%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NLP267^1 : 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 : n013.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 1.60s 1.96s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 73 ( 48 unt; 0 typ; 1 def)
% Number of atoms : 412 ( 79 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 386 ( 11 ~; 22 |; 10 &; 303 @)
% ( 1 <=>; 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 : 23 ( 19 usr; 9 con; 0-3 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 80 ( 67 ^; 13 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mrel: mworld > mworld > $o ).
thf(func_def_2,type,
mactual: mworld ).
thf(func_def_3,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_5,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_17,type,
price: $i > mworld > $o ).
thf(func_def_18,type,
dest: $i > mworld > $o ).
thf(func_def_19,type,
class: $i > mworld > $o ).
thf(func_def_20,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_35,type,
sK1: mworld ).
thf(f164,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f158,f163]) ).
thf(f163,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f162]) ).
thf(f162,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f161]) ).
thf(f161,plain,
( ( $false = $true )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f113,f142]) ).
thf(f142,plain,
( ( $false
= ( dest @ paris @ sK1 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f140]) ).
thf(f140,definition,
( spl0_3
<=> ( $false
= ( dest @ paris @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f113,plain,
( ( dest @ paris @ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
( ( ( dest @ paris @ sK1 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f80,f106]) ).
thf(f106,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( dest @ paris @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( dest @ paris @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f104]) ).
thf(f104,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,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)],[f53,f55,f58]) ).
thf(f58,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f45]) ).
thf(f45,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/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',mbox_def) ).
thf(f55,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,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/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',mlocal_def) ).
thf(f53,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f29]) ).
thf(f29,plain,
mlocal @ ( mbox @ ( dest @ paris ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
mlocal @ ( mbox @ ( dest @ paris ) ),
file('/export/starexec/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',belief1) ).
thf(f80,plain,
( $true
= ( mrel @ mactual @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ( mrel @ mactual @ sK1 )
=> ( price @ seventy @ sK1 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,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)],[f59,f55,f58]) ).
thf(f59,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(flattening,[status(thm)],[f42]) ).
thf(f42,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f41]) ).
thf(f41,plain,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,negated_conjecture,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f15,conjecture,
mlocal @ ( mbox @ ( price @ seventy ) ),
file('/export/starexec/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',con) ).
thf(f158,plain,
spl0_3,
inference(avatar_split_clause,[status(thm)],[f157,f140]) ).
thf(f157,plain,
( $false
= ( dest @ paris @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f156]) ).
thf(f156,plain,
( ( $false = $true )
| ( $false
= ( dest @ paris @ sK1 ) ) ),
inference(forward_demodulation,[status(thm)],[f155,f79]) ).
thf(f79,plain,
( ( price @ seventy @ sK1 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f155,plain,
( ( ( price @ seventy @ sK1 )
= $true )
| ( $false
= ( dest @ paris @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
( ( ( price @ seventy @ sK1 )
= $true )
| ( $false
= ( dest @ paris @ sK1 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f147,f109]) ).
thf(f109,plain,
( ( class @ second @ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ( ( class @ second @ sK1 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f96,f80]) ).
thf(f96,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( class @ second @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( class @ second @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f94]) ).
thf(f94,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( class @ second ) ) ) ),
inference(definition_unfolding,[status(thm)],[f48,f55,f58]) ).
thf(f48,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
mlocal @ ( mbox @ ( class @ second ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
mlocal @ ( mbox @ ( class @ second ) ),
file('/export/starexec/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',belief2) ).
thf(f147,plain,
( ( $false
= ( class @ second @ sK1 ) )
| ( ( price @ seventy @ sK1 )
= $true )
| ( $false
= ( dest @ paris @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f145]) ).
thf(f145,plain,
( ( ( price @ seventy @ sK1 )
= $true )
| ( $false
= ( dest @ paris @ sK1 ) )
| ( $false
= ( class @ second @ sK1 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f86,f80]) ).
thf(f86,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( price @ seventy @ X1 )
= $true )
| ( ( class @ second @ X1 )
= $false )
| ( $false
= ( dest @ paris @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( price @ seventy @ X1 )
= $true )
| ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
=> ( price @ seventy @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
=> ( price @ seventy @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,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)],[f56,f55,f58,f50,f49]) ).
thf(f49,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f35]) ).
thf(f35,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/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',mand_def) ).
thf(f50,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/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',mimplies_def) ).
thf(f56,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',law2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.19 % Problem : NLP267^1 : TPTP v9.2.1. Released v8.1.0.
% 0.09/0.20 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.48 % Computer : n013.cluster.edu
% 0.15/0.48 % Model : x86_64 x86_64
% 0.15/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.48 % Memory : 8042.1875MB
% 0.15/0.48 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.48 % CPULimit : 300
% 0.15/0.48 % WCLimit : 300
% 0.15/0.48 % DateTime : Tue Feb 24 10:54:09 EST 2026
% 0.15/0.48 % CPUTime :
% 0.15/0.48 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.75 ---- Original DTF file ---
% 0.29/0.75 thf(spec,logic,$$dhol).
% 0.29/0.75 %------------------------------------------------------------------------------
% 0.29/0.75 % File : NLP267^1 : TPTP v9.2.1. Released v8.1.0.
% 0.29/0.75 % Domain : Natural Language Processing
% 0.29/0.75 % Problem : Ticket example
% 0.29/0.75 % Version : [BP13] axioms.
% 0.29/0.75 % English :
% 0.29/0.75
% 0.29/0.75 % Refs : [FH+98] Farinas del Cerro et al. (1998), Belief Reconstruction
% 0.29/0.75 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.29/0.75 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.29/0.75 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.29/0.75 % Source : [TPTP]
% 0.29/0.75 % Names : APM001+1 [QMLTP]
% 0.29/0.75
% 0.29/0.75 % Status : Theorem
% 0.29/0.75 % Rating : 0.00 v8.2.0, 0.15 v8.1.0
% 0.29/0.75 % Syntax : Number of formulae : 34 ( 8 unt; 19 typ; 8 def)
% 0.29/0.75 % Number of atoms : 53 ( 8 equ; 0 cnn)
% 0.29/0.75 % Maximal formula atoms : 7 ( 3 avg)
% 0.29/0.75 % Number of connectives : 64 ( 1 ~; 1 |; 2 &; 57 @)
% 0.29/0.75 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.29/0.75 % Maximal formula depth : 8 ( 3 avg)
% 0.29/0.75 % Number of types : 3 ( 1 usr)
% 0.29/0.75 % Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% 0.29/0.75 % Number of symbols : 19 ( 18 usr; 6 con; 0-3 aty)
% 0.29/0.75 % Number of variables : 21 ( 19 ^; 1 !; 1 ?; 21 :)
% 0.29/0.75 % SPC : TH0_THM_EQU_NAR
% 0.29/0.75
% 0.29/0.75 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.29/0.75 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.29/0.75 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.29/0.75 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.29/0.75 % $modalities == $modal_system_K].
% 0.29/0.75 %------------------------------------------------------------------------------
% 0.29/0.75 thf(mworld,type,
% 0.29/0.75 mworld: $tType ).
% 0.29/0.75
% 0.29/0.75 thf(mrel_type,type,
% 0.29/0.75 mrel: mworld > mworld > $o ).
% 0.29/0.75
% 0.29/0.75 thf(mactual_type,type,
% 0.29/0.75 mactual: mworld ).
% 0.29/0.75
% 0.29/0.75 thf(mlocal_type,type,
% 0.29/0.75 mlocal: ( mworld > $o ) > $o ).
% 0.29/0.75
% 0.29/0.75 thf(mlocal_def,definition,
% 0.29/0.75 ( mlocal
% 0.29/0.75 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(mnot_type,type,
% 0.29/0.75 mnot: ( mworld > $o ) > mworld > $o ).
% 0.29/0.75
% 0.29/0.75 thf(mand_type,type,
% 0.29/0.75 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.75
% 0.29/0.75 thf(mor_type,type,
% 0.29/0.75 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.75
% 0.29/0.75 thf(mimplies_type,type,
% 0.29/0.75 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.75
% 0.29/0.75 thf(mequiv_type,type,
% 0.29/0.75 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.75
% 0.29/0.75 thf(mnot_def,definition,
% 0.29/0.75 ( mnot
% 0.29/0.75 = ( ^ [A: mworld > $o,W: mworld] :
% 0.29/0.75 ~ ( A @ W ) ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(mand_def,definition,
% 0.29/0.75 ( mand
% 0.29/0.75 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.75 ( ( A @ W )
% 0.29/0.75 & ( B @ W ) ) ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(mor_def,definition,
% 0.29/0.75 ( mor
% 0.29/0.75 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.75 ( ( A @ W )
% 0.29/0.75 | ( B @ W ) ) ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(mimplies_def,definition,
% 0.29/0.75 ( mimplies
% 0.29/0.75 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.75 ( ( A @ W )
% 0.29/0.75 => ( B @ W ) ) ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(mequiv_def,definition,
% 0.29/0.75 ( mequiv
% 0.29/0.75 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.75 ( ( A @ W )
% 0.29/0.75 <=> ( B @ W ) ) ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(mbox_type,type,
% 0.29/0.75 mbox: ( mworld > $o ) > mworld > $o ).
% 0.29/0.75
% 0.29/0.75 thf(mbox_def,definition,
% 0.29/0.75 ( mbox
% 0.29/0.75 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/0.75 ! [V: mworld] :
% 0.29/0.75 ( ( mrel @ W @ V )
% 0.29/0.75 => ( Phi @ V ) ) ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(mdia_type,type,
% 0.29/0.75 mdia: ( mworld > $o ) > mworld > $o ).
% 0.29/0.75
% 0.29/0.75 thf(mdia_def,definition,
% 0.29/0.75 ( mdia
% 0.29/0.75 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/0.75 ? [V: mworld] :
% 0.29/0.75 ( ( mrel @ W @ V )
% 0.29/0.75 & ( Phi @ V ) ) ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(seventy_decl,type,
% 0.29/0.75 seventy: $i ).
% 0.29/0.75
% 0.29/0.75 thf(ninetyfive_decl,type,
% 0.29/0.75 ninetyfive: $i ).
% 0.29/0.75
% 0.29/0.75 thf(second_decl,type,
% 0.29/0.75 second: $i ).
% 0.29/0.75
% 0.29/0.75 thf(paris_decl,type,
% 0.29/0.75 paris: $i ).
% 0.29/0.75
% 0.29/0.75 thf(first_decl,type,
% 0.29/0.75 first: $i ).
% 0.29/0.75
% 0.29/0.75 thf(price_decl,type,
% 0.29/0.75 price: $i > mworld > $o ).
% 0.29/0.75
% 0.29/0.75 thf(dest_decl,type,
% 0.29/0.75 dest: $i > mworld > $o ).
% 0.29/0.75
% 0.29/0.75 thf(class_decl,type,
% 0.29/0.75 class: $i > mworld > $o ).
% 0.29/0.75
% 0.29/0.75 thf(law1,axiom,
% 0.29/0.75 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(law2,axiom,
% 0.29/0.75 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(law3,axiom,
% 0.29/0.75 mlocal @ ( mbox @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(law4,axiom,
% 0.29/0.75 mlocal @ ( mbox @ ( mnot @ ( mand @ ( price @ ninetyfive ) @ ( price @ seventy ) ) ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(belief1,axiom,
% 0.29/0.75 mlocal @ ( mbox @ ( dest @ paris ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(belief2,axiom,
% 0.29/0.75 mlocal @ ( mbox @ ( class @ second ) ) ).
% 0.29/0.75
% 0.29/0.75 thf(con,conjecture,
% 0.29/0.75 mlocal @ ( mbox @ ( price @ seventy ) ) ).
% 0.29/0.75
% 0.29/0.75 %------------------------------------------------------------------------------
% 0.29/0.75 ------------------------
% 1.60/1.92 ---- Embedded in THF ---
% 1.60/1.93 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.60/1.93 %%% Generated on Tue Feb 24 10:54:11 EST 2026
% 1.60/1.93 %%% using '$$dhol' embedding, version 1.3.0.
% 1.60/1.93 %%% Logic specification used:
% 1.60/1.93 %%% thf(spec, logic, $$dhol).
% 1.60/1.93
% 1.60/1.93 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2DTF13351.p
% See solution above
% 1.60/1.93 ------------------------
% 1.60/1.94 ---- Cleaned THF ---
% 1.60/1.94 thf(mworld,type,
% 1.60/1.94 mworld: $tType ).
% 1.60/1.94
% 1.60/1.94 thf(mrel_type,type,
% 1.60/1.94 mrel: mworld > mworld > $o ).
% 1.60/1.94
% 1.60/1.94 thf(mactual_type,type,
% 1.60/1.94 mactual: mworld ).
% 1.60/1.94
% 1.60/1.94 thf(mlocal_type,type,
% 1.60/1.94 mlocal: ( mworld > $o ) > $o ).
% 1.60/1.94
% 1.60/1.94 thf(mlocal_def,definition,
% 1.60/1.94 ( mlocal
% 1.60/1.94 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(mnot_type,type,
% 1.60/1.94 mnot: ( mworld > $o ) > mworld > $o ).
% 1.60/1.94
% 1.60/1.94 thf(mand_type,type,
% 1.60/1.94 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.60/1.94
% 1.60/1.94 thf(mor_type,type,
% 1.60/1.94 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.60/1.94
% 1.60/1.94 thf(mimplies_type,type,
% 1.60/1.94 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.60/1.94
% 1.60/1.94 thf(mequiv_type,type,
% 1.60/1.94 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.60/1.94
% 1.60/1.94 thf(mnot_def,definition,
% 1.60/1.94 ( mnot
% 1.60/1.94 = ( ^ [A: mworld > $o,W: mworld] :
% 1.60/1.94 ~ ( A @ W ) ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(mand_def,definition,
% 1.60/1.94 ( mand
% 1.60/1.94 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.60/1.94 ( ( A @ W )
% 1.60/1.94 & ( B @ W ) ) ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(mor_def,definition,
% 1.60/1.94 ( mor
% 1.60/1.94 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.60/1.94 ( ( A @ W )
% 1.60/1.94 | ( B @ W ) ) ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(mimplies_def,definition,
% 1.60/1.94 ( mimplies
% 1.60/1.94 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.60/1.94 ( ( A @ W )
% 1.60/1.94 => ( B @ W ) ) ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(mequiv_def,definition,
% 1.60/1.94 ( mequiv
% 1.60/1.94 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.60/1.94 ( ( A @ W )
% 1.60/1.94 <=> ( B @ W ) ) ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(mbox_type,type,
% 1.60/1.94 mbox: ( mworld > $o ) > mworld > $o ).
% 1.60/1.94
% 1.60/1.94 thf(mbox_def,definition,
% 1.60/1.94 ( mbox
% 1.60/1.94 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.60/1.94 ! [V: mworld] :
% 1.60/1.94 ( ( mrel @ W @ V )
% 1.60/1.94 => ( Phi @ V ) ) ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(mdia_type,type,
% 1.60/1.94 mdia: ( mworld > $o ) > mworld > $o ).
% 1.60/1.94
% 1.60/1.94 thf(mdia_def,definition,
% 1.60/1.94 ( mdia
% 1.60/1.94 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.60/1.94 ? [V: mworld] :
% 1.60/1.94 ( ( mrel @ W @ V )
% 1.60/1.94 & ( Phi @ V ) ) ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(seventy_decl,type,
% 1.60/1.94 seventy: $i ).
% 1.60/1.94
% 1.60/1.94 thf(ninetyfive_decl,type,
% 1.60/1.94 ninetyfive: $i ).
% 1.60/1.94
% 1.60/1.94 thf(second_decl,type,
% 1.60/1.94 second: $i ).
% 1.60/1.94
% 1.60/1.94 thf(paris_decl,type,
% 1.60/1.94 paris: $i ).
% 1.60/1.94
% 1.60/1.94 thf(first_decl,type,
% 1.60/1.94 first: $i ).
% 1.60/1.94
% 1.60/1.94 thf(price_decl,type,
% 1.60/1.94 price: $i > mworld > $o ).
% 1.60/1.94
% 1.60/1.94 thf(dest_decl,type,
% 1.60/1.94 dest: $i > mworld > $o ).
% 1.60/1.94
% 1.60/1.94 thf(class_decl,type,
% 1.60/1.94 class: $i > mworld > $o ).
% 1.60/1.94
% 1.60/1.94 thf(law1,axiom,
% 1.60/1.94 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(law2,axiom,
% 1.60/1.94 mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(law3,axiom,
% 1.60/1.94 mlocal @ ( mbox @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(law4,axiom,
% 1.60/1.94 mlocal @ ( mbox @ ( mnot @ ( mand @ ( price @ ninetyfive ) @ ( price @ seventy ) ) ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(belief1,axiom,
% 1.60/1.94 mlocal @ ( mbox @ ( dest @ paris ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(belief2,axiom,
% 1.60/1.94 mlocal @ ( mbox @ ( class @ second ) ) ).
% 1.60/1.94
% 1.60/1.94 thf(con,conjecture,
% 1.60/1.94 mlocal @ ( mbox @ ( price @ seventy ) ) ).
% 1.60/1.94 ------------------------
% 1.60/1.95 % (13669)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_13351 for (2999ds/27Mi)
% 1.60/1.96 % (13669)First to succeed.
% 1.60/1.96 % (13668)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_13351 for (2999ds/4Mi)
% 1.60/1.96 % (13667)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13351 for (2999ds/183Mi)
% 1.60/1.96 % (13669)Refutation found. Thanks to Tanya!
% 1.60/1.96 % SZS status Theorem for DTF2THF_13351
% 1.60/1.96 % SZS output start Proof for DTF2THF_13351
% 1.60/1.96 thf(type_def_5, type, mworld: $tType).
% 1.60/1.96 thf(func_def_0, type, mworld: $tType).
% 1.60/1.96 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.60/1.96 thf(func_def_2, type, mactual: mworld).
% 1.60/1.96 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.60/1.96 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.60/1.96 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.60/1.96 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.60/1.96 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.60/1.96 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.60/1.96 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.60/1.96 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.60/1.96 thf(func_def_17, type, price: $i > mworld > $o).
% 1.60/1.96 thf(func_def_18, type, dest: $i > mworld > $o).
% 1.60/1.96 thf(func_def_19, type, class: $i > mworld > $o).
% 1.60/1.96 thf(func_def_20, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.60/1.96 thf(func_def_35, type, sK1: mworld).
% 1.60/1.96 thf(f164,plain,(
% 1.60/1.96 $false),
% 1.60/1.96 inference(avatar_sat_refutation,[status(thm)],[f158,f163])).
% 1.60/1.96 thf(f163,plain,(
% 1.60/1.96 ~spl0_3),
% 1.60/1.96 inference(avatar_contradiction_clause,[status(thm)],[f162])).
% 1.60/1.96 thf(f162,plain,(
% 1.60/1.96 $false | ~spl0_3),
% 1.60/1.96 inference(trivial_inequality_removal,[status(thm)],[f161])).
% 1.60/1.96 thf(f161,plain,(
% 1.60/1.96 ($false = $true) | ~spl0_3),
% 1.60/1.96 inference(backward_demodulation,[status(thm)],[f113,f142])).
% 1.60/1.96 thf(f142,plain,(
% 1.60/1.96 ($false = (dest @ paris @ sK1)) | ~spl0_3),
% 1.60/1.96 inference(avatar_component_clause,[status(thm)],[f140])).
% 1.60/1.96 thf(f140,definition,(
% 1.60/1.96 spl0_3 <=> ($false = (dest @ paris @ sK1))),
% 1.60/1.96 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.60/1.96 thf(f113,plain,(
% 1.60/1.96 ((dest @ paris @ sK1) = $true)),
% 1.60/1.96 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.60/1.96 thf(f112,plain,(
% 1.60/1.96 ((dest @ paris @ sK1) = $true) | ($false = $true)),
% 1.60/1.96 inference(superposition,[status(thm)],[f80,f106])).
% 1.60/1.96 thf(f106,plain,(
% 1.60/1.96 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((dest @ paris @ X1) = $true)) )),
% 1.60/1.96 inference(binary_proxy_clausification,[status(thm)],[f105])).
% 1.60/1.96 thf(f105,plain,(
% 1.60/1.96 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (dest @ paris @ X1)))) )),
% 1.60/1.96 inference(beta_eta_normalization,[status(thm)],[f104])).
% 1.60/1.96 thf(f104,plain,(
% 1.60/1.96 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (dest @ paris @ Y0))) @ X1) = $true)) )),
% 1.60/1.96 inference(pi_clausification,[status(thm)],[f103])).
% 1.60/1.96 thf(f103,plain,(
% 1.60/1.96 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (dest @ paris @ Y0)))))),
% 1.60/1.96 inference(beta_eta_normalization,[status(thm)],[f65])).
% 1.60/1.96 thf(f65,plain,(
% 1.60/1.96 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (dest @ paris))) = $true)),
% 1.60/1.96 inference(definition_unfolding,[status(thm)],[f53,f55,f58])).
% 1.60/1.96 thf(f58,plain,(
% 1.60/1.96 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.60/1.96 inference(cnf_transformation,[status(thm)],[f46])).
% 1.60/1.96 thf(f46,plain,(
% 1.60/1.96 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.60/1.96 inference(fool_elimination,[status(thm)],[f45])).
% 1.60/1.96 thf(f45,plain,(
% 1.60/1.96 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 1.60/1.96 inference(rectify,[status(thm)],[f7])).
% 1.60/1.96 thf(f7,axiom,(
% 1.60/1.96 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 1.60/1.96 file('/export/starexec/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',mbox_def)).
% 1.60/1.96 thf(f55,plain,(
% 1.60/1.96 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.60/1.96 inference(cnf_transformation,[status(thm)],[f24])).
% 1.60/1.96 thf(f24,plain,(
% 1.60/1.96 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.60/1.96 inference(fool_elimination,[status(thm)],[f1])).
% 1.60/1.96 thf(f1,axiom,(
% 1.60/1.96 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.60/1.96 file('/export/starexec/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',mlocal_def)).
% 1.60/1.96 thf(f53,plain,(
% 1.60/1.96 ((mlocal @ (mbox @ (dest @ paris))) = $true)),
% 1.60/1.96 inference(cnf_transformation,[status(thm)],[f30])).
% 1.60/1.96 thf(f30,plain,(
% 1.60/1.96 ((mlocal @ (mbox @ (dest @ paris))) = $true)),
% 1.60/1.96 inference(fool_elimination,[status(thm)],[f29])).
% 1.60/1.96 thf(f29,plain,(
% 1.60/1.96 (mlocal @ (mbox @ (dest @ paris)))),
% 1.60/1.96 inference(rectify,[status(thm)],[f13])).
% 1.60/1.96 thf(f13,axiom,(
% 1.60/1.96 (mlocal @ (mbox @ (dest @ paris)))),
% 1.60/1.96 file('/export/starexec/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',belief1)).
% 1.60/1.96 thf(f80,plain,(
% 1.60/1.96 ($true = (mrel @ mactual @ sK1))),
% 1.60/1.96 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.60/1.96 thf(f78,plain,(
% 1.60/1.96 (((mrel @ mactual @ sK1) => (price @ seventy @ sK1)) = $false)),
% 1.60/1.96 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.60/1.96 thf(f77,plain,(
% 1.60/1.96 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (price @ seventy @ Y0))) @ sK1))),
% 1.60/1.96 inference(sigma_clausification,[status(thm)],[f76])).
% 1.60/1.96 thf(f76,plain,(
% 1.60/1.96 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (price @ seventy @ Y0)))) != $true)),
% 1.60/1.96 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.60/1.96 thf(f68,plain,(
% 1.60/1.96 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (price @ seventy))) != $true)),
% 1.60/1.96 inference(definition_unfolding,[status(thm)],[f59,f55,f58])).
% 1.60/1.96 thf(f59,plain,(
% 1.60/1.96 ((mlocal @ (mbox @ (price @ seventy))) != $true)),
% 1.60/1.96 inference(cnf_transformation,[status(thm)],[f47])).
% 1.60/1.96 thf(f47,plain,(
% 1.60/1.96 ((mlocal @ (mbox @ (price @ seventy))) != $true)),
% 1.60/1.96 inference(flattening,[status(thm)],[f42])).
% 1.60/1.96 thf(f42,plain,(
% 1.60/1.96 ~((mlocal @ (mbox @ (price @ seventy))) = $true)),
% 1.60/1.96 inference(fool_elimination,[status(thm)],[f41])).
% 1.60/1.96 thf(f41,plain,(
% 1.60/1.96 ~(mlocal @ (mbox @ (price @ seventy)))),
% 1.60/1.96 inference(rectify,[status(thm)],[f16])).
% 1.60/1.96 thf(f16,negated_conjecture,(
% 1.60/1.96 ~(mlocal @ (mbox @ (price @ seventy)))),
% 1.60/1.96 inference(negated_conjecture,[status(cth)],[f15])).
% 1.60/1.96 thf(f15,conjecture,(
% 1.60/1.96 (mlocal @ (mbox @ (price @ seventy)))),
% 1.60/1.96 file('/export/starexec/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',con)).
% 1.60/1.96 thf(f158,plain,(
% 1.60/1.96 spl0_3),
% 1.60/1.96 inference(avatar_split_clause,[status(thm)],[f157,f140])).
% 1.60/1.96 thf(f157,plain,(
% 1.60/1.96 ($false = (dest @ paris @ sK1))),
% 1.60/1.96 inference(trivial_inequality_removal,[status(thm)],[f156])).
% 1.60/1.96 thf(f156,plain,(
% 1.60/1.96 ($false = $true) | ($false = (dest @ paris @ sK1))),
% 1.60/1.96 inference(forward_demodulation,[status(thm)],[f155,f79])).
% 1.60/1.96 thf(f79,plain,(
% 1.60/1.96 ((price @ seventy @ sK1) = $false)),
% 1.60/1.96 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.60/1.96 thf(f155,plain,(
% 1.60/1.96 ((price @ seventy @ sK1) = $true) | ($false = (dest @ paris @ sK1))),
% 1.60/1.96 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 1.60/1.96 thf(f154,plain,(
% 1.60/1.96 ((price @ seventy @ sK1) = $true) | ($false = (dest @ paris @ sK1)) | ($false = $true)),
% 1.60/1.96 inference(forward_demodulation,[status(thm)],[f147,f109])).
% 1.60/1.96 thf(f109,plain,(
% 1.60/1.96 ((class @ second @ sK1) = $true)),
% 1.60/1.96 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.60/1.96 thf(f107,plain,(
% 1.60/1.96 ((class @ second @ sK1) = $true) | ($false = $true)),
% 1.60/1.96 inference(superposition,[status(thm)],[f96,f80])).
% 1.60/1.96 thf(f96,plain,(
% 1.60/1.96 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((class @ second @ X1) = $true)) )),
% 1.60/1.96 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.60/1.96 thf(f95,plain,(
% 1.60/1.96 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (class @ second @ X1)) = $true)) )),
% 1.60/1.96 inference(beta_eta_normalization,[status(thm)],[f94])).
% 1.60/1.96 thf(f94,plain,(
% 1.60/1.96 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (class @ second @ Y0))) @ X1))) )),
% 1.60/1.96 inference(pi_clausification,[status(thm)],[f93])).
% 1.60/1.96 thf(f93,plain,(
% 1.60/1.96 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (class @ second @ Y0)))) = $true)),
% 1.60/1.96 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.60/1.96 thf(f63,plain,(
% 1.60/1.96 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (class @ second))))),
% 1.60/1.96 inference(definition_unfolding,[status(thm)],[f48,f55,f58])).
% 1.60/1.96 thf(f48,plain,(
% 1.60/1.96 ((mlocal @ (mbox @ (class @ second))) = $true)),
% 1.60/1.96 inference(cnf_transformation,[status(thm)],[f23])).
% 1.60/1.96 thf(f23,plain,(
% 1.60/1.96 ((mlocal @ (mbox @ (class @ second))) = $true)),
% 1.60/1.96 inference(fool_elimination,[status(thm)],[f22])).
% 1.60/1.96 thf(f22,plain,(
% 1.60/1.96 (mlocal @ (mbox @ (class @ second)))),
% 1.60/1.96 inference(rectify,[status(thm)],[f14])).
% 1.60/1.96 thf(f14,axiom,(
% 1.60/1.96 (mlocal @ (mbox @ (class @ second)))),
% 1.60/1.96 file('/export/starexec/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',belief2)).
% 1.60/1.96 thf(f147,plain,(
% 1.60/1.96 ($false = (class @ second @ sK1)) | ((price @ seventy @ sK1) = $true) | ($false = (dest @ paris @ sK1))),
% 1.60/1.96 inference(trivial_inequality_removal,[status(thm)],[f145])).
% 1.60/1.96 thf(f145,plain,(
% 1.60/1.96 ((price @ seventy @ sK1) = $true) | ($false = (dest @ paris @ sK1)) | ($false = (class @ second @ sK1)) | ($false = $true)),
% 1.60/1.96 inference(superposition,[status(thm)],[f86,f80])).
% 1.60/1.96 thf(f86,plain,(
% 1.60/1.96 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((price @ seventy @ X1) = $true) | ((class @ second @ X1) = $false) | ($false = (dest @ paris @ X1))) )),
% 1.60/1.96 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 1.60/1.96 thf(f85,plain,(
% 1.60/1.96 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((price @ seventy @ X1) = $true) | (((dest @ paris @ X1) & (class @ second @ X1)) = $false)) )),
% 1.60/1.96 inference(binary_proxy_clausification,[status(thm)],[f84])).
% 1.60/1.96 thf(f84,plain,(
% 1.60/1.96 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((((dest @ paris @ X1) & (class @ second @ X1)) => (price @ seventy @ X1)) = $true)) )),
% 1.60/1.96 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.60/1.96 thf(f83,plain,(
% 1.60/1.96 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (((dest @ paris @ X1) & (class @ second @ X1)) => (price @ seventy @ X1))) = $true)) )),
% 1.60/1.96 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.60/1.96 thf(f82,plain,(
% 1.60/1.96 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (((dest @ paris @ Y0) & (class @ second @ Y0)) => (price @ seventy @ Y0)))) @ X1))) )),
% 1.60/1.96 inference(pi_clausification,[status(thm)],[f81])).
% 1.60/1.96 thf(f81,plain,(
% 1.60/1.96 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (((dest @ paris @ Y0) & (class @ second @ Y0)) => (price @ seventy @ Y0))))) = $true)),
% 1.60/1.96 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.60/1.96 thf(f67,plain,(
% 1.60/1.96 (((^[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)),
% 1.60/1.96 inference(definition_unfolding,[status(thm)],[f56,f55,f58,f50,f49])).
% 1.60/1.96 thf(f49,plain,(
% 1.60/1.96 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.60/1.96 inference(cnf_transformation,[status(thm)],[f36])).
% 1.60/1.96 thf(f36,plain,(
% 1.60/1.96 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.60/1.96 inference(fool_elimination,[status(thm)],[f35])).
% 1.60/1.96 thf(f35,plain,(
% 1.60/1.96 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))) = mand)),
% 1.60/1.96 inference(rectify,[status(thm)],[f3])).
% 1.60/1.96 thf(f3,axiom,(
% 1.60/1.96 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))) = mand)),
% 1.60/1.96 file('/export/starexec/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',mand_def)).
% 1.60/1.96 thf(f50,plain,(
% 1.60/1.96 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.60/1.96 inference(cnf_transformation,[status(thm)],[f34])).
% 1.60/1.96 thf(f34,plain,(
% 1.60/1.96 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.60/1.96 inference(fool_elimination,[status(thm)],[f33])).
% 1.60/1.96 thf(f33,plain,(
% 1.60/1.96 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.60/1.96 inference(rectify,[status(thm)],[f5])).
% 1.60/1.96 thf(f5,axiom,(
% 1.60/1.96 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.60/1.96 file('/export/starexec/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',mimplies_def)).
% 1.60/1.96 thf(f56,plain,(
% 1.60/1.96 ((mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.60/1.96 inference(cnf_transformation,[status(thm)],[f26])).
% 1.60/1.96 thf(f26,plain,(
% 1.60/1.96 ((mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy)))) = $true)),
% 1.60/1.96 inference(fool_elimination,[status(thm)],[f25])).
% 1.60/1.96 thf(f25,plain,(
% 1.60/1.96 (mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy))))),
% 1.60/1.96 inference(rectify,[status(thm)],[f10])).
% 1.60/1.96 thf(f10,axiom,(
% 1.60/1.96 (mlocal @ (mbox @ (mimplies @ (mand @ (dest @ paris) @ (class @ second)) @ (price @ seventy))))),
% 1.60/1.96 file('/export/starexec/sandbox2/tmp/tmp.KVwaBLsq2V/DTF2THF_13351.p',law2)).
% 1.60/1.96 % SZS output end Proof for DTF2THF_13351
% 1.60/1.96 % (13669)------------------------------
% 1.60/1.96 % (13669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.96 % (13669)Termination reason: Refutation
% 1.60/1.96
% 1.60/1.96 % (13669)Memory used [KB]: 5628
% 1.60/1.96 % (13669)Time elapsed: 0.007 s
% 1.60/1.96 % (13669)Instructions burned: 12 (million)
% 1.60/1.96 % (13669)------------------------------
% 1.60/1.96 % (13669)------------------------------
% 1.60/1.96 % (13666)Success in time 0.018 s
%------------------------------------------------------------------------------