%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO890^16 : 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 : n026.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 09:55:07 AM UTC 2026
% Result : Theorem 1.87s 1.51s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 344 ( 70 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 474 ( 20 ~; 15 |; 33 &; 358 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 18 usr; 7 con; 0-3 aty)
% ( 11 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 129 ( 98 ^; 29 !; 2 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mrel: mworld > mworld > $o ).
thf(func_def_2,type,
mactual: mworld ).
thf(func_def_3,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_5,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
eiw_di: $i > mworld > $o ).
thf(func_def_13,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_15,type,
e: $i > mworld > $o ).
thf(func_def_16,type,
f: $i > mworld > $o ).
thf(func_def_30,type,
sK0: mworld > $i ).
thf(func_def_34,type,
sK3: mworld ).
thf(f116,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f113,f76]) ).
thf(f76,plain,
( $true
= ( eiw_di @ sK2 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( $true
= ( ( eiw_di @ sK2 @ mactual )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( e @ sK2 @ Y0 )
& ( f @ sK2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( ( e @ Y0 @ Y1 )
& ( f @ Y0 @ Y1 ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( ( e @ Y0 @ Y1 )
& ( f @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( ( e @ Y0 @ Y1 )
& ( f @ Y0 @ Y1 ) ) ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( f @ Y1 @ Y0 ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) )
@ ( e @ Y0 )
@ ( f @ Y0 ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f57,f60,f62,f58,f56,f54,f56,f58]) ).
thf(f54,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,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/sandbox/tmp/tmp.ZOUo0mCqqG/DTF2THF_6113.p',mand_def) ).
thf(f56,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,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.ZOUo0mCqqG/DTF2THF_6113.p',mbox_def) ).
thf(f58,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) )
= mexists_di ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X6: $i] :
( ( X1 @ X6 @ X2 )
& ( eiw_di @ X6 @ X2 ) ) )
= mexists_di ),
file('/export/starexec/sandbox/tmp/tmp.ZOUo0mCqqG/DTF2THF_6113.p',mexists_di_def) ).
thf(f62,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox/tmp/tmp.ZOUo0mCqqG/DTF2THF_6113.p',mimplies_def) ).
thf(f60,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,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.ZOUo0mCqqG/DTF2THF_6113.p',mlocal_def) ).
thf(f57,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( e @ Y0 ) @ ( f @ Y0 ) ) ) )
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( e @ Y0 ) @ ( f @ Y0 ) ) ) )
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f42]) ).
thf(f42,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( e @ Y0 ) @ ( f @ Y0 ) ) ) )
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f41]) ).
thf(f41,plain,
~ ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( mand @ ( e @ X0 ) @ ( f @ X0 ) ) ) )
@ ( mbox
@ ( mexists_di
@ ^ [X1: $i] : ( f @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [X6: $i] : ( mbox @ ( mand @ ( e @ X6 ) @ ( f @ X6 ) ) ) )
@ ( mbox
@ ( mexists_di
@ ^ [X6: $i] : ( f @ X6 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f15,conjecture,
( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [X6: $i] : ( mbox @ ( mand @ ( e @ X6 ) @ ( f @ X6 ) ) ) )
@ ( mbox
@ ( mexists_di
@ ^ [X6: $i] : ( f @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZOUo0mCqqG/DTF2THF_6113.p',con) ).
thf(f113,plain,
( $true
!= ( eiw_di @ sK2 @ mactual ) ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
( ( $true != $true )
| ( $true
!= ( eiw_di @ sK2 @ mactual ) ) ),
inference(superposition,[status(thm)],[f108,f85]) ).
thf(f85,plain,
( ( mrel @ mactual @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
( $false
= ( ( mrel @ mactual @ sK3 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK3 )
& ( f @ Y0 @ sK3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( f @ Y1 @ Y0 ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( f @ Y1 @ Y0 ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f108,plain,
! [X0: mworld] :
( ( $true
!= ( mrel @ X0 @ sK3 ) )
| ( $true
!= ( eiw_di @ sK2 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
! [X0: mworld] :
( ( $true
!= ( mrel @ X0 @ sK3 ) )
| ( $true = $false )
| ( $true
!= ( eiw_di @ sK2 @ X0 ) ) ),
inference(superposition,[status(thm)],[f68,f100]) ).
thf(f100,plain,
( ( eiw_di @ sK2 @ sK3 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( ( eiw_di @ sK2 @ sK3 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f88,f95]) ).
thf(f95,plain,
( $true
= ( f @ sK2 @ sK3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
( ( $true = $false )
| ( $true
= ( f @ sK2 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f85,f80]) ).
thf(f80,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( f @ sK2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( e @ sK2 @ X1 )
& ( f @ sK2 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( e @ sK2 @ X1 )
& ( f @ sK2 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( e @ sK2 @ Y0 )
& ( f @ sK2 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( e @ sK2 @ Y0 )
& ( f @ sK2 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f88,plain,
! [X1: $i] :
( ( $false
= ( f @ X1 @ sK3 ) )
| ( $false
= ( eiw_di @ X1 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: $i] :
( $false
= ( ( eiw_di @ X1 @ sK3 )
& ( f @ X1 @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK3 )
& ( f @ Y0 @ sK3 ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK3 )
& ( f @ Y0 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f68,plain,
! [X2: $i,X0: mworld,X1: mworld] :
( ( $true
= ( eiw_di @ X2 @ X0 ) )
| ( $true
!= ( eiw_di @ X2 @ X1 ) )
| ( $true
!= ( mrel @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( $true
!= ( eiw_di @ X2 @ X1 ) )
| ( $true
!= ( mrel @ X1 @ X0 ) )
| ( $true
= ( eiw_di @ X2 @ X0 ) ) ),
inference(flattening,[status(thm)],[f50]) ).
thf(f50,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( $true
= ( eiw_di @ X2 @ X0 ) )
| ( $true
!= ( eiw_di @ X2 @ X1 ) )
| ( $true
!= ( mrel @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( $true
= ( eiw_di @ X2 @ X1 ) )
& ( $true
= ( mrel @ X1 @ X0 ) ) )
=> ( $true
= ( eiw_di @ X2 @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( eiw_di @ X2 @ X1 )
& ( mrel @ X1 @ X0 ) )
=> ( eiw_di @ X2 @ X0 ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
! [X4: mworld,X2: mworld,X6: $i] :
( ( ( eiw_di @ X6 @ X2 )
& ( mrel @ X2 @ X4 ) )
=> ( eiw_di @ X6 @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.ZOUo0mCqqG/DTF2THF_6113.p',eiw_di_cumul) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO890^16 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Feb 24 14:53:25 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SYO890^16 : TPTP v9.2.1. Released v8.1.0.
% 0.20/0.46 % Domain : Syntactic
% 0.20/0.46 % Problem : Forbes problem
% 0.20/0.46 % Version : [BP13] axioms.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.20/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.20/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.20/0.46 % Source : [TPTP]
% 0.20/0.46 % Names : SYM045+1 [QMLTP]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.20/0.46 % Syntax : Number of formulae : 31 ( 12 unt; 16 typ; 10 def)
% 0.20/0.46 % Number of atoms : 42 ( 10 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 10 ( 2 avg)
% 0.20/0.46 % Number of connectives : 65 ( 1 ~; 1 |; 5 &; 52 @)
% 0.20/0.46 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 10 ( 3 avg)
% 0.20/0.46 % Number of types : 3 ( 1 usr)
% 0.20/0.46 % Number of type conns : 63 ( 63 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 16 ( 15 usr; 1 con; 0-3 aty)
% 0.20/0.46 % Number of variables : 38 ( 25 ^; 10 !; 3 ?; 38 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.20/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.20/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.20/0.46 % $modal == [$constants == $rigid,$quantification == $cumulative,
% 0.20/0.46 % $modalities == $modal_system_S4].
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(mworld,type,
% 0.20/0.46 mworld: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(mrel_type,type,
% 0.20/0.46 mrel: mworld > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mactual_type,type,
% 0.20/0.46 mactual: mworld ).
% 0.20/0.46
% 0.20/0.46 thf(mlocal_type,type,
% 0.20/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mlocal_def,definition,
% 0.20/0.46 ( mlocal
% 0.20/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mnot_type,type,
% 0.20/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mand_type,type,
% 0.20/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mor_type,type,
% 0.20/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mimplies_type,type,
% 0.20/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mequiv_type,type,
% 0.20/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mnot_def,definition,
% 0.20/0.46 ( mnot
% 0.20/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.20/0.46 ~ ( A @ W ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mand_def,definition,
% 0.20/0.46 ( mand
% 0.20/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.46 ( ( A @ W )
% 0.20/0.46 & ( B @ W ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mor_def,definition,
% 0.20/0.46 ( mor
% 0.20/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.46 ( ( A @ W )
% 0.20/0.46 | ( B @ W ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mimplies_def,definition,
% 0.20/0.46 ( mimplies
% 0.20/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.46 ( ( A @ W )
% 0.20/0.46 => ( B @ W ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mequiv_def,definition,
% 0.20/0.46 ( mequiv
% 0.20/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.46 ( ( A @ W )
% 0.20/0.46 <=> ( B @ W ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mbox_type,type,
% 0.20/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mbox_def,definition,
% 0.20/0.46 ( mbox
% 0.20/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.46 ! [V: mworld] :
% 0.20/0.46 ( ( mrel @ W @ V )
% 0.20/0.46 => ( Phi @ V ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mdia_type,type,
% 0.20/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mdia_def,definition,
% 0.20/0.46 ( mdia
% 0.20/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.46 ? [V: mworld] :
% 0.20/0.46 ( ( mrel @ W @ V )
% 0.20/0.46 & ( Phi @ V ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mrel_reflexive,axiom,
% 0.20/0.46 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.20/0.46
% 0.20/0.46 thf(mrel_transitive,axiom,
% 0.20/0.46 ! [W: mworld,V: mworld,U: mworld] :
% 0.20/0.46 ( ( ( mrel @ W @ V )
% 0.20/0.46 & ( mrel @ V @ U ) )
% 0.20/0.46 => ( mrel @ W @ U ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eiw_di_type,type,
% 0.20/0.46 eiw_di: $i > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(eiw_di_nonempty,axiom,
% 0.20/0.46 ! [W: mworld] :
% 0.20/0.46 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.20/0.46
% 0.20/0.46 thf(eiw_di_cumul,axiom,
% 0.20/0.46 ! [W: mworld,V: mworld,X: $i] :
% 0.20/0.46 ( ( ( eiw_di @ X @ W )
% 0.20/0.46 & ( mrel @ W @ V ) )
% 0.20/0.46 => ( eiw_di @ X @ V ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mforall_di_type,type,
% 0.20/0.46 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mforall_di_def,definition,
% 0.20/0.46 ( mforall_di
% 0.20/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.20/0.46 ! [X: $i] :
% 0.20/0.46 ( ( eiw_di @ X @ W )
% 0.20/0.46 => ( A @ X @ W ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(mexists_di_type,type,
% 0.20/0.46 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(mexists_di_def,definition,
% 0.20/0.46 ( mexists_di
% 0.20/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.20/0.46 ? [X: $i] :
% 0.20/0.46 ( ( eiw_di @ X @ W )
% 0.20/0.46 & ( A @ X @ W ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(e_decl,type,
% 0.20/0.46 e: $i > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(f_decl,type,
% 0.20/0.46 f: $i > mworld > $o ).
% 0.20/0.46
% 0.20/0.46 thf(con,conjecture,
% 0.20/0.46 ( mlocal
% 0.20/0.46 @ ( mimplies
% 0.20/0.46 @ ( mexists_di
% 0.20/0.46 @ ^ [X: $i] : ( mbox @ ( mand @ ( e @ X ) @ ( f @ X ) ) ) )
% 0.20/0.46 @ ( mbox
% 0.20/0.46 @ ( mexists_di
% 0.20/0.46 @ ^ [X: $i] : ( f @ X ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.72/1.47 ---- Embedded in THF ---
% 1.72/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.72/1.47 %%% Generated on Tue Feb 24 14:53:26 EST 2026
% 1.72/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 1.72/1.47 %%% Logic specification used:
% 1.72/1.47 %%% thf(spec, logic, $$dhol).
% 1.72/1.47
% 1.72/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ZOUo0mCqqG/DTF2DTF6113.p
% See solution above
% 1.72/1.47 ------------------------
% 1.72/1.48 ---- Cleaned THF ---
% 1.72/1.48 thf(mworld,type,
% 1.72/1.48 mworld: $tType ).
% 1.72/1.48
% 1.72/1.48 thf(mrel_type,type,
% 1.72/1.48 mrel: mworld > mworld > $o ).
% 1.72/1.48
% 1.72/1.48 thf(mactual_type,type,
% 1.72/1.48 mactual: mworld ).
% 1.72/1.48
% 1.72/1.48 thf(mlocal_type,type,
% 1.72/1.48 mlocal: ( mworld > $o ) > $o ).
% 1.72/1.48
% 1.72/1.48 thf(mlocal_def,definition,
% 1.72/1.48 ( mlocal
% 1.72/1.48 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.72/1.48
% 1.72/1.48 thf(mnot_type,type,
% 1.72/1.48 mnot: ( mworld > $o ) > mworld > $o ).
% 1.72/1.48
% 1.72/1.48 thf(mand_type,type,
% 1.72/1.48 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.72/1.48
% 1.72/1.48 thf(mor_type,type,
% 1.72/1.48 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.72/1.48
% 1.72/1.48 thf(mimplies_type,type,
% 1.72/1.48 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.72/1.48
% 1.72/1.48 thf(mequiv_type,type,
% 1.72/1.48 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.72/1.48
% 1.72/1.48 thf(mnot_def,definition,
% 1.72/1.48 ( mnot
% 1.72/1.48 = ( ^ [A: mworld > $o,W: mworld] :
% 1.72/1.48 ~ ( A @ W ) ) ) ).
% 1.72/1.48
% 1.72/1.48 thf(mand_def,definition,
% 1.72/1.48 ( mand
% 1.72/1.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.72/1.48 ( ( A @ W )
% 1.72/1.48 & ( B @ W ) ) ) ) ).
% 1.72/1.48
% 1.72/1.48 thf(mor_def,definition,
% 1.72/1.48 ( mor
% 1.72/1.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.72/1.48 ( ( A @ W )
% 1.72/1.48 | ( B @ W ) ) ) ) ).
% 1.72/1.48
% 1.72/1.48 thf(mimplies_def,definition,
% 1.72/1.48 ( mimplies
% 1.72/1.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.72/1.48 ( ( A @ W )
% 1.72/1.48 => ( B @ W ) ) ) ) ).
% 1.72/1.48
% 1.72/1.48 thf(mequiv_def,definition,
% 1.72/1.48 ( mequiv
% 1.72/1.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.72/1.48 ( ( A @ W )
% 1.72/1.48 <=> ( B @ W ) ) ) ) ).
% 1.72/1.48
% 1.72/1.48 thf(mbox_type,type,
% 1.72/1.48 mbox: ( mworld > $o ) > mworld > $o ).
% 1.72/1.48
% 1.72/1.48 thf(mbox_def,definition,
% 1.72/1.48 ( mbox
% 1.72/1.48 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.72/1.48 ! [V: mworld] :
% 1.72/1.48 ( ( mrel @ W @ V )
% 1.72/1.48 => ( Phi @ V ) ) ) ) ).
% 1.72/1.48
% 1.72/1.48 thf(mdia_type,type,
% 1.72/1.48 mdia: ( mworld > $o ) > mworld > $o ).
% 1.72/1.48
% 1.72/1.48 thf(mdia_def,definition,
% 1.72/1.48 ( mdia
% 1.72/1.48 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.72/1.48 ? [V: mworld] :
% 1.72/1.48 ( ( mrel @ W @ V )
% 1.72/1.48 & ( Phi @ V ) ) ) ) ).
% 1.72/1.48
% 1.72/1.48 thf(mrel_reflexive,axiom,
% 1.72/1.48 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.72/1.48
% 1.72/1.48 thf(mrel_transitive,axiom,
% 1.72/1.48 ! [W: mworld,V: mworld,U: mworld] :
% 1.72/1.48 ( ( ( mrel @ W @ V )
% 1.72/1.48 & ( mrel @ V @ U ) )
% 1.72/1.48 => ( mrel @ W @ U ) ) ).
% 1.72/1.48
% 1.72/1.48 thf(eiw_di_type,type,
% 1.72/1.48 eiw_di: $i > mworld > $o ).
% 1.72/1.48
% 1.72/1.48 thf(eiw_di_nonempty,axiom,
% 1.72/1.48 ! [W: mworld] :
% 1.72/1.48 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 1.72/1.48
% 1.72/1.48 thf(eiw_di_cumul,axiom,
% 1.72/1.48 ! [W: mworld,V: mworld,X: $i] :
% 1.72/1.48 ( ( ( eiw_di @ X @ W )
% 1.72/1.48 & ( mrel @ W @ V ) )
% 1.72/1.48 => ( eiw_di @ X @ V ) ) ).
% 1.72/1.48
% 1.72/1.48 thf(mforall_di_type,type,
% 1.72/1.48 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.72/1.48
% 1.72/1.48 thf(mforall_di_def,definition,
% 1.72/1.48 ( mforall_di
% 1.72/1.48 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.72/1.48 ! [X: $i] :
% 1.72/1.48 ( ( eiw_di @ X @ W )
% 1.72/1.48 => ( A @ X @ W ) ) ) ) ).
% 1.72/1.48
% 1.72/1.48 thf(mexists_di_type,type,
% 1.72/1.48 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.72/1.48
% 1.72/1.48 thf(mexists_di_def,definition,
% 1.72/1.48 ( mexists_di
% 1.72/1.48 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.72/1.48 ? [X: $i] :
% 1.72/1.48 ( ( eiw_di @ X @ W )
% 1.72/1.48 & ( A @ X @ W ) ) ) ) ).
% 1.72/1.48
% 1.72/1.48 thf(e_decl,type,
% 1.72/1.48 e: $i > mworld > $o ).
% 1.72/1.48
% 1.72/1.48 thf(f_decl,type,
% 1.72/1.48 f: $i > mworld > $o ).
% 1.72/1.48
% 1.72/1.48 thf(con,conjecture,
% 1.72/1.48 ( mlocal
% 1.72/1.48 @ ( mimplies
% 1.72/1.48 @ ( mexists_di
% 1.72/1.48 @ ^ [X: $i] : ( mbox @ ( mand @ ( e @ X ) @ ( f @ X ) ) ) )
% 1.72/1.48 @ ( mbox
% 1.72/1.48 @ ( mexists_di
% 1.72/1.48 @ ^ [X: $i] : ( f @ X ) ) ) ) ) ).
% 1.72/1.48 ------------------------
% 1.87/1.50 % (6212)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_6113 for (2999ds/27Mi)
% 1.87/1.50 % (6210)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6113 for (2999ds/183Mi)
% 1.87/1.50 % (6211)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_6113 for (2999ds/4Mi)
% 1.87/1.50 % (6213)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6113 for (2999ds/2Mi)
% 1.87/1.50 % (6214)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_6113 for (2999ds/2Mi)
% 1.87/1.50 % (6215)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_6113 for (2999ds/275Mi)
% 1.87/1.50 % (6216)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6113 for (2999ds/18Mi)
% 1.87/1.50 % (6213)Instruction limit reached!
% 1.87/1.50 % (6213)------------------------------
% 1.87/1.50 % (6213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.50 % (6213)Termination reason: Unknown
% 1.87/1.50 % (6213)Termination phase: Property scanning
% 1.87/1.50 % (6214)Instruction limit reached!
% 1.87/1.50 % (6214)------------------------------
% 1.87/1.50 % (6214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.50 % (6214)Termination reason: Unknown
% 1.87/1.50 % (6214)Termination phase: Property scanning
% 1.87/1.50
% 1.87/1.50 % (6214)Memory used [KB]: 1023
% 1.87/1.50 % (6214)Time elapsed: 0.003 s
% 1.87/1.50 % (6214)Instructions burned: 3 (million)
% 1.87/1.50 % (6214)------------------------------
% 1.87/1.50 % (6214)------------------------------
% 1.87/1.50
% 1.87/1.50 % (6213)Memory used [KB]: 1023
% 1.87/1.50 % (6213)Time elapsed: 0.003 s
% 1.87/1.50 % (6213)Instructions burned: 3 (million)
% 1.87/1.50 % (6213)------------------------------
% 1.87/1.50 % (6213)------------------------------
% 1.87/1.50 % (6211)Instruction limit reached!
% 1.87/1.50 % (6211)------------------------------
% 1.87/1.50 % (6211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.50 % (6211)Termination reason: Unknown
% 1.87/1.50 % (6211)Termination phase: Saturation
% 1.87/1.50
% 1.87/1.50 % (6211)Memory used [KB]: 5500
% 1.87/1.50 % (6211)Time elapsed: 0.004 s
% 1.87/1.50 % (6211)Instructions burned: 5 (million)
% 1.87/1.50 % (6211)------------------------------
% 1.87/1.50 % (6211)------------------------------
% 1.87/1.50 % (6215)Refutation not found, incomplete strategy
% 1.87/1.50 % (6215)------------------------------
% 1.87/1.50 % (6215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.50 % (6215)Termination reason: Refutation not found, incomplete strategy
% 1.87/1.50
% 1.87/1.50
% 1.87/1.50 % (6215)Memory used [KB]: 5500
% 1.87/1.50 % (6215)Time elapsed: 0.004 s
% 1.87/1.50 % (6215)Instructions burned: 5 (million)
% 1.87/1.50 % (6215)------------------------------
% 1.87/1.50 % (6215)------------------------------
% 1.87/1.51 % (6210)First to succeed.
% 1.87/1.51 % (6216)Also succeeded, but the first one will report.
% 1.87/1.51 % (6212)Also succeeded, but the first one will report.
% 1.87/1.51 % (6210)Refutation found. Thanks to Tanya!
% 1.87/1.51 % SZS status Theorem for DTF2THF_6113
% 1.87/1.51 % SZS output start Proof for DTF2THF_6113
% 1.87/1.51 thf(type_def_5, type, mworld: $tType).
% 1.87/1.51 thf(func_def_0, type, mworld: $tType).
% 1.87/1.51 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.87/1.51 thf(func_def_2, type, mactual: mworld).
% 1.87/1.51 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.87/1.51 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.87/1.51 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.87/1.51 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.87/1.51 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.87/1.51 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.87/1.51 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.87/1.51 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.87/1.51 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 1.87/1.51 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.87/1.51 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.87/1.51 thf(func_def_15, type, e: $i > mworld > $o).
% 1.87/1.51 thf(func_def_16, type, f: $i > mworld > $o).
% 1.87/1.51 thf(func_def_30, type, sK0: mworld > $i).
% 1.87/1.51 thf(func_def_34, type, sK3: mworld).
% 1.87/1.51 thf(f116,plain,(
% 1.87/1.51 $false),
% 1.87/1.51 inference(subsumption_resolution,[status(thm)],[f113,f76])).
% 1.87/1.51 thf(f76,plain,(
% 1.87/1.51 ($true = (eiw_di @ sK2 @ mactual))),
% 1.87/1.51 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.87/1.51 thf(f74,plain,(
% 1.87/1.51 ($true = ((eiw_di @ sK2 @ mactual) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((e @ sK2 @ Y0) & (f @ sK2 @ Y0)))))))),
% 1.87/1.51 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.87/1.51 thf(f73,plain,(
% 1.87/1.51 ($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => ((e @ Y0 @ Y1) & (f @ Y0 @ Y1))))))) @ sK2))),
% 1.87/1.51 inference(sigma_clausification,[status(thm)],[f72])).
% 1.87/1.51 thf(f72,plain,(
% 1.87/1.51 ($true = (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => ((e @ Y0 @ Y1) & (f @ Y0 @ Y1)))))))))),
% 1.87/1.51 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.87/1.51 thf(f70,plain,(
% 1.87/1.51 (((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => ((e @ Y0 @ Y1) & (f @ Y0 @ Y1)))))))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (f @ Y1 @ Y0)))))))) != $true)),
% 1.87/1.51 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.87/1.51 thf(f69,plain,(
% 1.87/1.51 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ ((^[Y1 : mworld > $o]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: ((Y1 @ Y3) & (Y2 @ Y3))))))) @ (e @ Y0) @ (f @ Y0))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: (f @ Y0)))))))),
% 1.87/1.51 inference(definition_unfolding,[status(thm)],[f57,f60,f62,f58,f56,f54,f56,f58])).
% 1.87/1.51 thf(f54,plain,(
% 1.87/1.51 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.87/1.51 inference(cnf_transformation,[status(thm)],[f25])).
% 1.87/1.51 thf(f25,plain,(
% 1.87/1.51 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.87/1.51 inference(fool_elimination,[status(thm)],[f24])).
% 1.87/1.51 thf(f24,plain,(
% 1.87/1.51 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 1.87/1.51 inference(rectify,[status(thm)],[f3])).
% 1.87/1.51 thf(f3,axiom,(
% 1.87/1.51 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))))),
% 1.87/1.51 file('/export/starexec/sandbox/tmp/tmp.ZOUo0mCqqG/DTF2THF_6113.p',mand_def)).
% 1.87/1.51 thf(f56,plain,(
% 1.87/1.51 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.87/1.51 inference(cnf_transformation,[status(thm)],[f29])).
% 1.87/1.51 thf(f29,plain,(
% 1.87/1.51 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.87/1.51 inference(fool_elimination,[status(thm)],[f28])).
% 1.87/1.51 thf(f28,plain,(
% 1.87/1.51 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 1.87/1.51 inference(rectify,[status(thm)],[f7])).
% 1.87/1.51 thf(f7,axiom,(
% 1.87/1.51 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 1.87/1.51 file('/export/starexec/sandbox/tmp/tmp.ZOUo0mCqqG/DTF2THF_6113.p',mbox_def)).
% 1.87/1.51 thf(f58,plain,(
% 1.87/1.51 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 1.87/1.51 inference(cnf_transformation,[status(thm)],[f19])).
% 1.87/1.51 thf(f19,plain,(
% 1.87/1.51 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 1.87/1.51 inference(fool_elimination,[status(thm)],[f18])).
% 1.87/1.51 thf(f18,plain,(
% 1.87/1.51 ((^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))) = mexists_di)),
% 1.87/1.51 inference(rectify,[status(thm)],[f14])).
% 1.87/1.51 thf(f14,axiom,(
% 1.87/1.51 ((^[X1 : $i > mworld > $o, X2 : mworld] : (? [X6 : $i] : ((X1 @ X6 @ X2) & (eiw_di @ X6 @ X2)))) = mexists_di)),
% 1.87/1.51 file('/export/starexec/sandbox/tmp/tmp.ZOUo0mCqqG/DTF2THF_6113.p',mexists_di_def)).
% 1.87/1.51 thf(f62,plain,(
% 1.87/1.51 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.87/1.51 inference(cnf_transformation,[status(thm)],[f21])).
% 1.87/1.51 thf(f21,plain,(
% 1.87/1.51 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.87/1.51 inference(fool_elimination,[status(thm)],[f20])).
% 1.87/1.51 thf(f20,plain,(
% 1.87/1.51 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 1.87/1.51 inference(rectify,[status(thm)],[f5])).
% 1.87/1.51 thf(f5,axiom,(
% 1.87/1.51 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 1.87/1.51 file('/export/starexec/sandbox/tmp/tmp.ZOUo0mCqqG/DTF2THF_6113.p',mimplies_def)).
% 1.87/1.51 thf(f60,plain,(
% 1.87/1.51 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.87/1.51 inference(cnf_transformation,[status(thm)],[f34])).
% 1.87/1.51 thf(f34,plain,(
% 1.87/1.51 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.87/1.51 inference(fool_elimination,[status(thm)],[f1])).
% 1.87/1.51 thf(f1,axiom,(
% 1.87/1.51 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.87/1.51 file('/export/starexec/sandbox/tmp/tmp.ZOUo0mCqqG/DTF2THF_6113.p',mlocal_def)).
% 1.87/1.51 thf(f57,plain,(
% 1.87/1.51 ($true != (mlocal @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (e @ Y0) @ (f @ Y0))))) @ (mbox @ (mexists_di @ (^[Y0 : $i]: (f @ Y0)))))))),
% 1.87/1.51 inference(cnf_transformation,[status(thm)],[f47])).
% 1.87/1.51 thf(f47,plain,(
% 1.87/1.51 ($true != (mlocal @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (e @ Y0) @ (f @ Y0))))) @ (mbox @ (mexists_di @ (^[Y0 : $i]: (f @ Y0)))))))),
% 1.87/1.51 inference(flattening,[status(thm)],[f42])).
% 1.87/1.51 thf(f42,plain,(
% 1.87/1.51 ~($true = (mlocal @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (e @ Y0) @ (f @ Y0))))) @ (mbox @ (mexists_di @ (^[Y0 : $i]: (f @ Y0)))))))),
% 1.87/1.51 inference(fool_elimination,[status(thm)],[f41])).
% 1.87/1.51 thf(f41,plain,(
% 1.87/1.51 ~(mlocal @ (mimplies @ (mexists_di @ (^[X0 : $i] : (mbox @ (mand @ (e @ X0) @ (f @ X0))))) @ (mbox @ (mexists_di @ (^[X1 : $i] : (f @ X1))))))),
% 1.87/1.51 inference(rectify,[status(thm)],[f16])).
% 1.87/1.51 thf(f16,negated_conjecture,(
% 1.87/1.51 ~(mlocal @ (mimplies @ (mexists_di @ (^[X6 : $i] : (mbox @ (mand @ (e @ X6) @ (f @ X6))))) @ (mbox @ (mexists_di @ (^[X6 : $i] : (f @ X6))))))),
% 1.87/1.51 inference(negated_conjecture,[status(cth)],[f15])).
% 1.87/1.51 thf(f15,conjecture,(
% 1.87/1.51 (mlocal @ (mimplies @ (mexists_di @ (^[X6 : $i] : (mbox @ (mand @ (e @ X6) @ (f @ X6))))) @ (mbox @ (mexists_di @ (^[X6 : $i] : (f @ X6))))))),
% 1.87/1.51 file('/export/starexec/sandbox/tmp/tmp.ZOUo0mCqqG/DTF2THF_6113.p',con)).
% 1.87/1.51 thf(f113,plain,(
% 1.87/1.51 ($true != (eiw_di @ sK2 @ mactual))),
% 1.87/1.51 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.87/1.51 thf(f111,plain,(
% 1.87/1.51 ($true != $true) | ($true != (eiw_di @ sK2 @ mactual))),
% 1.87/1.51 inference(superposition,[status(thm)],[f108,f85])).
% 1.87/1.51 thf(f85,plain,(
% 1.87/1.51 ((mrel @ mactual @ sK3) = $true)),
% 1.87/1.51 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.87/1.51 thf(f83,plain,(
% 1.87/1.51 ($false = ((mrel @ mactual @ sK3) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (f @ Y0 @ sK3))))))),
% 1.87/1.51 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.87/1.51 thf(f82,plain,(
% 1.87/1.51 (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (f @ Y1 @ Y0)))))) @ sK3) = $false)),
% 1.87/1.51 inference(sigma_clausification,[status(thm)],[f71])).
% 1.87/1.51 thf(f71,plain,(
% 1.87/1.51 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (f @ Y1 @ Y0))))))) = $false)),
% 1.87/1.51 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.87/1.51 thf(f108,plain,(
% 1.87/1.51 ( ! [X0 : mworld] : (($true != (mrel @ X0 @ sK3)) | ($true != (eiw_di @ sK2 @ X0))) )),
% 1.87/1.51 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.87/1.51 thf(f105,plain,(
% 1.87/1.51 ( ! [X0 : mworld] : (($true != (mrel @ X0 @ sK3)) | ($true = $false) | ($true != (eiw_di @ sK2 @ X0))) )),
% 1.87/1.51 inference(superposition,[status(thm)],[f68,f100])).
% 1.87/1.51 thf(f100,plain,(
% 1.87/1.51 ((eiw_di @ sK2 @ sK3) = $false)),
% 1.87/1.51 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.87/1.51 thf(f98,plain,(
% 1.87/1.51 ((eiw_di @ sK2 @ sK3) = $false) | ($true = $false)),
% 1.87/1.51 inference(superposition,[status(thm)],[f88,f95])).
% 1.87/1.51 thf(f95,plain,(
% 1.87/1.51 ($true = (f @ sK2 @ sK3))),
% 1.87/1.51 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.87/1.51 thf(f91,plain,(
% 1.87/1.51 ($true = $false) | ($true = (f @ sK2 @ sK3))),
% 1.87/1.51 inference(superposition,[status(thm)],[f85,f80])).
% 1.87/1.51 thf(f80,plain,(
% 1.87/1.51 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((f @ sK2 @ X1) = $true)) )),
% 1.87/1.51 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.87/1.51 thf(f79,plain,(
% 1.87/1.51 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = ((e @ sK2 @ X1) & (f @ sK2 @ X1)))) )),
% 1.87/1.51 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.87/1.51 thf(f78,plain,(
% 1.87/1.51 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => ((e @ sK2 @ X1) & (f @ sK2 @ X1))) = $true)) )),
% 1.87/1.51 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.87/1.51 thf(f77,plain,(
% 1.87/1.51 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((e @ sK2 @ Y0) & (f @ sK2 @ Y0)))) @ X1))) )),
% 1.87/1.51 inference(pi_clausification,[status(thm)],[f75])).
% 1.87/1.51 thf(f75,plain,(
% 1.87/1.51 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((e @ sK2 @ Y0) & (f @ sK2 @ Y0))))))),
% 1.87/1.51 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.87/1.51 thf(f88,plain,(
% 1.87/1.51 ( ! [X1 : $i] : (($false = (f @ X1 @ sK3)) | ($false = (eiw_di @ X1 @ sK3))) )),
% 1.87/1.51 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.87/1.51 thf(f87,plain,(
% 1.87/1.51 ( ! [X1 : $i] : (($false = ((eiw_di @ X1 @ sK3) & (f @ X1 @ sK3)))) )),
% 1.87/1.51 inference(beta_eta_normalization,[status(thm)],[f86])).
% 1.87/1.51 thf(f86,plain,(
% 1.87/1.51 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (f @ Y0 @ sK3))) @ X1) = $false)) )),
% 1.87/1.51 inference(pi_clausification,[status(thm)],[f84])).
% 1.87/1.51 thf(f84,plain,(
% 1.87/1.51 ($false = (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (f @ Y0 @ sK3)))))),
% 1.87/1.51 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.87/1.51 thf(f68,plain,(
% 1.87/1.51 ( ! [X2 : $i,X0 : mworld,X1 : mworld] : (($true = (eiw_di @ X2 @ X0)) | ($true != (eiw_di @ X2 @ X1)) | ($true != (mrel @ X1 @ X0))) )),
% 1.87/1.51 inference(cnf_transformation,[status(thm)],[f51])).
% 1.87/1.51 thf(f51,plain,(
% 1.87/1.51 ! [X0 : mworld,X1 : mworld,X2 : $i] : (($true != (eiw_di @ X2 @ X1)) | ($true != (mrel @ X1 @ X0)) | ($true = (eiw_di @ X2 @ X0)))),
% 1.87/1.51 inference(flattening,[status(thm)],[f50])).
% 1.87/1.51 thf(f50,plain,(
% 1.87/1.51 ! [X0 : mworld,X1 : mworld,X2 : $i] : (($true = (eiw_di @ X2 @ X0)) | (($true != (eiw_di @ X2 @ X1)) | ($true != (mrel @ X1 @ X0))))),
% 1.87/1.51 inference(ennf_transformation,[status(thm)],[f40])).
% 1.87/1.51 thf(f40,plain,(
% 1.87/1.51 ! [X0 : mworld,X1 : mworld,X2 : $i] : ((($true = (eiw_di @ X2 @ X1)) & ($true = (mrel @ X1 @ X0))) => ($true = (eiw_di @ X2 @ X0)))),
% 1.87/1.51 inference(fool_elimination,[status(thm)],[f39])).
% 1.87/1.51 thf(f39,plain,(
% 1.87/1.51 ! [X0 : mworld,X1 : mworld,X2 : $i] : (((eiw_di @ X2 @ X1) & (mrel @ X1 @ X0)) => (eiw_di @ X2 @ X0))),
% 1.87/1.51 inference(rectify,[status(thm)],[f12])).
% 1.87/1.51 thf(f12,axiom,(
% 1.87/1.51 ! [X4 : mworld,X2 : mworld,X6 : $i] : (((eiw_di @ X6 @ X2) & (mrel @ X2 @ X4)) => (eiw_di @ X6 @ X4))),
% 1.87/1.51 file('/export/starexec/sandbox/tmp/tmp.ZOUo0mCqqG/DTF2THF_6113.p',eiw_di_cumul)).
% 1.87/1.51 % SZS output end Proof for DTF2THF_6113
% 1.87/1.51 % (6210)------------------------------
% 1.87/1.51 % (6210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.51 % (6210)Termination reason: Refutation
% 1.87/1.51
% 1.87/1.51 % (6210)Memory used [KB]: 5628
% 1.87/1.51 % (6210)Time elapsed: 0.009 s
% 1.87/1.51 % (6210)Instructions burned: 9 (million)
% 1.87/1.51 % (6210)------------------------------
% 1.87/1.51 % (6210)------------------------------
% 1.87/1.51 % (6209)Success in time 0.022 s
%------------------------------------------------------------------------------