%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NLP267^18 : 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 : n025.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 1.61s 2.01s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 385 ( 74 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 420 ( 7 ~; 20 |; 15 &; 345 @)
% ( 0 <=>; 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 : 24 ( 20 usr; 10 con; 0-3 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 101 ( 71 ^; 30 !; 0 ?; 101 :)
% 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(f188,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f186]) ).
thf(f186,plain,
$false = $true,
inference(superposition,[status(thm)],[f110,f180]) ).
thf(f180,plain,
! [X0: mworld] :
( ( price @ seventy @ X0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f178]) ).
thf(f178,plain,
! [X0: mworld] :
( ( ( price @ seventy @ X0 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f175,f66]) ).
thf(f66,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ '#b_s' @ X0 @ X1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ '#b_s' @ X0 @ X1 )
= $true ),
inference(fool_elimination,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: mworld,X1: mworld] : ( mrel @ '#b_s' @ X0 @ X1 ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
! [X2: mworld,X5: mworld] : ( mrel @ '#b_s' @ X2 @ X5 ),
file('/export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p','mrel_#b_s_universal') ).
thf(f175,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) )
| ( ( price @ seventy @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f172]) ).
thf(f172,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) )
| ( $false = $true )
| ( ( price @ seventy @ X1 )
= $true ) ),
inference(backward_demodulation,[status(thm)],[f159,f170]) ).
thf(f170,plain,
! [X0: mworld] :
( $true
= ( dest @ paris @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f169]) ).
thf(f169,plain,
! [X0: mworld] :
( ( $true
= ( dest @ paris @ X0 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f66,f129]) ).
thf(f129,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) )
| ( ( dest @ paris @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f127]) ).
thf(f127,plain,
! [X1: mworld] :
( ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
= $true )
| ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f126]) ).
thf(f126,plain,
! [X1: mworld] :
( ( ( mrel @ '#b_s' @ mactual @ X1 )
=> ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f125]) ).
thf(f125,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ '#b_s' @ mactual @ Y0 )
=> ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_s' @ mactual @ Y0 )
=> ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,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 ) )
@ ( dest @ paris )
@ ( class @ second ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f57,f71,f70,f68]) ).
thf(f68,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
thf(f55,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f54]) ).
thf(f54,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/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.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)],[f24]) ).
thf(f24,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,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/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p',mbox_def) ).
thf(f71,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f45,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p',mlocal_def) ).
thf(f57,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f41]) ).
thf(f41,plain,
mlocal @ ( mbox @ '#b_s' @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,axiom,
mlocal @ ( mbox @ '#b_s' @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p',axiom_5) ).
thf(f159,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) )
| ( ( price @ seventy @ X1 )
= $true )
| ( $false
= ( dest @ paris @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) )
| ( $false = $true )
| ( ( price @ seventy @ X1 )
= $true )
| ( $false
= ( dest @ paris @ X1 ) ) ),
inference(backward_demodulation,[status(thm)],[f106,f152]) ).
thf(f152,plain,
! [X0: mworld] :
( $true
= ( class @ second @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
! [X0: mworld] :
( ( $true
= ( class @ second @ X0 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f128,f66]) ).
thf(f128,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) )
| ( $true
= ( class @ second @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f127]) ).
thf(f106,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) )
| ( $false
= ( dest @ paris @ X1 ) )
| ( ( price @ seventy @ X1 )
= $true )
| ( $false
= ( class @ second @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,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)],[f104]) ).
thf(f104,plain,
! [X1: mworld] :
( ( ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
=> ( price @ seventy @ X1 ) )
= $true )
| ( $false
= ( mrel @ '#b_s' @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X1: mworld] :
( ( ( mrel @ '#b_s' @ mactual @ X1 )
=> ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
=> ( price @ seventy @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f102]) ).
thf(f102,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ '#b_s' @ mactual @ Y0 )
=> ( ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_s' @ mactual @ Y0 )
=> ( ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f76]) ).
thf(f76,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 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( dest @ paris )
@ ( class @ second ) )
@ ( price @ seventy ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f60,f71,f70,f73,f68]) ).
thf(f73,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f35]) ).
thf(f35,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.BQLjuivjMC/DTF2THF_14124.p',mimplies_def) ).
thf(f60,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f46]) ).
thf(f46,plain,
mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p',axiom_2) ).
thf(f110,plain,
( $false
= ( price @ seventy @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
( $false
= ( ( mrel @ '#b_s' @ mactual @ sK1 )
=> ( price @ seventy @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f108]) ).
thf(f108,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#b_s' @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_s' @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ^ [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 ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f74,f71,f70]) ).
thf(f74,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f56]) ).
thf(f56,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) )
!= $true ),
inference(flattening,[status(thm)],[f51]) ).
thf(f51,plain,
( ( mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f50]) ).
thf(f50,plain,
~ ( mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,negated_conjecture,
~ ( mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
thf(f18,conjecture,
mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ),
file('/export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p',con) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.24 % Problem : NLP267^18 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.25 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.52 % Computer : n025.cluster.edu
% 0.17/0.52 % Model : x86_64 x86_64
% 0.17/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.52 % Memory : 8042.1875MB
% 0.17/0.52 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.52 % CPULimit : 300
% 0.17/0.52 % WCLimit : 300
% 0.17/0.52 % DateTime : Tue Feb 24 10:54:29 EST 2026
% 0.17/0.52 % CPUTime :
% 0.17/0.52 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.85 ---- Original DTF file ---
% 0.19/0.85 thf(spec,logic,$$dhol).
% 0.19/0.85 %------------------------------------------------------------------------------
% 0.19/0.85 % File : NLP267^18 : TPTP v9.2.1. Released v8.1.0.
% 0.19/0.85 % Domain : Natural Language Processing
% 0.19/0.85 % Problem : Ticket example
% 0.19/0.85 % Version : [BP13] axioms.
% 0.19/0.85 % English :
% 0.19/0.85
% 0.19/0.85 % Refs : [FH+98] Farinas del Cerro et al. (1998), Belief Reconstruction
% 0.19/0.85 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.19/0.85 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.19/0.85 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.19/0.85 % Source : [TPTP]
% 0.19/0.85 % Names : MML016+1 [QMLTP]
% 0.19/0.85
% 0.19/0.85 % Status : Theorem
% 0.19/0.85 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0
% 0.19/0.85 % Syntax : Number of formulae : 40 ( 10 unt; 22 typ; 8 def)
% 0.19/0.85 % Number of atoms : 66 ( 8 equ; 0 cnn)
% 0.19/0.85 % Maximal formula atoms : 7 ( 3 avg)
% 0.19/0.85 % Number of connectives : 94 ( 1 ~; 1 |; 2 &; 87 @)
% 0.19/0.85 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.85 % Maximal formula depth : 8 ( 4 avg)
% 0.19/0.85 % Number of types : 4 ( 2 usr)
% 0.19/0.85 % Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% 0.19/0.85 % Number of symbols : 21 ( 20 usr; 8 con; 0-3 aty)
% 0.19/0.85 % Number of variables : 27 ( 21 ^; 5 !; 1 ?; 27 :)
% 0.19/0.85 % SPC : TH0_THM_EQU_NAR
% 0.19/0.85
% 0.19/0.85 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.19/0.85 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.19/0.85 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.19/0.85 % $modal == [$constants == $rigid,$quantification == $cumulative,
% 0.19/0.85 % $modalities == $modal_system_S5U].
% 0.19/0.85 %------------------------------------------------------------------------------
% 0.19/0.85 thf(mworld,type,
% 0.19/0.85 mworld: $tType ).
% 0.19/0.85
% 0.19/0.85 thf(mindex,type,
% 0.19/0.85 mindex: $tType ).
% 0.19/0.85
% 0.19/0.85 thf(mrel_type,type,
% 0.19/0.85 mrel: mindex > mworld > mworld > $o ).
% 0.19/0.85
% 0.19/0.85 thf('#b_u_type',type,
% 0.19/0.85 '#b_u': mindex ).
% 0.19/0.85
% 0.19/0.85 thf('#b_s_type',type,
% 0.19/0.85 '#b_s': mindex ).
% 0.19/0.85
% 0.19/0.85 thf(mactual_type,type,
% 0.19/0.85 mactual: mworld ).
% 0.19/0.85
% 0.19/0.85 thf(mlocal_type,type,
% 0.19/0.85 mlocal: ( mworld > $o ) > $o ).
% 0.19/0.85
% 0.19/0.85 thf(mlocal_def,definition,
% 0.19/0.85 ( mlocal
% 0.19/0.85 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(mnot_type,type,
% 0.19/0.85 mnot: ( mworld > $o ) > mworld > $o ).
% 0.19/0.85
% 0.19/0.85 thf(mand_type,type,
% 0.19/0.85 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.85
% 0.19/0.85 thf(mor_type,type,
% 0.19/0.85 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.85
% 0.19/0.85 thf(mimplies_type,type,
% 0.19/0.85 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.85
% 0.19/0.85 thf(mequiv_type,type,
% 0.19/0.85 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.85
% 0.19/0.85 thf(mnot_def,definition,
% 0.19/0.85 ( mnot
% 0.19/0.85 = ( ^ [A: mworld > $o,W: mworld] :
% 0.19/0.85 ~ ( A @ W ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(mand_def,definition,
% 0.19/0.85 ( mand
% 0.19/0.85 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.85 ( ( A @ W )
% 0.19/0.85 & ( B @ W ) ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(mor_def,definition,
% 0.19/0.85 ( mor
% 0.19/0.85 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.85 ( ( A @ W )
% 0.19/0.85 | ( B @ W ) ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(mimplies_def,definition,
% 0.19/0.85 ( mimplies
% 0.19/0.85 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.85 ( ( A @ W )
% 0.19/0.85 => ( B @ W ) ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(mequiv_def,definition,
% 0.19/0.85 ( mequiv
% 0.19/0.85 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.85 ( ( A @ W )
% 0.19/0.85 <=> ( B @ W ) ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(mbox_type,type,
% 0.19/0.85 mbox: mindex > ( mworld > $o ) > mworld > $o ).
% 0.19/0.85
% 0.19/0.85 thf(mbox_def,definition,
% 0.19/0.85 ( mbox
% 0.19/0.85 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.19/0.85 ! [V: mworld] :
% 0.19/0.85 ( ( mrel @ R @ W @ V )
% 0.19/0.85 => ( Phi @ V ) ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(mdia_type,type,
% 0.19/0.85 mdia: mindex > ( mworld > $o ) > mworld > $o ).
% 0.19/0.85
% 0.19/0.85 thf(mdia_def,definition,
% 0.19/0.85 ( mdia
% 0.19/0.85 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.19/0.85 ? [V: mworld] :
% 0.19/0.85 ( ( mrel @ R @ W @ V )
% 0.19/0.85 & ( Phi @ V ) ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf('mrel_#b_u_universal',axiom,
% 0.19/0.85 ! [W: mworld,V: mworld] : ( mrel @ '#b_u' @ W @ V ) ).
% 0.19/0.85
% 0.19/0.85 thf('mrel_#b_s_universal',axiom,
% 0.19/0.85 ! [W: mworld,V: mworld] : ( mrel @ '#b_s' @ W @ V ) ).
% 0.19/0.85
% 0.19/0.85 thf(seventy_decl,type,
% 0.19/0.85 seventy: $i ).
% 0.19/0.85
% 0.19/0.85 thf(ninetyfive_decl,type,
% 0.19/0.85 ninetyfive: $i ).
% 0.19/0.85
% 0.19/0.85 thf(second_decl,type,
% 0.19/0.85 second: $i ).
% 0.19/0.85
% 0.19/0.85 thf(paris_decl,type,
% 0.19/0.85 paris: $i ).
% 0.19/0.85
% 0.19/0.85 thf(first_decl,type,
% 0.19/0.85 first: $i ).
% 0.19/0.85
% 0.19/0.85 thf(price_decl,type,
% 0.19/0.85 price: $i > mworld > $o ).
% 0.19/0.85
% 0.19/0.85 thf(dest_decl,type,
% 0.19/0.85 dest: $i > mworld > $o ).
% 0.19/0.85
% 0.19/0.85 thf(class_decl,type,
% 0.19/0.85 class: $i > mworld > $o ).
% 0.19/0.85
% 0.19/0.85 thf(axiom_1,axiom,
% 0.19/0.85 mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(axiom_2,axiom,
% 0.19/0.85 mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(axiom_3_s,axiom,
% 0.19/0.85 mlocal @ ( mbox @ '#b_s' @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(axiom_3_u,axiom,
% 0.19/0.85 mlocal @ ( mbox @ '#b_u' @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(axiom_4_s,axiom,
% 0.19/0.85 mlocal @ ( mbox @ '#b_s' @ ( mnot @ ( mand @ ( price @ seventy ) @ ( price @ ninetyfive ) ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(axiom_4_u,axiom,
% 0.19/0.85 mlocal @ ( mbox @ '#b_u' @ ( mnot @ ( mand @ ( price @ seventy ) @ ( price @ ninetyfive ) ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(axiom_5,axiom,
% 0.19/0.85 mlocal @ ( mbox @ '#b_s' @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) ) ).
% 0.19/0.85
% 0.19/0.85 thf(con,conjecture,
% 0.19/0.85 mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) ).
% 0.19/0.85
% 0.19/0.85 %------------------------------------------------------------------------------
% 0.19/0.85 ------------------------
% 1.61/1.96 ---- Embedded in THF ---
% 1.61/1.96 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.96 %%% Generated on Tue Feb 24 10:54:30 EST 2026
% 1.61/1.96 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.96 %%% Logic specification used:
% 1.61/1.96 %%% thf(spec, logic, $$dhol).
% 1.61/1.96
% 1.61/1.96 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2DTF14124.p
% See solution above
% 1.61/1.96 ------------------------
% 1.61/1.98 ---- Cleaned THF ---
% 1.61/1.98 thf(mworld,type,
% 1.61/1.98 mworld: $tType ).
% 1.61/1.98
% 1.61/1.98 thf(mindex,type,
% 1.61/1.98 mindex: $tType ).
% 1.61/1.98
% 1.61/1.98 thf(mrel_type,type,
% 1.61/1.98 mrel: mindex > mworld > mworld > $o ).
% 1.61/1.98
% 1.61/1.98 thf('#b_u_type',type,
% 1.61/1.98 '#b_u': mindex ).
% 1.61/1.98
% 1.61/1.98 thf('#b_s_type',type,
% 1.61/1.98 '#b_s': mindex ).
% 1.61/1.98
% 1.61/1.98 thf(mactual_type,type,
% 1.61/1.98 mactual: mworld ).
% 1.61/1.98
% 1.61/1.98 thf(mlocal_type,type,
% 1.61/1.98 mlocal: ( mworld > $o ) > $o ).
% 1.61/1.98
% 1.61/1.98 thf(mlocal_def,definition,
% 1.61/1.98 ( mlocal
% 1.61/1.98 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(mnot_type,type,
% 1.61/1.98 mnot: ( mworld > $o ) > mworld > $o ).
% 1.61/1.98
% 1.61/1.98 thf(mand_type,type,
% 1.61/1.98 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.61/1.98
% 1.61/1.98 thf(mor_type,type,
% 1.61/1.98 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.61/1.98
% 1.61/1.98 thf(mimplies_type,type,
% 1.61/1.98 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.61/1.98
% 1.61/1.98 thf(mequiv_type,type,
% 1.61/1.98 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.61/1.98
% 1.61/1.98 thf(mnot_def,definition,
% 1.61/1.98 ( mnot
% 1.61/1.98 = ( ^ [A: mworld > $o,W: mworld] :
% 1.61/1.98 ~ ( A @ W ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(mand_def,definition,
% 1.61/1.98 ( mand
% 1.61/1.98 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.61/1.98 ( ( A @ W )
% 1.61/1.98 & ( B @ W ) ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(mor_def,definition,
% 1.61/1.98 ( mor
% 1.61/1.98 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.61/1.98 ( ( A @ W )
% 1.61/1.98 | ( B @ W ) ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(mimplies_def,definition,
% 1.61/1.98 ( mimplies
% 1.61/1.98 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.61/1.98 ( ( A @ W )
% 1.61/1.98 => ( B @ W ) ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(mequiv_def,definition,
% 1.61/1.98 ( mequiv
% 1.61/1.98 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.61/1.98 ( ( A @ W )
% 1.61/1.98 <=> ( B @ W ) ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(mbox_type,type,
% 1.61/1.98 mbox: mindex > ( mworld > $o ) > mworld > $o ).
% 1.61/1.98
% 1.61/1.98 thf(mbox_def,definition,
% 1.61/1.98 ( mbox
% 1.61/1.98 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 1.61/1.98 ! [V: mworld] :
% 1.61/1.98 ( ( mrel @ R @ W @ V )
% 1.61/1.98 => ( Phi @ V ) ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(mdia_type,type,
% 1.61/1.98 mdia: mindex > ( mworld > $o ) > mworld > $o ).
% 1.61/1.98
% 1.61/1.98 thf(mdia_def,definition,
% 1.61/1.98 ( mdia
% 1.61/1.98 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 1.61/1.98 ? [V: mworld] :
% 1.61/1.98 ( ( mrel @ R @ W @ V )
% 1.61/1.98 & ( Phi @ V ) ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf('mrel_#b_u_universal',axiom,
% 1.61/1.98 ! [W: mworld,V: mworld] : ( mrel @ '#b_u' @ W @ V ) ).
% 1.61/1.98
% 1.61/1.98 thf('mrel_#b_s_universal',axiom,
% 1.61/1.98 ! [W: mworld,V: mworld] : ( mrel @ '#b_s' @ W @ V ) ).
% 1.61/1.98
% 1.61/1.98 thf(seventy_decl,type,
% 1.61/1.98 seventy: $i ).
% 1.61/1.98
% 1.61/1.98 thf(ninetyfive_decl,type,
% 1.61/1.98 ninetyfive: $i ).
% 1.61/1.98
% 1.61/1.98 thf(second_decl,type,
% 1.61/1.98 second: $i ).
% 1.61/1.98
% 1.61/1.98 thf(paris_decl,type,
% 1.61/1.98 paris: $i ).
% 1.61/1.98
% 1.61/1.98 thf(first_decl,type,
% 1.61/1.98 first: $i ).
% 1.61/1.98
% 1.61/1.98 thf(price_decl,type,
% 1.61/1.98 price: $i > mworld > $o ).
% 1.61/1.98
% 1.61/1.98 thf(dest_decl,type,
% 1.61/1.98 dest: $i > mworld > $o ).
% 1.61/1.98
% 1.61/1.98 thf(class_decl,type,
% 1.61/1.98 class: $i > mworld > $o ).
% 1.61/1.98
% 1.61/1.98 thf(axiom_1,axiom,
% 1.61/1.98 mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(axiom_2,axiom,
% 1.61/1.98 mlocal @ ( mbox @ '#b_s' @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(axiom_3_s,axiom,
% 1.61/1.98 mlocal @ ( mbox @ '#b_s' @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(axiom_3_u,axiom,
% 1.61/1.98 mlocal @ ( mbox @ '#b_u' @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(axiom_4_s,axiom,
% 1.61/1.98 mlocal @ ( mbox @ '#b_s' @ ( mnot @ ( mand @ ( price @ seventy ) @ ( price @ ninetyfive ) ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(axiom_4_u,axiom,
% 1.61/1.98 mlocal @ ( mbox @ '#b_u' @ ( mnot @ ( mand @ ( price @ seventy ) @ ( price @ ninetyfive ) ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(axiom_5,axiom,
% 1.61/1.98 mlocal @ ( mbox @ '#b_s' @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(con,conjecture,
% 1.61/1.98 mlocal @ ( mbox @ '#b_s' @ ( price @ seventy ) ) ).
% 1.61/1.98 ------------------------
% 1.61/2.00 % (14296)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_14124 for (2999ds/27Mi)
% 1.61/2.00 % (14295)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_14124 for (2999ds/4Mi)
% 1.61/2.00 % (14297)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14124 for (2999ds/2Mi)
% 1.61/2.00 % (14295)Instruction limit reached!
% 1.61/2.00 % (14295)------------------------------
% 1.61/2.00 % (14295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/2.00 % (14295)Termination reason: Unknown
% 1.61/2.00 % (14295)Termination phase: Property scanning
% 1.61/2.00
% 1.61/2.00 % (14295)Memory used [KB]: 1023
% 1.61/2.00 % (14295)Time elapsed: 0.004 s
% 1.61/2.00 % (14295)Instructions burned: 5 (million)
% 1.61/2.00 % (14295)------------------------------
% 1.61/2.00 % (14295)------------------------------
% 1.61/2.00 % (14297)Instruction limit reached!
% 1.61/2.00 % (14297)------------------------------
% 1.61/2.00 % (14297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/2.00 % (14297)Termination reason: Unknown
% 1.61/2.00 % (14297)Termination phase: shuffling
% 1.61/2.00
% 1.61/2.00 % (14297)Memory used [KB]: 1023
% 1.61/2.00 % (14297)Time elapsed: 0.003 s
% 1.61/2.00 % (14297)Instructions burned: 2 (million)
% 1.61/2.00 % (14297)------------------------------
% 1.61/2.00 % (14297)------------------------------
% 1.61/2.00 % (14296)First to succeed.
% 1.61/2.01 % (14296)Refutation found. Thanks to Tanya!
% 1.61/2.01 % SZS status Theorem for DTF2THF_14124
% 1.61/2.01 % SZS output start Proof for DTF2THF_14124
% 1.61/2.01 thf(type_def_5, type, mindex: $tType).
% 1.61/2.01 thf(type_def_6, type, mworld: $tType).
% 1.61/2.01 thf(func_def_0, type, mworld: $tType).
% 1.61/2.01 thf(func_def_1, type, mindex: $tType).
% 1.61/2.01 thf(func_def_2, type, mrel: mindex > mworld > mworld > $o).
% 1.61/2.01 thf(func_def_3, type, '#b_u': mindex).
% 1.61/2.01 thf(func_def_4, type, '#b_s': mindex).
% 1.61/2.01 thf(func_def_5, type, mactual: mworld).
% 1.61/2.01 thf(func_def_6, type, mlocal: (mworld > $o) > $o).
% 1.61/2.01 thf(func_def_8, type, mnot: (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_9, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_10, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_11, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_12, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_13, type, mbox: mindex > (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_14, type, mdia: mindex > (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_20, type, price: $i > mworld > $o).
% 1.61/2.01 thf(func_def_21, type, dest: $i > mworld > $o).
% 1.61/2.01 thf(func_def_22, type, class: $i > mworld > $o).
% 1.61/2.01 thf(func_def_23, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.61/2.01 thf(func_def_39, type, sK1: mworld).
% 1.61/2.01 thf(f188,plain,(
% 1.61/2.01 $false),
% 1.61/2.01 inference(trivial_inequality_removal,[status(thm)],[f186])).
% 1.61/2.01 thf(f186,plain,(
% 1.61/2.01 ($false = $true)),
% 1.61/2.01 inference(superposition,[status(thm)],[f110,f180])).
% 1.61/2.01 thf(f180,plain,(
% 1.61/2.01 ( ! [X0 : mworld] : (((price @ seventy @ X0) = $true)) )),
% 1.61/2.01 inference(trivial_inequality_removal,[status(thm)],[f178])).
% 1.61/2.01 thf(f178,plain,(
% 1.61/2.01 ( ! [X0 : mworld] : (((price @ seventy @ X0) = $true) | ($false = $true)) )),
% 1.61/2.01 inference(superposition,[status(thm)],[f175,f66])).
% 1.61/2.01 thf(f66,plain,(
% 1.61/2.01 ( ! [X0 : mworld,X1 : mworld] : (((mrel @ '#b_s' @ X0 @ X1) = $true)) )),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f30])).
% 1.61/2.01 thf(f30,plain,(
% 1.61/2.01 ! [X0 : mworld,X1 : mworld] : ((mrel @ '#b_s' @ X0 @ X1) = $true)),
% 1.61/2.01 inference(fool_elimination,[status(thm)],[f29])).
% 1.61/2.01 thf(f29,plain,(
% 1.61/2.01 ! [X0 : mworld,X1 : mworld] : (mrel @ '#b_s' @ X0 @ X1)),
% 1.61/2.01 inference(rectify,[status(thm)],[f10])).
% 1.61/2.01 thf(f10,axiom,(
% 1.61/2.01 ! [X2 : mworld,X5 : mworld] : (mrel @ '#b_s' @ X2 @ X5)),
% 1.61/2.01 file('/export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p','mrel_#b_s_universal')).
% 1.61/2.01 thf(f175,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : (($false = (mrel @ '#b_s' @ mactual @ X1)) | ((price @ seventy @ X1) = $true)) )),
% 1.61/2.01 inference(trivial_inequality_removal,[status(thm)],[f172])).
% 1.61/2.01 thf(f172,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : (($false = (mrel @ '#b_s' @ mactual @ X1)) | ($false = $true) | ((price @ seventy @ X1) = $true)) )),
% 1.61/2.01 inference(backward_demodulation,[status(thm)],[f159,f170])).
% 1.61/2.01 thf(f170,plain,(
% 1.61/2.01 ( ! [X0 : mworld] : (($true = (dest @ paris @ X0))) )),
% 1.61/2.01 inference(trivial_inequality_removal,[status(thm)],[f169])).
% 1.61/2.01 thf(f169,plain,(
% 1.61/2.01 ( ! [X0 : mworld] : (($true = (dest @ paris @ X0)) | ($false = $true)) )),
% 1.61/2.01 inference(superposition,[status(thm)],[f66,f129])).
% 1.61/2.01 thf(f129,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : (($false = (mrel @ '#b_s' @ mactual @ X1)) | ((dest @ paris @ X1) = $true)) )),
% 1.61/2.01 inference(binary_proxy_clausification,[status(thm)],[f127])).
% 1.61/2.01 thf(f127,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : ((((dest @ paris @ X1) & (class @ second @ X1)) = $true) | ($false = (mrel @ '#b_s' @ mactual @ X1))) )),
% 1.61/2.01 inference(binary_proxy_clausification,[status(thm)],[f126])).
% 1.61/2.01 thf(f126,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : ((((mrel @ '#b_s' @ mactual @ X1) => ((dest @ paris @ X1) & (class @ second @ X1))) = $true)) )),
% 1.61/2.01 inference(beta_eta_normalization,[status(thm)],[f125])).
% 1.61/2.01 thf(f125,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ '#b_s' @ mactual @ Y0) => ((dest @ paris @ Y0) & (class @ second @ Y0)))) @ X1) = $true)) )),
% 1.61/2.01 inference(pi_clausification,[status(thm)],[f124])).
% 1.61/2.01 thf(f124,plain,(
% 1.61/2.01 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#b_s' @ mactual @ Y0) => ((dest @ paris @ Y0) & (class @ second @ Y0))))) = $true)),
% 1.61/2.01 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.61/2.01 thf(f75,plain,(
% 1.61/2.01 ($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))))))) @ (dest @ paris) @ (class @ second)))))),
% 1.61/2.01 inference(definition_unfolding,[status(thm)],[f57,f71,f70,f68])).
% 1.61/2.01 thf(f68,plain,(
% 1.61/2.01 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f55])).
% 1.61/2.01 thf(f55,plain,(
% 1.61/2.01 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.61/2.01 inference(fool_elimination,[status(thm)],[f54])).
% 1.61/2.01 thf(f54,plain,(
% 1.61/2.01 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 1.61/2.01 inference(rectify,[status(thm)],[f3])).
% 1.61/2.01 thf(f3,axiom,(
% 1.61/2.01 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))))),
% 1.61/2.01 file('/export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p',mand_def)).
% 1.61/2.01 thf(f70,plain,(
% 1.61/2.01 (mbox = (^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f24])).
% 1.61/2.01 thf(f24,plain,(
% 1.61/2.01 (mbox = (^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 1.61/2.01 inference(fool_elimination,[status(thm)],[f23])).
% 1.61/2.01 thf(f23,plain,(
% 1.61/2.01 (mbox = (^[X0 : mindex, X1 : mworld > $o, X2 : mworld] : (! [X3 : mworld] : ((mrel @ X0 @ X2 @ X3) => (X1 @ X3)))))),
% 1.61/2.01 inference(rectify,[status(thm)],[f7])).
% 1.61/2.01 thf(f7,axiom,(
% 1.61/2.01 (mbox = (^[X4 : mindex, X0 : mworld > $o, X2 : mworld] : (! [X5 : mworld] : ((mrel @ X4 @ X2 @ X5) => (X0 @ X5)))))),
% 1.61/2.01 file('/export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p',mbox_def)).
% 1.61/2.01 thf(f71,plain,(
% 1.61/2.01 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f45])).
% 1.61/2.01 thf(f45,plain,(
% 1.61/2.01 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.61/2.01 inference(fool_elimination,[status(thm)],[f1])).
% 1.61/2.01 thf(f1,axiom,(
% 1.61/2.01 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.61/2.01 file('/export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p',mlocal_def)).
% 1.61/2.01 thf(f57,plain,(
% 1.61/2.01 ((mlocal @ (mbox @ '#b_s' @ (mand @ (dest @ paris) @ (class @ second)))) = $true)),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f42])).
% 1.61/2.01 thf(f42,plain,(
% 1.61/2.01 ((mlocal @ (mbox @ '#b_s' @ (mand @ (dest @ paris) @ (class @ second)))) = $true)),
% 1.61/2.01 inference(fool_elimination,[status(thm)],[f41])).
% 1.61/2.01 thf(f41,plain,(
% 1.61/2.01 (mlocal @ (mbox @ '#b_s' @ (mand @ (dest @ paris) @ (class @ second))))),
% 1.61/2.01 inference(rectify,[status(thm)],[f17])).
% 1.61/2.01 thf(f17,axiom,(
% 1.61/2.01 (mlocal @ (mbox @ '#b_s' @ (mand @ (dest @ paris) @ (class @ second))))),
% 1.61/2.01 file('/export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p',axiom_5)).
% 1.61/2.01 thf(f159,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : (($false = (mrel @ '#b_s' @ mactual @ X1)) | ((price @ seventy @ X1) = $true) | ($false = (dest @ paris @ X1))) )),
% 1.61/2.01 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 1.61/2.01 thf(f154,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : (($false = (mrel @ '#b_s' @ mactual @ X1)) | ($false = $true) | ((price @ seventy @ X1) = $true) | ($false = (dest @ paris @ X1))) )),
% 1.61/2.01 inference(backward_demodulation,[status(thm)],[f106,f152])).
% 1.61/2.01 thf(f152,plain,(
% 1.61/2.01 ( ! [X0 : mworld] : (($true = (class @ second @ X0))) )),
% 1.61/2.01 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.61/2.01 thf(f150,plain,(
% 1.61/2.01 ( ! [X0 : mworld] : (($true = (class @ second @ X0)) | ($false = $true)) )),
% 1.61/2.01 inference(superposition,[status(thm)],[f128,f66])).
% 1.61/2.01 thf(f128,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : (($false = (mrel @ '#b_s' @ mactual @ X1)) | ($true = (class @ second @ X1))) )),
% 1.61/2.01 inference(binary_proxy_clausification,[status(thm)],[f127])).
% 1.61/2.01 thf(f106,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : (($false = (mrel @ '#b_s' @ mactual @ X1)) | ($false = (dest @ paris @ X1)) | ((price @ seventy @ X1) = $true) | ($false = (class @ second @ X1))) )),
% 1.61/2.01 inference(binary_proxy_clausification,[status(thm)],[f105])).
% 1.61/2.01 thf(f105,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : (($false = (mrel @ '#b_s' @ mactual @ X1)) | ($false = ((dest @ paris @ X1) & (class @ second @ X1))) | ((price @ seventy @ X1) = $true)) )),
% 1.61/2.01 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 1.61/2.01 thf(f104,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : (((((dest @ paris @ X1) & (class @ second @ X1)) => (price @ seventy @ X1)) = $true) | ($false = (mrel @ '#b_s' @ mactual @ X1))) )),
% 1.61/2.01 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.61/2.01 thf(f103,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : ((((mrel @ '#b_s' @ mactual @ X1) => (((dest @ paris @ X1) & (class @ second @ X1)) => (price @ seventy @ X1))) = $true)) )),
% 1.61/2.01 inference(beta_eta_normalization,[status(thm)],[f102])).
% 1.61/2.01 thf(f102,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ '#b_s' @ mactual @ Y0) => (((dest @ paris @ Y0) & (class @ second @ Y0)) => (price @ seventy @ Y0)))) @ X1) = $true)) )),
% 1.61/2.01 inference(pi_clausification,[status(thm)],[f101])).
% 1.61/2.01 thf(f101,plain,(
% 1.61/2.01 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#b_s' @ mactual @ Y0) => (((dest @ paris @ Y0) & (class @ second @ Y0)) => (price @ seventy @ Y0))))) = $true)),
% 1.61/2.01 inference(beta_eta_normalization,[status(thm)],[f76])).
% 1.61/2.01 thf(f76,plain,(
% 1.61/2.01 (((^[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)))) = $true)),
% 1.61/2.01 inference(definition_unfolding,[status(thm)],[f60,f71,f70,f73,f68])).
% 1.61/2.01 thf(f73,plain,(
% 1.61/2.01 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f36])).
% 1.61/2.01 thf(f36,plain,(
% 1.61/2.01 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.61/2.01 inference(fool_elimination,[status(thm)],[f35])).
% 1.61/2.01 thf(f35,plain,(
% 1.61/2.01 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.61/2.01 inference(rectify,[status(thm)],[f5])).
% 1.61/2.01 thf(f5,axiom,(
% 1.61/2.01 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.61/2.01 file('/export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p',mimplies_def)).
% 1.61/2.01 thf(f60,plain,(
% 1.61/2.01 ((mlocal @ (mbox @ '#b_s' @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f47])).
% 1.61/2.01 thf(f47,plain,(
% 1.61/2.01 ((mlocal @ (mbox @ '#b_s' @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.61/2.01 inference(fool_elimination,[status(thm)],[f46])).
% 1.61/2.01 thf(f46,plain,(
% 1.61/2.01 (mlocal @ (mbox @ '#b_s' @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy))))),
% 1.61/2.01 inference(rectify,[status(thm)],[f12])).
% 1.61/2.01 thf(f12,axiom,(
% 1.61/2.01 (mlocal @ (mbox @ '#b_s' @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy))))),
% 1.61/2.01 file('/export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p',axiom_2)).
% 1.61/2.01 thf(f110,plain,(
% 1.61/2.01 ($false = (price @ seventy @ sK1))),
% 1.61/2.01 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.61/2.01 thf(f109,plain,(
% 1.61/2.01 ($false = ((mrel @ '#b_s' @ mactual @ sK1) => (price @ seventy @ sK1)))),
% 1.61/2.01 inference(beta_eta_normalization,[status(thm)],[f108])).
% 1.61/2.01 thf(f108,plain,(
% 1.61/2.01 ($false = ((^[Y0 : mworld]: ((mrel @ '#b_s' @ mactual @ Y0) => (price @ seventy @ Y0))) @ sK1))),
% 1.61/2.01 inference(sigma_clausification,[status(thm)],[f107])).
% 1.61/2.01 thf(f107,plain,(
% 1.61/2.01 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#b_s' @ mactual @ Y0) => (price @ seventy @ Y0)))) != $true)),
% 1.61/2.01 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.61/2.01 thf(f82,plain,(
% 1.61/2.01 (((^[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))) != $true)),
% 1.61/2.01 inference(definition_unfolding,[status(thm)],[f74,f71,f70])).
% 1.61/2.01 thf(f74,plain,(
% 1.61/2.01 ((mlocal @ (mbox @ '#b_s' @ (price @ seventy))) != $true)),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f56])).
% 1.61/2.01 thf(f56,plain,(
% 1.61/2.01 ((mlocal @ (mbox @ '#b_s' @ (price @ seventy))) != $true)),
% 1.61/2.01 inference(flattening,[status(thm)],[f51])).
% 1.61/2.01 thf(f51,plain,(
% 1.61/2.01 ~((mlocal @ (mbox @ '#b_s' @ (price @ seventy))) = $true)),
% 1.61/2.01 inference(fool_elimination,[status(thm)],[f50])).
% 1.61/2.01 thf(f50,plain,(
% 1.61/2.01 ~(mlocal @ (mbox @ '#b_s' @ (price @ seventy)))),
% 1.61/2.01 inference(rectify,[status(thm)],[f19])).
% 1.61/2.01 thf(f19,negated_conjecture,(
% 1.61/2.01 ~(mlocal @ (mbox @ '#b_s' @ (price @ seventy)))),
% 1.61/2.01 inference(negated_conjecture,[status(cth)],[f18])).
% 1.61/2.01 thf(f18,conjecture,(
% 1.61/2.01 (mlocal @ (mbox @ '#b_s' @ (price @ seventy)))),
% 1.61/2.01 file('/export/starexec/sandbox2/tmp/tmp.BQLjuivjMC/DTF2THF_14124.p',con)).
% 1.61/2.01 % SZS output end Proof for DTF2THF_14124
% 1.61/2.01 % (14296)------------------------------
% 1.61/2.01 % (14296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/2.01 % (14296)Termination reason: Refutation
% 1.61/2.01
% 1.61/2.01 % (14296)Memory used [KB]: 5628
% 1.61/2.01 % (14296)Time elapsed: 0.010 s
% 1.61/2.01 % (14296)Instructions burned: 21 (million)
% 1.61/2.01 % (14296)------------------------------
% 1.61/2.01 % (14296)------------------------------
% 1.61/2.01 % (14286)Success in time 0.024 s
%------------------------------------------------------------------------------