%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NLP267^4 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 09:22:27 AM UTC 2026
% Result : Theorem 1.67s 1.38s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 79 ( 46 unt; 0 typ; 3 def)
% Number of atoms : 416 ( 77 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 404 ( 21 ~; 30 |; 10 &; 301 @)
% ( 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(f261,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f210,f230,f243,f260]) ).
thf(f260,plain,
( spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f259]) ).
thf(f259,plain,
( $false
| spl0_7
| ~ spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f255,f193]) ).
thf(f193,plain,
( ( $false
!= ( mrel @ mactual @ sK1 ) )
| spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f192]) ).
thf(f192,definition,
( spl0_7
<=> ( $false
= ( mrel @ mactual @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f255,plain,
( ( $false
= ( mrel @ mactual @ sK1 ) )
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f253]) ).
thf(f253,plain,
( ( $false
= ( mrel @ mactual @ sK1 ) )
| ( $false = $true )
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f198,f88]) ).
thf(f88,plain,
! [X1: mworld] :
( ( $true
= ( dest @ paris @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( dest @ paris @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,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)],[f69,f59,f60]) ).
thf(f60,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f36]) ).
thf(f36,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/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',mbox_def) ).
thf(f59,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,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.jrKK0qiVno/DTF2THF_19175.p',mlocal_def) ).
thf(f69,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f32]) ).
thf(f32,plain,
mlocal @ ( mbox @ ( dest @ paris ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
mlocal @ ( mbox @ ( dest @ paris ) ),
file('/export/starexec/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',belief1) ).
thf(f198,plain,
( ( ( dest @ paris @ sK1 )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f196]) ).
thf(f196,definition,
( spl0_8
<=> ( ( dest @ paris @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f243,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[status(thm)],[f242]) ).
thf(f242,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f235]) ).
thf(f235,plain,
( ( $false = $true )
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f194,f84]) ).
thf(f84,plain,
( $true
= ( mrel @ mactual @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( $false
= ( ( mrel @ mactual @ sK1 )
=> ( price @ seventy @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( price @ seventy ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f64,f59,f60]) ).
thf(f64,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f53,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,negated_conjecture,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
thf(f17,conjecture,
mlocal @ ( mbox @ ( price @ seventy ) ),
file('/export/starexec/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',con) ).
thf(f194,plain,
( ( $false
= ( mrel @ mactual @ sK1 ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f192]) ).
thf(f230,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[status(thm)],[f229]) ).
thf(f229,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f223]) ).
thf(f223,plain,
( ( $false = $true )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f179,f124]) ).
thf(f124,plain,
( $true
= ( class @ second @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ( $false = $true )
| ( $true
= ( class @ second @ sK1 ) ) ),
inference(superposition,[status(thm)],[f84,f110]) ).
thf(f110,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( class @ second @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( class @ second @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f108]) ).
thf(f108,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( class @ second ) ) ) ),
inference(definition_unfolding,[status(thm)],[f58,f59,f60]) ).
thf(f58,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f52]) ).
thf(f52,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f51]) ).
thf(f51,plain,
mlocal @ ( mbox @ ( class @ second ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
mlocal @ ( mbox @ ( class @ second ) ),
file('/export/starexec/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',belief2) ).
thf(f179,plain,
( ( $false
= ( class @ second @ sK1 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f177]) ).
thf(f177,definition,
( spl0_6
<=> ( $false
= ( class @ second @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f210,plain,
( spl0_8
| spl0_7
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f187,f177,f192,f196]) ).
thf(f187,plain,
( ( $false
= ( class @ second @ sK1 ) )
| ( $false
= ( mrel @ mactual @ sK1 ) )
| ( ( dest @ paris @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f185]) ).
thf(f185,plain,
( ( ( dest @ paris @ sK1 )
= $false )
| ( $false
= ( mrel @ mactual @ sK1 ) )
| ( $false
= ( class @ second @ sK1 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f83,f94]) ).
thf(f94,plain,
! [X1: mworld] :
( ( $true
= ( price @ seventy @ X1 ) )
| ( ( class @ second @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( dest @ paris @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X1: mworld] :
( ( $true
= ( price @ seventy @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( class @ second @ X1 )
& ( dest @ paris @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( ( class @ second @ X1 )
& ( dest @ paris @ X1 ) )
=> ( price @ seventy @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( ( class @ second @ X1 )
& ( dest @ paris @ X1 ) )
=> ( price @ seventy @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f90]) ).
thf(f90,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( class @ second @ Y0 )
& ( dest @ paris @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( class @ second @ Y0 )
& ( dest @ paris @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,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)],[f57,f59,f60,f62,f70]) ).
thf(f70,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f45]) ).
thf(f45,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/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',mand_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,
( 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.jrKK0qiVno/DTF2THF_19175.p',mimplies_def) ).
thf(f57,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,plain,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',law2) ).
thf(f83,plain,
( ( price @ seventy @ sK1 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NLP267^4 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n014.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 10:54:42 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : NLP267^4 : 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 : 36 ( 9 unt; 19 typ; 8 def)
% 0.30/0.46 % Number of atoms : 57 ( 8 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 7 ( 3 avg)
% 0.30/0.46 % Number of connectives : 74 ( 1 ~; 1 |; 3 &; 65 @)
% 0.30/0.46 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 8 ( 4 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 : 25 ( 19 ^; 5 !; 1 ?; 25 :)
% 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_S4].
% 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(mrel_transitive,axiom,
% 0.30/0.46 ! [W: mworld,V: mworld,U: mworld] :
% 0.30/0.46 ( ( ( mrel @ W @ V )
% 0.30/0.46 & ( mrel @ V @ U ) )
% 0.30/0.46 => ( mrel @ W @ U ) ) ).
% 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 ------------------------
% 1.67/1.34 ---- Embedded in THF ---
% 1.67/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.34 %%% Generated on Tue Feb 24 10:54:43 EST 2026
% 1.67/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.34 %%% Logic specification used:
% 1.67/1.34 %%% thf(spec, logic, $$dhol).
% 1.67/1.34
% 1.67/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.jrKK0qiVno/DTF2DTF19175.p
% See solution above
% 1.67/1.34 ------------------------
% 1.67/1.36 ---- Cleaned THF ---
% 1.67/1.36 thf(mworld,type,
% 1.67/1.36 mworld: $tType ).
% 1.67/1.36
% 1.67/1.36 thf(mrel_type,type,
% 1.67/1.36 mrel: mworld > mworld > $o ).
% 1.67/1.36
% 1.67/1.36 thf(mactual_type,type,
% 1.67/1.36 mactual: mworld ).
% 1.67/1.36
% 1.67/1.36 thf(mlocal_type,type,
% 1.67/1.36 mlocal: ( mworld > $o ) > $o ).
% 1.67/1.36
% 1.67/1.36 thf(mlocal_def,definition,
% 1.67/1.36 ( mlocal
% 1.67/1.36 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(mnot_type,type,
% 1.67/1.36 mnot: ( mworld > $o ) > mworld > $o ).
% 1.67/1.36
% 1.67/1.36 thf(mand_type,type,
% 1.67/1.36 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.67/1.36
% 1.67/1.36 thf(mor_type,type,
% 1.67/1.36 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.67/1.36
% 1.67/1.36 thf(mimplies_type,type,
% 1.67/1.36 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.67/1.36
% 1.67/1.36 thf(mequiv_type,type,
% 1.67/1.36 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.67/1.36
% 1.67/1.36 thf(mnot_def,definition,
% 1.67/1.36 ( mnot
% 1.67/1.36 = ( ^ [A: mworld > $o,W: mworld] :
% 1.67/1.36 ~ ( A @ W ) ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(mand_def,definition,
% 1.67/1.36 ( mand
% 1.67/1.36 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.67/1.36 ( ( A @ W )
% 1.67/1.36 & ( B @ W ) ) ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(mor_def,definition,
% 1.67/1.36 ( mor
% 1.67/1.36 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.67/1.36 ( ( A @ W )
% 1.67/1.36 | ( B @ W ) ) ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(mimplies_def,definition,
% 1.67/1.36 ( mimplies
% 1.67/1.36 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.67/1.36 ( ( A @ W )
% 1.67/1.36 => ( B @ W ) ) ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(mequiv_def,definition,
% 1.67/1.36 ( mequiv
% 1.67/1.36 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.67/1.36 ( ( A @ W )
% 1.67/1.36 <=> ( B @ W ) ) ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(mbox_type,type,
% 1.67/1.36 mbox: ( mworld > $o ) > mworld > $o ).
% 1.67/1.36
% 1.67/1.36 thf(mbox_def,definition,
% 1.67/1.36 ( mbox
% 1.67/1.36 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.67/1.36 ! [V: mworld] :
% 1.67/1.36 ( ( mrel @ W @ V )
% 1.67/1.36 => ( Phi @ V ) ) ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(mdia_type,type,
% 1.67/1.36 mdia: ( mworld > $o ) > mworld > $o ).
% 1.67/1.36
% 1.67/1.36 thf(mdia_def,definition,
% 1.67/1.36 ( mdia
% 1.67/1.36 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.67/1.36 ? [V: mworld] :
% 1.67/1.36 ( ( mrel @ W @ V )
% 1.67/1.36 & ( Phi @ V ) ) ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(mrel_reflexive,axiom,
% 1.67/1.36 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.67/1.36
% 1.67/1.36 thf(mrel_transitive,axiom,
% 1.67/1.36 ! [W: mworld,V: mworld,U: mworld] :
% 1.67/1.36 ( ( ( mrel @ W @ V )
% 1.67/1.36 & ( mrel @ V @ U ) )
% 1.67/1.36 => ( mrel @ W @ U ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(seventy_decl,type,
% 1.67/1.36 seventy: $i ).
% 1.67/1.36
% 1.67/1.36 thf(ninetyfive_decl,type,
% 1.67/1.36 ninetyfive: $i ).
% 1.67/1.36
% 1.67/1.36 thf(second_decl,type,
% 1.67/1.36 second: $i ).
% 1.67/1.36
% 1.67/1.36 thf(paris_decl,type,
% 1.67/1.36 paris: $i ).
% 1.67/1.36
% 1.67/1.36 thf(first_decl,type,
% 1.67/1.36 first: $i ).
% 1.67/1.36
% 1.67/1.36 thf(price_decl,type,
% 1.67/1.36 price: $i > mworld > $o ).
% 1.67/1.36
% 1.67/1.36 thf(dest_decl,type,
% 1.67/1.36 dest: $i > mworld > $o ).
% 1.67/1.36
% 1.67/1.36 thf(class_decl,type,
% 1.67/1.36 class: $i > mworld > $o ).
% 1.67/1.36
% 1.67/1.36 thf(law1,axiom,
% 1.67/1.36 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(law2,axiom,
% 1.67/1.36 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(law3,axiom,
% 1.67/1.36 mlocal @ ( mbox @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(law4,axiom,
% 1.67/1.36 mlocal @ ( mbox @ ( mnot @ ( mand @ ( price @ ninetyfive ) @ ( price @ seventy ) ) ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(belief1,axiom,
% 1.67/1.36 mlocal @ ( mbox @ ( dest @ paris ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(belief2,axiom,
% 1.67/1.36 mlocal @ ( mbox @ ( class @ second ) ) ).
% 1.67/1.36
% 1.67/1.36 thf(con,conjecture,
% 1.67/1.36 mlocal @ ( mbox @ ( price @ seventy ) ) ).
% 1.67/1.36 ------------------------
% 1.67/1.37 % (19334)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_19175 for (2999ds/4Mi)
% 1.67/1.37 % (19333)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19175 for (2999ds/183Mi)
% 1.67/1.37 % (19337)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_19175 for (2999ds/2Mi)
% 1.67/1.37 % (19334)Instruction limit reached!
% 1.67/1.37 % (19334)------------------------------
% 1.67/1.37 % (19334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (19334)Termination reason: Unknown
% 1.67/1.37 % (19334)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (19334)Memory used [KB]: 5500
% 1.67/1.37 % (19334)Time elapsed: 0.003 s
% 1.67/1.37 % (19334)Instructions burned: 5 (million)
% 1.67/1.37 % (19334)------------------------------
% 1.67/1.37 % (19334)------------------------------
% 1.67/1.37 % (19337)Instruction limit reached!
% 1.67/1.37 % (19337)------------------------------
% 1.67/1.37 % (19337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (19337)Termination reason: Unknown
% 1.67/1.37 % (19337)Termination phase: Function definition elimination
% 1.67/1.37
% 1.67/1.37 % (19337)Memory used [KB]: 1023
% 1.67/1.37 % (19337)Time elapsed: 0.002 s
% 1.67/1.37 % (19337)Instructions burned: 3 (million)
% 1.67/1.37 % (19337)------------------------------
% 1.67/1.37 % (19337)------------------------------
% 1.67/1.38 % (19333)First to succeed.
% 1.67/1.38 % (19335)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_19175 for (2999ds/27Mi)
% 1.67/1.38 % (19336)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19175 for (2999ds/2Mi)
% 1.67/1.38 % (19338)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_19175 for (2999ds/275Mi)
% 1.67/1.38 % (19336)Instruction limit reached!
% 1.67/1.38 % (19336)------------------------------
% 1.67/1.38 % (19336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.38 % (19336)Termination reason: Unknown
% 1.67/1.38 % (19336)Termination phase: shuffling
% 1.67/1.38
% 1.67/1.38 % (19336)Memory used [KB]: 1023
% 1.67/1.38 % (19336)Time elapsed: 0.003 s
% 1.67/1.38 % (19336)Instructions burned: 2 (million)
% 1.67/1.38 % (19336)------------------------------
% 1.67/1.38 % (19336)------------------------------
% 1.67/1.38 % (19333)Refutation found. Thanks to Tanya!
% 1.67/1.38 % SZS status Theorem for DTF2THF_19175
% 1.67/1.38 % SZS output start Proof for DTF2THF_19175
% 1.67/1.38 thf(type_def_5, type, mworld: $tType).
% 1.67/1.38 thf(func_def_0, type, mworld: $tType).
% 1.67/1.38 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.67/1.38 thf(func_def_2, type, mactual: mworld).
% 1.67/1.38 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.67/1.38 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.67/1.38 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.67/1.38 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.67/1.38 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.67/1.38 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.67/1.38 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.67/1.38 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.67/1.38 thf(func_def_17, type, price: $i > mworld > $o).
% 1.67/1.38 thf(func_def_18, type, dest: $i > mworld > $o).
% 1.67/1.38 thf(func_def_19, type, class: $i > mworld > $o).
% 1.67/1.38 thf(func_def_34, type, sK1: mworld).
% 1.67/1.38 thf(f261,plain,(
% 1.67/1.38 $false),
% 1.67/1.38 inference(avatar_sat_refutation,[status(thm)],[f210,f230,f243,f260])).
% 1.67/1.38 thf(f260,plain,(
% 1.67/1.38 spl0_7 | ~spl0_8),
% 1.67/1.38 inference(avatar_contradiction_clause,[status(thm)],[f259])).
% 1.67/1.38 thf(f259,plain,(
% 1.67/1.38 $false | (spl0_7 | ~spl0_8)),
% 1.67/1.38 inference(subsumption_resolution,[status(thm)],[f255,f193])).
% 1.67/1.38 thf(f193,plain,(
% 1.67/1.38 ($false != (mrel @ mactual @ sK1)) | spl0_7),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f192])).
% 1.67/1.38 thf(f192,definition,(
% 1.67/1.38 spl0_7 <=> ($false = (mrel @ mactual @ sK1))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.67/1.38 thf(f255,plain,(
% 1.67/1.38 ($false = (mrel @ mactual @ sK1)) | ~spl0_8),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f253])).
% 1.67/1.38 thf(f253,plain,(
% 1.67/1.38 ($false = (mrel @ mactual @ sK1)) | ($false = $true) | ~spl0_8),
% 1.67/1.38 inference(superposition,[status(thm)],[f198,f88])).
% 1.67/1.38 thf(f88,plain,(
% 1.67/1.38 ( ! [X1 : mworld] : (($true = (dest @ paris @ X1)) | ($false = (mrel @ mactual @ X1))) )),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.67/1.38 thf(f87,plain,(
% 1.67/1.38 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (dest @ paris @ X1)) = $true)) )),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f86])).
% 1.67/1.38 thf(f86,plain,(
% 1.67/1.38 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (dest @ paris @ Y0))) @ X1) = $true)) )),
% 1.67/1.38 inference(pi_clausification,[status(thm)],[f85])).
% 1.67/1.38 thf(f85,plain,(
% 1.67/1.38 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (dest @ paris @ Y0)))) = $true)),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.67/1.38 thf(f78,plain,(
% 1.67/1.38 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (dest @ paris))))),
% 1.67/1.38 inference(definition_unfolding,[status(thm)],[f69,f59,f60])).
% 1.67/1.38 thf(f60,plain,(
% 1.67/1.38 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f37])).
% 1.67/1.38 thf(f37,plain,(
% 1.67/1.38 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.67/1.38 inference(fool_elimination,[status(thm)],[f36])).
% 1.67/1.38 thf(f36,plain,(
% 1.67/1.38 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 1.67/1.38 inference(rectify,[status(thm)],[f7])).
% 1.67/1.38 thf(f7,axiom,(
% 1.67/1.38 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 1.67/1.38 file('/export/starexec/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',mbox_def)).
% 1.67/1.38 thf(f59,plain,(
% 1.67/1.38 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f42])).
% 1.67/1.38 thf(f42,plain,(
% 1.67/1.38 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.67/1.38 inference(fool_elimination,[status(thm)],[f1])).
% 1.67/1.38 thf(f1,axiom,(
% 1.67/1.38 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.67/1.38 file('/export/starexec/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',mlocal_def)).
% 1.67/1.38 thf(f69,plain,(
% 1.67/1.38 ((mlocal @ (mbox @ (dest @ paris))) = $true)),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f33])).
% 1.67/1.38 thf(f33,plain,(
% 1.67/1.38 ((mlocal @ (mbox @ (dest @ paris))) = $true)),
% 1.67/1.38 inference(fool_elimination,[status(thm)],[f32])).
% 1.67/1.38 thf(f32,plain,(
% 1.67/1.38 (mlocal @ (mbox @ (dest @ paris)))),
% 1.67/1.38 inference(rectify,[status(thm)],[f15])).
% 1.67/1.38 thf(f15,axiom,(
% 1.67/1.38 (mlocal @ (mbox @ (dest @ paris)))),
% 1.67/1.38 file('/export/starexec/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',belief1)).
% 1.67/1.38 thf(f198,plain,(
% 1.67/1.38 ((dest @ paris @ sK1) = $false) | ~spl0_8),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f196])).
% 1.67/1.38 thf(f196,definition,(
% 1.67/1.38 spl0_8 <=> ((dest @ paris @ sK1) = $false)),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.67/1.38 thf(f243,plain,(
% 1.67/1.38 ~spl0_7),
% 1.67/1.38 inference(avatar_contradiction_clause,[status(thm)],[f242])).
% 1.67/1.38 thf(f242,plain,(
% 1.67/1.38 $false | ~spl0_7),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f235])).
% 1.67/1.38 thf(f235,plain,(
% 1.67/1.38 ($false = $true) | ~spl0_7),
% 1.67/1.38 inference(superposition,[status(thm)],[f194,f84])).
% 1.67/1.38 thf(f84,plain,(
% 1.67/1.38 ($true = (mrel @ mactual @ sK1))),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.67/1.38 thf(f82,plain,(
% 1.67/1.38 ($false = ((mrel @ mactual @ sK1) => (price @ seventy @ sK1)))),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f81])).
% 1.67/1.38 thf(f81,plain,(
% 1.67/1.38 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (price @ seventy @ Y0))) @ sK1))),
% 1.67/1.38 inference(sigma_clausification,[status(thm)],[f80])).
% 1.67/1.38 thf(f80,plain,(
% 1.67/1.38 ($true != (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (price @ seventy @ Y0)))))),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.67/1.38 thf(f77,plain,(
% 1.67/1.38 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (price @ seventy))) != $true)),
% 1.67/1.38 inference(definition_unfolding,[status(thm)],[f64,f59,f60])).
% 1.67/1.38 thf(f64,plain,(
% 1.67/1.38 ((mlocal @ (mbox @ (price @ seventy))) != $true)),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f53])).
% 1.67/1.38 thf(f53,plain,(
% 1.67/1.38 ((mlocal @ (mbox @ (price @ seventy))) != $true)),
% 1.67/1.38 inference(flattening,[status(thm)],[f27])).
% 1.67/1.38 thf(f27,plain,(
% 1.67/1.38 ~((mlocal @ (mbox @ (price @ seventy))) = $true)),
% 1.67/1.38 inference(fool_elimination,[status(thm)],[f26])).
% 1.67/1.38 thf(f26,plain,(
% 1.67/1.38 ~(mlocal @ (mbox @ (price @ seventy)))),
% 1.67/1.38 inference(rectify,[status(thm)],[f18])).
% 1.67/1.38 thf(f18,negated_conjecture,(
% 1.67/1.38 ~(mlocal @ (mbox @ (price @ seventy)))),
% 1.67/1.38 inference(negated_conjecture,[status(cth)],[f17])).
% 1.67/1.38 thf(f17,conjecture,(
% 1.67/1.38 (mlocal @ (mbox @ (price @ seventy)))),
% 1.67/1.38 file('/export/starexec/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',con)).
% 1.67/1.38 thf(f194,plain,(
% 1.67/1.38 ($false = (mrel @ mactual @ sK1)) | ~spl0_7),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f192])).
% 1.67/1.38 thf(f230,plain,(
% 1.67/1.38 ~spl0_6),
% 1.67/1.38 inference(avatar_contradiction_clause,[status(thm)],[f229])).
% 1.67/1.38 thf(f229,plain,(
% 1.67/1.38 $false | ~spl0_6),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f223])).
% 1.67/1.38 thf(f223,plain,(
% 1.67/1.38 ($false = $true) | ~spl0_6),
% 1.67/1.38 inference(superposition,[status(thm)],[f179,f124])).
% 1.67/1.38 thf(f124,plain,(
% 1.67/1.38 ($true = (class @ second @ sK1))),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.67/1.38 thf(f119,plain,(
% 1.67/1.38 ($false = $true) | ($true = (class @ second @ sK1))),
% 1.67/1.38 inference(superposition,[status(thm)],[f84,f110])).
% 1.67/1.38 thf(f110,plain,(
% 1.67/1.38 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((class @ second @ X1) = $true)) )),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.67/1.38 thf(f109,plain,(
% 1.67/1.38 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (class @ second @ X1)) = $true)) )),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f108])).
% 1.67/1.38 thf(f108,plain,(
% 1.67/1.38 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (class @ second @ Y0))) @ X1) = $true)) )),
% 1.67/1.38 inference(pi_clausification,[status(thm)],[f107])).
% 1.67/1.38 thf(f107,plain,(
% 1.67/1.38 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (class @ second @ Y0)))) = $true)),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.67/1.38 thf(f75,plain,(
% 1.67/1.38 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (class @ second))))),
% 1.67/1.38 inference(definition_unfolding,[status(thm)],[f58,f59,f60])).
% 1.67/1.38 thf(f58,plain,(
% 1.67/1.38 ((mlocal @ (mbox @ (class @ second))) = $true)),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f52])).
% 1.67/1.38 thf(f52,plain,(
% 1.67/1.38 ((mlocal @ (mbox @ (class @ second))) = $true)),
% 1.67/1.38 inference(fool_elimination,[status(thm)],[f51])).
% 1.67/1.38 thf(f51,plain,(
% 1.67/1.38 (mlocal @ (mbox @ (class @ second)))),
% 1.67/1.38 inference(rectify,[status(thm)],[f16])).
% 1.67/1.38 thf(f16,axiom,(
% 1.67/1.38 (mlocal @ (mbox @ (class @ second)))),
% 1.67/1.38 file('/export/starexec/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',belief2)).
% 1.67/1.38 thf(f179,plain,(
% 1.67/1.38 ($false = (class @ second @ sK1)) | ~spl0_6),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f177])).
% 1.67/1.38 thf(f177,definition,(
% 1.67/1.38 spl0_6 <=> ($false = (class @ second @ sK1))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.67/1.38 thf(f210,plain,(
% 1.67/1.38 spl0_8 | spl0_7 | spl0_6),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f187,f177,f192,f196])).
% 1.67/1.38 thf(f187,plain,(
% 1.67/1.38 ($false = (class @ second @ sK1)) | ($false = (mrel @ mactual @ sK1)) | ((dest @ paris @ sK1) = $false)),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f185])).
% 1.67/1.38 thf(f185,plain,(
% 1.67/1.38 ((dest @ paris @ sK1) = $false) | ($false = (mrel @ mactual @ sK1)) | ($false = (class @ second @ sK1)) | ($false = $true)),
% 1.67/1.38 inference(superposition,[status(thm)],[f83,f94])).
% 1.67/1.38 thf(f94,plain,(
% 1.67/1.38 ( ! [X1 : mworld] : (($true = (price @ seventy @ X1)) | ((class @ second @ X1) = $false) | ($false = (mrel @ mactual @ X1)) | ($false = (dest @ paris @ X1))) )),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.67/1.38 thf(f93,plain,(
% 1.67/1.38 ( ! [X1 : mworld] : (($true = (price @ seventy @ X1)) | ($false = (mrel @ mactual @ X1)) | ($false = ((class @ second @ X1) & (dest @ paris @ X1)))) )),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.67/1.38 thf(f92,plain,(
% 1.67/1.38 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (((class @ second @ X1) & (dest @ paris @ X1)) => (price @ seventy @ X1)))) )),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 1.67/1.38 thf(f91,plain,(
% 1.67/1.38 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (((class @ second @ X1) & (dest @ paris @ X1)) => (price @ seventy @ X1))))) )),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f90])).
% 1.67/1.38 thf(f90,plain,(
% 1.67/1.38 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (((class @ second @ Y0) & (dest @ paris @ Y0)) => (price @ seventy @ Y0)))) @ X1))) )),
% 1.67/1.38 inference(pi_clausification,[status(thm)],[f89])).
% 1.67/1.38 thf(f89,plain,(
% 1.67/1.38 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (((class @ second @ Y0) & (dest @ paris @ Y0)) => (price @ seventy @ Y0))))) = $true)),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.67/1.38 thf(f74,plain,(
% 1.67/1.38 (((^[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)),
% 1.67/1.38 inference(definition_unfolding,[status(thm)],[f57,f59,f60,f62,f70])).
% 1.67/1.38 thf(f70,plain,(
% 1.67/1.38 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f46])).
% 1.67/1.38 thf(f46,plain,(
% 1.67/1.38 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.67/1.38 inference(fool_elimination,[status(thm)],[f45])).
% 1.67/1.38 thf(f45,plain,(
% 1.67/1.38 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 1.67/1.38 inference(rectify,[status(thm)],[f3])).
% 1.67/1.38 thf(f3,axiom,(
% 1.67/1.38 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))) = mand)),
% 1.67/1.38 file('/export/starexec/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',mand_def)).
% 1.67/1.38 thf(f62,plain,(
% 1.67/1.38 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f21])).
% 1.67/1.38 thf(f21,plain,(
% 1.67/1.38 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.67/1.38 inference(fool_elimination,[status(thm)],[f20])).
% 1.67/1.38 thf(f20,plain,(
% 1.67/1.38 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.67/1.38 inference(rectify,[status(thm)],[f5])).
% 1.67/1.38 thf(f5,axiom,(
% 1.67/1.38 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.67/1.38 file('/export/starexec/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',mimplies_def)).
% 1.67/1.38 thf(f57,plain,(
% 1.67/1.38 ((mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.38 thf(f29,plain,(
% 1.67/1.38 ((mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.67/1.38 inference(fool_elimination,[status(thm)],[f28])).
% 1.67/1.38 thf(f28,plain,(
% 1.67/1.38 (mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy))))),
% 1.67/1.38 inference(rectify,[status(thm)],[f12])).
% 1.67/1.38 thf(f12,axiom,(
% 1.67/1.38 (mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy))))),
% 1.67/1.38 file('/export/starexec/sandbox2/tmp/tmp.jrKK0qiVno/DTF2THF_19175.p',law2)).
% 1.67/1.38 thf(f83,plain,(
% 1.67/1.38 ((price @ seventy @ sK1) = $false)),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.67/1.38 % SZS output end Proof for DTF2THF_19175
% 1.67/1.38 % (19333)------------------------------
% 1.67/1.38 % (19333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.38 % (19333)Termination reason: Refutation
% 1.67/1.38
% 1.67/1.38 % (19333)Memory used [KB]: 5628
% 1.67/1.38 % (19333)Time elapsed: 0.009 s
% 1.67/1.38 % (19333)Instructions burned: 16 (million)
% 1.67/1.38 % (19333)------------------------------
% 1.67/1.38 % (19333)------------------------------
% 1.67/1.38 % (19332)Success in time 0.017 s
%------------------------------------------------------------------------------