%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PLA053^2 : 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 : 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 1.75s 1.30s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% 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 : 27 ( 22 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_17,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_34,type,
sK1: mworld > $i > $i ).
thf(func_def_35,type,
sK2: mworld > $i ).
thf(func_def_37,type,
sK4: mworld ).
thf(f158,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f124,f146,f157]) ).
thf(f157,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f156]) ).
thf(f156,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f155]) ).
thf(f155,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f103,f151]) ).
thf(f151,plain,
( ( $false
= ( mrel @ mactual @ sK4 ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ( $false
= ( mrel @ mactual @ sK4 ) )
| ( $false = $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f60,f119]) ).
thf(f119,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ X0 @ sK4 ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f118]) ).
thf(f118,definition,
( spl0_1
<=> ! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ X0 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f60,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X2: mworld] : ( mrel @ X2 @ X2 ),
file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',mrel_reflexive) ).
thf(f103,plain,
( $true
= ( mrel @ mactual @ sK4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
( ( ( mrel @ mactual @ sK4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( h @ Y1 @ sK4 )
& ( bomb @ Y0 @ sK4 ) )
=> ( defused @ Y0 @ sK4 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f100]) ).
thf(f100,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( h @ Y2 @ Y0 )
& ( bomb @ Y1 @ Y0 ) )
=> ( defused @ Y1 @ Y0 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ( h @ Y2 @ Y0 )
& ( bomb @ Y1 @ Y0 ) )
=> ( defused @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,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] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( bomb @ Y0 )
@ ( h @ Y1 ) )
@ ( defused @ Y0 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f52,f48,f55,f61,f54,f50,f58]) ).
thf(f58,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,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.r7rDaqw3uO/DTF2THF_6739.p',mand_def) ).
thf(f50,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( mimplies
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',mimplies_def) ).
thf(f54,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) )
= mexists_di ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X5: $i] : ( X1 @ X5 @ X2 ) )
= mexists_di ),
file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',mexists_di_def) ).
thf(f61,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X5: $i] : ( X1 @ X5 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',mforall_di_def) ).
thf(f55,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) )
= mbox ),
file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',mbox_def) ).
thf(f48,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',mlocal_def) ).
thf(f52,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)],[f47]) ).
thf(f47,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f29]) ).
thf(f29,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)],[f28]) ).
thf(f28,plain,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,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)],[f15]) ).
thf(f15,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.r7rDaqw3uO/DTF2THF_6739.p',con) ).
thf(f146,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f145]) ).
thf(f145,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f132,f108]) ).
thf(f108,plain,
( $false
= ( defused @ sK5 @ sK4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
! [X1: $i] :
( $false
= ( ( ( h @ X1 @ sK4 )
& ( bomb @ sK5 @ sK4 ) )
=> ( defused @ sK5 @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f106]) ).
thf(f106,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( ( h @ Y0 @ sK4 )
& ( bomb @ sK5 @ sK4 ) )
=> ( defused @ sK5 @ sK4 ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( h @ Y0 @ sK4 )
& ( bomb @ sK5 @ sK4 ) )
=> ( defused @ sK5 @ sK4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f104]) ).
thf(f104,plain,
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( h @ Y1 @ sK4 )
& ( bomb @ Y0 @ sK4 ) )
=> ( defused @ Y0 @ sK4 ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( h @ Y1 @ sK4 )
& ( bomb @ Y0 @ sK4 ) )
=> ( defused @ Y0 @ sK4 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f132,plain,
( ( $true
= ( defused @ sK5 @ sK4 ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f130]) ).
thf(f130,plain,
( ( $false = $true )
| ( $true
= ( defused @ sK5 @ sK4 ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f110,f122]) ).
thf(f122,plain,
( ! [X1: $i] :
( ( $false
= ( bomb @ X1 @ sK4 ) )
| ( ( defused @ X1 @ sK4 )
= $true ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f121]) ).
thf(f121,definition,
( spl0_2
<=> ! [X1: $i] :
( ( ( defused @ X1 @ sK4 )
= $true )
| ( $false
= ( bomb @ X1 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f110,plain,
( $true
= ( bomb @ sK5 @ sK4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X1: $i] :
( ( ( h @ X1 @ sK4 )
& ( bomb @ sK5 @ sK4 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f124,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f115,f118,f121]) ).
thf(f115,plain,
! [X0: mworld,X1: $i] :
( ( ( defused @ X1 @ sK4 )
= $true )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( bomb @ X1 @ sK4 ) )
| ( $false
= ( mrel @ X0 @ sK4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f114]) ).
thf(f114,plain,
! [X0: mworld,X1: $i] :
( ( $false = $true )
| ( $false
= ( mrel @ X0 @ sK4 ) )
| ( $false
= ( bomb @ X1 @ sK4 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( defused @ X1 @ sK4 )
= $true ) ),
inference(superposition,[status(thm)],[f79,f111]) ).
thf(f111,plain,
! [X1: $i] :
( ( h @ X1 @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f79,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( h @ ( sK1 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( defused @ X2 @ X3 ) )
| ( $false
= ( bomb @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( defused @ X2 @ X3 ) )
| ( $false
= ( ( h @ ( sK1 @ X1 @ X2 ) @ X3 )
& ( bomb @ X2 @ X3 ) ) )
| ( $false
= ( mrel @ X1 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( ( ( ( h @ ( sK1 @ X1 @ X2 ) @ X3 )
& ( bomb @ X2 @ X3 ) )
=> ( defused @ X2 @ X3 ) )
= $true )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X3 )
=> ( ( ( h @ ( sK1 @ X1 @ X2 ) @ X3 )
& ( bomb @ X2 @ X3 ) )
=> ( defused @ X2 @ X3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( h @ ( sK1 @ X1 @ X2 ) @ Y0 )
& ( bomb @ X2 @ Y0 ) )
=> ( defused @ X2 @ Y0 ) ) )
@ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( h @ ( sK1 @ X1 @ X2 ) @ Y0 )
& ( bomb @ X2 @ Y0 ) )
=> ( defused @ X2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( h @ Y0 @ Y1 )
& ( bomb @ X2 @ Y1 ) )
=> ( defused @ X2 @ Y1 ) ) ) )
@ ( sK1 @ X1 @ X2 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( h @ Y0 @ Y1 )
& ( bomb @ X2 @ Y1 ) )
=> ( defused @ X2 @ Y1 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X1: mworld] :
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( h @ Y1 @ Y2 )
& ( bomb @ Y0 @ Y2 ) )
=> ( defused @ Y0 @ Y2 ) ) ) ) )
@ X2 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: mworld] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( h @ Y1 @ Y2 )
& ( bomb @ Y0 @ Y2 ) )
=> ( defused @ Y0 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( h @ Y1 @ Y2 )
& ( bomb @ Y0 @ Y2 ) )
=> ( defused @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( ( ( h @ Y2 @ Y3 )
& ( bomb @ Y1 @ Y3 ) )
=> ( defused @ Y1 @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( ( ( h @ Y2 @ Y3 )
& ( bomb @ Y1 @ Y3 ) )
=> ( defused @ Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,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] :
( !! @ 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)],[f57,f48,f55,f61,f54,f55,f50,f58]) ).
thf(f57,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f36]) ).
thf(f36,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,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.r7rDaqw3uO/DTF2THF_6739.p',ax3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PLA053^2 : 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
% 0.16/0.34 % Computer : n008.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:28:09 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : PLA053^2 : TPTP v9.2.1. Released v8.1.0.
% 0.19/0.45 % Domain : Planning
% 0.19/0.45 % Problem : Abductive planning: Bomb-in-the-toilet with detector
% 0.19/0.45 % Version : [BP13] axioms.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Sto98] Stone (1998), Abductive Planning with Sensing
% 0.19/0.45 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.19/0.45 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.19/0.45 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.19/0.45 % Source : [TPTP]
% 0.19/0.45 % Names : APM004+1 [QMLTP]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.19/0.45 % Syntax : Number of formulae : 31 ( 11 unt; 16 typ; 10 def)
% 0.19/0.45 % Number of atoms : 56 ( 10 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 10 ( 3 avg)
% 0.19/0.45 % Number of connectives : 68 ( 1 ~; 1 |; 2 &; 61 @)
% 0.19/0.45 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 13 ( 4 avg)
% 0.19/0.45 % Number of types : 3 ( 1 usr)
% 0.19/0.45 % Number of type conns : 63 ( 63 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 16 ( 15 usr; 1 con; 0-3 aty)
% 0.19/0.45 % Number of variables : 35 ( 30 ^; 3 !; 2 ?; 35 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.19/0.45 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.19/0.45 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.19/0.45 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.19/0.45 % $modalities == $modal_system_T].
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(mworld,type,
% 0.19/0.45 mworld: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(mrel_type,type,
% 0.19/0.45 mrel: mworld > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mactual_type,type,
% 0.19/0.45 mactual: mworld ).
% 0.19/0.45
% 0.19/0.45 thf(mlocal_type,type,
% 0.19/0.45 mlocal: ( mworld > $o ) > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mlocal_def,definition,
% 0.19/0.45 ( mlocal
% 0.19/0.45 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(mnot_type,type,
% 0.19/0.45 mnot: ( mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mand_type,type,
% 0.19/0.45 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mor_type,type,
% 0.19/0.45 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mimplies_type,type,
% 0.19/0.45 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mequiv_type,type,
% 0.19/0.45 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mnot_def,definition,
% 0.19/0.45 ( mnot
% 0.19/0.45 = ( ^ [A: mworld > $o,W: mworld] :
% 0.19/0.45 ~ ( A @ W ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(mand_def,definition,
% 0.19/0.45 ( mand
% 0.19/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.45 ( ( A @ W )
% 0.19/0.45 & ( B @ W ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(mor_def,definition,
% 0.19/0.45 ( mor
% 0.19/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.45 ( ( A @ W )
% 0.19/0.45 | ( B @ W ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(mimplies_def,definition,
% 0.19/0.45 ( mimplies
% 0.19/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.45 ( ( A @ W )
% 0.19/0.46 => ( B @ W ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(mequiv_def,definition,
% 0.19/0.46 ( mequiv
% 0.19/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.46 ( ( A @ W )
% 0.19/0.46 <=> ( B @ W ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(mbox_type,type,
% 0.19/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.19/0.46
% 0.19/0.46 thf(mbox_def,definition,
% 0.19/0.46 ( mbox
% 0.19/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.19/0.46 ! [V: mworld] :
% 0.19/0.46 ( ( mrel @ W @ V )
% 0.19/0.46 => ( Phi @ V ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(mdia_type,type,
% 0.19/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.19/0.46
% 0.19/0.46 thf(mdia_def,definition,
% 0.19/0.46 ( mdia
% 0.19/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.19/0.46 ? [V: mworld] :
% 0.19/0.46 ( ( mrel @ W @ V )
% 0.19/0.46 & ( Phi @ V ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(mrel_reflexive,axiom,
% 0.19/0.46 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.19/0.46
% 0.19/0.46 thf(mforall_di_type,type,
% 0.19/0.46 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.19/0.46
% 0.19/0.46 thf(mforall_di_def,definition,
% 0.19/0.46 ( mforall_di
% 0.19/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.19/0.46 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(mexists_di_type,type,
% 0.19/0.46 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.19/0.46
% 0.19/0.46 thf(mexists_di_def,definition,
% 0.19/0.46 ( mexists_di
% 0.19/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.19/0.46 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(h_decl,type,
% 0.19/0.46 h: $i > mworld > $o ).
% 0.19/0.46
% 0.19/0.46 thf(bomb_decl,type,
% 0.19/0.46 bomb: $i > mworld > $o ).
% 0.19/0.46
% 0.19/0.46 thf(defused_decl,type,
% 0.19/0.46 defused: $i > mworld > $o ).
% 0.19/0.46
% 0.19/0.46 thf(ax1,axiom,
% 0.19/0.46 ( mlocal
% 0.19/0.46 @ ( mbox
% 0.19/0.46 @ ( mexists_di
% 0.19/0.46 @ ^ [B: $i] : ( bomb @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(ax2,axiom,
% 0.19/0.46 ( mlocal
% 0.19/0.46 @ ( mexists_di
% 0.19/0.46 @ ^ [A: $i] :
% 0.19/0.46 ( mbox
% 0.19/0.46 @ ( mforall_di
% 0.19/0.46 @ ^ [X: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ A ) ) @ ( mbox @ ( bomb @ X ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(ax3,axiom,
% 0.19/0.46 ( mlocal
% 0.19/0.46 @ ( mbox
% 0.19/0.46 @ ( mforall_di
% 0.19/0.46 @ ^ [X: $i] :
% 0.19/0.46 ( mexists_di
% 0.19/0.46 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(con,conjecture,
% 0.19/0.46 ( mlocal
% 0.19/0.46 @ ( mbox
% 0.19/0.46 @ ( mforall_di
% 0.19/0.46 @ ^ [X: $i] :
% 0.19/0.46 ( mexists_di
% 0.19/0.46 @ ^ [D: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.55/1.27 ---- Embedded in THF ---
% 1.55/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.27 %%% Generated on Tue Feb 24 11:28:10 EST 2026
% 1.55/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.27 %%% Logic specification used:
% 1.55/1.27 %%% thf(spec, logic, $$dhol).
% 1.55/1.27
% 1.55/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2DTF6739.p
% See solution above
% 1.55/1.27 ------------------------
% 1.55/1.28 ---- Cleaned THF ---
% 1.55/1.28 thf(mworld,type,
% 1.55/1.28 mworld: $tType ).
% 1.55/1.28
% 1.55/1.28 thf(mrel_type,type,
% 1.55/1.28 mrel: mworld > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mactual_type,type,
% 1.55/1.28 mactual: mworld ).
% 1.55/1.28
% 1.55/1.28 thf(mlocal_type,type,
% 1.55/1.28 mlocal: ( mworld > $o ) > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mlocal_def,definition,
% 1.55/1.28 ( mlocal
% 1.55/1.28 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mnot_type,type,
% 1.55/1.28 mnot: ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mand_type,type,
% 1.55/1.28 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mor_type,type,
% 1.55/1.28 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mimplies_type,type,
% 1.55/1.28 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mequiv_type,type,
% 1.55/1.28 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mnot_def,definition,
% 1.55/1.28 ( mnot
% 1.55/1.28 = ( ^ [A: mworld > $o,W: mworld] :
% 1.55/1.28 ~ ( A @ W ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mand_def,definition,
% 1.55/1.28 ( mand
% 1.55/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.55/1.28 ( ( A @ W )
% 1.55/1.28 & ( B @ W ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mor_def,definition,
% 1.55/1.28 ( mor
% 1.55/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.55/1.28 ( ( A @ W )
% 1.55/1.28 | ( B @ W ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mimplies_def,definition,
% 1.55/1.28 ( mimplies
% 1.55/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.55/1.28 ( ( A @ W )
% 1.55/1.28 => ( B @ W ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mequiv_def,definition,
% 1.55/1.28 ( mequiv
% 1.55/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.55/1.28 ( ( A @ W )
% 1.55/1.28 <=> ( B @ W ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mbox_type,type,
% 1.55/1.28 mbox: ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mbox_def,definition,
% 1.55/1.28 ( mbox
% 1.55/1.28 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.55/1.28 ! [V: mworld] :
% 1.55/1.28 ( ( mrel @ W @ V )
% 1.55/1.28 => ( Phi @ V ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mdia_type,type,
% 1.55/1.28 mdia: ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mdia_def,definition,
% 1.55/1.28 ( mdia
% 1.55/1.28 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.55/1.28 ? [V: mworld] :
% 1.55/1.28 ( ( mrel @ W @ V )
% 1.55/1.28 & ( Phi @ V ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mrel_reflexive,axiom,
% 1.55/1.28 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.55/1.28
% 1.55/1.28 thf(mforall_di_type,type,
% 1.55/1.28 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mforall_di_def,definition,
% 1.55/1.28 ( mforall_di
% 1.55/1.28 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.55/1.28 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mexists_di_type,type,
% 1.55/1.28 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mexists_di_def,definition,
% 1.55/1.28 ( mexists_di
% 1.55/1.28 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.55/1.28 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(h_decl,type,
% 1.55/1.28 h: $i > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(bomb_decl,type,
% 1.55/1.28 bomb: $i > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(defused_decl,type,
% 1.55/1.28 defused: $i > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(ax1,axiom,
% 1.55/1.28 ( mlocal
% 1.55/1.28 @ ( mbox
% 1.55/1.28 @ ( mexists_di
% 1.55/1.28 @ ^ [B: $i] : ( bomb @ B ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(ax2,axiom,
% 1.55/1.28 ( mlocal
% 1.55/1.28 @ ( mexists_di
% 1.55/1.28 @ ^ [A: $i] :
% 1.55/1.28 ( mbox
% 1.55/1.28 @ ( mforall_di
% 1.55/1.28 @ ^ [X: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ A ) ) @ ( mbox @ ( bomb @ X ) ) ) ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(ax3,axiom,
% 1.55/1.28 ( mlocal
% 1.55/1.28 @ ( mbox
% 1.55/1.28 @ ( mforall_di
% 1.55/1.28 @ ^ [X: $i] :
% 1.55/1.28 ( mexists_di
% 1.55/1.28 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(con,conjecture,
% 1.55/1.28 ( mlocal
% 1.55/1.28 @ ( mbox
% 1.55/1.28 @ ( mforall_di
% 1.55/1.28 @ ^ [X: $i] :
% 1.55/1.28 ( mexists_di
% 1.55/1.28 @ ^ [D: $i] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ).
% 1.55/1.28 ------------------------
% 1.55/1.30 % (6932)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_6739 for (2999ds/27Mi)
% 1.75/1.30 % (6933)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6739 for (2999ds/2Mi)
% 1.75/1.30 % (6936)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6739 for (2999ds/18Mi)
% 1.75/1.30 % (6933)Instruction limit reached!
% 1.75/1.30 % (6933)------------------------------
% 1.75/1.30 % (6933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.30 % (6933)Termination reason: Unknown
% 1.75/1.30 % (6933)Termination phase: Function definition elimination
% 1.75/1.30
% 1.75/1.30 % (6933)Memory used [KB]: 1023
% 1.75/1.30 % (6933)Time elapsed: 0.002 s
% 1.75/1.30 % (6933)Instructions burned: 4 (million)
% 1.75/1.30 % (6933)------------------------------
% 1.75/1.30 % (6933)------------------------------
% 1.75/1.30 % (6932)First to succeed.
% 1.75/1.30 % (6931)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_6739 for (2999ds/4Mi)
% 1.75/1.30 % (6936)Instruction limit reached!
% 1.75/1.30 % (6936)------------------------------
% 1.75/1.30 % (6936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.30 % (6936)Termination reason: Unknown
% 1.75/1.30 % (6936)Termination phase: Saturation
% 1.75/1.30
% 1.75/1.30 % (6936)Memory used [KB]: 5628
% 1.75/1.30 % (6936)Time elapsed: 0.007 s
% 1.75/1.30 % (6936)Instructions burned: 19 (million)
% 1.75/1.30 % (6936)------------------------------
% 1.75/1.30 % (6936)------------------------------
% 1.75/1.30 % (6932)Refutation found. Thanks to Tanya!
% 1.75/1.30 % SZS status Theorem for DTF2THF_6739
% 1.75/1.30 % SZS output start Proof for DTF2THF_6739
% 1.75/1.30 thf(type_def_5, type, mworld: $tType).
% 1.75/1.30 thf(func_def_0, type, mworld: $tType).
% 1.75/1.30 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.75/1.30 thf(func_def_2, type, mactual: mworld).
% 1.75/1.30 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.75/1.30 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.75/1.30 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.75/1.30 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.75/1.30 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.75/1.30 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.75/1.30 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.75/1.30 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.75/1.30 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.75/1.30 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.75/1.30 thf(func_def_14, type, h: $i > mworld > $o).
% 1.75/1.30 thf(func_def_15, type, bomb: $i > mworld > $o).
% 1.75/1.30 thf(func_def_16, type, defused: $i > mworld > $o).
% 1.75/1.30 thf(func_def_17, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.75/1.30 thf(func_def_34, type, sK1: mworld > $i > $i).
% 1.75/1.30 thf(func_def_35, type, sK2: mworld > $i).
% 1.75/1.30 thf(func_def_37, type, sK4: mworld).
% 1.75/1.30 thf(f158,plain,(
% 1.75/1.30 $false),
% 1.75/1.30 inference(avatar_sat_refutation,[status(thm)],[f124,f146,f157])).
% 1.75/1.30 thf(f157,plain,(
% 1.75/1.30 ~spl0_1),
% 1.75/1.30 inference(avatar_contradiction_clause,[status(thm)],[f156])).
% 1.75/1.30 thf(f156,plain,(
% 1.75/1.30 $false | ~spl0_1),
% 1.75/1.30 inference(trivial_inequality_removal,[status(thm)],[f155])).
% 1.75/1.30 thf(f155,plain,(
% 1.75/1.30 ($false = $true) | ~spl0_1),
% 1.75/1.30 inference(backward_demodulation,[status(thm)],[f103,f151])).
% 1.75/1.30 thf(f151,plain,(
% 1.75/1.30 ($false = (mrel @ mactual @ sK4)) | ~spl0_1),
% 1.75/1.30 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.75/1.30 thf(f150,plain,(
% 1.75/1.30 ($false = (mrel @ mactual @ sK4)) | ($false = $true) | ~spl0_1),
% 1.75/1.30 inference(superposition,[status(thm)],[f60,f119])).
% 1.75/1.30 thf(f119,plain,(
% 1.75/1.30 ( ! [X0 : mworld] : (($false = (mrel @ mactual @ X0)) | ($false = (mrel @ X0 @ sK4))) ) | ~spl0_1),
% 1.75/1.30 inference(avatar_component_clause,[status(thm)],[f118])).
% 1.75/1.30 thf(f118,definition,(
% 1.75/1.30 spl0_1 <=> ! [X0 : mworld] : (($false = (mrel @ mactual @ X0)) | ($false = (mrel @ X0 @ sK4)))),
% 1.75/1.30 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.75/1.30 thf(f60,plain,(
% 1.75/1.30 ( ! [X0 : mworld] : (((mrel @ X0 @ X0) = $true)) )),
% 1.75/1.30 inference(cnf_transformation,[status(thm)],[f33])).
% 1.75/1.30 thf(f33,plain,(
% 1.75/1.30 ! [X0 : mworld] : ((mrel @ X0 @ X0) = $true)),
% 1.75/1.30 inference(fool_elimination,[status(thm)],[f32])).
% 1.75/1.30 thf(f32,plain,(
% 1.75/1.30 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 1.75/1.30 inference(rectify,[status(thm)],[f9])).
% 1.75/1.30 thf(f9,axiom,(
% 1.75/1.30 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 1.75/1.30 file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',mrel_reflexive)).
% 1.75/1.30 thf(f103,plain,(
% 1.75/1.30 ($true = (mrel @ mactual @ sK4))),
% 1.75/1.30 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.75/1.30 thf(f101,plain,(
% 1.75/1.30 (((mrel @ mactual @ sK4) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((h @ Y1 @ sK4) & (bomb @ Y0 @ sK4)) => (defused @ Y0 @ sK4))))))) = $false)),
% 1.75/1.30 inference(beta_eta_normalization,[status(thm)],[f100])).
% 1.75/1.30 thf(f100,plain,(
% 1.75/1.30 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((h @ Y2 @ Y0) & (bomb @ Y1 @ Y0)) => (defused @ Y1 @ Y0)))))))) @ sK4))),
% 1.75/1.30 inference(sigma_clausification,[status(thm)],[f99])).
% 1.75/1.30 thf(f99,plain,(
% 1.75/1.30 ($true != (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((h @ Y2 @ Y0) & (bomb @ Y1 @ Y0)) => (defused @ Y1 @ Y0))))))))))),
% 1.75/1.30 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.75/1.30 thf(f63,plain,(
% 1.75/1.30 (((^[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]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) != $true)),
% 1.75/1.30 inference(definition_unfolding,[status(thm)],[f52,f48,f55,f61,f54,f50,f58])).
% 1.75/1.30 thf(f58,plain,(
% 1.75/1.30 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.75/1.30 inference(cnf_transformation,[status(thm)],[f25])).
% 1.75/1.30 thf(f25,plain,(
% 1.75/1.30 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.75/1.30 inference(fool_elimination,[status(thm)],[f24])).
% 1.75/1.30 thf(f24,plain,(
% 1.75/1.30 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 1.75/1.30 inference(rectify,[status(thm)],[f3])).
% 1.75/1.30 thf(f3,axiom,(
% 1.75/1.30 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))) = mand)),
% 1.75/1.30 file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',mand_def)).
% 1.75/1.30 thf(f50,plain,(
% 1.75/1.30 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.75/1.30 inference(cnf_transformation,[status(thm)],[f31])).
% 1.75/1.30 thf(f31,plain,(
% 1.75/1.30 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.75/1.30 inference(fool_elimination,[status(thm)],[f30])).
% 1.75/1.30 thf(f30,plain,(
% 1.75/1.30 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.75/1.30 inference(rectify,[status(thm)],[f5])).
% 1.75/1.30 thf(f5,axiom,(
% 1.75/1.30 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.75/1.30 file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',mimplies_def)).
% 1.75/1.30 thf(f54,plain,(
% 1.75/1.30 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.75/1.30 inference(cnf_transformation,[status(thm)],[f23])).
% 1.75/1.30 thf(f23,plain,(
% 1.75/1.30 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.75/1.30 inference(fool_elimination,[status(thm)],[f22])).
% 1.75/1.30 thf(f22,plain,(
% 1.75/1.30 ((^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : (X0 @ X2 @ X1))) = mexists_di)),
% 1.75/1.30 inference(rectify,[status(thm)],[f11])).
% 1.75/1.30 thf(f11,axiom,(
% 1.75/1.30 ((^[X1 : $i > mworld > $o, X2 : mworld] : (? [X5 : $i] : (X1 @ X5 @ X2))) = mexists_di)),
% 1.75/1.30 file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',mexists_di_def)).
% 1.75/1.30 thf(f61,plain,(
% 1.75/1.30 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.75/1.30 inference(cnf_transformation,[status(thm)],[f27])).
% 1.75/1.30 thf(f27,plain,(
% 1.75/1.30 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.75/1.30 inference(fool_elimination,[status(thm)],[f26])).
% 1.75/1.30 thf(f26,plain,(
% 1.75/1.30 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))))),
% 1.75/1.30 inference(rectify,[status(thm)],[f10])).
% 1.75/1.30 thf(f10,axiom,(
% 1.75/1.30 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5 : $i] : (X1 @ X5 @ X2))))),
% 1.75/1.30 file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',mforall_di_def)).
% 1.75/1.30 thf(f55,plain,(
% 1.75/1.30 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.75/1.30 inference(cnf_transformation,[status(thm)],[f44])).
% 1.75/1.30 thf(f44,plain,(
% 1.75/1.30 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.75/1.30 inference(fool_elimination,[status(thm)],[f43])).
% 1.75/1.30 thf(f43,plain,(
% 1.75/1.30 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 1.75/1.30 inference(rectify,[status(thm)],[f7])).
% 1.75/1.30 thf(f7,axiom,(
% 1.75/1.30 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 1.75/1.30 file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',mbox_def)).
% 1.75/1.30 thf(f48,plain,(
% 1.75/1.30 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.75/1.30 inference(cnf_transformation,[status(thm)],[f40])).
% 1.75/1.30 thf(f40,plain,(
% 1.75/1.30 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.75/1.30 inference(fool_elimination,[status(thm)],[f1])).
% 1.75/1.30 thf(f1,axiom,(
% 1.75/1.30 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.75/1.30 file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',mlocal_def)).
% 1.75/1.30 thf(f52,plain,(
% 1.75/1.30 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) != $true)),
% 1.75/1.30 inference(cnf_transformation,[status(thm)],[f47])).
% 1.75/1.30 thf(f47,plain,(
% 1.75/1.30 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) != $true)),
% 1.75/1.30 inference(flattening,[status(thm)],[f29])).
% 1.75/1.30 thf(f29,plain,(
% 1.75/1.30 ~((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) = $true)),
% 1.75/1.30 inference(fool_elimination,[status(thm)],[f28])).
% 1.75/1.30 thf(f28,plain,(
% 1.75/1.30 ~(mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : (mexists_di @ (^[X1 : $i] : (mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0))))))))),
% 1.75/1.30 inference(rectify,[status(thm)],[f16])).
% 1.75/1.30 thf(f16,negated_conjecture,(
% 1.75/1.30 ~(mlocal @ (mbox @ (mforall_di @ (^[X5 : $i] : (mexists_di @ (^[X6 : $i] : (mimplies @ (mand @ (bomb @ X5) @ (h @ X6)) @ (defused @ X5))))))))),
% 1.75/1.30 inference(negated_conjecture,[status(cth)],[f15])).
% 1.75/1.30 thf(f15,conjecture,(
% 1.75/1.30 (mlocal @ (mbox @ (mforall_di @ (^[X5 : $i] : (mexists_di @ (^[X6 : $i] : (mimplies @ (mand @ (bomb @ X5) @ (h @ X6)) @ (defused @ X5))))))))),
% 1.75/1.30 file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',con)).
% 1.75/1.30 thf(f146,plain,(
% 1.75/1.30 ~spl0_2),
% 1.75/1.30 inference(avatar_contradiction_clause,[status(thm)],[f145])).
% 1.75/1.30 thf(f145,plain,(
% 1.75/1.30 $false | ~spl0_2),
% 1.75/1.30 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.75/1.30 thf(f144,plain,(
% 1.75/1.30 ($false = $true) | ~spl0_2),
% 1.75/1.30 inference(forward_demodulation,[status(thm)],[f132,f108])).
% 1.75/1.30 thf(f108,plain,(
% 1.75/1.30 ($false = (defused @ sK5 @ sK4))),
% 1.75/1.30 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.75/1.30 thf(f107,plain,(
% 1.75/1.30 ( ! [X1 : $i] : (($false = (((h @ X1 @ sK4) & (bomb @ sK5 @ sK4)) => (defused @ sK5 @ sK4)))) )),
% 1.75/1.30 inference(beta_eta_normalization,[status(thm)],[f106])).
% 1.75/1.30 thf(f106,plain,(
% 1.75/1.30 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((h @ Y0 @ sK4) & (bomb @ sK5 @ sK4)) => (defused @ sK5 @ sK4))) @ X1) = $false)) )),
% 1.75/1.30 inference(pi_clausification,[status(thm)],[f105])).
% 1.75/1.30 thf(f105,plain,(
% 1.75/1.30 ($false = (?? @ $i @ (^[Y0 : $i]: (((h @ Y0 @ sK4) & (bomb @ sK5 @ sK4)) => (defused @ sK5 @ sK4)))))),
% 1.75/1.30 inference(beta_eta_normalization,[status(thm)],[f104])).
% 1.75/1.30 thf(f104,plain,(
% 1.75/1.30 ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((h @ Y1 @ sK4) & (bomb @ Y0 @ sK4)) => (defused @ Y0 @ sK4))))) @ sK5))),
% 1.75/1.30 inference(sigma_clausification,[status(thm)],[f102])).
% 1.75/1.30 thf(f102,plain,(
% 1.75/1.30 ($false = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((h @ Y1 @ sK4) & (bomb @ Y0 @ sK4)) => (defused @ Y0 @ sK4)))))))),
% 1.75/1.30 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.75/1.30 thf(f132,plain,(
% 1.75/1.30 ($true = (defused @ sK5 @ sK4)) | ~spl0_2),
% 1.75/1.30 inference(trivial_inequality_removal,[status(thm)],[f130])).
% 1.75/1.30 thf(f130,plain,(
% 1.75/1.30 ($false = $true) | ($true = (defused @ sK5 @ sK4)) | ~spl0_2),
% 1.75/1.30 inference(superposition,[status(thm)],[f110,f122])).
% 1.75/1.30 thf(f122,plain,(
% 1.75/1.30 ( ! [X1 : $i] : (($false = (bomb @ X1 @ sK4)) | ((defused @ X1 @ sK4) = $true)) ) | ~spl0_2),
% 1.75/1.30 inference(avatar_component_clause,[status(thm)],[f121])).
% 1.75/1.30 thf(f121,definition,(
% 1.75/1.30 spl0_2 <=> ! [X1 : $i] : (((defused @ X1 @ sK4) = $true) | ($false = (bomb @ X1 @ sK4)))),
% 1.75/1.30 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.75/1.30 thf(f110,plain,(
% 1.75/1.30 ($true = (bomb @ sK5 @ sK4))),
% 1.75/1.30 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.75/1.30 thf(f109,plain,(
% 1.75/1.30 ( ! [X1 : $i] : ((((h @ X1 @ sK4) & (bomb @ sK5 @ sK4)) = $true)) )),
% 1.75/1.30 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.75/1.30 thf(f124,plain,(
% 1.75/1.30 spl0_2 | spl0_1),
% 1.75/1.30 inference(avatar_split_clause,[status(thm)],[f115,f118,f121])).
% 1.75/1.30 thf(f115,plain,(
% 1.75/1.30 ( ! [X0 : mworld,X1 : $i] : (((defused @ X1 @ sK4) = $true) | ($false = (mrel @ mactual @ X0)) | ($false = (bomb @ X1 @ sK4)) | ($false = (mrel @ X0 @ sK4))) )),
% 1.75/1.30 inference(trivial_inequality_removal,[status(thm)],[f114])).
% 1.75/1.30 thf(f114,plain,(
% 1.75/1.30 ( ! [X0 : mworld,X1 : $i] : (($false = $true) | ($false = (mrel @ X0 @ sK4)) | ($false = (bomb @ X1 @ sK4)) | ($false = (mrel @ mactual @ X0)) | ((defused @ X1 @ sK4) = $true)) )),
% 1.75/1.30 inference(superposition,[status(thm)],[f79,f111])).
% 1.75/1.30 thf(f111,plain,(
% 1.75/1.30 ( ! [X1 : $i] : (((h @ X1 @ sK4) = $true)) )),
% 1.75/1.30 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.75/1.30 thf(f79,plain,(
% 1.75/1.30 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (h @ (sK1 @ X1 @ X2) @ X3)) | ($false = (mrel @ X1 @ X3)) | ($true = (defused @ X2 @ X3)) | ($false = (bomb @ X2 @ X3)) | ($false = (mrel @ mactual @ X1))) )),
% 1.75/1.30 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.75/1.30 thf(f78,plain,(
% 1.75/1.30 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (defused @ X2 @ X3)) | ($false = ((h @ (sK1 @ X1 @ X2) @ X3) & (bomb @ X2 @ X3))) | ($false = (mrel @ X1 @ X3))) )),
% 1.75/1.30 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.75/1.30 thf(f77,plain,(
% 1.75/1.30 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (((((h @ (sK1 @ X1 @ X2) @ X3) & (bomb @ X2 @ X3)) => (defused @ X2 @ X3)) = $true) | ($false = (mrel @ X1 @ X3)) | ($false = (mrel @ mactual @ X1))) )),
% 1.75/1.30 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.75/1.30 thf(f76,plain,(
% 1.75/1.30 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((mrel @ X1 @ X3) => (((h @ (sK1 @ X1 @ X2) @ X3) & (bomb @ X2 @ X3)) => (defused @ X2 @ X3))))) )),
% 1.75/1.30 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.75/1.30 thf(f75,plain,(
% 1.75/1.30 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((h @ (sK1 @ X1 @ X2) @ Y0) & (bomb @ X2 @ Y0)) => (defused @ X2 @ Y0)))) @ X3))) )),
% 1.75/1.30 inference(pi_clausification,[status(thm)],[f74])).
% 1.75/1.30 thf(f74,plain,(
% 1.75/1.30 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((h @ (sK1 @ X1 @ X2) @ Y0) & (bomb @ X2 @ Y0)) => (defused @ X2 @ Y0))))))) )),
% 1.75/1.30 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.75/1.30 thf(f73,plain,(
% 1.75/1.30 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((h @ Y0 @ Y1) & (bomb @ X2 @ Y1)) => (defused @ X2 @ Y1)))))) @ (sK1 @ X1 @ X2)))) )),
% 1.75/1.30 inference(sigma_clausification,[status(thm)],[f72])).
% 1.75/1.30 thf(f72,plain,(
% 1.75/1.30 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((h @ Y0 @ Y1) & (bomb @ X2 @ Y1)) => (defused @ X2 @ Y1))))))) = $true)) )),
% 1.75/1.30 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.75/1.30 thf(f71,plain,(
% 1.75/1.30 ( ! [X2 : $i,X1 : mworld] : ((((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((h @ Y1 @ Y2) & (bomb @ Y0 @ Y2)) => (defused @ Y0 @ Y2)))))))) @ X2) = $true) | ($false = (mrel @ mactual @ X1))) )),
% 1.75/1.30 inference(pi_clausification,[status(thm)],[f70])).
% 1.75/1.30 thf(f70,plain,(
% 1.75/1.30 ( ! [X1 : mworld] : (($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((h @ Y1 @ Y2) & (bomb @ Y0 @ Y2)) => (defused @ Y0 @ Y2)))))))))) | ($false = (mrel @ mactual @ X1))) )),
% 1.75/1.30 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 1.75/1.30 thf(f69,plain,(
% 1.75/1.30 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((h @ Y1 @ Y2) & (bomb @ Y0 @ Y2)) => (defused @ Y0 @ Y2)))))))))))) )),
% 1.75/1.30 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.75/1.30 thf(f68,plain,(
% 1.75/1.30 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (((h @ Y2 @ Y3) & (bomb @ Y1 @ Y3)) => (defused @ Y1 @ Y3))))))))))) @ X1))) )),
% 1.75/1.30 inference(pi_clausification,[status(thm)],[f67])).
% 1.75/1.30 thf(f67,plain,(
% 1.75/1.30 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (((h @ Y2 @ Y3) & (bomb @ Y1 @ Y3)) => (defused @ Y1 @ Y3)))))))))))))),
% 1.75/1.30 inference(beta_eta_normalization,[status(thm)],[f65])).
% 1.75/1.30 thf(f65,plain,(
% 1.75/1.30 (((^[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]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))) = $true)),
% 1.75/1.30 inference(definition_unfolding,[status(thm)],[f57,f48,f55,f61,f54,f55,f50,f58])).
% 1.75/1.30 thf(f57,plain,(
% 1.75/1.30 ($true = (mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))))),
% 1.75/1.30 inference(cnf_transformation,[status(thm)],[f37])).
% 1.75/1.30 thf(f37,plain,(
% 1.75/1.30 ($true = (mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))))),
% 1.75/1.30 inference(fool_elimination,[status(thm)],[f36])).
% 1.75/1.30 thf(f36,plain,(
% 1.75/1.30 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : (mexists_di @ (^[X1 : $i] : (mbox @ (mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0)))))))))),
% 1.75/1.30 inference(rectify,[status(thm)],[f14])).
% 1.75/1.30 thf(f14,axiom,(
% 1.75/1.30 (mlocal @ (mbox @ (mforall_di @ (^[X5 : $i] : (mexists_di @ (^[X6 : $i] : (mbox @ (mimplies @ (mand @ (bomb @ X5) @ (h @ X6)) @ (defused @ X5)))))))))),
% 1.75/1.30 file('/export/starexec/sandbox/tmp/tmp.r7rDaqw3uO/DTF2THF_6739.p',ax3)).
% 1.75/1.30 % SZS output end Proof for DTF2THF_6739
% 1.75/1.30 % (6932)------------------------------
% 1.75/1.30 % (6932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.30 % (6932)Termination reason: Refutation
% 1.75/1.30
% 1.75/1.30 % (6932)Memory used [KB]: 5756
% 1.75/1.30 % (6932)Time elapsed: 0.008 s
% 1.75/1.30 % (6932)Instructions burned: 15 (million)
% 1.75/1.30 % (6932)------------------------------
% 1.75/1.30 % (6932)------------------------------
% 1.75/1.30 % (6929)Success in time 0.006 s
%------------------------------------------------------------------------------