%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PLA053^18 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:27:54 AM UTC 2026
% Result : Theorem 1.91s 1.54s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 17
% Syntax : Number of formulae : 117 ( 52 unt; 0 typ; 8 def)
% Number of atoms : 815 ( 161 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 1148 ( 49 ~; 113 |; 55 &; 804 @)
% ( 8 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 29 usr; 15 con; 0-3 aty)
% ( 29 !!; 18 ??; 0 @@+; 0 @@-)
% Number of variables : 222 ( 157 ^; 63 !; 2 ?; 222 :)
% 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_15,type,
h: $i > mworld > $o ).
thf(func_def_16,type,
bomb: $i > mworld > $o ).
thf(func_def_17,type,
defused: $i > mworld > $o ).
thf(func_def_31,type,
sK0: mworld > $i ).
thf(func_def_36,type,
sK3: mworld > $i ).
thf(func_def_37,type,
sK4: mworld ).
thf(func_def_39,type,
sK6: mworld > $i > $i ).
thf(f344,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f143,f148,f154,f189,f195,f269,f294,f304,f343]) ).
thf(f343,plain,
( ~ spl1_1
| ~ spl1_3
| spl1_11
| ~ spl1_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f342]) ).
thf(f342,plain,
( $false
| ~ spl1_1
| ~ spl1_3
| spl1_11
| ~ spl1_14 ),
inference(trivial_inequality_removal,[status(thm)],[f338]) ).
thf(f338,plain,
( ( $false = $true )
| ~ spl1_1
| ~ spl1_3
| spl1_11
| ~ spl1_14 ),
inference(superposition,[status(thm)],[f325,f139]) ).
thf(f139,plain,
( ( $false
= ( defused @ sK5 @ sK4 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f137]) ).
thf(f137,definition,
( spl1_1
<=> ( $false
= ( defused @ sK5 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f325,plain,
( ( $true
= ( defused @ sK5 @ sK4 ) )
| ~ spl1_3
| spl1_11
| ~ spl1_14 ),
inference(subsumption_resolution,[status(thm)],[f324,f242]) ).
thf(f242,plain,
( ( $false
!= ( eiw_di @ sK5 @ sK4 ) )
| spl1_11 ),
inference(avatar_component_clause,[status(thm)],[f241]) ).
thf(f241,definition,
( spl1_11
<=> ( $false
= ( eiw_di @ sK5 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition]) ).
thf(f324,plain,
( ( $false
= ( eiw_di @ sK5 @ sK4 ) )
| ( $true
= ( defused @ sK5 @ sK4 ) )
| ~ spl1_3
| ~ spl1_14 ),
inference(trivial_inequality_removal,[status(thm)],[f313]) ).
thf(f313,plain,
( ( $true
= ( defused @ sK5 @ sK4 ) )
| ( $false
= ( eiw_di @ sK5 @ sK4 ) )
| ( $false = $true )
| ~ spl1_3
| ~ spl1_14 ),
inference(superposition,[status(thm)],[f147,f291]) ).
thf(f291,plain,
( ! [X0: $i] :
( ( $false
= ( bomb @ X0 @ sK4 ) )
| ( $false
= ( eiw_di @ X0 @ sK4 ) )
| ( ( defused @ X0 @ sK4 )
= $true ) )
| ~ spl1_14 ),
inference(avatar_component_clause,[status(thm)],[f290]) ).
thf(f290,definition,
( spl1_14
<=> ! [X0: $i] :
( ( ( defused @ X0 @ sK4 )
= $true )
| ( $false
= ( eiw_di @ X0 @ sK4 ) )
| ( $false
= ( bomb @ X0 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_14])],[avatar_definition]) ).
thf(f147,plain,
( ( ( bomb @ sK5 @ sK4 )
= $true )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f145]) ).
thf(f145,definition,
( spl1_3
<=> ( ( bomb @ sK5 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f304,plain,
~ spl1_13,
inference(avatar_contradiction_clause,[status(thm)],[f303]) ).
thf(f303,plain,
( $false
| ~ spl1_13 ),
inference(trivial_inequality_removal,[status(thm)],[f299]) ).
thf(f299,plain,
( ( $false = $true )
| ~ spl1_13 ),
inference(superposition,[status(thm)],[f288,f69]) ).
thf(f69,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( mrel @ X0 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
thf(f52,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( mrel @ X0 @ X1 ) ),
inference(fool_elimination,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X2: mworld,X4: mworld] : ( mrel @ X2 @ X4 ),
file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mrel_universal) ).
thf(f288,plain,
( ( $false
= ( mrel @ sK4 @ sK4 ) )
| ~ spl1_13 ),
inference(avatar_component_clause,[status(thm)],[f286]) ).
thf(f286,definition,
( spl1_13
<=> ( $false
= ( mrel @ sK4 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_13])],[avatar_definition]) ).
thf(f294,plain,
( spl1_13
| spl1_14
| spl1_4
| ~ spl1_6 ),
inference(avatar_split_clause,[status(thm)],[f293,f186,f172,f290,f286]) ).
thf(f172,definition,
( spl1_4
<=> ( $false
= ( mrel @ mactual @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f186,definition,
( spl1_6
<=> ! [X0: $i] :
( ( $false
= ( eiw_di @ X0 @ sK4 ) )
| ( $true
= ( h @ ( sK6 @ sK4 @ X0 ) @ sK4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition]) ).
thf(f293,plain,
( ! [X0: $i] :
( ( ( defused @ X0 @ sK4 )
= $true )
| ( $false
= ( eiw_di @ X0 @ sK4 ) )
| ( $false
= ( bomb @ X0 @ sK4 ) )
| ( $false
= ( mrel @ sK4 @ sK4 ) ) )
| spl1_4
| ~ spl1_6 ),
inference(subsumption_resolution,[status(thm)],[f279,f173]) ).
thf(f173,plain,
( ( $false
!= ( mrel @ mactual @ sK4 ) )
| spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f172]) ).
thf(f279,plain,
( ! [X0: $i] :
( ( $false
= ( eiw_di @ X0 @ sK4 ) )
| ( $false
= ( bomb @ X0 @ sK4 ) )
| ( $false
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( mrel @ sK4 @ sK4 ) )
| ( ( defused @ X0 @ sK4 )
= $true ) )
| ~ spl1_6 ),
inference(trivial_inequality_removal,[status(thm)],[f278]) ).
thf(f278,plain,
( ! [X0: $i] :
( ( ( defused @ X0 @ sK4 )
= $true )
| ( $false
= ( eiw_di @ X0 @ sK4 ) )
| ( $false
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( bomb @ X0 @ sK4 ) )
| ( $false
= ( mrel @ sK4 @ sK4 ) )
| ( $false = $true ) )
| ~ spl1_6 ),
inference(duplicate_literal_removal,[status(thm)],[f274]) ).
thf(f274,plain,
( ! [X0: $i] :
( ( $false
= ( bomb @ X0 @ sK4 ) )
| ( $false
= ( mrel @ mactual @ sK4 ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ X0 @ sK4 ) )
| ( $false
= ( eiw_di @ X0 @ sK4 ) )
| ( $false
= ( mrel @ sK4 @ sK4 ) )
| ( ( defused @ X0 @ sK4 )
= $true ) )
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f134,f187]) ).
thf(f187,plain,
( ! [X0: $i] :
( ( $true
= ( h @ ( sK6 @ sK4 @ X0 ) @ sK4 ) )
| ( $false
= ( eiw_di @ X0 @ sK4 ) ) )
| ~ spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f186]) ).
thf(f134,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( h @ ( sK6 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( bomb @ X2 @ X3 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( ( defused @ X2 @ X3 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f133]) ).
thf(f133,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( h @ ( sK6 @ X1 @ X2 ) @ X3 )
& ( bomb @ X2 @ X3 ) ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( ( defused @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( ( h @ ( sK6 @ X1 @ X2 ) @ X3 )
& ( bomb @ X2 @ X3 ) )
=> ( defused @ X2 @ X3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( mrel @ X1 @ X3 )
=> ( ( ( h @ ( sK6 @ X1 @ X2 ) @ X3 )
& ( bomb @ X2 @ X3 ) )
=> ( defused @ X2 @ X3 ) ) )
= $true )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f130]) ).
thf(f130,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( h @ ( sK6 @ X1 @ X2 ) @ Y0 )
& ( bomb @ X2 @ Y0 ) )
=> ( defused @ X2 @ Y0 ) ) )
@ X3 )
= $true )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( h @ ( sK6 @ X1 @ X2 ) @ Y0 )
& ( bomb @ X2 @ Y0 ) )
=> ( defused @ X2 @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f127]) ).
thf(f127,plain,
! [X2: $i,X1: mworld] :
( ( ( ( eiw_di @ ( sK6 @ X1 @ X2 ) @ X1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( h @ ( sK6 @ X1 @ X2 ) @ Y0 )
& ( bomb @ X2 @ Y0 ) )
=> ( defused @ X2 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f126]) ).
thf(f126,plain,
! [X2: $i,X1: mworld] :
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( h @ Y0 @ Y1 )
& ( bomb @ X2 @ Y1 ) )
=> ( defused @ X2 @ Y1 ) ) ) ) )
@ ( sK6 @ X1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f125]) ).
thf(f125,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( h @ Y0 @ Y1 )
& ( bomb @ X2 @ Y1 ) )
=> ( defused @ X2 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( eiw_di @ X2 @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( h @ Y0 @ Y1 )
& ( bomb @ X2 @ Y1 ) )
=> ( defused @ X2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f123]) ).
thf(f123,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( h @ Y1 @ Y2 )
& ( bomb @ Y0 @ Y2 ) )
=> ( defused @ Y0 @ Y2 ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( h @ Y1 @ Y2 )
& ( bomb @ Y0 @ Y2 ) )
=> ( defused @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ X1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( h @ Y1 @ Y2 )
& ( bomb @ Y0 @ Y2 ) )
=> ( defused @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f120]) ).
thf(f120,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y0 )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( ( ( h @ Y2 @ Y3 )
& ( bomb @ Y1 @ Y3 ) )
=> ( defused @ Y1 @ Y3 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y0 )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( ( ( h @ Y2 @ Y3 )
& ( bomb @ Y1 @ Y3 ) )
=> ( defused @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
( ( ^ [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: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( bomb @ Y0 )
@ ( h @ Y1 ) )
@ ( defused @ Y0 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f64,f72,f70,f63,f62,f70,f67,f61]) ).
thf(f61,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/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mand_def) ).
thf(f67,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f45,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mimplies_def) ).
thf(f62,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f50,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f49]) ).
thf(f49,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X5: $i] :
( ( X1 @ X5 @ X2 )
& ( eiw_di @ X5 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mexists_di_def) ).
thf(f63,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_di ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X5: $i] :
( ( eiw_di @ X5 @ X2 )
=> ( X1 @ X5 @ X2 ) ) )
= mforall_di ),
file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mforall_di_def) ).
thf(f70,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/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mbox_def) ).
thf(f72,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mlocal_def) ).
thf(f64,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f34]) ).
thf(f34,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X5: $i] :
( mexists_di
@ ^ [X6: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X5 ) @ ( h @ X6 ) ) @ ( defused @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',ax3) ).
thf(f269,plain,
~ spl1_11,
inference(avatar_contradiction_clause,[status(thm)],[f268]) ).
thf(f268,plain,
( $false
| ~ spl1_11 ),
inference(trivial_inequality_removal,[status(thm)],[f262]) ).
thf(f262,plain,
( ( $false = $true )
| ~ spl1_11 ),
inference(superposition,[status(thm)],[f111,f243]) ).
thf(f243,plain,
( ( $false
= ( eiw_di @ sK5 @ sK4 ) )
| ~ spl1_11 ),
inference(avatar_component_clause,[status(thm)],[f241]) ).
thf(f111,plain,
( $true
= ( eiw_di @ sK5 @ sK4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
( $false
= ( ( eiw_di @ sK5 @ sK4 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK4 )
& ( ( ( h @ Y0 @ sK4 )
& ( bomb @ sK5 @ sK4 ) )
=> ( defused @ sK5 @ sK4 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f108]) ).
thf(f108,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK4 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ sK4 )
& ( ( ( h @ Y1 @ sK4 )
& ( bomb @ Y0 @ sK4 ) )
=> ( defused @ Y0 @ sK4 ) ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK4 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ sK4 )
& ( ( ( h @ Y1 @ sK4 )
& ( bomb @ Y0 @ sK4 ) )
=> ( defused @ Y0 @ sK4 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( $false
= ( ( mrel @ mactual @ sK4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK4 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ sK4 )
& ( ( ( h @ Y1 @ sK4 )
& ( bomb @ Y0 @ sK4 ) )
=> ( defused @ Y0 @ sK4 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f104]) ).
thf(f104,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y0 )
& ( ( ( h @ Y2 @ Y0 )
& ( bomb @ Y1 @ Y0 ) )
=> ( defused @ Y1 @ Y0 ) ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y0 )
& ( ( ( h @ Y2 @ Y0 )
& ( bomb @ Y1 @ Y0 ) )
=> ( defused @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,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: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( bomb @ Y0 )
@ ( h @ Y1 ) )
@ ( defused @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f68,f72,f70,f63,f62,f67,f61]) ).
thf(f68,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f53,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X5: $i] :
( mexists_di
@ ^ [X6: $i] : ( mimplies @ ( mand @ ( bomb @ X5 ) @ ( h @ X6 ) ) @ ( defused @ X5 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
thf(f17,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X5: $i] :
( mexists_di
@ ^ [X6: $i] : ( mimplies @ ( mand @ ( bomb @ X5 ) @ ( h @ X6 ) ) @ ( defused @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',con) ).
thf(f195,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[status(thm)],[f194]) ).
thf(f194,plain,
( $false
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f191]) ).
thf(f191,plain,
( ( $false = $true )
| ~ spl1_4 ),
inference(superposition,[status(thm)],[f69,f174]) ).
thf(f174,plain,
( ( $false
= ( mrel @ mactual @ sK4 ) )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f172]) ).
thf(f189,plain,
( spl1_6
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f183,f172,f186]) ).
thf(f183,plain,
! [X0: $i] :
( ( $true
= ( h @ ( sK6 @ sK4 @ X0 ) @ sK4 ) )
| ( $false
= ( mrel @ mactual @ sK4 ) )
| ( $false
= ( eiw_di @ X0 @ sK4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f181]) ).
thf(f181,plain,
! [X0: $i] :
( ( $false
= ( eiw_di @ X0 @ sK4 ) )
| ( $true
= ( h @ ( sK6 @ sK4 @ X0 ) @ sK4 ) )
| ( $false
= ( mrel @ mactual @ sK4 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f129,f118]) ).
thf(f118,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ sK4 ) )
| ( ( h @ X1 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ sK4 ) )
| ( $true
= ( ( h @ X1 @ sK4 )
& ( bomb @ sK5 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ sK4 ) )
| ( $false
= ( ( ( h @ X1 @ sK4 )
& ( bomb @ sK5 @ sK4 ) )
=> ( defused @ sK5 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
! [X1: $i] :
( $false
= ( ( eiw_di @ X1 @ sK4 )
& ( ( ( h @ X1 @ sK4 )
& ( bomb @ sK5 @ sK4 ) )
=> ( defused @ sK5 @ sK4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f112]) ).
thf(f112,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK4 )
& ( ( ( h @ Y0 @ sK4 )
& ( bomb @ sK5 @ sK4 ) )
=> ( defused @ sK5 @ sK4 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK4 )
& ( ( ( h @ Y0 @ sK4 )
& ( bomb @ sK5 @ sK4 ) )
=> ( defused @ sK5 @ sK4 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f129,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( eiw_di @ ( sK6 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f127]) ).
thf(f154,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[status(thm)],[f153]) ).
thf(f153,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f149]) ).
thf(f149,plain,
( ( $false = $true )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f142,f111]) ).
thf(f142,plain,
( ! [X1: $i] :
( $false
= ( eiw_di @ X1 @ sK4 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f141]) ).
thf(f141,definition,
( spl1_2
<=> ! [X1: $i] :
( $false
= ( eiw_di @ X1 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f148,plain,
( spl1_3
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f117,f141,f145]) ).
thf(f117,plain,
! [X1: $i] :
( ( ( bomb @ sK5 @ sK4 )
= $true )
| ( $false
= ( eiw_di @ X1 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f116]) ).
thf(f143,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f115,f141,f137]) ).
thf(f115,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ sK4 ) )
| ( $false
= ( defused @ sK5 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PLA053^18 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n005.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:27:59 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.49 ---- Original DTF file ---
% 0.27/0.49 thf(spec,logic,$$dhol).
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 % File : PLA053^18 : TPTP v9.2.1. Released v8.1.0.
% 0.27/0.49 % Domain : Planning
% 0.27/0.49 % Problem : Abductive planning: Bomb-in-the-toilet with detector
% 0.27/0.49 % Version : [BP13] axioms.
% 0.27/0.49 % English :
% 0.27/0.49
% 0.27/0.49 % Refs : [Sto98] Stone (1998), Abductive Planning with Sensing
% 0.27/0.49 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.27/0.49 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.27/0.49 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.27/0.49 % Source : [TPTP]
% 0.27/0.49 % Names : APM004+1 [QMLTP]
% 0.27/0.49
% 0.27/0.49 % Status : Theorem
% 0.27/0.49 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.27/0.49 % Syntax : Number of formulae : 34 ( 12 unt; 17 typ; 10 def)
% 0.27/0.49 % Number of atoms : 62 ( 10 equ; 0 cnn)
% 0.27/0.49 % Maximal formula atoms : 10 ( 3 avg)
% 0.27/0.49 % Number of connectives : 84 ( 1 ~; 1 |; 4 &; 73 @)
% 0.27/0.49 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.27/0.49 % Maximal formula depth : 13 ( 4 avg)
% 0.27/0.49 % Number of types : 3 ( 1 usr)
% 0.27/0.49 % Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% 0.27/0.49 % Number of symbols : 17 ( 16 usr; 1 con; 0-3 aty)
% 0.27/0.49 % Number of variables : 41 ( 30 ^; 8 !; 3 ?; 41 :)
% 0.27/0.49 % SPC : TH0_THM_EQU_NAR
% 0.27/0.49
% 0.27/0.49 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.27/0.49 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.27/0.49 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.27/0.49 % $modal == [$constants == $rigid,$quantification == $cumulative,
% 0.27/0.49 % $modalities == $modal_system_S5U].
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 thf(mworld,type,
% 0.27/0.49 mworld: $tType ).
% 0.27/0.49
% 0.27/0.49 thf(mrel_type,type,
% 0.27/0.49 mrel: mworld > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(mactual_type,type,
% 0.27/0.49 mactual: mworld ).
% 0.27/0.49
% 0.27/0.49 thf(mlocal_type,type,
% 0.27/0.49 mlocal: ( mworld > $o ) > $o ).
% 0.27/0.49
% 0.27/0.49 thf(mlocal_def,definition,
% 0.27/0.49 ( mlocal
% 0.27/0.49 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(mnot_type,type,
% 0.27/0.49 mnot: ( mworld > $o ) > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(mand_type,type,
% 0.27/0.49 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(mor_type,type,
% 0.27/0.49 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(mimplies_type,type,
% 0.27/0.49 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(mequiv_type,type,
% 0.27/0.49 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(mnot_def,definition,
% 0.27/0.49 ( mnot
% 0.27/0.49 = ( ^ [A: mworld > $o,W: mworld] :
% 0.27/0.49 ~ ( A @ W ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(mand_def,definition,
% 0.27/0.49 ( mand
% 0.27/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.27/0.49 ( ( A @ W )
% 0.27/0.49 & ( B @ W ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(mor_def,definition,
% 0.27/0.49 ( mor
% 0.27/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.27/0.49 ( ( A @ W )
% 0.27/0.49 | ( B @ W ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(mimplies_def,definition,
% 0.27/0.49 ( mimplies
% 0.27/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.27/0.49 ( ( A @ W )
% 0.27/0.49 => ( B @ W ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(mequiv_def,definition,
% 0.27/0.49 ( mequiv
% 0.27/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.27/0.49 ( ( A @ W )
% 0.27/0.49 <=> ( B @ W ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(mbox_type,type,
% 0.27/0.49 mbox: ( mworld > $o ) > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(mbox_def,definition,
% 0.27/0.49 ( mbox
% 0.27/0.49 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.27/0.49 ! [V: mworld] :
% 0.27/0.49 ( ( mrel @ W @ V )
% 0.27/0.49 => ( Phi @ V ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(mdia_type,type,
% 0.27/0.49 mdia: ( mworld > $o ) > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(mdia_def,definition,
% 0.27/0.49 ( mdia
% 0.27/0.49 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.27/0.49 ? [V: mworld] :
% 0.27/0.49 ( ( mrel @ W @ V )
% 0.27/0.49 & ( Phi @ V ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(mrel_universal,axiom,
% 0.27/0.49 ! [W: mworld,V: mworld] : ( mrel @ W @ V ) ).
% 0.27/0.49
% 0.27/0.49 thf(eiw_di_type,type,
% 0.27/0.49 eiw_di: $i > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(eiw_di_nonempty,axiom,
% 0.27/0.49 ! [W: mworld] :
% 0.27/0.49 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.27/0.49
% 0.27/0.49 thf(eiw_di_cumul,axiom,
% 0.27/0.49 ! [W: mworld,V: mworld,X: $i] :
% 0.27/0.49 ( ( ( eiw_di @ X @ W )
% 0.27/0.49 & ( mrel @ W @ V ) )
% 0.27/0.49 => ( eiw_di @ X @ V ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(mforall_di_type,type,
% 0.27/0.49 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(mforall_di_def,definition,
% 0.27/0.49 ( mforall_di
% 0.27/0.49 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.27/0.49 ! [X: $i] :
% 0.27/0.49 ( ( eiw_di @ X @ W )
% 0.27/0.49 => ( A @ X @ W ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(mexists_di_type,type,
% 0.27/0.49 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(mexists_di_def,definition,
% 0.27/0.49 ( mexists_di
% 0.27/0.49 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.27/0.49 ? [X: $i] :
% 0.27/0.49 ( ( eiw_di @ X @ W )
% 0.27/0.49 & ( A @ X @ W ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 %%% This output was generated by tptputils, version 1.2.
% 0.27/0.49 %%% Generated on Wed Apr 27 15:22:07 CEST 2022 using command 'downgrade(tff)'.
% 0.27/0.49 thf(h_decl,type,
% 0.27/0.49 h: $i > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(bomb_decl,type,
% 0.27/0.49 bomb: $i > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(defused_decl,type,
% 0.27/0.49 defused: $i > mworld > $o ).
% 0.27/0.49
% 0.27/0.49 thf(ax1,axiom,
% 0.27/0.49 ( mlocal
% 0.27/0.49 @ ( mbox
% 0.27/0.49 @ ( mexists_di
% 0.27/0.49 @ ^ [B: $i] : ( bomb @ B ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(ax2,axiom,
% 0.27/0.49 ( mlocal
% 0.27/0.49 @ ( mexists_di
% 0.27/0.49 @ ^ [A: $i] :
% 0.27/0.49 ( mbox
% 0.27/0.49 @ ( mforall_di
% 0.27/0.49 @ ^ [X: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ A ) ) @ ( mbox @ ( bomb @ X ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(ax3,axiom,
% 0.27/0.49 ( mlocal
% 0.27/0.49 @ ( mbox
% 0.27/0.49 @ ( mforall_di
% 0.27/0.49 @ ^ [X: $i] :
% 0.27/0.49 ( mexists_di
% 0.27/0.49 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(con,conjecture,
% 0.27/0.49 ( mlocal
% 0.27/0.49 @ ( mbox
% 0.27/0.49 @ ( mforall_di
% 0.27/0.49 @ ^ [X: $i] :
% 0.27/0.49 ( mexists_di
% 0.27/0.49 @ ^ [D: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 ------------------------
% 1.72/1.48 ---- Embedded in THF ---
% 1.72/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.72/1.48 %%% Generated on Tue Feb 24 11:28:00 EST 2026
% 1.72/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 1.72/1.48 %%% Logic specification used:
% 1.72/1.48 %%% thf(spec, logic, $$dhol).
% 1.72/1.48
% 1.72/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2DTF13713.p
% See solution above
% 1.72/1.48 ------------------------
% 1.72/1.49 ---- Cleaned THF ---
% 1.72/1.49 thf(mworld,type,
% 1.72/1.49 mworld: $tType ).
% 1.72/1.49
% 1.72/1.49 thf(mrel_type,type,
% 1.72/1.49 mrel: mworld > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(mactual_type,type,
% 1.72/1.49 mactual: mworld ).
% 1.72/1.49
% 1.72/1.49 thf(mlocal_type,type,
% 1.72/1.49 mlocal: ( mworld > $o ) > $o ).
% 1.72/1.49
% 1.72/1.49 thf(mlocal_def,definition,
% 1.72/1.49 ( mlocal
% 1.72/1.49 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(mnot_type,type,
% 1.72/1.49 mnot: ( mworld > $o ) > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(mand_type,type,
% 1.72/1.49 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(mor_type,type,
% 1.72/1.49 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(mimplies_type,type,
% 1.72/1.49 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(mequiv_type,type,
% 1.72/1.49 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(mnot_def,definition,
% 1.72/1.49 ( mnot
% 1.72/1.49 = ( ^ [A: mworld > $o,W: mworld] :
% 1.72/1.49 ~ ( A @ W ) ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(mand_def,definition,
% 1.72/1.49 ( mand
% 1.72/1.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.72/1.49 ( ( A @ W )
% 1.72/1.49 & ( B @ W ) ) ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(mor_def,definition,
% 1.72/1.49 ( mor
% 1.72/1.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.72/1.49 ( ( A @ W )
% 1.72/1.49 | ( B @ W ) ) ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(mimplies_def,definition,
% 1.72/1.49 ( mimplies
% 1.72/1.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.72/1.49 ( ( A @ W )
% 1.72/1.49 => ( B @ W ) ) ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(mequiv_def,definition,
% 1.72/1.49 ( mequiv
% 1.72/1.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.72/1.49 ( ( A @ W )
% 1.72/1.49 <=> ( B @ W ) ) ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(mbox_type,type,
% 1.72/1.49 mbox: ( mworld > $o ) > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(mbox_def,definition,
% 1.72/1.49 ( mbox
% 1.72/1.49 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.72/1.49 ! [V: mworld] :
% 1.72/1.49 ( ( mrel @ W @ V )
% 1.72/1.49 => ( Phi @ V ) ) ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(mdia_type,type,
% 1.72/1.49 mdia: ( mworld > $o ) > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(mdia_def,definition,
% 1.72/1.49 ( mdia
% 1.72/1.49 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.72/1.49 ? [V: mworld] :
% 1.72/1.49 ( ( mrel @ W @ V )
% 1.72/1.49 & ( Phi @ V ) ) ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(mrel_universal,axiom,
% 1.72/1.49 ! [W: mworld,V: mworld] : ( mrel @ W @ V ) ).
% 1.72/1.49
% 1.72/1.49 thf(eiw_di_type,type,
% 1.72/1.49 eiw_di: $i > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(eiw_di_nonempty,axiom,
% 1.72/1.49 ! [W: mworld] :
% 1.72/1.49 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 1.72/1.49
% 1.72/1.49 thf(eiw_di_cumul,axiom,
% 1.72/1.49 ! [W: mworld,V: mworld,X: $i] :
% 1.72/1.49 ( ( ( eiw_di @ X @ W )
% 1.72/1.49 & ( mrel @ W @ V ) )
% 1.72/1.49 => ( eiw_di @ X @ V ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(mforall_di_type,type,
% 1.72/1.49 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(mforall_di_def,definition,
% 1.72/1.49 ( mforall_di
% 1.72/1.49 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.72/1.49 ! [X: $i] :
% 1.72/1.49 ( ( eiw_di @ X @ W )
% 1.72/1.49 => ( A @ X @ W ) ) ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(mexists_di_type,type,
% 1.72/1.49 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(mexists_di_def,definition,
% 1.72/1.49 ( mexists_di
% 1.72/1.49 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.72/1.49 ? [X: $i] :
% 1.72/1.49 ( ( eiw_di @ X @ W )
% 1.72/1.49 & ( A @ X @ W ) ) ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(h_decl,type,
% 1.72/1.49 h: $i > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(bomb_decl,type,
% 1.72/1.49 bomb: $i > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(defused_decl,type,
% 1.72/1.49 defused: $i > mworld > $o ).
% 1.72/1.49
% 1.72/1.49 thf(ax1,axiom,
% 1.72/1.49 ( mlocal
% 1.72/1.49 @ ( mbox
% 1.72/1.49 @ ( mexists_di
% 1.72/1.49 @ ^ [B: $i] : ( bomb @ B ) ) ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(ax2,axiom,
% 1.72/1.49 ( mlocal
% 1.72/1.49 @ ( mexists_di
% 1.72/1.49 @ ^ [A: $i] :
% 1.72/1.49 ( mbox
% 1.72/1.49 @ ( mforall_di
% 1.72/1.49 @ ^ [X: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ A ) ) @ ( mbox @ ( bomb @ X ) ) ) ) ) ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(ax3,axiom,
% 1.72/1.49 ( mlocal
% 1.72/1.49 @ ( mbox
% 1.72/1.49 @ ( mforall_di
% 1.72/1.49 @ ^ [X: $i] :
% 1.72/1.49 ( mexists_di
% 1.72/1.49 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ) ).
% 1.72/1.49
% 1.72/1.49 thf(con,conjecture,
% 1.72/1.49 ( mlocal
% 1.72/1.49 @ ( mbox
% 1.72/1.49 @ ( mforall_di
% 1.72/1.49 @ ^ [X: $i] :
% 1.72/1.49 ( mexists_di
% 1.72/1.49 @ ^ [D: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ).
% 1.72/1.49 ------------------------
% 1.91/1.51 % (13871)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13713 for (2999ds/183Mi)
% 1.91/1.51 % (13873)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_13713 for (2999ds/27Mi)
% 1.91/1.51 % (13872)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_13713 for (2999ds/4Mi)
% 1.91/1.51 % (13874)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13713 for (2999ds/2Mi)
% 1.91/1.51 % (13875)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_13713 for (2999ds/2Mi)
% 1.91/1.51 % (13876)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_13713 for (2999ds/275Mi)
% 1.91/1.51 % (13877)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13713 for (2999ds/18Mi)
% 1.91/1.52 % (13874)Instruction limit reached!
% 1.91/1.52 % (13874)------------------------------
% 1.91/1.52 % (13874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.52 % (13874)Termination reason: Unknown
% 1.91/1.52 % (13874)Termination phase: Property scanning
% 1.91/1.52
% 1.91/1.52 % (13875)Instruction limit reached!
% 1.91/1.52 % (13875)------------------------------
% 1.91/1.52 % (13875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.52 % (13875)Termination reason: Unknown
% 1.91/1.52 % (13875)Termination phase: Property scanning
% 1.91/1.52
% 1.91/1.52 % (13875)Memory used [KB]: 1023
% 1.91/1.52 % (13875)Time elapsed: 0.003 s
% 1.91/1.52 % (13875)Instructions burned: 3 (million)
% 1.91/1.52 % (13875)------------------------------
% 1.91/1.52 % (13875)------------------------------
% 1.91/1.52 % (13874)Memory used [KB]: 1023
% 1.91/1.52 % (13874)Time elapsed: 0.003 s
% 1.91/1.52 % (13874)Instructions burned: 3 (million)
% 1.91/1.52 % (13874)------------------------------
% 1.91/1.52 % (13874)------------------------------
% 1.91/1.52 % (13872)Instruction limit reached!
% 1.91/1.52 % (13872)------------------------------
% 1.91/1.52 % (13872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.52 % (13872)Termination reason: Unknown
% 1.91/1.52 % (13872)Termination phase: Property scanning
% 1.91/1.52
% 1.91/1.52 % (13872)Memory used [KB]: 1023
% 1.91/1.52 % (13872)Time elapsed: 0.004 s
% 1.91/1.52 % (13872)Instructions burned: 5 (million)
% 1.91/1.52 % (13872)------------------------------
% 1.91/1.52 % (13872)------------------------------
% 1.91/1.52 % (13876)Refutation not found, incomplete strategy
% 1.91/1.52 % (13876)------------------------------
% 1.91/1.52 % (13876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.52 % (13876)Termination reason: Refutation not found, incomplete strategy
% 1.91/1.52
% 1.91/1.52
% 1.91/1.52 % (13876)Memory used [KB]: 5500
% 1.91/1.52 % (13876)Time elapsed: 0.004 s
% 1.91/1.52 % (13876)Instructions burned: 3 (million)
% 1.91/1.52 % (13876)------------------------------
% 1.91/1.52 % (13876)------------------------------
% 1.91/1.52 % (13877)Instruction limit reached!
% 1.91/1.52 % (13877)------------------------------
% 1.91/1.52 % (13877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.52 % (13877)Termination reason: Unknown
% 1.91/1.52 % (13877)Termination phase: Saturation
% 1.91/1.52
% 1.91/1.52 % (13877)Memory used [KB]: 5756
% 1.91/1.52 % (13877)Time elapsed: 0.011 s
% 1.91/1.52 % (13877)Instructions burned: 18 (million)
% 1.91/1.52 % (13877)------------------------------
% 1.91/1.52 % (13877)------------------------------
% 1.91/1.53 % (13873)Instruction limit reached!
% 1.91/1.53 % (13873)------------------------------
% 1.91/1.53 % (13873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.53 % (13873)Termination reason: Unknown
% 1.91/1.53 % (13873)Termination phase: Saturation
% 1.91/1.53
% 1.91/1.53 % (13873)Memory used [KB]: 5756
% 1.91/1.53 % (13873)Time elapsed: 0.016 s
% 1.91/1.53 % (13873)Instructions burned: 27 (million)
% 1.91/1.53 % (13873)------------------------------
% 1.91/1.53 % (13873)------------------------------
% 1.91/1.53 % (13878)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13713 for (2999ds/3Mi)
% 1.91/1.53 % (13879)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_13713 for (2999ds/37Mi)
% 1.91/1.53 % (13880)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_13713 for (2999ds/15Mi)
% 1.91/1.53 % (13871)First to succeed.
% 1.91/1.53 % (13881)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_13713 for (2999ds/3Mi)
% 1.91/1.53 % (13878)Instruction limit reached!
% 1.91/1.53 % (13878)------------------------------
% 1.91/1.53 % (13878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.53 % (13878)Termination reason: Unknown
% 1.91/1.53 % (13878)Termination phase: Property scanning
% 1.91/1.53
% 1.91/1.53 % (13878)Memory used [KB]: 1023
% 1.91/1.53 % (13878)Time elapsed: 0.003 s
% 1.91/1.53 % (13878)Instructions burned: 3 (million)
% 1.91/1.53 % (13878)------------------------------
% 1.91/1.53 % (13878)------------------------------
% 1.91/1.53 % (13881)Instruction limit reached!
% 1.91/1.53 % (13881)------------------------------
% 1.91/1.53 % (13881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.53 % (13881)Termination reason: Unknown
% 1.91/1.53 % (13881)Termination phase: Property scanning
% 1.91/1.53
% 1.91/1.53 % (13881)Memory used [KB]: 1023
% 1.91/1.53 % (13881)Time elapsed: 0.003 s
% 1.91/1.53 % (13881)Instructions burned: 3 (million)
% 1.91/1.53 % (13881)------------------------------
% 1.91/1.53 % (13881)------------------------------
% 1.91/1.54 % (13871)Refutation found. Thanks to Tanya!
% 1.91/1.54 % SZS status Theorem for DTF2THF_13713
% 1.91/1.54 % SZS output start Proof for DTF2THF_13713
% 1.91/1.54 thf(type_def_5, type, mworld: $tType).
% 1.91/1.54 thf(func_def_0, type, mworld: $tType).
% 1.91/1.54 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.91/1.54 thf(func_def_2, type, mactual: mworld).
% 1.91/1.54 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.91/1.54 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.91/1.54 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.91/1.54 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.91/1.54 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.91/1.54 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.91/1.54 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.91/1.54 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.91/1.54 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 1.91/1.54 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.91/1.54 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.91/1.54 thf(func_def_15, type, h: $i > mworld > $o).
% 1.91/1.54 thf(func_def_16, type, bomb: $i > mworld > $o).
% 1.91/1.54 thf(func_def_17, type, defused: $i > mworld > $o).
% 1.91/1.54 thf(func_def_31, type, sK0: mworld > $i).
% 1.91/1.54 thf(func_def_36, type, sK3: mworld > $i).
% 1.91/1.54 thf(func_def_37, type, sK4: mworld).
% 1.91/1.54 thf(func_def_39, type, sK6: mworld > $i > $i).
% 1.91/1.54 thf(f344,plain,(
% 1.91/1.54 $false),
% 1.91/1.54 inference(avatar_sat_refutation,[status(thm)],[f143,f148,f154,f189,f195,f269,f294,f304,f343])).
% 1.91/1.54 thf(f343,plain,(
% 1.91/1.54 ~spl1_1 | ~spl1_3 | spl1_11 | ~spl1_14),
% 1.91/1.54 inference(avatar_contradiction_clause,[status(thm)],[f342])).
% 1.91/1.54 thf(f342,plain,(
% 1.91/1.54 $false | (~spl1_1 | ~spl1_3 | spl1_11 | ~spl1_14)),
% 1.91/1.54 inference(trivial_inequality_removal,[status(thm)],[f338])).
% 1.91/1.54 thf(f338,plain,(
% 1.91/1.54 ($false = $true) | (~spl1_1 | ~spl1_3 | spl1_11 | ~spl1_14)),
% 1.91/1.54 inference(superposition,[status(thm)],[f325,f139])).
% 1.91/1.54 thf(f139,plain,(
% 1.91/1.54 ($false = (defused @ sK5 @ sK4)) | ~spl1_1),
% 1.91/1.54 inference(avatar_component_clause,[status(thm)],[f137])).
% 1.91/1.54 thf(f137,definition,(
% 1.91/1.54 spl1_1 <=> ($false = (defused @ sK5 @ sK4))),
% 1.91/1.54 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.91/1.54 thf(f325,plain,(
% 1.91/1.54 ($true = (defused @ sK5 @ sK4)) | (~spl1_3 | spl1_11 | ~spl1_14)),
% 1.91/1.54 inference(subsumption_resolution,[status(thm)],[f324,f242])).
% 1.91/1.54 thf(f242,plain,(
% 1.91/1.54 ($false != (eiw_di @ sK5 @ sK4)) | spl1_11),
% 1.91/1.54 inference(avatar_component_clause,[status(thm)],[f241])).
% 1.91/1.54 thf(f241,definition,(
% 1.91/1.54 spl1_11 <=> ($false = (eiw_di @ sK5 @ sK4))),
% 1.91/1.54 introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition])).
% 1.91/1.54 thf(f324,plain,(
% 1.91/1.54 ($false = (eiw_di @ sK5 @ sK4)) | ($true = (defused @ sK5 @ sK4)) | (~spl1_3 | ~spl1_14)),
% 1.91/1.54 inference(trivial_inequality_removal,[status(thm)],[f313])).
% 1.91/1.54 thf(f313,plain,(
% 1.91/1.54 ($true = (defused @ sK5 @ sK4)) | ($false = (eiw_di @ sK5 @ sK4)) | ($false = $true) | (~spl1_3 | ~spl1_14)),
% 1.91/1.54 inference(superposition,[status(thm)],[f147,f291])).
% 1.91/1.54 thf(f291,plain,(
% 1.91/1.54 ( ! [X0 : $i] : (($false = (bomb @ X0 @ sK4)) | ($false = (eiw_di @ X0 @ sK4)) | ((defused @ X0 @ sK4) = $true)) ) | ~spl1_14),
% 1.91/1.54 inference(avatar_component_clause,[status(thm)],[f290])).
% 1.91/1.54 thf(f290,definition,(
% 1.91/1.54 spl1_14 <=> ! [X0 : $i] : (((defused @ X0 @ sK4) = $true) | ($false = (eiw_di @ X0 @ sK4)) | ($false = (bomb @ X0 @ sK4)))),
% 1.91/1.54 introduced(definition,[new_symbols(naming,[spl1_14])],[avatar_definition])).
% 1.91/1.54 thf(f147,plain,(
% 1.91/1.54 ((bomb @ sK5 @ sK4) = $true) | ~spl1_3),
% 1.91/1.54 inference(avatar_component_clause,[status(thm)],[f145])).
% 1.91/1.54 thf(f145,definition,(
% 1.91/1.54 spl1_3 <=> ((bomb @ sK5 @ sK4) = $true)),
% 1.91/1.54 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.91/1.54 thf(f304,plain,(
% 1.91/1.54 ~spl1_13),
% 1.91/1.54 inference(avatar_contradiction_clause,[status(thm)],[f303])).
% 1.91/1.54 thf(f303,plain,(
% 1.91/1.54 $false | ~spl1_13),
% 1.91/1.54 inference(trivial_inequality_removal,[status(thm)],[f299])).
% 1.91/1.54 thf(f299,plain,(
% 1.91/1.54 ($false = $true) | ~spl1_13),
% 1.91/1.54 inference(superposition,[status(thm)],[f288,f69])).
% 1.91/1.54 thf(f69,plain,(
% 1.91/1.54 ( ! [X0 : mworld,X1 : mworld] : (($true = (mrel @ X0 @ X1))) )),
% 1.91/1.54 inference(cnf_transformation,[status(thm)],[f52])).
% 1.91/1.54 thf(f52,plain,(
% 1.91/1.54 ! [X0 : mworld,X1 : mworld] : ($true = (mrel @ X0 @ X1))),
% 1.91/1.54 inference(fool_elimination,[status(thm)],[f51])).
% 1.91/1.54 thf(f51,plain,(
% 1.91/1.54 ! [X0 : mworld,X1 : mworld] : (mrel @ X0 @ X1)),
% 1.91/1.54 inference(rectify,[status(thm)],[f9])).
% 1.91/1.54 thf(f9,axiom,(
% 1.91/1.54 ! [X2 : mworld,X4 : mworld] : (mrel @ X2 @ X4)),
% 1.91/1.54 file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mrel_universal)).
% 1.91/1.54 thf(f288,plain,(
% 1.91/1.54 ($false = (mrel @ sK4 @ sK4)) | ~spl1_13),
% 1.91/1.54 inference(avatar_component_clause,[status(thm)],[f286])).
% 1.91/1.54 thf(f286,definition,(
% 1.91/1.54 spl1_13 <=> ($false = (mrel @ sK4 @ sK4))),
% 1.91/1.54 introduced(definition,[new_symbols(naming,[spl1_13])],[avatar_definition])).
% 1.91/1.54 thf(f294,plain,(
% 1.91/1.54 spl1_13 | spl1_14 | spl1_4 | ~spl1_6),
% 1.91/1.54 inference(avatar_split_clause,[status(thm)],[f293,f186,f172,f290,f286])).
% 1.91/1.54 thf(f172,definition,(
% 1.91/1.54 spl1_4 <=> ($false = (mrel @ mactual @ sK4))),
% 1.91/1.54 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.91/1.54 thf(f186,definition,(
% 1.91/1.54 spl1_6 <=> ! [X0 : $i] : (($false = (eiw_di @ X0 @ sK4)) | ($true = (h @ (sK6 @ sK4 @ X0) @ sK4)))),
% 1.91/1.54 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 1.91/1.54 thf(f293,plain,(
% 1.91/1.54 ( ! [X0 : $i] : (((defused @ X0 @ sK4) = $true) | ($false = (eiw_di @ X0 @ sK4)) | ($false = (bomb @ X0 @ sK4)) | ($false = (mrel @ sK4 @ sK4))) ) | (spl1_4 | ~spl1_6)),
% 1.91/1.54 inference(subsumption_resolution,[status(thm)],[f279,f173])).
% 1.91/1.54 thf(f173,plain,(
% 1.91/1.54 ($false != (mrel @ mactual @ sK4)) | spl1_4),
% 1.91/1.54 inference(avatar_component_clause,[status(thm)],[f172])).
% 1.91/1.54 thf(f279,plain,(
% 1.91/1.54 ( ! [X0 : $i] : (($false = (eiw_di @ X0 @ sK4)) | ($false = (bomb @ X0 @ sK4)) | ($false = (mrel @ mactual @ sK4)) | ($false = (mrel @ sK4 @ sK4)) | ((defused @ X0 @ sK4) = $true)) ) | ~spl1_6),
% 1.91/1.54 inference(trivial_inequality_removal,[status(thm)],[f278])).
% 1.91/1.54 thf(f278,plain,(
% 1.91/1.54 ( ! [X0 : $i] : (((defused @ X0 @ sK4) = $true) | ($false = (eiw_di @ X0 @ sK4)) | ($false = (mrel @ mactual @ sK4)) | ($false = (bomb @ X0 @ sK4)) | ($false = (mrel @ sK4 @ sK4)) | ($false = $true)) ) | ~spl1_6),
% 1.91/1.54 inference(duplicate_literal_removal,[status(thm)],[f274])).
% 1.91/1.54 thf(f274,plain,(
% 1.91/1.54 ( ! [X0 : $i] : (($false = (bomb @ X0 @ sK4)) | ($false = (mrel @ mactual @ sK4)) | ($false = $true) | ($false = (eiw_di @ X0 @ sK4)) | ($false = (eiw_di @ X0 @ sK4)) | ($false = (mrel @ sK4 @ sK4)) | ((defused @ X0 @ sK4) = $true)) ) | ~spl1_6),
% 1.91/1.54 inference(superposition,[status(thm)],[f134,f187])).
% 1.91/1.54 thf(f187,plain,(
% 1.91/1.54 ( ! [X0 : $i] : (($true = (h @ (sK6 @ sK4 @ X0) @ sK4)) | ($false = (eiw_di @ X0 @ sK4))) ) | ~spl1_6),
% 1.91/1.54 inference(avatar_component_clause,[status(thm)],[f186])).
% 1.91/1.54 thf(f134,plain,(
% 1.91/1.54 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (h @ (sK6 @ X1 @ X2) @ X3)) | ($false = (bomb @ X2 @ X3)) | ($false = (mrel @ X1 @ X3)) | ($false = (eiw_di @ X2 @ X1)) | ((defused @ X2 @ X3) = $true) | ($false = (mrel @ mactual @ X1))) )),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f133])).
% 1.91/1.54 thf(f133,plain,(
% 1.91/1.54 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (mrel @ X1 @ X3)) | ($false = (mrel @ mactual @ X1)) | ($false = ((h @ (sK6 @ X1 @ X2) @ X3) & (bomb @ X2 @ X3))) | ($false = (eiw_di @ X2 @ X1)) | ((defused @ X2 @ X3) = $true)) )),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f132])).
% 1.91/1.54 thf(f132,plain,(
% 1.91/1.54 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (eiw_di @ X2 @ X1)) | ($false = (mrel @ X1 @ X3)) | ($false = (mrel @ mactual @ X1)) | ($true = (((h @ (sK6 @ X1 @ X2) @ X3) & (bomb @ X2 @ X3)) => (defused @ X2 @ X3)))) )),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.91/1.54 thf(f131,plain,(
% 1.91/1.54 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | (((mrel @ X1 @ X3) => (((h @ (sK6 @ X1 @ X2) @ X3) & (bomb @ X2 @ X3)) => (defused @ X2 @ X3))) = $true) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.91/1.54 inference(beta_eta_normalization,[status(thm)],[f130])).
% 1.91/1.54 thf(f130,plain,(
% 1.91/1.54 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((h @ (sK6 @ X1 @ X2) @ Y0) & (bomb @ X2 @ Y0)) => (defused @ X2 @ Y0)))) @ X3) = $true) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.91/1.54 inference(pi_clausification,[status(thm)],[f128])).
% 1.91/1.54 thf(f128,plain,(
% 1.91/1.54 ( ! [X2 : $i,X1 : mworld] : (($false = (eiw_di @ X2 @ X1)) | ($false = (mrel @ mactual @ X1)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((h @ (sK6 @ X1 @ X2) @ Y0) & (bomb @ X2 @ Y0)) => (defused @ X2 @ Y0))))) = $true)) )),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f127])).
% 1.91/1.54 thf(f127,plain,(
% 1.91/1.54 ( ! [X2 : $i,X1 : mworld] : ((((eiw_di @ (sK6 @ X1 @ X2) @ X1) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((h @ (sK6 @ X1 @ X2) @ Y0) & (bomb @ X2 @ Y0)) => (defused @ X2 @ Y0)))))) = $true) | ($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.91/1.54 inference(beta_eta_normalization,[status(thm)],[f126])).
% 1.91/1.54 thf(f126,plain,(
% 1.91/1.54 ( ! [X2 : $i,X1 : mworld] : ((((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((h @ Y0 @ Y1) & (bomb @ X2 @ Y1)) => (defused @ X2 @ Y1))))))) @ (sK6 @ X1 @ X2)) = $true) | ($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.91/1.54 inference(sigma_clausification,[status(thm)],[f125])).
% 1.91/1.54 thf(f125,plain,(
% 1.91/1.54 ( ! [X2 : $i,X1 : mworld] : (($false = (eiw_di @ X2 @ X1)) | ($true = (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((h @ Y0 @ Y1) & (bomb @ X2 @ Y1)) => (defused @ X2 @ Y1))))))))) | ($false = (mrel @ mactual @ X1))) )),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f124])).
% 1.91/1.54 thf(f124,plain,(
% 1.91/1.54 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((eiw_di @ X2 @ X1) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((h @ Y0 @ Y1) & (bomb @ X2 @ Y1)) => (defused @ X2 @ Y1))))))))))) )),
% 1.91/1.54 inference(beta_eta_normalization,[status(thm)],[f123])).
% 1.91/1.54 thf(f123,plain,(
% 1.91/1.54 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((h @ Y1 @ Y2) & (bomb @ Y0 @ Y2)) => (defused @ Y0 @ Y2)))))))))) @ X2))) )),
% 1.91/1.54 inference(pi_clausification,[status(thm)],[f122])).
% 1.91/1.54 thf(f122,plain,(
% 1.91/1.54 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((h @ Y1 @ Y2) & (bomb @ Y0 @ Y2)) => (defused @ Y0 @ Y2))))))))))))) )),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f121])).
% 1.91/1.54 thf(f121,plain,(
% 1.91/1.54 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((h @ Y1 @ Y2) & (bomb @ Y0 @ Y2)) => (defused @ Y0 @ Y2)))))))))))))) )),
% 1.91/1.54 inference(beta_eta_normalization,[status(thm)],[f120])).
% 1.91/1.54 thf(f120,plain,(
% 1.91/1.54 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y0) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (((h @ Y2 @ Y3) & (bomb @ Y1 @ Y3)) => (defused @ Y1 @ Y3))))))))))))) @ X1) = $true)) )),
% 1.91/1.54 inference(pi_clausification,[status(thm)],[f119])).
% 1.91/1.54 thf(f119,plain,(
% 1.91/1.54 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y0) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (((h @ Y2 @ Y3) & (bomb @ Y1 @ Y3)) => (defused @ Y1 @ Y3)))))))))))))) = $true)),
% 1.91/1.54 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.91/1.54 thf(f77,plain,(
% 1.91/1.54 (((^[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 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))) = $true)),
% 1.91/1.54 inference(definition_unfolding,[status(thm)],[f64,f72,f70,f63,f62,f70,f67,f61])).
% 1.91/1.54 thf(f61,plain,(
% 1.91/1.54 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.91/1.54 inference(cnf_transformation,[status(thm)],[f27])).
% 1.91/1.54 thf(f27,plain,(
% 1.91/1.54 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.91/1.54 inference(fool_elimination,[status(thm)],[f26])).
% 1.91/1.54 thf(f26,plain,(
% 1.91/1.54 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 1.91/1.54 inference(rectify,[status(thm)],[f3])).
% 1.91/1.54 thf(f3,axiom,(
% 1.91/1.54 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))) = mand)),
% 1.91/1.54 file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mand_def)).
% 1.91/1.54 thf(f67,plain,(
% 1.91/1.54 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.91/1.54 inference(cnf_transformation,[status(thm)],[f45])).
% 1.91/1.54 thf(f45,plain,(
% 1.91/1.54 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.91/1.54 inference(fool_elimination,[status(thm)],[f44])).
% 1.91/1.54 thf(f44,plain,(
% 1.91/1.54 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 1.91/1.54 inference(rectify,[status(thm)],[f5])).
% 1.91/1.54 thf(f5,axiom,(
% 1.91/1.54 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 1.91/1.54 file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mimplies_def)).
% 1.91/1.54 thf(f62,plain,(
% 1.91/1.54 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 1.91/1.54 inference(cnf_transformation,[status(thm)],[f50])).
% 1.91/1.54 thf(f50,plain,(
% 1.91/1.54 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 1.91/1.54 inference(fool_elimination,[status(thm)],[f49])).
% 1.91/1.54 thf(f49,plain,(
% 1.91/1.54 (mexists_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))))),
% 1.91/1.54 inference(rectify,[status(thm)],[f13])).
% 1.91/1.54 thf(f13,axiom,(
% 1.91/1.54 (mexists_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (? [X5 : $i] : ((X1 @ X5 @ X2) & (eiw_di @ X5 @ X2)))))),
% 1.91/1.54 file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mexists_di_def)).
% 1.91/1.54 thf(f63,plain,(
% 1.91/1.54 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.91/1.54 inference(cnf_transformation,[status(thm)],[f23])).
% 1.91/1.54 thf(f23,plain,(
% 1.91/1.54 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.91/1.54 inference(fool_elimination,[status(thm)],[f22])).
% 1.91/1.54 thf(f22,plain,(
% 1.91/1.54 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))) = mforall_di)),
% 1.91/1.54 inference(rectify,[status(thm)],[f12])).
% 1.91/1.54 thf(f12,axiom,(
% 1.91/1.54 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5 : $i] : ((eiw_di @ X5 @ X2) => (X1 @ X5 @ X2)))) = mforall_di)),
% 1.91/1.54 file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mforall_di_def)).
% 1.91/1.54 thf(f70,plain,(
% 1.91/1.54 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.91/1.54 inference(cnf_transformation,[status(thm)],[f37])).
% 1.91/1.54 thf(f37,plain,(
% 1.91/1.54 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.91/1.54 inference(fool_elimination,[status(thm)],[f36])).
% 1.91/1.54 thf(f36,plain,(
% 1.91/1.54 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 1.91/1.54 inference(rectify,[status(thm)],[f7])).
% 1.91/1.54 thf(f7,axiom,(
% 1.91/1.54 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 1.91/1.54 file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mbox_def)).
% 1.91/1.54 thf(f72,plain,(
% 1.91/1.54 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.91/1.54 inference(cnf_transformation,[status(thm)],[f46])).
% 1.91/1.54 thf(f46,plain,(
% 1.91/1.54 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.91/1.54 inference(fool_elimination,[status(thm)],[f1])).
% 1.91/1.54 thf(f1,axiom,(
% 1.91/1.54 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.91/1.54 file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',mlocal_def)).
% 1.91/1.54 thf(f64,plain,(
% 1.91/1.54 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))) = $true)),
% 1.91/1.54 inference(cnf_transformation,[status(thm)],[f35])).
% 1.91/1.54 thf(f35,plain,(
% 1.91/1.54 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))) = $true)),
% 1.91/1.54 inference(fool_elimination,[status(thm)],[f34])).
% 1.91/1.54 thf(f34,plain,(
% 1.91/1.54 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : (mexists_di @ (^[X1 : $i] : (mbox @ (mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0)))))))))),
% 1.91/1.54 inference(rectify,[status(thm)],[f16])).
% 1.91/1.54 thf(f16,axiom,(
% 1.91/1.54 (mlocal @ (mbox @ (mforall_di @ (^[X5 : $i] : (mexists_di @ (^[X6 : $i] : (mbox @ (mimplies @ (mand @ (bomb @ X5) @ (h @ X6)) @ (defused @ X5)))))))))),
% 1.91/1.54 file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',ax3)).
% 1.91/1.54 thf(f269,plain,(
% 1.91/1.54 ~spl1_11),
% 1.91/1.54 inference(avatar_contradiction_clause,[status(thm)],[f268])).
% 1.91/1.54 thf(f268,plain,(
% 1.91/1.54 $false | ~spl1_11),
% 1.91/1.54 inference(trivial_inequality_removal,[status(thm)],[f262])).
% 1.91/1.54 thf(f262,plain,(
% 1.91/1.54 ($false = $true) | ~spl1_11),
% 1.91/1.54 inference(superposition,[status(thm)],[f111,f243])).
% 1.91/1.54 thf(f243,plain,(
% 1.91/1.54 ($false = (eiw_di @ sK5 @ sK4)) | ~spl1_11),
% 1.91/1.54 inference(avatar_component_clause,[status(thm)],[f241])).
% 1.91/1.54 thf(f111,plain,(
% 1.91/1.54 ($true = (eiw_di @ sK5 @ sK4))),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.91/1.54 thf(f109,plain,(
% 1.91/1.54 ($false = ((eiw_di @ sK5 @ sK4) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK4) & (((h @ Y0 @ sK4) & (bomb @ sK5 @ sK4)) => (defused @ sK5 @ sK4)))))))),
% 1.91/1.54 inference(beta_eta_normalization,[status(thm)],[f108])).
% 1.91/1.54 thf(f108,plain,(
% 1.91/1.54 ($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ sK4) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK4) & (((h @ Y1 @ sK4) & (bomb @ Y0 @ sK4)) => (defused @ Y0 @ sK4))))))) @ sK5))),
% 1.91/1.54 inference(sigma_clausification,[status(thm)],[f106])).
% 1.91/1.54 thf(f106,plain,(
% 1.91/1.54 ($false = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK4) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK4) & (((h @ Y1 @ sK4) & (bomb @ Y0 @ sK4)) => (defused @ Y0 @ sK4)))))))))),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f105])).
% 1.91/1.54 thf(f105,plain,(
% 1.91/1.54 ($false = ((mrel @ mactual @ sK4) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK4) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK4) & (((h @ Y1 @ sK4) & (bomb @ Y0 @ sK4)) => (defused @ Y0 @ sK4))))))))))),
% 1.91/1.54 inference(beta_eta_normalization,[status(thm)],[f104])).
% 1.91/1.54 thf(f104,plain,(
% 1.91/1.54 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y0) & (((h @ Y2 @ Y0) & (bomb @ Y1 @ Y0)) => (defused @ Y1 @ Y0)))))))))) @ sK4))),
% 1.91/1.54 inference(sigma_clausification,[status(thm)],[f103])).
% 1.91/1.54 thf(f103,plain,(
% 1.91/1.54 ($true != (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y0) & (((h @ Y2 @ Y0) & (bomb @ Y1 @ Y0)) => (defused @ Y1 @ Y0))))))))))))),
% 1.91/1.54 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.91/1.54 thf(f78,plain,(
% 1.91/1.54 ($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 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))))),
% 1.91/1.54 inference(definition_unfolding,[status(thm)],[f68,f72,f70,f63,f62,f67,f61])).
% 1.91/1.54 thf(f68,plain,(
% 1.91/1.54 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) != $true)),
% 1.91/1.54 inference(cnf_transformation,[status(thm)],[f53])).
% 1.91/1.54 thf(f53,plain,(
% 1.91/1.54 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) != $true)),
% 1.91/1.54 inference(flattening,[status(thm)],[f21])).
% 1.91/1.54 thf(f21,plain,(
% 1.91/1.54 ~((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) = $true)),
% 1.91/1.54 inference(fool_elimination,[status(thm)],[f20])).
% 1.91/1.54 thf(f20,plain,(
% 1.91/1.54 ~(mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : (mexists_di @ (^[X1 : $i] : (mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0))))))))),
% 1.91/1.54 inference(rectify,[status(thm)],[f18])).
% 1.91/1.54 thf(f18,negated_conjecture,(
% 1.91/1.54 ~(mlocal @ (mbox @ (mforall_di @ (^[X5 : $i] : (mexists_di @ (^[X6 : $i] : (mimplies @ (mand @ (bomb @ X5) @ (h @ X6)) @ (defused @ X5))))))))),
% 1.91/1.54 inference(negated_conjecture,[status(cth)],[f17])).
% 1.91/1.54 thf(f17,conjecture,(
% 1.91/1.54 (mlocal @ (mbox @ (mforall_di @ (^[X5 : $i] : (mexists_di @ (^[X6 : $i] : (mimplies @ (mand @ (bomb @ X5) @ (h @ X6)) @ (defused @ X5))))))))),
% 1.91/1.54 file('/export/starexec/sandbox/tmp/tmp.2WcgN7XUqU/DTF2THF_13713.p',con)).
% 1.91/1.54 thf(f195,plain,(
% 1.91/1.54 ~spl1_4),
% 1.91/1.54 inference(avatar_contradiction_clause,[status(thm)],[f194])).
% 1.91/1.54 thf(f194,plain,(
% 1.91/1.54 $false | ~spl1_4),
% 1.91/1.54 inference(trivial_inequality_removal,[status(thm)],[f191])).
% 1.91/1.54 thf(f191,plain,(
% 1.91/1.54 ($false = $true) | ~spl1_4),
% 1.91/1.54 inference(superposition,[status(thm)],[f69,f174])).
% 1.91/1.54 thf(f174,plain,(
% 1.91/1.54 ($false = (mrel @ mactual @ sK4)) | ~spl1_4),
% 1.91/1.54 inference(avatar_component_clause,[status(thm)],[f172])).
% 1.91/1.54 thf(f189,plain,(
% 1.91/1.54 spl1_6 | spl1_4),
% 1.91/1.54 inference(avatar_split_clause,[status(thm)],[f183,f172,f186])).
% 1.91/1.54 thf(f183,plain,(
% 1.91/1.54 ( ! [X0 : $i] : (($true = (h @ (sK6 @ sK4 @ X0) @ sK4)) | ($false = (mrel @ mactual @ sK4)) | ($false = (eiw_di @ X0 @ sK4))) )),
% 1.91/1.54 inference(trivial_inequality_removal,[status(thm)],[f181])).
% 1.91/1.54 thf(f181,plain,(
% 1.91/1.54 ( ! [X0 : $i] : (($false = (eiw_di @ X0 @ sK4)) | ($true = (h @ (sK6 @ sK4 @ X0) @ sK4)) | ($false = (mrel @ mactual @ sK4)) | ($false = $true)) )),
% 1.91/1.54 inference(superposition,[status(thm)],[f129,f118])).
% 1.91/1.54 thf(f118,plain,(
% 1.91/1.54 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ sK4)) | ((h @ X1 @ sK4) = $true)) )),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f116])).
% 1.91/1.54 thf(f116,plain,(
% 1.91/1.54 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ sK4)) | ($true = ((h @ X1 @ sK4) & (bomb @ sK5 @ sK4)))) )),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f114])).
% 1.91/1.54 thf(f114,plain,(
% 1.91/1.54 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ sK4)) | ($false = (((h @ X1 @ sK4) & (bomb @ sK5 @ sK4)) => (defused @ sK5 @ sK4)))) )),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.91/1.54 thf(f113,plain,(
% 1.91/1.54 ( ! [X1 : $i] : (($false = ((eiw_di @ X1 @ sK4) & (((h @ X1 @ sK4) & (bomb @ sK5 @ sK4)) => (defused @ sK5 @ sK4))))) )),
% 1.91/1.54 inference(beta_eta_normalization,[status(thm)],[f112])).
% 1.91/1.54 thf(f112,plain,(
% 1.91/1.54 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ sK4) & (((h @ Y0 @ sK4) & (bomb @ sK5 @ sK4)) => (defused @ sK5 @ sK4)))) @ X1))) )),
% 1.91/1.54 inference(pi_clausification,[status(thm)],[f110])).
% 1.91/1.54 thf(f110,plain,(
% 1.91/1.54 ($false = (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK4) & (((h @ Y0 @ sK4) & (bomb @ sK5 @ sK4)) => (defused @ sK5 @ sK4))))))),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.91/1.54 thf(f129,plain,(
% 1.91/1.54 ( ! [X2 : $i,X1 : mworld] : (($true = (eiw_di @ (sK6 @ X1 @ X2) @ X1)) | ($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f127])).
% 1.91/1.54 thf(f154,plain,(
% 1.91/1.54 ~spl1_2),
% 1.91/1.54 inference(avatar_contradiction_clause,[status(thm)],[f153])).
% 1.91/1.54 thf(f153,plain,(
% 1.91/1.54 $false | ~spl1_2),
% 1.91/1.54 inference(trivial_inequality_removal,[status(thm)],[f149])).
% 1.91/1.54 thf(f149,plain,(
% 1.91/1.54 ($false = $true) | ~spl1_2),
% 1.91/1.54 inference(superposition,[status(thm)],[f142,f111])).
% 1.91/1.54 thf(f142,plain,(
% 1.91/1.54 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ sK4))) ) | ~spl1_2),
% 1.91/1.54 inference(avatar_component_clause,[status(thm)],[f141])).
% 1.91/1.54 thf(f141,definition,(
% 1.91/1.54 spl1_2 <=> ! [X1 : $i] : ($false = (eiw_di @ X1 @ sK4))),
% 1.91/1.54 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.91/1.54 thf(f148,plain,(
% 1.91/1.54 spl1_3 | spl1_2),
% 1.91/1.54 inference(avatar_split_clause,[status(thm)],[f117,f141,f145])).
% 1.91/1.54 thf(f117,plain,(
% 1.91/1.54 ( ! [X1 : $i] : (((bomb @ sK5 @ sK4) = $true) | ($false = (eiw_di @ X1 @ sK4))) )),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f116])).
% 1.91/1.54 thf(f143,plain,(
% 1.91/1.54 spl1_1 | spl1_2),
% 1.91/1.54 inference(avatar_split_clause,[status(thm)],[f115,f141,f137])).
% 1.91/1.54 thf(f115,plain,(
% 1.91/1.54 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ sK4)) | ($false = (defused @ sK5 @ sK4))) )),
% 1.91/1.54 inference(binary_proxy_clausification,[status(thm)],[f114])).
% 1.91/1.54 % SZS output end Proof for DTF2THF_13713
% 1.91/1.54 % (13871)------------------------------
% 1.91/1.54 % (13871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.91/1.54 % (13871)Termination reason: Refutation
% 1.91/1.54
% 1.91/1.54 % (13871)Memory used [KB]: 5884
% 1.91/1.54 % (13871)Time elapsed: 0.023 s
% 1.91/1.54 % (13871)Instructions burned: 35 (million)
% 1.91/1.54 % (13871)------------------------------
% 1.91/1.54 % (13871)------------------------------
% 1.91/1.54 % (13870)Success in time 0.035 s
%------------------------------------------------------------------------------