%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO899^8 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 09:55:09 AM UTC 2026
% Result : Theorem 1.76s 1.42s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 63 ( 41 unt; 0 typ; 2 def)
% Number of atoms : 332 ( 64 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 394 ( 17 ~; 21 |; 15 &; 283 @)
% ( 2 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 15 usr; 8 con; 0-3 aty)
% ( 13 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 94 ( 75 ^; 17 !; 2 ?; 94 :)
% 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,
p: mworld > $o ).
thf(func_def_13,type,
q: mworld > $o ).
thf(func_def_28,type,
sK1: mworld ).
thf(f104,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f70,f84,f103]) ).
thf(f103,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f102]) ).
thf(f102,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f97,f92]) ).
thf(f92,plain,
( ( q @ sK1 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ( q @ sK1 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f49,f62]) ).
thf(f62,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X1: mworld] :
( ( ( q @ X1 )
& ( mrel @ mactual @ X1 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( q @ Y0 )
& ( mrel @ mactual @ Y0 ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( q @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( q @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ( p @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( mrel @ mactual @ Y0 ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( q @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ p
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ q ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f36,f42,f37,f41,f37,f33,f37,f33,f41]) ).
thf(f33,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) )
= mbox ),
file('/export/starexec/sandbox2/tmp/tmp.P7EKUgqaKq/DTF2THF_7025.p',mbox_def) ).
thf(f41,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f29]) ).
thf(f29,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X2: mworld] :
? [X4: mworld] :
( ( mrel @ X2 @ X4 )
& ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.P7EKUgqaKq/DTF2THF_7025.p',mdia_def) ).
thf(f37,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,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/sandbox2/tmp/tmp.P7EKUgqaKq/DTF2THF_7025.p',mimplies_def) ).
thf(f42,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,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/sandbox2/tmp/tmp.P7EKUgqaKq/DTF2THF_7025.p',mlocal_def) ).
thf(f36,plain,
( ( mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f28]) ).
thf(f28,plain,
( ( mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f27]) ).
thf(f27,plain,
~ ( mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f10,conjecture,
mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.P7EKUgqaKq/DTF2THF_7025.p',con) ).
thf(f49,plain,
( $true
= ( mrel @ mactual @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( ( p @ sK1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( mrel @ mactual @ sK1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ^ [Y0: mworld] :
( ( ( p @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( mrel @ mactual @ Y0 ) )
@ sK1 )
= $true ),
inference(sigma_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ( p @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( mrel @ mactual @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f97,plain,
( ( $true
= ( q @ sK1 ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ( $true = $false )
| ( $true
= ( q @ sK1 ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f65,f39]) ).
thf(f39,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X2: mworld] : ( mrel @ X2 @ X2 ),
file('/export/starexec/sandbox2/tmp/tmp.P7EKUgqaKq/DTF2THF_7025.p',mrel_reflexive) ).
thf(f65,plain,
( ! [X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( $true
= ( q @ X1 ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl0_1
<=> ! [X1: mworld] :
( ( $true
= ( q @ X1 ) )
| ( ( mrel @ sK1 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f84,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f83]) ).
thf(f83,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f69,f77]) ).
thf(f77,plain,
( $true
= ( p @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $true = $false )
| ( $true
= ( p @ sK1 ) ) ),
inference(superposition,[status(thm)],[f59,f49]) ).
thf(f59,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( p @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( p @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f69,plain,
( ( ( p @ sK1 )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f67,definition,
( spl0_2
<=> ( ( p @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f70,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f54,f67,f64]) ).
thf(f54,plain,
! [X1: mworld] :
( ( ( p @ sK1 )
= $false )
| ( $true
= ( q @ X1 ) )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ sK1 @ X1 )
=> ( q @ X1 ) ) )
| ( ( p @ sK1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: mworld] :
( ( ( p @ sK1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) )
= $true )
| ( ( p @ sK1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( p @ sK1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO899^8 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.35 % Computer : n006.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 14:53:30 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SYO899^8 : TPTP v9.2.1. Released v8.1.0.
% 0.20/0.45 % Domain : Syntactic
% 0.20/0.45 % Problem : Modal propositional logic theorems. problem 37
% 0.20/0.45 % Version : [BP13] axioms.
% 0.20/0.45 % English :
% 0.20/0.45
% 0.20/0.45 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.20/0.45 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.20/0.45 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.20/0.45 % Source : [TPTP]
% 0.20/0.45 % Names : SYM137+1 [QMLTP]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 0.00 v8.2.0, 0.15 v8.1.0
% 0.20/0.45 % Syntax : Number of formulae : 23 ( 9 unt; 13 typ; 8 def)
% 0.20/0.45 % Number of atoms : 31 ( 8 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 12 ( 3 avg)
% 0.20/0.45 % Number of connectives : 36 ( 1 ~; 1 |; 2 &; 29 @)
% 0.20/0.45 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 7 ( 2 avg)
% 0.20/0.45 % Number of types : 2 ( 1 usr)
% 0.20/0.45 % Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 13 ( 12 usr; 1 con; 0-3 aty)
% 0.20/0.45 % Number of variables : 22 ( 19 ^; 2 !; 1 ?; 22 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.20/0.45 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.20/0.45 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.20/0.45 % $modal == [$constants == $rigid,$quantification == $varying,
% 0.20/0.45 % $modalities == $modal_system_T].
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(mworld,type,
% 0.20/0.45 mworld: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(mrel_type,type,
% 0.20/0.45 mrel: mworld > mworld > $o ).
% 0.20/0.45
% 0.20/0.45 thf(mactual_type,type,
% 0.20/0.45 mactual: mworld ).
% 0.20/0.45
% 0.20/0.45 thf(mlocal_type,type,
% 0.20/0.45 mlocal: ( mworld > $o ) > $o ).
% 0.20/0.45
% 0.20/0.45 thf(mlocal_def,definition,
% 0.20/0.45 ( mlocal
% 0.20/0.45 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(mnot_type,type,
% 0.20/0.45 mnot: ( mworld > $o ) > mworld > $o ).
% 0.20/0.45
% 0.20/0.45 thf(mand_type,type,
% 0.20/0.45 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.45
% 0.20/0.45 thf(mor_type,type,
% 0.20/0.45 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.45
% 0.20/0.45 thf(mimplies_type,type,
% 0.20/0.45 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.45
% 0.20/0.45 thf(mequiv_type,type,
% 0.20/0.45 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.45
% 0.20/0.45 thf(mnot_def,definition,
% 0.20/0.45 ( mnot
% 0.20/0.45 = ( ^ [A: mworld > $o,W: mworld] :
% 0.20/0.45 ~ ( A @ W ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(mand_def,definition,
% 0.20/0.45 ( mand
% 0.20/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.45 ( ( A @ W )
% 0.20/0.45 & ( B @ W ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(mor_def,definition,
% 0.20/0.45 ( mor
% 0.20/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.45 ( ( A @ W )
% 0.20/0.45 | ( B @ W ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(mimplies_def,definition,
% 0.20/0.45 ( mimplies
% 0.20/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.45 ( ( A @ W )
% 0.20/0.45 => ( B @ W ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(mequiv_def,definition,
% 0.20/0.45 ( mequiv
% 0.20/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.45 ( ( A @ W )
% 0.20/0.45 <=> ( B @ W ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(mbox_type,type,
% 0.20/0.45 mbox: ( mworld > $o ) > mworld > $o ).
% 0.20/0.45
% 0.20/0.45 thf(mbox_def,definition,
% 0.20/0.45 ( mbox
% 0.20/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.45 ! [V: mworld] :
% 0.20/0.45 ( ( mrel @ W @ V )
% 0.20/0.45 => ( Phi @ V ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(mdia_type,type,
% 0.20/0.45 mdia: ( mworld > $o ) > mworld > $o ).
% 0.20/0.45
% 0.20/0.45 thf(mdia_def,definition,
% 0.20/0.45 ( mdia
% 0.20/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.45 ? [V: mworld] :
% 0.20/0.45 ( ( mrel @ W @ V )
% 0.20/0.45 & ( Phi @ V ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(mrel_reflexive,axiom,
% 0.20/0.45 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.20/0.45
% 0.20/0.45 thf(p_decl,type,
% 0.20/0.45 p: mworld > $o ).
% 0.20/0.45
% 0.20/0.45 thf(q_decl,type,
% 0.20/0.45 q: mworld > $o ).
% 0.20/0.45
% 0.20/0.45 thf(con,conjecture,
% 0.20/0.45 mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.56/1.38 ---- Embedded in THF ---
% 1.56/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.38 %%% Generated on Tue Feb 24 14:53:31 EST 2026
% 1.56/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.38 %%% Logic specification used:
% 1.56/1.38 %%% thf(spec, logic, $$dhol).
% 1.56/1.38
% 1.56/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.P7EKUgqaKq/DTF2DTF7025.p
% See solution above
% 1.56/1.38 ------------------------
% 1.56/1.39 ---- Cleaned THF ---
% 1.56/1.39 thf(mworld,type,
% 1.56/1.39 mworld: $tType ).
% 1.56/1.39
% 1.56/1.39 thf(mrel_type,type,
% 1.56/1.39 mrel: mworld > mworld > $o ).
% 1.56/1.39
% 1.56/1.39 thf(mactual_type,type,
% 1.56/1.39 mactual: mworld ).
% 1.56/1.39
% 1.56/1.39 thf(mlocal_type,type,
% 1.56/1.39 mlocal: ( mworld > $o ) > $o ).
% 1.56/1.39
% 1.56/1.39 thf(mlocal_def,definition,
% 1.56/1.39 ( mlocal
% 1.56/1.39 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.56/1.39
% 1.56/1.39 thf(mnot_type,type,
% 1.56/1.39 mnot: ( mworld > $o ) > mworld > $o ).
% 1.56/1.39
% 1.56/1.39 thf(mand_type,type,
% 1.56/1.39 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.56/1.39
% 1.56/1.39 thf(mor_type,type,
% 1.56/1.39 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.56/1.39
% 1.56/1.39 thf(mimplies_type,type,
% 1.56/1.39 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.56/1.39
% 1.56/1.39 thf(mequiv_type,type,
% 1.56/1.39 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.56/1.39
% 1.56/1.39 thf(mnot_def,definition,
% 1.56/1.39 ( mnot
% 1.56/1.39 = ( ^ [A: mworld > $o,W: mworld] :
% 1.56/1.39 ~ ( A @ W ) ) ) ).
% 1.56/1.39
% 1.56/1.39 thf(mand_def,definition,
% 1.56/1.39 ( mand
% 1.56/1.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.56/1.39 ( ( A @ W )
% 1.56/1.39 & ( B @ W ) ) ) ) ).
% 1.56/1.39
% 1.56/1.39 thf(mor_def,definition,
% 1.56/1.39 ( mor
% 1.56/1.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.56/1.39 ( ( A @ W )
% 1.56/1.39 | ( B @ W ) ) ) ) ).
% 1.56/1.39
% 1.56/1.39 thf(mimplies_def,definition,
% 1.56/1.39 ( mimplies
% 1.56/1.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.56/1.39 ( ( A @ W )
% 1.56/1.39 => ( B @ W ) ) ) ) ).
% 1.56/1.39
% 1.56/1.39 thf(mequiv_def,definition,
% 1.56/1.39 ( mequiv
% 1.56/1.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.56/1.39 ( ( A @ W )
% 1.56/1.39 <=> ( B @ W ) ) ) ) ).
% 1.56/1.39
% 1.56/1.39 thf(mbox_type,type,
% 1.56/1.39 mbox: ( mworld > $o ) > mworld > $o ).
% 1.56/1.39
% 1.56/1.39 thf(mbox_def,definition,
% 1.56/1.39 ( mbox
% 1.56/1.39 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.56/1.39 ! [V: mworld] :
% 1.56/1.39 ( ( mrel @ W @ V )
% 1.56/1.39 => ( Phi @ V ) ) ) ) ).
% 1.56/1.39
% 1.56/1.39 thf(mdia_type,type,
% 1.56/1.39 mdia: ( mworld > $o ) > mworld > $o ).
% 1.56/1.39
% 1.56/1.39 thf(mdia_def,definition,
% 1.56/1.39 ( mdia
% 1.56/1.39 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.56/1.39 ? [V: mworld] :
% 1.56/1.39 ( ( mrel @ W @ V )
% 1.56/1.39 & ( Phi @ V ) ) ) ) ).
% 1.56/1.39
% 1.56/1.39 thf(mrel_reflexive,axiom,
% 1.56/1.39 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.56/1.39
% 1.56/1.39 thf(p_decl,type,
% 1.56/1.39 p: mworld > $o ).
% 1.56/1.39
% 1.56/1.39 thf(q_decl,type,
% 1.56/1.39 q: mworld > $o ).
% 1.56/1.39
% 1.56/1.39 thf(con,conjecture,
% 1.56/1.39 mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) ).
% 1.56/1.39 ------------------------
% 1.76/1.41 % (7126)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_7025 for (2999ds/2Mi)
% 1.76/1.41 % (7125)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7025 for (2999ds/2Mi)
% 1.76/1.41 % (7124)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_7025 for (2999ds/27Mi)
% 1.76/1.41 % (7123)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_7025 for (2999ds/4Mi)
% 1.76/1.41 % (7122)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7025 for (2999ds/183Mi)
% 1.76/1.41 % (7127)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_7025 for (2999ds/275Mi)
% 1.76/1.41 % (7128)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7025 for (2999ds/18Mi)
% 1.76/1.42 % (7125)Instruction limit reached!
% 1.76/1.42 % (7125)------------------------------
% 1.76/1.42 % (7125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.42 % (7125)Termination reason: Unknown
% 1.76/1.42 % (7126)Instruction limit reached!
% 1.76/1.42 % (7126)------------------------------
% 1.76/1.42 % (7126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.42 % (7126)Termination reason: Unknown
% 1.76/1.42 % (7126)Termination phase: Property scanning
% 1.76/1.42
% 1.76/1.42 % (7126)Memory used [KB]: 1023
% 1.76/1.42 % (7126)Time elapsed: 0.003 s
% 1.76/1.42 % (7126)Instructions burned: 3 (million)
% 1.76/1.42 % (7126)------------------------------
% 1.76/1.42 % (7126)------------------------------
% 1.76/1.42 % (7125)Termination phase: Property scanning
% 1.76/1.42
% 1.76/1.42 % (7125)Memory used [KB]: 1023
% 1.76/1.42 % (7125)Time elapsed: 0.003 s
% 1.76/1.42 % (7125)Instructions burned: 3 (million)
% 1.76/1.42 % (7125)------------------------------
% 1.76/1.42 % (7125)------------------------------
% 1.76/1.42 % (7127)Refutation not found, incomplete strategy
% 1.76/1.42 % (7127)------------------------------
% 1.76/1.42 % (7127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.42 % (7127)Termination reason: Refutation not found, incomplete strategy
% 1.76/1.42
% 1.76/1.42
% 1.76/1.42 % (7127)Memory used [KB]: 5500
% 1.76/1.42 % (7123)Instruction limit reached!
% 1.76/1.42 % (7123)------------------------------
% 1.76/1.42 % (7123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.42 % (7127)Time elapsed: 0.003 s
% 1.76/1.42 % (7127)Instructions burned: 3 (million)
% 1.76/1.42 % (7127)------------------------------
% 1.76/1.42 % (7127)------------------------------
% 1.76/1.42 % (7123)Termination reason: Unknown
% 1.76/1.42 % (7123)Termination phase: Saturation
% 1.76/1.42
% 1.76/1.42 % (7123)Memory used [KB]: 5500
% 1.76/1.42 % (7123)Time elapsed: 0.004 s
% 1.76/1.42 % (7123)Instructions burned: 4 (million)
% 1.76/1.42 % (7123)------------------------------
% 1.76/1.42 % (7123)------------------------------
% 1.76/1.42 % (7122)First to succeed.
% 1.76/1.42 % (7124)Also succeeded, but the first one will report.
% 1.76/1.42 % (7122)Refutation found. Thanks to Tanya!
% 1.76/1.42 % SZS status Theorem for DTF2THF_7025
% 1.76/1.42 % SZS output start Proof for DTF2THF_7025
% 1.76/1.42 thf(type_def_5, type, mworld: $tType).
% 1.76/1.42 thf(func_def_0, type, mworld: $tType).
% 1.76/1.42 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.76/1.42 thf(func_def_2, type, mactual: mworld).
% 1.76/1.42 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.76/1.42 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.76/1.42 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.76/1.42 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.76/1.42 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.76/1.42 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.76/1.42 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.76/1.42 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.76/1.42 thf(func_def_12, type, p: mworld > $o).
% 1.76/1.42 thf(func_def_13, type, q: mworld > $o).
% 1.76/1.42 thf(func_def_28, type, sK1: mworld).
% 1.76/1.42 thf(f104,plain,(
% 1.76/1.42 $false),
% 1.76/1.42 inference(avatar_sat_refutation,[status(thm)],[f70,f84,f103])).
% 1.76/1.42 thf(f103,plain,(
% 1.76/1.42 ~spl0_1),
% 1.76/1.42 inference(avatar_contradiction_clause,[status(thm)],[f102])).
% 1.76/1.42 thf(f102,plain,(
% 1.76/1.42 $false | ~spl0_1),
% 1.76/1.42 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.76/1.42 thf(f98,plain,(
% 1.76/1.42 ($true = $false) | ~spl0_1),
% 1.76/1.42 inference(superposition,[status(thm)],[f97,f92])).
% 1.76/1.42 thf(f92,plain,(
% 1.76/1.42 ((q @ sK1) = $false)),
% 1.76/1.42 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.76/1.42 thf(f89,plain,(
% 1.76/1.42 ((q @ sK1) = $false) | ($true = $false)),
% 1.76/1.42 inference(superposition,[status(thm)],[f49,f62])).
% 1.76/1.42 thf(f62,plain,(
% 1.76/1.42 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (q @ X1))) )),
% 1.76/1.42 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.76/1.42 thf(f61,plain,(
% 1.76/1.42 ( ! [X1 : mworld] : ((((q @ X1) & (mrel @ mactual @ X1)) = $false)) )),
% 1.76/1.42 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.76/1.42 thf(f60,plain,(
% 1.76/1.42 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((q @ Y0) & (mrel @ mactual @ Y0))) @ X1) = $false)) )),
% 1.76/1.42 inference(pi_clausification,[status(thm)],[f55])).
% 1.76/1.42 thf(f55,plain,(
% 1.76/1.42 ($false = (?? @ mworld @ (^[Y0 : mworld]: ((q @ Y0) & (mrel @ mactual @ Y0)))))),
% 1.76/1.42 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.76/1.42 thf(f45,plain,(
% 1.76/1.42 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0)))) => (?? @ mworld @ (^[Y0 : mworld]: ((q @ Y0) & (mrel @ mactual @ Y0))))) = $false)),
% 1.76/1.42 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.76/1.42 thf(f44,plain,(
% 1.76/1.42 (((?? @ mworld @ (^[Y0 : mworld]: (((p @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1))))) & (mrel @ mactual @ Y0)))) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0)))) => (?? @ mworld @ (^[Y0 : mworld]: ((q @ Y0) & (mrel @ mactual @ Y0)))))) != $true)),
% 1.76/1.42 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.76/1.42 thf(f43,plain,(
% 1.76/1.42 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ p @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ q))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ p) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ q)))))),
% 1.76/1.42 inference(definition_unfolding,[status(thm)],[f36,f42,f37,f41,f37,f33,f37,f33,f41])).
% 1.76/1.42 thf(f33,plain,(
% 1.76/1.42 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.76/1.42 inference(cnf_transformation,[status(thm)],[f24])).
% 1.76/1.42 thf(f24,plain,(
% 1.76/1.42 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.76/1.42 inference(fool_elimination,[status(thm)],[f23])).
% 1.76/1.42 thf(f23,plain,(
% 1.76/1.42 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 1.76/1.42 inference(rectify,[status(thm)],[f7])).
% 1.76/1.42 thf(f7,axiom,(
% 1.76/1.42 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 1.76/1.42 file('/export/starexec/sandbox2/tmp/tmp.P7EKUgqaKq/DTF2THF_7025.p',mbox_def)).
% 1.76/1.42 thf(f41,plain,(
% 1.76/1.42 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 1.76/1.42 inference(cnf_transformation,[status(thm)],[f30])).
% 1.76/1.42 thf(f30,plain,(
% 1.76/1.42 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 1.76/1.42 inference(fool_elimination,[status(thm)],[f29])).
% 1.76/1.42 thf(f29,plain,(
% 1.76/1.42 (mdia = (^[X0 : mworld > $o, X1 : mworld] : (? [X2 : mworld] : ((mrel @ X1 @ X2) & (X0 @ X2)))))),
% 1.76/1.42 inference(rectify,[status(thm)],[f8])).
% 1.76/1.42 thf(f8,axiom,(
% 1.76/1.42 (mdia = (^[X0 : mworld > $o, X2 : mworld] : (? [X4 : mworld] : ((mrel @ X2 @ X4) & (X0 @ X4)))))),
% 1.76/1.42 file('/export/starexec/sandbox2/tmp/tmp.P7EKUgqaKq/DTF2THF_7025.p',mdia_def)).
% 1.76/1.42 thf(f37,plain,(
% 1.76/1.42 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.76/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.76/1.42 thf(f18,plain,(
% 1.76/1.42 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.76/1.42 inference(fool_elimination,[status(thm)],[f17])).
% 1.76/1.42 thf(f17,plain,(
% 1.76/1.42 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.76/1.42 inference(rectify,[status(thm)],[f5])).
% 1.76/1.42 thf(f5,axiom,(
% 1.76/1.42 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.76/1.42 file('/export/starexec/sandbox2/tmp/tmp.P7EKUgqaKq/DTF2THF_7025.p',mimplies_def)).
% 1.76/1.42 thf(f42,plain,(
% 1.76/1.42 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.76/1.42 inference(cnf_transformation,[status(thm)],[f31])).
% 1.76/1.42 thf(f31,plain,(
% 1.76/1.42 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.76/1.42 inference(fool_elimination,[status(thm)],[f1])).
% 1.76/1.42 thf(f1,axiom,(
% 1.76/1.42 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.76/1.42 file('/export/starexec/sandbox2/tmp/tmp.P7EKUgqaKq/DTF2THF_7025.p',mlocal_def)).
% 1.76/1.42 thf(f36,plain,(
% 1.76/1.42 ((mlocal @ (mimplies @ (mdia @ (mimplies @ p @ (mbox @ q))) @ (mimplies @ (mbox @ p) @ (mdia @ q)))) != $true)),
% 1.76/1.42 inference(cnf_transformation,[status(thm)],[f32])).
% 1.76/1.42 thf(f32,plain,(
% 1.76/1.42 ((mlocal @ (mimplies @ (mdia @ (mimplies @ p @ (mbox @ q))) @ (mimplies @ (mbox @ p) @ (mdia @ q)))) != $true)),
% 1.76/1.42 inference(flattening,[status(thm)],[f28])).
% 1.76/1.42 thf(f28,plain,(
% 1.76/1.42 ~((mlocal @ (mimplies @ (mdia @ (mimplies @ p @ (mbox @ q))) @ (mimplies @ (mbox @ p) @ (mdia @ q)))) = $true)),
% 1.76/1.42 inference(fool_elimination,[status(thm)],[f27])).
% 1.76/1.42 thf(f27,plain,(
% 1.76/1.42 ~(mlocal @ (mimplies @ (mdia @ (mimplies @ p @ (mbox @ q))) @ (mimplies @ (mbox @ p) @ (mdia @ q))))),
% 1.76/1.42 inference(rectify,[status(thm)],[f11])).
% 1.76/1.42 thf(f11,negated_conjecture,(
% 1.76/1.42 ~(mlocal @ (mimplies @ (mdia @ (mimplies @ p @ (mbox @ q))) @ (mimplies @ (mbox @ p) @ (mdia @ q))))),
% 1.76/1.42 inference(negated_conjecture,[status(cth)],[f10])).
% 1.76/1.42 thf(f10,conjecture,(
% 1.76/1.42 (mlocal @ (mimplies @ (mdia @ (mimplies @ p @ (mbox @ q))) @ (mimplies @ (mbox @ p) @ (mdia @ q))))),
% 1.76/1.42 file('/export/starexec/sandbox2/tmp/tmp.P7EKUgqaKq/DTF2THF_7025.p',con)).
% 1.76/1.42 thf(f49,plain,(
% 1.76/1.42 ($true = (mrel @ mactual @ sK1))),
% 1.76/1.42 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.76/1.42 thf(f48,plain,(
% 1.76/1.42 ((((p @ sK1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0))))) & (mrel @ mactual @ sK1)) = $true)),
% 1.76/1.42 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.76/1.42 thf(f47,plain,(
% 1.76/1.42 (((^[Y0 : mworld]: (((p @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1))))) & (mrel @ mactual @ Y0))) @ sK1) = $true)),
% 1.76/1.42 inference(sigma_clausification,[status(thm)],[f46])).
% 1.76/1.42 thf(f46,plain,(
% 1.76/1.42 ($true = (?? @ mworld @ (^[Y0 : mworld]: (((p @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1))))) & (mrel @ mactual @ Y0)))))),
% 1.76/1.42 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.76/1.42 thf(f97,plain,(
% 1.76/1.42 ($true = (q @ sK1)) | ~spl0_1),
% 1.76/1.42 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.76/1.42 thf(f94,plain,(
% 1.76/1.42 ($true = $false) | ($true = (q @ sK1)) | ~spl0_1),
% 1.76/1.42 inference(superposition,[status(thm)],[f65,f39])).
% 1.76/1.42 thf(f39,plain,(
% 1.76/1.42 ( ! [X0 : mworld] : (($true = (mrel @ X0 @ X0))) )),
% 1.76/1.42 inference(cnf_transformation,[status(thm)],[f26])).
% 1.76/1.42 thf(f26,plain,(
% 1.76/1.42 ! [X0 : mworld] : ($true = (mrel @ X0 @ X0))),
% 1.76/1.42 inference(fool_elimination,[status(thm)],[f25])).
% 1.76/1.42 thf(f25,plain,(
% 1.76/1.42 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 1.76/1.42 inference(rectify,[status(thm)],[f9])).
% 1.76/1.42 thf(f9,axiom,(
% 1.76/1.42 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 1.76/1.42 file('/export/starexec/sandbox2/tmp/tmp.P7EKUgqaKq/DTF2THF_7025.p',mrel_reflexive)).
% 1.76/1.42 thf(f65,plain,(
% 1.76/1.42 ( ! [X1 : mworld] : (((mrel @ sK1 @ X1) = $false) | ($true = (q @ X1))) ) | ~spl0_1),
% 1.76/1.42 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.76/1.42 thf(f64,definition,(
% 1.76/1.42 spl0_1 <=> ! [X1 : mworld] : (($true = (q @ X1)) | ((mrel @ sK1 @ X1) = $false))),
% 1.76/1.42 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.76/1.42 thf(f84,plain,(
% 1.76/1.42 ~spl0_2),
% 1.76/1.42 inference(avatar_contradiction_clause,[status(thm)],[f83])).
% 1.76/1.42 thf(f83,plain,(
% 1.76/1.42 $false | ~spl0_2),
% 1.76/1.42 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.76/1.42 thf(f80,plain,(
% 1.76/1.42 ($true = $false) | ~spl0_2),
% 1.76/1.42 inference(superposition,[status(thm)],[f69,f77])).
% 1.76/1.42 thf(f77,plain,(
% 1.76/1.42 ($true = (p @ sK1))),
% 1.76/1.42 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.76/1.42 thf(f72,plain,(
% 1.76/1.42 ($true = $false) | ($true = (p @ sK1))),
% 1.76/1.42 inference(superposition,[status(thm)],[f59,f49])).
% 1.76/1.42 thf(f59,plain,(
% 1.76/1.42 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((p @ X1) = $true)) )),
% 1.76/1.42 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.76/1.42 thf(f58,plain,(
% 1.76/1.42 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (p @ X1)))) )),
% 1.76/1.42 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.76/1.42 thf(f57,plain,(
% 1.76/1.42 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0))) @ X1))) )),
% 1.76/1.42 inference(pi_clausification,[status(thm)],[f56])).
% 1.76/1.42 thf(f56,plain,(
% 1.76/1.42 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0)))))),
% 1.76/1.42 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.76/1.42 thf(f69,plain,(
% 1.76/1.42 ((p @ sK1) = $false) | ~spl0_2),
% 1.76/1.42 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.76/1.42 thf(f67,definition,(
% 1.76/1.42 spl0_2 <=> ((p @ sK1) = $false)),
% 1.76/1.42 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.76/1.42 thf(f70,plain,(
% 1.76/1.42 spl0_1 | spl0_2),
% 1.76/1.42 inference(avatar_split_clause,[status(thm)],[f54,f67,f64])).
% 1.76/1.42 thf(f54,plain,(
% 1.76/1.42 ( ! [X1 : mworld] : (((p @ sK1) = $false) | ($true = (q @ X1)) | ((mrel @ sK1 @ X1) = $false)) )),
% 1.76/1.42 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.76/1.42 thf(f53,plain,(
% 1.76/1.42 ( ! [X1 : mworld] : (($true = ((mrel @ sK1 @ X1) => (q @ X1))) | ((p @ sK1) = $false)) )),
% 1.76/1.42 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.76/1.42 thf(f52,plain,(
% 1.76/1.42 ( ! [X1 : mworld] : (((p @ sK1) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0))) @ X1))) )),
% 1.76/1.42 inference(pi_clausification,[status(thm)],[f51])).
% 1.76/1.42 thf(f51,plain,(
% 1.76/1.42 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0)))) = $true) | ((p @ sK1) = $false)),
% 1.76/1.42 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.76/1.42 thf(f50,plain,(
% 1.76/1.42 (((p @ sK1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0))))) = $true)),
% 1.76/1.42 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.76/1.42 % SZS output end Proof for DTF2THF_7025
% 1.76/1.42 % (7122)------------------------------
% 1.76/1.42 % (7122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.42 % (7122)Termination reason: Refutation
% 1.76/1.42
% 1.76/1.42 % (7122)Memory used [KB]: 5500
% 1.76/1.42 % (7122)Time elapsed: 0.007 s
% 1.76/1.42 % (7122)Instructions burned: 5 (million)
% 1.76/1.42 % (7122)------------------------------
% 1.76/1.42 % (7122)------------------------------
% 1.76/1.42 % (7121)Success in time 0.021 s
%------------------------------------------------------------------------------