[status(thm)],[f52])).
% 1.87/2.07 thf(f52,plain,(
% 1.87/2.07 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X1 @ X2) != $true) | ($true != (mrel @ X0 @ X1)) | ($true = (mrel @ X0 @ X2)))),
% 1.87/2.07 inference(flattening,[status(thm)],[f51])).
% 1.87/2.07 thf(f51,plain,(
% 1.87/2.07 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (($true = (mrel @ X0 @ X2)) | (($true != (mrel @ X0 @ X1)) | ((mrel @ X1 @ X2) != $true)))),
% 1.87/2.07 inference(ennf_transformation,[status(thm)],[f41])).
% 1.87/2.07 thf(f41,plain,(
% 1.87/2.07 ! [X0 : mworld,X1 : mworld,X2 : mworld] : ((($true = (mrel @ X0 @ X1)) & ((mrel @ X1 @ X2) = $true)) => ($true = (mrel @ X0 @ X2)))),
% 1.87/2.07 inference(fool_elimination,[status(thm)],[f40])).
% 1.87/2.07 thf(f40,plain,(
% 1.87/2.07 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X1 @ X2) & (mrel @ X0 @ X1)) => (mrel @ X0 @ X2))),
% 1.87/2.07 inference(rectify,[status(thm)],[f10])).
% 1.87/2.07 thf(f10,axiom,(
% 1.87/2.07 ! [X2 : mworld,X4 : mworld,X5 : mworld] : (((mrel @ X4 @ X5) & (mrel @ X2 @ X4)) => (mrel @ X2 @ X5))),
% 1.87/2.07 file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',mrel_transitive)).
% 1.87/2.07 thf(f322,plain,(
% 1.87/2.07 ((mrel @ mactual @ (sK6 @ (sK1 @ mactual) @ sK3)) = $false) | ~spl0_8),
% 1.87/2.07 inference(avatar_component_clause,[status(thm)],[f320])).
% 1.87/2.07 thf(f320,definition,(
% 1.87/2.07 spl0_8 <=> ((mrel @ mactual @ (sK6 @ (sK1 @ mactual) @ sK3)) = $false)),
% 1.87/2.07 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.87/2.07 thf(f367,plain,(
% 1.87/2.07 spl0_8 | ~spl0_9),
% 1.87/2.07 inference(avatar_split_clause,[status(thm)],[f364,f324,f320])).
% 1.87/2.07 thf(f324,definition,(
% 1.87/2.07 spl0_9 <=> ((entry_box @ sK3 @ (sK6 @ (sK1 @ mactual) @ sK3)) = $false)),
% 1.87/2.07 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.87/2.07 thf(f364,plain,(
% 1.87/2.07 ((mrel @ mactual @ (sK6 @ (sK1 @ mactual) @ sK3)) = $false) | ~spl0_9),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f363])).
% 1.87/2.07 thf(f363,plain,(
% 1.87/2.07 ((mrel @ mactual @ (sK6 @ (sK1 @ mactual) @ sK3)) = $false) | ($true = $false) | ~spl0_9),
% 1.87/2.07 inference(superposition,[status(thm)],[f111,f326])).
% 1.87/2.07 thf(f326,plain,(
% 1.87/2.07 ((entry_box @ sK3 @ (sK6 @ (sK1 @ mactual) @ sK3)) = $false) | ~spl0_9),
% 1.87/2.07 inference(avatar_component_clause,[status(thm)],[f324])).
% 1.87/2.07 thf(f111,plain,(
% 1.87/2.07 ( ! [X1 : mworld] : (($true = (entry_box @ sK3 @ X1)) | ((mrel @ mactual @ X1) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.87/2.07 thf(f109,plain,(
% 1.87/2.07 ( ! [X1 : mworld] : ((((entry_box @ sK3 @ X1) & (number @ sK3 @ one @ X1)) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f108])).
% 1.87/2.07 thf(f108,plain,(
% 1.87/2.07 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => ((entry_box @ sK3 @ X1) & (number @ sK3 @ one @ X1))))) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f107])).
% 1.87/2.07 thf(f107,plain,(
% 1.87/2.07 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((entry_box @ sK3 @ Y0) & (number @ sK3 @ one @ Y0)))) @ X1) = $true)) )),
% 1.87/2.07 inference(pi_clausification,[status(thm)],[f106])).
% 1.87/2.07 thf(f106,plain,(
% 1.87/2.07 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((entry_box @ sK3 @ Y0) & (number @ sK3 @ one @ Y0))))) = $true)),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f105])).
% 1.87/2.07 thf(f105,plain,(
% 1.87/2.07 ($true = ((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => ((entry_box @ Y0 @ Y1) & (number @ Y0 @ one @ Y1)))))) @ sK3))),
% 1.87/2.07 inference(sigma_clausification,[status(thm)],[f104])).
% 1.87/2.07 thf(f104,plain,(
% 1.87/2.07 ((?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => ((entry_box @ Y0 @ Y1) & (number @ Y0 @ one @ Y1))))))) = $true)),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.87/2.07 thf(f69,plain,(
% 1.87/2.07 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ ((^[Y1 : mworld > $o]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: ((Y1 @ Y3) & (Y2 @ Y3))))))) @ (entry_box @ Y0) @ (number @ Y0 @ one)))))))),
% 1.87/2.07 inference(definition_unfolding,[status(thm)],[f57,f65,f55,f54,f61])).
% 1.87/2.07 thf(f57,plain,(
% 1.87/2.07 ($true = (mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (entry_box @ Y0) @ (number @ Y0 @ one)))))))),
% 1.87/2.07 inference(cnf_transformation,[status(thm)],[f20])).
% 1.87/2.07 thf(f20,plain,(
% 1.87/2.07 ($true = (mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (entry_box @ Y0) @ (number @ Y0 @ one)))))))),
% 1.87/2.07 inference(fool_elimination,[status(thm)],[f19])).
% 1.87/2.07 thf(f19,plain,(
% 1.87/2.07 (mlocal @ (mexists_di @ (^[X0 : $i] : (mbox @ (mand @ (entry_box @ X0) @ (number @ X0 @ one))))))),
% 1.87/2.07 inference(rectify,[status(thm)],[f14])).
% 1.87/2.07 thf(f14,axiom,(
% 1.87/2.07 (mlocal @ (mexists_di @ (^[X3 : $i] : (mbox @ (mand @ (entry_box @ X3) @ (number @ X3 @ one))))))),
% 1.87/2.07 file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',ax2)).
% 1.87/2.07 thf(f345,plain,(
% 1.87/2.07 ~spl0_6),
% 1.87/2.07 inference(avatar_contradiction_clause,[status(thm)],[f344])).
% 1.87/2.07 thf(f344,plain,(
% 1.87/2.07 $false | ~spl0_6),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f338])).
% 1.87/2.07 thf(f338,plain,(
% 1.87/2.07 ($true = $false) | ~spl0_6),
% 1.87/2.07 inference(superposition,[status(thm)],[f59,f314])).
% 1.87/2.07 thf(f314,plain,(
% 1.87/2.07 ((mrel @ mactual @ mactual) = $false) | ~spl0_6),
% 1.87/2.07 inference(avatar_component_clause,[status(thm)],[f312])).
% 1.87/2.07 thf(f312,definition,(
% 1.87/2.07 spl0_6 <=> ((mrel @ mactual @ mactual) = $false)),
% 1.87/2.07 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.87/2.07 thf(f59,plain,(
% 1.87/2.07 ( ! [X0 : mworld] : (($true = (mrel @ X0 @ X0))) )),
% 1.87/2.07 inference(cnf_transformation,[status(thm)],[f37])).
% 1.87/2.07 thf(f37,plain,(
% 1.87/2.07 ! [X0 : mworld] : ($true = (mrel @ X0 @ X0))),
% 1.87/2.07 inference(fool_elimination,[status(thm)],[f36])).
% 1.87/2.07 thf(f36,plain,(
% 1.87/2.07 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 1.87/2.07 inference(rectify,[status(thm)],[f9])).
% 1.87/2.07 thf(f9,axiom,(
% 1.87/2.07 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 1.87/2.07 file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',mrel_reflexive)).
% 1.87/2.07 thf(f335,plain,(
% 1.87/2.07 spl0_6 | spl0_2 | ~spl0_7),
% 1.87/2.07 inference(avatar_split_clause,[status(thm)],[f334,f316,f182,f312])).
% 1.87/2.07 thf(f182,definition,(
% 1.87/2.07 spl0_2 <=> ((mrel @ mactual @ sK4) = $false)),
% 1.87/2.07 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.87/2.07 thf(f334,plain,(
% 1.87/2.07 ((mrel @ mactual @ mactual) = $false) | (spl0_2 | ~spl0_7)),
% 1.87/2.07 inference(subsumption_resolution,[status(thm)],[f330,f183])).
% 1.87/2.07 thf(f183,plain,(
% 1.87/2.07 ((mrel @ mactual @ sK4) != $false) | spl0_2),
% 1.87/2.07 inference(avatar_component_clause,[status(thm)],[f182])).
% 1.87/2.07 thf(f330,plain,(
% 1.87/2.07 ((mrel @ mactual @ mactual) = $false) | ((mrel @ mactual @ sK4) = $false) | ~spl0_7),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f328])).
% 1.87/2.07 thf(f328,plain,(
% 1.87/2.07 ($true = $false) | ((mrel @ mactual @ mactual) = $false) | ((mrel @ mactual @ sK4) = $false) | ~spl0_7),
% 1.87/2.07 inference(superposition,[status(thm)],[f318,f82])).
% 1.87/2.07 thf(f82,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X1 : mworld] : (((string @ (sK1 @ X1) @ X2) = $true) | ((mrel @ mactual @ X1) = $false) | ((mrel @ X1 @ X2) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f81])).
% 1.87/2.07 thf(f81,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ X1 @ X2) = $false) | ($true = ((userid @ u @ (sK1 @ X1) @ X2) & (string @ (sK1 @ X1) @ X2))) | ((mrel @ mactual @ X1) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.87/2.07 thf(f80,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | (((mrel @ X1 @ X2) => ((userid @ u @ (sK1 @ X1) @ X2) & (string @ (sK1 @ X1) @ X2))) = $true)) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f79])).
% 1.87/2.07 thf(f79,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((userid @ u @ (sK1 @ X1) @ Y0) & (string @ (sK1 @ X1) @ Y0)))) @ X2) = $true)) )),
% 1.87/2.07 inference(pi_clausification,[status(thm)],[f78])).
% 1.87/2.07 thf(f78,plain,(
% 1.87/2.07 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((userid @ u @ (sK1 @ X1) @ Y0) & (string @ (sK1 @ X1) @ Y0))))))) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.87/2.07 thf(f77,plain,(
% 1.87/2.07 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = ((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => ((userid @ u @ Y0 @ Y1) & (string @ Y0 @ Y1)))))) @ (sK1 @ X1)))) )),
% 1.87/2.07 inference(sigma_clausification,[status(thm)],[f76])).
% 1.87/2.07 thf(f76,plain,(
% 1.87/2.07 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => ((userid @ u @ Y0 @ Y1) & (string @ Y0 @ Y1))))))) = $true)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.87/2.07 thf(f75,plain,(
% 1.87/2.07 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => ((userid @ u @ Y0 @ Y1) & (string @ Y0 @ Y1)))))))))) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.87/2.07 thf(f74,plain,(
% 1.87/2.07 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((userid @ u @ Y1 @ Y2) & (string @ Y1 @ Y2))))))))) @ X1))) )),
% 1.87/2.07 inference(pi_clausification,[status(thm)],[f73])).
% 1.87/2.07 thf(f73,plain,(
% 1.87/2.07 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((userid @ u @ Y1 @ Y2) & (string @ Y1 @ Y2)))))))))) = $true)),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.87/2.07 thf(f72,plain,(
% 1.87/2.07 ($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 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ ((^[Y1 : mworld > $o]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: ((Y1 @ Y3) & (Y2 @ Y3))))))) @ (userid @ u @ Y0) @ (string @ Y0))))))))),
% 1.87/2.07 inference(definition_unfolding,[status(thm)],[f68,f65,f54,f55,f54,f61])).
% 1.87/2.07 thf(f68,plain,(
% 1.87/2.07 ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (userid @ u @ Y0) @ (string @ Y0))))))) = $true)),
% 1.87/2.07 inference(cnf_transformation,[status(thm)],[f49])).
% 1.87/2.07 thf(f49,plain,(
% 1.87/2.07 ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (userid @ u @ Y0) @ (string @ Y0))))))) = $true)),
% 1.87/2.07 inference(fool_elimination,[status(thm)],[f48])).
% 1.87/2.07 thf(f48,plain,(
% 1.87/2.07 (mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : (mbox @ (mand @ (userid @ u @ X0) @ (string @ X0)))))))),
% 1.87/2.07 inference(rectify,[status(thm)],[f13])).
% 1.87/2.07 thf(f13,axiom,(
% 1.87/2.07 (mlocal @ (mbox @ (mexists_di @ (^[X7 : $i] : (mbox @ (mand @ (userid @ u @ X7) @ (string @ X7)))))))),
% 1.87/2.07 file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',ax1)).
% 1.87/2.07 thf(f318,plain,(
% 1.87/2.07 ((string @ (sK1 @ mactual) @ sK4) = $false) | ~spl0_7),
% 1.87/2.07 inference(avatar_component_clause,[status(thm)],[f316])).
% 1.87/2.07 thf(f327,plain,(
% 1.87/2.07 spl0_6 | spl0_7 | spl0_8 | spl0_9 | ~spl0_4),
% 1.87/2.07 inference(avatar_split_clause,[status(thm)],[f308,f288,f324,f320,f316,f312])).
% 1.87/2.07 thf(f288,definition,(
% 1.87/2.07 spl0_4 <=> ! [X0 : mworld] : (($false = (string @ (sK1 @ X0) @ sK4)) | ((entry_box @ sK3 @ (sK6 @ (sK1 @ X0) @ sK3)) = $false) | ((mrel @ X0 @ (sK6 @ (sK1 @ X0) @ sK3)) = $false) | ($false = (mrel @ mactual @ X0)) | ((mrel @ mactual @ (sK6 @ (sK1 @ X0) @ sK3)) = $false))),
% 1.87/2.07 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.87/2.07 thf(f308,plain,(
% 1.87/2.07 ((entry_box @ sK3 @ (sK6 @ (sK1 @ mactual) @ sK3)) = $false) | ((mrel @ mactual @ mactual) = $false) | ((mrel @ mactual @ (sK6 @ (sK1 @ mactual) @ sK3)) = $false) | ((string @ (sK1 @ mactual) @ sK4) = $false) | ~spl0_4),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f307])).
% 1.87/2.07 thf(f307,plain,(
% 1.87/2.07 ($false != $false) | ((mrel @ mactual @ (sK6 @ (sK1 @ mactual) @ sK3)) = $false) | ((mrel @ mactual @ mactual) = $false) | ((string @ (sK1 @ mactual) @ sK4) = $false) | ((entry_box @ sK3 @ (sK6 @ (sK1 @ mactual) @ sK3)) = $false) | ~spl0_4),
% 1.87/2.07 inference(equality_factoring,[status(thm)],[f289])).
% 1.87/2.07 thf(f289,plain,(
% 1.87/2.07 ( ! [X0 : mworld] : (((mrel @ mactual @ (sK6 @ (sK1 @ X0) @ sK3)) = $false) | ($false = (string @ (sK1 @ X0) @ sK4)) | ((mrel @ X0 @ (sK6 @ (sK1 @ X0) @ sK3)) = $false) | ((entry_box @ sK3 @ (sK6 @ (sK1 @ X0) @ sK3)) = $false) | ($false = (mrel @ mactual @ X0))) ) | ~spl0_4),
% 1.87/2.07 inference(avatar_component_clause,[status(thm)],[f288])).
% 1.87/2.07 thf(f303,plain,(
% 1.87/2.07 spl0_2 | ~spl0_5),
% 1.87/2.07 inference(avatar_contradiction_clause,[status(thm)],[f302])).
% 1.87/2.07 thf(f302,plain,(
% 1.87/2.07 $false | (spl0_2 | ~spl0_5)),
% 1.87/2.07 inference(subsumption_resolution,[status(thm)],[f298,f183])).
% 1.87/2.07 thf(f298,plain,(
% 1.87/2.07 ((mrel @ mactual @ sK4) = $false) | ~spl0_5),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f296])).
% 1.87/2.07 thf(f296,plain,(
% 1.87/2.07 ($true = $false) | ((mrel @ mactual @ sK4) = $false) | ~spl0_5),
% 1.87/2.07 inference(superposition,[status(thm)],[f293,f111])).
% 1.87/2.07 thf(f293,plain,(
% 1.87/2.07 ((entry_box @ sK3 @ sK4) = $false) | ~spl0_5),
% 1.87/2.07 inference(avatar_component_clause,[status(thm)],[f291])).
% 1.87/2.07 thf(f295,plain,(
% 1.87/2.07 spl0_5 | spl0_4 | spl0_2),
% 1.87/2.07 inference(avatar_split_clause,[status(thm)],[f285,f182,f288,f291])).
% 1.87/2.07 thf(f285,plain,(
% 1.87/2.07 ( ! [X0 : mworld] : (((mrel @ X0 @ (sK6 @ (sK1 @ X0) @ sK3)) = $false) | ($false = (mrel @ mactual @ X0)) | ((mrel @ mactual @ (sK6 @ (sK1 @ X0) @ sK3)) = $false) | ($false = (string @ (sK1 @ X0) @ sK4)) | ((entry_box @ sK3 @ sK4) = $false) | ((entry_box @ sK3 @ (sK6 @ (sK1 @ X0) @ sK3)) = $false)) ) | spl0_2),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f284])).
% 1.87/2.07 thf(f284,plain,(
% 1.87/2.07 ( ! [X0 : mworld] : (($true = $false) | ((mrel @ mactual @ (sK6 @ (sK1 @ X0) @ sK3)) = $false) | ((mrel @ X0 @ (sK6 @ (sK1 @ X0) @ sK3)) = $false) | ($false = (mrel @ mactual @ X0)) | ($false = (string @ (sK1 @ X0) @ sK4)) | ((entry_box @ sK3 @ (sK6 @ (sK1 @ X0) @ sK3)) = $false) | ((entry_box @ sK3 @ sK4) = $false)) ) | spl0_2),
% 1.87/2.07 inference(superposition,[status(thm)],[f110,f282])).
% 1.87/2.07 thf(f282,plain,(
% 1.87/2.07 ( ! [X0 : mworld,X1 : $i] : (((number @ X1 @ one @ (sK6 @ (sK1 @ X0) @ X1)) = $false) | ((entry_box @ X1 @ sK4) = $false) | ((entry_box @ X1 @ (sK6 @ (sK1 @ X0) @ X1)) = $false) | ((mrel @ X0 @ (sK6 @ (sK1 @ X0) @ X1)) = $false) | ($false = (mrel @ mactual @ X0)) | ($false = (string @ (sK1 @ X0) @ sK4))) ) | spl0_2),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f279])).
% 1.87/2.07 thf(f279,plain,(
% 1.87/2.07 ( ! [X0 : mworld,X1 : $i] : (((entry_box @ X1 @ (sK6 @ (sK1 @ X0) @ X1)) = $false) | ($true = $false) | ($false = (mrel @ mactual @ X0)) | ((mrel @ X0 @ (sK6 @ (sK1 @ X0) @ X1)) = $false) | ($false = (string @ (sK1 @ X0) @ sK4)) | ((number @ X1 @ one @ (sK6 @ (sK1 @ X0) @ X1)) = $false) | ((entry_box @ X1 @ sK4) = $false)) ) | spl0_2),
% 1.87/2.07 inference(superposition,[status(thm)],[f278,f83])).
% 1.87/2.07 thf(f83,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X1 : mworld] : (($true = (userid @ u @ (sK1 @ X1) @ X2)) | ((mrel @ mactual @ X1) = $false) | ((mrel @ X1 @ X2) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f81])).
% 1.87/2.07 thf(f278,plain,(
% 1.87/2.07 ( ! [X0 : $i,X1 : $i] : (((userid @ u @ X0 @ (sK6 @ X0 @ X1)) = $false) | ((entry_box @ X1 @ (sK6 @ X0 @ X1)) = $false) | ((string @ X0 @ sK4) = $false) | ((number @ X1 @ one @ (sK6 @ X0 @ X1)) = $false) | ((entry_box @ X1 @ sK4) = $false)) ) | spl0_2),
% 1.87/2.07 inference(subsumption_resolution,[status(thm)],[f277,f183])).
% 1.87/2.07 thf(f277,plain,(
% 1.87/2.07 ( ! [X0 : $i,X1 : $i] : (((entry_box @ X1 @ (sK6 @ X0 @ X1)) = $false) | ((userid @ u @ X0 @ (sK6 @ X0 @ X1)) = $false) | ((mrel @ mactual @ sK4) = $false) | ((entry_box @ X1 @ sK4) = $false) | ((string @ X0 @ sK4) = $false) | ((number @ X1 @ one @ (sK6 @ X0 @ X1)) = $false)) )),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f276])).
% 1.87/2.07 thf(f276,plain,(
% 1.87/2.07 ( ! [X0 : $i,X1 : $i] : (((number @ X1 @ one @ (sK6 @ X0 @ X1)) = $false) | ((userid @ u @ X0 @ (sK6 @ X0 @ X1)) = $false) | ((entry_box @ X1 @ (sK6 @ X0 @ X1)) = $false) | ((mrel @ mactual @ sK4) = $false) | ((entry_box @ X1 @ sK4) = $false) | ($true = $false) | ((string @ X0 @ sK4) = $false)) )),
% 1.87/2.07 inference(duplicate_literal_removal,[status(thm)],[f264])).
% 1.87/2.07 thf(f264,plain,(
% 1.87/2.07 ( ! [X0 : $i,X1 : $i] : (((userid @ u @ X0 @ (sK6 @ X0 @ X1)) = $false) | ((string @ X0 @ sK4) = $false) | ((entry_box @ X1 @ (sK6 @ X0 @ X1)) = $false) | ((entry_box @ X1 @ sK4) = $false) | ((entry_box @ X1 @ (sK6 @ X0 @ X1)) = $false) | ((userid @ u @ X0 @ (sK6 @ X0 @ X1)) = $false) | ((number @ X1 @ one @ (sK6 @ X0 @ X1)) = $false) | ((mrel @ mactual @ sK4) = $false) | ((number @ X1 @ one @ (sK6 @ X0 @ X1)) = $false) | ($true = $false)) )),
% 1.87/2.07 inference(superposition,[status(thm)],[f141,f209])).
% 1.87/2.07 thf(f209,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (((mrel @ X2 @ (sK5 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1)) = $false) | ((mrel @ mactual @ X2) = $false) | ((userid @ u @ X0 @ (sK6 @ X0 @ X1)) = $false) | ((number @ X1 @ one @ (sK6 @ X0 @ X1)) = $false) | ((string @ X0 @ X2) = $false) | ((entry_box @ X1 @ (sK6 @ X0 @ X1)) = $false) | ((entry_box @ X1 @ X2) = $false)) )),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f208])).
% 1.87/2.07 thf(f208,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (((entry_box @ X1 @ X2) = $false) | ((string @ X0 @ X2) = $false) | ((number @ X1 @ one @ (sK6 @ X0 @ X1)) = $false) | ((userid @ u @ X0 @ (sK6 @ X0 @ X1)) = $false) | ((mrel @ X2 @ (sK5 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1)) = $false) | ((entry_box @ X1 @ (sK6 @ X0 @ X1)) = $false) | ($true = $false) | ((mrel @ mactual @ X2) = $false)) )),
% 1.87/2.07 inference(duplicate_literal_removal,[status(thm)],[f204])).
% 1.87/2.07 thf(f204,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (((mrel @ mactual @ X2) = $false) | ((entry_box @ X1 @ (sK6 @ X0 @ X1)) = $false) | ((mrel @ X2 @ (sK5 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1)) = $false) | ((entry_box @ X1 @ (sK6 @ X0 @ X1)) = $false) | ((entry_box @ X1 @ X2) = $false) | ($true = $false) | ((number @ X1 @ one @ (sK6 @ X0 @ X1)) = $false) | ((userid @ u @ X0 @ (sK6 @ X0 @ X1)) = $false) | ((userid @ u @ X0 @ (sK6 @ X0 @ X1)) = $false) | ((number @ X1 @ one @ (sK6 @ X0 @ X1)) = $false) | ((string @ X0 @ X2) = $false)) )),
% 1.87/2.07 inference(superposition,[status(thm)],[f157,f149])).
% 1.87/2.07 thf(f149,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X1 @ X2 @ (sK8 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2))) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ((entry_box @ X2 @ (sK6 @ X1 @ X2)) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f148])).
% 1.87/2.07 thf(f148,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X1 @ X2 @ (sK8 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2))) | (((entry_box @ X2 @ (sK6 @ X1 @ X2)) & (number @ X2 @ one @ (sK6 @ X1 @ X2))) = $false) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f144])).
% 1.87/2.07 thf(f144,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((userid @ u @ X1 @ (sK6 @ X1 @ X2)) & ((entry_box @ X2 @ (sK6 @ X1 @ X2)) & (number @ X2 @ one @ (sK6 @ X1 @ X2)))) = $false) | ($false = (in @ X1 @ X2 @ (sK8 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2)))) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.87/2.07 thf(f143,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((do @ X4 @ X3 @ (sK8 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ (sK8 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2)))) | (((userid @ u @ X1 @ (sK6 @ X1 @ X2)) & ((entry_box @ X2 @ (sK6 @ X1 @ X2)) & (number @ X2 @ one @ (sK6 @ X1 @ X2)))) = $false)) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f142])).
% 1.87/2.07 thf(f142,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)))) @ (sK8 @ X1 @ X3 @ X4 @ X2)) = $false) | (((userid @ u @ X1 @ (sK6 @ X1 @ X2)) & ((entry_box @ X2 @ (sK6 @ X1 @ X2)) & (number @ X2 @ one @ (sK6 @ X1 @ X2)))) = $false)) )),
% 1.87/2.07 inference(sigma_clausification,[status(thm)],[f138])).
% 1.87/2.07 thf(f138,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2))))) = $false) | (((userid @ u @ X1 @ (sK6 @ X1 @ X2)) & ((entry_box @ X2 @ (sK6 @ X1 @ X2)) & (number @ X2 @ one @ (sK6 @ X1 @ X2)))) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 1.87/2.07 thf(f130,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((mrel @ sK4 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)))))) = $false) | (((userid @ u @ X1 @ (sK6 @ X1 @ X2)) & ((entry_box @ X2 @ (sK6 @ X1 @ X2)) & (number @ X2 @ one @ (sK6 @ X1 @ X2)))) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f129])).
% 1.87/2.07 thf(f129,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((mrel @ sK4 @ (sK6 @ X1 @ X2)) => ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) & ((entry_box @ X2 @ (sK6 @ X1 @ X2)) & (number @ X2 @ one @ (sK6 @ X1 @ X2))))) = $false) | (((mrel @ sK4 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)))))) = $false)) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f128])).
% 1.87/2.07 thf(f128,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((mrel @ sK4 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)))))) = $false) | (((^[Y0 : mworld]: ((mrel @ sK4 @ Y0) => ((userid @ u @ X1 @ Y0) & ((entry_box @ X2 @ Y0) & (number @ X2 @ one @ Y0))))) @ (sK6 @ X1 @ X2)) = $false)) )),
% 1.87/2.07 inference(sigma_clausification,[status(thm)],[f127])).
% 1.87/2.07 thf(f127,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK4 @ Y0) => ((userid @ u @ X1 @ Y0) & ((entry_box @ X2 @ Y0) & (number @ X2 @ one @ Y0)))))) = $false) | (((mrel @ sK4 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)))))) = $false)) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f126])).
% 1.87/2.07 thf(f126,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK4 @ Y0) => ((userid @ u @ X1 @ Y0) & ((entry_box @ X2 @ Y0) & (number @ X2 @ one @ Y0)))))) = $false) | (((^[Y0 : mworld]: ((mrel @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0)))))) @ (sK5 @ X3 @ X1 @ X4 @ X2)) = $false)) )),
% 1.87/2.07 inference(sigma_clausification,[status(thm)],[f125])).
% 1.87/2.07 thf(f125,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0))))))) = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK4 @ Y0) => ((userid @ u @ X1 @ Y0) & ((entry_box @ X2 @ Y0) & (number @ X2 @ one @ Y0)))))) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f124])).
% 1.87/2.07 thf(f124,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK4 @ Y0) => ((userid @ u @ X1 @ Y0) & ((entry_box @ X2 @ Y0) & (number @ X2 @ one @ Y0)))))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0)))))))) = $false)) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f123])).
% 1.87/2.07 thf(f123,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK4 @ Y1) => ((userid @ u @ X1 @ Y1) & ((entry_box @ X2 @ Y1) & (number @ X2 @ one @ Y1)))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK4 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((do @ Y0 @ X3 @ Y2 @ Y1) => (in @ X1 @ X2 @ Y2 @ Y1))))))))) @ X4) = $false)) )),
% 1.87/2.07 inference(pi_clausification,[status(thm)],[f122])).
% 1.87/2.07 thf(f122,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK4 @ Y1) => ((userid @ u @ X1 @ Y1) & ((entry_box @ X2 @ Y1) & (number @ X2 @ one @ Y1)))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK4 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((do @ Y0 @ X3 @ Y2 @ Y1) => (in @ X1 @ X2 @ Y2 @ Y1)))))))))) = $false)) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f121])).
% 1.87/2.07 thf(f121,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK4 @ Y2) => ((userid @ u @ X1 @ Y2) & ((entry_box @ X2 @ Y2) & (number @ X2 @ one @ Y2)))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK4 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((do @ Y1 @ Y0 @ Y3 @ Y2) => (in @ X1 @ X2 @ Y3 @ Y2))))))))))) @ X3))) )),
% 1.87/2.07 inference(pi_clausification,[status(thm)],[f120])).
% 1.87/2.07 thf(f120,plain,(
% 1.87/2.07 ( ! [X2 : $i,X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK4 @ Y2) => ((userid @ u @ X1 @ Y2) & ((entry_box @ X2 @ Y2) & (number @ X2 @ one @ Y2)))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK4 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((do @ Y1 @ Y0 @ Y3 @ Y2) => (in @ X1 @ X2 @ Y3 @ Y2)))))))))))))) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f119])).
% 1.87/2.07 thf(f119,plain,(
% 1.87/2.07 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK4 @ Y3) => ((userid @ u @ X1 @ Y3) & ((entry_box @ Y0 @ Y3) & (number @ Y0 @ one @ Y3)))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK4 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((do @ Y2 @ Y1 @ Y4 @ Y3) => (in @ X1 @ Y0 @ Y4 @ Y3))))))))))))) @ X2) = $false)) )),
% 1.87/2.07 inference(pi_clausification,[status(thm)],[f118])).
% 1.87/2.07 thf(f118,plain,(
% 1.87/2.07 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK4 @ Y3) => ((userid @ u @ X1 @ Y3) & ((entry_box @ Y0 @ Y3) & (number @ Y0 @ one @ Y3)))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK4 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((do @ Y2 @ Y1 @ Y4 @ Y3) => (in @ X1 @ Y0 @ Y4 @ Y3)))))))))))))) = $false)) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f117])).
% 1.87/2.07 thf(f117,plain,(
% 1.87/2.07 ( ! [X1 : $i] : ((((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK4 @ Y4) => ((userid @ u @ Y0 @ Y4) & ((entry_box @ Y1 @ Y4) & (number @ Y1 @ one @ Y4)))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK4 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((do @ Y3 @ Y2 @ Y5 @ Y4) => (in @ Y0 @ Y1 @ Y5 @ Y4))))))))))))))) @ X1) = $false)) )),
% 1.87/2.07 inference(pi_clausification,[status(thm)],[f115])).
% 1.87/2.07 thf(f115,plain,(
% 1.87/2.07 ($false = (?? @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK4 @ Y4) => ((userid @ u @ Y0 @ Y4) & ((entry_box @ Y1 @ Y4) & (number @ Y1 @ one @ Y4)))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK4 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((do @ Y3 @ Y2 @ Y5 @ Y4) => (in @ Y0 @ Y1 @ Y5 @ Y4)))))))))))))))))),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f114])).
% 1.87/2.07 thf(f157,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = (in @ X1 @ X3 @ (sK8 @ X4 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) | ((userid @ u @ X4 @ (sK6 @ X4 @ X5)) = $false) | ((mrel @ mactual @ X2) = $false) | ((entry_box @ X3 @ X2) = $false) | ((mrel @ X2 @ (sK5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5)) = $false) | ((string @ X1 @ X2) = $false) | ((number @ X5 @ one @ (sK6 @ X4 @ X5)) = $false) | ((entry_box @ X5 @ (sK6 @ X4 @ X5)) = $false)) )),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f155])).
% 1.87/2.07 thf(f155,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((entry_box @ X3 @ X2) = $false) | ((string @ X1 @ X2) = $false) | ((entry_box @ X5 @ (sK6 @ X4 @ X5)) = $false) | ((userid @ u @ X4 @ (sK6 @ X4 @ X5)) = $false) | ((mrel @ X2 @ (sK5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5)) = $false) | ($true = $false) | ((number @ X5 @ one @ (sK6 @ X4 @ X5)) = $false) | ($true = (in @ X1 @ X3 @ (sK8 @ X4 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) | ((mrel @ mactual @ X2) = $false)) )),
% 1.87/2.07 inference(superposition,[status(thm)],[f103,f147])).
% 1.87/2.07 thf(f147,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (do @ X4 @ X3 @ (sK8 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2))) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ((entry_box @ X2 @ (sK6 @ X1 @ X2)) = $false) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f146])).
% 1.87/2.07 thf(f146,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | (((entry_box @ X2 @ (sK6 @ X1 @ X2)) & (number @ X2 @ one @ (sK6 @ X1 @ X2))) = $false) | ($true = (do @ X4 @ X3 @ (sK8 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2)))) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f145])).
% 1.87/2.07 thf(f145,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (do @ X4 @ X3 @ (sK8 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2))) | (((userid @ u @ X1 @ (sK6 @ X1 @ X2)) & ((entry_box @ X2 @ (sK6 @ X1 @ X2)) & (number @ X2 @ one @ (sK6 @ X1 @ X2)))) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.87/2.07 thf(f103,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld,X6 : $i,X4 : $i,X5 : mworld] : (((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ X6 @ X5) = $false) | ($false = (string @ X3 @ X1)) | ($false = (mrel @ X1 @ X5)) | ((in @ X3 @ X4 @ X6 @ X5) = $true) | ((entry_box @ X4 @ X1) = $false) | ((mrel @ mactual @ X1) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f102])).
% 1.87/2.07 thf(f102,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld,X6 : $i,X4 : $i,X5 : mworld] : (($true = ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ X6 @ X5) => (in @ X3 @ X4 @ X6 @ X5))) | ($false = (mrel @ X1 @ X5)) | ((entry_box @ X4 @ X1) = $false) | ($false = (string @ X3 @ X1)) | ((mrel @ mactual @ X1) = $false)) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f101])).
% 1.87/2.07 thf(f101,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld,X6 : $i,X4 : $i,X5 : mworld] : (((mrel @ mactual @ X1) = $false) | ($false = (string @ X3 @ X1)) | ($false = (mrel @ X1 @ X5)) | ((entry_box @ X4 @ X1) = $false) | ($true = ((^[Y0 : $i]: ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ Y0 @ X5) => (in @ X3 @ X4 @ Y0 @ X5))) @ X6))) )),
% 1.87/2.07 inference(pi_clausification,[status(thm)],[f100])).
% 1.87/2.07 thf(f100,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i,X5 : mworld] : (($false = (string @ X3 @ X1)) | ((mrel @ mactual @ X1) = $false) | ((entry_box @ X4 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ Y0 @ X5) => (in @ X3 @ X4 @ Y0 @ X5)))) = $true) | ($false = (mrel @ X1 @ X5))) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.87/2.07 thf(f99,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i,X5 : mworld] : (((mrel @ mactual @ X1) = $false) | ($false = (string @ X3 @ X1)) | ((entry_box @ X4 @ X1) = $false) | (((mrel @ X1 @ X5) => (!! @ $i @ (^[Y0 : $i]: ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ Y0 @ X5) => (in @ X3 @ X4 @ Y0 @ X5))))) = $true)) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f98])).
% 1.87/2.07 thf(f98,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ Y1 @ Y0) => (in @ X3 @ X4 @ Y1 @ Y0)))))) @ X5) = $true) | ((entry_box @ X4 @ X1) = $false) | ((mrel @ mactual @ X1) = $false) | ($false = (string @ X3 @ X1))) )),
% 1.87/2.07 inference(pi_clausification,[status(thm)],[f97])).
% 1.87/2.07 thf(f97,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ Y1 @ Y0) => (in @ X3 @ X4 @ Y1 @ Y0))))))) = $true) | ($false = (string @ X3 @ X1)) | ((entry_box @ X4 @ X1) = $false) | ((mrel @ mactual @ X1) = $false)) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f96])).
% 1.87/2.07 thf(f96,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (((entry_box @ X4 @ X1) = $false) | ($false = (string @ X3 @ X1)) | ((mrel @ mactual @ X1) = $false) | ($true = ((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((do @ X2 @ Y0 @ Y2 @ Y1) => (in @ X3 @ X4 @ Y2 @ Y1)))))))) @ (sK2 @ X3 @ X1 @ X4 @ X2)))) )),
% 1.87/2.07 inference(sigma_clausification,[status(thm)],[f95])).
% 1.87/2.07 thf(f95,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (((entry_box @ X4 @ X1) = $false) | ($true = (?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((do @ X2 @ Y0 @ Y2 @ Y1) => (in @ X3 @ X4 @ Y2 @ Y1)))))))))) | ($false = (string @ X3 @ X1)) | ((mrel @ mactual @ X1) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.87/2.07 thf(f94,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (($false = ((string @ X3 @ X1) & (entry_box @ X4 @ X1))) | ($true = (?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((do @ X2 @ Y0 @ Y2 @ Y1) => (in @ X3 @ X4 @ Y2 @ Y1)))))))))) | ((mrel @ mactual @ X1) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.87/2.07 thf(f93,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (((mrel @ mactual @ X1) = $false) | ((((string @ X3 @ X1) & (entry_box @ X4 @ X1)) => (?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((do @ X2 @ Y0 @ Y2 @ Y1) => (in @ X3 @ X4 @ Y2 @ Y1)))))))))) = $true)) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f92])).
% 1.87/2.07 thf(f92,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (((mrel @ mactual @ X1) = $false) | (((^[Y0 : $i]: (((string @ X3 @ X1) & (entry_box @ Y0 @ X1)) => (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((do @ X2 @ Y1 @ Y3 @ Y2) => (in @ X3 @ Y0 @ Y3 @ Y2))))))))))) @ X4) = $true)) )),
% 1.87/2.07 inference(pi_clausification,[status(thm)],[f91])).
% 1.87/2.07 thf(f91,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (((!! @ $i @ (^[Y0 : $i]: (((string @ X3 @ X1) & (entry_box @ Y0 @ X1)) => (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((do @ X2 @ Y1 @ Y3 @ Y2) => (in @ X3 @ Y0 @ Y3 @ Y2)))))))))))) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f90])).
% 1.87/2.07 thf(f90,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : mworld] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((string @ Y0 @ X1) & (entry_box @ Y1 @ X1)) => (?? @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((do @ X2 @ Y2 @ Y4 @ Y3) => (in @ Y0 @ Y1 @ Y4 @ Y3))))))))))))) @ X3) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 1.87/2.07 inference(pi_clausification,[status(thm)],[f89])).
% 1.87/2.07 thf(f89,plain,(
% 1.87/2.07 ( ! [X2 : $i,X1 : mworld] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((string @ Y0 @ X1) & (entry_box @ Y1 @ X1)) => (?? @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((do @ X2 @ Y2 @ Y4 @ Y3) => (in @ Y0 @ Y1 @ Y4 @ Y3))))))))))))))) | ((mrel @ mactual @ X1) = $false)) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f88])).
% 1.87/2.07 thf(f88,plain,(
% 1.87/2.07 ( ! [X2 : $i,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((string @ Y1 @ X1) & (entry_box @ Y2 @ X1)) => (?? @ $i @ (^[Y3 : $i]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ X1 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((do @ Y0 @ Y3 @ Y5 @ Y4) => (in @ Y1 @ Y2 @ Y5 @ Y4))))))))))))))) @ X2))) )),
% 1.87/2.07 inference(pi_clausification,[status(thm)],[f87])).
% 1.87/2.07 thf(f87,plain,(
% 1.87/2.07 ( ! [X1 : mworld] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((string @ Y1 @ X1) & (entry_box @ Y2 @ X1)) => (?? @ $i @ (^[Y3 : $i]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ X1 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((do @ Y0 @ Y3 @ Y5 @ Y4) => (in @ Y1 @ Y2 @ Y5 @ Y4)))))))))))))))) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f86])).
% 1.87/2.07 thf(f86,plain,(
% 1.87/2.07 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((string @ Y1 @ X1) & (entry_box @ Y2 @ X1)) => (?? @ $i @ (^[Y3 : $i]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ X1 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((do @ Y0 @ Y3 @ Y5 @ Y4) => (in @ Y1 @ Y2 @ Y5 @ Y4))))))))))))))))))) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.87/2.07 thf(f85,plain,(
% 1.87/2.07 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((string @ Y2 @ Y0) & (entry_box @ Y3 @ Y0)) => (?? @ $i @ (^[Y4 : $i]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (!! @ $i @ (^[Y6 : $i]: ((do @ Y1 @ Y4 @ Y6 @ Y5) => (in @ Y2 @ Y3 @ Y6 @ Y5)))))))))))))))))) @ X1))) )),
% 1.87/2.07 inference(pi_clausification,[status(thm)],[f84])).
% 1.87/2.07 thf(f84,plain,(
% 1.87/2.07 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((string @ Y2 @ Y0) & (entry_box @ Y3 @ Y0)) => (?? @ $i @ (^[Y4 : $i]: (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (!! @ $i @ (^[Y6 : $i]: ((do @ Y1 @ Y4 @ Y6 @ Y5) => (in @ Y2 @ Y3 @ Y6 @ Y5))))))))))))))))))) = $true)),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.87/2.07 thf(f70,plain,(
% 1.87/2.07 ($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 > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ (string @ Y1) @ (entry_box @ Y2)) @ ((^[Y3 : $i > mworld > $o]: ((^[Y4 : mworld]: (?? @ $i @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))) @ (^[Y3 : $i]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ ((^[Y4 : $i > mworld > $o]: ((^[Y5 : mworld]: (!! @ $i @ (^[Y6 : $i]: (Y4 @ Y6 @ Y5)))))) @ (^[Y4 : $i]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld > $o]: ((^[Y7 : mworld]: ((Y5 @ Y7) => (Y6 @ Y7))))))) @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4)))))))))))))))))),
% 1.87/2.07 inference(definition_unfolding,[status(thm)],[f58,f65,f54,f66,f66,f66,f64,f61,f55,f54,f66,f64])).
% 1.87/2.07 thf(f58,plain,(
% 1.87/2.07 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mimplies @ (mand @ (string @ Y1) @ (entry_box @ Y2)) @ (mexists_di @ (^[Y3 : $i]: (mbox @ (mforall_di @ (^[Y4 : $i]: (mimplies @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4)))))))))))))))) = $true)),
% 1.87/2.07 inference(cnf_transformation,[status(thm)],[f31])).
% 1.87/2.07 thf(f31,plain,(
% 1.87/2.07 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mimplies @ (mand @ (string @ Y1) @ (entry_box @ Y2)) @ (mexists_di @ (^[Y3 : $i]: (mbox @ (mforall_di @ (^[Y4 : $i]: (mimplies @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4)))))))))))))))) = $true)),
% 1.87/2.07 inference(fool_elimination,[status(thm)],[f30])).
% 1.87/2.07 thf(f30,plain,(
% 1.87/2.07 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X2 : $i] : (mimplies @ (mand @ (string @ X1) @ (entry_box @ X2)) @ (mexists_di @ (^[X3 : $i] : (mbox @ (mforall_di @ (^[X4 : $i] : (mimplies @ (do @ X0 @ X3 @ X4) @ (in @ X1 @ X2 @ X4))))))))))))))))),
% 1.87/2.07 inference(rectify,[status(thm)],[f15])).
% 1.87/2.07 thf(f15,axiom,(
% 1.87/2.07 (mlocal @ (mbox @ (mforall_di @ (^[X8 : $i] : (mforall_di @ (^[X7 : $i] : (mforall_di @ (^[X3 : $i] : (mimplies @ (mand @ (string @ X7) @ (entry_box @ X3)) @ (mexists_di @ (^[X1 : $i] : (mbox @ (mforall_di @ (^[X9 : $i] : (mimplies @ (do @ X8 @ X1 @ X9) @ (in @ X7 @ X3 @ X9))))))))))))))))),
% 1.87/2.07 file('/export/starexec/sandbox/tmp/tmp.l3lOMfjeXj/DTF2THF_4164.p',ax3)).
% 1.87/2.07 thf(f141,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (mrel @ sK4 @ (sK5 @ X3 @ X1 @ X4 @ X2))) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ((entry_box @ X2 @ (sK6 @ X1 @ X2)) = $false) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 1.87/2.07 thf(f140,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | (((entry_box @ X2 @ (sK6 @ X1 @ X2)) & (number @ X2 @ one @ (sK6 @ X1 @ X2))) = $false) | ($true = (mrel @ sK4 @ (sK5 @ X3 @ X1 @ X4 @ X2)))) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 1.87/2.07 thf(f139,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((userid @ u @ X1 @ (sK6 @ X1 @ X2)) & ((entry_box @ X2 @ (sK6 @ X1 @ X2)) & (number @ X2 @ one @ (sK6 @ X1 @ X2)))) = $false) | ($true = (mrel @ sK4 @ (sK5 @ X3 @ X1 @ X4 @ X2)))) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 1.87/2.07 thf(f110,plain,(
% 1.87/2.07 ( ! [X1 : mworld] : (($true = (number @ sK3 @ one @ X1)) | ((mrel @ mactual @ X1) = $false)) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.87/2.07 thf(f200,plain,(
% 1.87/2.07 ~spl0_2),
% 1.87/2.07 inference(avatar_contradiction_clause,[status(thm)],[f199])).
% 1.87/2.07 thf(f199,plain,(
% 1.87/2.07 $false | ~spl0_2),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f192])).
% 1.87/2.07 thf(f192,plain,(
% 1.87/2.07 ($true = $false) | ~spl0_2),
% 1.87/2.07 inference(superposition,[status(thm)],[f184,f116])).
% 1.87/2.07 thf(f184,plain,(
% 1.87/2.07 ((mrel @ mactual @ sK4) = $false) | ~spl0_2),
% 1.87/2.07 inference(avatar_component_clause,[status(thm)],[f182])).
% 1.87/2.07 thf(f186,plain,(
% 1.87/2.07 spl0_2 | spl0_1),
% 1.87/2.07 inference(avatar_split_clause,[status(thm)],[f174,f179,f182])).
% 1.87/2.07 thf(f174,plain,(
% 1.87/2.07 ( ! [X0 : $i,X1 : $i] : (((mrel @ mactual @ sK4) = $false) | ((entry_box @ X1 @ sK4) = $false) | ((string @ X0 @ sK4) = $false) | ((mrel @ sK4 @ (sK6 @ X0 @ X1)) = $true)) )),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f173])).
% 1.87/2.07 thf(f173,plain,(
% 1.87/2.07 ( ! [X0 : $i,X1 : $i] : (((string @ X0 @ sK4) = $false) | ((mrel @ sK4 @ (sK6 @ X0 @ X1)) = $true) | ($true = $false) | ((entry_box @ X1 @ sK4) = $false) | ((mrel @ mactual @ sK4) = $false)) )),
% 1.87/2.07 inference(duplicate_literal_removal,[status(thm)],[f169])).
% 1.87/2.07 thf(f169,plain,(
% 1.87/2.07 ( ! [X0 : $i,X1 : $i] : (((entry_box @ X1 @ sK4) = $false) | ($true = $false) | ((mrel @ sK4 @ (sK6 @ X0 @ X1)) = $true) | ((mrel @ mactual @ sK4) = $false) | ((string @ X0 @ sK4) = $false) | ((mrel @ sK4 @ (sK6 @ X0 @ X1)) = $true)) )),
% 1.87/2.07 inference(superposition,[status(thm)],[f133,f163])).
% 1.87/2.07 thf(f163,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (((mrel @ X2 @ (sK5 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1)) = $false) | ((mrel @ sK4 @ (sK6 @ X0 @ X1)) = $true) | ((entry_box @ X1 @ X2) = $false) | ((mrel @ mactual @ X2) = $false) | ((string @ X0 @ X2) = $false)) )),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f162])).
% 1.87/2.07 thf(f162,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (((entry_box @ X1 @ X2) = $false) | ((mrel @ sK4 @ (sK6 @ X0 @ X1)) = $true) | ((mrel @ X2 @ (sK5 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1)) = $false) | ($true = $false) | ((string @ X0 @ X2) = $false) | ((mrel @ mactual @ X2) = $false)) )),
% 1.87/2.07 inference(duplicate_literal_removal,[status(thm)],[f159])).
% 1.87/2.07 thf(f159,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (((mrel @ sK4 @ (sK6 @ X0 @ X1)) = $true) | ($true = $false) | ((mrel @ sK4 @ (sK6 @ X0 @ X1)) = $true) | ((mrel @ X2 @ (sK5 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1)) = $false) | ((string @ X0 @ X2) = $false) | ((mrel @ mactual @ X2) = $false) | ((entry_box @ X1 @ X2) = $false)) )),
% 1.87/2.07 inference(superposition,[status(thm)],[f136,f153])).
% 1.87/2.07 thf(f153,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((in @ X1 @ X3 @ (sK7 @ X4 @ X5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5)) = $true) | ((mrel @ X2 @ (sK5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5)) = $false) | ((entry_box @ X3 @ X2) = $false) | ((mrel @ sK4 @ (sK6 @ X4 @ X5)) = $true) | ((mrel @ mactual @ X2) = $false) | ((string @ X1 @ X2) = $false)) )),
% 1.87/2.07 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.87/2.07 thf(f150,plain,(
% 1.87/2.07 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((mrel @ X2 @ (sK5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5)) = $false) | ((string @ X1 @ X2) = $false) | ((mrel @ sK4 @ (sK6 @ X4 @ X5)) = $true) | ((entry_box @ X3 @ X2) = $false) | ((mrel @ mactual @ X2) = $false) | ($true = $false) | ((in @ X1 @ X3 @ (sK7 @ X4 @ X5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5)) = $true)) )),
% 1.87/2.07 inference(superposition,[status(thm)],[f137,f103])).
% 1.87/2.07 thf(f137,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((do @ X4 @ X3 @ (sK7 @ X1 @ X2 @ X3 @ X4) @ (sK5 @ X3 @ X1 @ X4 @ X2)) = $true) | ($true = (mrel @ sK4 @ (sK6 @ X1 @ X2)))) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 1.87/2.07 thf(f135,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((do @ X4 @ X3 @ (sK7 @ X1 @ X2 @ X3 @ X4) @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ (sK7 @ X1 @ X2 @ X3 @ X4) @ (sK5 @ X3 @ X1 @ X4 @ X2))) = $false) | ($true = (mrel @ sK4 @ (sK6 @ X1 @ X2)))) )),
% 1.87/2.07 inference(beta_eta_normalization,[status(thm)],[f134])).
% 1.87/2.07 thf(f134,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)))) @ (sK7 @ X1 @ X2 @ X3 @ X4)) = $false) | ($true = (mrel @ sK4 @ (sK6 @ X1 @ X2)))) )),
% 1.87/2.07 inference(sigma_clausification,[status(thm)],[f132])).
% 1.87/2.07 thf(f132,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2))))) = $false) | ($true = (mrel @ sK4 @ (sK6 @ X1 @ X2)))) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.87/2.07 thf(f131,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((mrel @ sK4 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)))))) = $false) | ($true = (mrel @ sK4 @ (sK6 @ X1 @ X2)))) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f129])).
% 1.87/2.07 thf(f136,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X1 @ X2 @ (sK7 @ X1 @ X2 @ X3 @ X4) @ (sK5 @ X3 @ X1 @ X4 @ X2))) | ($true = (mrel @ sK4 @ (sK6 @ X1 @ X2)))) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 1.87/2.07 thf(f133,plain,(
% 1.87/2.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (mrel @ sK4 @ (sK5 @ X3 @ X1 @ X4 @ X2))) | ($true = (mrel @ sK4 @ (sK6 @ X1 @ X2)))) )),
% 1.87/2.07 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.87/2.07 % SZS output end Proof for DTF2THF_4164
% 1.87/2.07 % (4474)------------------------------
% 1.87/2.07 % (4474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/2.07 % (4474)Termination reason: Refutation
% 1.87/2.07
% 1.87/2.07 % (4474)Memory used [KB]: 6268
% 1.87/2.07 % (4474)Time elapsed: 0.049 s
% 1.87/2.07 % (4474)Instructions burned: 88 (million)
% 1.87/2.07 % (4474)------------------------------
% 1.87/2.07 % (4474)------------------------------
% 1.87/2.07 % (4473)Success in time 0.05 s
%------------------------------------------------------------------------------