%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NLP267^17 : 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 : n018.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 1.67s 2.10s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 41 unt; 0 typ; 2 def)
% Number of atoms : 406 ( 75 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 427 ( 15 ~; 26 |; 15 &; 336 @)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 12 con; 0-3 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 83 ( 71 ^; 12 !; 0 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mindex: $tType ).
thf(type_def_6,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mindex: $tType ).
thf(func_def_2,type,
mrel: mindex > mworld > mworld > $o ).
thf(func_def_3,type,
'#b_u': mindex ).
thf(func_def_4,type,
'#b_s': mindex ).
thf(func_def_5,type,
mactual: mworld ).
thf(func_def_6,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_8,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mbox: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
mdia: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_20,type,
price: $i > mworld > $o ).
thf(func_def_21,type,
dest: $i > mworld > $o ).
thf(func_def_22,type,
class: $i > mworld > $o ).
thf(func_def_23,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_39,type,
sK1: mworld ).
thf(f293,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f213,f230,f286]) ).
thf(f286,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[status(thm)],[f285]) ).
thf(f285,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f284]) ).
thf(f284,plain,
( ( $false = $true )
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f279,f209]) ).
thf(f209,plain,
( ( ( dest @ paris @ sK1 )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f207]) ).
thf(f207,definition,
( spl0_7
<=> ( ( dest @ paris @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f279,plain,
( ( dest @ paris @ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f275]) ).
thf(f275,plain,
( ( $false = $true )
| ( ( dest @ paris @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f99,f117]) ).
thf(f117,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) )
| ( $true
= ( dest @ paris @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) )
| ( $true
= ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ '#b_s' @ mactual @ X1 )
=> ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f113]) ).
thf(f113,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ '#b_s' @ mactual @ Y0 )
=> ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_s' @ mactual @ Y0 )
=> ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f93]) ).
thf(f93,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b_s'
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( dest @ paris )
@ ( class @ second ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f81,f84,f70,f83]) ).
thf(f83,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox/tmp/tmp.ORMnaX0hXp/DTF2THF_4317.p',mand_def) ).
thf(f70,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
thf(f51,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f50]) ).
thf(f50,plain,
( mbox
= ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( mbox
= ( ^ [X4: mindex,X0: mworld > $o,X2: mworld] :
! [X5: mworld] :
( ( mrel @ X4 @ X2 @ X5 )
=> ( X0 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ORMnaX0hXp/DTF2THF_4317.p',mbox_def) ).
thf(f84,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,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.ORMnaX0hXp/DTF2THF_4317.p',mlocal_def) ).
thf(f81,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f48]) ).
thf(f48,plain,
mlocal @ ( mbox @ '#b_s' @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,axiom,
mlocal @ ( mbox @ '#b_s' @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ORMnaX0hXp/DTF2THF_4317.p',axiom_5) ).
thf(f99,plain,
( ( mrel @ '#b_s' @ mactual @ sK1 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
( $false
= ( ( mrel @ '#b_s' @ mactual @ sK1 )
=> ( price @ seventy @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f96]) ).
thf(f96,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ '#b_s' @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) )
@ sK1 )
= $false ),
inference(sigma_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_s' @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f94]) ).
thf(f94,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b_s'
@ ( price @ seventy ) ) ) ),
inference(definition_unfolding,[status(thm)],[f86,f84,f70]) ).
thf(f86,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f62]) ).
thf(f62,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) )
!= $true ),
inference(flattening,[status(thm)],[f39]) ).
thf(f39,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f38]) ).
thf(f38,plain,
~ ( mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,negated_conjecture,
~ ( mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
thf(f20,conjecture,
mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ),
file('/export/starexec/sandbox/tmp/tmp.ORMnaX0hXp/DTF2THF_4317.p',con) ).
thf(f230,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f229]) ).
thf(f229,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f228]) ).
thf(f228,plain,
( ( $false = $true )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f219,f167]) ).
thf(f167,plain,
( ( ( class @ second @ sK1 )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f165]) ).
thf(f165,definition,
( spl0_4
<=> ( ( class @ second @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f219,plain,
( ( class @ second @ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f217]) ).
thf(f217,plain,
( ( $false = $true )
| ( ( class @ second @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f99,f116]) ).
thf(f116,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) )
| ( ( class @ second @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f115]) ).
thf(f213,plain,
( spl0_4
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f212,f207,f165]) ).
thf(f212,plain,
( ( ( class @ second @ sK1 )
= $false )
| ( ( dest @ paris @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f211]) ).
thf(f211,plain,
( ( ( dest @ paris @ sK1 )
= $false )
| ( ( class @ second @ sK1 )
= $false )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f200,f98]) ).
thf(f98,plain,
( ( price @ seventy @ sK1 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f200,plain,
( ( ( price @ seventy @ sK1 )
= $true )
| ( ( class @ second @ sK1 )
= $false )
| ( ( dest @ paris @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f199]) ).
thf(f199,plain,
( ( ( price @ seventy @ sK1 )
= $true )
| ( ( dest @ paris @ sK1 )
= $false )
| ( ( class @ second @ sK1 )
= $false )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f99,f111]) ).
thf(f111,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) )
| ( ( price @ seventy @ X1 )
= $true )
| ( $false
= ( dest @ paris @ X1 ) )
| ( ( class @ second @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) )
| ( $false
= ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) ) )
| ( ( price @ seventy @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X1: mworld] :
( ( $true
= ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
=> ( price @ seventy @ X1 ) ) )
| ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
! [X1: mworld] :
( ( ( mrel @ '#b_s' @ mactual @ X1 )
=> ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
=> ( price @ seventy @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f107]) ).
thf(f107,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#b_s' @ mactual @ Y0 )
=> ( ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_s' @ mactual @ Y0 )
=> ( ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f92]) ).
thf(f92,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b_s'
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( dest @ paris )
@ ( class @ second ) )
@ ( price @ seventy ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f79,f84,f70,f80,f83]) ).
thf(f80,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
thf(f59,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f58]) ).
thf(f58,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.ORMnaX0hXp/DTF2THF_4317.p',mimplies_def) ).
thf(f79,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f36]) ).
thf(f36,plain,
mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ORMnaX0hXp/DTF2THF_4317.p',axiom_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.19 % Problem : NLP267^17 : TPTP v9.2.1. Released v8.1.0.
% 0.10/0.20 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 % Computer : n018.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8042.1875MB
% 0.16/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Tue Feb 24 10:54:17 EST 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.63 ---- Original DTF file ---
% 0.30/0.63 thf(spec,logic,$$dhol).
% 0.30/0.63 %------------------------------------------------------------------------------
% 0.30/0.63 % File : NLP267^17 : TPTP v9.2.1. Released v8.1.0.
% 0.30/0.63 % Domain : Natural Language Processing
% 0.30/0.63 % Problem : Ticket example
% 0.30/0.63 % Version : [BP13] axioms.
% 0.30/0.63 % English :
% 0.30/0.63
% 0.30/0.63 % Refs : [FH+98] Farinas del Cerro et al. (1998), Belief Reconstruction
% 0.30/0.63 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.30/0.63 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.30/0.63 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.30/0.63 % Source : [TPTP]
% 0.30/0.63 % Names : MML016+1 [QMLTP]
% 0.30/0.63
% 0.30/0.63 % Status : Theorem
% 0.30/0.63 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0
% 0.30/0.63 % Syntax : Number of formulae : 42 ( 10 unt; 22 typ; 8 def)
% 0.30/0.63 % Number of atoms : 72 ( 8 equ; 0 cnn)
% 0.30/0.63 % Maximal formula atoms : 7 ( 3 avg)
% 0.30/0.63 % Number of connectives : 116 ( 1 ~; 1 |; 4 &; 105 @)
% 0.30/0.63 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.30/0.63 % Maximal formula depth : 9 ( 5 avg)
% 0.30/0.63 % Number of types : 4 ( 2 usr)
% 0.30/0.63 % Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% 0.30/0.63 % Number of symbols : 21 ( 20 usr; 8 con; 0-3 aty)
% 0.30/0.63 % Number of variables : 31 ( 21 ^; 9 !; 1 ?; 31 :)
% 0.30/0.63 % SPC : TH0_THM_EQU_NAR
% 0.30/0.63
% 0.30/0.63 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.30/0.63 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.30/0.63 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.30/0.63 % $modal == [$constants == $rigid,$quantification == $cumulative,
% 0.30/0.63 % $modalities == $modal_system_S5].
% 0.30/0.63 %------------------------------------------------------------------------------
% 0.30/0.63 thf(mworld,type,
% 0.30/0.63 mworld: $tType ).
% 0.30/0.63
% 0.30/0.63 thf(mindex,type,
% 0.30/0.63 mindex: $tType ).
% 0.30/0.63
% 0.30/0.63 thf(mrel_type,type,
% 0.30/0.63 mrel: mindex > mworld > mworld > $o ).
% 0.30/0.63
% 0.30/0.63 thf('#b_u_type',type,
% 0.30/0.63 '#b_u': mindex ).
% 0.30/0.63
% 0.30/0.63 thf('#b_s_type',type,
% 0.30/0.63 '#b_s': mindex ).
% 0.30/0.63
% 0.30/0.63 thf(mactual_type,type,
% 0.30/0.63 mactual: mworld ).
% 0.30/0.63
% 0.30/0.63 thf(mlocal_type,type,
% 0.30/0.63 mlocal: ( mworld > $o ) > $o ).
% 0.30/0.63
% 0.30/0.63 thf(mlocal_def,definition,
% 0.30/0.63 ( mlocal
% 0.30/0.63 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(mnot_type,type,
% 0.30/0.63 mnot: ( mworld > $o ) > mworld > $o ).
% 0.30/0.63
% 0.30/0.63 thf(mand_type,type,
% 0.30/0.63 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.63
% 0.30/0.63 thf(mor_type,type,
% 0.30/0.63 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.63
% 0.30/0.63 thf(mimplies_type,type,
% 0.30/0.63 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.63
% 0.30/0.63 thf(mequiv_type,type,
% 0.30/0.63 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.63
% 0.30/0.63 thf(mnot_def,definition,
% 0.30/0.63 ( mnot
% 0.30/0.63 = ( ^ [A: mworld > $o,W: mworld] :
% 0.30/0.63 ~ ( A @ W ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(mand_def,definition,
% 0.30/0.63 ( mand
% 0.30/0.63 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.63 ( ( A @ W )
% 0.30/0.63 & ( B @ W ) ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(mor_def,definition,
% 0.30/0.63 ( mor
% 0.30/0.63 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.63 ( ( A @ W )
% 0.30/0.63 | ( B @ W ) ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(mimplies_def,definition,
% 0.30/0.63 ( mimplies
% 0.30/0.63 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.63 ( ( A @ W )
% 0.30/0.63 => ( B @ W ) ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(mequiv_def,definition,
% 0.30/0.63 ( mequiv
% 0.30/0.63 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.63 ( ( A @ W )
% 0.30/0.63 <=> ( B @ W ) ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(mbox_type,type,
% 0.30/0.63 mbox: mindex > ( mworld > $o ) > mworld > $o ).
% 0.30/0.63
% 0.30/0.63 thf(mbox_def,definition,
% 0.30/0.63 ( mbox
% 0.30/0.63 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.30/0.63 ! [V: mworld] :
% 0.30/0.63 ( ( mrel @ R @ W @ V )
% 0.30/0.63 => ( Phi @ V ) ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(mdia_type,type,
% 0.30/0.63 mdia: mindex > ( mworld > $o ) > mworld > $o ).
% 0.30/0.63
% 0.30/0.63 thf(mdia_def,definition,
% 0.30/0.63 ( mdia
% 0.30/0.63 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.30/0.63 ? [V: mworld] :
% 0.30/0.63 ( ( mrel @ R @ W @ V )
% 0.30/0.63 & ( Phi @ V ) ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf('mrel_#b_u_reflexive',axiom,
% 0.30/0.63 ! [W: mworld] : ( mrel @ '#b_u' @ W @ W ) ).
% 0.30/0.63
% 0.30/0.63 thf('mrel_#b_u_euclidean',axiom,
% 0.30/0.63 ! [W: mworld,V: mworld,U: mworld] :
% 0.30/0.63 ( ( ( mrel @ '#b_u' @ W @ U )
% 0.30/0.63 & ( mrel @ '#b_u' @ W @ V ) )
% 0.30/0.63 => ( mrel @ '#b_u' @ U @ V ) ) ).
% 0.30/0.63
% 0.30/0.63 thf('mrel_#b_s_reflexive',axiom,
% 0.30/0.63 ! [W: mworld] : ( mrel @ '#b_s' @ W @ W ) ).
% 0.30/0.63
% 0.30/0.63 thf('mrel_#b_s_euclidean',axiom,
% 0.30/0.63 ! [W: mworld,V: mworld,U: mworld] :
% 0.30/0.63 ( ( ( mrel @ '#b_s' @ W @ U )
% 0.30/0.63 & ( mrel @ '#b_s' @ W @ V ) )
% 0.30/0.63 => ( mrel @ '#b_s' @ U @ V ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(seventy_decl,type,
% 0.30/0.63 seventy: $i ).
% 0.30/0.63
% 0.30/0.63 thf(ninetyfive_decl,type,
% 0.30/0.63 ninetyfive: $i ).
% 0.30/0.63
% 0.30/0.63 thf(second_decl,type,
% 0.30/0.63 second: $i ).
% 0.30/0.63
% 0.30/0.63 thf(paris_decl,type,
% 0.30/0.63 paris: $i ).
% 0.30/0.63
% 0.30/0.63 thf(first_decl,type,
% 0.30/0.63 first: $i ).
% 0.30/0.63
% 0.30/0.63 thf(price_decl,type,
% 0.30/0.63 price: $i > mworld > $o ).
% 0.30/0.63
% 0.30/0.63 thf(dest_decl,type,
% 0.30/0.63 dest: $i > mworld > $o ).
% 0.30/0.63
% 0.30/0.63 thf(class_decl,type,
% 0.30/0.63 class: $i > mworld > $o ).
% 0.30/0.63
% 0.30/0.63 thf(axiom_1,axiom,
% 0.30/0.63 mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(axiom_2,axiom,
% 0.30/0.63 mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(axiom_3_s,axiom,
% 0.30/0.63 mlocal @ ( mbox @ '#b_s' @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(axiom_3_u,axiom,
% 0.30/0.63 mlocal @ ( mbox @ '#b_u' @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(axiom_4_s,axiom,
% 0.30/0.63 mlocal @ ( mbox @ '#b_s' @ ( mnot @ ( mand @ ( price @ seventy ) @ ( price @ ninetyfive ) ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(axiom_4_u,axiom,
% 0.30/0.63 mlocal @ ( mbox @ '#b_u' @ ( mnot @ ( mand @ ( price @ seventy ) @ ( price @ ninetyfive ) ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(axiom_5,axiom,
% 0.30/0.63 mlocal @ ( mbox @ '#b_s' @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) ) ).
% 0.30/0.63
% 0.30/0.63 thf(con,conjecture,
% 0.30/0.63 mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) ).
% 0.30/0.63
% 0.30/0.63 %------------------------------------------------------------------------------
% 0.30/0.63 ------------------------
% 1.67/2.06 ---- Embedded in THF ---
% 1.67/2.06 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/2.06 %%% Generated on Tue Feb 24 10:54:18 EST 2026
% 1.67/2.06 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/2.06 %%% Logic specification used:
% 1.67/2.06 %%% thf(spec, logic, $$dhol).
% 1.67/2.06
% 1.67/2.06 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ORMnaX0hXp/DTF2DTF4317.p
% See solution above
% 1.67/2.06 ------------------------
% 1.67/2.07 ---- Cleaned THF ---
% 1.67/2.07 thf(mworld,type,
% 1.67/2.07 mworld: $tType ).
% 1.67/2.07
% 1.67/2.07 thf(mindex,type,
% 1.67/2.07 mindex: $tType ).
% 1.67/2.07
% 1.67/2.07 thf(mrel_type,type,
% 1.67/2.07 mrel: mindex > mworld > mworld > $o ).
% 1.67/2.07
% 1.67/2.07 thf('#b_u_type',type,
% 1.67/2.07 '#b_u': mindex ).
% 1.67/2.07
% 1.67/2.07 thf('#b_s_type',type,
% 1.67/2.07 '#b_s': mindex ).
% 1.67/2.07
% 1.67/2.07 thf(mactual_type,type,
% 1.67/2.07 mactual: mworld ).
% 1.67/2.07
% 1.67/2.07 thf(mlocal_type,type,
% 1.67/2.07 mlocal: ( mworld > $o ) > $o ).
% 1.67/2.07
% 1.67/2.07 thf(mlocal_def,definition,
% 1.67/2.07 ( mlocal
% 1.67/2.07 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(mnot_type,type,
% 1.67/2.07 mnot: ( mworld > $o ) > mworld > $o ).
% 1.67/2.07
% 1.67/2.07 thf(mand_type,type,
% 1.67/2.07 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.67/2.07
% 1.67/2.07 thf(mor_type,type,
% 1.67/2.07 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.67/2.07
% 1.67/2.07 thf(mimplies_type,type,
% 1.67/2.07 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.67/2.07
% 1.67/2.07 thf(mequiv_type,type,
% 1.67/2.07 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.67/2.07
% 1.67/2.07 thf(mnot_def,definition,
% 1.67/2.07 ( mnot
% 1.67/2.07 = ( ^ [A: mworld > $o,W: mworld] :
% 1.67/2.07 ~ ( A @ W ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(mand_def,definition,
% 1.67/2.07 ( mand
% 1.67/2.07 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.67/2.07 ( ( A @ W )
% 1.67/2.07 & ( B @ W ) ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(mor_def,definition,
% 1.67/2.07 ( mor
% 1.67/2.07 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.67/2.07 ( ( A @ W )
% 1.67/2.07 | ( B @ W ) ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(mimplies_def,definition,
% 1.67/2.07 ( mimplies
% 1.67/2.07 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.67/2.07 ( ( A @ W )
% 1.67/2.07 => ( B @ W ) ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(mequiv_def,definition,
% 1.67/2.07 ( mequiv
% 1.67/2.07 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.67/2.07 ( ( A @ W )
% 1.67/2.07 <=> ( B @ W ) ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(mbox_type,type,
% 1.67/2.07 mbox: mindex > ( mworld > $o ) > mworld > $o ).
% 1.67/2.07
% 1.67/2.07 thf(mbox_def,definition,
% 1.67/2.07 ( mbox
% 1.67/2.07 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 1.67/2.07 ! [V: mworld] :
% 1.67/2.07 ( ( mrel @ R @ W @ V )
% 1.67/2.07 => ( Phi @ V ) ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(mdia_type,type,
% 1.67/2.07 mdia: mindex > ( mworld > $o ) > mworld > $o ).
% 1.67/2.07
% 1.67/2.07 thf(mdia_def,definition,
% 1.67/2.07 ( mdia
% 1.67/2.07 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 1.67/2.07 ? [V: mworld] :
% 1.67/2.07 ( ( mrel @ R @ W @ V )
% 1.67/2.07 & ( Phi @ V ) ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf('mrel_#b_u_reflexive',axiom,
% 1.67/2.07 ! [W: mworld] : ( mrel @ '#b_u' @ W @ W ) ).
% 1.67/2.07
% 1.67/2.07 thf('mrel_#b_u_euclidean',axiom,
% 1.67/2.07 ! [W: mworld,V: mworld,U: mworld] :
% 1.67/2.07 ( ( ( mrel @ '#b_u' @ W @ U )
% 1.67/2.07 & ( mrel @ '#b_u' @ W @ V ) )
% 1.67/2.07 => ( mrel @ '#b_u' @ U @ V ) ) ).
% 1.67/2.07
% 1.67/2.07 thf('mrel_#b_s_reflexive',axiom,
% 1.67/2.07 ! [W: mworld] : ( mrel @ '#b_s' @ W @ W ) ).
% 1.67/2.07
% 1.67/2.07 thf('mrel_#b_s_euclidean',axiom,
% 1.67/2.07 ! [W: mworld,V: mworld,U: mworld] :
% 1.67/2.07 ( ( ( mrel @ '#b_s' @ W @ U )
% 1.67/2.07 & ( mrel @ '#b_s' @ W @ V ) )
% 1.67/2.07 => ( mrel @ '#b_s' @ U @ V ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(seventy_decl,type,
% 1.67/2.07 seventy: $i ).
% 1.67/2.07
% 1.67/2.07 thf(ninetyfive_decl,type,
% 1.67/2.07 ninetyfive: $i ).
% 1.67/2.07
% 1.67/2.07 thf(second_decl,type,
% 1.67/2.07 second: $i ).
% 1.67/2.07
% 1.67/2.07 thf(paris_decl,type,
% 1.67/2.07 paris: $i ).
% 1.67/2.07
% 1.67/2.07 thf(first_decl,type,
% 1.67/2.07 first: $i ).
% 1.67/2.07
% 1.67/2.07 thf(price_decl,type,
% 1.67/2.07 price: $i > mworld > $o ).
% 1.67/2.07
% 1.67/2.07 thf(dest_decl,type,
% 1.67/2.07 dest: $i > mworld > $o ).
% 1.67/2.07
% 1.67/2.07 thf(class_decl,type,
% 1.67/2.07 class: $i > mworld > $o ).
% 1.67/2.07
% 1.67/2.07 thf(axiom_1,axiom,
% 1.67/2.07 mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(axiom_2,axiom,
% 1.67/2.07 mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(axiom_3_s,axiom,
% 1.67/2.07 mlocal @ ( mbox @ '#b_s' @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(axiom_3_u,axiom,
% 1.67/2.07 mlocal @ ( mbox @ '#b_u' @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(axiom_4_s,axiom,
% 1.67/2.07 mlocal @ ( mbox @ '#b_s' @ ( mnot @ ( mand @ ( price @ seventy ) @ ( price @ ninetyfive ) ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(axiom_4_u,axiom,
% 1.67/2.07 mlocal @ ( mbox @ '#b_u' @ ( mnot @ ( mand @ ( price @ seventy ) @ ( price @ ninetyfive ) ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(axiom_5,axiom,
% 1.67/2.07 mlocal @ ( mbox @ '#b_s' @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) ) ).
% 1.67/2.07
% 1.67/2.07 thf(con,conjecture,
% 1.67/2.07 mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) ).
% 1.67/2.07 ------------------------
% 1.67/2.09 % (4416)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_4317 for (2999ds/27Mi)
% 1.67/2.09 % (4417)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4317 for (2999ds/2Mi)
% 1.67/2.09 % (4417)Instruction limit reached!
% 1.67/2.09 % (4417)------------------------------
% 1.67/2.09 % (4417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/2.09 % (4417)Termination reason: Unknown
% 1.67/2.09 % (4417)Termination phase: Property scanning
% 1.67/2.09
% 1.67/2.09 % (4417)Memory used [KB]: 1023
% 1.67/2.09 % (4417)Time elapsed: 0.003 s
% 1.67/2.09 % (4417)Instructions burned: 4 (million)
% 1.67/2.09 % (4417)------------------------------
% 1.67/2.09 % (4417)------------------------------
% 1.67/2.09 % (4414)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4317 for (2999ds/183Mi)
% 1.67/2.09 % (4415)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_4317 for (2999ds/4Mi)
% 1.67/2.09 % (4416)First to succeed.
% 1.67/2.09 % (4420)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4317 for (2999ds/18Mi)
% 1.67/2.09 % (4415)Instruction limit reached!
% 1.67/2.09 % (4415)------------------------------
% 1.67/2.09 % (4415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/2.09 % (4415)Termination reason: Unknown
% 1.67/2.09 % (4415)Termination phase: Property scanning
% 1.67/2.09
% 1.67/2.09 % (4415)Memory used [KB]: 1023
% 1.67/2.09 % (4415)Time elapsed: 0.004 s
% 1.67/2.09 % (4415)Instructions burned: 4 (million)
% 1.67/2.09 % (4415)------------------------------
% 1.67/2.09 % (4415)------------------------------
% 1.67/2.10 % (4416)Refutation found. Thanks to Tanya!
% 1.67/2.10 % SZS status Theorem for DTF2THF_4317
% 1.67/2.10 % SZS output start Proof for DTF2THF_4317
% 1.67/2.10 thf(type_def_5, type, mindex: $tType).
% 1.67/2.10 thf(type_def_6, type, mworld: $tType).
% 1.67/2.10 thf(func_def_0, type, mworld: $tType).
% 1.67/2.10 thf(func_def_1, type, mindex: $tType).
% 1.67/2.10 thf(func_def_2, type, mrel: mindex > mworld > mworld > $o).
% 1.67/2.10 thf(func_def_3, type, '#b_u': mindex).
% 1.67/2.10 thf(func_def_4, type, '#b_s': mindex).
% 1.67/2.10 thf(func_def_5, type, mactual: mworld).
% 1.67/2.10 thf(func_def_6, type, mlocal: (mworld > $o) > $o).
% 1.67/2.10 thf(func_def_8, type, mnot: (mworld > $o) > mworld > $o).
% 1.67/2.10 thf(func_def_9, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.67/2.10 thf(func_def_10, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.67/2.10 thf(func_def_11, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.67/2.10 thf(func_def_12, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.67/2.10 thf(func_def_13, type, mbox: mindex > (mworld > $o) > mworld > $o).
% 1.67/2.10 thf(func_def_14, type, mdia: mindex > (mworld > $o) > mworld > $o).
% 1.67/2.10 thf(func_def_20, type, price: $i > mworld > $o).
% 1.67/2.10 thf(func_def_21, type, dest: $i > mworld > $o).
% 1.67/2.10 thf(func_def_22, type, class: $i > mworld > $o).
% 1.67/2.10 thf(func_def_23, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.67/2.10 thf(func_def_39, type, sK1: mworld).
% 1.67/2.10 thf(f293,plain,(
% 1.67/2.10 $false),
% 1.67/2.10 inference(avatar_sat_refutation,[status(thm)],[f213,f230,f286])).
% 1.67/2.10 thf(f286,plain,(
% 1.67/2.10 ~spl0_7),
% 1.67/2.10 inference(avatar_contradiction_clause,[status(thm)],[f285])).
% 1.67/2.10 thf(f285,plain,(
% 1.67/2.10 $false | ~spl0_7),
% 1.67/2.10 inference(trivial_inequality_removal,[status(thm)],[f284])).
% 1.67/2.10 thf(f284,plain,(
% 1.67/2.10 ($false = $true) | ~spl0_7),
% 1.67/2.10 inference(forward_demodulation,[status(thm)],[f279,f209])).
% 1.67/2.10 thf(f209,plain,(
% 1.67/2.10 ((dest @ paris @ sK1) = $false) | ~spl0_7),
% 1.67/2.10 inference(avatar_component_clause,[status(thm)],[f207])).
% 1.67/2.10 thf(f207,definition,(
% 1.67/2.10 spl0_7 <=> ((dest @ paris @ sK1) = $false)),
% 1.67/2.10 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.67/2.10 thf(f279,plain,(
% 1.67/2.10 ((dest @ paris @ sK1) = $true)),
% 1.67/2.10 inference(trivial_inequality_removal,[status(thm)],[f275])).
% 1.67/2.10 thf(f275,plain,(
% 1.67/2.10 ($false = $true) | ((dest @ paris @ sK1) = $true)),
% 1.67/2.10 inference(superposition,[status(thm)],[f99,f117])).
% 1.67/2.10 thf(f117,plain,(
% 1.67/2.10 ( ! [X1 : mworld] : (($false = (mrel @ '#b_s' @ mactual @ X1)) | ($true = (dest @ paris @ X1))) )),
% 1.67/2.10 inference(binary_proxy_clausification,[status(thm)],[f115])).
% 1.67/2.10 thf(f115,plain,(
% 1.67/2.10 ( ! [X1 : mworld] : (($false = (mrel @ '#b_s' @ mactual @ X1)) | ($true = ((dest @ paris @ X1) & (class @ second @ X1)))) )),
% 1.67/2.10 inference(binary_proxy_clausification,[status(thm)],[f114])).
% 1.67/2.10 thf(f114,plain,(
% 1.67/2.10 ( ! [X1 : mworld] : (($true = ((mrel @ '#b_s' @ mactual @ X1) => ((dest @ paris @ X1) & (class @ second @ X1))))) )),
% 1.67/2.10 inference(beta_eta_normalization,[status(thm)],[f113])).
% 1.67/2.10 thf(f113,plain,(
% 1.67/2.10 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ '#b_s' @ mactual @ Y0) => ((dest @ paris @ Y0) & (class @ second @ Y0)))) @ X1) = $true)) )),
% 1.67/2.10 inference(pi_clausification,[status(thm)],[f112])).
% 1.67/2.10 thf(f112,plain,(
% 1.67/2.10 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#b_s' @ mactual @ Y0) => ((dest @ paris @ Y0) & (class @ second @ Y0))))) = $true)),
% 1.67/2.10 inference(beta_eta_normalization,[status(thm)],[f93])).
% 1.67/2.10 thf(f93,plain,(
% 1.67/2.10 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ '#b_s' @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ (dest @ paris) @ (class @ second)))) = $true)),
% 1.67/2.10 inference(definition_unfolding,[status(thm)],[f81,f84,f70,f83])).
% 1.67/2.10 thf(f83,plain,(
% 1.67/2.10 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.67/2.10 inference(cnf_transformation,[status(thm)],[f35])).
% 1.67/2.10 thf(f35,plain,(
% 1.67/2.10 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.67/2.10 inference(fool_elimination,[status(thm)],[f34])).
% 1.67/2.10 thf(f34,plain,(
% 1.67/2.10 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))) = mand)),
% 1.67/2.10 inference(rectify,[status(thm)],[f3])).
% 1.67/2.10 thf(f3,axiom,(
% 1.67/2.10 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))) = mand)),
% 1.67/2.10 file('/export/starexec/sandbox/tmp/tmp.ORMnaX0hXp/DTF2THF_4317.p',mand_def)).
% 1.67/2.10 thf(f70,plain,(
% 1.67/2.10 (mbox = (^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 1.67/2.10 inference(cnf_transformation,[status(thm)],[f51])).
% 1.67/2.10 thf(f51,plain,(
% 1.67/2.10 (mbox = (^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 1.67/2.10 inference(fool_elimination,[status(thm)],[f50])).
% 1.67/2.10 thf(f50,plain,(
% 1.67/2.10 (mbox = (^[X0 : mindex, X1 : mworld > $o, X2 : mworld] : (! [X3 : mworld] : ((mrel @ X0 @ X2 @ X3) => (X1 @ X3)))))),
% 1.67/2.10 inference(rectify,[status(thm)],[f7])).
% 1.67/2.10 thf(f7,axiom,(
% 1.67/2.10 (mbox = (^[X4 : mindex, X0 : mworld > $o, X2 : mworld] : (! [X5 : mworld] : ((mrel @ X4 @ X2 @ X5) => (X0 @ X5)))))),
% 1.67/2.10 file('/export/starexec/sandbox/tmp/tmp.ORMnaX0hXp/DTF2THF_4317.p',mbox_def)).
% 1.67/2.10 thf(f84,plain,(
% 1.67/2.10 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.67/2.10 inference(cnf_transformation,[status(thm)],[f33])).
% 1.67/2.10 thf(f33,plain,(
% 1.67/2.10 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.67/2.10 inference(fool_elimination,[status(thm)],[f1])).
% 1.67/2.10 thf(f1,axiom,(
% 1.67/2.10 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.67/2.10 file('/export/starexec/sandbox/tmp/tmp.ORMnaX0hXp/DTF2THF_4317.p',mlocal_def)).
% 1.67/2.10 thf(f81,plain,(
% 1.67/2.10 ((mlocal @ (mbox @ '#b_s' @ (mand @ (dest @ paris) @ (class @ second)))) = $true)),
% 1.67/2.10 inference(cnf_transformation,[status(thm)],[f49])).
% 1.67/2.10 thf(f49,plain,(
% 1.67/2.10 ((mlocal @ (mbox @ '#b_s' @ (mand @ (dest @ paris) @ (class @ second)))) = $true)),
% 1.67/2.10 inference(fool_elimination,[status(thm)],[f48])).
% 1.67/2.10 thf(f48,plain,(
% 1.67/2.10 (mlocal @ (mbox @ '#b_s' @ (mand @ (dest @ paris) @ (class @ second))))),
% 1.67/2.10 inference(rectify,[status(thm)],[f19])).
% 1.67/2.10 thf(f19,axiom,(
% 1.67/2.10 (mlocal @ (mbox @ '#b_s' @ (mand @ (dest @ paris) @ (class @ second))))),
% 1.67/2.10 file('/export/starexec/sandbox/tmp/tmp.ORMnaX0hXp/DTF2THF_4317.p',axiom_5)).
% 1.67/2.10 thf(f99,plain,(
% 1.67/2.10 ((mrel @ '#b_s' @ mactual @ sK1) = $true)),
% 1.67/2.10 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.67/2.10 thf(f97,plain,(
% 1.67/2.10 ($false = ((mrel @ '#b_s' @ mactual @ sK1) => (price @ seventy @ sK1)))),
% 1.67/2.10 inference(beta_eta_normalization,[status(thm)],[f96])).
% 1.67/2.10 thf(f96,plain,(
% 1.67/2.10 (((^[Y0 : mworld]: ((mrel @ '#b_s' @ mactual @ Y0) => (price @ seventy @ Y0))) @ sK1) = $false)),
% 1.67/2.10 inference(sigma_clausification,[status(thm)],[f95])).
% 1.67/2.10 thf(f95,plain,(
% 1.67/2.10 ($true != (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#b_s' @ mactual @ Y0) => (price @ seventy @ Y0)))))),
% 1.67/2.10 inference(beta_eta_normalization,[status(thm)],[f94])).
% 1.67/2.10 thf(f94,plain,(
% 1.67/2.10 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ '#b_s' @ (price @ seventy))))),
% 1.67/2.10 inference(definition_unfolding,[status(thm)],[f86,f84,f70])).
% 1.67/2.10 thf(f86,plain,(
% 1.67/2.10 ((mlocal @ (mbox @ '#b_s' @ (price @ seventy))) != $true)),
% 1.67/2.10 inference(cnf_transformation,[status(thm)],[f62])).
% 1.67/2.10 thf(f62,plain,(
% 1.67/2.10 ((mlocal @ (mbox @ '#b_s' @ (price @ seventy))) != $true)),
% 1.67/2.10 inference(flattening,[status(thm)],[f39])).
% 1.67/2.10 thf(f39,plain,(
% 1.67/2.10 ~((mlocal @ (mbox @ '#b_s' @ (price @ seventy))) = $true)),
% 1.67/2.10 inference(fool_elimination,[status(thm)],[f38])).
% 1.67/2.10 thf(f38,plain,(
% 1.67/2.10 ~(mlocal @ (mbox @ '#b_s' @ (price @ seventy)))),
% 1.67/2.10 inference(rectify,[status(thm)],[f21])).
% 1.67/2.10 thf(f21,negated_conjecture,(
% 1.67/2.10 ~(mlocal @ (mbox @ '#b_s' @ (price @ seventy)))),
% 1.67/2.10 inference(negated_conjecture,[status(cth)],[f20])).
% 1.67/2.10 thf(f20,conjecture,(
% 1.67/2.10 (mlocal @ (mbox @ '#b_s' @ (price @ seventy)))),
% 1.67/2.10 file('/export/starexec/sandbox/tmp/tmp.ORMnaX0hXp/DTF2THF_4317.p',con)).
% 1.67/2.10 thf(f230,plain,(
% 1.67/2.10 ~spl0_4),
% 1.67/2.10 inference(avatar_contradiction_clause,[status(thm)],[f229])).
% 1.67/2.10 thf(f229,plain,(
% 1.67/2.10 $false | ~spl0_4),
% 1.67/2.10 inference(trivial_inequality_removal,[status(thm)],[f228])).
% 1.67/2.10 thf(f228,plain,(
% 1.67/2.10 ($false = $true) | ~spl0_4),
% 1.67/2.10 inference(forward_demodulation,[status(thm)],[f219,f167])).
% 1.67/2.10 thf(f167,plain,(
% 1.67/2.10 ((class @ second @ sK1) = $false) | ~spl0_4),
% 1.67/2.10 inference(avatar_component_clause,[status(thm)],[f165])).
% 1.67/2.10 thf(f165,definition,(
% 1.67/2.10 spl0_4 <=> ((class @ second @ sK1) = $false)),
% 1.67/2.10 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.67/2.10 thf(f219,plain,(
% 1.67/2.10 ((class @ second @ sK1) = $true)),
% 1.67/2.10 inference(trivial_inequality_removal,[status(thm)],[f217])).
% 1.67/2.10 thf(f217,plain,(
% 1.67/2.10 ($false = $true) | ((class @ second @ sK1) = $true)),
% 1.67/2.10 inference(superposition,[status(thm)],[f99,f116])).
% 1.67/2.10 thf(f116,plain,(
% 1.67/2.10 ( ! [X1 : mworld] : (($false = (mrel @ '#b_s' @ mactual @ X1)) | ((class @ second @ X1) = $true)) )),
% 1.67/2.10 inference(binary_proxy_clausification,[status(thm)],[f115])).
% 1.67/2.10 thf(f213,plain,(
% 1.67/2.10 spl0_4 | spl0_7),
% 1.67/2.10 inference(avatar_split_clause,[status(thm)],[f212,f207,f165])).
% 1.67/2.10 thf(f212,plain,(
% 1.67/2.10 ((class @ second @ sK1) = $false) | ((dest @ paris @ sK1) = $false)),
% 1.67/2.10 inference(trivial_inequality_removal,[status(thm)],[f211])).
% 1.67/2.10 thf(f211,plain,(
% 1.67/2.10 ((dest @ paris @ sK1) = $false) | ((class @ second @ sK1) = $false) | ($false = $true)),
% 1.67/2.10 inference(forward_demodulation,[status(thm)],[f200,f98])).
% 1.67/2.10 thf(f98,plain,(
% 1.67/2.10 ((price @ seventy @ sK1) = $false)),
% 1.67/2.10 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.67/2.10 thf(f200,plain,(
% 1.67/2.10 ((price @ seventy @ sK1) = $true) | ((class @ second @ sK1) = $false) | ((dest @ paris @ sK1) = $false)),
% 1.67/2.10 inference(trivial_inequality_removal,[status(thm)],[f199])).
% 1.67/2.10 thf(f199,plain,(
% 1.67/2.10 ((price @ seventy @ sK1) = $true) | ((dest @ paris @ sK1) = $false) | ((class @ second @ sK1) = $false) | ($false = $true)),
% 1.67/2.10 inference(superposition,[status(thm)],[f99,f111])).
% 1.67/2.10 thf(f111,plain,(
% 1.67/2.10 ( ! [X1 : mworld] : (($false = (mrel @ '#b_s' @ mactual @ X1)) | ((price @ seventy @ X1) = $true) | ($false = (dest @ paris @ X1)) | ((class @ second @ X1) = $false)) )),
% 1.67/2.10 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 1.67/2.10 thf(f110,plain,(
% 1.67/2.10 ( ! [X1 : mworld] : (($false = (mrel @ '#b_s' @ mactual @ X1)) | ($false = ((dest @ paris @ X1) & (class @ second @ X1))) | ((price @ seventy @ X1) = $true)) )),
% 1.67/2.10 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.67/2.10 thf(f109,plain,(
% 1.67/2.10 ( ! [X1 : mworld] : (($true = (((dest @ paris @ X1) & (class @ second @ X1)) => (price @ seventy @ X1))) | ($false = (mrel @ '#b_s' @ mactual @ X1))) )),
% 1.67/2.10 inference(binary_proxy_clausification,[status(thm)],[f108])).
% 1.67/2.10 thf(f108,plain,(
% 1.67/2.10 ( ! [X1 : mworld] : ((((mrel @ '#b_s' @ mactual @ X1) => (((dest @ paris @ X1) & (class @ second @ X1)) => (price @ seventy @ X1))) = $true)) )),
% 1.67/2.10 inference(beta_eta_normalization,[status(thm)],[f107])).
% 1.67/2.10 thf(f107,plain,(
% 1.67/2.10 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ '#b_s' @ mactual @ Y0) => (((dest @ paris @ Y0) & (class @ second @ Y0)) => (price @ seventy @ Y0)))) @ X1))) )),
% 1.67/2.10 inference(pi_clausification,[status(thm)],[f106])).
% 1.67/2.10 thf(f106,plain,(
% 1.67/2.10 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#b_s' @ mactual @ Y0) => (((dest @ paris @ Y0) & (class @ second @ Y0)) => (price @ seventy @ Y0))))))),
% 1.67/2.10 inference(beta_eta_normalization,[status(thm)],[f92])).
% 1.67/2.10 thf(f92,plain,(
% 1.67/2.10 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ '#b_s' @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))))),
% 1.67/2.10 inference(definition_unfolding,[status(thm)],[f79,f84,f70,f80,f83])).
% 1.67/2.10 thf(f80,plain,(
% 1.67/2.10 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.67/2.10 inference(cnf_transformation,[status(thm)],[f59])).
% 1.67/2.10 thf(f59,plain,(
% 1.67/2.10 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.67/2.10 inference(fool_elimination,[status(thm)],[f58])).
% 1.67/2.10 thf(f58,plain,(
% 1.67/2.10 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.67/2.10 inference(rectify,[status(thm)],[f5])).
% 1.67/2.10 thf(f5,axiom,(
% 1.67/2.10 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.67/2.10 file('/export/starexec/sandbox/tmp/tmp.ORMnaX0hXp/DTF2THF_4317.p',mimplies_def)).
% 1.67/2.10 thf(f79,plain,(
% 1.67/2.10 ((mlocal @ (mbox @ '#b_s' @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.67/2.10 inference(cnf_transformation,[status(thm)],[f37])).
% 1.67/2.10 thf(f37,plain,(
% 1.67/2.10 ((mlocal @ (mbox @ '#b_s' @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.67/2.10 inference(fool_elimination,[status(thm)],[f36])).
% 1.67/2.10 thf(f36,plain,(
% 1.67/2.10 (mlocal @ (mbox @ '#b_s' @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy))))),
% 1.67/2.10 inference(rectify,[status(thm)],[f14])).
% 1.67/2.10 thf(f14,axiom,(
% 1.67/2.10 (mlocal @ (mbox @ '#b_s' @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy))))),
% 1.67/2.10 file('/export/starexec/sandbox/tmp/tmp.ORMnaX0hXp/DTF2THF_4317.p',axiom_2)).
% 1.67/2.10 % SZS output end Proof for DTF2THF_4317
% 1.67/2.10 % (4416)------------------------------
% 1.67/2.10 % (4416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/2.10 % (4416)Termination reason: Refutation
% 1.67/2.10
% 1.67/2.10 % (4416)Memory used [KB]: 5756
% 1.67/2.10 % (4416)Time elapsed: 0.010 s
% 1.67/2.10 % (4416)Instructions burned: 23 (million)
% 1.67/2.10 % (4416)------------------------------
% 1.67/2.10 % (4416)------------------------------
% 1.67/2.10 % (4413)Success in time 0.02 s
%------------------------------------------------------------------------------