%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NLP267^3 : 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 : n023.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 1.72s 1.30s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 67 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 401 ( 79 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 381 ( 7 ~; 22 |; 10 &; 303 @)
% ( 0 <=>; 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 : 22 ( 18 usr; 8 con; 0-3 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 83 ( 67 ^; 16 !; 0 ?; 83 :)
% 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_33,type,
sK0: mworld > mworld ).
thf(func_def_35,type,
sK2: mworld ).
thf(f138,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f137]) ).
thf(f137,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f119,f136]) ).
thf(f136,plain,
( ( class @ second @ sK2 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $false = $true )
| ( ( class @ second @ sK2 )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f134,f85]) ).
thf(f85,plain,
( $false
= ( price @ seventy @ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( ( ( mrel @ mactual @ sK2 )
=> ( price @ seventy @ sK2 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f83]) ).
thf(f83,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,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)],[f56,f62,f67]) ).
thf(f67,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) )
= mbox ),
file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',mbox_def) ).
thf(f62,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,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.RlgiO9hvUd/DTF2THF_2492.p',mlocal_def) ).
thf(f56,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f50,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,negated_conjecture,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f16,conjecture,
mlocal @ ( mbox @ ( price @ seventy ) ),
file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',con) ).
thf(f134,plain,
( ( ( class @ second @ sK2 )
= $false )
| ( $true
= ( price @ seventy @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f127]) ).
thf(f127,plain,
( ( ( class @ second @ sK2 )
= $false )
| ( $false = $true )
| ( $true
= ( price @ seventy @ sK2 ) ) ),
inference(superposition,[status(thm)],[f126,f86]) ).
thf(f86,plain,
( ( mrel @ mactual @ sK2 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f84]) ).
thf(f126,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( price @ seventy @ X0 )
= $true )
| ( $false
= ( class @ second @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
! [X0: mworld] :
( ( ( price @ seventy @ X0 )
= $true )
| ( $false
= ( class @ second @ X0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f121]) ).
thf(f121,plain,
! [X0: mworld] :
( ( $false
= ( class @ second @ X0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false = $true )
| ( ( price @ seventy @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f102,f96]) ).
thf(f96,plain,
! [X1: mworld] :
( ( $true
= ( dest @ paris @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( dest @ paris @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f94]) ).
thf(f94,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( dest @ paris ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f63,f62,f67]) ).
thf(f63,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f27]) ).
thf(f27,plain,
mlocal @ ( mbox @ ( dest @ paris ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
mlocal @ ( mbox @ ( dest @ paris ) ),
file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',belief1) ).
thf(f102,plain,
! [X1: mworld] :
( ( $false
= ( dest @ paris @ X1 ) )
| ( ( class @ second @ X1 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( price @ seventy @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X1: mworld] :
( ( ( price @ seventy @ X1 )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X1: mworld] :
( ( ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
=> ( price @ seventy @ X1 ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
=> ( price @ seventy @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f98]) ).
thf(f98,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,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] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( dest @ paris )
@ ( class @ second ) )
@ ( price @ seventy ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f54,f62,f67,f58,f57]) ).
thf(f57,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f46]) ).
thf(f46,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( mand
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',mand_def) ).
thf(f58,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f33]) ).
thf(f33,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( mimplies
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',mimplies_def) ).
thf(f54,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f35]) ).
thf(f35,plain,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',law2) ).
thf(f119,plain,
( ( class @ second @ sK2 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
( ( $false = $true )
| ( ( class @ second @ sK2 )
= $true ) ),
inference(superposition,[status(thm)],[f86,f112]) ).
thf(f112,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( class @ second @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( class @ second @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f110]) ).
thf(f110,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( class @ second ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f65,f62,f67]) ).
thf(f65,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
mlocal @ ( mbox @ ( class @ second ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
mlocal @ ( mbox @ ( class @ second ) ),
file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',belief2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NLP267^3 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n023.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 10:55:19 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : NLP267^3 : TPTP v9.2.1. Released v8.1.0.
% 0.29/0.45 % Domain : Natural Language Processing
% 0.29/0.45 % Problem : Ticket example
% 0.29/0.45 % Version : [BP13] axioms.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [FH+98] Farinas del Cerro et al. (1998), Belief Reconstruction
% 0.29/0.45 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.29/0.45 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.29/0.45 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.29/0.45 % Source : [TPTP]
% 0.29/0.45 % Names : APM001+1 [QMLTP]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.00 v8.2.0, 0.15 v8.1.0
% 0.29/0.45 % Syntax : Number of formulae : 35 ( 9 unt; 19 typ; 8 def)
% 0.29/0.45 % Number of atoms : 54 ( 8 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 7 ( 3 avg)
% 0.29/0.45 % Number of connectives : 66 ( 1 ~; 1 |; 2 &; 59 @)
% 0.29/0.45 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 8 ( 3 avg)
% 0.29/0.45 % Number of types : 3 ( 1 usr)
% 0.29/0.45 % Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 19 ( 18 usr; 6 con; 0-3 aty)
% 0.29/0.45 % Number of variables : 23 ( 19 ^; 2 !; 2 ?; 23 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.29/0.45 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.29/0.45 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.29/0.45 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.29/0.45 % $modalities == $modal_system_D].
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(mworld,type,
% 0.29/0.45 mworld: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(mrel_type,type,
% 0.29/0.45 mrel: mworld > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mactual_type,type,
% 0.29/0.45 mactual: mworld ).
% 0.29/0.45
% 0.29/0.45 thf(mlocal_type,type,
% 0.29/0.45 mlocal: ( mworld > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mlocal_def,definition,
% 0.29/0.45 ( mlocal
% 0.29/0.45 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mnot_type,type,
% 0.29/0.45 mnot: ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mand_type,type,
% 0.29/0.45 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mor_type,type,
% 0.29/0.45 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mimplies_type,type,
% 0.29/0.45 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mequiv_type,type,
% 0.29/0.45 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mnot_def,definition,
% 0.29/0.45 ( mnot
% 0.29/0.45 = ( ^ [A: mworld > $o,W: mworld] :
% 0.29/0.45 ~ ( A @ W ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mand_def,definition,
% 0.29/0.45 ( mand
% 0.29/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.45 ( ( A @ W )
% 0.29/0.45 & ( B @ W ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mor_def,definition,
% 0.29/0.45 ( mor
% 0.29/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.45 ( ( A @ W )
% 0.29/0.45 | ( B @ W ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mimplies_def,definition,
% 0.29/0.45 ( mimplies
% 0.29/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.45 ( ( A @ W )
% 0.29/0.45 => ( B @ W ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mequiv_def,definition,
% 0.29/0.45 ( mequiv
% 0.29/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.45 ( ( A @ W )
% 0.29/0.45 <=> ( B @ W ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mbox_type,type,
% 0.29/0.45 mbox: ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mbox_def,definition,
% 0.29/0.45 ( mbox
% 0.29/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/0.45 ! [V: mworld] :
% 0.29/0.45 ( ( mrel @ W @ V )
% 0.29/0.45 => ( Phi @ V ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mdia_type,type,
% 0.29/0.45 mdia: ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mdia_def,definition,
% 0.29/0.45 ( mdia
% 0.29/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/0.45 ? [V: mworld] :
% 0.29/0.45 ( ( mrel @ W @ V )
% 0.29/0.45 & ( Phi @ V ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mrel_serial,axiom,
% 0.29/0.45 ! [W: mworld] :
% 0.29/0.45 ? [V: mworld] : ( mrel @ W @ V ) ).
% 0.29/0.45
% 0.29/0.45 thf(seventy_decl,type,
% 0.29/0.45 seventy: $i ).
% 0.29/0.45
% 0.29/0.45 thf(ninetyfive_decl,type,
% 0.29/0.45 ninetyfive: $i ).
% 0.29/0.45
% 0.29/0.45 thf(second_decl,type,
% 0.29/0.45 second: $i ).
% 0.29/0.45
% 0.29/0.45 thf(paris_decl,type,
% 0.29/0.45 paris: $i ).
% 0.29/0.45
% 0.29/0.45 thf(first_decl,type,
% 0.29/0.45 first: $i ).
% 0.29/0.45
% 0.29/0.45 thf(price_decl,type,
% 0.29/0.45 price: $i > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(dest_decl,type,
% 0.29/0.45 dest: $i > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(class_decl,type,
% 0.29/0.45 class: $i > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(law1,axiom,
% 0.29/0.45 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(law2,axiom,
% 0.29/0.45 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(law3,axiom,
% 0.29/0.45 mlocal @ ( mbox @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(law4,axiom,
% 0.29/0.45 mlocal @ ( mbox @ ( mnot @ ( mand @ ( price @ ninetyfive ) @ ( price @ seventy ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(belief1,axiom,
% 0.29/0.45 mlocal @ ( mbox @ ( dest @ paris ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(belief2,axiom,
% 0.29/0.45 mlocal @ ( mbox @ ( class @ second ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(con,conjecture,
% 0.29/0.45 mlocal @ ( mbox @ ( price @ seventy ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.55/1.27 ---- Embedded in THF ---
% 1.55/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.27 %%% Generated on Tue Feb 24 10:55:20 EST 2026
% 1.55/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.27 %%% Logic specification used:
% 1.55/1.27 %%% thf(spec, logic, $$dhol).
% 1.55/1.27
% 1.55/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2DTF2492.p
% See solution above
% 1.55/1.27 ------------------------
% 1.55/1.28 ---- Cleaned THF ---
% 1.55/1.28 thf(mworld,type,
% 1.55/1.28 mworld: $tType ).
% 1.55/1.28
% 1.55/1.28 thf(mrel_type,type,
% 1.55/1.28 mrel: mworld > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mactual_type,type,
% 1.55/1.28 mactual: mworld ).
% 1.55/1.28
% 1.55/1.28 thf(mlocal_type,type,
% 1.55/1.28 mlocal: ( mworld > $o ) > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mlocal_def,definition,
% 1.55/1.28 ( mlocal
% 1.55/1.28 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mnot_type,type,
% 1.55/1.28 mnot: ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mand_type,type,
% 1.55/1.28 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mor_type,type,
% 1.55/1.28 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mimplies_type,type,
% 1.55/1.28 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mequiv_type,type,
% 1.55/1.28 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mnot_def,definition,
% 1.55/1.28 ( mnot
% 1.55/1.28 = ( ^ [A: mworld > $o,W: mworld] :
% 1.55/1.28 ~ ( A @ W ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mand_def,definition,
% 1.55/1.28 ( mand
% 1.55/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.55/1.28 ( ( A @ W )
% 1.55/1.28 & ( B @ W ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mor_def,definition,
% 1.55/1.28 ( mor
% 1.55/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.55/1.28 ( ( A @ W )
% 1.55/1.28 | ( B @ W ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mimplies_def,definition,
% 1.55/1.28 ( mimplies
% 1.55/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.55/1.28 ( ( A @ W )
% 1.55/1.28 => ( B @ W ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mequiv_def,definition,
% 1.55/1.28 ( mequiv
% 1.55/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.55/1.28 ( ( A @ W )
% 1.55/1.28 <=> ( B @ W ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mbox_type,type,
% 1.55/1.28 mbox: ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mbox_def,definition,
% 1.55/1.28 ( mbox
% 1.55/1.28 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.55/1.28 ! [V: mworld] :
% 1.55/1.28 ( ( mrel @ W @ V )
% 1.55/1.28 => ( Phi @ V ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mdia_type,type,
% 1.55/1.28 mdia: ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mdia_def,definition,
% 1.55/1.28 ( mdia
% 1.55/1.28 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.55/1.28 ? [V: mworld] :
% 1.55/1.28 ( ( mrel @ W @ V )
% 1.55/1.28 & ( Phi @ V ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mrel_serial,axiom,
% 1.55/1.28 ! [W: mworld] :
% 1.55/1.28 ? [V: mworld] : ( mrel @ W @ V ) ).
% 1.55/1.28
% 1.55/1.28 thf(seventy_decl,type,
% 1.55/1.28 seventy: $i ).
% 1.55/1.28
% 1.55/1.28 thf(ninetyfive_decl,type,
% 1.55/1.28 ninetyfive: $i ).
% 1.55/1.28
% 1.55/1.28 thf(second_decl,type,
% 1.55/1.28 second: $i ).
% 1.55/1.28
% 1.55/1.28 thf(paris_decl,type,
% 1.55/1.28 paris: $i ).
% 1.55/1.28
% 1.55/1.28 thf(first_decl,type,
% 1.55/1.28 first: $i ).
% 1.55/1.28
% 1.55/1.28 thf(price_decl,type,
% 1.55/1.28 price: $i > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(dest_decl,type,
% 1.55/1.28 dest: $i > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(class_decl,type,
% 1.55/1.28 class: $i > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(law1,axiom,
% 1.55/1.28 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(law2,axiom,
% 1.55/1.28 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(law3,axiom,
% 1.55/1.28 mlocal @ ( mbox @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(law4,axiom,
% 1.55/1.28 mlocal @ ( mbox @ ( mnot @ ( mand @ ( price @ ninetyfive ) @ ( price @ seventy ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(belief1,axiom,
% 1.55/1.28 mlocal @ ( mbox @ ( dest @ paris ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(belief2,axiom,
% 1.55/1.28 mlocal @ ( mbox @ ( class @ second ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(con,conjecture,
% 1.55/1.28 mlocal @ ( mbox @ ( price @ seventy ) ) ).
% 1.55/1.28 ------------------------
% 1.55/1.29 % (2766)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2492 for (2999ds/183Mi)
% 1.55/1.29 % (2772)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2492 for (2999ds/18Mi)
% 1.72/1.30 % (2772)First to succeed.
% 1.72/1.30 % (2766)Also succeeded, but the first one will report.
% 1.72/1.30 % (2772)Refutation found. Thanks to Tanya!
% 1.72/1.30 % SZS status Theorem for DTF2THF_2492
% 1.72/1.30 % SZS output start Proof for DTF2THF_2492
% 1.72/1.30 thf(type_def_5, type, mworld: $tType).
% 1.72/1.30 thf(func_def_0, type, mworld: $tType).
% 1.72/1.30 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.72/1.30 thf(func_def_2, type, mactual: mworld).
% 1.72/1.30 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.72/1.30 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.72/1.30 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.72/1.30 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.72/1.30 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.72/1.30 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.72/1.30 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.72/1.30 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.72/1.30 thf(func_def_17, type, price: $i > mworld > $o).
% 1.72/1.30 thf(func_def_18, type, dest: $i > mworld > $o).
% 1.72/1.30 thf(func_def_19, type, class: $i > mworld > $o).
% 1.72/1.30 thf(func_def_33, type, sK0: mworld > mworld).
% 1.72/1.30 thf(func_def_35, type, sK2: mworld).
% 1.72/1.30 thf(f138,plain,(
% 1.72/1.30 $false),
% 1.72/1.30 inference(trivial_inequality_removal,[status(thm)],[f137])).
% 1.72/1.30 thf(f137,plain,(
% 1.72/1.30 ($false = $true)),
% 1.72/1.30 inference(backward_demodulation,[status(thm)],[f119,f136])).
% 1.72/1.30 thf(f136,plain,(
% 1.72/1.30 ((class @ second @ sK2) = $false)),
% 1.72/1.30 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.72/1.30 thf(f135,plain,(
% 1.72/1.30 ($false = $true) | ((class @ second @ sK2) = $false)),
% 1.72/1.30 inference(forward_demodulation,[status(thm)],[f134,f85])).
% 1.72/1.30 thf(f85,plain,(
% 1.72/1.30 ($false = (price @ seventy @ sK2))),
% 1.72/1.30 inference(binary_proxy_clausification,[status(thm)],[f84])).
% 1.72/1.30 thf(f84,plain,(
% 1.72/1.30 (((mrel @ mactual @ sK2) => (price @ seventy @ sK2)) = $false)),
% 1.72/1.30 inference(beta_eta_normalization,[status(thm)],[f83])).
% 1.72/1.30 thf(f83,plain,(
% 1.72/1.30 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (price @ seventy @ Y0))) @ sK2))),
% 1.72/1.30 inference(sigma_clausification,[status(thm)],[f82])).
% 1.72/1.30 thf(f82,plain,(
% 1.72/1.30 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (price @ seventy @ Y0)))) != $true)),
% 1.72/1.30 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.72/1.30 thf(f71,plain,(
% 1.72/1.30 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (price @ seventy))) != $true)),
% 1.72/1.30 inference(definition_unfolding,[status(thm)],[f56,f62,f67])).
% 1.72/1.30 thf(f67,plain,(
% 1.72/1.30 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.72/1.30 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.30 thf(f24,plain,(
% 1.72/1.30 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.72/1.30 inference(fool_elimination,[status(thm)],[f23])).
% 1.72/1.30 thf(f23,plain,(
% 1.72/1.30 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 1.72/1.30 inference(rectify,[status(thm)],[f7])).
% 1.72/1.30 thf(f7,axiom,(
% 1.72/1.30 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 1.72/1.30 file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',mbox_def)).
% 1.72/1.30 thf(f62,plain,(
% 1.72/1.30 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.72/1.30 inference(cnf_transformation,[status(thm)],[f39])).
% 1.72/1.30 thf(f39,plain,(
% 1.72/1.30 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.72/1.30 inference(fool_elimination,[status(thm)],[f1])).
% 1.72/1.30 thf(f1,axiom,(
% 1.72/1.30 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.72/1.30 file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',mlocal_def)).
% 1.72/1.30 thf(f56,plain,(
% 1.72/1.30 ((mlocal @ (mbox @ (price @ seventy))) != $true)),
% 1.72/1.30 inference(cnf_transformation,[status(thm)],[f50])).
% 1.72/1.30 thf(f50,plain,(
% 1.72/1.30 ((mlocal @ (mbox @ (price @ seventy))) != $true)),
% 1.72/1.30 inference(flattening,[status(thm)],[f26])).
% 1.72/1.30 thf(f26,plain,(
% 1.72/1.30 ~((mlocal @ (mbox @ (price @ seventy))) = $true)),
% 1.72/1.30 inference(fool_elimination,[status(thm)],[f25])).
% 1.72/1.30 thf(f25,plain,(
% 1.72/1.30 ~(mlocal @ (mbox @ (price @ seventy)))),
% 1.72/1.30 inference(rectify,[status(thm)],[f17])).
% 1.72/1.30 thf(f17,negated_conjecture,(
% 1.72/1.30 ~(mlocal @ (mbox @ (price @ seventy)))),
% 1.72/1.30 inference(negated_conjecture,[status(cth)],[f16])).
% 1.72/1.30 thf(f16,conjecture,(
% 1.72/1.30 (mlocal @ (mbox @ (price @ seventy)))),
% 1.72/1.30 file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',con)).
% 1.72/1.30 thf(f134,plain,(
% 1.72/1.30 ((class @ second @ sK2) = $false) | ($true = (price @ seventy @ sK2))),
% 1.72/1.30 inference(trivial_inequality_removal,[status(thm)],[f127])).
% 1.72/1.30 thf(f127,plain,(
% 1.72/1.30 ((class @ second @ sK2) = $false) | ($false = $true) | ($true = (price @ seventy @ sK2))),
% 1.72/1.30 inference(superposition,[status(thm)],[f126,f86])).
% 1.72/1.30 thf(f86,plain,(
% 1.72/1.30 ((mrel @ mactual @ sK2) = $true)),
% 1.72/1.30 inference(binary_proxy_clausification,[status(thm)],[f84])).
% 1.72/1.30 thf(f126,plain,(
% 1.72/1.30 ( ! [X0 : mworld] : (($false = (mrel @ mactual @ X0)) | ((price @ seventy @ X0) = $true) | ($false = (class @ second @ X0))) )),
% 1.72/1.30 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.72/1.30 thf(f125,plain,(
% 1.72/1.30 ( ! [X0 : mworld] : (((price @ seventy @ X0) = $true) | ($false = (class @ second @ X0)) | ($false = (mrel @ mactual @ X0)) | ($false = $true)) )),
% 1.72/1.30 inference(duplicate_literal_removal,[status(thm)],[f121])).
% 1.72/1.30 thf(f121,plain,(
% 1.72/1.30 ( ! [X0 : mworld] : (($false = (class @ second @ X0)) | ($false = (mrel @ mactual @ X0)) | ($false = (mrel @ mactual @ X0)) | ($false = $true) | ((price @ seventy @ X0) = $true)) )),
% 1.72/1.30 inference(superposition,[status(thm)],[f102,f96])).
% 1.72/1.30 thf(f96,plain,(
% 1.72/1.30 ( ! [X1 : mworld] : (($true = (dest @ paris @ X1)) | ((mrel @ mactual @ X1) = $false)) )),
% 1.72/1.30 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.72/1.30 thf(f95,plain,(
% 1.72/1.30 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (dest @ paris @ X1)) = $true)) )),
% 1.72/1.30 inference(beta_eta_normalization,[status(thm)],[f94])).
% 1.72/1.30 thf(f94,plain,(
% 1.72/1.30 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (dest @ paris @ Y0))) @ X1) = $true)) )),
% 1.72/1.30 inference(pi_clausification,[status(thm)],[f93])).
% 1.72/1.30 thf(f93,plain,(
% 1.72/1.30 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (dest @ paris @ Y0)))) = $true)),
% 1.72/1.30 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.72/1.30 thf(f73,plain,(
% 1.72/1.30 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (dest @ paris))) = $true)),
% 1.72/1.30 inference(definition_unfolding,[status(thm)],[f63,f62,f67])).
% 1.72/1.30 thf(f63,plain,(
% 1.72/1.30 ((mlocal @ (mbox @ (dest @ paris))) = $true)),
% 1.72/1.30 inference(cnf_transformation,[status(thm)],[f28])).
% 1.72/1.30 thf(f28,plain,(
% 1.72/1.30 ((mlocal @ (mbox @ (dest @ paris))) = $true)),
% 1.72/1.30 inference(fool_elimination,[status(thm)],[f27])).
% 1.72/1.30 thf(f27,plain,(
% 1.72/1.30 (mlocal @ (mbox @ (dest @ paris)))),
% 1.72/1.30 inference(rectify,[status(thm)],[f14])).
% 1.72/1.30 thf(f14,axiom,(
% 1.72/1.30 (mlocal @ (mbox @ (dest @ paris)))),
% 1.72/1.30 file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',belief1)).
% 1.72/1.30 thf(f102,plain,(
% 1.72/1.30 ( ! [X1 : mworld] : (($false = (dest @ paris @ X1)) | ((class @ second @ X1) = $false) | ((mrel @ mactual @ X1) = $false) | ((price @ seventy @ X1) = $true)) )),
% 1.72/1.30 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.72/1.30 thf(f101,plain,(
% 1.72/1.30 ( ! [X1 : mworld] : (((price @ seventy @ X1) = $true) | ((mrel @ mactual @ X1) = $false) | (((dest @ paris @ X1) & (class @ second @ X1)) = $false)) )),
% 1.72/1.30 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.72/1.30 thf(f100,plain,(
% 1.72/1.30 ( ! [X1 : mworld] : (((((dest @ paris @ X1) & (class @ second @ X1)) => (price @ seventy @ X1)) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 1.72/1.30 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.72/1.30 thf(f99,plain,(
% 1.72/1.30 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (((dest @ paris @ X1) & (class @ second @ X1)) => (price @ seventy @ X1))) = $true)) )),
% 1.72/1.30 inference(beta_eta_normalization,[status(thm)],[f98])).
% 1.72/1.30 thf(f98,plain,(
% 1.72/1.30 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (((dest @ paris @ Y0) & (class @ second @ Y0)) => (price @ seventy @ Y0)))) @ X1) = $true)) )),
% 1.72/1.30 inference(pi_clausification,[status(thm)],[f97])).
% 1.72/1.30 thf(f97,plain,(
% 1.72/1.30 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (((dest @ paris @ Y0) & (class @ second @ Y0)) => (price @ seventy @ Y0))))) = $true)),
% 1.72/1.30 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.72/1.30 thf(f69,plain,(
% 1.72/1.30 (((^[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]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.72/1.30 inference(definition_unfolding,[status(thm)],[f54,f62,f67,f58,f57])).
% 1.72/1.30 thf(f57,plain,(
% 1.72/1.30 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.72/1.30 inference(cnf_transformation,[status(thm)],[f47])).
% 1.72/1.30 thf(f47,plain,(
% 1.72/1.30 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.72/1.30 inference(fool_elimination,[status(thm)],[f46])).
% 1.72/1.30 thf(f46,plain,(
% 1.72/1.30 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 1.72/1.30 inference(rectify,[status(thm)],[f3])).
% 1.72/1.30 thf(f3,axiom,(
% 1.72/1.30 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))))),
% 1.72/1.30 file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',mand_def)).
% 1.72/1.30 thf(f58,plain,(
% 1.72/1.30 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.72/1.30 inference(cnf_transformation,[status(thm)],[f34])).
% 1.72/1.30 thf(f34,plain,(
% 1.72/1.30 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.72/1.30 inference(fool_elimination,[status(thm)],[f33])).
% 1.72/1.30 thf(f33,plain,(
% 1.72/1.30 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.72/1.30 inference(rectify,[status(thm)],[f5])).
% 1.72/1.30 thf(f5,axiom,(
% 1.72/1.30 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.72/1.30 file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',mimplies_def)).
% 1.72/1.30 thf(f54,plain,(
% 1.72/1.30 ((mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.72/1.30 inference(cnf_transformation,[status(thm)],[f36])).
% 1.72/1.30 thf(f36,plain,(
% 1.72/1.30 ((mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.72/1.30 inference(fool_elimination,[status(thm)],[f35])).
% 1.72/1.30 thf(f35,plain,(
% 1.72/1.30 (mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy))))),
% 1.72/1.30 inference(rectify,[status(thm)],[f11])).
% 1.72/1.30 thf(f11,axiom,(
% 1.72/1.30 (mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy))))),
% 1.72/1.30 file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',law2)).
% 1.72/1.30 thf(f119,plain,(
% 1.72/1.30 ((class @ second @ sK2) = $true)),
% 1.72/1.30 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.72/1.30 thf(f116,plain,(
% 1.72/1.30 ($false = $true) | ((class @ second @ sK2) = $true)),
% 1.72/1.30 inference(superposition,[status(thm)],[f86,f112])).
% 1.72/1.30 thf(f112,plain,(
% 1.72/1.30 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((class @ second @ X1) = $true)) )),
% 1.72/1.30 inference(binary_proxy_clausification,[status(thm)],[f111])).
% 1.72/1.30 thf(f111,plain,(
% 1.72/1.30 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (class @ second @ X1)) = $true)) )),
% 1.72/1.30 inference(beta_eta_normalization,[status(thm)],[f110])).
% 1.72/1.30 thf(f110,plain,(
% 1.72/1.30 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (class @ second @ Y0))) @ X1) = $true)) )),
% 1.72/1.30 inference(pi_clausification,[status(thm)],[f109])).
% 1.72/1.30 thf(f109,plain,(
% 1.72/1.30 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (class @ second @ Y0)))) = $true)),
% 1.72/1.30 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.72/1.30 thf(f75,plain,(
% 1.72/1.30 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (class @ second))) = $true)),
% 1.72/1.30 inference(definition_unfolding,[status(thm)],[f65,f62,f67])).
% 1.72/1.30 thf(f65,plain,(
% 1.72/1.30 ((mlocal @ (mbox @ (class @ second))) = $true)),
% 1.72/1.30 inference(cnf_transformation,[status(thm)],[f22])).
% 1.72/1.30 thf(f22,plain,(
% 1.72/1.30 ((mlocal @ (mbox @ (class @ second))) = $true)),
% 1.72/1.30 inference(fool_elimination,[status(thm)],[f21])).
% 1.72/1.30 thf(f21,plain,(
% 1.72/1.30 (mlocal @ (mbox @ (class @ second)))),
% 1.72/1.30 inference(rectify,[status(thm)],[f15])).
% 1.72/1.30 thf(f15,axiom,(
% 1.72/1.30 (mlocal @ (mbox @ (class @ second)))),
% 1.72/1.30 file('/export/starexec/sandbox/tmp/tmp.RlgiO9hvUd/DTF2THF_2492.p',belief2)).
% 1.72/1.30 % SZS output end Proof for DTF2THF_2492
% 1.72/1.30 % (2772)------------------------------
% 1.72/1.30 % (2772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.30 % (2772)Termination reason: Refutation
% 1.72/1.30
% 1.72/1.30 % (2772)Memory used [KB]: 5628
% 1.72/1.30 % (2772)Time elapsed: 0.006 s
% 1.72/1.30 % (2772)Instructions burned: 11 (million)
% 1.72/1.30 % (2772)------------------------------
% 1.72/1.30 % (2772)------------------------------
% 1.72/1.30 % (2765)Success in time 0.017 s
%------------------------------------------------------------------------------