%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PLA053^4 : 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 : n008.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 1.73s 1.33s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 83 ( 53 unt; 0 typ; 2 def)
% Number of atoms : 506 ( 99 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 741 ( 19 ~; 40 |; 27 &; 562 @)
% ( 2 <=>; 48 =>; 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 : 26 ( 21 usr; 9 con; 0-3 aty)
% ( 27 !!; 16 ??; 0 @@+; 0 @@-)
% Number of variables : 201 ( 153 ^; 46 !; 2 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mrel: mworld > mworld > $o ).
thf(func_def_2,type,
mactual: mworld ).
thf(func_def_3,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_5,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
h: $i > mworld > $o ).
thf(func_def_15,type,
bomb: $i > mworld > $o ).
thf(func_def_16,type,
defused: $i > mworld > $o ).
thf(func_def_34,type,
sK2: mworld > $i > $i ).
thf(func_def_35,type,
sK3: mworld ).
thf(func_def_37,type,
sK5: mworld > $i ).
thf(f167,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f130,f152,f166]) ).
thf(f166,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f165]) ).
thf(f165,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f157]) ).
thf(f157,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f156,f111]) ).
thf(f111,plain,
( $true
= ( bomb @ sK4 @ sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X1: $i] :
( ( ( bomb @ sK4 @ sK3 )
& ( h @ X1 @ sK3 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
! [X1: $i] :
( $false
= ( ( ( bomb @ sK4 @ sK3 )
& ( h @ X1 @ sK3 ) )
=> ( defused @ sK4 @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f106]) ).
thf(f106,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( ( bomb @ sK4 @ sK3 )
& ( h @ Y0 @ sK3 ) )
=> ( defused @ sK4 @ sK3 ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( bomb @ sK4 @ sK3 )
& ( h @ Y0 @ sK3 ) )
=> ( defused @ sK4 @ sK3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f104]) ).
thf(f104,plain,
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( bomb @ Y0 @ sK3 )
& ( h @ Y1 @ sK3 ) )
=> ( defused @ Y0 @ sK3 ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( bomb @ Y0 @ sK3 )
& ( h @ Y1 @ sK3 ) )
=> ( defused @ Y0 @ sK3 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
( $false
= ( ( mrel @ mactual @ sK3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( bomb @ Y0 @ sK3 )
& ( h @ Y1 @ sK3 ) )
=> ( defused @ Y0 @ sK3 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f100]) ).
thf(f100,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( bomb @ Y1 @ Y0 )
& ( h @ Y2 @ Y0 ) )
=> ( defused @ Y1 @ Y0 ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( bomb @ Y1 @ Y0 )
& ( h @ Y2 @ Y0 ) )
=> ( defused @ Y1 @ Y0 ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,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] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ ( bomb @ Y0 )
@ ( h @ Y1 ) )
@ ( defused @ Y0 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f63,f59,f56,f57,f62,f60,f61]) ).
thf(f61,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f36]) ).
thf(f36,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( mand
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',mand_def) ).
thf(f60,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ^ [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.K4VIEEeA0P/DTF2THF_6802.p',mimplies_def) ).
thf(f62,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X6: $i] : ( X1 @ X6 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',mexists_di_def) ).
thf(f57,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f32]) ).
thf(f32,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X6: $i] : ( X1 @ X6 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',mforall_di_def) ).
thf(f56,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) )
= mbox ),
file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',mbox_def) ).
thf(f59,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,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.K4VIEEeA0P/DTF2THF_6802.p',mlocal_def) ).
thf(f63,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)],[f50]) ).
thf(f50,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f25]) ).
thf(f25,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)],[f24]) ).
thf(f24,plain,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X6: $i] :
( mexists_di
@ ^ [X7: $i] : ( mimplies @ ( mand @ ( bomb @ X6 ) @ ( h @ X7 ) ) @ ( defused @ X6 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f16,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X6: $i] :
( mexists_di
@ ^ [X7: $i] : ( mimplies @ ( mand @ ( bomb @ X6 ) @ ( h @ X7 ) ) @ ( defused @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',con) ).
thf(f156,plain,
( ( $false
= ( bomb @ sK4 @ sK3 ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
( ( $false = $true )
| ( $false
= ( bomb @ sK4 @ sK3 ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f108,f125]) ).
thf(f125,plain,
( ! [X1: $i] :
( ( $true
= ( defused @ X1 @ sK3 ) )
| ( $false
= ( bomb @ X1 @ sK3 ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f124]) ).
thf(f124,definition,
( spl0_1
<=> ! [X1: $i] :
( ( $false
= ( bomb @ X1 @ sK3 ) )
| ( $true
= ( defused @ X1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f108,plain,
( ( defused @ sK4 @ sK3 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f152,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f151]) ).
thf(f151,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f143]) ).
thf(f143,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f140,f103]) ).
thf(f103,plain,
( ( mrel @ mactual @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f140,plain,
( ( $false
= ( mrel @ mactual @ sK3 ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ sK3 ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f67,f128]) ).
thf(f128,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ X0 @ sK3 ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f127]) ).
thf(f127,definition,
( spl0_2
<=> ! [X0: mworld] :
( ( $false
= ( mrel @ X0 @ sK3 ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f67,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,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.K4VIEEeA0P/DTF2THF_6802.p',mrel_reflexive) ).
thf(f130,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f121,f124,f127]) ).
thf(f121,plain,
! [X0: mworld,X1: $i] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( bomb @ X1 @ sK3 ) )
| ( $false
= ( mrel @ X0 @ sK3 ) )
| ( $true
= ( defused @ X1 @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
! [X0: mworld,X1: $i] :
( ( $false
= ( bomb @ X1 @ sK3 ) )
| ( $true
= ( defused @ X1 @ sK3 ) )
| ( $false
= ( mrel @ X0 @ sK3 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X0 ) ) ),
inference(superposition,[status(thm)],[f110,f98]) ).
thf(f98,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( h @ ( sK2 @ X1 @ X2 ) @ X3 ) )
| ( ( defused @ X2 @ X3 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( bomb @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( ( defused @ X2 @ X3 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( ( bomb @ X2 @ X3 )
& ( h @ ( sK2 @ X1 @ X2 ) @ X3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $true
= ( ( ( bomb @ X2 @ X3 )
& ( h @ ( sK2 @ X1 @ X2 ) @ X3 ) )
=> ( defused @ X2 @ X3 ) ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X3 )
=> ( ( ( bomb @ X2 @ X3 )
& ( h @ ( sK2 @ X1 @ X2 ) @ X3 ) )
=> ( defused @ X2 @ X3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( bomb @ X2 @ Y0 )
& ( h @ ( sK2 @ X1 @ X2 ) @ Y0 ) )
=> ( defused @ X2 @ Y0 ) ) )
@ X3 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( bomb @ X2 @ Y0 )
& ( h @ ( sK2 @ X1 @ X2 ) @ Y0 ) )
=> ( defused @ X2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( bomb @ X2 @ Y1 )
& ( h @ Y0 @ Y1 ) )
=> ( defused @ X2 @ Y1 ) ) ) )
@ ( sK2 @ X1 @ X2 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( bomb @ X2 @ Y1 )
& ( h @ Y0 @ Y1 ) )
=> ( defused @ X2 @ Y1 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( bomb @ Y0 @ Y2 )
& ( h @ Y1 @ Y2 ) )
=> ( defused @ Y0 @ Y2 ) ) ) ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
! [X1: mworld] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( bomb @ Y0 @ Y2 )
& ( h @ Y1 @ Y2 ) )
=> ( defused @ Y0 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( bomb @ Y0 @ Y2 )
& ( h @ Y1 @ Y2 ) )
=> ( defused @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( ( ( bomb @ Y1 @ Y3 )
& ( h @ Y2 @ Y3 ) )
=> ( defused @ Y1 @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( ( ( bomb @ Y1 @ Y3 )
& ( h @ Y2 @ Y3 ) )
=> ( defused @ Y1 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ 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] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ ( bomb @ Y0 )
@ ( h @ Y1 ) )
@ ( defused @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f53,f59,f56,f57,f62,f56,f60,f61]) ).
thf(f53,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)],[f47]) ).
thf(f47,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)],[f46]) ).
thf(f46,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X6: $i] :
( mexists_di
@ ^ [X7: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X6 ) @ ( h @ X7 ) ) @ ( defused @ X6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',ax3) ).
thf(f110,plain,
! [X1: $i] :
( ( h @ X1 @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PLA053^4 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n008.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 11:28:09 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.44 ---- Original DTF file ---
% 0.20/0.44 thf(spec,logic,$$dhol).
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 % File : PLA053^4 : TPTP v9.2.1. Released v8.1.0.
% 0.20/0.44 % Domain : Planning
% 0.20/0.44 % Problem : Abductive planning: Bomb-in-the-toilet with detector
% 0.20/0.44 % Version : [BP13] axioms.
% 0.20/0.44 % English :
% 0.20/0.44
% 0.20/0.44 % Refs : [Sto98] Stone (1998), Abductive Planning with Sensing
% 0.20/0.44 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.20/0.44 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.20/0.44 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.20/0.44 % Source : [TPTP]
% 0.20/0.44 % Names : APM004+1 [QMLTP]
% 0.20/0.44
% 0.20/0.44 % Status : Theorem
% 0.20/0.44 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.20/0.44 % Syntax : Number of formulae : 32 ( 11 unt; 16 typ; 10 def)
% 0.20/0.44 % Number of atoms : 59 ( 10 equ; 0 cnn)
% 0.20/0.44 % Maximal formula atoms : 10 ( 3 avg)
% 0.20/0.44 % Number of connectives : 76 ( 1 ~; 1 |; 3 &; 67 @)
% 0.20/0.44 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.44 % Maximal formula depth : 13 ( 4 avg)
% 0.20/0.44 % Number of types : 3 ( 1 usr)
% 0.20/0.44 % Number of type conns : 63 ( 63 >; 0 *; 0 +; 0 <<)
% 0.20/0.44 % Number of symbols : 16 ( 15 usr; 1 con; 0-3 aty)
% 0.20/0.44 % Number of variables : 38 ( 30 ^; 6 !; 2 ?; 38 :)
% 0.20/0.44 % SPC : TH0_THM_EQU_NAR
% 0.20/0.44
% 0.20/0.44 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.20/0.44 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.20/0.44 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.20/0.44 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.20/0.44 % $modalities == $modal_system_S4].
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 thf(mworld,type,
% 0.20/0.44 mworld: $tType ).
% 0.20/0.44
% 0.20/0.44 thf(mrel_type,type,
% 0.20/0.44 mrel: mworld > mworld > $o ).
% 0.20/0.44
% 0.20/0.44 thf(mactual_type,type,
% 0.20/0.44 mactual: mworld ).
% 0.20/0.44
% 0.20/0.44 thf(mlocal_type,type,
% 0.20/0.44 mlocal: ( mworld > $o ) > $o ).
% 0.20/0.44
% 0.20/0.44 thf(mlocal_def,definition,
% 0.20/0.44 ( mlocal
% 0.20/0.44 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(mnot_type,type,
% 0.20/0.44 mnot: ( mworld > $o ) > mworld > $o ).
% 0.20/0.44
% 0.20/0.44 thf(mand_type,type,
% 0.20/0.44 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.44
% 0.20/0.44 thf(mor_type,type,
% 0.20/0.44 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.44
% 0.20/0.44 thf(mimplies_type,type,
% 0.20/0.44 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.44
% 0.20/0.44 thf(mequiv_type,type,
% 0.20/0.44 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.44
% 0.20/0.44 thf(mnot_def,definition,
% 0.20/0.44 ( mnot
% 0.20/0.44 = ( ^ [A: mworld > $o,W: mworld] :
% 0.20/0.44 ~ ( A @ W ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(mand_def,definition,
% 0.20/0.44 ( mand
% 0.20/0.44 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.44 ( ( A @ W )
% 0.20/0.44 & ( B @ W ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(mor_def,definition,
% 0.20/0.44 ( mor
% 0.20/0.44 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.44 ( ( A @ W )
% 0.20/0.44 | ( B @ W ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(mimplies_def,definition,
% 0.20/0.44 ( mimplies
% 0.20/0.44 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.44 ( ( A @ W )
% 0.20/0.44 => ( B @ W ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(mequiv_def,definition,
% 0.20/0.44 ( mequiv
% 0.20/0.44 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.44 ( ( A @ W )
% 0.20/0.44 <=> ( B @ W ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(mbox_type,type,
% 0.20/0.44 mbox: ( mworld > $o ) > mworld > $o ).
% 0.20/0.44
% 0.20/0.44 thf(mbox_def,definition,
% 0.20/0.44 ( mbox
% 0.20/0.44 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.44 ! [V: mworld] :
% 0.20/0.44 ( ( mrel @ W @ V )
% 0.20/0.44 => ( Phi @ V ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(mdia_type,type,
% 0.20/0.44 mdia: ( mworld > $o ) > mworld > $o ).
% 0.20/0.44
% 0.20/0.44 thf(mdia_def,definition,
% 0.20/0.44 ( mdia
% 0.20/0.44 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.44 ? [V: mworld] :
% 0.20/0.44 ( ( mrel @ W @ V )
% 0.20/0.44 & ( Phi @ V ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(mrel_reflexive,axiom,
% 0.20/0.44 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.20/0.44
% 0.20/0.44 thf(mrel_transitive,axiom,
% 0.20/0.44 ! [W: mworld,V: mworld,U: mworld] :
% 0.20/0.44 ( ( ( mrel @ W @ V )
% 0.20/0.44 & ( mrel @ V @ U ) )
% 0.20/0.44 => ( mrel @ W @ U ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(mforall_di_type,type,
% 0.20/0.44 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.20/0.44
% 0.20/0.44 thf(mforall_di_def,definition,
% 0.20/0.44 ( mforall_di
% 0.20/0.44 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.20/0.44 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(mexists_di_type,type,
% 0.20/0.44 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.20/0.44
% 0.20/0.44 thf(mexists_di_def,definition,
% 0.20/0.44 ( mexists_di
% 0.20/0.44 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.20/0.44 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(h_decl,type,
% 0.20/0.44 h: $i > mworld > $o ).
% 0.20/0.44
% 0.20/0.44 thf(bomb_decl,type,
% 0.20/0.44 bomb: $i > mworld > $o ).
% 0.20/0.44
% 0.20/0.44 thf(defused_decl,type,
% 0.20/0.44 defused: $i > mworld > $o ).
% 0.20/0.44
% 0.20/0.44 thf(ax1,axiom,
% 0.20/0.44 ( mlocal
% 0.20/0.44 @ ( mbox
% 0.20/0.44 @ ( mexists_di
% 0.20/0.44 @ ^ [B: $i] : ( bomb @ B ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(ax2,axiom,
% 0.20/0.44 ( mlocal
% 0.20/0.44 @ ( mexists_di
% 0.20/0.44 @ ^ [A: $i] :
% 0.20/0.44 ( mbox
% 0.20/0.44 @ ( mforall_di
% 0.20/0.44 @ ^ [X: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ A ) ) @ ( mbox @ ( bomb @ X ) ) ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(ax3,axiom,
% 0.20/0.44 ( mlocal
% 0.20/0.44 @ ( mbox
% 0.20/0.44 @ ( mforall_di
% 0.20/0.44 @ ^ [X: $i] :
% 0.20/0.44 ( mexists_di
% 0.20/0.44 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(con,conjecture,
% 0.20/0.44 ( mlocal
% 0.20/0.44 @ ( mbox
% 0.20/0.44 @ ( mforall_di
% 0.20/0.44 @ ^ [X: $i] :
% 0.20/0.44 ( mexists_di
% 0.20/0.44 @ ^ [D: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 ------------------------
% 1.54/1.29 ---- Embedded in THF ---
% 1.54/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.29 %%% Generated on Tue Feb 24 11:28:10 EST 2026
% 1.54/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.29 %%% Logic specification used:
% 1.54/1.29 %%% thf(spec, logic, $$dhol).
% 1.54/1.29
% 1.54/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2DTF6802.p
% See solution above
% 1.54/1.29 ------------------------
% 1.73/1.30 ---- Cleaned THF ---
% 1.73/1.30 thf(mworld,type,
% 1.73/1.30 mworld: $tType ).
% 1.73/1.30
% 1.73/1.30 thf(mrel_type,type,
% 1.73/1.30 mrel: mworld > mworld > $o ).
% 1.73/1.30
% 1.73/1.30 thf(mactual_type,type,
% 1.73/1.30 mactual: mworld ).
% 1.73/1.30
% 1.73/1.30 thf(mlocal_type,type,
% 1.73/1.30 mlocal: ( mworld > $o ) > $o ).
% 1.73/1.30
% 1.73/1.30 thf(mlocal_def,definition,
% 1.73/1.30 ( mlocal
% 1.73/1.30 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(mnot_type,type,
% 1.73/1.30 mnot: ( mworld > $o ) > mworld > $o ).
% 1.73/1.30
% 1.73/1.30 thf(mand_type,type,
% 1.73/1.30 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.73/1.30
% 1.73/1.30 thf(mor_type,type,
% 1.73/1.30 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.73/1.30
% 1.73/1.30 thf(mimplies_type,type,
% 1.73/1.30 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.73/1.30
% 1.73/1.30 thf(mequiv_type,type,
% 1.73/1.30 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.73/1.30
% 1.73/1.30 thf(mnot_def,definition,
% 1.73/1.30 ( mnot
% 1.73/1.30 = ( ^ [A: mworld > $o,W: mworld] :
% 1.73/1.30 ~ ( A @ W ) ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(mand_def,definition,
% 1.73/1.30 ( mand
% 1.73/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.73/1.30 ( ( A @ W )
% 1.73/1.30 & ( B @ W ) ) ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(mor_def,definition,
% 1.73/1.30 ( mor
% 1.73/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.73/1.30 ( ( A @ W )
% 1.73/1.30 | ( B @ W ) ) ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(mimplies_def,definition,
% 1.73/1.30 ( mimplies
% 1.73/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.73/1.30 ( ( A @ W )
% 1.73/1.30 => ( B @ W ) ) ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(mequiv_def,definition,
% 1.73/1.30 ( mequiv
% 1.73/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.73/1.30 ( ( A @ W )
% 1.73/1.30 <=> ( B @ W ) ) ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(mbox_type,type,
% 1.73/1.30 mbox: ( mworld > $o ) > mworld > $o ).
% 1.73/1.30
% 1.73/1.30 thf(mbox_def,definition,
% 1.73/1.30 ( mbox
% 1.73/1.30 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.73/1.30 ! [V: mworld] :
% 1.73/1.30 ( ( mrel @ W @ V )
% 1.73/1.30 => ( Phi @ V ) ) ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(mdia_type,type,
% 1.73/1.30 mdia: ( mworld > $o ) > mworld > $o ).
% 1.73/1.30
% 1.73/1.30 thf(mdia_def,definition,
% 1.73/1.30 ( mdia
% 1.73/1.30 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.73/1.30 ? [V: mworld] :
% 1.73/1.30 ( ( mrel @ W @ V )
% 1.73/1.30 & ( Phi @ V ) ) ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(mrel_reflexive,axiom,
% 1.73/1.30 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.73/1.30
% 1.73/1.30 thf(mrel_transitive,axiom,
% 1.73/1.30 ! [W: mworld,V: mworld,U: mworld] :
% 1.73/1.30 ( ( ( mrel @ W @ V )
% 1.73/1.30 & ( mrel @ V @ U ) )
% 1.73/1.30 => ( mrel @ W @ U ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(mforall_di_type,type,
% 1.73/1.30 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.73/1.30
% 1.73/1.30 thf(mforall_di_def,definition,
% 1.73/1.30 ( mforall_di
% 1.73/1.30 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.73/1.30 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(mexists_di_type,type,
% 1.73/1.30 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.73/1.30
% 1.73/1.30 thf(mexists_di_def,definition,
% 1.73/1.30 ( mexists_di
% 1.73/1.30 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.73/1.30 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(h_decl,type,
% 1.73/1.30 h: $i > mworld > $o ).
% 1.73/1.30
% 1.73/1.30 thf(bomb_decl,type,
% 1.73/1.30 bomb: $i > mworld > $o ).
% 1.73/1.30
% 1.73/1.30 thf(defused_decl,type,
% 1.73/1.30 defused: $i > mworld > $o ).
% 1.73/1.30
% 1.73/1.30 thf(ax1,axiom,
% 1.73/1.30 ( mlocal
% 1.73/1.30 @ ( mbox
% 1.73/1.30 @ ( mexists_di
% 1.73/1.30 @ ^ [B: $i] : ( bomb @ B ) ) ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(ax2,axiom,
% 1.73/1.30 ( mlocal
% 1.73/1.30 @ ( mexists_di
% 1.73/1.30 @ ^ [A: $i] :
% 1.73/1.30 ( mbox
% 1.73/1.30 @ ( mforall_di
% 1.73/1.30 @ ^ [X: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ A ) ) @ ( mbox @ ( bomb @ X ) ) ) ) ) ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(ax3,axiom,
% 1.73/1.30 ( mlocal
% 1.73/1.30 @ ( mbox
% 1.73/1.30 @ ( mforall_di
% 1.73/1.30 @ ^ [X: $i] :
% 1.73/1.30 ( mexists_di
% 1.73/1.30 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ) ).
% 1.73/1.30
% 1.73/1.30 thf(con,conjecture,
% 1.73/1.30 ( mlocal
% 1.73/1.30 @ ( mbox
% 1.73/1.30 @ ( mforall_di
% 1.73/1.30 @ ^ [X: $i] :
% 1.73/1.30 ( mexists_di
% 1.73/1.30 @ ^ [D: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ).
% 1.73/1.30 ------------------------
% 1.73/1.31 % (6952)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_6802 for (3000ds/275Mi)
% 1.73/1.31 % (6951)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_6802 for (3000ds/2Mi)
% 1.73/1.31 % (6952)Refutation not found, incomplete strategy
% 1.73/1.31 % (6952)------------------------------
% 1.73/1.31 % (6952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.31 % (6952)Termination reason: Refutation not found, incomplete strategy
% 1.73/1.31
% 1.73/1.31
% 1.73/1.31 % (6952)Memory used [KB]: 5500
% 1.73/1.31 % (6952)Time elapsed: 0.002 s
% 1.73/1.31 % (6952)Instructions burned: 3 (million)
% 1.73/1.31 % (6952)------------------------------
% 1.73/1.31 % (6952)------------------------------
% 1.73/1.31 % (6951)Instruction limit reached!
% 1.73/1.31 % (6951)------------------------------
% 1.73/1.31 % (6951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.31 % (6951)Termination reason: Unknown
% 1.73/1.31 % (6951)Termination phase: Property scanning
% 1.73/1.31
% 1.73/1.31 % (6951)Memory used [KB]: 1023
% 1.73/1.31 % (6951)Time elapsed: 0.002 s
% 1.73/1.31 % (6951)Instructions burned: 4 (million)
% 1.73/1.31 % (6951)------------------------------
% 1.73/1.31 % (6951)------------------------------
% 1.73/1.32 % (6953)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6802 for (3000ds/18Mi)
% 1.73/1.32 % (6947)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6802 for (3000ds/183Mi)
% 1.73/1.32 % (6948)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_6802 for (3000ds/4Mi)
% 1.73/1.32 % (6949)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_6802 for (3000ds/27Mi)
% 1.73/1.32 % (6950)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6802 for (3000ds/2Mi)
% 1.73/1.32 % (6950)Instruction limit reached!
% 1.73/1.32 % (6950)------------------------------
% 1.73/1.32 % (6950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.32 % (6950)Termination reason: Unknown
% 1.73/1.32 % (6950)Termination phase: shuffling
% 1.73/1.32
% 1.73/1.32 % (6950)Memory used [KB]: 1023
% 1.73/1.32 % (6950)Time elapsed: 0.003 s
% 1.73/1.32 % (6950)Instructions burned: 2 (million)
% 1.73/1.32 % (6950)------------------------------
% 1.73/1.32 % (6950)------------------------------
% 1.73/1.32 % (6948)Instruction limit reached!
% 1.73/1.32 % (6948)------------------------------
% 1.73/1.32 % (6948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.32 % (6948)Termination reason: Unknown
% 1.73/1.32 % (6948)Termination phase: Property scanning
% 1.73/1.32
% 1.73/1.32 % (6948)Memory used [KB]: 1023
% 1.73/1.32 % (6948)Time elapsed: 0.004 s
% 1.73/1.32 % (6948)Instructions burned: 4 (million)
% 1.73/1.32 % (6948)------------------------------
% 1.73/1.32 % (6948)------------------------------
% 1.73/1.32 % (6954)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6802 for (2999ds/3Mi)
% 1.73/1.32 % (6955)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_6802 for (2999ds/37Mi)
% 1.73/1.32 % (6954)Instruction limit reached!
% 1.73/1.32 % (6954)------------------------------
% 1.73/1.32 % (6954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.32 % (6954)Termination reason: Unknown
% 1.73/1.32 % (6954)Termination phase: Function definition elimination
% 1.73/1.32
% 1.73/1.32 % (6954)Memory used [KB]: 1023
% 1.73/1.32 % (6954)Time elapsed: 0.002 s
% 1.73/1.32 % (6954)Instructions burned: 4 (million)
% 1.73/1.32 % (6954)------------------------------
% 1.73/1.32 % (6954)------------------------------
% 1.73/1.33 % (6947)First to succeed.
% 1.73/1.33 % (6953)Instruction limit reached!
% 1.73/1.33 % (6953)------------------------------
% 1.73/1.33 % (6953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.33 % (6953)Termination reason: Unknown
% 1.73/1.33 % (6953)Termination phase: Saturation
% 1.73/1.33
% 1.73/1.33 % (6953)Memory used [KB]: 5628
% 1.73/1.33 % (6953)Time elapsed: 0.013 s
% 1.73/1.33 % (6953)Instructions burned: 19 (million)
% 1.73/1.33 % (6953)------------------------------
% 1.73/1.33 % (6953)------------------------------
% 1.73/1.33 % (6947)Refutation found. Thanks to Tanya!
% 1.73/1.33 % SZS status Theorem for DTF2THF_6802
% 1.73/1.33 % SZS output start Proof for DTF2THF_6802
% 1.73/1.33 thf(type_def_5, type, mworld: $tType).
% 1.73/1.33 thf(func_def_0, type, mworld: $tType).
% 1.73/1.33 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.73/1.33 thf(func_def_2, type, mactual: mworld).
% 1.73/1.33 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.73/1.33 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.73/1.33 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.73/1.33 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.73/1.33 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.73/1.33 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.73/1.33 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.73/1.33 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.73/1.33 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.73/1.33 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.73/1.33 thf(func_def_14, type, h: $i > mworld > $o).
% 1.73/1.33 thf(func_def_15, type, bomb: $i > mworld > $o).
% 1.73/1.33 thf(func_def_16, type, defused: $i > mworld > $o).
% 1.73/1.33 thf(func_def_34, type, sK2: mworld > $i > $i).
% 1.73/1.33 thf(func_def_35, type, sK3: mworld).
% 1.73/1.33 thf(func_def_37, type, sK5: mworld > $i).
% 1.73/1.33 thf(f167,plain,(
% 1.73/1.33 $false),
% 1.73/1.33 inference(avatar_sat_refutation,[status(thm)],[f130,f152,f166])).
% 1.73/1.33 thf(f166,plain,(
% 1.73/1.33 ~spl0_1),
% 1.73/1.33 inference(avatar_contradiction_clause,[status(thm)],[f165])).
% 1.73/1.33 thf(f165,plain,(
% 1.73/1.33 $false | ~spl0_1),
% 1.73/1.33 inference(trivial_inequality_removal,[status(thm)],[f157])).
% 1.73/1.33 thf(f157,plain,(
% 1.73/1.33 ($false = $true) | ~spl0_1),
% 1.73/1.33 inference(superposition,[status(thm)],[f156,f111])).
% 1.73/1.33 thf(f111,plain,(
% 1.73/1.33 ($true = (bomb @ sK4 @ sK3))),
% 1.73/1.33 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.73/1.33 thf(f109,plain,(
% 1.73/1.33 ( ! [X1 : $i] : ((((bomb @ sK4 @ sK3) & (h @ X1 @ sK3)) = $true)) )),
% 1.73/1.33 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.73/1.33 thf(f107,plain,(
% 1.73/1.33 ( ! [X1 : $i] : (($false = (((bomb @ sK4 @ sK3) & (h @ X1 @ sK3)) => (defused @ sK4 @ sK3)))) )),
% 1.73/1.33 inference(beta_eta_normalization,[status(thm)],[f106])).
% 1.73/1.33 thf(f106,plain,(
% 1.73/1.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((bomb @ sK4 @ sK3) & (h @ Y0 @ sK3)) => (defused @ sK4 @ sK3))) @ X1) = $false)) )),
% 1.73/1.33 inference(pi_clausification,[status(thm)],[f105])).
% 1.73/1.33 thf(f105,plain,(
% 1.73/1.33 ($false = (?? @ $i @ (^[Y0 : $i]: (((bomb @ sK4 @ sK3) & (h @ Y0 @ sK3)) => (defused @ sK4 @ sK3)))))),
% 1.73/1.33 inference(beta_eta_normalization,[status(thm)],[f104])).
% 1.73/1.33 thf(f104,plain,(
% 1.73/1.33 ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((bomb @ Y0 @ sK3) & (h @ Y1 @ sK3)) => (defused @ Y0 @ sK3))))) @ sK4))),
% 1.73/1.33 inference(sigma_clausification,[status(thm)],[f102])).
% 1.73/1.33 thf(f102,plain,(
% 1.73/1.33 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((bomb @ Y0 @ sK3) & (h @ Y1 @ sK3)) => (defused @ Y0 @ sK3)))))) = $false)),
% 1.73/1.33 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.73/1.33 thf(f101,plain,(
% 1.73/1.33 ($false = ((mrel @ mactual @ sK3) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((bomb @ Y0 @ sK3) & (h @ Y1 @ sK3)) => (defused @ Y0 @ sK3))))))))),
% 1.73/1.33 inference(beta_eta_normalization,[status(thm)],[f100])).
% 1.73/1.33 thf(f100,plain,(
% 1.73/1.33 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((bomb @ Y1 @ Y0) & (h @ Y2 @ Y0)) => (defused @ Y1 @ Y0)))))))) @ sK3))),
% 1.73/1.33 inference(sigma_clausification,[status(thm)],[f99])).
% 1.73/1.33 thf(f99,plain,(
% 1.73/1.33 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((bomb @ Y1 @ Y0) & (h @ Y2 @ Y0)) => (defused @ Y1 @ Y0))))))))) != $true)),
% 1.73/1.33 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.73/1.33 thf(f70,plain,(
% 1.73/1.33 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (?? @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) != $true)),
% 1.73/1.33 inference(definition_unfolding,[status(thm)],[f63,f59,f56,f57,f62,f60,f61])).
% 1.73/1.33 thf(f61,plain,(
% 1.73/1.33 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.73/1.33 inference(cnf_transformation,[status(thm)],[f37])).
% 1.73/1.33 thf(f37,plain,(
% 1.73/1.33 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.73/1.33 inference(fool_elimination,[status(thm)],[f36])).
% 1.73/1.33 thf(f36,plain,(
% 1.73/1.33 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 1.73/1.33 inference(rectify,[status(thm)],[f3])).
% 1.73/1.33 thf(f3,axiom,(
% 1.73/1.33 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))))),
% 1.73/1.33 file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',mand_def)).
% 1.73/1.33 thf(f60,plain,(
% 1.73/1.33 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.73/1.33 inference(cnf_transformation,[status(thm)],[f49])).
% 1.73/1.33 thf(f49,plain,(
% 1.73/1.33 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.73/1.33 inference(fool_elimination,[status(thm)],[f48])).
% 1.73/1.33 thf(f48,plain,(
% 1.73/1.33 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 1.73/1.33 inference(rectify,[status(thm)],[f5])).
% 1.73/1.33 thf(f5,axiom,(
% 1.73/1.33 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 1.73/1.33 file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',mimplies_def)).
% 1.73/1.33 thf(f62,plain,(
% 1.73/1.33 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.73/1.33 inference(cnf_transformation,[status(thm)],[f31])).
% 1.73/1.33 thf(f31,plain,(
% 1.73/1.33 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.73/1.33 inference(fool_elimination,[status(thm)],[f30])).
% 1.73/1.33 thf(f30,plain,(
% 1.73/1.33 (mexists_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : (X0 @ X2 @ X1))))),
% 1.73/1.33 inference(rectify,[status(thm)],[f12])).
% 1.73/1.33 thf(f12,axiom,(
% 1.73/1.33 (mexists_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (? [X6 : $i] : (X1 @ X6 @ X2))))),
% 1.73/1.33 file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',mexists_di_def)).
% 1.73/1.33 thf(f57,plain,(
% 1.73/1.33 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.73/1.33 inference(cnf_transformation,[status(thm)],[f33])).
% 1.73/1.33 thf(f33,plain,(
% 1.73/1.33 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.73/1.33 inference(fool_elimination,[status(thm)],[f32])).
% 1.73/1.33 thf(f32,plain,(
% 1.73/1.33 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))))),
% 1.73/1.33 inference(rectify,[status(thm)],[f11])).
% 1.73/1.33 thf(f11,axiom,(
% 1.73/1.33 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X6 : $i] : (X1 @ X6 @ X2))))),
% 1.73/1.33 file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',mforall_di_def)).
% 1.73/1.33 thf(f56,plain,(
% 1.73/1.33 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.73/1.33 inference(cnf_transformation,[status(thm)],[f39])).
% 1.73/1.33 thf(f39,plain,(
% 1.73/1.33 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.73/1.33 inference(fool_elimination,[status(thm)],[f38])).
% 1.73/1.33 thf(f38,plain,(
% 1.73/1.33 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 1.73/1.33 inference(rectify,[status(thm)],[f7])).
% 1.73/1.33 thf(f7,axiom,(
% 1.73/1.33 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 1.73/1.33 file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',mbox_def)).
% 1.73/1.33 thf(f59,plain,(
% 1.73/1.33 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.73/1.33 inference(cnf_transformation,[status(thm)],[f21])).
% 1.73/1.33 thf(f21,plain,(
% 1.73/1.33 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.73/1.33 inference(fool_elimination,[status(thm)],[f1])).
% 1.73/1.33 thf(f1,axiom,(
% 1.73/1.33 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.73/1.33 file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',mlocal_def)).
% 1.73/1.33 thf(f63,plain,(
% 1.73/1.33 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) != $true)),
% 1.73/1.33 inference(cnf_transformation,[status(thm)],[f50])).
% 1.73/1.33 thf(f50,plain,(
% 1.73/1.33 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) != $true)),
% 1.73/1.33 inference(flattening,[status(thm)],[f25])).
% 1.73/1.33 thf(f25,plain,(
% 1.73/1.33 ~((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) = $true)),
% 1.73/1.33 inference(fool_elimination,[status(thm)],[f24])).
% 1.73/1.33 thf(f24,plain,(
% 1.73/1.33 ~(mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : (mexists_di @ (^[X1 : $i] : (mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0))))))))),
% 1.73/1.33 inference(rectify,[status(thm)],[f17])).
% 1.73/1.33 thf(f17,negated_conjecture,(
% 1.73/1.33 ~(mlocal @ (mbox @ (mforall_di @ (^[X6 : $i] : (mexists_di @ (^[X7 : $i] : (mimplies @ (mand @ (bomb @ X6) @ (h @ X7)) @ (defused @ X6))))))))),
% 1.73/1.33 inference(negated_conjecture,[status(cth)],[f16])).
% 1.73/1.33 thf(f16,conjecture,(
% 1.73/1.33 (mlocal @ (mbox @ (mforall_di @ (^[X6 : $i] : (mexists_di @ (^[X7 : $i] : (mimplies @ (mand @ (bomb @ X6) @ (h @ X7)) @ (defused @ X6))))))))),
% 1.73/1.33 file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',con)).
% 1.73/1.33 thf(f156,plain,(
% 1.73/1.33 ($false = (bomb @ sK4 @ sK3)) | ~spl0_1),
% 1.73/1.33 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 1.73/1.33 thf(f154,plain,(
% 1.73/1.33 ($false = $true) | ($false = (bomb @ sK4 @ sK3)) | ~spl0_1),
% 1.73/1.33 inference(superposition,[status(thm)],[f108,f125])).
% 1.73/1.33 thf(f125,plain,(
% 1.73/1.33 ( ! [X1 : $i] : (($true = (defused @ X1 @ sK3)) | ($false = (bomb @ X1 @ sK3))) ) | ~spl0_1),
% 1.73/1.33 inference(avatar_component_clause,[status(thm)],[f124])).
% 1.73/1.33 thf(f124,definition,(
% 1.73/1.33 spl0_1 <=> ! [X1 : $i] : (($false = (bomb @ X1 @ sK3)) | ($true = (defused @ X1 @ sK3)))),
% 1.73/1.33 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.73/1.33 thf(f108,plain,(
% 1.73/1.33 ((defused @ sK4 @ sK3) = $false)),
% 1.73/1.33 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.73/1.33 thf(f152,plain,(
% 1.73/1.33 ~spl0_2),
% 1.73/1.33 inference(avatar_contradiction_clause,[status(thm)],[f151])).
% 1.73/1.33 thf(f151,plain,(
% 1.73/1.33 $false | ~spl0_2),
% 1.73/1.33 inference(trivial_inequality_removal,[status(thm)],[f143])).
% 1.73/1.33 thf(f143,plain,(
% 1.73/1.33 ($false = $true) | ~spl0_2),
% 1.73/1.33 inference(superposition,[status(thm)],[f140,f103])).
% 1.73/1.33 thf(f103,plain,(
% 1.73/1.33 ((mrel @ mactual @ sK3) = $true)),
% 1.73/1.33 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.73/1.33 thf(f140,plain,(
% 1.73/1.33 ($false = (mrel @ mactual @ sK3)) | ~spl0_2),
% 1.73/1.33 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.73/1.33 thf(f135,plain,(
% 1.73/1.33 ($false = $true) | ($false = (mrel @ mactual @ sK3)) | ~spl0_2),
% 1.73/1.33 inference(superposition,[status(thm)],[f67,f128])).
% 1.73/1.33 thf(f128,plain,(
% 1.73/1.33 ( ! [X0 : mworld] : (($false = (mrel @ mactual @ X0)) | ($false = (mrel @ X0 @ sK3))) ) | ~spl0_2),
% 1.73/1.33 inference(avatar_component_clause,[status(thm)],[f127])).
% 1.73/1.33 thf(f127,definition,(
% 1.73/1.33 spl0_2 <=> ! [X0 : mworld] : (($false = (mrel @ X0 @ sK3)) | ($false = (mrel @ mactual @ X0)))),
% 1.73/1.33 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.73/1.33 thf(f67,plain,(
% 1.73/1.33 ( ! [X0 : mworld] : (((mrel @ X0 @ X0) = $true)) )),
% 1.73/1.33 inference(cnf_transformation,[status(thm)],[f27])).
% 1.73/1.33 thf(f27,plain,(
% 1.73/1.33 ! [X0 : mworld] : ((mrel @ X0 @ X0) = $true)),
% 1.73/1.33 inference(fool_elimination,[status(thm)],[f26])).
% 1.73/1.33 thf(f26,plain,(
% 1.73/1.33 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 1.73/1.33 inference(rectify,[status(thm)],[f9])).
% 1.73/1.33 thf(f9,axiom,(
% 1.73/1.33 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 1.73/1.33 file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',mrel_reflexive)).
% 1.73/1.33 thf(f130,plain,(
% 1.73/1.33 spl0_2 | spl0_1),
% 1.73/1.33 inference(avatar_split_clause,[status(thm)],[f121,f124,f127])).
% 1.73/1.33 thf(f121,plain,(
% 1.73/1.33 ( ! [X0 : mworld,X1 : $i] : (($false = (mrel @ mactual @ X0)) | ($false = (bomb @ X1 @ sK3)) | ($false = (mrel @ X0 @ sK3)) | ($true = (defused @ X1 @ sK3))) )),
% 1.73/1.33 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.73/1.33 thf(f120,plain,(
% 1.73/1.33 ( ! [X0 : mworld,X1 : $i] : (($false = (bomb @ X1 @ sK3)) | ($true = (defused @ X1 @ sK3)) | ($false = (mrel @ X0 @ sK3)) | ($false = $true) | ($false = (mrel @ mactual @ X0))) )),
% 1.73/1.33 inference(superposition,[status(thm)],[f110,f98])).
% 1.73/1.33 thf(f98,plain,(
% 1.73/1.33 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (h @ (sK2 @ X1 @ X2) @ X3)) | ((defused @ X2 @ X3) = $true) | ($false = (mrel @ mactual @ X1)) | ($false = (mrel @ X1 @ X3)) | ($false = (bomb @ X2 @ X3))) )),
% 1.73/1.33 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.73/1.33 thf(f97,plain,(
% 1.73/1.33 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (((defused @ X2 @ X3) = $true) | ($false = (mrel @ mactual @ X1)) | ($false = (mrel @ X1 @ X3)) | ($false = ((bomb @ X2 @ X3) & (h @ (sK2 @ X1 @ X2) @ X3)))) )),
% 1.73/1.33 inference(binary_proxy_clausification,[status(thm)],[f96])).
% 1.73/1.33 thf(f96,plain,(
% 1.73/1.33 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($true = (((bomb @ X2 @ X3) & (h @ (sK2 @ X1 @ X2) @ X3)) => (defused @ X2 @ X3))) | ($false = (mrel @ X1 @ X3)) | ($false = (mrel @ mactual @ X1))) )),
% 1.73/1.33 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.73/1.33 thf(f95,plain,(
% 1.73/1.33 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((mrel @ X1 @ X3) => (((bomb @ X2 @ X3) & (h @ (sK2 @ X1 @ X2) @ X3)) => (defused @ X2 @ X3))))) )),
% 1.73/1.33 inference(beta_eta_normalization,[status(thm)],[f94])).
% 1.73/1.33 thf(f94,plain,(
% 1.73/1.33 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((bomb @ X2 @ Y0) & (h @ (sK2 @ X1 @ X2) @ Y0)) => (defused @ X2 @ Y0)))) @ X3) = $true) | ($false = (mrel @ mactual @ X1))) )),
% 1.73/1.33 inference(pi_clausification,[status(thm)],[f93])).
% 1.73/1.33 thf(f93,plain,(
% 1.73/1.33 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((bomb @ X2 @ Y0) & (h @ (sK2 @ X1 @ X2) @ Y0)) => (defused @ X2 @ Y0))))))) )),
% 1.73/1.33 inference(beta_eta_normalization,[status(thm)],[f92])).
% 1.73/1.33 thf(f92,plain,(
% 1.73/1.33 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((bomb @ X2 @ Y1) & (h @ Y0 @ Y1)) => (defused @ X2 @ Y1)))))) @ (sK2 @ X1 @ X2)))) )),
% 1.73/1.33 inference(sigma_clausification,[status(thm)],[f91])).
% 1.73/1.33 thf(f91,plain,(
% 1.73/1.33 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((bomb @ X2 @ Y1) & (h @ Y0 @ Y1)) => (defused @ X2 @ Y1))))))) = $true)) )),
% 1.73/1.33 inference(beta_eta_normalization,[status(thm)],[f90])).
% 1.73/1.33 thf(f90,plain,(
% 1.73/1.33 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((bomb @ Y0 @ Y2) & (h @ Y1 @ Y2)) => (defused @ Y0 @ Y2)))))))) @ X2))) )),
% 1.73/1.33 inference(pi_clausification,[status(thm)],[f89])).
% 1.73/1.33 thf(f89,plain,(
% 1.73/1.33 ( ! [X1 : mworld] : (($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((bomb @ Y0 @ Y2) & (h @ Y1 @ Y2)) => (defused @ Y0 @ Y2)))))))))) | ($false = (mrel @ mactual @ X1))) )),
% 1.73/1.33 inference(binary_proxy_clausification,[status(thm)],[f88])).
% 1.73/1.33 thf(f88,plain,(
% 1.73/1.33 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((bomb @ Y0 @ Y2) & (h @ Y1 @ Y2)) => (defused @ Y0 @ Y2)))))))))))) )),
% 1.73/1.33 inference(beta_eta_normalization,[status(thm)],[f87])).
% 1.73/1.33 thf(f87,plain,(
% 1.73/1.33 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (((bomb @ Y1 @ Y3) & (h @ Y2 @ Y3)) => (defused @ Y1 @ Y3))))))))))) @ X1))) )),
% 1.73/1.33 inference(pi_clausification,[status(thm)],[f86])).
% 1.73/1.33 thf(f86,plain,(
% 1.73/1.33 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (((bomb @ Y1 @ Y3) & (h @ Y2 @ Y3)) => (defused @ Y1 @ Y3)))))))))))) = $true)),
% 1.73/1.33 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.73/1.33 thf(f69,plain,(
% 1.73/1.33 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (?? @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ 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]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))))),
% 1.73/1.33 inference(definition_unfolding,[status(thm)],[f53,f59,f56,f57,f62,f56,f60,f61])).
% 1.73/1.33 thf(f53,plain,(
% 1.73/1.33 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))) = $true)),
% 1.73/1.33 inference(cnf_transformation,[status(thm)],[f47])).
% 1.73/1.33 thf(f47,plain,(
% 1.73/1.33 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))) = $true)),
% 1.73/1.33 inference(fool_elimination,[status(thm)],[f46])).
% 1.73/1.33 thf(f46,plain,(
% 1.73/1.33 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : (mexists_di @ (^[X1 : $i] : (mbox @ (mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0)))))))))),
% 1.73/1.33 inference(rectify,[status(thm)],[f15])).
% 1.73/1.33 thf(f15,axiom,(
% 1.73/1.33 (mlocal @ (mbox @ (mforall_di @ (^[X6 : $i] : (mexists_di @ (^[X7 : $i] : (mbox @ (mimplies @ (mand @ (bomb @ X6) @ (h @ X7)) @ (defused @ X6)))))))))),
% 1.73/1.33 file('/export/starexec/sandbox2/tmp/tmp.K4VIEEeA0P/DTF2THF_6802.p',ax3)).
% 1.73/1.33 thf(f110,plain,(
% 1.73/1.33 ( ! [X1 : $i] : (((h @ X1 @ sK3) = $true)) )),
% 1.73/1.33 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.73/1.33 % SZS output end Proof for DTF2THF_6802
% 1.73/1.33 % (6947)------------------------------
% 1.73/1.33 % (6947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.33 % (6947)Termination reason: Refutation
% 1.73/1.33
% 1.73/1.33 % (6947)Memory used [KB]: 5756
% 1.73/1.33 % (6947)Time elapsed: 0.012 s
% 1.73/1.33 % (6947)Instructions burned: 17 (million)
% 1.73/1.33 % (6947)------------------------------
% 1.73/1.33 % (6947)------------------------------
% 1.73/1.33 % (6946)Success in time 0.014 s
%------------------------------------------------------------------------------