%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NLP267^2 : 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 : n014.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 09:22:26 AM UTC 2026
% Result : Theorem 1.74s 1.38s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 79 ( 48 unt; 0 typ; 3 def)
% Number of atoms : 418 ( 77 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 396 ( 19 ~; 26 |; 10 &; 299 @)
% ( 3 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 11 con; 0-3 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 80 ( 67 ^; 13 !; 0 ?; 80 :)
% 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_17,type,
price: $i > mworld > $o ).
thf(func_def_18,type,
dest: $i > mworld > $o ).
thf(func_def_19,type,
class: $i > mworld > $o ).
thf(func_def_34,type,
sK1: mworld ).
thf(f253,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f217,f238,f245,f252]) ).
thf(f252,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[status(thm)],[f251]) ).
thf(f251,plain,
( $false
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f247]) ).
thf(f247,plain,
( ( $false = $true )
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f215,f87]) ).
thf(f87,plain,
( $false
= ( price @ seventy @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( ( ( mrel @ mactual @ sK1 )
=> ( price @ seventy @ sK1 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( price @ seventy ) ) ) ),
inference(definition_unfolding,[status(thm)],[f63,f65,f55]) ).
thf(f55,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f46]) ).
thf(f46,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',mbox_def) ).
thf(f65,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f45,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',mlocal_def) ).
thf(f63,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f50,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,negated_conjecture,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f16,conjecture,
mlocal @ ( mbox @ ( price @ seventy ) ),
file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',con) ).
thf(f215,plain,
( ( ( price @ seventy @ sK1 )
= $true )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f213]) ).
thf(f213,definition,
( spl0_10
<=> ( ( price @ seventy @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f245,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[status(thm)],[f244]) ).
thf(f244,plain,
( $false
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f240]) ).
thf(f240,plain,
( ( $false = $true )
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f211,f125]) ).
thf(f125,plain,
( ( dest @ paris @ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $false = $true )
| ( ( dest @ paris @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f88,f92]) ).
thf(f92,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( dest @ paris @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( dest @ paris @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f90]) ).
thf(f90,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( dest @ paris ) ) ) ),
inference(definition_unfolding,[status(thm)],[f54,f65,f55]) ).
thf(f54,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f41]) ).
thf(f41,plain,
mlocal @ ( mbox @ ( dest @ paris ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
mlocal @ ( mbox @ ( dest @ paris ) ),
file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',belief1) ).
thf(f88,plain,
( ( mrel @ mactual @ sK1 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f86]) ).
thf(f211,plain,
( ( $false
= ( dest @ paris @ sK1 ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f209]) ).
thf(f209,definition,
( spl0_9
<=> ( $false
= ( dest @ paris @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f238,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f237]) ).
thf(f237,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f233]) ).
thf(f233,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f138,f117]) ).
thf(f117,plain,
( ( class @ second @ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
( ( ( class @ second @ sK1 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f77,f88]) ).
thf(f77,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( class @ second @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( class @ second @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( class @ second ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f62,f65,f55]) ).
thf(f62,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f31]) ).
thf(f31,plain,
mlocal @ ( mbox @ ( class @ second ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
mlocal @ ( mbox @ ( class @ second ) ),
file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',belief2) ).
thf(f138,plain,
( ( $false
= ( class @ second @ sK1 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f136]) ).
thf(f136,definition,
( spl0_1
<=> ( $false
= ( class @ second @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f217,plain,
( spl0_9
| spl0_1
| spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f192,f213,f136,f209]) ).
thf(f192,plain,
( ( $false
= ( dest @ paris @ sK1 ) )
| ( ( price @ seventy @ sK1 )
= $true )
| ( $false
= ( class @ second @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f188]) ).
thf(f188,plain,
( ( $false = $true )
| ( ( price @ seventy @ sK1 )
= $true )
| ( $false
= ( class @ second @ sK1 ) )
| ( $false
= ( dest @ paris @ sK1 ) ) ),
inference(superposition,[status(thm)],[f104,f88]) ).
thf(f104,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( price @ seventy @ X1 )
= $true )
| ( $false
= ( dest @ paris @ X1 ) )
| ( ( class @ second @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X1: mworld] :
( ( ( price @ seventy @ X1 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( class @ second @ X1 )
& ( dest @ paris @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( ( class @ second @ X1 )
& ( dest @ paris @ X1 ) )
=> ( price @ seventy @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( ( class @ second @ X1 )
& ( dest @ paris @ X1 ) )
=> ( price @ seventy @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f100]) ).
thf(f100,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( class @ second @ Y0 )
& ( dest @ paris @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( class @ second @ Y0 )
& ( dest @ paris @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( dest @ paris )
@ ( class @ second ) )
@ ( price @ seventy ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f59,f65,f55,f64,f60]) ).
thf(f60,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,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.1rDyWn3FMy/DTF2THF_19128.p',mand_def) ).
thf(f64,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f33]) ).
thf(f33,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.1rDyWn3FMy/DTF2THF_19128.p',mimplies_def) ).
thf(f59,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f27]) ).
thf(f27,plain,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',law2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NLP267^2 : 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
% 0.15/0.34 % Computer : n014.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 10:54:42 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : NLP267^2 : TPTP v9.2.1. Released v8.1.0.
% 0.30/0.46 % Domain : Natural Language Processing
% 0.30/0.46 % Problem : Ticket example
% 0.30/0.46 % Version : [BP13] axioms.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [FH+98] Farinas del Cerro et al. (1998), Belief Reconstruction
% 0.30/0.46 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.30/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.30/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.30/0.46 % Source : [TPTP]
% 0.30/0.46 % Names : APM001+1 [QMLTP]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.30/0.46 % Syntax : Number of formulae : 35 ( 9 unt; 19 typ; 8 def)
% 0.30/0.46 % Number of atoms : 54 ( 8 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 7 ( 3 avg)
% 0.30/0.46 % Number of connectives : 66 ( 1 ~; 1 |; 2 &; 59 @)
% 0.30/0.46 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 8 ( 3 avg)
% 0.30/0.46 % Number of types : 3 ( 1 usr)
% 0.30/0.46 % Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 19 ( 18 usr; 6 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 22 ( 19 ^; 2 !; 1 ?; 22 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.30/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.30/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.30/0.46 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.30/0.46 % $modalities == $modal_system_T].
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(mworld,type,
% 0.30/0.46 mworld: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(mrel_type,type,
% 0.30/0.46 mrel: mworld > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mactual_type,type,
% 0.30/0.46 mactual: mworld ).
% 0.30/0.46
% 0.30/0.46 thf(mlocal_type,type,
% 0.30/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mlocal_def,definition,
% 0.30/0.46 ( mlocal
% 0.30/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mnot_type,type,
% 0.30/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mand_type,type,
% 0.30/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mor_type,type,
% 0.30/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mimplies_type,type,
% 0.30/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mequiv_type,type,
% 0.30/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mnot_def,definition,
% 0.30/0.46 ( mnot
% 0.30/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.30/0.46 ~ ( A @ W ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mand_def,definition,
% 0.30/0.46 ( mand
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 & ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mor_def,definition,
% 0.30/0.46 ( mor
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 | ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mimplies_def,definition,
% 0.30/0.46 ( mimplies
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 => ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mequiv_def,definition,
% 0.30/0.46 ( mequiv
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 <=> ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mbox_type,type,
% 0.30/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mbox_def,definition,
% 0.30/0.46 ( mbox
% 0.30/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.46 ! [V: mworld] :
% 0.30/0.46 ( ( mrel @ W @ V )
% 0.30/0.46 => ( Phi @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mdia_type,type,
% 0.30/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mdia_def,definition,
% 0.30/0.46 ( mdia
% 0.30/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.46 ? [V: mworld] :
% 0.30/0.46 ( ( mrel @ W @ V )
% 0.30/0.46 & ( Phi @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mrel_reflexive,axiom,
% 0.30/0.46 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.30/0.46
% 0.30/0.46 thf(seventy_decl,type,
% 0.30/0.46 seventy: $i ).
% 0.30/0.46
% 0.30/0.46 thf(ninetyfive_decl,type,
% 0.30/0.46 ninetyfive: $i ).
% 0.30/0.46
% 0.30/0.46 thf(second_decl,type,
% 0.30/0.46 second: $i ).
% 0.30/0.46
% 0.30/0.46 thf(paris_decl,type,
% 0.30/0.46 paris: $i ).
% 0.30/0.46
% 0.30/0.46 thf(first_decl,type,
% 0.30/0.46 first: $i ).
% 0.30/0.46
% 0.30/0.46 thf(price_decl,type,
% 0.30/0.46 price: $i > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(dest_decl,type,
% 0.30/0.46 dest: $i > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(class_decl,type,
% 0.30/0.46 class: $i > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(law1,axiom,
% 0.30/0.46 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(law2,axiom,
% 0.30/0.46 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(law3,axiom,
% 0.30/0.46 mlocal @ ( mbox @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(law4,axiom,
% 0.30/0.46 mlocal @ ( mbox @ ( mnot @ ( mand @ ( price @ ninetyfive ) @ ( price @ seventy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(belief1,axiom,
% 0.30/0.46 mlocal @ ( mbox @ ( dest @ paris ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(belief2,axiom,
% 0.30/0.46 mlocal @ ( mbox @ ( class @ second ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(con,conjecture,
% 0.30/0.46 mlocal @ ( mbox @ ( price @ seventy ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.74/1.35 ---- Embedded in THF ---
% 1.74/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.74/1.35 %%% Generated on Tue Feb 24 10:54:43 EST 2026
% 1.74/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.74/1.35 %%% Logic specification used:
% 1.74/1.35 %%% thf(spec, logic, $$dhol).
% 1.74/1.35
% 1.74/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2DTF19128.p
% See solution above
% 1.74/1.35 ------------------------
% 1.74/1.36 ---- Cleaned THF ---
% 1.74/1.36 thf(mworld,type,
% 1.74/1.36 mworld: $tType ).
% 1.74/1.36
% 1.74/1.36 thf(mrel_type,type,
% 1.74/1.36 mrel: mworld > mworld > $o ).
% 1.74/1.36
% 1.74/1.36 thf(mactual_type,type,
% 1.74/1.36 mactual: mworld ).
% 1.74/1.36
% 1.74/1.36 thf(mlocal_type,type,
% 1.74/1.36 mlocal: ( mworld > $o ) > $o ).
% 1.74/1.36
% 1.74/1.36 thf(mlocal_def,definition,
% 1.74/1.36 ( mlocal
% 1.74/1.36 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(mnot_type,type,
% 1.74/1.36 mnot: ( mworld > $o ) > mworld > $o ).
% 1.74/1.36
% 1.74/1.36 thf(mand_type,type,
% 1.74/1.36 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.74/1.36
% 1.74/1.36 thf(mor_type,type,
% 1.74/1.36 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.74/1.36
% 1.74/1.36 thf(mimplies_type,type,
% 1.74/1.36 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.74/1.36
% 1.74/1.36 thf(mequiv_type,type,
% 1.74/1.36 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.74/1.36
% 1.74/1.36 thf(mnot_def,definition,
% 1.74/1.36 ( mnot
% 1.74/1.36 = ( ^ [A: mworld > $o,W: mworld] :
% 1.74/1.36 ~ ( A @ W ) ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(mand_def,definition,
% 1.74/1.36 ( mand
% 1.74/1.36 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.74/1.36 ( ( A @ W )
% 1.74/1.36 & ( B @ W ) ) ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(mor_def,definition,
% 1.74/1.36 ( mor
% 1.74/1.36 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.74/1.36 ( ( A @ W )
% 1.74/1.36 | ( B @ W ) ) ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(mimplies_def,definition,
% 1.74/1.36 ( mimplies
% 1.74/1.36 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.74/1.36 ( ( A @ W )
% 1.74/1.36 => ( B @ W ) ) ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(mequiv_def,definition,
% 1.74/1.36 ( mequiv
% 1.74/1.36 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.74/1.36 ( ( A @ W )
% 1.74/1.36 <=> ( B @ W ) ) ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(mbox_type,type,
% 1.74/1.36 mbox: ( mworld > $o ) > mworld > $o ).
% 1.74/1.36
% 1.74/1.36 thf(mbox_def,definition,
% 1.74/1.36 ( mbox
% 1.74/1.36 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.74/1.36 ! [V: mworld] :
% 1.74/1.36 ( ( mrel @ W @ V )
% 1.74/1.36 => ( Phi @ V ) ) ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(mdia_type,type,
% 1.74/1.36 mdia: ( mworld > $o ) > mworld > $o ).
% 1.74/1.36
% 1.74/1.36 thf(mdia_def,definition,
% 1.74/1.36 ( mdia
% 1.74/1.36 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.74/1.36 ? [V: mworld] :
% 1.74/1.36 ( ( mrel @ W @ V )
% 1.74/1.36 & ( Phi @ V ) ) ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(mrel_reflexive,axiom,
% 1.74/1.36 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.74/1.36
% 1.74/1.36 thf(seventy_decl,type,
% 1.74/1.36 seventy: $i ).
% 1.74/1.36
% 1.74/1.36 thf(ninetyfive_decl,type,
% 1.74/1.36 ninetyfive: $i ).
% 1.74/1.36
% 1.74/1.36 thf(second_decl,type,
% 1.74/1.36 second: $i ).
% 1.74/1.36
% 1.74/1.36 thf(paris_decl,type,
% 1.74/1.36 paris: $i ).
% 1.74/1.36
% 1.74/1.36 thf(first_decl,type,
% 1.74/1.36 first: $i ).
% 1.74/1.36
% 1.74/1.36 thf(price_decl,type,
% 1.74/1.36 price: $i > mworld > $o ).
% 1.74/1.36
% 1.74/1.36 thf(dest_decl,type,
% 1.74/1.36 dest: $i > mworld > $o ).
% 1.74/1.36
% 1.74/1.36 thf(class_decl,type,
% 1.74/1.36 class: $i > mworld > $o ).
% 1.74/1.36
% 1.74/1.36 thf(law1,axiom,
% 1.74/1.36 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(law2,axiom,
% 1.74/1.36 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(law3,axiom,
% 1.74/1.36 mlocal @ ( mbox @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(law4,axiom,
% 1.74/1.36 mlocal @ ( mbox @ ( mnot @ ( mand @ ( price @ ninetyfive ) @ ( price @ seventy ) ) ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(belief1,axiom,
% 1.74/1.36 mlocal @ ( mbox @ ( dest @ paris ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(belief2,axiom,
% 1.74/1.36 mlocal @ ( mbox @ ( class @ second ) ) ).
% 1.74/1.36
% 1.74/1.36 thf(con,conjecture,
% 1.74/1.36 mlocal @ ( mbox @ ( price @ seventy ) ) ).
% 1.74/1.36 ------------------------
% 1.74/1.38 % (19317)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19128 for (2999ds/183Mi)
% 1.74/1.38 % (19319)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_19128 for (2999ds/27Mi)
% 1.74/1.38 % (19318)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_19128 for (2999ds/4Mi)
% 1.74/1.38 % (19317)First to succeed.
% 1.74/1.38 % (19318)Instruction limit reached!
% 1.74/1.38 % (19318)------------------------------
% 1.74/1.38 % (19318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.38 % (19318)Termination reason: Unknown
% 1.74/1.38 % (19318)Termination phase: Saturation
% 1.74/1.38
% 1.74/1.38 % (19318)Memory used [KB]: 1023
% 1.74/1.38 % (19318)Time elapsed: 0.003 s
% 1.74/1.38 % (19318)Instructions burned: 4 (million)
% 1.74/1.38 % (19318)------------------------------
% 1.74/1.38 % (19318)------------------------------
% 1.74/1.38 % (19317)Refutation found. Thanks to Tanya!
% 1.74/1.38 % SZS status Theorem for DTF2THF_19128
% 1.74/1.38 % SZS output start Proof for DTF2THF_19128
% 1.74/1.38 thf(type_def_5, type, mworld: $tType).
% 1.74/1.38 thf(func_def_0, type, mworld: $tType).
% 1.74/1.38 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.74/1.38 thf(func_def_2, type, mactual: mworld).
% 1.74/1.38 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.74/1.38 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.74/1.38 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.74/1.38 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.74/1.38 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.74/1.38 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.74/1.38 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.74/1.38 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.74/1.38 thf(func_def_17, type, price: $i > mworld > $o).
% 1.74/1.38 thf(func_def_18, type, dest: $i > mworld > $o).
% 1.74/1.38 thf(func_def_19, type, class: $i > mworld > $o).
% 1.74/1.38 thf(func_def_34, type, sK1: mworld).
% 1.74/1.38 thf(f253,plain,(
% 1.74/1.38 $false),
% 1.74/1.38 inference(avatar_sat_refutation,[status(thm)],[f217,f238,f245,f252])).
% 1.74/1.38 thf(f252,plain,(
% 1.74/1.38 ~spl0_10),
% 1.74/1.38 inference(avatar_contradiction_clause,[status(thm)],[f251])).
% 1.74/1.38 thf(f251,plain,(
% 1.74/1.38 $false | ~spl0_10),
% 1.74/1.38 inference(trivial_inequality_removal,[status(thm)],[f247])).
% 1.74/1.38 thf(f247,plain,(
% 1.74/1.38 ($false = $true) | ~spl0_10),
% 1.74/1.38 inference(superposition,[status(thm)],[f215,f87])).
% 1.74/1.38 thf(f87,plain,(
% 1.74/1.38 ($false = (price @ seventy @ sK1))),
% 1.74/1.38 inference(binary_proxy_clausification,[status(thm)],[f86])).
% 1.74/1.38 thf(f86,plain,(
% 1.74/1.38 (((mrel @ mactual @ sK1) => (price @ seventy @ sK1)) = $false)),
% 1.74/1.38 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.74/1.38 thf(f85,plain,(
% 1.74/1.38 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (price @ seventy @ Y0))) @ sK1))),
% 1.74/1.38 inference(sigma_clausification,[status(thm)],[f84])).
% 1.74/1.38 thf(f84,plain,(
% 1.74/1.38 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (price @ seventy @ Y0)))) != $true)),
% 1.74/1.38 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.74/1.38 thf(f73,plain,(
% 1.74/1.38 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (price @ seventy))))),
% 1.74/1.38 inference(definition_unfolding,[status(thm)],[f63,f65,f55])).
% 1.74/1.38 thf(f55,plain,(
% 1.74/1.38 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.74/1.38 inference(cnf_transformation,[status(thm)],[f47])).
% 1.74/1.38 thf(f47,plain,(
% 1.74/1.38 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.74/1.38 inference(fool_elimination,[status(thm)],[f46])).
% 1.74/1.38 thf(f46,plain,(
% 1.74/1.38 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 1.74/1.38 inference(rectify,[status(thm)],[f7])).
% 1.74/1.38 thf(f7,axiom,(
% 1.74/1.38 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 1.74/1.38 file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',mbox_def)).
% 1.74/1.38 thf(f65,plain,(
% 1.74/1.38 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.74/1.38 inference(cnf_transformation,[status(thm)],[f45])).
% 1.74/1.38 thf(f45,plain,(
% 1.74/1.38 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.74/1.38 inference(fool_elimination,[status(thm)],[f1])).
% 1.74/1.38 thf(f1,axiom,(
% 1.74/1.38 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.74/1.38 file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',mlocal_def)).
% 1.74/1.38 thf(f63,plain,(
% 1.74/1.38 ((mlocal @ (mbox @ (price @ seventy))) != $true)),
% 1.74/1.38 inference(cnf_transformation,[status(thm)],[f50])).
% 1.74/1.38 thf(f50,plain,(
% 1.74/1.38 ((mlocal @ (mbox @ (price @ seventy))) != $true)),
% 1.74/1.38 inference(flattening,[status(thm)],[f24])).
% 1.74/1.38 thf(f24,plain,(
% 1.74/1.38 ~((mlocal @ (mbox @ (price @ seventy))) = $true)),
% 1.74/1.38 inference(fool_elimination,[status(thm)],[f23])).
% 1.74/1.38 thf(f23,plain,(
% 1.74/1.38 ~(mlocal @ (mbox @ (price @ seventy)))),
% 1.74/1.38 inference(rectify,[status(thm)],[f17])).
% 1.74/1.38 thf(f17,negated_conjecture,(
% 1.74/1.38 ~(mlocal @ (mbox @ (price @ seventy)))),
% 1.74/1.38 inference(negated_conjecture,[status(cth)],[f16])).
% 1.74/1.38 thf(f16,conjecture,(
% 1.74/1.38 (mlocal @ (mbox @ (price @ seventy)))),
% 1.74/1.38 file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',con)).
% 1.74/1.38 thf(f215,plain,(
% 1.74/1.38 ((price @ seventy @ sK1) = $true) | ~spl0_10),
% 1.74/1.38 inference(avatar_component_clause,[status(thm)],[f213])).
% 1.74/1.38 thf(f213,definition,(
% 1.74/1.38 spl0_10 <=> ((price @ seventy @ sK1) = $true)),
% 1.74/1.38 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.74/1.38 thf(f245,plain,(
% 1.74/1.38 ~spl0_9),
% 1.74/1.38 inference(avatar_contradiction_clause,[status(thm)],[f244])).
% 1.74/1.38 thf(f244,plain,(
% 1.74/1.38 $false | ~spl0_9),
% 1.74/1.38 inference(trivial_inequality_removal,[status(thm)],[f240])).
% 1.74/1.38 thf(f240,plain,(
% 1.74/1.38 ($false = $true) | ~spl0_9),
% 1.74/1.38 inference(superposition,[status(thm)],[f211,f125])).
% 1.74/1.38 thf(f125,plain,(
% 1.74/1.38 ((dest @ paris @ sK1) = $true)),
% 1.74/1.38 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.74/1.38 thf(f121,plain,(
% 1.74/1.38 ($false = $true) | ((dest @ paris @ sK1) = $true)),
% 1.74/1.38 inference(superposition,[status(thm)],[f88,f92])).
% 1.74/1.38 thf(f92,plain,(
% 1.74/1.38 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((dest @ paris @ X1) = $true)) )),
% 1.74/1.38 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 1.74/1.38 thf(f91,plain,(
% 1.74/1.38 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (dest @ paris @ X1)) = $true)) )),
% 1.74/1.38 inference(beta_eta_normalization,[status(thm)],[f90])).
% 1.74/1.38 thf(f90,plain,(
% 1.74/1.38 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (dest @ paris @ Y0))) @ X1) = $true)) )),
% 1.74/1.38 inference(pi_clausification,[status(thm)],[f89])).
% 1.74/1.38 thf(f89,plain,(
% 1.74/1.38 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (dest @ paris @ Y0)))))),
% 1.74/1.38 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.74/1.38 thf(f68,plain,(
% 1.74/1.38 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (dest @ paris))))),
% 1.74/1.38 inference(definition_unfolding,[status(thm)],[f54,f65,f55])).
% 1.74/1.38 thf(f54,plain,(
% 1.74/1.38 ((mlocal @ (mbox @ (dest @ paris))) = $true)),
% 1.74/1.38 inference(cnf_transformation,[status(thm)],[f42])).
% 1.74/1.38 thf(f42,plain,(
% 1.74/1.38 ((mlocal @ (mbox @ (dest @ paris))) = $true)),
% 1.74/1.38 inference(fool_elimination,[status(thm)],[f41])).
% 1.74/1.38 thf(f41,plain,(
% 1.74/1.38 (mlocal @ (mbox @ (dest @ paris)))),
% 1.74/1.38 inference(rectify,[status(thm)],[f14])).
% 1.74/1.38 thf(f14,axiom,(
% 1.74/1.38 (mlocal @ (mbox @ (dest @ paris)))),
% 1.74/1.38 file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',belief1)).
% 1.74/1.38 thf(f88,plain,(
% 1.74/1.38 ((mrel @ mactual @ sK1) = $true)),
% 1.74/1.38 inference(binary_proxy_clausification,[status(thm)],[f86])).
% 1.74/1.38 thf(f211,plain,(
% 1.74/1.38 ($false = (dest @ paris @ sK1)) | ~spl0_9),
% 1.74/1.38 inference(avatar_component_clause,[status(thm)],[f209])).
% 1.74/1.38 thf(f209,definition,(
% 1.74/1.38 spl0_9 <=> ($false = (dest @ paris @ sK1))),
% 1.74/1.38 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.74/1.38 thf(f238,plain,(
% 1.74/1.38 ~spl0_1),
% 1.74/1.38 inference(avatar_contradiction_clause,[status(thm)],[f237])).
% 1.74/1.38 thf(f237,plain,(
% 1.74/1.38 $false | ~spl0_1),
% 1.74/1.38 inference(trivial_inequality_removal,[status(thm)],[f233])).
% 1.74/1.38 thf(f233,plain,(
% 1.74/1.38 ($false = $true) | ~spl0_1),
% 1.74/1.38 inference(superposition,[status(thm)],[f138,f117])).
% 1.74/1.38 thf(f117,plain,(
% 1.74/1.38 ((class @ second @ sK1) = $true)),
% 1.74/1.38 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.74/1.38 thf(f111,plain,(
% 1.74/1.38 ((class @ second @ sK1) = $true) | ($false = $true)),
% 1.74/1.38 inference(superposition,[status(thm)],[f77,f88])).
% 1.74/1.38 thf(f77,plain,(
% 1.74/1.38 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((class @ second @ X1) = $true)) )),
% 1.74/1.38 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.74/1.38 thf(f76,plain,(
% 1.74/1.38 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (class @ second @ X1)) = $true)) )),
% 1.74/1.38 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.74/1.38 thf(f75,plain,(
% 1.74/1.38 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (class @ second @ Y0))) @ X1) = $true)) )),
% 1.74/1.38 inference(pi_clausification,[status(thm)],[f74])).
% 1.74/1.38 thf(f74,plain,(
% 1.74/1.38 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (class @ second @ Y0)))) = $true)),
% 1.74/1.38 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.74/1.38 thf(f72,plain,(
% 1.74/1.38 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (class @ second))) = $true)),
% 1.74/1.38 inference(definition_unfolding,[status(thm)],[f62,f65,f55])).
% 1.74/1.39 thf(f62,plain,(
% 1.74/1.39 ((mlocal @ (mbox @ (class @ second))) = $true)),
% 1.74/1.39 inference(cnf_transformation,[status(thm)],[f32])).
% 1.74/1.39 thf(f32,plain,(
% 1.74/1.39 ((mlocal @ (mbox @ (class @ second))) = $true)),
% 1.74/1.39 inference(fool_elimination,[status(thm)],[f31])).
% 1.74/1.39 thf(f31,plain,(
% 1.74/1.39 (mlocal @ (mbox @ (class @ second)))),
% 1.74/1.39 inference(rectify,[status(thm)],[f15])).
% 1.74/1.39 thf(f15,axiom,(
% 1.74/1.39 (mlocal @ (mbox @ (class @ second)))),
% 1.74/1.39 file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',belief2)).
% 1.74/1.39 thf(f138,plain,(
% 1.74/1.39 ($false = (class @ second @ sK1)) | ~spl0_1),
% 1.74/1.39 inference(avatar_component_clause,[status(thm)],[f136])).
% 1.74/1.39 thf(f136,definition,(
% 1.74/1.39 spl0_1 <=> ($false = (class @ second @ sK1))),
% 1.74/1.39 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.74/1.39 thf(f217,plain,(
% 1.74/1.39 spl0_9 | spl0_1 | spl0_10),
% 1.74/1.39 inference(avatar_split_clause,[status(thm)],[f192,f213,f136,f209])).
% 1.74/1.39 thf(f192,plain,(
% 1.74/1.39 ($false = (dest @ paris @ sK1)) | ((price @ seventy @ sK1) = $true) | ($false = (class @ second @ sK1))),
% 1.74/1.39 inference(trivial_inequality_removal,[status(thm)],[f188])).
% 1.74/1.39 thf(f188,plain,(
% 1.74/1.39 ($false = $true) | ((price @ seventy @ sK1) = $true) | ($false = (class @ second @ sK1)) | ($false = (dest @ paris @ sK1))),
% 1.74/1.39 inference(superposition,[status(thm)],[f104,f88])).
% 1.74/1.39 thf(f104,plain,(
% 1.74/1.39 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((price @ seventy @ X1) = $true) | ($false = (dest @ paris @ X1)) | ((class @ second @ X1) = $false)) )),
% 1.74/1.39 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.74/1.39 thf(f103,plain,(
% 1.74/1.39 ( ! [X1 : mworld] : (((price @ seventy @ X1) = $true) | ($false = (mrel @ mactual @ X1)) | ($false = ((class @ second @ X1) & (dest @ paris @ X1)))) )),
% 1.74/1.39 inference(binary_proxy_clausification,[status(thm)],[f102])).
% 1.74/1.39 thf(f102,plain,(
% 1.74/1.39 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (((class @ second @ X1) & (dest @ paris @ X1)) => (price @ seventy @ X1)))) )),
% 1.74/1.39 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.74/1.39 thf(f101,plain,(
% 1.74/1.39 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (((class @ second @ X1) & (dest @ paris @ X1)) => (price @ seventy @ X1))) = $true)) )),
% 1.74/1.39 inference(beta_eta_normalization,[status(thm)],[f100])).
% 1.74/1.39 thf(f100,plain,(
% 1.74/1.39 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (((class @ second @ Y0) & (dest @ paris @ Y0)) => (price @ seventy @ Y0)))) @ X1) = $true)) )),
% 1.74/1.39 inference(pi_clausification,[status(thm)],[f99])).
% 1.74/1.39 thf(f99,plain,(
% 1.74/1.39 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (((class @ second @ Y0) & (dest @ paris @ Y0)) => (price @ seventy @ Y0))))) = $true)),
% 1.74/1.39 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.74/1.39 thf(f70,plain,(
% 1.74/1.39 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))) @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.74/1.39 inference(definition_unfolding,[status(thm)],[f59,f65,f55,f64,f60])).
% 1.74/1.39 thf(f60,plain,(
% 1.74/1.39 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.74/1.39 inference(cnf_transformation,[status(thm)],[f26])).
% 1.74/1.39 thf(f26,plain,(
% 1.74/1.39 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.74/1.39 inference(fool_elimination,[status(thm)],[f25])).
% 1.74/1.39 thf(f25,plain,(
% 1.74/1.39 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 1.74/1.39 inference(rectify,[status(thm)],[f3])).
% 1.74/1.39 thf(f3,axiom,(
% 1.74/1.39 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))) = mand)),
% 1.74/1.39 file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',mand_def)).
% 1.74/1.39 thf(f64,plain,(
% 1.74/1.39 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.74/1.39 inference(cnf_transformation,[status(thm)],[f34])).
% 1.74/1.39 thf(f34,plain,(
% 1.74/1.39 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.74/1.39 inference(fool_elimination,[status(thm)],[f33])).
% 1.74/1.39 thf(f33,plain,(
% 1.74/1.39 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.74/1.39 inference(rectify,[status(thm)],[f5])).
% 1.74/1.39 thf(f5,axiom,(
% 1.74/1.39 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.74/1.39 file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',mimplies_def)).
% 1.74/1.39 thf(f59,plain,(
% 1.74/1.39 ((mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.74/1.39 inference(cnf_transformation,[status(thm)],[f28])).
% 1.74/1.39 thf(f28,plain,(
% 1.74/1.39 ((mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.74/1.39 inference(fool_elimination,[status(thm)],[f27])).
% 1.74/1.39 thf(f27,plain,(
% 1.74/1.39 (mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy))))),
% 1.74/1.39 inference(rectify,[status(thm)],[f11])).
% 1.74/1.39 thf(f11,axiom,(
% 1.74/1.39 (mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy))))),
% 1.74/1.39 file('/export/starexec/sandbox/tmp/tmp.1rDyWn3FMy/DTF2THF_19128.p',law2)).
% 1.74/1.39 % SZS output end Proof for DTF2THF_19128
% 1.74/1.39 % (19317)------------------------------
% 1.74/1.39 % (19317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.39 % (19317)Termination reason: Refutation
% 1.74/1.39
% 1.74/1.39 % (19317)Memory used [KB]: 5628
% 1.74/1.39 % (19317)Time elapsed: 0.008 s
% 1.74/1.39 % (19317)Instructions burned: 14 (million)
% 1.74/1.39 % (19317)------------------------------
% 1.74/1.39 % (19317)------------------------------
% 1.74/1.39 % (19316)Success in time 0.017 s
%------------------------------------------------------------------------------