%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NLP266^23 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 1.81s 2.52s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 23
% Syntax : Number of formulae : 282 ( 74 unt; 0 typ; 8 def)
% Number of atoms : 4677 (1146 equ; 0 cnn)
% Maximal formula atoms : 23 ( 16 avg)
% Number of connectives : 7454 ( 113 ~; 983 |; 189 &;5669 @)
% ( 8 <=>; 276 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 93 ( 93 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 38 usr; 17 con; 0-4 aty)
% ( 154 !!; 62 ??; 0 @@+; 0 @@-)
% Number of variables : 894 ( 429 ^; 459 !; 6 ?; 894 :)
% 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,
eiw_di: $i > mworld > $o ).
thf(func_def_13,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_17,type,
number: $i > $i > mworld > $o ).
thf(func_def_18,type,
string: $i > mworld > $o ).
thf(func_def_19,type,
in: $i > $i > $i > mworld > $o ).
thf(func_def_20,type,
do: $i > $i > $i > mworld > $o ).
thf(func_def_21,type,
entry_box: $i > mworld > $o ).
thf(func_def_22,type,
userid: $i > $i > mworld > $o ).
thf(func_def_38,type,
sK0: mworld > $i ).
thf(func_def_43,type,
sK2: $i > mworld > $i > $i > $i ).
thf(func_def_45,type,
sK4: mworld > $i ).
thf(func_def_46,type,
sK5: mworld ).
thf(func_def_47,type,
sK6: $i > $i > mworld ).
thf(func_def_48,type,
sK7: $i > $i > $i > $i > mworld ).
thf(func_def_49,type,
sK8: $i > $i > $i > $i > $i ).
thf(func_def_50,type,
sK9: $i > $i > $i > $i > $i ).
thf(f1524,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f346,f376,f393,f1348,f1355,f1444,f1495,f1513,f1523]) ).
thf(f1523,plain,
( spl1_9
| ~ spl1_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f1522]) ).
thf(f1522,plain,
( $false
| spl1_9
| ~ spl1_11 ),
inference(subsumption_resolution,[status(thm)],[f1518,f1398]) ).
thf(f1398,plain,
( ( $false
!= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| spl1_9 ),
inference(avatar_component_clause,[status(thm)],[f1397]) ).
thf(f1397,definition,
( spl1_9
<=> ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition]) ).
thf(f1518,plain,
( ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ~ spl1_11 ),
inference(trivial_inequality_removal,[status(thm)],[f1517]) ).
thf(f1517,plain,
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ~ spl1_11 ),
inference(superposition,[status(thm)],[f119,f1407]) ).
thf(f1407,plain,
( ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ~ spl1_11 ),
inference(avatar_component_clause,[status(thm)],[f1405]) ).
thf(f1405,definition,
( spl1_11
<=> ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition]) ).
thf(f119,plain,
! [X1: mworld] :
( ( $true
= ( entry_box @ sK3 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f118]) ).
thf(f118,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( number @ sK3 @ one @ X1 )
& ( entry_box @ sK3 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( number @ sK3 @ one @ X1 )
& ( entry_box @ sK3 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f116]) ).
thf(f116,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( number @ sK3 @ one @ Y0 )
& ( entry_box @ sK3 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( number @ sK3 @ one @ Y0 )
& ( entry_box @ sK3 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
( $true
= ( ( eiw_di @ sK3 @ mactual )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( number @ sK3 @ one @ Y0 )
& ( entry_box @ sK3 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f112]) ).
thf(f112,plain,
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( ( number @ Y0 @ one @ Y1 )
& ( entry_box @ Y0 @ Y1 ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( ( number @ Y0 @ one @ Y1 )
& ( entry_box @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( 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] :
( ( Y2 @ Y3 )
& ( Y1 @ Y3 ) )
@ ( entry_box @ Y0 )
@ ( number @ Y0 @ one ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f72,f65,f68,f64,f70]) ).
thf(f70,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X3 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mand_def) ).
thf(f64,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f36]) ).
thf(f36,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/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mbox_def) ).
thf(f68,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) )
= mexists_di ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X6: $i] :
( ( X1 @ X6 @ X2 )
& ( eiw_di @ X6 @ X2 ) ) )
= mexists_di ),
file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mexists_di_def) ).
thf(f65,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mlocal_def) ).
thf(f72,plain,
( $true
= ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( entry_box @ Y0 ) @ ( number @ Y0 @ one ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( $true
= ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( entry_box @ Y0 ) @ ( number @ Y0 @ one ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f46]) ).
thf(f46,plain,
( mlocal
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( mand @ ( entry_box @ X0 ) @ ( number @ X0 @ one ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
( mlocal
@ ( mexists_di
@ ^ [X3: $i] : ( mbox @ ( mand @ ( entry_box @ X3 ) @ ( number @ X3 @ one ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',ax2) ).
thf(f1513,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[status(thm)],[f1512]) ).
thf(f1512,plain,
( $false
| ~ spl1_10 ),
inference(trivial_inequality_removal,[status(thm)],[f1507]) ).
thf(f1507,plain,
( ( $false = $true )
| ~ spl1_10 ),
inference(superposition,[status(thm)],[f79,f1501]) ).
thf(f1501,plain,
( ( $false
= ( mrel @ sK5 @ sK5 ) )
| ~ spl1_10 ),
inference(trivial_inequality_removal,[status(thm)],[f1500]) ).
thf(f1500,plain,
( ( $false
= ( mrel @ sK5 @ sK5 ) )
| ( $false = $true )
| ~ spl1_10 ),
inference(forward_demodulation,[status(thm)],[f1499,f138]) ).
thf(f138,plain,
( ( mrel @ mactual @ sK5 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
( $false
= ( ( mrel @ mactual @ sK5 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK5 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ sK5 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ sK5 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ sK5 )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK5 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( eiw_di @ Y5 @ Y4 )
=> ( ( do @ Y3 @ Y2 @ Y5 @ Y4 )
=> ( in @ Y0 @ Y1 @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK5 @ Y4 )
=> ( ( number @ Y1 @ one @ Y4 )
& ( entry_box @ Y1 @ Y4 )
& ( userid @ u @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f135]) ).
thf(f135,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y0 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y0 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y0 )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( eiw_di @ Y6 @ Y5 )
=> ( ( do @ Y4 @ Y3 @ Y6 @ Y5 )
=> ( in @ Y1 @ Y2 @ Y6 @ Y5 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( ( number @ Y2 @ one @ Y5 )
& ( entry_box @ Y2 @ Y5 )
& ( userid @ u @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y0 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y0 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y0 )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( eiw_di @ Y6 @ Y5 )
=> ( ( do @ Y4 @ Y3 @ Y6 @ Y5 )
=> ( in @ Y1 @ Y2 @ Y6 @ Y5 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( ( number @ Y2 @ one @ Y5 )
& ( entry_box @ Y2 @ Y5 )
& ( userid @ u @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,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] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
& ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
& ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: $i] :
( ^ [Y3: $i > mworld > $o,Y4: mworld] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( eiw_di @ Y5 @ Y4 )
& ( Y3 @ Y5 @ Y4 ) ) )
@ ^ [Y3: $i] :
( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y5 @ Y6 )
& ( Y4 @ Y6 ) )
@ ( ^ [Y4: mworld > $o,Y5: mworld] :
( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ ( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y5 @ Y6 )
& ( Y4 @ Y6 ) )
@ ( userid @ u @ Y0 )
@ ( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y5 @ Y6 )
& ( Y4 @ 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] :
( ( eiw_di @ Y6 @ Y5 )
=> ( 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)],[f80,f65,f64,f68,f68,f68,f68,f70,f64,f70,f70,f64,f78,f76]) ).
thf(f76,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/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mimplies_def) ).
thf(f78,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_di ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ X2 )
=> ( X1 @ X6 @ X2 ) ) )
= mforall_di ),
file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mforall_di_def) ).
thf(f80,plain,
( $true
!= ( 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 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
thf(f56,plain,
( $true
!= ( 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 ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f35]) ).
thf(f35,plain,
( $true
!= ( 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 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f34]) ).
thf(f34,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)],[f19]) ).
thf(f19,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)],[f18]) ).
thf(f18,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/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',con) ).
thf(f1499,plain,
( ( $false
= ( mrel @ sK5 @ sK5 ) )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ~ spl1_10 ),
inference(trivial_inequality_removal,[status(thm)],[f1497]) ).
thf(f1497,plain,
( ( $false
= ( mrel @ sK5 @ sK5 ) )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ( $false = $true )
| ~ spl1_10 ),
inference(superposition,[status(thm)],[f133,f1403]) ).
thf(f1403,plain,
( ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ~ spl1_10 ),
inference(avatar_component_clause,[status(thm)],[f1401]) ).
thf(f1401,definition,
( spl1_10
<=> ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_10])],[avatar_definition]) ).
thf(f133,plain,
! [X2: mworld,X1: mworld] :
( ( ( string @ ( sK4 @ X1 ) @ X2 )
= $true )
| ( $false
= ( mrel @ X1 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ X1 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( string @ ( sK4 @ X1 ) @ X2 )
& ( userid @ u @ ( sK4 @ X1 ) @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ X1 @ X2 )
=> ( ( string @ ( sK4 @ X1 ) @ X2 )
& ( userid @ u @ ( sK4 @ X1 ) @ X2 ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f129]) ).
thf(f129,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( string @ ( sK4 @ X1 ) @ Y0 )
& ( userid @ u @ ( sK4 @ X1 ) @ Y0 ) ) )
@ X2 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f127]) ).
thf(f127,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( string @ ( sK4 @ X1 ) @ Y0 )
& ( userid @ u @ ( sK4 @ X1 ) @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f126]) ).
thf(f126,plain,
! [X1: mworld] :
( ( $true
= ( ( eiw_di @ ( sK4 @ X1 ) @ X1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( string @ ( sK4 @ X1 ) @ Y0 )
& ( userid @ u @ ( sK4 @ X1 ) @ Y0 ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f125]) ).
thf(f125,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( string @ Y0 @ Y1 )
& ( userid @ u @ Y0 @ Y1 ) ) ) ) )
@ ( sK4 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( string @ Y0 @ Y1 )
& ( userid @ u @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f123]) ).
thf(f123,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( string @ Y0 @ Y1 )
& ( userid @ u @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f122]) ).
thf(f122,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( string @ Y1 @ Y2 )
& ( userid @ u @ Y1 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( string @ Y1 @ Y2 )
& ( userid @ u @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,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] :
( ( eiw_di @ Y2 @ Y1 )
& ( 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] :
( ( Y2 @ Y3 )
& ( Y1 @ Y3 ) )
@ ( userid @ u @ Y0 )
@ ( string @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f67,f65,f64,f68,f64,f70]) ).
thf(f67,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( string @ Y0 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( string @ Y0 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f42]) ).
thf(f42,plain,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( mand @ ( userid @ u @ X0 ) @ ( string @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X7: $i] : ( mbox @ ( mand @ ( userid @ u @ X7 ) @ ( string @ X7 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',ax1) ).
thf(f79,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X2: mworld] : ( mrel @ X2 @ X2 ),
file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mrel_reflexive) ).
thf(f1495,plain,
( spl1_10
| ~ spl1_2
| spl1_7
| ~ spl1_9 ),
inference(avatar_split_clause,[status(thm)],[f1494,f1397,f1339,f337,f1401]) ).
thf(f337,definition,
( spl1_2
<=> ! [X0: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $false
= ( entry_box @ X1 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f1339,definition,
( spl1_7
<=> ( $false
= ( entry_box @ sK3 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition]) ).
thf(f1494,plain,
( ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ~ spl1_2
| spl1_7
| ~ spl1_9 ),
inference(trivial_inequality_removal,[status(thm)],[f1493]) ).
thf(f1493,plain,
( ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false = $true )
| ~ spl1_2
| spl1_7
| ~ spl1_9 ),
inference(forward_demodulation,[status(thm)],[f1492,f228]) ).
thf(f228,plain,
( ( eiw_di @ sK3 @ sK5 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f220]) ).
thf(f220,plain,
( ( $true != $true )
| ( ( eiw_di @ sK3 @ sK5 )
= $true ) ),
inference(superposition,[status(thm)],[f205,f115]) ).
thf(f115,plain,
( $true
= ( eiw_di @ sK3 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f205,plain,
! [X0: $i] :
( ( $true
!= ( eiw_di @ X0 @ mactual ) )
| ( ( eiw_di @ X0 @ sK5 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f199]) ).
thf(f199,plain,
! [X0: $i] :
( ( ( eiw_di @ X0 @ sK5 )
= $true )
| ( $true != $true )
| ( $true
!= ( eiw_di @ X0 @ mactual ) ) ),
inference(superposition,[status(thm)],[f66,f182]) ).
thf(f182,plain,
( $true
= ( mrel @ sK5 @ mactual ) ),
inference(trivial_inequality_removal,[status(thm)],[f180]) ).
thf(f180,plain,
( ( $true
= ( mrel @ sK5 @ mactual ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f178,f79]) ).
thf(f178,plain,
! [X0: mworld] :
( ( $true
!= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ sK5 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f176]) ).
thf(f176,plain,
! [X0: mworld] :
( ( $true != $true )
| ( ( mrel @ sK5 @ X0 )
= $true )
| ( $true
!= ( mrel @ mactual @ X0 ) ) ),
inference(superposition,[status(thm)],[f63,f138]) ).
thf(f63,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ X2 ) )
| ( ( mrel @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( $true
= ( mrel @ X1 @ X2 ) )
| ( ( mrel @ X0 @ X2 )
!= $true )
| ( $true
!= ( mrel @ X0 @ X1 ) ) ),
inference(flattening,[status(thm)],[f57]) ).
thf(f57,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( $true
= ( mrel @ X1 @ X2 ) )
| ( ( mrel @ X0 @ X2 )
!= $true )
| ( $true
!= ( mrel @ X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f55]) ).
thf(f55,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( ( mrel @ X0 @ X2 )
= $true )
& ( $true
= ( mrel @ X0 @ X1 ) ) )
=> ( $true
= ( mrel @ X1 @ X2 ) ) ),
inference(fool_elimination,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X1 )
& ( mrel @ X0 @ X2 ) )
=> ( mrel @ X1 @ X2 ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
! [X2: mworld,X5: mworld,X4: mworld] :
( ( ( mrel @ X2 @ X5 )
& ( mrel @ X2 @ X4 ) )
=> ( mrel @ X5 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mrel_euclidean) ).
thf(f66,plain,
! [X2: mworld,X0: mworld,X1: $i] :
( ( ( mrel @ X2 @ X0 )
!= $true )
| ( ( eiw_di @ X1 @ X0 )
!= $true )
| ( ( eiw_di @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: mworld,X1: $i,X2: mworld] :
( ( ( eiw_di @ X1 @ X0 )
!= $true )
| ( ( eiw_di @ X1 @ X2 )
= $true )
| ( ( mrel @ X2 @ X0 )
!= $true ) ),
inference(flattening,[status(thm)],[f59]) ).
thf(f59,plain,
! [X0: mworld,X1: $i,X2: mworld] :
( ( ( eiw_di @ X1 @ X2 )
= $true )
| ( ( mrel @ X2 @ X0 )
!= $true )
| ( ( eiw_di @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: mworld,X1: $i,X2: mworld] :
( ( ( ( mrel @ X2 @ X0 )
= $true )
& ( ( eiw_di @ X1 @ X0 )
= $true ) )
=> ( ( eiw_di @ X1 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f50]) ).
thf(f50,plain,
! [X0: mworld,X1: $i,X2: mworld] :
( ( ( eiw_di @ X1 @ X0 )
& ( mrel @ X2 @ X0 ) )
=> ( eiw_di @ X1 @ X2 ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
! [X2: mworld,X6: $i,X4: mworld] :
( ( ( eiw_di @ X6 @ X2 )
& ( mrel @ X4 @ X2 ) )
=> ( eiw_di @ X6 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',eiw_di_decr) ).
thf(f1492,plain,
( ( $false
= ( eiw_di @ sK3 @ sK5 ) )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ~ spl1_2
| spl1_7
| ~ spl1_9 ),
inference(trivial_inequality_removal,[status(thm)],[f1491]) ).
thf(f1491,plain,
( ( $false = $true )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( eiw_di @ sK3 @ sK5 ) )
| ~ spl1_2
| spl1_7
| ~ spl1_9 ),
inference(forward_demodulation,[status(thm)],[f1490,f226]) ).
thf(f226,plain,
( ( eiw_di @ ( sK4 @ sK5 ) @ sK5 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f222]) ).
thf(f222,plain,
( ( ( eiw_di @ ( sK4 @ sK5 ) @ sK5 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f205,f213]) ).
thf(f213,plain,
( ( eiw_di @ ( sK4 @ sK5 ) @ mactual )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f212]) ).
thf(f212,plain,
( ( $false = $true )
| ( ( eiw_di @ ( sK4 @ sK5 ) @ mactual )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f211,f138]) ).
thf(f211,plain,
( ( ( mrel @ mactual @ sK5 )
= $false )
| ( ( eiw_di @ ( sK4 @ sK5 ) @ mactual )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f206]) ).
thf(f206,plain,
( ( ( eiw_di @ ( sK4 @ sK5 ) @ mactual )
= $true )
| ( $true != $true )
| ( ( mrel @ mactual @ sK5 )
= $false ) ),
inference(superposition,[status(thm)],[f202,f128]) ).
thf(f128,plain,
! [X1: mworld] :
( ( ( eiw_di @ ( sK4 @ X1 ) @ X1 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f126]) ).
thf(f202,plain,
! [X0: $i] :
( ( ( eiw_di @ X0 @ sK5 )
!= $true )
| ( $true
= ( eiw_di @ X0 @ mactual ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f197]) ).
thf(f197,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( eiw_di @ X0 @ mactual ) )
| ( ( eiw_di @ X0 @ sK5 )
!= $true ) ),
inference(superposition,[status(thm)],[f66,f138]) ).
thf(f1490,plain,
( ( $false
= ( eiw_di @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( eiw_di @ sK3 @ sK5 ) )
| ~ spl1_2
| spl1_7
| ~ spl1_9 ),
inference(subsumption_resolution,[status(thm)],[f1482,f1340]) ).
thf(f1340,plain,
( ( $false
!= ( entry_box @ sK3 @ sK5 ) )
| spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f1339]) ).
thf(f1482,plain,
( ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( entry_box @ sK3 @ sK5 ) )
| ( $false
= ( eiw_di @ sK3 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK4 @ sK5 ) @ sK5 ) )
| ~ spl1_2
| ~ spl1_9 ),
inference(trivial_inequality_removal,[status(thm)],[f1475]) ).
thf(f1475,plain,
( ( $false
= ( entry_box @ sK3 @ sK5 ) )
| ( $false
= ( eiw_di @ sK3 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false = $true )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ~ spl1_2
| ~ spl1_9 ),
inference(superposition,[status(thm)],[f1399,f350]) ).
thf(f350,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( mrel @ mactual @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( entry_box @ X1 @ sK5 ) ) )
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f347]) ).
thf(f347,plain,
( ! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $true
= ( mrel @ mactual @ ( sK6 @ X0 @ X1 ) ) ) )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f184,f338]) ).
thf(f338,plain,
( ! [X0: $i,X1: $i] :
( ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false
= ( string @ X0 @ sK5 ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f337]) ).
thf(f184,plain,
! [X0: mworld] :
( ( ( mrel @ sK5 @ X0 )
!= $true )
| ( $true
= ( mrel @ mactual @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f183]) ).
thf(f183,plain,
! [X0: mworld] :
( ( ( mrel @ sK5 @ X0 )
!= $true )
| ( $true
= ( mrel @ mactual @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f63,f182]) ).
thf(f1399,plain,
( ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ~ spl1_9 ),
inference(avatar_component_clause,[status(thm)],[f1397]) ).
thf(f1444,plain,
( spl1_10
| spl1_11
| spl1_9
| ~ spl1_2
| spl1_7
| ~ spl1_8 ),
inference(avatar_split_clause,[status(thm)],[f1443,f1343,f1339,f337,f1397,f1405,f1401]) ).
thf(f1343,definition,
( spl1_8
<=> ! [X0: mworld] :
( ( ( mrel @ mactual @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) )
= $false )
| ( ( eiw_di @ ( sK4 @ X0 ) @ sK5 )
= $false )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ X0 @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) ) )
| ( $false
= ( string @ ( sK4 @ X0 ) @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition]) ).
thf(f1443,plain,
( ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ~ spl1_2
| spl1_7
| ~ spl1_8 ),
inference(trivial_inequality_removal,[status(thm)],[f1442]) ).
thf(f1442,plain,
( ( $false = $true )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ~ spl1_2
| spl1_7
| ~ spl1_8 ),
inference(forward_demodulation,[status(thm)],[f1441,f138]) ).
thf(f1441,plain,
( ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ~ spl1_2
| spl1_7
| ~ spl1_8 ),
inference(trivial_inequality_removal,[status(thm)],[f1440]) ).
thf(f1440,plain,
( ( ( mrel @ mactual @ sK5 )
= $false )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ~ spl1_2
| spl1_7
| ~ spl1_8 ),
inference(forward_demodulation,[status(thm)],[f1439,f228]) ).
thf(f1439,plain,
( ( $false
= ( eiw_di @ sK3 @ sK5 ) )
| ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ~ spl1_2
| spl1_7
| ~ spl1_8 ),
inference(trivial_inequality_removal,[status(thm)],[f1438]) ).
thf(f1438,plain,
( ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( eiw_di @ sK3 @ sK5 ) )
| ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false = $true )
| ~ spl1_2
| spl1_7
| ~ spl1_8 ),
inference(forward_demodulation,[status(thm)],[f1437,f226]) ).
thf(f1437,plain,
( ( $false
= ( eiw_di @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false
= ( eiw_di @ sK3 @ sK5 ) )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ~ spl1_2
| spl1_7
| ~ spl1_8 ),
inference(subsumption_resolution,[status(thm)],[f1382,f1340]) ).
thf(f1382,plain,
( ( ( mrel @ mactual @ sK5 )
= $false )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false
= ( eiw_di @ sK3 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false
= ( entry_box @ sK3 @ sK5 ) )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ~ spl1_2
| ~ spl1_8 ),
inference(trivial_inequality_removal,[status(thm)],[f1381]) ).
thf(f1381,plain,
( ( ( mrel @ mactual @ sK5 )
= $false )
| ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false
= ( entry_box @ sK3 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false = $true )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( eiw_di @ sK3 @ sK5 ) )
| ~ spl1_2
| ~ spl1_8 ),
inference(duplicate_literal_removal,[status(thm)],[f1377]) ).
thf(f1377,plain,
( ( $false
= ( mrel @ mactual @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( entry_box @ sK3 @ sK5 ) )
| ( $false
= ( eiw_di @ sK3 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false = $true )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ sK5 ) @ sK3 ) ) )
| ( $false
= ( string @ ( sK4 @ sK5 ) @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK4 @ sK5 ) @ sK5 ) )
| ~ spl1_2
| ~ spl1_8 ),
inference(superposition,[status(thm)],[f338,f1344]) ).
thf(f1344,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( eiw_di @ ( sK4 @ X0 ) @ sK5 )
= $false )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) ) )
| ( ( mrel @ mactual @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) )
= $false )
| ( $false
= ( string @ ( sK4 @ X0 ) @ sK5 ) ) )
| ~ spl1_8 ),
inference(avatar_component_clause,[status(thm)],[f1343]) ).
thf(f1355,plain,
~ spl1_7,
inference(avatar_contradiction_clause,[status(thm)],[f1354]) ).
thf(f1354,plain,
( $false
| ~ spl1_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1353]) ).
thf(f1353,plain,
( ( $false = $true )
| ~ spl1_7 ),
inference(backward_demodulation,[status(thm)],[f138,f1352]) ).
thf(f1352,plain,
( ( ( mrel @ mactual @ sK5 )
= $false )
| ~ spl1_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1350]) ).
thf(f1350,plain,
( ( $false = $true )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ~ spl1_7 ),
inference(superposition,[status(thm)],[f119,f1341]) ).
thf(f1341,plain,
( ( $false
= ( entry_box @ sK3 @ sK5 ) )
| ~ spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f1339]) ).
thf(f1348,plain,
( spl1_7
| spl1_8
| ~ spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f1347,f367,f1343,f1339]) ).
thf(f367,definition,
( spl1_3
<=> ! [X0: $i,X1: $i] :
( ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f1347,plain,
( ! [X0: mworld] :
( ( $false
= ( entry_box @ sK3 @ sK5 ) )
| ( ( eiw_di @ ( sK4 @ X0 ) @ sK5 )
= $false )
| ( $false
= ( mrel @ X0 @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) ) )
| ( $false
= ( string @ ( sK4 @ X0 ) @ sK5 ) )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ mactual @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) )
= $false ) )
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f1346]) ).
thf(f1346,plain,
( ! [X0: mworld] :
( ( ( mrel @ mactual @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) )
= $false )
| ( $false
= ( mrel @ X0 @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) ) )
| ( ( eiw_di @ ( sK4 @ X0 ) @ sK5 )
= $false )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) ) )
| ( $false
= ( string @ ( sK4 @ X0 ) @ sK5 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( entry_box @ sK3 @ sK5 ) )
| ( $false = $true ) )
| ~ spl1_3 ),
inference(forward_demodulation,[status(thm)],[f1334,f228]) ).
thf(f1334,plain,
( ! [X0: mworld] :
( ( ( eiw_di @ ( sK4 @ X0 ) @ sK5 )
= $false )
| ( $false
= ( eiw_di @ sK3 @ sK5 ) )
| ( $false
= ( mrel @ X0 @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) ) )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) ) )
| ( $false
= ( string @ ( sK4 @ X0 ) @ sK5 ) )
| ( $false
= ( entry_box @ sK3 @ sK5 ) )
| ( ( mrel @ mactual @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) ) )
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f1332]) ).
thf(f1332,plain,
( ! [X0: mworld] :
( ( $false
= ( string @ ( sK4 @ X0 ) @ sK5 ) )
| ( $false
= ( mrel @ X0 @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) ) )
| ( ( eiw_di @ ( sK4 @ X0 ) @ sK5 )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ mactual @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) )
= $false )
| ( $false
= ( entry_box @ sK3 @ ( sK6 @ ( sK4 @ X0 ) @ sK3 ) ) )
| ( $false
= ( entry_box @ sK3 @ sK5 ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ sK3 @ sK5 ) ) )
| ~ spl1_3 ),
inference(superposition,[status(thm)],[f1235,f120]) ).
thf(f120,plain,
! [X1: mworld] :
( ( $true
= ( number @ sK3 @ one @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f118]) ).
thf(f1235,plain,
( ! [X0: mworld,X1: $i] :
( ( $false
= ( number @ X1 @ one @ ( sK6 @ ( sK4 @ X0 ) @ X1 ) ) )
| ( $false
= ( mrel @ X0 @ ( sK6 @ ( sK4 @ X0 ) @ X1 ) ) )
| ( ( eiw_di @ ( sK4 @ X0 ) @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ ( sK4 @ X0 ) @ X1 ) ) )
| ( $false
= ( string @ ( sK4 @ X0 ) @ sK5 ) ) )
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f1233]) ).
thf(f1233,plain,
( ! [X0: mworld,X1: $i] :
( ( $false
= ( string @ ( sK4 @ X0 ) @ sK5 ) )
| ( $false
= ( mrel @ X0 @ ( sK6 @ ( sK4 @ X0 ) @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ ( sK4 @ X0 ) @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ ( sK4 @ X0 ) @ X1 ) ) )
| ( ( eiw_di @ ( sK4 @ X0 ) @ sK5 )
= $false )
| ( $false = $true )
| ( $false
= ( entry_box @ X1 @ sK5 ) ) )
| ~ spl1_3 ),
inference(superposition,[status(thm)],[f132,f368]) ).
thf(f368,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f367]) ).
thf(f132,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( userid @ u @ ( sK4 @ X1 ) @ X2 ) )
| ( $false
= ( mrel @ X1 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f393,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[status(thm)],[f392]) ).
thf(f392,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f382]) ).
thf(f382,plain,
( ( $false = $true )
| ~ spl1_1 ),
inference(backward_demodulation,[status(thm)],[f227,f335]) ).
thf(f335,plain,
( ! [X2: $i] :
( $false
= ( eiw_di @ X2 @ sK5 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f334]) ).
thf(f334,definition,
( spl1_1
<=> ! [X2: $i] :
( $false
= ( eiw_di @ X2 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f227,plain,
( $true
= ( eiw_di @ ( sK0 @ mactual ) @ sK5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f224]) ).
thf(f224,plain,
( ( $true
= ( eiw_di @ ( sK0 @ mactual ) @ sK5 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f205,f74]) ).
thf(f74,plain,
! [X0: mworld] :
( ( eiw_di @ ( sK0 @ X0 ) @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f62]) ).
thf(f62,plain,
! [X0: mworld] :
( ( eiw_di @ ( sK0 @ X0 ) @ X0 )
= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f61]) ).
thf(f61,plain,
! [X0: mworld] :
( ? [X1: $i] :
( ( eiw_di @ X1 @ X0 )
= $true )
=> ( ( eiw_di @ ( sK0 @ X0 ) @ X0 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
! [X0: mworld] :
? [X1: $i] :
( ( eiw_di @ X1 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: mworld] :
? [X1: $i] : ( eiw_di @ X1 @ X0 ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
! [X2: mworld] :
? [X6: $i] : ( eiw_di @ X6 @ X2 ),
file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',eiw_di_nonempty) ).
thf(f376,plain,
( spl1_1
| spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f375,f367,f334]) ).
thf(f375,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f374]) ).
thf(f374,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false = $true )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f359,f138]) ).
thf(f359,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f358]) ).
thf(f358,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f356]) ).
thf(f356,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false = $true )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(superposition,[status(thm)],[f103,f317]) ).
thf(f317,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK5 @ X1 @ X2 ) @ sK5 ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f316]) ).
thf(f316,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK5 @ X1 @ X2 ) @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) ) ),
inference(forward_demodulation,[status(thm)],[f313,f138]) ).
thf(f313,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( string @ X0 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK5 @ X1 @ X2 ) @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( ( mrel @ mactual @ sK5 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f312]) ).
thf(f312,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK5 @ X1 @ X2 ) @ sK5 ) )
| ( ( mrel @ mactual @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f299]) ).
thf(f299,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( mrel @ mactual @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK5 @ X1 @ X2 ) @ sK5 ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK5 @ X1 @ X2 ) @ sK5 ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) ) ),
inference(superposition,[status(thm)],[f273,f169]) ).
thf(f169,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( mrel @ sK5 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
= $true )
| ( $false
= ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f167]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( ( ( mrel @ sK5 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( ( do @ X4 @ X3 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) ) ) ) )
= $false )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) ) ) )
| ( ( ( mrel @ sK5 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( ( do @ X4 @ X3 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) ) ) ) )
= $false )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f156]) ).
thf(f156,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( ( mrel @ sK5 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( ( do @ X4 @ X3 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) ) ) ) )
= $false )
| ( $false
= ( eiw_di @ X3 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f155]) ).
thf(f155,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( mrel @ sK5 @ ( sK6 @ X1 @ X2 ) )
=> ( ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( ( mrel @ sK5 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( ( do @ X4 @ X3 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f154]) ).
thf(f154,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) ) )
@ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( ( mrel @ sK5 @ ( sK6 @ X1 @ X2 ) )
=> ( ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) ) ),
inference(sigma_clausification,[status(thm)],[f153]) ).
thf(f153,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( ( mrel @ sK5 @ ( sK6 @ X1 @ X2 ) )
=> ( ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) )
& ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) ) ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f152]) ).
thf(f152,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( ( number @ X2 @ one @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( userid @ u @ X1 @ Y0 ) ) )
@ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f151]) ).
thf(f151,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( ( number @ X2 @ one @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( userid @ u @ X1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( ( number @ X2 @ one @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( userid @ u @ X1 @ Y0 ) ) ) ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f149]) ).
thf(f149,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( ( eiw_di @ X4 @ sK5 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( ( number @ X2 @ one @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( userid @ u @ X1 @ Y0 ) ) ) ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f148]) ).
thf(f148,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK5 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK5 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ( do @ Y0 @ X3 @ Y2 @ Y1 )
=> ( in @ X1 @ X2 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK5 @ Y1 )
=> ( ( number @ X2 @ one @ Y1 )
& ( entry_box @ X2 @ Y1 )
& ( userid @ u @ X1 @ Y1 ) ) ) ) )
@ X4 ) ) ),
inference(pi_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK5 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK5 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ( do @ Y0 @ X3 @ Y2 @ Y1 )
=> ( in @ X1 @ X2 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK5 @ Y1 )
=> ( ( number @ X2 @ one @ Y1 )
& ( entry_box @ X2 @ Y1 )
& ( userid @ u @ X1 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f146]) ).
thf(f146,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( ( eiw_di @ X3 @ sK5 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK5 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK5 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ( do @ Y0 @ X3 @ Y2 @ Y1 )
=> ( in @ X1 @ X2 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK5 @ Y1 )
=> ( ( number @ X2 @ one @ Y1 )
& ( entry_box @ X2 @ Y1 )
& ( userid @ u @ X1 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f145]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK5 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ sK5 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK5 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( ( do @ Y1 @ Y0 @ Y3 @ Y2 )
=> ( in @ X1 @ X2 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK5 @ Y2 )
=> ( ( number @ X2 @ one @ Y2 )
& ( entry_box @ X2 @ Y2 )
& ( userid @ u @ X1 @ Y2 ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK5 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ sK5 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK5 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( ( do @ Y1 @ Y0 @ Y3 @ Y2 )
=> ( in @ X1 @ X2 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK5 @ Y2 )
=> ( ( number @ X2 @ one @ Y2 )
& ( entry_box @ X2 @ Y2 )
& ( userid @ u @ X1 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( eiw_di @ X2 @ sK5 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK5 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ sK5 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK5 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( ( do @ Y1 @ Y0 @ Y3 @ Y2 )
=> ( in @ X1 @ X2 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK5 @ Y2 )
=> ( ( number @ X2 @ one @ Y2 )
& ( entry_box @ X2 @ Y2 )
& ( userid @ u @ X1 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f142]) ).
thf(f142,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK5 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ sK5 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ sK5 )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK5 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( ( do @ Y2 @ Y1 @ Y4 @ Y3 )
=> ( in @ X1 @ Y0 @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK5 @ Y3 )
=> ( ( number @ Y0 @ one @ Y3 )
& ( entry_box @ Y0 @ Y3 )
& ( userid @ u @ X1 @ Y3 ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(pi_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK5 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ sK5 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ sK5 )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK5 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( ( do @ Y2 @ Y1 @ Y4 @ Y3 )
=> ( in @ X1 @ Y0 @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK5 @ Y3 )
=> ( ( number @ Y0 @ one @ Y3 )
& ( entry_box @ Y0 @ Y3 )
& ( userid @ u @ X1 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
! [X1: $i] :
( $false
= ( ( eiw_di @ X1 @ sK5 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK5 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ sK5 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ sK5 )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK5 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( ( do @ Y2 @ Y1 @ Y4 @ Y3 )
=> ( in @ X1 @ Y0 @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK5 @ Y3 )
=> ( ( number @ Y0 @ one @ Y3 )
& ( entry_box @ Y0 @ Y3 )
& ( userid @ u @ X1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f139]) ).
thf(f139,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK5 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ sK5 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ sK5 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ sK5 )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK5 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( eiw_di @ Y5 @ Y4 )
=> ( ( do @ Y3 @ Y2 @ Y5 @ Y4 )
=> ( in @ Y0 @ Y1 @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK5 @ Y4 )
=> ( ( number @ Y1 @ one @ Y4 )
& ( entry_box @ Y1 @ Y4 )
& ( userid @ u @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f137]) ).
thf(f137,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK5 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ sK5 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ sK5 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ sK5 )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK5 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( eiw_di @ Y5 @ Y4 )
=> ( ( do @ Y3 @ Y2 @ Y5 @ Y4 )
=> ( in @ Y0 @ Y1 @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK5 @ Y4 )
=> ( ( number @ Y1 @ one @ Y4 )
& ( entry_box @ Y1 @ Y4 )
& ( userid @ u @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f273,plain,
! [X2: $i,X3: $i,X0: $i,X1: mworld] :
( ( $false
= ( mrel @ X1 @ ( sK7 @ ( sK2 @ X0 @ X1 @ X2 @ X3 ) @ X0 @ X3 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( string @ X0 @ X1 ) )
| ( $false
= ( entry_box @ X2 @ X1 ) )
| ( $false
= ( entry_box @ X2 @ ( sK6 @ X0 @ X2 ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X0 @ X2 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( ( eiw_di @ ( sK2 @ X0 @ X1 @ X2 @ X3 ) @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f272]) ).
thf(f272,plain,
! [X2: $i,X3: $i,X0: $i,X1: mworld] :
( ( $false = $true )
| ( $false
= ( string @ X0 @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X0 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( mrel @ X1 @ ( sK7 @ ( sK2 @ X0 @ X1 @ X2 @ X3 ) @ X0 @ X3 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK6 @ X0 @ X2 ) ) )
| ( ( eiw_di @ ( sK2 @ X0 @ X1 @ X2 @ X3 ) @ sK5 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X0 @ X1 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( entry_box @ X2 @ X1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f269]) ).
thf(f269,plain,
! [X2: $i,X3: $i,X0: $i,X1: mworld] :
( ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X0 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( ( eiw_di @ ( sK2 @ X0 @ X1 @ X2 @ X3 ) @ sK5 )
= $false )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X0 @ X1 ) )
| ( $false
= ( entry_box @ X2 @ ( sK6 @ X0 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( entry_box @ X2 @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X0 @ X2 ) ) )
| ( $false
= ( string @ X0 @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK6 @ X0 @ X2 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false = $true )
| ( ( eiw_di @ ( sK2 @ X0 @ X1 @ X2 @ X3 ) @ sK5 )
= $false )
| ( $false
= ( mrel @ X1 @ ( sK7 @ ( sK2 @ X0 @ X1 @ X2 @ X3 ) @ X0 @ X3 @ X2 ) ) ) ),
inference(superposition,[status(thm)],[f173,f257]) ).
thf(f257,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( eiw_di @ ( sK9 @ X0 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X3 @ X1 ) @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X1 @ X2 ) )
| ( $false
= ( mrel @ X2 @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X3 @ X2 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ sK5 ) )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f256]) ).
thf(f256,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( $false
= ( eiw_di @ X3 @ X2 ) )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( eiw_di @ X1 @ X2 ) )
| ( $false
= ( eiw_di @ ( sK9 @ X0 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X3 @ X1 ) @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ X2 ) )
| ( $false
= ( mrel @ X2 @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f252]) ).
thf(f252,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( eiw_di @ X3 @ X2 ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ ( sK9 @ X0 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X3 @ X1 ) @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ X2 ) )
| ( $false
= ( mrel @ X2 @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ X2 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ sK5 ) )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ sK5 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( entry_box @ X1 @ ( sK6 @ X0 @ X1 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( number @ X1 @ one @ ( sK6 @ X0 @ X1 ) ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false = $true )
| ( $false
= ( userid @ u @ X0 @ ( sK6 @ X0 @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f241,f174]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X2 @ ( sK9 @ X1 @ X3 @ X4 @ X2 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f172]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) )
| ( ( ( do @ X4 @ X3 @ ( sK9 @ X1 @ X3 @ X4 @ X2 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ ( sK9 @ X1 @ X3 @ X4 @ X2 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) )
= $false )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f171]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( ( eiw_di @ ( sK9 @ X1 @ X3 @ X4 @ X2 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( ( do @ X4 @ X3 @ ( sK9 @ X1 @ X3 @ X4 @ X2 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ ( sK9 @ X1 @ X3 @ X4 @ X2 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f170]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( ( do @ X4 @ X3 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) ) )
@ ( sK9 @ X1 @ X3 @ X4 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) ) ),
inference(sigma_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( ( do @ X4 @ X3 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) ) ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f167]) ).
thf(f241,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ X1 @ X3 @ ( sK9 @ X4 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X0 @ X5 ) @ ( sK7 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) )
= $true )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( number @ X5 @ one @ ( sK6 @ X4 @ X5 ) ) )
| ( $false
= ( eiw_di @ X1 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( entry_box @ X3 @ X2 ) )
| ( $false
= ( eiw_di @ X3 @ X2 ) )
| ( $false
= ( eiw_di @ X5 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ sK5 ) )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( $false
= ( entry_box @ X5 @ ( sK6 @ X4 @ X5 ) ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK9 @ X4 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X0 @ X5 ) @ ( sK7 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( mrel @ X2 @ ( sK7 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( string @ X1 @ X2 ) )
| ( $false
= ( userid @ u @ X4 @ ( sK6 @ X4 @ X5 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f238]) ).
thf(f238,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( ( in @ X1 @ X3 @ ( sK9 @ X4 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X0 @ X5 ) @ ( sK7 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) )
= $true )
| ( $false
= ( entry_box @ X3 @ X2 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ sK5 ) )
| ( $false
= ( userid @ u @ X4 @ ( sK6 @ X4 @ X5 ) ) )
| ( $false
= ( string @ X1 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( eiw_di @ X5 @ sK5 ) )
| ( $false
= ( mrel @ X2 @ ( sK7 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( eiw_di @ X3 @ X2 ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( number @ X5 @ one @ ( sK6 @ X4 @ X5 ) ) )
| ( $false
= ( entry_box @ X5 @ ( sK6 @ X4 @ X5 ) ) )
| ( $false
= ( eiw_di @ X1 @ X2 ) )
| ( $false
= ( eiw_di @ ( sK9 @ X4 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X0 @ X5 ) @ ( sK7 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) ) ),
inference(superposition,[status(thm)],[f175,f110]) ).
thf(f110,plain,
! [X2: $i,X3: $i,X1: mworld,X6: $i,X4: $i,X5: mworld] :
( ( $false
= ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ X6 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( in @ X3 @ X4 @ X6 @ X5 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( eiw_di @ X4 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( eiw_di @ X6 @ X5 ) )
| ( $false
= ( string @ X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X2: $i,X3: $i,X1: mworld,X6: $i,X4: $i,X5: mworld] :
( ( $false
= ( string @ X3 @ X1 ) )
| ( $true
= ( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ X6 @ X5 )
=> ( in @ X3 @ X4 @ X6 @ X5 ) ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X6 @ X5 ) )
| ( $false
= ( eiw_di @ X4 @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
! [X2: $i,X3: $i,X1: mworld,X6: $i,X4: $i,X5: mworld] :
( ( ( ( eiw_di @ X6 @ X5 )
=> ( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ X6 @ X5 )
=> ( in @ X3 @ X4 @ X6 @ X5 ) ) )
= $true )
| ( $false
= ( eiw_di @ X4 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( string @ X3 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f107]) ).
thf(f107,plain,
! [X2: $i,X3: $i,X1: mworld,X6: $i,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ X1 @ X5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X5 )
=> ( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ Y0 @ X5 )
=> ( in @ X3 @ X4 @ Y0 @ X5 ) ) )
@ X6 ) )
| ( $false
= ( string @ X3 @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( eiw_di @ X4 @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( eiw_di @ X4 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( string @ X3 @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X5 )
=> ( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ Y0 @ X5 )
=> ( in @ X3 @ X4 @ Y0 @ X5 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( eiw_di @ X4 @ X1 ) )
| ( $false
= ( string @ X3 @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( ( ( mrel @ X1 @ X5 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X5 )
=> ( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ Y0 @ X5 )
=> ( in @ X3 @ X4 @ Y0 @ X5 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f104]) ).
thf(f104,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( string @ X3 @ X1 ) )
| ( $false
= ( eiw_di @ X4 @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ Y1 @ Y0 )
=> ( in @ X3 @ X4 @ Y1 @ Y0 ) ) ) ) )
@ X5 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( string @ X3 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ Y1 @ Y0 )
=> ( in @ X3 @ X4 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( eiw_di @ X4 @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( string @ X3 @ X1 ) )
| ( ( ( eiw_di @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ X1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ Y1 @ Y0 )
=> ( in @ X3 @ X4 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( eiw_di @ X4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( eiw_di @ X4 @ X1 ) )
| ( $false
= ( ( entry_box @ X4 @ X1 )
& ( string @ X3 @ X1 ) ) )
| ( ( ( eiw_di @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ X1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ( do @ X2 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ Y1 @ Y0 )
=> ( in @ X3 @ X4 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true )
| ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( eiw_di @ X4 @ X1 ) )
| ( $false
= ( ( entry_box @ X4 @ X1 )
& ( string @ X3 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) ) ) )
@ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( eiw_di @ X4 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( ( entry_box @ X4 @ X1 )
& ( string @ X3 @ X1 ) ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( eiw_di @ X4 @ X1 ) )
| ( ( ( ( entry_box @ X4 @ X1 )
& ( string @ X3 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( eiw_di @ X4 @ X1 )
=> ( ( ( entry_box @ X4 @ X1 )
& ( string @ X3 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ( ( entry_box @ Y0 @ X1 )
& ( string @ X3 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( ( do @ X2 @ Y1 @ Y3 @ Y2 )
=> ( in @ X3 @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ( ( entry_box @ Y0 @ X1 )
& ( string @ X3 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( ( do @ X2 @ Y1 @ Y3 @ Y2 )
=> ( in @ X3 @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( eiw_di @ X3 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ( ( entry_box @ Y0 @ X1 )
& ( string @ X3 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( ( do @ X2 @ Y1 @ Y3 @ Y2 )
=> ( in @ X3 @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
=> ( ( ( entry_box @ Y1 @ X1 )
& ( string @ Y0 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ X1 )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( ( do @ X2 @ Y2 @ Y4 @ Y3 )
=> ( in @ Y0 @ Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
=> ( ( ( entry_box @ Y1 @ X1 )
& ( string @ Y0 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ X1 )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( ( do @ X2 @ Y2 @ Y4 @ Y3 )
=> ( in @ Y0 @ Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( ( eiw_di @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
=> ( ( ( entry_box @ Y1 @ X1 )
& ( string @ Y0 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ X1 )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( ( do @ X2 @ Y2 @ Y4 @ Y3 )
=> ( in @ Y0 @ Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ X1 )
=> ( ( ( entry_box @ Y2 @ X1 )
& ( string @ Y1 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ X1 )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ X1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( eiw_di @ Y5 @ Y4 )
=> ( ( do @ Y0 @ Y3 @ Y5 @ Y4 )
=> ( in @ Y1 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ X1 )
=> ( ( ( entry_box @ Y2 @ X1 )
& ( string @ Y1 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ X1 )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ X1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( eiw_di @ Y5 @ Y4 )
=> ( ( do @ Y0 @ Y3 @ Y5 @ Y4 )
=> ( in @ Y1 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ X1 )
=> ( ( ( entry_box @ Y2 @ X1 )
& ( string @ Y1 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ X1 )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ X1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( eiw_di @ Y5 @ Y4 )
=> ( ( do @ Y0 @ Y3 @ Y5 @ Y4 )
=> ( in @ Y1 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y0 )
=> ( ( ( entry_box @ Y3 @ Y0 )
& ( string @ Y2 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y0 )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( eiw_di @ Y6 @ Y5 )
=> ( ( do @ Y1 @ Y4 @ Y6 @ Y5 )
=> ( in @ Y2 @ Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y0 )
=> ( ( ( entry_box @ Y3 @ Y0 )
& ( string @ Y2 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y0 )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( eiw_di @ Y6 @ Y5 )
=> ( ( do @ Y1 @ Y4 @ Y6 @ Y5 )
=> ( in @ Y2 @ Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f83]) ).
thf(f83,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] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( 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] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( string @ Y1 )
@ ( entry_box @ Y2 ) )
@ ( ^ [Y3: $i > mworld > $o,Y4: mworld] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( eiw_di @ Y5 @ Y4 )
& ( 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] :
( ( eiw_di @ Y6 @ Y5 )
=> ( 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)],[f73,f65,f64,f78,f78,f78,f76,f70,f68,f64,f78,f76]) ).
thf(f73,plain,
( $true
= ( 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 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( 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 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,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)],[f17]) ).
thf(f17,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/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',ax3) ).
thf(f175,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( do @ X4 @ X3 @ ( sK9 @ X1 @ X3 @ X4 @ X2 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f172]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( eiw_di @ ( sK9 @ X1 @ X3 @ X4 @ X2 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( userid @ u @ X1 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f171]) ).
thf(f103,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $true
= ( eiw_di @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) @ X1 ) )
| ( $false
= ( string @ X3 @ X1 ) )
| ( $false
= ( eiw_di @ X4 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( eiw_di @ X3 @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f346,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f345,f337,f334]) ).
thf(f345,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f344]) ).
thf(f344,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $false = $true )
| ( $false
= ( entry_box @ X1 @ sK5 ) ) ),
inference(forward_demodulation,[status(thm)],[f326,f138]) ).
thf(f326,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f325]) ).
thf(f325,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false = $true )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( ( eiw_di @ X0 @ sK5 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f321]) ).
thf(f321,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false = $true )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( string @ X0 @ sK5 ) ) ),
inference(superposition,[status(thm)],[f296,f103]) ).
thf(f296,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK5 @ X1 @ X2 ) @ sK5 ) )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f295]) ).
thf(f295,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK5 @ X1 @ X2 ) @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $false = $true )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(forward_demodulation,[status(thm)],[f287,f138]) ).
thf(f287,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK5 @ X1 @ X2 ) @ sK5 ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ( $false
= ( entry_box @ X1 @ sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f286]) ).
thf(f286,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK5 @ X1 @ X2 ) @ sK5 ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ( $false
= ( entry_box @ X1 @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f277]) ).
thf(f277,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( ( mrel @ mactual @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK5 @ X1 @ X2 ) @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( string @ X0 @ sK5 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ sK5 @ X1 @ X2 ) @ sK5 ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true ) ),
inference(superposition,[status(thm)],[f265,f159]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( mrel @ sK5 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
= $true )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $true
= ( mrel @ sK5 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f157]) ).
thf(f157,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( ( ( mrel @ sK5 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( ( do @ X4 @ X3 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) ) ) ) )
= $false )
| ( $true
= ( mrel @ sK5 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f155]) ).
thf(f265,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( mrel @ X2 @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X1 @ X2 ) )
| ( $false
= ( eiw_di @ X3 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ X2 ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f264]) ).
thf(f264,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( entry_box @ X1 @ X2 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X3 @ X2 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ X2 ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ X2 @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ sK5 ) )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f261]) ).
thf(f261,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false = $true )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $false
= ( entry_box @ X1 @ X2 ) )
| ( $false
= ( eiw_di @ X3 @ X2 ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ sK5 ) )
| ( $false
= ( mrel @ X2 @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ sK5 ) )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X1 @ X2 ) ) ),
inference(superposition,[status(thm)],[f163,f249]) ).
thf(f249,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( eiw_di @ ( sK8 @ X0 @ X1 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X3 ) @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( entry_box @ X1 @ X2 ) )
| ( $false
= ( eiw_di @ X1 @ X2 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X3 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( mrel @ X2 @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f248]) ).
thf(f248,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ X2 ) )
| ( $false
= ( mrel @ X2 @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( $false
= ( eiw_di @ X1 @ X2 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ ( sK8 @ X0 @ X1 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X3 ) @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ X3 @ X2 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ sK5 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f245]) ).
thf(f245,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( entry_box @ X1 @ X2 ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( ( mrel @ sK5 @ ( sK6 @ X0 @ X1 ) )
= $true )
| ( $false
= ( eiw_di @ ( sK8 @ X0 @ X1 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X3 ) @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( eiw_di @ X3 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ X2 @ ( sK7 @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ sK5 ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( eiw_di @ X1 @ X2 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X0 @ X2 @ X1 @ X3 ) @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(superposition,[status(thm)],[f164,f219]) ).
thf(f219,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X1 @ X3 @ ( sK8 @ X4 @ X5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK7 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( eiw_di @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ sK5 ) )
| ( $false
= ( entry_box @ X3 @ X2 ) )
| ( $false
= ( eiw_di @ X3 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( eiw_di @ ( sK8 @ X4 @ X5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK7 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( string @ X1 @ X2 ) )
| ( $false
= ( mrel @ X2 @ ( sK7 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $true
= ( mrel @ sK5 @ ( sK6 @ X4 @ X5 ) ) )
| ( $false
= ( eiw_di @ X5 @ sK5 ) )
| ( $false
= ( eiw_di @ X0 @ X2 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f217]) ).
thf(f217,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( entry_box @ X3 @ X2 ) )
| ( $false
= ( mrel @ X2 @ ( sK7 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( string @ X1 @ X2 ) )
| ( ( eiw_di @ X0 @ sK5 )
= $false )
| ( $false
= ( eiw_di @ X3 @ X2 ) )
| ( $false
= ( eiw_di @ ( sK8 @ X4 @ X5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK7 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $true
= ( in @ X1 @ X3 @ ( sK8 @ X4 @ X5 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK7 @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false = $true )
| ( $true
= ( mrel @ sK5 @ ( sK6 @ X4 @ X5 ) ) )
| ( $false
= ( eiw_di @ X1 @ X2 ) )
| ( $false
= ( eiw_di @ ( sK2 @ X1 @ X2 @ X3 @ X0 ) @ sK5 ) )
| ( $false
= ( eiw_di @ X5 @ sK5 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( eiw_di @ X0 @ X2 ) ) ),
inference(superposition,[status(thm)],[f110,f165]) ).
thf(f165,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( do @ X4 @ X3 @ ( sK8 @ X1 @ X2 @ X3 @ X4 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $true
= ( mrel @ sK5 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f162]) ).
thf(f162,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( ( do @ X4 @ X3 @ ( sK8 @ X1 @ X2 @ X3 @ X4 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ ( sK8 @ X1 @ X2 @ X3 @ X4 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $true
= ( mrel @ sK5 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f161]) ).
thf(f161,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( ( eiw_di @ ( sK8 @ X1 @ X2 @ X3 @ X4 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( ( do @ X4 @ X3 @ ( sK8 @ X1 @ X2 @ X3 @ X4 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ ( sK8 @ X1 @ X2 @ X3 @ X4 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $true
= ( mrel @ sK5 @ ( sK6 @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f160]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( mrel @ sK5 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( ( do @ X4 @ X3 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) ) )
@ ( sK8 @ X1 @ X2 @ X3 @ X4 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) ) ),
inference(sigma_clausification,[status(thm)],[f158]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( ( do @ X4 @ X3 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) ) ) ) )
| ( $true
= ( mrel @ sK5 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f157]) ).
thf(f164,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X2 @ ( sK8 @ X1 @ X2 @ X3 @ X4 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) )
| ( $true
= ( mrel @ sK5 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f162]) ).
thf(f163,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( eiw_di @ ( sK8 @ X1 @ X2 @ X3 @ X4 ) @ ( sK7 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( eiw_di @ X3 @ sK5 ) )
| ( $false
= ( eiw_di @ X4 @ sK5 ) )
| ( $true
= ( mrel @ sK5 @ ( sK6 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK5 ) )
| ( $false
= ( eiw_di @ X1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.28 % Problem : NLP266^23 : TPTP v9.2.1. Released v8.1.0.
% 0.11/0.29 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.55 % Computer : n002.cluster.edu
% 0.16/0.55 % Model : x86_64 x86_64
% 0.16/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.55 % Memory : 8042.1875MB
% 0.16/0.55 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.55 % CPULimit : 300
% 0.16/0.55 % WCLimit : 300
% 0.16/0.55 % DateTime : Tue Feb 24 10:54:35 EST 2026
% 0.16/0.55 % CPUTime :
% 0.16/0.55 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.79 ---- Original DTF file ---
% 0.19/0.79 thf(spec,logic,$$dhol).
% 0.19/0.79 %------------------------------------------------------------------------------
% 0.19/0.79 % File : NLP266^23 : TPTP v9.2.1. Released v8.1.0.
% 0.19/0.79 % Domain : Natural Language Processing
% 0.19/0.79 % Problem : Generation of abstract instructions: enter a number in a box
% 0.19/0.79 % Version : [BP13] axioms.
% 0.19/0.79 % English :
% 0.19/0.79
% 0.19/0.79 % Refs : [Sto00] Stone (2000), Towards a Computational Account of Knowl
% 0.19/0.79 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.19/0.79 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.19/0.79 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.19/0.79 % Source : [TPTP]
% 0.19/0.79 % Names : APM003+1 [QMLTP]
% 0.19/0.79
% 0.19/0.79 % Status : Theorem
% 0.19/0.79 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.60 v8.2.0, 0.77 v8.1.0
% 0.19/0.79 % Syntax : Number of formulae : 40 ( 12 unt; 22 typ; 10 def)
% 0.19/0.79 % Number of atoms : 78 ( 10 equ; 0 cnn)
% 0.19/0.79 % Maximal formula atoms : 18 ( 4 avg)
% 0.19/0.79 % Number of connectives : 120 ( 1 ~; 1 |; 5 &; 107 @)
% 0.19/0.79 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.19/0.79 % Maximal formula depth : 20 ( 5 avg)
% 0.19/0.79 % Number of types : 3 ( 1 usr)
% 0.19/0.79 % Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% 0.19/0.79 % Number of symbols : 22 ( 21 usr; 3 con; 0-4 aty)
% 0.19/0.79 % Number of variables : 48 ( 35 ^; 10 !; 3 ?; 48 :)
% 0.19/0.79 % SPC : TH0_THM_EQU_NAR
% 0.19/0.79
% 0.19/0.79 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.19/0.79 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.19/0.79 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.19/0.79 % $modal == [$constants == $rigid,$quantification == $decreasing,
% 0.19/0.79 % $modalities == $modal_system_S5].
% 0.19/0.79 %------------------------------------------------------------------------------
% 0.19/0.79 thf(mworld,type,
% 0.19/0.79 mworld: $tType ).
% 0.19/0.79
% 0.19/0.79 thf(mrel_type,type,
% 0.19/0.79 mrel: mworld > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(mactual_type,type,
% 0.19/0.79 mactual: mworld ).
% 0.19/0.79
% 0.19/0.79 thf(mlocal_type,type,
% 0.19/0.79 mlocal: ( mworld > $o ) > $o ).
% 0.19/0.79
% 0.19/0.79 thf(mlocal_def,definition,
% 0.19/0.79 ( mlocal
% 0.19/0.79 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(mnot_type,type,
% 0.19/0.79 mnot: ( mworld > $o ) > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(mand_type,type,
% 0.19/0.79 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(mor_type,type,
% 0.19/0.79 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(mimplies_type,type,
% 0.19/0.79 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(mequiv_type,type,
% 0.19/0.79 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(mnot_def,definition,
% 0.19/0.79 ( mnot
% 0.19/0.79 = ( ^ [A: mworld > $o,W: mworld] :
% 0.19/0.79 ~ ( A @ W ) ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(mand_def,definition,
% 0.19/0.79 ( mand
% 0.19/0.79 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.79 ( ( A @ W )
% 0.19/0.79 & ( B @ W ) ) ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(mor_def,definition,
% 0.19/0.79 ( mor
% 0.19/0.79 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.79 ( ( A @ W )
% 0.19/0.79 | ( B @ W ) ) ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(mimplies_def,definition,
% 0.19/0.79 ( mimplies
% 0.19/0.79 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.79 ( ( A @ W )
% 0.19/0.79 => ( B @ W ) ) ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(mequiv_def,definition,
% 0.19/0.79 ( mequiv
% 0.19/0.79 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.79 ( ( A @ W )
% 0.19/0.79 <=> ( B @ W ) ) ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(mbox_type,type,
% 0.19/0.79 mbox: ( mworld > $o ) > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(mbox_def,definition,
% 0.19/0.79 ( mbox
% 0.19/0.79 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.19/0.79 ! [V: mworld] :
% 0.19/0.79 ( ( mrel @ W @ V )
% 0.19/0.79 => ( Phi @ V ) ) ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(mdia_type,type,
% 0.19/0.79 mdia: ( mworld > $o ) > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(mdia_def,definition,
% 0.19/0.79 ( mdia
% 0.19/0.79 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.19/0.79 ? [V: mworld] :
% 0.19/0.79 ( ( mrel @ W @ V )
% 0.19/0.79 & ( Phi @ V ) ) ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(mrel_reflexive,axiom,
% 0.19/0.79 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.19/0.79
% 0.19/0.79 thf(mrel_euclidean,axiom,
% 0.19/0.79 ! [W: mworld,V: mworld,U: mworld] :
% 0.19/0.79 ( ( ( mrel @ W @ U )
% 0.19/0.79 & ( mrel @ W @ V ) )
% 0.19/0.79 => ( mrel @ U @ V ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(eiw_di_type,type,
% 0.19/0.79 eiw_di: $i > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(eiw_di_nonempty,axiom,
% 0.19/0.79 ! [W: mworld] :
% 0.19/0.79 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.19/0.79
% 0.19/0.79 thf(eiw_di_decr,axiom,
% 0.19/0.79 ! [W: mworld,V: mworld,X: $i] :
% 0.19/0.79 ( ( ( eiw_di @ X @ W )
% 0.19/0.79 & ( mrel @ V @ W ) )
% 0.19/0.79 => ( eiw_di @ X @ V ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(mforall_di_type,type,
% 0.19/0.79 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(mforall_di_def,definition,
% 0.19/0.79 ( mforall_di
% 0.19/0.79 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.19/0.79 ! [X: $i] :
% 0.19/0.79 ( ( eiw_di @ X @ W )
% 0.19/0.79 => ( A @ X @ W ) ) ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(mexists_di_type,type,
% 0.19/0.79 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(mexists_di_def,definition,
% 0.19/0.79 ( mexists_di
% 0.19/0.79 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.19/0.79 ? [X: $i] :
% 0.19/0.79 ( ( eiw_di @ X @ W )
% 0.19/0.79 & ( A @ X @ W ) ) ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(u_decl,type,
% 0.19/0.79 u: $i ).
% 0.19/0.79
% 0.19/0.79 thf(one_decl,type,
% 0.19/0.79 one: $i ).
% 0.19/0.79
% 0.19/0.79 thf(number_decl,type,
% 0.19/0.79 number: $i > $i > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(string_decl,type,
% 0.19/0.79 string: $i > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(in_decl,type,
% 0.19/0.79 in: $i > $i > $i > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(do_decl,type,
% 0.19/0.79 do: $i > $i > $i > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(entry_box_decl,type,
% 0.19/0.79 entry_box: $i > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(userid_decl,type,
% 0.19/0.79 userid: $i > $i > mworld > $o ).
% 0.19/0.79
% 0.19/0.79 thf(ax1,axiom,
% 0.19/0.79 ( mlocal
% 0.19/0.79 @ ( mbox
% 0.19/0.79 @ ( mexists_di
% 0.19/0.79 @ ^ [I: $i] : ( mbox @ ( mand @ ( userid @ u @ I ) @ ( string @ I ) ) ) ) ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(ax2,axiom,
% 0.19/0.79 ( mlocal
% 0.19/0.79 @ ( mexists_di
% 0.19/0.79 @ ^ [B: $i] : ( mbox @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(ax3,axiom,
% 0.19/0.79 ( mlocal
% 0.19/0.79 @ ( mbox
% 0.19/0.79 @ ( mforall_di
% 0.19/0.79 @ ^ [S: $i] :
% 0.19/0.79 ( mforall_di
% 0.19/0.79 @ ^ [I: $i] :
% 0.19/0.79 ( mforall_di
% 0.19/0.79 @ ^ [B: $i] :
% 0.19/0.79 ( mimplies @ ( mand @ ( string @ I ) @ ( entry_box @ B ) )
% 0.19/0.79 @ ( mexists_di
% 0.19/0.79 @ ^ [A: $i] :
% 0.19/0.79 ( mbox
% 0.19/0.79 @ ( mforall_di
% 0.19/0.79 @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.79
% 0.19/0.79 thf(con,conjecture,
% 0.19/0.79 ( mlocal
% 0.19/0.79 @ ( mbox
% 0.19/0.79 @ ( mexists_di
% 0.19/0.79 @ ^ [I: $i] :
% 0.19/0.79 ( mexists_di
% 0.19/0.79 @ ^ [B: $i] :
% 0.19/0.79 ( mexists_di
% 0.19/0.79 @ ^ [A: $i] :
% 0.19/0.79 ( mexists_di
% 0.19/0.79 @ ^ [S: $i] :
% 0.19/0.79 ( mand @ ( mbox @ ( mand @ ( userid @ u @ I ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
% 0.19/0.79 @ ( mbox
% 0.19/0.79 @ ( mforall_di
% 0.19/0.79 @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.79
% 0.19/0.79 %------------------------------------------------------------------------------
% 0.19/0.79 ------------------------
% 1.75/2.15 ---- Embedded in THF ---
% 1.75/2.15 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.75/2.15 %%% Generated on Tue Feb 24 10:54:36 EST 2026
% 1.75/2.15 %%% using '$$dhol' embedding, version 1.3.0.
% 1.75/2.15 %%% Logic specification used:
% 1.75/2.15 %%% thf(spec, logic, $$dhol).
% 1.75/2.15
% 1.75/2.15 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2DTF11589.p
% See solution above
% 1.75/2.15 ------------------------
% 1.75/2.16 ---- Cleaned THF ---
% 1.75/2.16 thf(mworld,type,
% 1.75/2.16 mworld: $tType ).
% 1.75/2.16
% 1.75/2.16 thf(mrel_type,type,
% 1.75/2.16 mrel: mworld > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(mactual_type,type,
% 1.75/2.16 mactual: mworld ).
% 1.75/2.16
% 1.75/2.16 thf(mlocal_type,type,
% 1.75/2.16 mlocal: ( mworld > $o ) > $o ).
% 1.75/2.16
% 1.75/2.16 thf(mlocal_def,definition,
% 1.75/2.16 ( mlocal
% 1.75/2.16 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(mnot_type,type,
% 1.75/2.16 mnot: ( mworld > $o ) > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(mand_type,type,
% 1.75/2.16 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(mor_type,type,
% 1.75/2.16 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(mimplies_type,type,
% 1.75/2.16 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(mequiv_type,type,
% 1.75/2.16 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(mnot_def,definition,
% 1.75/2.16 ( mnot
% 1.75/2.16 = ( ^ [A: mworld > $o,W: mworld] :
% 1.75/2.16 ~ ( A @ W ) ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(mand_def,definition,
% 1.75/2.16 ( mand
% 1.75/2.16 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.75/2.16 ( ( A @ W )
% 1.75/2.16 & ( B @ W ) ) ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(mor_def,definition,
% 1.75/2.16 ( mor
% 1.75/2.16 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.75/2.16 ( ( A @ W )
% 1.75/2.16 | ( B @ W ) ) ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(mimplies_def,definition,
% 1.75/2.16 ( mimplies
% 1.75/2.16 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.75/2.16 ( ( A @ W )
% 1.75/2.16 => ( B @ W ) ) ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(mequiv_def,definition,
% 1.75/2.16 ( mequiv
% 1.75/2.16 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.75/2.16 ( ( A @ W )
% 1.75/2.16 <=> ( B @ W ) ) ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(mbox_type,type,
% 1.75/2.16 mbox: ( mworld > $o ) > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(mbox_def,definition,
% 1.75/2.16 ( mbox
% 1.75/2.16 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.75/2.16 ! [V: mworld] :
% 1.75/2.16 ( ( mrel @ W @ V )
% 1.75/2.16 => ( Phi @ V ) ) ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(mdia_type,type,
% 1.75/2.16 mdia: ( mworld > $o ) > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(mdia_def,definition,
% 1.75/2.16 ( mdia
% 1.75/2.16 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.75/2.16 ? [V: mworld] :
% 1.75/2.16 ( ( mrel @ W @ V )
% 1.75/2.16 & ( Phi @ V ) ) ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(mrel_reflexive,axiom,
% 1.75/2.16 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.75/2.16
% 1.75/2.16 thf(mrel_euclidean,axiom,
% 1.75/2.16 ! [W: mworld,V: mworld,U: mworld] :
% 1.75/2.16 ( ( ( mrel @ W @ U )
% 1.75/2.16 & ( mrel @ W @ V ) )
% 1.75/2.16 => ( mrel @ U @ V ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(eiw_di_type,type,
% 1.75/2.16 eiw_di: $i > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(eiw_di_nonempty,axiom,
% 1.75/2.16 ! [W: mworld] :
% 1.75/2.16 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 1.75/2.16
% 1.75/2.16 thf(eiw_di_decr,axiom,
% 1.75/2.16 ! [W: mworld,V: mworld,X: $i] :
% 1.75/2.16 ( ( ( eiw_di @ X @ W )
% 1.75/2.16 & ( mrel @ V @ W ) )
% 1.75/2.16 => ( eiw_di @ X @ V ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(mforall_di_type,type,
% 1.75/2.16 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(mforall_di_def,definition,
% 1.75/2.16 ( mforall_di
% 1.75/2.16 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.75/2.16 ! [X: $i] :
% 1.75/2.16 ( ( eiw_di @ X @ W )
% 1.75/2.16 => ( A @ X @ W ) ) ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(mexists_di_type,type,
% 1.75/2.16 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(mexists_di_def,definition,
% 1.75/2.16 ( mexists_di
% 1.75/2.16 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.75/2.16 ? [X: $i] :
% 1.75/2.16 ( ( eiw_di @ X @ W )
% 1.75/2.16 & ( A @ X @ W ) ) ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(u_decl,type,
% 1.75/2.16 u: $i ).
% 1.75/2.16
% 1.75/2.16 thf(one_decl,type,
% 1.75/2.16 one: $i ).
% 1.75/2.16
% 1.75/2.16 thf(number_decl,type,
% 1.75/2.16 number: $i > $i > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(string_decl,type,
% 1.75/2.16 string: $i > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(in_decl,type,
% 1.75/2.16 in: $i > $i > $i > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(do_decl,type,
% 1.75/2.16 do: $i > $i > $i > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(entry_box_decl,type,
% 1.75/2.16 entry_box: $i > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(userid_decl,type,
% 1.75/2.16 userid: $i > $i > mworld > $o ).
% 1.75/2.16
% 1.75/2.16 thf(ax1,axiom,
% 1.75/2.16 ( mlocal
% 1.75/2.16 @ ( mbox
% 1.75/2.16 @ ( mexists_di
% 1.75/2.16 @ ^ [I: $i] : ( mbox @ ( mand @ ( userid @ u @ I ) @ ( string @ I ) ) ) ) ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(ax2,axiom,
% 1.75/2.16 ( mlocal
% 1.75/2.16 @ ( mexists_di
% 1.75/2.16 @ ^ [B: $i] : ( mbox @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(ax3,axiom,
% 1.75/2.16 ( mlocal
% 1.75/2.16 @ ( mbox
% 1.75/2.16 @ ( mforall_di
% 1.75/2.16 @ ^ [S: $i] :
% 1.75/2.16 ( mforall_di
% 1.75/2.16 @ ^ [I: $i] :
% 1.75/2.16 ( mforall_di
% 1.75/2.16 @ ^ [B: $i] :
% 1.75/2.16 ( mimplies @ ( mand @ ( string @ I ) @ ( entry_box @ B ) )
% 1.75/2.16 @ ( mexists_di
% 1.75/2.16 @ ^ [A: $i] :
% 1.75/2.16 ( mbox
% 1.75/2.16 @ ( mforall_di
% 1.75/2.16 @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ).
% 1.75/2.16
% 1.75/2.16 thf(con,conjecture,
% 1.75/2.16 ( mlocal
% 1.75/2.16 @ ( mbox
% 1.75/2.16 @ ( mexists_di
% 1.75/2.16 @ ^ [I: $i] :
% 1.75/2.16 ( mexists_di
% 1.75/2.16 @ ^ [B: $i] :
% 1.75/2.16 ( mexists_di
% 1.75/2.16 @ ^ [A: $i] :
% 1.75/2.16 ( mexists_di
% 1.75/2.16 @ ^ [S: $i] :
% 1.75/2.16 ( mand @ ( mbox @ ( mand @ ( userid @ u @ I ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
% 1.75/2.16 @ ( mbox
% 1.75/2.16 @ ( mforall_di
% 1.75/2.16 @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ).
% 1.75/2.16 ------------------------
% 1.75/2.17 % (11729)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_11589 for (2999ds/4Mi)
% 1.75/2.17 % (11728)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/183Mi)
% 1.75/2.17 % (11729)Instruction limit reached!
% 1.75/2.17 % (11729)------------------------------
% 1.75/2.17 % (11729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/2.17 % (11729)Termination reason: Unknown
% 1.75/2.17 % (11729)Termination phase: Function definition elimination
% 1.75/2.17
% 1.75/2.17 % (11729)Memory used [KB]: 1023
% 1.75/2.17 % (11729)Time elapsed: 0.003 s
% 1.75/2.17 % (11729)Instructions burned: 5 (million)
% 1.75/2.17 % (11729)------------------------------
% 1.75/2.17 % (11729)------------------------------
% 1.75/2.18 % (11730)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_11589 for (2999ds/27Mi)
% 1.75/2.18 % (11731)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/2Mi)
% 1.75/2.18 % (11732)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_11589 for (2999ds/2Mi)
% 1.75/2.18 % (11734)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/18Mi)
% 1.75/2.18 % (11733)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_11589 for (2999ds/275Mi)
% 1.75/2.18 % (11732)Instruction limit reached!
% 1.75/2.18 % (11732)------------------------------
% 1.75/2.18 % (11732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/2.18 % (11732)Termination reason: Unknown
% 1.75/2.18 % (11732)Termination phase: shuffling
% 1.75/2.18
% 1.75/2.18 % (11732)Memory used [KB]: 1023
% 1.75/2.18 % (11732)Time elapsed: 0.003 s
% 1.75/2.18 % (11732)Instructions burned: 2 (million)
% 1.75/2.18 % (11732)------------------------------
% 1.75/2.18 % (11732)------------------------------
% 1.75/2.18 % (11731)Instruction limit reached!
% 1.75/2.18 % (11731)------------------------------
% 1.75/2.18 % (11731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/2.18 % (11731)Termination reason: Unknown
% 1.75/2.18 % (11731)Termination phase: Property scanning
% 1.75/2.18
% 1.75/2.18 % (11731)Memory used [KB]: 1023
% 1.75/2.18 % (11731)Time elapsed: 0.004 s
% 1.75/2.18 % (11731)Instructions burned: 3 (million)
% 1.75/2.18 % (11731)------------------------------
% 1.75/2.18 % (11731)------------------------------
% 1.75/2.18 % (11735)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/3Mi)
% 1.75/2.18 % (11735)Instruction limit reached!
% 1.75/2.18 % (11735)------------------------------
% 1.75/2.18 % (11735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/2.18 % (11735)Termination reason: Unknown
% 1.75/2.18 % (11735)Termination phase: Property scanning
% 1.75/2.18
% 1.75/2.18 % (11735)Memory used [KB]: 1023
% 1.75/2.18 % (11735)Time elapsed: 0.002 s
% 1.75/2.18 % (11735)Instructions burned: 3 (million)
% 1.75/2.18 % (11735)------------------------------
% 1.75/2.18 % (11735)------------------------------
% 1.75/2.19 % (11733)Refutation not found, incomplete strategy
% 1.75/2.19 % (11733)------------------------------
% 1.75/2.19 % (11733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/2.19 % (11733)Termination reason: Refutation not found, incomplete strategy
% 1.75/2.19
% 1.75/2.19
% 1.75/2.19 % (11733)Memory used [KB]: 5500
% 1.75/2.19 % (11733)Time elapsed: 0.006 s
% 1.75/2.19 % (11733)Instructions burned: 6 (million)
% 1.75/2.19 % (11733)------------------------------
% 1.75/2.19 % (11733)------------------------------
% 1.75/2.19 % (11734)Instruction limit reached!
% 1.75/2.19 % (11734)------------------------------
% 1.75/2.19 % (11734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/2.19 % (11734)Termination reason: Unknown
% 1.75/2.19 % (11734)Termination phase: Saturation
% 1.75/2.19
% 1.75/2.19 % (11734)Memory used [KB]: 5628
% 1.75/2.19 % (11734)Time elapsed: 0.011 s
% 1.75/2.19 % (11734)Instructions burned: 18 (million)
% 1.75/2.19 % (11734)------------------------------
% 1.75/2.19 % (11734)------------------------------
% 1.75/2.19 % (11738)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_11589 for (2999ds/3Mi)
% 1.75/2.20 % (11738)Instruction limit reached!
% 1.75/2.20 % (11738)------------------------------
% 1.75/2.20 % (11738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/2.20 % (11738)Termination reason: Unknown
% 1.75/2.20 % (11738)Termination phase: Naming
% 1.75/2.20
% 1.75/2.20 % (11738)Memory used [KB]: 1023
% 1.75/2.20 % (11738)Time elapsed: 0.002 s
% 1.75/2.20 % (11738)Instructions burned: 4 (million)
% 1.75/2.20 % (11738)------------------------------
% 1.75/2.20 % (11738)------------------------------
% 1.75/2.20 % (11730)Instruction limit reached!
% 1.75/2.20 % (11730)------------------------------
% 1.75/2.20 % (11730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/2.20 % (11730)Termination reason: Unknown
% 1.75/2.20 % (11730)Termination phase: Saturation
% 1.75/2.20
% 1.75/2.20 % (11730)Memory used [KB]: 5756
% 1.75/2.20 % (11730)Time elapsed: 0.017 s
% 1.75/2.20 % (11730)Instructions burned: 27 (million)
% 1.75/2.20 % (11730)------------------------------
% 1.75/2.20 % (11730)------------------------------
% 1.81/2.20 % (11736)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_11589 for (2999ds/37Mi)
% 1.81/2.20 % (11737)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_11589 for (2999ds/15Mi)
% 1.81/2.20 % (11740)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/7Mi)
% 1.81/2.20 % (11739)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_11589 for (2999ds/1041Mi)
% 1.81/2.20 % (11741)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/16Mi)
% 1.81/2.21 % (11740)Instruction limit reached!
% 1.81/2.21 % (11740)------------------------------
% 1.81/2.21 % (11740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.21 % (11740)Termination reason: Unknown
% 1.81/2.21 % (11740)Termination phase: Saturation
% 1.81/2.21
% 1.81/2.21 % (11740)Memory used [KB]: 1023
% 1.81/2.21 % (11740)Time elapsed: 0.004 s
% 1.81/2.21 % (11740)Instructions burned: 8 (million)
% 1.81/2.21 % (11740)------------------------------
% 1.81/2.21 % (11740)------------------------------
% 1.81/2.21 % (11737)Instruction limit reached!
% 1.81/2.21 % (11737)------------------------------
% 1.81/2.21 % (11737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.21 % (11737)Termination reason: Unknown
% 1.81/2.21 % (11737)Termination phase: Saturation
% 1.81/2.21
% 1.81/2.21 % (11737)Memory used [KB]: 5628
% 1.81/2.21 % (11737)Time elapsed: 0.010 s
% 1.81/2.21 % (11737)Instructions burned: 16 (million)
% 1.81/2.21 % (11737)------------------------------
% 1.81/2.21 % (11737)------------------------------
% 1.81/2.21 % (11741)Instruction limit reached!
% 1.81/2.21 % (11741)------------------------------
% 1.81/2.21 % (11741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.21 % (11741)Termination reason: Unknown
% 1.81/2.21 % (11741)Termination phase: Saturation
% 1.81/2.21
% 1.81/2.21 % (11741)Memory used [KB]: 5628
% 1.81/2.21 % (11741)Time elapsed: 0.006 s
% 1.81/2.21 % (11741)Instructions burned: 16 (million)
% 1.81/2.21 % (11741)------------------------------
% 1.81/2.21 % (11741)------------------------------
% 1.81/2.21 % (11742)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_11589 for (2999ds/3Mi)
% 1.81/2.21 % (11742)Instruction limit reached!
% 1.81/2.21 % (11742)------------------------------
% 1.81/2.21 % (11742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.21 % (11742)Termination reason: Unknown
% 1.81/2.21 % (11742)Termination phase: Property scanning
% 1.81/2.21
% 1.81/2.21 % (11742)Memory used [KB]: 1023
% 1.81/2.21 % (11742)Time elapsed: 0.003 s
% 1.81/2.21 % (11742)Instructions burned: 3 (million)
% 1.81/2.21 % (11742)------------------------------
% 1.81/2.21 % (11742)------------------------------
% 1.81/2.22 % (11743)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_11589 for (2999ds/3Mi)
% 1.81/2.22 % (11743)Instruction limit reached!
% 1.81/2.22 % (11743)------------------------------
% 1.81/2.22 % (11743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.22 % (11743)Termination reason: Unknown
% 1.81/2.22 % (11743)Termination phase: shuffling
% 1.81/2.22
% 1.81/2.22 % (11743)Memory used [KB]: 1023
% 1.81/2.22 % (11743)Time elapsed: 0.002 s
% 1.81/2.22 % (11743)Instructions burned: 4 (million)
% 1.81/2.22 % (11743)------------------------------
% 1.81/2.22 % (11743)------------------------------
% 1.81/2.22 % (11745)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/3Mi)
% 1.81/2.22 % (11745)Instruction limit reached!
% 1.81/2.22 % (11745)------------------------------
% 1.81/2.22 % (11745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.22 % (11745)Termination reason: Unknown
% 1.81/2.22 % (11745)Termination phase: Property scanning
% 1.81/2.22
% 1.81/2.22 % (11745)Memory used [KB]: 1023
% 1.81/2.22 % (11745)Time elapsed: 0.002 s
% 1.81/2.22 % (11745)Instructions burned: 4 (million)
% 1.81/2.22 % (11745)------------------------------
% 1.81/2.22 % (11745)------------------------------
% 1.81/2.22 % (11736)Instruction limit reached!
% 1.81/2.22 % (11736)------------------------------
% 1.81/2.22 % (11736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.22 % (11736)Termination reason: Unknown
% 1.81/2.22 % (11736)Termination phase: Saturation
% 1.81/2.22
% 1.81/2.22 % (11736)Memory used [KB]: 5756
% 1.81/2.22 % (11736)Time elapsed: 0.023 s
% 1.81/2.22 % (11736)Instructions burned: 37 (million)
% 1.81/2.22 % (11736)------------------------------
% 1.81/2.22 % (11736)------------------------------
% 1.81/2.23 % (11744)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/7Mi)
% 1.81/2.23 % (11747)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/18Mi)
% 1.81/2.23 % (11746)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/4Mi)
% 1.81/2.23 % (11748)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/710Mi)
% 1.81/2.23 % (11746)Instruction limit reached!
% 1.81/2.23 % (11746)------------------------------
% 1.81/2.23 % (11746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.23 % (11744)Instruction limit reached!
% 1.81/2.23 % (11744)------------------------------
% 1.81/2.23 % (11744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.23 % (11746)Termination reason: Unknown
% 1.81/2.23 % (11744)Termination reason: Unknown
% 1.81/2.23 % (11746)Termination phase: Property scanning
% 1.81/2.23
% 1.81/2.23 % (11744)Termination phase: Saturation
% 1.81/2.23 % (11746)Memory used [KB]: 1023
% 1.81/2.23
% 1.81/2.23 % (11746)Time elapsed: 0.003 s
% 1.81/2.23 % (11746)Instructions burned: 7 (million)
% 1.81/2.23 % (11746)------------------------------
% 1.81/2.23 % (11746)------------------------------
% 1.81/2.23 % (11744)Memory used [KB]: 5500
% 1.81/2.23 % (11744)Time elapsed: 0.006 s
% 1.81/2.23 % (11744)Instructions burned: 8 (million)
% 1.81/2.23 % (11744)------------------------------
% 1.81/2.23 % (11744)------------------------------
% 1.81/2.23 % (11747)Instruction limit reached!
% 1.81/2.23 % (11747)------------------------------
% 1.81/2.23 % (11747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.23 % (11747)Termination reason: Unknown
% 1.81/2.23 % (11747)Termination phase: Saturation
% 1.81/2.23
% 1.81/2.23 % (11747)Memory used [KB]: 5628
% 1.81/2.23 % (11747)Time elapsed: 0.008 s
% 1.81/2.23 % (11747)Instructions burned: 18 (million)
% 1.81/2.23 % (11747)------------------------------
% 1.81/2.23 % (11747)------------------------------
% 1.81/2.23 % (11728)Instruction limit reached!
% 1.81/2.23 % (11728)------------------------------
% 1.81/2.23 % (11728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.23 % (11728)Termination reason: Unknown
% 1.81/2.23 % (11728)Termination phase: Saturation
% 1.81/2.23
% 1.81/2.23 % (11728)Memory used [KB]: 6268
% 1.81/2.23 % (11728)Time elapsed: 0.061 s
% 1.81/2.23 % (11728)Instructions burned: 185 (million)
% 1.81/2.23 % (11728)------------------------------
% 1.81/2.23 % (11728)------------------------------
% 1.81/2.24 % (11749)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/6Mi)
% 1.81/2.24 % (11750)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/902Mi)
% 1.81/2.24 % (11749)Instruction limit reached!
% 1.81/2.24 % (11749)------------------------------
% 1.81/2.24 % (11749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.24 % (11749)Termination reason: Unknown
% 1.81/2.24 % (11749)Termination phase: Property scanning
% 1.81/2.24
% 1.81/2.24 % (11749)Memory used [KB]: 1023
% 1.81/2.24 % (11749)Time elapsed: 0.005 s
% 1.81/2.24 % (11749)Instructions burned: 6 (million)
% 1.81/2.24 % (11749)------------------------------
% 1.81/2.24 % (11749)------------------------------
% 1.81/2.24 % (11750)Refutation not found, incomplete strategy
% 1.81/2.24 % (11750)------------------------------
% 1.81/2.24 % (11750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.24 % (11750)Termination reason: Refutation not found, incomplete strategy
% 1.81/2.24
% 1.81/2.24
% 1.81/2.24 % (11750)Memory used [KB]: 5500
% 1.81/2.24 % (11750)Time elapsed: 0.003 s
% 1.81/2.24 % (11750)Instructions burned: 5 (million)
% 1.81/2.24 % (11750)------------------------------
% 1.81/2.24 % (11750)------------------------------
% 1.81/2.24 % (11752)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/5Mi)
% 1.81/2.24 % (11753)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/6Mi)
% 1.81/2.24 % (11752)Instruction limit reached!
% 1.81/2.24 % (11752)------------------------------
% 1.81/2.24 % (11752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.24 % (11752)Termination reason: Unknown
% 1.81/2.24 % (11752)Termination phase: Property scanning
% 1.81/2.24
% 1.81/2.24 % (11752)Memory used [KB]: 1023
% 1.81/2.24 % (11752)Time elapsed: 0.003 s
% 1.81/2.24 % (11752)Instructions burned: 5 (million)
% 1.81/2.24 % (11752)------------------------------
% 1.81/2.24 % (11752)------------------------------
% 1.81/2.25 % (11753)Instruction limit reached!
% 1.81/2.25 % (11753)------------------------------
% 1.81/2.25 % (11753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.25 % (11753)Termination reason: Unknown
% 1.81/2.25 % (11753)Termination phase: Saturation
% 1.81/2.25
% 1.81/2.25 % (11753)Memory used [KB]: 5500
% 1.81/2.25 % (11753)Time elapsed: 0.004 s
% 1.81/2.25 % (11753)Instructions burned: 8 (million)
% 1.81/2.25 % (11753)------------------------------
% 1.81/2.25 % (11753)------------------------------
% 1.81/2.25 % (11751)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/21Mi)
% 1.81/2.25 % (11755)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/779Mi)
% 1.81/2.25 % (11756)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/19Mi)
% 1.81/2.26 % (11757)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/879Mi)
% 1.81/2.26 % (11751)Instruction limit reached!
% 1.81/2.26 % (11751)------------------------------
% 1.81/2.26 % (11751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.26 % (11751)Termination reason: Unknown
% 1.81/2.26 % (11751)Termination phase: Saturation
% 1.81/2.26
% 1.81/2.26 % (11751)Memory used [KB]: 5756
% 1.81/2.26 % (11751)Time elapsed: 0.013 s
% 1.81/2.26 % (11751)Instructions burned: 21 (million)
% 1.81/2.26 % (11751)------------------------------
% 1.81/2.26 % (11751)------------------------------
% 1.81/2.26 % (11754)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/377Mi)
% 1.81/2.26 % (11756)Refutation not found, incomplete strategy
% 1.81/2.26 % (11756)------------------------------
% 1.81/2.26 % (11756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.26 % (11756)Termination reason: Refutation not found, incomplete strategy
% 1.81/2.26
% 1.81/2.26
% 1.81/2.26 % (11756)Memory used [KB]: 5628
% 1.81/2.26 % (11756)Time elapsed: 0.006 s
% 1.81/2.26 % (11756)Instructions burned: 14 (million)
% 1.81/2.26 % (11756)------------------------------
% 1.81/2.26 % (11756)------------------------------
% 1.81/2.27 % (11759)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/3Mi)
% 1.81/2.27 % (11759)Instruction limit reached!
% 1.81/2.27 % (11759)------------------------------
% 1.81/2.27 % (11759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.27 % (11759)Termination reason: Unknown
% 1.81/2.27 % (11759)Termination phase: Property scanning
% 1.81/2.27
% 1.81/2.27 % (11759)Memory used [KB]: 1023
% 1.81/2.27 % (11759)Time elapsed: 0.003 s
% 1.81/2.27 % (11759)Instructions burned: 4 (million)
% 1.81/2.27 % (11759)------------------------------
% 1.81/2.27 % (11759)------------------------------
% 1.81/2.27 % (11758)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/17Mi)
% 1.81/2.28 % (11758)Instruction limit reached!
% 1.81/2.28 % (11758)------------------------------
% 1.81/2.28 % (11758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.28 % (11758)Termination reason: Unknown
% 1.81/2.28 % (11758)Termination phase: Saturation
% 1.81/2.28
% 1.81/2.28 % (11758)Memory used [KB]: 5628
% 1.81/2.28 % (11758)Time elapsed: 0.007 s
% 1.81/2.28 % (11758)Instructions burned: 19 (million)
% 1.81/2.28 % (11758)------------------------------
% 1.81/2.28 % (11758)------------------------------
% 1.81/2.28 % (11760)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_11589 for (2999ds/30Mi)
% 1.81/2.29 % (11761)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_11589 for (2998ds/127Mi)
% 1.81/2.29 % (11760)Instruction limit reached!
% 1.81/2.29 % (11760)------------------------------
% 1.81/2.29 % (11760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.29 % (11760)Termination reason: Unknown
% 1.81/2.29 % (11760)Termination phase: Saturation
% 1.81/2.29
% 1.81/2.29 % (11760)Memory used [KB]: 5756
% 1.81/2.29 % (11760)Time elapsed: 0.012 s
% 1.81/2.29 % (11760)Instructions burned: 33 (million)
% 1.81/2.29 % (11760)------------------------------
% 1.81/2.29 % (11760)------------------------------
% 1.81/2.30 % (11762)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_11589 for (2998ds/100Mi)
% 1.81/2.33 % (11761)Instruction limit reached!
% 1.81/2.33 % (11761)------------------------------
% 1.81/2.33 % (11761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.33 % (11761)Termination reason: Unknown
% 1.81/2.33 % (11761)Termination phase: Saturation
% 1.81/2.33
% 1.81/2.33 % (11761)Memory used [KB]: 6012
% 1.81/2.33 % (11761)Time elapsed: 0.044 s
% 1.81/2.33 % (11761)Instructions burned: 129 (million)
% 1.81/2.33 % (11761)------------------------------
% 1.81/2.33 % (11761)------------------------------
% 1.81/2.33 % (11762)Instruction limit reached!
% 1.81/2.33 % (11762)------------------------------
% 1.81/2.33 % (11762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.33 % (11762)Termination reason: Unknown
% 1.81/2.33 % (11762)Termination phase: Saturation
% 1.81/2.33
% 1.81/2.33 % (11762)Memory used [KB]: 6012
% 1.81/2.33 % (11762)Time elapsed: 0.033 s
% 1.81/2.33 % (11762)Instructions burned: 101 (million)
% 1.81/2.33 % (11762)------------------------------
% 1.81/2.33 % (11762)------------------------------
% 1.81/2.34 % (11763)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_11589 for (2998ds/3Mi)
% 1.81/2.34 % (11763)Instruction limit reached!
% 1.81/2.34 % (11763)------------------------------
% 1.81/2.34 % (11763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.34 % (11763)Termination reason: Unknown
% 1.81/2.34 % (11763)Termination phase: Property scanning
% 1.81/2.34
% 1.81/2.34 % (11763)Memory used [KB]: 1023
% 1.81/2.34 % (11763)Time elapsed: 0.003 s
% 1.81/2.34 % (11763)Instructions burned: 5 (million)
% 1.81/2.34 % (11763)------------------------------
% 1.81/2.34 % (11763)------------------------------
% 1.81/2.34 % (11764)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_11589 for (2998ds/20Mi)
% 1.81/2.35 % (11764)Refutation not found, incomplete strategy
% 1.81/2.35 % (11764)------------------------------
% 1.81/2.35 % (11764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.35 % (11764)Termination reason: Refutation not found, incomplete strategy
% 1.81/2.35
% 1.81/2.35
% 1.81/2.35 % (11764)Memory used [KB]: 5628
% 1.81/2.35 % (11764)Time elapsed: 0.004 s
% 1.81/2.35 % (11764)Instructions burned: 7 (million)
% 1.81/2.35 % (11764)------------------------------
% 1.81/2.35 % (11764)------------------------------
% 1.81/2.35 % (11765)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_11589 for (2998ds/86Mi)
% 1.81/2.36 % (11766)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_11589 for (2998ds/107Mi)
% 1.81/2.38 % (11765)Instruction limit reached!
% 1.81/2.38 % (11765)------------------------------
% 1.81/2.38 % (11765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.38 % (11765)Termination reason: Unknown
% 1.81/2.38 % (11765)Termination phase: Saturation
% 1.81/2.38
% 1.81/2.38 % (11765)Memory used [KB]: 6012
% 1.81/2.38 % (11765)Time elapsed: 0.052 s
% 1.81/2.38 % (11765)Instructions burned: 88 (million)
% 1.81/2.38 % (11765)------------------------------
% 1.81/2.38 % (11765)------------------------------
% 1.81/2.38 % (11754)Instruction limit reached!
% 1.81/2.38 % (11754)------------------------------
% 1.81/2.38 % (11754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.38 % (11754)Termination reason: Unknown
% 1.81/2.38 % (11754)Termination phase: Saturation
% 1.81/2.38
% 1.81/2.38 % (11754)Memory used [KB]: 6268
% 1.81/2.38 % (11754)Time elapsed: 0.126 s
% 1.81/2.38 % (11754)Instructions burned: 378 (million)
% 1.81/2.38 % (11754)------------------------------
% 1.81/2.38 % (11754)------------------------------
% 1.81/2.39 % (11767)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_11589 for (2997ds/39Mi)
% 1.81/2.39 % (11766)Instruction limit reached!
% 1.81/2.39 % (11766)------------------------------
% 1.81/2.39 % (11766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.39 % (11766)Termination reason: Unknown
% 1.81/2.39 % (11766)Termination phase: Saturation
% 1.81/2.39
% 1.81/2.39 % (11766)Memory used [KB]: 6012
% 1.81/2.39 % (11766)Time elapsed: 0.037 s
% 1.81/2.39 % (11766)Instructions burned: 107 (million)
% 1.81/2.39 % (11766)------------------------------
% 1.81/2.39 % (11766)------------------------------
% 1.81/2.39 % (11768)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_11589 for (2997ds/448Mi)
% 1.81/2.40 % (11769)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_11589 for (2997ds/46Mi)
% 1.81/2.40 % (11767)Instruction limit reached!
% 1.81/2.40 % (11767)------------------------------
% 1.81/2.40 % (11767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.40 % (11767)Termination reason: Unknown
% 1.81/2.40 % (11767)Termination phase: Saturation
% 1.81/2.40
% 1.81/2.40 % (11767)Memory used [KB]: 5884
% 1.81/2.40 % (11767)Time elapsed: 0.015 s
% 1.81/2.40 % (11767)Instructions burned: 40 (million)
% 1.81/2.40 % (11767)------------------------------
% 1.81/2.40 % (11767)------------------------------
% 1.81/2.41 % (11770)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_11589 for (2997ds/98Mi)
% 1.81/2.42 % (11769)Instruction limit reached!
% 1.81/2.42 % (11769)------------------------------
% 1.81/2.42 % (11769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.42 % (11769)Termination reason: Unknown
% 1.81/2.42 % (11769)Termination phase: Saturation
% 1.81/2.42
% 1.81/2.42 % (11769)Memory used [KB]: 5756
% 1.81/2.42 % (11769)Time elapsed: 0.018 s
% 1.81/2.42 % (11769)Instructions burned: 47 (million)
% 1.81/2.42 % (11769)------------------------------
% 1.81/2.42 % (11769)------------------------------
% 1.81/2.43 % (11771)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_11589 for (2997ds/507Mi)
% 1.81/2.43 % (11748)Refutation not found, incomplete strategy
% 1.81/2.43 % (11748)------------------------------
% 1.81/2.43 % (11748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.43 % (11748)Termination reason: Refutation not found, incomplete strategy
% 1.81/2.43
% 1.81/2.43
% 1.81/2.43 % (11748)Memory used [KB]: 6652
% 1.81/2.43 % (11748)Time elapsed: 0.201 s
% 1.81/2.43 % (11748)Instructions burned: 672 (million)
% 1.81/2.43 % (11748)------------------------------
% 1.81/2.43 % (11748)------------------------------
% 1.81/2.43 % (11771)Refutation not found, incomplete strategy
% 1.81/2.43 % (11771)------------------------------
% 1.81/2.43 % (11771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.43 % (11771)Termination reason: Refutation not found, incomplete strategy
% 1.81/2.43
% 1.81/2.43
% 1.81/2.43 % (11771)Memory used [KB]: 5628
% 1.81/2.43 % (11771)Time elapsed: 0.006 s
% 1.81/2.43 % (11771)Instructions burned: 14 (million)
% 1.81/2.43 % (11771)------------------------------
% 1.81/2.43 % (11771)------------------------------
% 1.81/2.44 % (11772)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_11589 for (2997ds/149Mi)
% 1.81/2.44 % (11773)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_11589 for (2997ds/39Mi)
% 1.81/2.45 % (11770)Instruction limit reached!
% 1.81/2.45 % (11770)------------------------------
% 1.81/2.45 % (11770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.45 % (11770)Termination reason: Unknown
% 1.81/2.45 % (11770)Termination phase: Saturation
% 1.81/2.45
% 1.81/2.45 % (11770)Memory used [KB]: 1535
% 1.81/2.45 % (11770)Time elapsed: 0.034 s
% 1.81/2.45 % (11770)Instructions burned: 99 (million)
% 1.81/2.45 % (11770)------------------------------
% 1.81/2.45 % (11770)------------------------------
% 1.81/2.46 % (11773)Instruction limit reached!
% 1.81/2.46 % (11773)------------------------------
% 1.81/2.46 % (11773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.46 % (11773)Termination reason: Unknown
% 1.81/2.46 % (11773)Termination phase: Saturation
% 1.81/2.46
% 1.81/2.46 % (11773)Memory used [KB]: 5884
% 1.81/2.46 % (11773)Time elapsed: 0.014 s
% 1.81/2.46 % (11773)Instructions burned: 39 (million)
% 1.81/2.46 % (11773)------------------------------
% 1.81/2.46 % (11773)------------------------------
% 1.81/2.46 % (11774)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_11589 for (2997ds/6Mi)
% 1.81/2.46 % (11774)Instruction limit reached!
% 1.81/2.46 % (11774)------------------------------
% 1.81/2.46 % (11774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.46 % (11774)Termination reason: Unknown
% 1.81/2.46 % (11774)Termination phase: Saturation
% 1.81/2.46
% 1.81/2.46 % (11774)Memory used [KB]: 9978
% 1.81/2.46 % (11774)Time elapsed: 0.004 s
% 1.81/2.46 % (11774)Instructions burned: 8 (million)
% 1.81/2.46 % (11774)------------------------------
% 1.81/2.46 % (11774)------------------------------
% 1.81/2.47 % (11775)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_11589 for (2997ds/1087Mi)
% 1.81/2.47 % (11776)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_11589 for (2997ds/47Mi)
% 1.81/2.47 % (11775)Refutation not found, incomplete strategy
% 1.81/2.47 % (11775)------------------------------
% 1.81/2.47 % (11775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.47 % (11775)Termination reason: Refutation not found, incomplete strategy
% 1.81/2.47
% 1.81/2.47
% 1.81/2.47 % (11775)Memory used [KB]: 5628
% 1.81/2.47 % (11775)Time elapsed: 0.006 s
% 1.81/2.47 % (11775)Instructions burned: 14 (million)
% 1.81/2.47 % (11775)------------------------------
% 1.81/2.47 % (11775)------------------------------
% 1.81/2.48 % (11777)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_11589 for (2996ds/44Mi)
% 1.81/2.48 % (11776)Instruction limit reached!
% 1.81/2.48 % (11776)------------------------------
% 1.81/2.48 % (11776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.48 % (11776)Termination reason: Unknown
% 1.81/2.48 % (11776)Termination phase: Saturation
% 1.81/2.48
% 1.81/2.48 % (11776)Memory used [KB]: 5756
% 1.81/2.48 % (11776)Time elapsed: 0.016 s
% 1.81/2.48 % (11776)Instructions burned: 47 (million)
% 1.81/2.48 % (11776)------------------------------
% 1.81/2.48 % (11776)------------------------------
% 1.81/2.49 % (11772)Instruction limit reached!
% 1.81/2.49 % (11772)------------------------------
% 1.81/2.49 % (11772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.49 % (11772)Termination reason: Unknown
% 1.81/2.49 % (11772)Termination phase: Saturation
% 1.81/2.49
% 1.81/2.49 % (11772)Memory used [KB]: 6140
% 1.81/2.49 % (11772)Time elapsed: 0.049 s
% 1.81/2.49 % (11772)Instructions burned: 151 (million)
% 1.81/2.49 % (11772)------------------------------
% 1.81/2.49 % (11772)------------------------------
% 1.81/2.49 % (11778)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_11589 for (2996ds/432Mi)
% 1.81/2.50 % (11777)Instruction limit reached!
% 1.81/2.50 % (11777)------------------------------
% 1.81/2.50 % (11777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.50 % (11777)Termination reason: Unknown
% 1.81/2.50 % (11777)Termination phase: Saturation
% 1.81/2.50
% 1.81/2.50 % (11777)Memory used [KB]: 1279
% 1.81/2.50 % (11777)Time elapsed: 0.016 s
% 1.81/2.50 % (11777)Instructions burned: 45 (million)
% 1.81/2.50 % (11777)------------------------------
% 1.81/2.50 % (11777)------------------------------
% 1.81/2.50 % (11779)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_11589 for (2996ds/62Mi)
% 1.81/2.50 % (11755)Instruction limit reached!
% 1.81/2.50 % (11755)------------------------------
% 1.81/2.50 % (11755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.50 % (11755)Termination reason: Unknown
% 1.81/2.50 % (11755)Termination phase: Saturation
% 1.81/2.50
% 1.81/2.50 % (11755)Memory used [KB]: 6268
% 1.81/2.50 % (11755)Time elapsed: 0.248 s
% 1.81/2.50 % (11755)Instructions burned: 781 (million)
% 1.81/2.50 % (11755)------------------------------
% 1.81/2.50 % (11755)------------------------------
% 1.81/2.51 % (11780)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_11589 for (2996ds/31Mi)
% 1.81/2.51 % (11781)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_11589 for (2996ds/96Mi)
% 1.81/2.51 % (11757)First to succeed.
% 1.81/2.51 % (11779)Instruction limit reached!
% 1.81/2.51 % (11779)------------------------------
% 1.81/2.51 % (11779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.51 % (11779)Termination reason: Unknown
% 1.81/2.51 % (11779)Termination phase: Saturation
% 1.81/2.51
% 1.81/2.51 % (11779)Memory used [KB]: 5884
% 1.81/2.51 % (11779)Time elapsed: 0.019 s
% 1.81/2.51 % (11779)Instructions burned: 62 (million)
% 1.81/2.51 % (11779)------------------------------
% 1.81/2.51 % (11779)------------------------------
% 1.81/2.52 % (11780)Instruction limit reached!
% 1.81/2.52 % (11780)------------------------------
% 1.81/2.52 % (11780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.52 % (11780)Termination reason: Unknown
% 1.81/2.52 % (11780)Termination phase: Saturation
% 1.81/2.52
% 1.81/2.52 % (11780)Memory used [KB]: 5884
% 1.81/2.52 % (11780)Time elapsed: 0.012 s
% 1.81/2.52 % (11780)Instructions burned: 33 (million)
% 1.81/2.52 % (11780)------------------------------
% 1.81/2.52 % (11780)------------------------------
% 1.81/2.52 % (11757)Refutation found. Thanks to Tanya!
% 1.81/2.52 % SZS status Theorem for DTF2THF_11589
% 1.81/2.52 % SZS output start Proof for DTF2THF_11589
% 1.81/2.52 thf(type_def_5, type, mworld: $tType).
% 1.81/2.52 thf(func_def_0, type, mworld: $tType).
% 1.81/2.52 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.81/2.52 thf(func_def_2, type, mactual: mworld).
% 1.81/2.52 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.81/2.52 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.81/2.52 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.81/2.52 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.81/2.52 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.81/2.52 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.81/2.52 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.81/2.52 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.81/2.52 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 1.81/2.52 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.81/2.52 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.81/2.52 thf(func_def_17, type, number: $i > $i > mworld > $o).
% 1.81/2.52 thf(func_def_18, type, string: $i > mworld > $o).
% 1.81/2.52 thf(func_def_19, type, in: $i > $i > $i > mworld > $o).
% 1.81/2.52 thf(func_def_20, type, do: $i > $i > $i > mworld > $o).
% 1.81/2.52 thf(func_def_21, type, entry_box: $i > mworld > $o).
% 1.81/2.52 thf(func_def_22, type, userid: $i > $i > mworld > $o).
% 1.81/2.52 thf(func_def_38, type, sK0: mworld > $i).
% 1.81/2.52 thf(func_def_43, type, sK2: $i > mworld > $i > $i > $i).
% 1.81/2.52 thf(func_def_45, type, sK4: mworld > $i).
% 1.81/2.52 thf(func_def_46, type, sK5: mworld).
% 1.81/2.52 thf(func_def_47, type, sK6: $i > $i > mworld).
% 1.81/2.52 thf(func_def_48, type, sK7: $i > $i > $i > $i > mworld).
% 1.81/2.52 thf(func_def_49, type, sK8: $i > $i > $i > $i > $i).
% 1.81/2.52 thf(func_def_50, type, sK9: $i > $i > $i > $i > $i).
% 1.81/2.52 thf(f1524,plain,(
% 1.81/2.52 $false),
% 1.81/2.52 inference(avatar_sat_refutation,[status(thm)],[f346,f376,f393,f1348,f1355,f1444,f1495,f1513,f1523])).
% 1.81/2.52 thf(f1523,plain,(
% 1.81/2.52 spl1_9 | ~spl1_11),
% 1.81/2.52 inference(avatar_contradiction_clause,[status(thm)],[f1522])).
% 1.81/2.52 thf(f1522,plain,(
% 1.81/2.52 $false | (spl1_9 | ~spl1_11)),
% 1.81/2.52 inference(subsumption_resolution,[status(thm)],[f1518,f1398])).
% 1.81/2.52 thf(f1398,plain,(
% 1.81/2.52 ($false != (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | spl1_9),
% 1.81/2.52 inference(avatar_component_clause,[status(thm)],[f1397])).
% 1.81/2.52 thf(f1397,definition,(
% 1.81/2.52 spl1_9 <=> ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3)))),
% 1.81/2.52 introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition])).
% 1.81/2.52 thf(f1518,plain,(
% 1.81/2.52 ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | ~spl1_11),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1517])).
% 1.81/2.52 thf(f1517,plain,(
% 1.81/2.52 ($false = $true) | ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | ~spl1_11),
% 1.81/2.52 inference(superposition,[status(thm)],[f119,f1407])).
% 1.81/2.52 thf(f1407,plain,(
% 1.81/2.52 ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ sK5) @ sK3))) | ~spl1_11),
% 1.81/2.52 inference(avatar_component_clause,[status(thm)],[f1405])).
% 1.81/2.52 thf(f1405,definition,(
% 1.81/2.52 spl1_11 <=> ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ sK5) @ sK3)))),
% 1.81/2.52 introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition])).
% 1.81/2.52 thf(f119,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($true = (entry_box @ sK3 @ X1)) | ($false = (mrel @ mactual @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f118])).
% 1.81/2.52 thf(f118,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | (((number @ sK3 @ one @ X1) & (entry_box @ sK3 @ X1)) = $true)) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f117])).
% 1.81/2.52 thf(f117,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => ((number @ sK3 @ one @ X1) & (entry_box @ sK3 @ X1))))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f116])).
% 1.81/2.52 thf(f116,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((number @ sK3 @ one @ Y0) & (entry_box @ sK3 @ Y0)))) @ X1))) )),
% 1.81/2.52 inference(pi_clausification,[status(thm)],[f114])).
% 1.81/2.52 thf(f114,plain,(
% 1.81/2.52 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((number @ sK3 @ one @ Y0) & (entry_box @ sK3 @ Y0))))) = $true)),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.81/2.52 thf(f113,plain,(
% 1.81/2.52 ($true = ((eiw_di @ sK3 @ mactual) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((number @ sK3 @ one @ Y0) & (entry_box @ sK3 @ Y0)))))))),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f112])).
% 1.81/2.52 thf(f112,plain,(
% 1.81/2.52 ($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => ((number @ Y0 @ one @ Y1) & (entry_box @ Y0 @ Y1))))))) @ sK3))),
% 1.81/2.52 inference(sigma_clausification,[status(thm)],[f111])).
% 1.81/2.52 thf(f111,plain,(
% 1.81/2.52 ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => ((number @ Y0 @ one @ Y1) & (entry_box @ Y0 @ Y1)))))))) = $true)),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.81/2.52 thf(f82,plain,(
% 1.81/2.52 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (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]: ((Y2 @ Y3) & (Y1 @ Y3))))))) @ (entry_box @ Y0) @ (number @ Y0 @ one)))))) = $true)),
% 1.81/2.52 inference(definition_unfolding,[status(thm)],[f72,f65,f68,f64,f70])).
% 1.81/2.52 thf(f70,plain,(
% 1.81/2.52 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f27])).
% 1.81/2.52 thf(f27,plain,(
% 1.81/2.52 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f26])).
% 1.81/2.52 thf(f26,plain,(
% 1.81/2.52 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 1.81/2.52 inference(rectify,[status(thm)],[f3])).
% 1.81/2.52 thf(f3,axiom,(
% 1.81/2.52 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))) = mand)),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mand_def)).
% 1.81/2.52 thf(f64,plain,(
% 1.81/2.52 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f37])).
% 1.81/2.52 thf(f37,plain,(
% 1.81/2.52 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f36])).
% 1.81/2.52 thf(f36,plain,(
% 1.81/2.52 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 1.81/2.52 inference(rectify,[status(thm)],[f7])).
% 1.81/2.52 thf(f7,axiom,(
% 1.81/2.52 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mbox_def)).
% 1.81/2.52 thf(f68,plain,(
% 1.81/2.52 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f29])).
% 1.81/2.52 thf(f29,plain,(
% 1.81/2.52 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f28])).
% 1.81/2.52 thf(f28,plain,(
% 1.81/2.52 ((^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))) = mexists_di)),
% 1.81/2.52 inference(rectify,[status(thm)],[f14])).
% 1.81/2.52 thf(f14,axiom,(
% 1.81/2.52 ((^[X1 : $i > mworld > $o, X2 : mworld] : (? [X6 : $i] : ((X1 @ X6 @ X2) & (eiw_di @ X6 @ X2)))) = mexists_di)),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mexists_di_def)).
% 1.81/2.52 thf(f65,plain,(
% 1.81/2.52 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f25])).
% 1.81/2.52 thf(f25,plain,(
% 1.81/2.52 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f1])).
% 1.81/2.52 thf(f1,axiom,(
% 1.81/2.52 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mlocal_def)).
% 1.81/2.52 thf(f72,plain,(
% 1.81/2.52 ($true = (mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (entry_box @ Y0) @ (number @ Y0 @ one)))))))),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f47])).
% 1.81/2.52 thf(f47,plain,(
% 1.81/2.52 ($true = (mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (entry_box @ Y0) @ (number @ Y0 @ one)))))))),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f46])).
% 1.81/2.52 thf(f46,plain,(
% 1.81/2.52 (mlocal @ (mexists_di @ (^[X0 : $i] : (mbox @ (mand @ (entry_box @ X0) @ (number @ X0 @ one))))))),
% 1.81/2.52 inference(rectify,[status(thm)],[f16])).
% 1.81/2.52 thf(f16,axiom,(
% 1.81/2.52 (mlocal @ (mexists_di @ (^[X3 : $i] : (mbox @ (mand @ (entry_box @ X3) @ (number @ X3 @ one))))))),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',ax2)).
% 1.81/2.52 thf(f1513,plain,(
% 1.81/2.52 ~spl1_10),
% 1.81/2.52 inference(avatar_contradiction_clause,[status(thm)],[f1512])).
% 1.81/2.52 thf(f1512,plain,(
% 1.81/2.52 $false | ~spl1_10),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1507])).
% 1.81/2.52 thf(f1507,plain,(
% 1.81/2.52 ($false = $true) | ~spl1_10),
% 1.81/2.52 inference(superposition,[status(thm)],[f79,f1501])).
% 1.81/2.52 thf(f1501,plain,(
% 1.81/2.52 ($false = (mrel @ sK5 @ sK5)) | ~spl1_10),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1500])).
% 1.81/2.52 thf(f1500,plain,(
% 1.81/2.52 ($false = (mrel @ sK5 @ sK5)) | ($false = $true) | ~spl1_10),
% 1.81/2.52 inference(forward_demodulation,[status(thm)],[f1499,f138])).
% 1.81/2.52 thf(f138,plain,(
% 1.81/2.52 ((mrel @ mactual @ sK5) = $true)),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.81/2.52 thf(f136,plain,(
% 1.81/2.52 ($false = ((mrel @ mactual @ sK5) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK5) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK5) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ sK5) & (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ sK5) & ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK5 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) => ((do @ Y3 @ Y2 @ Y5 @ Y4) => (in @ Y0 @ Y1 @ Y5 @ Y4)))))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK5 @ Y4) => (((number @ Y1 @ one @ Y4) & (entry_box @ Y1 @ Y4)) & (userid @ u @ Y0 @ Y4))))))))))))))))))))),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f135])).
% 1.81/2.52 thf(f135,plain,(
% 1.81/2.52 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y0) & (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y0) & ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (!! @ $i @ (^[Y6 : $i]: ((eiw_di @ Y6 @ Y5) => ((do @ Y4 @ Y3 @ Y6 @ Y5) => (in @ Y1 @ Y2 @ Y6 @ Y5)))))))) & (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (((number @ Y2 @ one @ Y5) & (entry_box @ Y2 @ Y5)) & (userid @ u @ Y1 @ Y5)))))))))))))))))))) @ sK5))),
% 1.81/2.52 inference(sigma_clausification,[status(thm)],[f134])).
% 1.81/2.52 thf(f134,plain,(
% 1.81/2.52 ($true != (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y0) & (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y0) & ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (!! @ $i @ (^[Y6 : $i]: ((eiw_di @ Y6 @ Y5) => ((do @ Y4 @ Y3 @ Y6 @ Y5) => (in @ Y1 @ Y2 @ Y6 @ Y5)))))))) & (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (((number @ Y2 @ one @ Y5) & (entry_box @ Y2 @ Y5)) & (userid @ u @ Y1 @ Y5))))))))))))))))))))))),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f84])).
% 1.81/2.52 thf(f84,plain,(
% 1.81/2.52 ($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]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) & (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (?? @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) & (Y2 @ Y4 @ Y3))))))) @ (^[Y2 : $i]: ((^[Y3 : $i > mworld > $o]: ((^[Y4 : mworld]: (?? @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) & (Y3 @ Y5 @ Y4))))))) @ (^[Y3 : $i]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ ((^[Y4 : mworld > $o]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ (userid @ u @ Y0) @ ((^[Y4 : mworld > $o]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld]: ((Y5 @ Y6) & (Y4 @ 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]: ((eiw_di @ Y6 @ Y5) => (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)))))))))))))))))),
% 1.81/2.52 inference(definition_unfolding,[status(thm)],[f80,f65,f64,f68,f68,f68,f68,f70,f64,f70,f70,f64,f78,f76])).
% 1.81/2.52 thf(f76,plain,(
% 1.81/2.52 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f33])).
% 1.81/2.52 thf(f33,plain,(
% 1.81/2.52 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f32])).
% 1.81/2.52 thf(f32,plain,(
% 1.81/2.52 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 1.81/2.52 inference(rectify,[status(thm)],[f5])).
% 1.81/2.52 thf(f5,axiom,(
% 1.81/2.52 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mimplies_def)).
% 1.81/2.52 thf(f78,plain,(
% 1.81/2.52 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f49])).
% 1.81/2.52 thf(f49,plain,(
% 1.81/2.52 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f48])).
% 1.81/2.52 thf(f48,plain,(
% 1.81/2.52 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))) = mforall_di)),
% 1.81/2.52 inference(rectify,[status(thm)],[f13])).
% 1.81/2.52 thf(f13,axiom,(
% 1.81/2.52 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X6 : $i] : ((eiw_di @ X6 @ X2) => (X1 @ X6 @ X2)))) = mforall_di)),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mforall_di_def)).
% 1.81/2.52 thf(f80,plain,(
% 1.81/2.52 ($true != (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 : $i]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))))),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f56])).
% 1.81/2.52 thf(f56,plain,(
% 1.81/2.52 ($true != (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 : $i]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))))),
% 1.81/2.52 inference(flattening,[status(thm)],[f35])).
% 1.81/2.52 thf(f35,plain,(
% 1.81/2.52 ~($true = (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)))))))))))))))))),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f34])).
% 1.81/2.52 thf(f34,plain,(
% 1.81/2.52 ~(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))))))))))))))))),
% 1.81/2.52 inference(rectify,[status(thm)],[f19])).
% 1.81/2.52 thf(f19,negated_conjecture,(
% 1.81/2.52 ~(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))))))))))))))))),
% 1.81/2.52 inference(negated_conjecture,[status(cth)],[f18])).
% 1.81/2.52 thf(f18,conjecture,(
% 1.81/2.52 (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 : $i] : (mimplies @ (do @ X8 @ X1 @ X9) @ (in @ X7 @ X3 @ X9))))))))))))))))),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',con)).
% 1.81/2.52 thf(f1499,plain,(
% 1.81/2.52 ($false = (mrel @ sK5 @ sK5)) | ((mrel @ mactual @ sK5) = $false) | ~spl1_10),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1497])).
% 1.81/2.52 thf(f1497,plain,(
% 1.81/2.52 ($false = (mrel @ sK5 @ sK5)) | ((mrel @ mactual @ sK5) = $false) | ($false = $true) | ~spl1_10),
% 1.81/2.52 inference(superposition,[status(thm)],[f133,f1403])).
% 1.81/2.52 thf(f1403,plain,(
% 1.81/2.52 ($false = (string @ (sK4 @ sK5) @ sK5)) | ~spl1_10),
% 1.81/2.52 inference(avatar_component_clause,[status(thm)],[f1401])).
% 1.81/2.52 thf(f1401,definition,(
% 1.81/2.52 spl1_10 <=> ($false = (string @ (sK4 @ sK5) @ sK5))),
% 1.81/2.52 introduced(definition,[new_symbols(naming,[spl1_10])],[avatar_definition])).
% 1.81/2.52 thf(f133,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X1 : mworld] : (((string @ (sK4 @ X1) @ X2) = $true) | ($false = (mrel @ X1 @ X2)) | ($false = (mrel @ mactual @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.81/2.52 thf(f131,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X1 : mworld] : (($false = (mrel @ X1 @ X2)) | ($false = (mrel @ mactual @ X1)) | ($true = ((string @ (sK4 @ X1) @ X2) & (userid @ u @ (sK4 @ X1) @ X2)))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 1.81/2.52 thf(f130,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ X1 @ X2) => ((string @ (sK4 @ X1) @ X2) & (userid @ u @ (sK4 @ X1) @ X2)))) | ($false = (mrel @ mactual @ X1))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f129])).
% 1.81/2.52 thf(f129,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((string @ (sK4 @ X1) @ Y0) & (userid @ u @ (sK4 @ X1) @ Y0)))) @ X2) = $true) | ($false = (mrel @ mactual @ X1))) )),
% 1.81/2.52 inference(pi_clausification,[status(thm)],[f127])).
% 1.81/2.52 thf(f127,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((string @ (sK4 @ X1) @ Y0) & (userid @ u @ (sK4 @ X1) @ Y0))))))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f126])).
% 1.81/2.52 thf(f126,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($true = ((eiw_di @ (sK4 @ X1) @ X1) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((string @ (sK4 @ X1) @ Y0) & (userid @ u @ (sK4 @ X1) @ Y0))))))) | ($false = (mrel @ mactual @ X1))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f125])).
% 1.81/2.52 thf(f125,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => ((string @ Y0 @ Y1) & (userid @ u @ Y0 @ Y1))))))) @ (sK4 @ X1)))) )),
% 1.81/2.52 inference(sigma_clausification,[status(thm)],[f124])).
% 1.81/2.52 thf(f124,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => ((string @ Y0 @ Y1) & (userid @ u @ Y0 @ Y1)))))))))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f123])).
% 1.81/2.52 thf(f123,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => ((string @ Y0 @ Y1) & (userid @ u @ Y0 @ Y1))))))))))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f122])).
% 1.81/2.52 thf(f122,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((string @ Y1 @ Y2) & (userid @ u @ Y1 @ Y2)))))))))) @ X1))) )),
% 1.81/2.52 inference(pi_clausification,[status(thm)],[f121])).
% 1.81/2.52 thf(f121,plain,(
% 1.81/2.52 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((string @ Y1 @ Y2) & (userid @ u @ Y1 @ Y2))))))))))))),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f81])).
% 1.81/2.52 thf(f81,plain,(
% 1.81/2.52 ($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]: ((eiw_di @ Y2 @ Y1) & (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]: ((Y2 @ Y3) & (Y1 @ Y3))))))) @ (userid @ u @ Y0) @ (string @ Y0))))))))),
% 1.81/2.52 inference(definition_unfolding,[status(thm)],[f67,f65,f64,f68,f64,f70])).
% 1.81/2.52 thf(f67,plain,(
% 1.81/2.52 ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (userid @ u @ Y0) @ (string @ Y0))))))) = $true)),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f43])).
% 1.81/2.52 thf(f43,plain,(
% 1.81/2.52 ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (userid @ u @ Y0) @ (string @ Y0))))))) = $true)),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f42])).
% 1.81/2.52 thf(f42,plain,(
% 1.81/2.52 (mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : (mbox @ (mand @ (userid @ u @ X0) @ (string @ X0)))))))),
% 1.81/2.52 inference(rectify,[status(thm)],[f15])).
% 1.81/2.52 thf(f15,axiom,(
% 1.81/2.52 (mlocal @ (mbox @ (mexists_di @ (^[X7 : $i] : (mbox @ (mand @ (userid @ u @ X7) @ (string @ X7)))))))),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',ax1)).
% 1.81/2.52 thf(f79,plain,(
% 1.81/2.52 ( ! [X0 : mworld] : (($true = (mrel @ X0 @ X0))) )),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f41])).
% 1.81/2.52 thf(f41,plain,(
% 1.81/2.52 ! [X0 : mworld] : ($true = (mrel @ X0 @ X0))),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f40])).
% 1.81/2.52 thf(f40,plain,(
% 1.81/2.52 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 1.81/2.52 inference(rectify,[status(thm)],[f9])).
% 1.81/2.52 thf(f9,axiom,(
% 1.81/2.52 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mrel_reflexive)).
% 1.81/2.52 thf(f1495,plain,(
% 1.81/2.52 spl1_10 | ~spl1_2 | spl1_7 | ~spl1_9),
% 1.81/2.52 inference(avatar_split_clause,[status(thm)],[f1494,f1397,f1339,f337,f1401])).
% 1.81/2.52 thf(f337,definition,(
% 1.81/2.52 spl1_2 <=> ! [X0 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ sK5)) | ($false = (string @ X0 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (entry_box @ X1 @ sK5)))),
% 1.81/2.52 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.81/2.52 thf(f1339,definition,(
% 1.81/2.52 spl1_7 <=> ($false = (entry_box @ sK3 @ sK5))),
% 1.81/2.52 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.81/2.52 thf(f1494,plain,(
% 1.81/2.52 ($false = (string @ (sK4 @ sK5) @ sK5)) | (~spl1_2 | spl1_7 | ~spl1_9)),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1493])).
% 1.81/2.52 thf(f1493,plain,(
% 1.81/2.52 ($false = (string @ (sK4 @ sK5) @ sK5)) | ($false = $true) | (~spl1_2 | spl1_7 | ~spl1_9)),
% 1.81/2.52 inference(forward_demodulation,[status(thm)],[f1492,f228])).
% 1.81/2.52 thf(f228,plain,(
% 1.81/2.52 ((eiw_di @ sK3 @ sK5) = $true)),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f220])).
% 1.81/2.52 thf(f220,plain,(
% 1.81/2.52 ($true != $true) | ((eiw_di @ sK3 @ sK5) = $true)),
% 1.81/2.52 inference(superposition,[status(thm)],[f205,f115])).
% 1.81/2.52 thf(f115,plain,(
% 1.81/2.52 ($true = (eiw_di @ sK3 @ mactual))),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.81/2.52 thf(f205,plain,(
% 1.81/2.52 ( ! [X0 : $i] : (($true != (eiw_di @ X0 @ mactual)) | ((eiw_di @ X0 @ sK5) = $true)) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f199])).
% 1.81/2.52 thf(f199,plain,(
% 1.81/2.52 ( ! [X0 : $i] : (((eiw_di @ X0 @ sK5) = $true) | ($true != $true) | ($true != (eiw_di @ X0 @ mactual))) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f66,f182])).
% 1.81/2.52 thf(f182,plain,(
% 1.81/2.52 ($true = (mrel @ sK5 @ mactual))),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f180])).
% 1.81/2.52 thf(f180,plain,(
% 1.81/2.52 ($true = (mrel @ sK5 @ mactual)) | ($true != $true)),
% 1.81/2.52 inference(superposition,[status(thm)],[f178,f79])).
% 1.81/2.52 thf(f178,plain,(
% 1.81/2.52 ( ! [X0 : mworld] : (($true != (mrel @ mactual @ X0)) | ((mrel @ sK5 @ X0) = $true)) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f176])).
% 1.81/2.52 thf(f176,plain,(
% 1.81/2.52 ( ! [X0 : mworld] : (($true != $true) | ((mrel @ sK5 @ X0) = $true) | ($true != (mrel @ mactual @ X0))) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f63,f138])).
% 1.81/2.52 thf(f63,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : (($true != (mrel @ X0 @ X1)) | ($true = (mrel @ X1 @ X2)) | ((mrel @ X0 @ X2) != $true)) )),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f58])).
% 1.81/2.52 thf(f58,plain,(
% 1.81/2.52 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (($true = (mrel @ X1 @ X2)) | ((mrel @ X0 @ X2) != $true) | ($true != (mrel @ X0 @ X1)))),
% 1.81/2.52 inference(flattening,[status(thm)],[f57])).
% 1.81/2.52 thf(f57,plain,(
% 1.81/2.52 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (($true = (mrel @ X1 @ X2)) | (((mrel @ X0 @ X2) != $true) | ($true != (mrel @ X0 @ X1))))),
% 1.81/2.52 inference(ennf_transformation,[status(thm)],[f55])).
% 1.81/2.52 thf(f55,plain,(
% 1.81/2.52 ! [X0 : mworld,X1 : mworld,X2 : mworld] : ((((mrel @ X0 @ X2) = $true) & ($true = (mrel @ X0 @ X1))) => ($true = (mrel @ X1 @ X2)))),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f54])).
% 1.81/2.52 thf(f54,plain,(
% 1.81/2.52 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X0 @ X1) & (mrel @ X0 @ X2)) => (mrel @ X1 @ X2))),
% 1.81/2.52 inference(rectify,[status(thm)],[f10])).
% 1.81/2.52 thf(f10,axiom,(
% 1.81/2.52 ! [X2 : mworld,X5 : mworld,X4 : mworld] : (((mrel @ X2 @ X5) & (mrel @ X2 @ X4)) => (mrel @ X5 @ X4))),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',mrel_euclidean)).
% 1.81/2.52 thf(f66,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X0 : mworld,X1 : $i] : (((mrel @ X2 @ X0) != $true) | ((eiw_di @ X1 @ X0) != $true) | ((eiw_di @ X1 @ X2) = $true)) )),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f60])).
% 1.81/2.52 thf(f60,plain,(
% 1.81/2.52 ! [X0 : mworld,X1 : $i,X2 : mworld] : (((eiw_di @ X1 @ X0) != $true) | ((eiw_di @ X1 @ X2) = $true) | ((mrel @ X2 @ X0) != $true))),
% 1.81/2.52 inference(flattening,[status(thm)],[f59])).
% 1.81/2.52 thf(f59,plain,(
% 1.81/2.52 ! [X0 : mworld,X1 : $i,X2 : mworld] : (((eiw_di @ X1 @ X2) = $true) | (((mrel @ X2 @ X0) != $true) | ((eiw_di @ X1 @ X0) != $true)))),
% 1.81/2.52 inference(ennf_transformation,[status(thm)],[f51])).
% 1.81/2.52 thf(f51,plain,(
% 1.81/2.52 ! [X0 : mworld,X1 : $i,X2 : mworld] : ((((mrel @ X2 @ X0) = $true) & ((eiw_di @ X1 @ X0) = $true)) => ((eiw_di @ X1 @ X2) = $true))),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f50])).
% 1.81/2.52 thf(f50,plain,(
% 1.81/2.52 ! [X0 : mworld,X1 : $i,X2 : mworld] : (((eiw_di @ X1 @ X0) & (mrel @ X2 @ X0)) => (eiw_di @ X1 @ X2))),
% 1.81/2.52 inference(rectify,[status(thm)],[f12])).
% 1.81/2.52 thf(f12,axiom,(
% 1.81/2.52 ! [X2 : mworld,X6 : $i,X4 : mworld] : (((eiw_di @ X6 @ X2) & (mrel @ X4 @ X2)) => (eiw_di @ X6 @ X4))),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',eiw_di_decr)).
% 1.81/2.52 thf(f1492,plain,(
% 1.81/2.52 ($false = (eiw_di @ sK3 @ sK5)) | ($false = (string @ (sK4 @ sK5) @ sK5)) | (~spl1_2 | spl1_7 | ~spl1_9)),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1491])).
% 1.81/2.52 thf(f1491,plain,(
% 1.81/2.52 ($false = $true) | ($false = (string @ (sK4 @ sK5) @ sK5)) | ($false = (eiw_di @ sK3 @ sK5)) | (~spl1_2 | spl1_7 | ~spl1_9)),
% 1.81/2.52 inference(forward_demodulation,[status(thm)],[f1490,f226])).
% 1.81/2.52 thf(f226,plain,(
% 1.81/2.52 ((eiw_di @ (sK4 @ sK5) @ sK5) = $true)),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f222])).
% 1.81/2.52 thf(f222,plain,(
% 1.81/2.52 ((eiw_di @ (sK4 @ sK5) @ sK5) = $true) | ($true != $true)),
% 1.81/2.52 inference(superposition,[status(thm)],[f205,f213])).
% 1.81/2.52 thf(f213,plain,(
% 1.81/2.52 ((eiw_di @ (sK4 @ sK5) @ mactual) = $true)),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f212])).
% 1.81/2.52 thf(f212,plain,(
% 1.81/2.52 ($false = $true) | ((eiw_di @ (sK4 @ sK5) @ mactual) = $true)),
% 1.81/2.52 inference(forward_demodulation,[status(thm)],[f211,f138])).
% 1.81/2.52 thf(f211,plain,(
% 1.81/2.52 ((mrel @ mactual @ sK5) = $false) | ((eiw_di @ (sK4 @ sK5) @ mactual) = $true)),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f206])).
% 1.81/2.52 thf(f206,plain,(
% 1.81/2.52 ((eiw_di @ (sK4 @ sK5) @ mactual) = $true) | ($true != $true) | ((mrel @ mactual @ sK5) = $false)),
% 1.81/2.52 inference(superposition,[status(thm)],[f202,f128])).
% 1.81/2.52 thf(f128,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (((eiw_di @ (sK4 @ X1) @ X1) = $true) | ($false = (mrel @ mactual @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f126])).
% 1.81/2.52 thf(f202,plain,(
% 1.81/2.52 ( ! [X0 : $i] : (((eiw_di @ X0 @ sK5) != $true) | ($true = (eiw_di @ X0 @ mactual))) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f197])).
% 1.81/2.52 thf(f197,plain,(
% 1.81/2.52 ( ! [X0 : $i] : (($true != $true) | ($true = (eiw_di @ X0 @ mactual)) | ((eiw_di @ X0 @ sK5) != $true)) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f66,f138])).
% 1.81/2.52 thf(f1490,plain,(
% 1.81/2.52 ($false = (eiw_di @ (sK4 @ sK5) @ sK5)) | ($false = (string @ (sK4 @ sK5) @ sK5)) | ($false = (eiw_di @ sK3 @ sK5)) | (~spl1_2 | spl1_7 | ~spl1_9)),
% 1.81/2.52 inference(subsumption_resolution,[status(thm)],[f1482,f1340])).
% 1.81/2.52 thf(f1340,plain,(
% 1.81/2.52 ($false != (entry_box @ sK3 @ sK5)) | spl1_7),
% 1.81/2.52 inference(avatar_component_clause,[status(thm)],[f1339])).
% 1.81/2.52 thf(f1482,plain,(
% 1.81/2.52 ($false = (string @ (sK4 @ sK5) @ sK5)) | ($false = (entry_box @ sK3 @ sK5)) | ($false = (eiw_di @ sK3 @ sK5)) | ($false = (eiw_di @ (sK4 @ sK5) @ sK5)) | (~spl1_2 | ~spl1_9)),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1475])).
% 1.81/2.52 thf(f1475,plain,(
% 1.81/2.52 ($false = (entry_box @ sK3 @ sK5)) | ($false = (eiw_di @ sK3 @ sK5)) | ($false = (eiw_di @ (sK4 @ sK5) @ sK5)) | ($false = $true) | ($false = (string @ (sK4 @ sK5) @ sK5)) | (~spl1_2 | ~spl1_9)),
% 1.81/2.52 inference(superposition,[status(thm)],[f1399,f350])).
% 1.81/2.52 thf(f350,plain,(
% 1.81/2.52 ( ! [X0 : $i,X1 : $i] : (($true = (mrel @ mactual @ (sK6 @ X0 @ X1))) | ($false = (string @ X0 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (entry_box @ X1 @ sK5))) ) | ~spl1_2),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f347])).
% 1.81/2.52 thf(f347,plain,(
% 1.81/2.52 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (string @ X0 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (entry_box @ X1 @ sK5)) | ($true = (mrel @ mactual @ (sK6 @ X0 @ X1)))) ) | ~spl1_2),
% 1.81/2.52 inference(superposition,[status(thm)],[f184,f338])).
% 1.81/2.52 thf(f338,plain,(
% 1.81/2.52 ( ! [X0 : $i,X1 : $i] : (((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ($false = (string @ X0 @ sK5))) ) | ~spl1_2),
% 1.81/2.52 inference(avatar_component_clause,[status(thm)],[f337])).
% 1.81/2.52 thf(f184,plain,(
% 1.81/2.52 ( ! [X0 : mworld] : (((mrel @ sK5 @ X0) != $true) | ($true = (mrel @ mactual @ X0))) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f183])).
% 1.81/2.52 thf(f183,plain,(
% 1.81/2.52 ( ! [X0 : mworld] : (((mrel @ sK5 @ X0) != $true) | ($true = (mrel @ mactual @ X0)) | ($true != $true)) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f63,f182])).
% 1.81/2.52 thf(f1399,plain,(
% 1.81/2.52 ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | ~spl1_9),
% 1.81/2.52 inference(avatar_component_clause,[status(thm)],[f1397])).
% 1.81/2.52 thf(f1444,plain,(
% 1.81/2.52 spl1_10 | spl1_11 | spl1_9 | ~spl1_2 | spl1_7 | ~spl1_8),
% 1.81/2.52 inference(avatar_split_clause,[status(thm)],[f1443,f1343,f1339,f337,f1397,f1405,f1401])).
% 1.81/2.52 thf(f1343,definition,(
% 1.81/2.52 spl1_8 <=> ! [X0 : mworld] : (((mrel @ mactual @ (sK6 @ (sK4 @ X0) @ sK3)) = $false) | ((eiw_di @ (sK4 @ X0) @ sK5) = $false) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ X0) @ sK3))) | ($false = (mrel @ mactual @ X0)) | ($false = (mrel @ X0 @ (sK6 @ (sK4 @ X0) @ sK3))) | ($false = (string @ (sK4 @ X0) @ sK5)))),
% 1.81/2.52 introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition])).
% 1.81/2.52 thf(f1443,plain,(
% 1.81/2.52 ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = (string @ (sK4 @ sK5) @ sK5)) | ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | (~spl1_2 | spl1_7 | ~spl1_8)),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1442])).
% 1.81/2.52 thf(f1442,plain,(
% 1.81/2.52 ($false = $true) | ($false = (string @ (sK4 @ sK5) @ sK5)) | ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ sK5) @ sK3))) | (~spl1_2 | spl1_7 | ~spl1_8)),
% 1.81/2.52 inference(forward_demodulation,[status(thm)],[f1441,f138])).
% 1.81/2.52 thf(f1441,plain,(
% 1.81/2.52 ($false = (string @ (sK4 @ sK5) @ sK5)) | ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | ((mrel @ mactual @ sK5) = $false) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ sK5) @ sK3))) | (~spl1_2 | spl1_7 | ~spl1_8)),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1440])).
% 1.81/2.52 thf(f1440,plain,(
% 1.81/2.52 ((mrel @ mactual @ sK5) = $false) | ($false = (string @ (sK4 @ sK5) @ sK5)) | ($false = $true) | ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ sK5) @ sK3))) | (~spl1_2 | spl1_7 | ~spl1_8)),
% 1.81/2.52 inference(forward_demodulation,[status(thm)],[f1439,f228])).
% 1.81/2.52 thf(f1439,plain,(
% 1.81/2.52 ($false = (eiw_di @ sK3 @ sK5)) | ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = (string @ (sK4 @ sK5) @ sK5)) | ((mrel @ mactual @ sK5) = $false) | (~spl1_2 | spl1_7 | ~spl1_8)),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1438])).
% 1.81/2.52 thf(f1438,plain,(
% 1.81/2.52 ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ sK5) @ sK3))) | ((mrel @ mactual @ sK5) = $false) | ($false = (string @ (sK4 @ sK5) @ sK5)) | ($false = (eiw_di @ sK3 @ sK5)) | ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = $true) | (~spl1_2 | spl1_7 | ~spl1_8)),
% 1.81/2.52 inference(forward_demodulation,[status(thm)],[f1437,f226])).
% 1.81/2.52 thf(f1437,plain,(
% 1.81/2.52 ($false = (eiw_di @ (sK4 @ sK5) @ sK5)) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = (string @ (sK4 @ sK5) @ sK5)) | ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = (eiw_di @ sK3 @ sK5)) | ((mrel @ mactual @ sK5) = $false) | (~spl1_2 | spl1_7 | ~spl1_8)),
% 1.81/2.52 inference(subsumption_resolution,[status(thm)],[f1382,f1340])).
% 1.81/2.52 thf(f1382,plain,(
% 1.81/2.52 ((mrel @ mactual @ sK5) = $false) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = (eiw_di @ sK3 @ sK5)) | ($false = (eiw_di @ (sK4 @ sK5) @ sK5)) | ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = (entry_box @ sK3 @ sK5)) | ($false = (string @ (sK4 @ sK5) @ sK5)) | (~spl1_2 | ~spl1_8)),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1381])).
% 1.81/2.52 thf(f1381,plain,(
% 1.81/2.52 ((mrel @ mactual @ sK5) = $false) | ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = (entry_box @ sK3 @ sK5)) | ($false = (eiw_di @ (sK4 @ sK5) @ sK5)) | ($false = $true) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = (string @ (sK4 @ sK5) @ sK5)) | ($false = (eiw_di @ sK3 @ sK5)) | (~spl1_2 | ~spl1_8)),
% 1.81/2.52 inference(duplicate_literal_removal,[status(thm)],[f1377])).
% 1.81/2.52 thf(f1377,plain,(
% 1.81/2.52 ($false = (mrel @ mactual @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = (string @ (sK4 @ sK5) @ sK5)) | ($false = (entry_box @ sK3 @ sK5)) | ($false = (eiw_di @ sK3 @ sK5)) | ($false = (eiw_di @ (sK4 @ sK5) @ sK5)) | ($false = $true) | ((mrel @ mactual @ sK5) = $false) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ sK5) @ sK3))) | ($false = (string @ (sK4 @ sK5) @ sK5)) | ($false = (eiw_di @ (sK4 @ sK5) @ sK5)) | (~spl1_2 | ~spl1_8)),
% 1.81/2.52 inference(superposition,[status(thm)],[f338,f1344])).
% 1.81/2.52 thf(f1344,plain,(
% 1.81/2.52 ( ! [X0 : mworld] : (($false = (mrel @ X0 @ (sK6 @ (sK4 @ X0) @ sK3))) | ($false = (mrel @ mactual @ X0)) | ((eiw_di @ (sK4 @ X0) @ sK5) = $false) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ X0) @ sK3))) | ((mrel @ mactual @ (sK6 @ (sK4 @ X0) @ sK3)) = $false) | ($false = (string @ (sK4 @ X0) @ sK5))) ) | ~spl1_8),
% 1.81/2.52 inference(avatar_component_clause,[status(thm)],[f1343])).
% 1.81/2.52 thf(f1355,plain,(
% 1.81/2.52 ~spl1_7),
% 1.81/2.52 inference(avatar_contradiction_clause,[status(thm)],[f1354])).
% 1.81/2.52 thf(f1354,plain,(
% 1.81/2.52 $false | ~spl1_7),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1353])).
% 1.81/2.52 thf(f1353,plain,(
% 1.81/2.52 ($false = $true) | ~spl1_7),
% 1.81/2.52 inference(backward_demodulation,[status(thm)],[f138,f1352])).
% 1.81/2.52 thf(f1352,plain,(
% 1.81/2.52 ((mrel @ mactual @ sK5) = $false) | ~spl1_7),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1350])).
% 1.81/2.52 thf(f1350,plain,(
% 1.81/2.52 ($false = $true) | ((mrel @ mactual @ sK5) = $false) | ~spl1_7),
% 1.81/2.52 inference(superposition,[status(thm)],[f119,f1341])).
% 1.81/2.52 thf(f1341,plain,(
% 1.81/2.52 ($false = (entry_box @ sK3 @ sK5)) | ~spl1_7),
% 1.81/2.52 inference(avatar_component_clause,[status(thm)],[f1339])).
% 1.81/2.52 thf(f1348,plain,(
% 1.81/2.52 spl1_7 | spl1_8 | ~spl1_3),
% 1.81/2.52 inference(avatar_split_clause,[status(thm)],[f1347,f367,f1343,f1339])).
% 1.81/2.52 thf(f367,definition,(
% 1.81/2.52 spl1_3 <=> ! [X0 : $i,X1 : $i] : (($false = (entry_box @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (string @ X0 @ sK5)) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X1 @ sK5)))),
% 1.81/2.52 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.81/2.52 thf(f1347,plain,(
% 1.81/2.52 ( ! [X0 : mworld] : (($false = (entry_box @ sK3 @ sK5)) | ((eiw_di @ (sK4 @ X0) @ sK5) = $false) | ($false = (mrel @ X0 @ (sK6 @ (sK4 @ X0) @ sK3))) | ($false = (string @ (sK4 @ X0) @ sK5)) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ X0) @ sK3))) | ($false = (mrel @ mactual @ X0)) | ((mrel @ mactual @ (sK6 @ (sK4 @ X0) @ sK3)) = $false)) ) | ~spl1_3),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1346])).
% 1.81/2.52 thf(f1346,plain,(
% 1.81/2.52 ( ! [X0 : mworld] : (((mrel @ mactual @ (sK6 @ (sK4 @ X0) @ sK3)) = $false) | ($false = (mrel @ X0 @ (sK6 @ (sK4 @ X0) @ sK3))) | ((eiw_di @ (sK4 @ X0) @ sK5) = $false) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ X0) @ sK3))) | ($false = (string @ (sK4 @ X0) @ sK5)) | ($false = (mrel @ mactual @ X0)) | ($false = (entry_box @ sK3 @ sK5)) | ($false = $true)) ) | ~spl1_3),
% 1.81/2.52 inference(forward_demodulation,[status(thm)],[f1334,f228])).
% 1.81/2.52 thf(f1334,plain,(
% 1.81/2.52 ( ! [X0 : mworld] : (((eiw_di @ (sK4 @ X0) @ sK5) = $false) | ($false = (eiw_di @ sK3 @ sK5)) | ($false = (mrel @ X0 @ (sK6 @ (sK4 @ X0) @ sK3))) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ X0) @ sK3))) | ($false = (string @ (sK4 @ X0) @ sK5)) | ($false = (entry_box @ sK3 @ sK5)) | ((mrel @ mactual @ (sK6 @ (sK4 @ X0) @ sK3)) = $false) | ($false = (mrel @ mactual @ X0))) ) | ~spl1_3),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1332])).
% 1.81/2.52 thf(f1332,plain,(
% 1.81/2.52 ( ! [X0 : mworld] : (($false = (string @ (sK4 @ X0) @ sK5)) | ($false = (mrel @ X0 @ (sK6 @ (sK4 @ X0) @ sK3))) | ((eiw_di @ (sK4 @ X0) @ sK5) = $false) | ($false = (mrel @ mactual @ X0)) | ((mrel @ mactual @ (sK6 @ (sK4 @ X0) @ sK3)) = $false) | ($false = (entry_box @ sK3 @ (sK6 @ (sK4 @ X0) @ sK3))) | ($false = (entry_box @ sK3 @ sK5)) | ($false = $true) | ($false = (eiw_di @ sK3 @ sK5))) ) | ~spl1_3),
% 1.81/2.52 inference(superposition,[status(thm)],[f1235,f120])).
% 1.81/2.52 thf(f120,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($true = (number @ sK3 @ one @ X1)) | ($false = (mrel @ mactual @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f118])).
% 1.81/2.52 thf(f1235,plain,(
% 1.81/2.52 ( ! [X0 : mworld,X1 : $i] : (($false = (number @ X1 @ one @ (sK6 @ (sK4 @ X0) @ X1))) | ($false = (mrel @ X0 @ (sK6 @ (sK4 @ X0) @ X1))) | ((eiw_di @ (sK4 @ X0) @ sK5) = $false) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ($false = (mrel @ mactual @ X0)) | ($false = (entry_box @ X1 @ (sK6 @ (sK4 @ X0) @ X1))) | ($false = (string @ (sK4 @ X0) @ sK5))) ) | ~spl1_3),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f1233])).
% 1.81/2.52 thf(f1233,plain,(
% 1.81/2.52 ( ! [X0 : mworld,X1 : $i] : (($false = (string @ (sK4 @ X0) @ sK5)) | ($false = (mrel @ X0 @ (sK6 @ (sK4 @ X0) @ X1))) | ($false = (entry_box @ X1 @ (sK6 @ (sK4 @ X0) @ X1))) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (mrel @ mactual @ X0)) | ($false = (number @ X1 @ one @ (sK6 @ (sK4 @ X0) @ X1))) | ((eiw_di @ (sK4 @ X0) @ sK5) = $false) | ($false = $true) | ($false = (entry_box @ X1 @ sK5))) ) | ~spl1_3),
% 1.81/2.52 inference(superposition,[status(thm)],[f132,f368])).
% 1.81/2.52 thf(f368,plain,(
% 1.81/2.52 ( ! [X0 : $i,X1 : $i] : (($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (entry_box @ X1 @ sK5)) | ($false = (string @ X0 @ sK5)) | ($false = (eiw_di @ X1 @ sK5))) ) | ~spl1_3),
% 1.81/2.52 inference(avatar_component_clause,[status(thm)],[f367])).
% 1.81/2.52 thf(f132,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X1 : mworld] : (($true = (userid @ u @ (sK4 @ X1) @ X2)) | ($false = (mrel @ X1 @ X2)) | ($false = (mrel @ mactual @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.81/2.52 thf(f393,plain,(
% 1.81/2.52 ~spl1_1),
% 1.81/2.52 inference(avatar_contradiction_clause,[status(thm)],[f392])).
% 1.81/2.52 thf(f392,plain,(
% 1.81/2.52 $false | ~spl1_1),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f382])).
% 1.81/2.52 thf(f382,plain,(
% 1.81/2.52 ($false = $true) | ~spl1_1),
% 1.81/2.52 inference(backward_demodulation,[status(thm)],[f227,f335])).
% 1.81/2.52 thf(f335,plain,(
% 1.81/2.52 ( ! [X2 : $i] : (($false = (eiw_di @ X2 @ sK5))) ) | ~spl1_1),
% 1.81/2.52 inference(avatar_component_clause,[status(thm)],[f334])).
% 1.81/2.52 thf(f334,definition,(
% 1.81/2.52 spl1_1 <=> ! [X2 : $i] : ($false = (eiw_di @ X2 @ sK5))),
% 1.81/2.52 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.81/2.52 thf(f227,plain,(
% 1.81/2.52 ($true = (eiw_di @ (sK0 @ mactual) @ sK5))),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f224])).
% 1.81/2.52 thf(f224,plain,(
% 1.81/2.52 ($true = (eiw_di @ (sK0 @ mactual) @ sK5)) | ($true != $true)),
% 1.81/2.52 inference(superposition,[status(thm)],[f205,f74])).
% 1.81/2.52 thf(f74,plain,(
% 1.81/2.52 ( ! [X0 : mworld] : (((eiw_di @ (sK0 @ X0) @ X0) = $true)) )),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f62])).
% 1.81/2.52 thf(f62,plain,(
% 1.81/2.52 ! [X0 : mworld] : ((eiw_di @ (sK0 @ X0) @ X0) = $true)),
% 1.81/2.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f61])).
% 1.81/2.52 thf(f61,plain,(
% 1.81/2.52 ! [X0 : mworld] : (? [X1 : $i] : ((eiw_di @ X1 @ X0) = $true) => ((eiw_di @ (sK0 @ X0) @ X0) = $true))),
% 1.81/2.52 introduced(definition,[],[choice_axiom])).
% 1.81/2.52 thf(f22,plain,(
% 1.81/2.52 ! [X0 : mworld] : ? [X1 : $i] : ((eiw_di @ X1 @ X0) = $true)),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f21])).
% 1.81/2.52 thf(f21,plain,(
% 1.81/2.52 ! [X0 : mworld] : ? [X1 : $i] : (eiw_di @ X1 @ X0)),
% 1.81/2.52 inference(rectify,[status(thm)],[f11])).
% 1.81/2.52 thf(f11,axiom,(
% 1.81/2.52 ! [X2 : mworld] : ? [X6 : $i] : (eiw_di @ X6 @ X2)),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',eiw_di_nonempty)).
% 1.81/2.52 thf(f376,plain,(
% 1.81/2.52 spl1_1 | spl1_3),
% 1.81/2.52 inference(avatar_split_clause,[status(thm)],[f375,f367,f334])).
% 1.81/2.52 thf(f375,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (string @ X0 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X2 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1)))) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f374])).
% 1.81/2.52 thf(f374,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (string @ X0 @ sK5)) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X2 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ($false = $true) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1)))) )),
% 1.81/2.52 inference(forward_demodulation,[status(thm)],[f359,f138])).
% 1.81/2.52 thf(f359,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (entry_box @ X1 @ sK5)) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ((mrel @ mactual @ sK5) = $false) | ($false = (string @ X0 @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1)))) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f358])).
% 1.81/2.52 thf(f358,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (entry_box @ X1 @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (string @ X0 @ sK5)) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X1 @ sK5)) | ((mrel @ mactual @ sK5) = $false) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = $true)) )),
% 1.81/2.52 inference(duplicate_literal_removal,[status(thm)],[f356])).
% 1.81/2.52 thf(f356,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (string @ X0 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ($false = $true) | ((mrel @ mactual @ sK5) = $false) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ($false = (string @ X0 @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f103,f317])).
% 1.81/2.52 thf(f317,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (eiw_di @ (sK2 @ X0 @ sK5 @ X1 @ X2) @ sK5)) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ($false = (entry_box @ X1 @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X2 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (string @ X0 @ sK5)) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f316])).
% 1.81/2.52 thf(f316,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = $true) | ($false = (entry_box @ X1 @ sK5)) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (string @ X0 @ sK5)) | ($false = (eiw_di @ (sK2 @ X0 @ sK5 @ X1 @ X2) @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X2 @ sK5))) )),
% 1.81/2.52 inference(forward_demodulation,[status(thm)],[f313,f138])).
% 1.81/2.52 thf(f313,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (string @ X0 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ (sK2 @ X0 @ sK5 @ X1 @ X2) @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ((mrel @ mactual @ sK5) = $false)) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f312])).
% 1.81/2.52 thf(f312,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = $true) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (string @ X0 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ($false = (entry_box @ X1 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ (sK2 @ X0 @ sK5 @ X1 @ X2) @ sK5)) | ((mrel @ mactual @ sK5) = $false)) )),
% 1.81/2.52 inference(duplicate_literal_removal,[status(thm)],[f299])).
% 1.81/2.52 thf(f299,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((mrel @ mactual @ sK5) = $false) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ($false = (eiw_di @ (sK2 @ X0 @ sK5 @ X1 @ X2) @ sK5)) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ (sK2 @ X0 @ sK5 @ X1 @ X2) @ sK5)) | ($false = $true) | ($false = (eiw_di @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (string @ X0 @ sK5)) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X2 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X2 @ sK5))) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f273,f169])).
% 1.81/2.52 thf(f169,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((mrel @ sK5 @ (sK7 @ X3 @ X1 @ X4 @ X2)) = $true) | ($false = (userid @ u @ X1 @ (sK6 @ X1 @ X2))) | ($false = (entry_box @ X2 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f167])).
% 1.81/2.52 thf(f167,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (entry_box @ X2 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (userid @ u @ X1 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X3 @ sK5)) | (((mrel @ sK5 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2))))))) = $false) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2)))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f166])).
% 1.81/2.52 thf(f166,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (userid @ u @ X1 @ (sK6 @ X1 @ X2))) | ($false = ((number @ X2 @ one @ (sK6 @ X1 @ X2)) & (entry_box @ X2 @ (sK6 @ X1 @ X2)))) | (((mrel @ sK5 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2))))))) = $false) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X3 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f156])).
% 1.81/2.52 thf(f156,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (((number @ X2 @ one @ (sK6 @ X1 @ X2)) & (entry_box @ X2 @ (sK6 @ X1 @ X2))) & (userid @ u @ X1 @ (sK6 @ X1 @ X2)))) | ($false = (eiw_di @ X1 @ sK5)) | (((mrel @ sK5 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2))))))) = $false) | ($false = (eiw_di @ X3 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f155])).
% 1.81/2.52 thf(f155,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((mrel @ sK5 @ (sK6 @ X1 @ X2)) => (((number @ X2 @ one @ (sK6 @ X1 @ X2)) & (entry_box @ X2 @ (sK6 @ X1 @ X2))) & (userid @ u @ X1 @ (sK6 @ X1 @ X2))))) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | (((mrel @ sK5 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2))))))) = $false)) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f154])).
% 1.81/2.52 thf(f154,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (eiw_di @ X4 @ sK5)) | ($false = ((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0))))))) @ (sK7 @ X3 @ X1 @ X4 @ X2))) | ($false = ((mrel @ sK5 @ (sK6 @ X1 @ X2)) => (((number @ X2 @ one @ (sK6 @ X1 @ X2)) & (entry_box @ X2 @ (sK6 @ X1 @ X2))) & (userid @ u @ X1 @ (sK6 @ X1 @ X2))))) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X3 @ sK5))) )),
% 1.81/2.52 inference(sigma_clausification,[status(thm)],[f153])).
% 1.81/2.52 thf(f153,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0))))))))) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X3 @ sK5)) | ($false = ((mrel @ sK5 @ (sK6 @ X1 @ X2)) => (((number @ X2 @ one @ (sK6 @ X1 @ X2)) & (entry_box @ X2 @ (sK6 @ X1 @ X2))) & (userid @ u @ X1 @ (sK6 @ X1 @ X2))))) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f152])).
% 1.81/2.52 thf(f152,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (eiw_di @ X2 @ sK5)) | ($false = ((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (((number @ X2 @ one @ Y0) & (entry_box @ X2 @ Y0)) & (userid @ u @ X1 @ Y0)))) @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0)))))))))) )),
% 1.81/2.52 inference(sigma_clausification,[status(thm)],[f151])).
% 1.81/2.52 thf(f151,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (((number @ X2 @ one @ Y0) & (entry_box @ X2 @ Y0)) & (userid @ u @ X1 @ Y0)))))) | ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0)))))))))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f150])).
% 1.81/2.52 thf(f150,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X4 @ sK5)) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0)))))))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (((number @ X2 @ one @ Y0) & (entry_box @ X2 @ Y0)) & (userid @ u @ X1 @ Y0))))))) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X3 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f149])).
% 1.81/2.52 thf(f149,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (eiw_di @ X3 @ sK5)) | ($false = ((eiw_di @ X4 @ sK5) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0)))))))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (((number @ X2 @ one @ Y0) & (entry_box @ X2 @ Y0)) & (userid @ u @ X1 @ Y0)))))))) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X2 @ sK5))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f148])).
% 1.81/2.52 thf(f148,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X3 @ sK5)) | ($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ sK5) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK5 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ Y0 @ X3 @ Y2 @ Y1) => (in @ X1 @ X2 @ Y2 @ Y1)))))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK5 @ Y1) => (((number @ X2 @ one @ Y1) & (entry_box @ X2 @ Y1)) & (userid @ u @ X1 @ Y1)))))))) @ X4))) )),
% 1.81/2.52 inference(pi_clausification,[status(thm)],[f147])).
% 1.81/2.52 thf(f147,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ sK5)) | ($false = (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK5) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK5 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ Y0 @ X3 @ Y2 @ Y1) => (in @ X1 @ X2 @ Y2 @ Y1)))))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK5 @ Y1) => (((number @ X2 @ one @ Y1) & (entry_box @ X2 @ Y1)) & (userid @ u @ X1 @ Y1)))))))))) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X2 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f146])).
% 1.81/2.52 thf(f146,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (eiw_di @ X2 @ sK5)) | ($false = ((eiw_di @ X3 @ sK5) & (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK5) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK5 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ Y0 @ X3 @ Y2 @ Y1) => (in @ X1 @ X2 @ Y2 @ Y1)))))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK5 @ Y1) => (((number @ X2 @ one @ Y1) & (entry_box @ X2 @ Y1)) & (userid @ u @ X1 @ Y1))))))))))) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f145])).
% 1.81/2.52 thf(f145,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ sK5) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK5) & ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK5 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => ((do @ Y1 @ Y0 @ Y3 @ Y2) => (in @ X1 @ X2 @ Y3 @ Y2)))))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK5 @ Y2) => (((number @ X2 @ one @ Y2) & (entry_box @ X2 @ Y2)) & (userid @ u @ X1 @ Y2))))))))))) @ X3))) )),
% 1.81/2.52 inference(pi_clausification,[status(thm)],[f144])).
% 1.81/2.52 thf(f144,plain,(
% 1.81/2.52 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ sK5)) | ($false = (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK5) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK5) & ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK5 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => ((do @ Y1 @ Y0 @ Y3 @ Y2) => (in @ X1 @ X2 @ Y3 @ Y2)))))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK5 @ Y2) => (((number @ X2 @ one @ Y2) & (entry_box @ X2 @ Y2)) & (userid @ u @ X1 @ Y2))))))))))))) | ($false = (eiw_di @ X2 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.81/2.52 thf(f143,plain,(
% 1.81/2.52 ( ! [X2 : $i,X1 : $i] : (($false = ((eiw_di @ X2 @ sK5) & (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK5) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK5) & ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK5 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => ((do @ Y1 @ Y0 @ Y3 @ Y2) => (in @ X1 @ X2 @ Y3 @ Y2)))))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK5 @ Y2) => (((number @ X2 @ one @ Y2) & (entry_box @ X2 @ Y2)) & (userid @ u @ X1 @ Y2)))))))))))))) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f142])).
% 1.81/2.52 thf(f142,plain,(
% 1.81/2.52 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ sK5) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK5) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ sK5) & ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK5 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => ((do @ Y2 @ Y1 @ Y4 @ Y3) => (in @ X1 @ Y0 @ Y4 @ Y3)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK5 @ Y3) => (((number @ Y0 @ one @ Y3) & (entry_box @ Y0 @ Y3)) & (userid @ u @ X1 @ Y3)))))))))))))) @ X2)) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(pi_clausification,[status(thm)],[f141])).
% 1.81/2.52 thf(f141,plain,(
% 1.81/2.52 ( ! [X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK5) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK5) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ sK5) & ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK5 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => ((do @ Y2 @ Y1 @ Y4 @ Y3) => (in @ X1 @ Y0 @ Y4 @ Y3)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK5 @ Y3) => (((number @ Y0 @ one @ Y3) & (entry_box @ Y0 @ Y3)) & (userid @ u @ X1 @ Y3)))))))))))))))) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 1.81/2.52 thf(f140,plain,(
% 1.81/2.52 ( ! [X1 : $i] : (($false = ((eiw_di @ X1 @ sK5) & (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK5) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK5) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ sK5) & ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK5 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => ((do @ Y2 @ Y1 @ Y4 @ Y3) => (in @ X1 @ Y0 @ Y4 @ Y3)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK5 @ Y3) => (((number @ Y0 @ one @ Y3) & (entry_box @ Y0 @ Y3)) & (userid @ u @ X1 @ Y3)))))))))))))))))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f139])).
% 1.81/2.52 thf(f139,plain,(
% 1.81/2.52 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ sK5) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK5) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ sK5) & (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ sK5) & ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK5 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) => ((do @ Y3 @ Y2 @ Y5 @ Y4) => (in @ Y0 @ Y1 @ Y5 @ Y4)))))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK5 @ Y4) => (((number @ Y1 @ one @ Y4) & (entry_box @ Y1 @ Y4)) & (userid @ u @ Y0 @ Y4))))))))))))))))) @ X1))) )),
% 1.81/2.52 inference(pi_clausification,[status(thm)],[f137])).
% 1.81/2.52 thf(f137,plain,(
% 1.81/2.52 ($false = (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK5) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK5) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ sK5) & (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ sK5) & ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK5 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) => ((do @ Y3 @ Y2 @ Y5 @ Y4) => (in @ Y0 @ Y1 @ Y5 @ Y4)))))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK5 @ Y4) => (((number @ Y1 @ one @ Y4) & (entry_box @ Y1 @ Y4)) & (userid @ u @ Y0 @ Y4)))))))))))))))))))),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.81/2.52 thf(f273,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : mworld] : (($false = (mrel @ X1 @ (sK7 @ (sK2 @ X0 @ X1 @ X2 @ X3) @ X0 @ X3 @ X2))) | ($false = (eiw_di @ X2 @ X1)) | ($false = (eiw_di @ X3 @ X1)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (string @ X0 @ X1)) | ($false = (entry_box @ X2 @ X1)) | ($false = (entry_box @ X2 @ (sK6 @ X0 @ X2))) | ($false = (number @ X2 @ one @ (sK6 @ X0 @ X2))) | ($false = (mrel @ mactual @ X1)) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X2))) | ($false = (eiw_di @ X3 @ sK5)) | ((eiw_di @ (sK2 @ X0 @ X1 @ X2 @ X3) @ sK5) = $false) | ($false = (eiw_di @ X0 @ X1))) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f272])).
% 1.81/2.52 thf(f272,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : mworld] : (($false = $true) | ($false = (string @ X0 @ X1)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X2))) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X3 @ X1)) | ($false = (number @ X2 @ one @ (sK6 @ X0 @ X2))) | ($false = (eiw_di @ X2 @ X1)) | ($false = (mrel @ X1 @ (sK7 @ (sK2 @ X0 @ X1 @ X2 @ X3) @ X0 @ X3 @ X2))) | ($false = (entry_box @ X2 @ (sK6 @ X0 @ X2))) | ((eiw_di @ (sK2 @ X0 @ X1 @ X2 @ X3) @ sK5) = $false) | ($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X0 @ X1)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (entry_box @ X2 @ X1))) )),
% 1.81/2.52 inference(duplicate_literal_removal,[status(thm)],[f269])).
% 1.81/2.52 thf(f269,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : mworld] : (($false = (eiw_di @ X3 @ X1)) | ($false = (number @ X2 @ one @ (sK6 @ X0 @ X2))) | ($false = (eiw_di @ X3 @ sK5)) | ((eiw_di @ (sK2 @ X0 @ X1 @ X2 @ X3) @ sK5) = $false) | ((eiw_di @ X0 @ sK5) = $false) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X0 @ X1)) | ($false = (entry_box @ X2 @ (sK6 @ X0 @ X2))) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (entry_box @ X2 @ X1)) | ($false = (eiw_di @ X2 @ X1)) | ($false = (mrel @ mactual @ X1)) | ($false = (number @ X2 @ one @ (sK6 @ X0 @ X2))) | ($false = (string @ X0 @ X1)) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X2))) | ($false = (entry_box @ X2 @ (sK6 @ X0 @ X2))) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X2))) | ($false = (eiw_di @ X2 @ sK5)) | ($false = $true) | ((eiw_di @ (sK2 @ X0 @ X1 @ X2 @ X3) @ sK5) = $false) | ($false = (mrel @ X1 @ (sK7 @ (sK2 @ X0 @ X1 @ X2 @ X3) @ X0 @ X3 @ X2)))) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f173,f257])).
% 1.81/2.52 thf(f257,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (($false = (eiw_di @ (sK9 @ X0 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X3 @ X1) @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X3 @ sK5)) | ((string @ X0 @ X2) = $false) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X1 @ X2)) | ($false = (mrel @ X2 @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X3 @ X2)) | ($false = (eiw_di @ (sK2 @ X0 @ X2 @ X1 @ X3) @ sK5)) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (entry_box @ X1 @ X2)) | ($false = (mrel @ mactual @ X2)) | ($false = (eiw_di @ X0 @ X2)) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f256])).
% 1.81/2.52 thf(f256,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (($false = $true) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X0 @ X2)) | ($false = (eiw_di @ X3 @ X2)) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ((string @ X0 @ X2) = $false) | ($false = (eiw_di @ X1 @ X2)) | ($false = (eiw_di @ (sK9 @ X0 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X3 @ X1) @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ($false = (mrel @ mactual @ X2)) | ($false = (eiw_di @ (sK2 @ X0 @ X2 @ X1 @ X3) @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (entry_box @ X1 @ X2)) | ($false = (mrel @ X2 @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1)))) )),
% 1.81/2.52 inference(duplicate_literal_removal,[status(thm)],[f252])).
% 1.81/2.52 thf(f252,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (($false = (eiw_di @ X3 @ X2)) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ (sK9 @ X0 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X3 @ X1) @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ($false = (entry_box @ X1 @ X2)) | ($false = (mrel @ X2 @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X1 @ X2)) | ($false = (eiw_di @ (sK2 @ X0 @ X2 @ X1 @ X3) @ sK5)) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1))) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X0 @ X2)) | ($false = (eiw_di @ (sK2 @ X0 @ X2 @ X1 @ X3) @ sK5)) | ($false = (mrel @ mactual @ X2)) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ((string @ X0 @ X2) = $false) | ($false = (eiw_di @ X1 @ sK5)) | ($false = $true) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X1)))) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f241,f174])).
% 1.81/2.52 thf(f174,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X1 @ X2 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X3 @ X1 @ X4 @ X2))) | ($false = (userid @ u @ X1 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (entry_box @ X2 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2)))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f172])).
% 1.81/2.52 thf(f172,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (entry_box @ X2 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (userid @ u @ X1 @ (sK6 @ X1 @ X2))) | (((do @ X4 @ X3 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X3 @ X1 @ X4 @ X2))) = $false) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f171])).
% 1.81/2.52 thf(f171,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (eiw_di @ X4 @ sK5)) | ($false = ((eiw_di @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X3 @ X1 @ X4 @ X2))))) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (entry_box @ X2 @ (sK6 @ X1 @ X2))) | ($false = (userid @ u @ X1 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f170])).
% 1.81/2.52 thf(f170,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (entry_box @ X2 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (userid @ u @ X1 @ (sK6 @ X1 @ X2))) | ($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2))))) @ (sK9 @ X1 @ X3 @ X4 @ X2))) | ($false = (eiw_di @ X2 @ sK5))) )),
% 1.81/2.52 inference(sigma_clausification,[status(thm)],[f168])).
% 1.81/2.52 thf(f168,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (userid @ u @ X1 @ (sK6 @ X1 @ X2))) | ($false = (entry_box @ X2 @ (sK6 @ X1 @ X2))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2))))))) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X3 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f167])).
% 1.81/2.52 thf(f241,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((in @ X1 @ X3 @ (sK9 @ X4 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK7 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5)) = $true) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (number @ X5 @ one @ (sK6 @ X4 @ X5))) | ($false = (eiw_di @ X1 @ X2)) | ($false = (mrel @ mactual @ X2)) | ($false = (entry_box @ X3 @ X2)) | ($false = (eiw_di @ X3 @ X2)) | ($false = (eiw_di @ X5 @ sK5)) | ($false = (eiw_di @ (sK2 @ X1 @ X2 @ X3 @ X0) @ sK5)) | ($false = (eiw_di @ X0 @ X2)) | ($false = (entry_box @ X5 @ (sK6 @ X4 @ X5))) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ (sK9 @ X4 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK7 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) | ($false = (mrel @ X2 @ (sK7 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) | ($false = (string @ X1 @ X2)) | ($false = (userid @ u @ X4 @ (sK6 @ X4 @ X5)))) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f238])).
% 1.81/2.52 thf(f238,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (((eiw_di @ X0 @ sK5) = $false) | ((in @ X1 @ X3 @ (sK9 @ X4 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK7 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5)) = $true) | ($false = (entry_box @ X3 @ X2)) | ($false = (eiw_di @ (sK2 @ X1 @ X2 @ X3 @ X0) @ sK5)) | ($false = (userid @ u @ X4 @ (sK6 @ X4 @ X5))) | ($false = (string @ X1 @ X2)) | ($false = (mrel @ mactual @ X2)) | ($false = (eiw_di @ X5 @ sK5)) | ($false = (mrel @ X2 @ (sK7 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) | ($false = (eiw_di @ X3 @ X2)) | ($false = $true) | ($false = (eiw_di @ X0 @ X2)) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (number @ X5 @ one @ (sK6 @ X4 @ X5))) | ($false = (entry_box @ X5 @ (sK6 @ X4 @ X5))) | ($false = (eiw_di @ X1 @ X2)) | ($false = (eiw_di @ (sK9 @ X4 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK7 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5)))) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f175,f110])).
% 1.81/2.52 thf(f110,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X6 : $i,X4 : $i,X5 : mworld] : (($false = (do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ X6 @ X5)) | ($false = (mrel @ mactual @ X1)) | ($true = (in @ X3 @ X4 @ X6 @ X5)) | ($false = (entry_box @ X4 @ X1)) | ($false = (eiw_di @ X3 @ X1)) | ($false = (eiw_di @ X4 @ X1)) | ($false = (mrel @ X1 @ X5)) | ($false = (eiw_di @ X2 @ X1)) | ($false = (eiw_di @ X6 @ X5)) | ($false = (string @ X3 @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.81/2.52 thf(f109,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X6 : $i,X4 : $i,X5 : mworld] : (($false = (string @ X3 @ X1)) | ($true = ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ X6 @ X5) => (in @ X3 @ X4 @ X6 @ X5))) | ($false = (mrel @ X1 @ X5)) | ($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X6 @ X5)) | ($false = (eiw_di @ X4 @ X1)) | ($false = (entry_box @ X4 @ X1)) | ($false = (eiw_di @ X2 @ X1)) | ($false = (eiw_di @ X3 @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f108])).
% 1.81/2.52 thf(f108,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X6 : $i,X4 : $i,X5 : mworld] : ((((eiw_di @ X6 @ X5) => ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ X6 @ X5) => (in @ X3 @ X4 @ X6 @ X5))) = $true) | ($false = (eiw_di @ X4 @ X1)) | ($false = (mrel @ X1 @ X5)) | ($false = (eiw_di @ X2 @ X1)) | ($false = (entry_box @ X4 @ X1)) | ($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X3 @ X1)) | ($false = (string @ X3 @ X1))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f107])).
% 1.81/2.52 thf(f107,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X6 : $i,X4 : $i,X5 : mworld] : (($false = (mrel @ X1 @ X5)) | ($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ X5) => ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ Y0 @ X5) => (in @ X3 @ X4 @ Y0 @ X5)))) @ X6)) | ($false = (string @ X3 @ X1)) | ($false = (eiw_di @ X3 @ X1)) | ($false = (eiw_di @ X4 @ X1)) | ($false = (eiw_di @ X2 @ X1)) | ($false = (mrel @ mactual @ X1)) | ($false = (entry_box @ X4 @ X1))) )),
% 1.81/2.52 inference(pi_clausification,[status(thm)],[f106])).
% 1.81/2.52 thf(f106,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i,X5 : mworld] : (($false = (eiw_di @ X4 @ X1)) | ($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X3 @ X1)) | ($false = (string @ X3 @ X1)) | ($false = (eiw_di @ X2 @ X1)) | ($false = (entry_box @ X4 @ X1)) | ($false = (mrel @ X1 @ X5)) | ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X5) => ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ Y0 @ X5) => (in @ X3 @ X4 @ Y0 @ X5))))) = $true)) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f105])).
% 1.81/2.52 thf(f105,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i,X5 : mworld] : (($false = (eiw_di @ X3 @ X1)) | ($false = (entry_box @ X4 @ X1)) | ($false = (eiw_di @ X4 @ X1)) | ($false = (string @ X3 @ X1)) | ($false = (eiw_di @ X2 @ X1)) | (((mrel @ X1 @ X5) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X5) => ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ Y0 @ X5) => (in @ X3 @ X4 @ Y0 @ X5)))))) = $true) | ($false = (mrel @ mactual @ X1))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f104])).
% 1.81/2.52 thf(f104,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i,X5 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X3 @ X1)) | ($false = (entry_box @ X4 @ X1)) | ($false = (string @ X3 @ X1)) | ($false = (eiw_di @ X4 @ X1)) | ($false = (eiw_di @ X2 @ X1)) | (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ Y1 @ Y0) => (in @ X3 @ X4 @ Y1 @ Y0))))))) @ X5) = $true)) )),
% 1.81/2.52 inference(pi_clausification,[status(thm)],[f102])).
% 1.81/2.52 thf(f102,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (($false = (string @ X3 @ X1)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ Y1 @ Y0) => (in @ X3 @ X4 @ Y1 @ Y0)))))))) = $true) | ($false = (entry_box @ X4 @ X1)) | ($false = (eiw_di @ X4 @ X1)) | ($false = (eiw_di @ X2 @ X1)) | ($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X3 @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.81/2.52 thf(f101,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (($false = (eiw_di @ X3 @ X1)) | ($false = (mrel @ mactual @ X1)) | ($false = (entry_box @ X4 @ X1)) | ($false = (string @ X3 @ X1)) | (((eiw_di @ (sK2 @ X3 @ X1 @ X4 @ X2) @ X1) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ Y1 @ Y0) => (in @ X3 @ X4 @ Y1 @ Y0))))))))) = $true) | ($false = (eiw_di @ X2 @ X1)) | ($false = (eiw_di @ X4 @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.81/2.52 thf(f100,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (($false = (eiw_di @ X4 @ X1)) | ($false = ((entry_box @ X4 @ X1) & (string @ X3 @ X1))) | (((eiw_di @ (sK2 @ X3 @ X1 @ X4 @ X2) @ X1) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X2 @ (sK2 @ X3 @ X1 @ X4 @ X2) @ Y1 @ Y0) => (in @ X3 @ X4 @ Y1 @ Y0))))))))) = $true) | ($false = (eiw_di @ X3 @ X1)) | ($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f99])).
% 1.81/2.52 thf(f99,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (($false = (eiw_di @ X4 @ X1)) | ($false = ((entry_box @ X4 @ X1) & (string @ X3 @ X1))) | ($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ X2 @ Y0 @ Y2 @ Y1) => (in @ X3 @ X4 @ Y2 @ Y1)))))))))) @ (sK2 @ X3 @ X1 @ X4 @ X2))) | ($false = (eiw_di @ X2 @ X1)) | ($false = (eiw_di @ X3 @ X1)) | ($false = (mrel @ mactual @ X1))) )),
% 1.81/2.52 inference(sigma_clausification,[status(thm)],[f98])).
% 1.81/2.52 thf(f98,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (($false = (eiw_di @ X4 @ X1)) | ($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X3 @ X1)) | ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ X2 @ Y0 @ Y2 @ Y1) => (in @ X3 @ X4 @ Y2 @ Y1))))))))))) = $true) | ($false = ((entry_box @ X4 @ X1) & (string @ X3 @ X1))) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.81/2.52 thf(f97,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (($false = (eiw_di @ X3 @ X1)) | ($false = (eiw_di @ X4 @ X1)) | ((((entry_box @ X4 @ X1) & (string @ X3 @ X1)) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ X2 @ Y0 @ Y2 @ Y1) => (in @ X3 @ X4 @ Y2 @ Y1)))))))))))) = $true) | ($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f96])).
% 1.81/2.52 thf(f96,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (($false = (eiw_di @ X2 @ X1)) | ($false = (eiw_di @ X3 @ X1)) | ($false = (mrel @ mactual @ X1)) | (((eiw_di @ X4 @ X1) => (((entry_box @ X4 @ X1) & (string @ X3 @ X1)) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ X2 @ Y0 @ Y2 @ Y1) => (in @ X3 @ X4 @ Y2 @ Y1))))))))))))) = $true)) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f95])).
% 1.81/2.52 thf(f95,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : ((((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (((entry_box @ Y0 @ X1) & (string @ X3 @ X1)) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => ((do @ X2 @ Y1 @ Y3 @ Y2) => (in @ X3 @ Y0 @ Y3 @ Y2)))))))))))))) @ X4) = $true) | ($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X3 @ X1)) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.81/2.52 inference(pi_clausification,[status(thm)],[f94])).
% 1.81/2.52 thf(f94,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X2 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (((entry_box @ Y0 @ X1) & (string @ X3 @ X1)) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => ((do @ X2 @ Y1 @ Y3 @ Y2) => (in @ X3 @ Y0 @ Y3 @ Y2)))))))))))))))) | ($false = (eiw_di @ X3 @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.81/2.52 thf(f93,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | (((eiw_di @ X3 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (((entry_box @ Y0 @ X1) & (string @ X3 @ X1)) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => ((do @ X2 @ Y1 @ Y3 @ Y2) => (in @ X3 @ Y0 @ Y3 @ Y2)))))))))))))))) = $true) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f92])).
% 1.81/2.52 thf(f92,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X2 @ X1)) | (((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) => (((entry_box @ Y1 @ X1) & (string @ Y0 @ X1)) => (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ X1) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => ((do @ X2 @ Y2 @ Y4 @ Y3) => (in @ Y0 @ Y1 @ Y4 @ Y3))))))))))))))))) @ X3) = $true)) )),
% 1.81/2.52 inference(pi_clausification,[status(thm)],[f91])).
% 1.81/2.52 thf(f91,plain,(
% 1.81/2.52 ( ! [X2 : $i,X1 : mworld] : (($false = (eiw_di @ X2 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) => (((entry_box @ Y1 @ X1) & (string @ Y0 @ X1)) => (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ X1) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => ((do @ X2 @ Y2 @ Y4 @ Y3) => (in @ Y0 @ Y1 @ Y4 @ Y3))))))))))))))))))) | ($false = (mrel @ mactual @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f90])).
% 1.81/2.52 thf(f90,plain,(
% 1.81/2.52 ( ! [X2 : $i,X1 : mworld] : (($true = ((eiw_di @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) => (((entry_box @ Y1 @ X1) & (string @ Y0 @ X1)) => (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ X1) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => ((do @ X2 @ Y2 @ Y4 @ Y3) => (in @ Y0 @ Y1 @ Y4 @ Y3)))))))))))))))))))) | ($false = (mrel @ mactual @ X1))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f89])).
% 1.81/2.52 thf(f89,plain,(
% 1.81/2.52 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | (((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ X1) => (((entry_box @ Y2 @ X1) & (string @ Y1 @ X1)) => (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ X1) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ X1 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) => ((do @ Y0 @ Y3 @ Y5 @ Y4) => (in @ Y1 @ Y2 @ Y5 @ Y4)))))))))))))))))))) @ X2) = $true)) )),
% 1.81/2.52 inference(pi_clausification,[status(thm)],[f88])).
% 1.81/2.52 thf(f88,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ X1) => (((entry_box @ Y2 @ X1) & (string @ Y1 @ X1)) => (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ X1) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ X1 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) => ((do @ Y0 @ Y3 @ Y5 @ Y4) => (in @ Y1 @ Y2 @ Y5 @ Y4))))))))))))))))))))))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.81/2.52 thf(f87,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ X1) => (((entry_box @ Y2 @ X1) & (string @ Y1 @ X1)) => (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ X1) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ X1 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) => ((do @ Y0 @ Y3 @ Y5 @ Y4) => (in @ Y1 @ Y2 @ Y5 @ Y4)))))))))))))))))))))))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f86])).
% 1.81/2.52 thf(f86,plain,(
% 1.81/2.52 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y0) => (((entry_box @ Y3 @ Y0) & (string @ Y2 @ Y0)) => (?? @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y0) & (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (!! @ $i @ (^[Y6 : $i]: ((eiw_di @ Y6 @ Y5) => ((do @ Y1 @ Y4 @ Y6 @ Y5) => (in @ Y2 @ Y3 @ Y6 @ Y5))))))))))))))))))))))) @ X1))) )),
% 1.81/2.52 inference(pi_clausification,[status(thm)],[f85])).
% 1.81/2.52 thf(f85,plain,(
% 1.81/2.52 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y0) => (((entry_box @ Y3 @ Y0) & (string @ Y2 @ Y0)) => (?? @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y0) & (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (!! @ $i @ (^[Y6 : $i]: ((eiw_di @ Y6 @ Y5) => ((do @ Y1 @ Y4 @ Y6 @ Y5) => (in @ Y2 @ Y3 @ Y6 @ Y5)))))))))))))))))))))))))),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f83])).
% 1.81/2.52 thf(f83,plain,(
% 1.81/2.52 ($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]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => (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]: ((Y4 @ Y5) & (Y3 @ Y5))))))) @ (string @ Y1) @ (entry_box @ Y2)) @ ((^[Y3 : $i > mworld > $o]: ((^[Y4 : mworld]: (?? @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) & (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]: ((eiw_di @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) @ (^[Y4 : $i]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld > $o]: ((^[Y7 : mworld]: ((Y5 @ Y7) => (Y6 @ Y7))))))) @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4)))))))))))))))))),
% 1.81/2.52 inference(definition_unfolding,[status(thm)],[f73,f65,f64,f78,f78,f78,f76,f70,f68,f64,f78,f76])).
% 1.81/2.52 thf(f73,plain,(
% 1.81/2.52 ($true = (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 : $i]: (mimplies @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4)))))))))))))))))),
% 1.81/2.52 inference(cnf_transformation,[status(thm)],[f24])).
% 1.81/2.52 thf(f24,plain,(
% 1.81/2.52 ($true = (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)))))))))))))))))),
% 1.81/2.52 inference(fool_elimination,[status(thm)],[f23])).
% 1.81/2.52 thf(f23,plain,(
% 1.81/2.52 (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))))))))))))))))),
% 1.81/2.52 inference(rectify,[status(thm)],[f17])).
% 1.81/2.52 thf(f17,axiom,(
% 1.81/2.52 (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))))))))))))))))),
% 1.81/2.52 file('/export/starexec/sandbox2/tmp/tmp.94OW5BL3pd/DTF2THF_11589.p',ax3)).
% 1.81/2.52 thf(f175,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (do @ X4 @ X3 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X3 @ X1 @ X4 @ X2))) | ($false = (userid @ u @ X1 @ (sK6 @ X1 @ X2))) | ($false = (entry_box @ X2 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X3 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f172])).
% 1.81/2.52 thf(f173,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (eiw_di @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X3 @ X1 @ X4 @ X2))) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (userid @ u @ X1 @ (sK6 @ X1 @ X2))) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (entry_box @ X2 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X2 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f171])).
% 1.81/2.52 thf(f103,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (($true = (eiw_di @ (sK2 @ X3 @ X1 @ X4 @ X2) @ X1)) | ($false = (string @ X3 @ X1)) | ($false = (eiw_di @ X4 @ X1)) | ($false = (mrel @ mactual @ X1)) | ($false = (entry_box @ X4 @ X1)) | ($false = (eiw_di @ X3 @ X1)) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.81/2.52 thf(f346,plain,(
% 1.81/2.52 spl1_1 | spl1_2),
% 1.81/2.52 inference(avatar_split_clause,[status(thm)],[f345,f337,f334])).
% 1.81/2.52 thf(f345,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (string @ X0 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false)) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f344])).
% 1.81/2.52 thf(f344,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (string @ X0 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = $true) | ($false = (entry_box @ X1 @ sK5))) )),
% 1.81/2.52 inference(forward_demodulation,[status(thm)],[f326,f138])).
% 1.81/2.52 thf(f326,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (entry_box @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (string @ X0 @ sK5)) | ((mrel @ mactual @ sK5) = $false) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f325])).
% 1.81/2.52 thf(f325,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (string @ X0 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ($false = $true) | ((mrel @ mactual @ sK5) = $false) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ((eiw_di @ X0 @ sK5) = $false)) )),
% 1.81/2.52 inference(duplicate_literal_removal,[status(thm)],[f321])).
% 1.81/2.52 thf(f321,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (entry_box @ X1 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (string @ X0 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = $true) | ((mrel @ mactual @ sK5) = $false) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (string @ X0 @ sK5))) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f296,f103])).
% 1.81/2.52 thf(f296,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (eiw_di @ (sK2 @ X0 @ sK5 @ X1 @ X2) @ sK5)) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (string @ X0 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (entry_box @ X1 @ sK5))) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f295])).
% 1.81/2.52 thf(f295,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ (sK2 @ X0 @ sK5 @ X1 @ X2) @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = $true) | ($false = (string @ X0 @ sK5)) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(forward_demodulation,[status(thm)],[f287,f138])).
% 1.81/2.52 thf(f287,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X1 @ sK5)) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ (sK2 @ X0 @ sK5 @ X1 @ X2) @ sK5)) | ($false = (string @ X0 @ sK5)) | ((mrel @ mactual @ sK5) = $false) | ($false = (entry_box @ X1 @ sK5))) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f286])).
% 1.81/2.52 thf(f286,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (eiw_di @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ (sK2 @ X0 @ sK5 @ X1 @ X2) @ sK5)) | ($false = $true) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (string @ X0 @ sK5)) | ((mrel @ mactual @ sK5) = $false) | ($false = (entry_box @ X1 @ sK5))) )),
% 1.81/2.52 inference(duplicate_literal_removal,[status(thm)],[f277])).
% 1.81/2.52 thf(f277,plain,(
% 1.81/2.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (eiw_di @ X2 @ sK5)) | ((mrel @ mactual @ sK5) = $false) | ($false = (eiw_di @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ (sK2 @ X0 @ sK5 @ X1 @ X2) @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (eiw_di @ X2 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (string @ X0 @ sK5)) | ($false = (eiw_di @ (sK2 @ X0 @ sK5 @ X1 @ X2) @ sK5)) | ($false = $true) | ($false = (eiw_di @ X1 @ sK5)) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true)) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f265,f159])).
% 1.81/2.52 thf(f159,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((mrel @ sK5 @ (sK7 @ X3 @ X1 @ X4 @ X2)) = $true) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($true = (mrel @ sK5 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X2 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f157])).
% 1.81/2.52 thf(f157,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (eiw_di @ X3 @ sK5)) | (((mrel @ sK5 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2))))))) = $false) | ($true = (mrel @ sK5 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f155])).
% 1.81/2.52 thf(f265,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (($false = (mrel @ X2 @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ($false = (eiw_di @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X1 @ X2)) | ($false = (eiw_di @ X3 @ X2)) | ($false = (mrel @ mactual @ X2)) | ($false = (eiw_di @ (sK2 @ X0 @ X2 @ X1 @ X3) @ sK5)) | ($false = (entry_box @ X1 @ X2)) | ((string @ X0 @ X2) = $false) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X0 @ X2)) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true)) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f264])).
% 1.81/2.52 thf(f264,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (($false = (entry_box @ X1 @ X2)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X3 @ X2)) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X1 @ X2)) | ((string @ X0 @ X2) = $false) | ($false = $true) | ($false = (mrel @ X2 @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ($false = (mrel @ mactual @ X2)) | ($false = (eiw_di @ (sK2 @ X0 @ X2 @ X1 @ X3) @ sK5)) | ($false = (eiw_di @ X0 @ X2)) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true)) )),
% 1.81/2.52 inference(duplicate_literal_removal,[status(thm)],[f261])).
% 1.81/2.52 thf(f261,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ sK5)) | ($false = $true) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (mrel @ mactual @ X2)) | ($false = (eiw_di @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (entry_box @ X1 @ X2)) | ($false = (eiw_di @ X3 @ X2)) | ((string @ X0 @ X2) = $false) | ($false = (eiw_di @ (sK2 @ X0 @ X2 @ X1 @ X3) @ sK5)) | ($false = (mrel @ X2 @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ($false = (eiw_di @ (sK2 @ X0 @ X2 @ X1 @ X3) @ sK5)) | ($false = (eiw_di @ X0 @ X2)) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X3 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X1 @ X2))) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f163,f249])).
% 1.81/2.52 thf(f249,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (($false = (eiw_di @ (sK8 @ X0 @ X1 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X3) @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ((string @ X0 @ X2) = $false) | ($false = (eiw_di @ X0 @ X2)) | ($false = (eiw_di @ (sK2 @ X0 @ X2 @ X1 @ X3) @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (entry_box @ X1 @ X2)) | ($false = (eiw_di @ X1 @ X2)) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X3 @ X2)) | ($false = (mrel @ mactual @ X2)) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (mrel @ X2 @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true)) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f248])).
% 1.81/2.52 thf(f248,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ sK5)) | ($false = (entry_box @ X1 @ X2)) | ($false = (mrel @ X2 @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ((string @ X0 @ X2) = $false) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (mrel @ mactual @ X2)) | ($false = (eiw_di @ X0 @ X2)) | ($false = (eiw_di @ X1 @ X2)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ (sK8 @ X0 @ X1 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X3) @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ($false = $true) | ($false = (eiw_di @ X3 @ X2)) | ($false = (eiw_di @ (sK2 @ X0 @ X2 @ X1 @ X3) @ sK5))) )),
% 1.81/2.52 inference(duplicate_literal_removal,[status(thm)],[f245])).
% 1.81/2.52 thf(f245,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X1 @ sK5)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (entry_box @ X1 @ X2)) | ($false = (eiw_di @ X3 @ sK5)) | ((mrel @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (eiw_di @ (sK8 @ X0 @ X1 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X3) @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ($false = (eiw_di @ X3 @ X2)) | ($false = (mrel @ mactual @ X2)) | ($false = (mrel @ X2 @ (sK7 @ (sK2 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) | ($false = (eiw_di @ X0 @ X2)) | ($false = $true) | ($false = (eiw_di @ (sK2 @ X0 @ X2 @ X1 @ X3) @ sK5)) | ((string @ X0 @ X2) = $false) | ($false = (eiw_di @ X1 @ X2)) | ($false = (eiw_di @ (sK2 @ X0 @ X2 @ X1 @ X3) @ sK5)) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f164,f219])).
% 1.81/2.52 thf(f219,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = (in @ X1 @ X3 @ (sK8 @ X4 @ X5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK7 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) | ($false = (eiw_di @ (sK2 @ X1 @ X2 @ X3 @ X0) @ sK5)) | ($false = (entry_box @ X3 @ X2)) | ($false = (eiw_di @ X3 @ X2)) | ($false = (mrel @ mactual @ X2)) | ($false = (eiw_di @ (sK8 @ X4 @ X5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK7 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (string @ X1 @ X2)) | ($false = (mrel @ X2 @ (sK7 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) | ($true = (mrel @ sK5 @ (sK6 @ X4 @ X5))) | ($false = (eiw_di @ X5 @ sK5)) | ($false = (eiw_di @ X0 @ X2)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X1 @ X2))) )),
% 1.81/2.52 inference(trivial_inequality_removal,[status(thm)],[f217])).
% 1.81/2.52 thf(f217,plain,(
% 1.81/2.52 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (eiw_di @ X4 @ sK5)) | ($false = (entry_box @ X3 @ X2)) | ($false = (mrel @ X2 @ (sK7 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) | ($false = (string @ X1 @ X2)) | ((eiw_di @ X0 @ sK5) = $false) | ($false = (eiw_di @ X3 @ X2)) | ($false = (eiw_di @ (sK8 @ X4 @ X5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK7 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) | ($true = (in @ X1 @ X3 @ (sK8 @ X4 @ X5 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK7 @ (sK2 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) | ($false = $true) | ($true = (mrel @ sK5 @ (sK6 @ X4 @ X5))) | ($false = (eiw_di @ X1 @ X2)) | ($false = (eiw_di @ (sK2 @ X1 @ X2 @ X3 @ X0) @ sK5)) | ($false = (eiw_di @ X5 @ sK5)) | ($false = (mrel @ mactual @ X2)) | ($false = (eiw_di @ X0 @ X2))) )),
% 1.81/2.52 inference(superposition,[status(thm)],[f110,f165])).
% 1.81/2.52 thf(f165,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (do @ X4 @ X3 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X3 @ X1 @ X4 @ X2))) | ($false = (eiw_di @ X3 @ sK5)) | ($true = (mrel @ sK5 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X4 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f162])).
% 1.81/2.52 thf(f162,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X4 @ sK5)) | ($false = ((do @ X4 @ X3 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X3 @ X1 @ X4 @ X2)))) | ($false = (eiw_di @ X1 @ sK5)) | ($true = (mrel @ sK5 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X3 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f161])).
% 1.81/2.52 thf(f161,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X4 @ sK5)) | ($false = ((eiw_di @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X3 @ X1 @ X4 @ X2))))) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($true = (mrel @ sK5 @ (sK6 @ X1 @ X2)))) )),
% 1.81/2.52 inference(beta_eta_normalization,[status(thm)],[f160])).
% 1.81/2.52 thf(f160,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (mrel @ sK5 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X3 @ sK5)) | ($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2))))) @ (sK8 @ X1 @ X2 @ X3 @ X4))) | ($false = (eiw_di @ X1 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X4 @ sK5))) )),
% 1.81/2.52 inference(sigma_clausification,[status(thm)],[f158])).
% 1.81/2.52 thf(f158,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (eiw_di @ X3 @ sK5)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK7 @ X3 @ X1 @ X4 @ X2))))))) | ($true = (mrel @ sK5 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f157])).
% 1.81/2.52 thf(f164,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X1 @ X2 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X3 @ X1 @ X4 @ X2))) | ($false = (eiw_di @ X4 @ sK5)) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X1 @ sK5)) | ($true = (mrel @ sK5 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X3 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f162])).
% 1.81/2.52 thf(f163,plain,(
% 1.81/2.52 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (eiw_di @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X3 @ X1 @ X4 @ X2))) | ($false = (eiw_di @ X3 @ sK5)) | ($false = (eiw_di @ X4 @ sK5)) | ($true = (mrel @ sK5 @ (sK6 @ X1 @ X2))) | ($false = (eiw_di @ X2 @ sK5)) | ($false = (eiw_di @ X1 @ sK5))) )),
% 1.81/2.52 inference(binary_proxy_clausification,[status(thm)],[f161])).
% 1.81/2.52 % SZS output end Proof for DTF2THF_11589
% 1.81/2.52 % (11757)------------------------------
% 1.81/2.52 % (11757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/2.52 % (11757)Termination reason: Refutation
% 1.81/2.52
% 1.81/2.52 % (11757)Memory used [KB]: 7036
% 1.81/2.52 % (11757)Time elapsed: 0.266 s
% 1.81/2.52 % (11757)Instructions burned: 848 (million)
% 1.81/2.52 % (11757)------------------------------
% 1.81/2.52 % (11757)------------------------------
% 1.81/2.52 % (11727)Success in time 0.357 s
%------------------------------------------------------------------------------