%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NLP265^17 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 09:22:24 AM UTC 2026
% Result : ContradictoryAxioms 1.61s 2.01s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 239 ( 53 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 299 ( 12 ~; 13 |; 0 &; 244 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 11 con; 0-3 aty)
% ( 11 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 76 ( 50 ^; 26 !; 0 ?; 76 :)
% 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,
'#i_alice': mindex ).
thf(func_def_4,type,
'#i_bob': mindex ).
thf(func_def_5,type,
'#b_alice': mindex ).
thf(func_def_6,type,
'#b_bob': mindex ).
thf(func_def_7,type,
mactual: mworld ).
thf(func_def_8,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_10,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_15,type,
mbox: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_16,type,
mdia: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_18,type,
bigcity: $i > mworld > $o ).
thf(func_def_34,type,
sK1: mworld > mworld ).
thf(func_def_35,type,
sK2: mworld > mworld ).
thf(func_def_36,type,
sK3: mworld ).
thf(func_def_37,type,
sK4: mworld ).
thf(func_def_38,type,
sK5: mworld > mworld ).
thf(func_def_39,type,
sK6: mworld > mworld ).
thf(f181,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f179]) ).
thf(f179,plain,
$true = $false,
inference(superposition,[status(thm)],[f178,f166]) ).
thf(f166,plain,
( $true
= ( bigcity @ portland @ mactual ) ),
inference(trivial_inequality_removal,[status(thm)],[f163]) ).
thf(f163,plain,
( ( $true
= ( bigcity @ portland @ mactual ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f162,f82]) ).
thf(f82,plain,
! [X0: mworld] :
( $true
= ( mrel @ '#b_alice' @ X0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
thf(f56,plain,
! [X0: mworld] :
( $true
= ( mrel @ '#b_alice' @ X0 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f55]) ).
thf(f55,plain,
! [X0: mworld] : ( mrel @ '#b_alice' @ X0 @ X0 ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
! [X2: mworld] : ( mrel @ '#b_alice' @ X2 @ X2 ),
file('/export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2THF_4642.p','mrel_#b_alice_reflexive') ).
thf(f162,plain,
! [X1: mworld] :
( ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false )
| ( $true
= ( bigcity @ portland @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f161]) ).
thf(f161,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ '#b_alice' @ mactual @ X1 )
=> ( bigcity @ portland @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f160]) ).
thf(f160,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#b_alice' @ mactual @ Y0 )
=> ( bigcity @ portland @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f159]) ).
thf(f159,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_alice' @ mactual @ Y0 )
=> ( bigcity @ portland @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b_alice'
@ ( bigcity @ portland ) ) ) ),
inference(definition_unfolding,[status(thm)],[f84,f78,f74]) ).
thf(f74,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
thf(f54,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X4: mindex,X0: mworld > $o,X2: mworld] :
! [X5: mworld] :
( ( mrel @ X4 @ X2 @ X5 )
=> ( X0 @ X5 ) ) )
= mbox ),
file('/export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2THF_4642.p',mbox_def) ).
thf(f78,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,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.LoG54obBQa/DTF2THF_4642.p',mlocal_def) ).
thf(f84,plain,
( ( mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f58]) ).
thf(f58,plain,
( ( mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f57]) ).
thf(f57,plain,
mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,axiom,
mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ),
file('/export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2THF_4642.p',axiom_2) ).
thf(f178,plain,
( ( bigcity @ portland @ mactual )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f175]) ).
thf(f175,plain,
( ( $true = $false )
| ( ( bigcity @ portland @ mactual )
= $false ) ),
inference(superposition,[status(thm)],[f172,f82]) ).
thf(f172,plain,
! [X0: mworld] :
( ( ( mrel @ '#b_alice' @ mactual @ X0 )
= $false )
| ( ( bigcity @ portland @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f167]) ).
thf(f167,plain,
! [X0: mworld] :
( ( ( mrel @ '#b_alice' @ mactual @ X0 )
= $false )
| ( ( bigcity @ portland @ X0 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f137,f87]) ).
thf(f87,plain,
! [X0: mworld] :
( ( mrel @ '#b_bob' @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f62]) ).
thf(f62,plain,
! [X0: mworld] :
( ( mrel @ '#b_bob' @ X0 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f61]) ).
thf(f61,plain,
! [X0: mworld] : ( mrel @ '#b_bob' @ X0 @ X0 ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
! [X2: mworld] : ( mrel @ '#b_bob' @ X2 @ X2 ),
file('/export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2THF_4642.p','mrel_#b_bob_reflexive') ).
thf(f137,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#b_bob' @ X1 @ X2 )
= $false )
| ( ( bigcity @ portland @ X2 )
= $false )
| ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false )
| ( ( mrel @ '#b_bob' @ X1 @ X2 )
= $false )
| ( ( ~ ( bigcity @ portland @ X2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false )
| ( ( ( mrel @ '#b_bob' @ X1 @ X2 )
=> ~ ( bigcity @ portland @ X2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f134]) ).
thf(f134,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#b_bob' @ X1 @ Y0 )
=> ~ ( bigcity @ portland @ Y0 ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f133]) ).
thf(f133,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_bob' @ X1 @ Y0 )
=> ~ ( bigcity @ portland @ Y0 ) ) ) )
| ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
! [X1: mworld] :
( ( ( mrel @ '#b_alice' @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_bob' @ X1 @ Y0 )
=> ~ ( bigcity @ portland @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f131]) ).
thf(f131,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ '#b_alice' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b_bob' @ Y0 @ Y1 )
=> ~ ( bigcity @ portland @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_alice' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b_bob' @ Y0 @ Y1 )
=> ~ ( bigcity @ portland @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f96]) ).
thf(f96,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b_alice'
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b_bob'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( bigcity @ portland ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f80,f78,f74,f74,f89]) ).
thf(f89,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f48,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f47]) ).
thf(f47,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2THF_4642.p',mnot_def) ).
thf(f80,plain,
( ( mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f29]) ).
thf(f29,plain,
mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,axiom,
mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2THF_4642.p',axiom_3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.25 % Problem : NLP265^17 : TPTP v9.2.1. Released v8.1.0.
% 0.11/0.26 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.52 % Computer : n016.cluster.edu
% 0.15/0.52 % Model : x86_64 x86_64
% 0.15/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.52 % Memory : 8042.1875MB
% 0.15/0.52 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.52 % CPULimit : 300
% 0.15/0.52 % WCLimit : 300
% 0.15/0.52 % DateTime : Tue Feb 24 10:54:52 EST 2026
% 0.15/0.52 % CPUTime :
% 0.15/0.52 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.84 ---- Original DTF file ---
% 0.31/0.84 thf(spec,logic,$$dhol).
% 0.31/0.84 %------------------------------------------------------------------------------
% 0.31/0.84 % File : NLP265^17 : TPTP v9.2.1. Released v8.1.0.
% 0.31/0.84 % Domain : Natural Language Processing
% 0.31/0.84 % Problem : Schema instantiation example
% 0.31/0.84 % Version : [BP13] axioms.
% 0.31/0.84 % English : Alice intends Bob to believe that Portland is a big city.
% 0.31/0.84
% 0.31/0.84 % Refs : [BS96] Bretier & Sadek (1996), Rational Agent as the Kernel o
% 0.31/0.84 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.31/0.84 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.31/0.84 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.31/0.84 % Source : [TPTP]
% 0.31/0.84 % Names : MML014+1 [QMLTP]
% 0.31/0.84
% 0.31/0.84 % Status : ContradictoryAxioms
% 0.31/0.84 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.31/0.84 % Syntax : Number of formulae : 39 ( 12 unt; 18 typ; 8 def)
% 0.31/0.84 % Number of atoms : 70 ( 8 equ; 0 cnn)
% 0.31/0.84 % Maximal formula atoms : 12 ( 3 avg)
% 0.31/0.84 % Number of connectives : 136 ( 1 ~; 1 |; 6 &; 121 @)
% 0.31/0.84 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 0.31/0.84 % Maximal formula depth : 10 ( 5 avg)
% 0.31/0.84 % Number of types : 4 ( 2 usr)
% 0.31/0.84 % Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% 0.31/0.84 % Number of symbols : 17 ( 16 usr; 6 con; 0-3 aty)
% 0.31/0.84 % Number of variables : 39 ( 21 ^; 17 !; 1 ?; 39 :)
% 0.31/0.84 % SPC : TH0_CAX_EQU_NAR
% 0.31/0.84
% 0.31/0.84 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.31/0.84 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.31/0.84 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.31/0.84 % $modal == [$constants == $rigid,$quantification == $cumulative,
% 0.31/0.84 % $modalities == $modal_system_S5].
% 0.31/0.84 %------------------------------------------------------------------------------
% 0.31/0.84 thf(mworld,type,
% 0.31/0.84 mworld: $tType ).
% 0.31/0.84
% 0.31/0.84 thf(mindex,type,
% 0.31/0.84 mindex: $tType ).
% 0.31/0.84
% 0.31/0.84 thf(mrel_type,type,
% 0.31/0.84 mrel: mindex > mworld > mworld > $o ).
% 0.31/0.84
% 0.31/0.84 thf('#i_alice_type',type,
% 0.31/0.84 '#i_alice': mindex ).
% 0.31/0.84
% 0.31/0.84 thf('#i_bob_type',type,
% 0.31/0.84 '#i_bob': mindex ).
% 0.31/0.84
% 0.31/0.84 thf('#b_alice_type',type,
% 0.31/0.84 '#b_alice': mindex ).
% 0.31/0.84
% 0.31/0.84 thf('#b_bob_type',type,
% 0.31/0.84 '#b_bob': mindex ).
% 0.31/0.84
% 0.31/0.84 thf(mactual_type,type,
% 0.31/0.84 mactual: mworld ).
% 0.31/0.84
% 0.31/0.84 thf(mlocal_type,type,
% 0.31/0.84 mlocal: ( mworld > $o ) > $o ).
% 0.31/0.84
% 0.31/0.84 thf(mlocal_def,definition,
% 0.31/0.84 ( mlocal
% 0.31/0.84 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.31/0.84
% 0.31/0.84 thf(mnot_type,type,
% 0.31/0.84 mnot: ( mworld > $o ) > mworld > $o ).
% 0.31/0.84
% 0.31/0.84 thf(mand_type,type,
% 0.31/0.84 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.84
% 0.31/0.84 thf(mor_type,type,
% 0.31/0.84 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.84
% 0.31/0.84 thf(mimplies_type,type,
% 0.31/0.84 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.84
% 0.31/0.84 thf(mequiv_type,type,
% 0.31/0.84 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.84
% 0.31/0.84 thf(mnot_def,definition,
% 0.31/0.84 ( mnot
% 0.31/0.84 = ( ^ [A: mworld > $o,W: mworld] :
% 0.31/0.84 ~ ( A @ W ) ) ) ).
% 0.31/0.84
% 0.31/0.84 thf(mand_def,definition,
% 0.31/0.84 ( mand
% 0.31/0.84 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.84 ( ( A @ W )
% 0.31/0.84 & ( B @ W ) ) ) ) ).
% 0.31/0.84
% 0.31/0.84 thf(mor_def,definition,
% 0.31/0.84 ( mor
% 0.31/0.84 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.84 ( ( A @ W )
% 0.31/0.84 | ( B @ W ) ) ) ) ).
% 0.31/0.84
% 0.31/0.84 thf(mimplies_def,definition,
% 0.31/0.84 ( mimplies
% 0.31/0.84 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.84 ( ( A @ W )
% 0.31/0.84 => ( B @ W ) ) ) ) ).
% 0.31/0.84
% 0.31/0.84 thf(mequiv_def,definition,
% 0.31/0.84 ( mequiv
% 0.31/0.84 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.84 ( ( A @ W )
% 0.31/0.84 <=> ( B @ W ) ) ) ) ).
% 0.31/0.84
% 0.31/0.84 thf(mbox_type,type,
% 0.31/0.84 mbox: mindex > ( mworld > $o ) > mworld > $o ).
% 0.31/0.84
% 0.31/0.84 thf(mbox_def,definition,
% 0.31/0.84 ( mbox
% 0.31/0.84 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.31/0.84 ! [V: mworld] :
% 0.31/0.84 ( ( mrel @ R @ W @ V )
% 0.31/0.84 => ( Phi @ V ) ) ) ) ).
% 0.31/0.84
% 0.31/0.84 thf(mdia_type,type,
% 0.31/0.84 mdia: mindex > ( mworld > $o ) > mworld > $o ).
% 0.31/0.84
% 0.31/0.84 thf(mdia_def,definition,
% 0.31/0.84 ( mdia
% 0.31/0.84 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.31/0.84 ? [V: mworld] :
% 0.31/0.84 ( ( mrel @ R @ W @ V )
% 0.31/0.84 & ( Phi @ V ) ) ) ) ).
% 0.31/0.84
% 0.31/0.84 thf('mrel_#i_alice_reflexive',axiom,
% 0.31/0.84 ! [W: mworld] : ( mrel @ '#i_alice' @ W @ W ) ).
% 0.31/0.84
% 0.31/0.84 thf('mrel_#i_alice_euclidean',axiom,
% 0.31/0.84 ! [W: mworld,V: mworld,U: mworld] :
% 0.31/0.84 ( ( ( mrel @ '#i_alice' @ W @ U )
% 0.31/0.84 & ( mrel @ '#i_alice' @ W @ V ) )
% 0.31/0.84 => ( mrel @ '#i_alice' @ U @ V ) ) ).
% 0.31/0.84
% 0.31/0.84 thf('mrel_#i_bob_reflexive',axiom,
% 0.31/0.84 ! [W: mworld] : ( mrel @ '#i_bob' @ W @ W ) ).
% 0.31/0.84
% 0.31/0.84 thf('mrel_#i_bob_euclidean',axiom,
% 0.31/0.84 ! [W: mworld,V: mworld,U: mworld] :
% 0.31/0.84 ( ( ( mrel @ '#i_bob' @ W @ U )
% 0.31/0.84 & ( mrel @ '#i_bob' @ W @ V ) )
% 0.31/0.84 => ( mrel @ '#i_bob' @ U @ V ) ) ).
% 0.31/0.84
% 0.31/0.84 thf('mrel_#b_alice_reflexive',axiom,
% 0.31/0.84 ! [W: mworld] : ( mrel @ '#b_alice' @ W @ W ) ).
% 0.31/0.84
% 0.31/0.84 thf('mrel_#b_alice_euclidean',axiom,
% 0.31/0.84 ! [W: mworld,V: mworld,U: mworld] :
% 0.31/0.84 ( ( ( mrel @ '#b_alice' @ W @ U )
% 0.31/0.84 & ( mrel @ '#b_alice' @ W @ V ) )
% 0.31/0.84 => ( mrel @ '#b_alice' @ U @ V ) ) ).
% 0.31/0.84
% 0.31/0.84 thf('mrel_#b_bob_reflexive',axiom,
% 0.31/0.84 ! [W: mworld] : ( mrel @ '#b_bob' @ W @ W ) ).
% 0.31/0.84
% 0.31/0.84 thf('mrel_#b_bob_euclidean',axiom,
% 0.31/0.84 ! [W: mworld,V: mworld,U: mworld] :
% 0.31/0.84 ( ( ( mrel @ '#b_bob' @ W @ U )
% 0.31/0.84 & ( mrel @ '#b_bob' @ W @ V ) )
% 0.31/0.84 => ( mrel @ '#b_bob' @ U @ V ) ) ).
% 0.31/0.84
% 0.31/0.84 thf(portland_decl,type,
% 0.31/0.84 portland: $i ).
% 0.31/0.84
% 0.31/0.84 thf(bigcity_decl,type,
% 0.31/0.84 bigcity: $i > mworld > $o ).
% 0.31/0.84
% 0.31/0.84 thf(axiom_1_alice,axiom,
% 0.31/0.84 mlocal @ ( mbox @ '#b_alice' @ ( mimplies @ ( mand @ ( bigcity @ portland ) @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ) ) @ ( mbox @ '#i_alice' @ ( mbox @ '#b_bob' @ ( bigcity @ portland ) ) ) ) ) ).
% 0.31/0.84
% 0.31/0.84 thf(axiom_1_bob,axiom,
% 0.31/0.84 mlocal @ ( mbox @ '#b_bob' @ ( mimplies @ ( mand @ ( bigcity @ portland ) @ ( mbox @ '#b_bob' @ ( mbox @ '#b_alice' @ ( mnot @ ( bigcity @ portland ) ) ) ) ) @ ( mbox @ '#i_bob' @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ) ) ) ) ).
% 0.31/0.84
% 0.31/0.84 thf(axiom_2,axiom,
% 0.31/0.84 mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ) ).
% 0.31/0.84
% 0.31/0.84 thf(axiom_3,axiom,
% 0.31/0.84 mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ) ).
% 0.31/0.84
% 0.31/0.84 thf(con,conjecture,
% 0.31/0.84 mlocal @ ( mbox @ '#i_alice' @ ( mbox @ '#b_bob' @ ( bigcity @ portland ) ) ) ).
% 0.31/0.84
% 0.31/0.84 %------------------------------------------------------------------------------
% 0.31/0.84 ------------------------
% 1.61/1.97 ---- Embedded in THF ---
% 1.61/1.98 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.98 %%% Generated on Tue Feb 24 10:54:54 EST 2026
% 1.61/1.98 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.98 %%% Logic specification used:
% 1.61/1.98 %%% thf(spec, logic, $$dhol).
% 1.61/1.98
% 1.61/1.98 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2DTF4642.p
% See solution above
% 1.61/1.98 ------------------------
% 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('#i_alice_type',type,
% 1.61/1.98 '#i_alice': mindex ).
% 1.61/1.98
% 1.61/1.98 thf('#i_bob_type',type,
% 1.61/1.98 '#i_bob': mindex ).
% 1.61/1.98
% 1.61/1.98 thf('#b_alice_type',type,
% 1.61/1.98 '#b_alice': mindex ).
% 1.61/1.98
% 1.61/1.98 thf('#b_bob_type',type,
% 1.61/1.98 '#b_bob': 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_#i_alice_reflexive',axiom,
% 1.61/1.98 ! [W: mworld] : ( mrel @ '#i_alice' @ W @ W ) ).
% 1.61/1.98
% 1.61/1.98 thf('mrel_#i_alice_euclidean',axiom,
% 1.61/1.98 ! [W: mworld,V: mworld,U: mworld] :
% 1.61/1.98 ( ( ( mrel @ '#i_alice' @ W @ U )
% 1.61/1.98 & ( mrel @ '#i_alice' @ W @ V ) )
% 1.61/1.98 => ( mrel @ '#i_alice' @ U @ V ) ) ).
% 1.61/1.98
% 1.61/1.98 thf('mrel_#i_bob_reflexive',axiom,
% 1.61/1.98 ! [W: mworld] : ( mrel @ '#i_bob' @ W @ W ) ).
% 1.61/1.98
% 1.61/1.98 thf('mrel_#i_bob_euclidean',axiom,
% 1.61/1.98 ! [W: mworld,V: mworld,U: mworld] :
% 1.61/1.98 ( ( ( mrel @ '#i_bob' @ W @ U )
% 1.61/1.98 & ( mrel @ '#i_bob' @ W @ V ) )
% 1.61/1.98 => ( mrel @ '#i_bob' @ U @ V ) ) ).
% 1.61/1.98
% 1.61/1.98 thf('mrel_#b_alice_reflexive',axiom,
% 1.61/1.98 ! [W: mworld] : ( mrel @ '#b_alice' @ W @ W ) ).
% 1.61/1.98
% 1.61/1.98 thf('mrel_#b_alice_euclidean',axiom,
% 1.61/1.98 ! [W: mworld,V: mworld,U: mworld] :
% 1.61/1.98 ( ( ( mrel @ '#b_alice' @ W @ U )
% 1.61/1.98 & ( mrel @ '#b_alice' @ W @ V ) )
% 1.61/1.98 => ( mrel @ '#b_alice' @ U @ V ) ) ).
% 1.61/1.98
% 1.61/1.98 thf('mrel_#b_bob_reflexive',axiom,
% 1.61/1.98 ! [W: mworld] : ( mrel @ '#b_bob' @ W @ W ) ).
% 1.61/1.98
% 1.61/1.98 thf('mrel_#b_bob_euclidean',axiom,
% 1.61/1.98 ! [W: mworld,V: mworld,U: mworld] :
% 1.61/1.98 ( ( ( mrel @ '#b_bob' @ W @ U )
% 1.61/1.98 & ( mrel @ '#b_bob' @ W @ V ) )
% 1.61/1.98 => ( mrel @ '#b_bob' @ U @ V ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(portland_decl,type,
% 1.61/1.98 portland: $i ).
% 1.61/1.98
% 1.61/1.98 thf(bigcity_decl,type,
% 1.61/1.98 bigcity: $i > mworld > $o ).
% 1.61/1.98
% 1.61/1.98 thf(axiom_1_alice,axiom,
% 1.61/1.98 mlocal @ ( mbox @ '#b_alice' @ ( mimplies @ ( mand @ ( bigcity @ portland ) @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ) ) @ ( mbox @ '#i_alice' @ ( mbox @ '#b_bob' @ ( bigcity @ portland ) ) ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(axiom_1_bob,axiom,
% 1.61/1.98 mlocal @ ( mbox @ '#b_bob' @ ( mimplies @ ( mand @ ( bigcity @ portland ) @ ( mbox @ '#b_bob' @ ( mbox @ '#b_alice' @ ( mnot @ ( bigcity @ portland ) ) ) ) ) @ ( mbox @ '#i_bob' @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ) ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(axiom_2,axiom,
% 1.61/1.98 mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(axiom_3,axiom,
% 1.61/1.98 mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ) ).
% 1.61/1.98
% 1.61/1.98 thf(con,conjecture,
% 1.61/1.98 mlocal @ ( mbox @ '#i_alice' @ ( mbox @ '#b_bob' @ ( bigcity @ portland ) ) ) ).
% 1.61/1.98 ------------------------
% 1.61/2.00 % (4954)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4642 for (2999ds/183Mi)
% 1.61/2.00 % (4960)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4642 for (2999ds/18Mi)
% 1.61/2.00 % (4954)First to succeed.
% 1.61/2.01 % (4954)Refutation found. Thanks to Tanya!
% 1.61/2.01 % SZS status ContradictoryAxioms for DTF2THF_4642
% 1.61/2.01 % SZS output start Proof for DTF2THF_4642
% 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, '#i_alice': mindex).
% 1.61/2.01 thf(func_def_4, type, '#i_bob': mindex).
% 1.61/2.01 thf(func_def_5, type, '#b_alice': mindex).
% 1.61/2.01 thf(func_def_6, type, '#b_bob': mindex).
% 1.61/2.01 thf(func_def_7, type, mactual: mworld).
% 1.61/2.01 thf(func_def_8, type, mlocal: (mworld > $o) > $o).
% 1.61/2.01 thf(func_def_10, type, mnot: (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_11, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_12, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_13, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_14, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_15, type, mbox: mindex > (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_16, type, mdia: mindex > (mworld > $o) > mworld > $o).
% 1.61/2.01 thf(func_def_18, type, bigcity: $i > mworld > $o).
% 1.61/2.01 thf(func_def_34, type, sK1: mworld > mworld).
% 1.61/2.01 thf(func_def_35, type, sK2: mworld > mworld).
% 1.61/2.01 thf(func_def_36, type, sK3: mworld).
% 1.61/2.01 thf(func_def_37, type, sK4: mworld).
% 1.61/2.01 thf(func_def_38, type, sK5: mworld > mworld).
% 1.61/2.01 thf(func_def_39, type, sK6: mworld > mworld).
% 1.61/2.01 thf(f181,plain,(
% 1.61/2.01 $false),
% 1.61/2.01 inference(trivial_inequality_removal,[status(thm)],[f179])).
% 1.61/2.01 thf(f179,plain,(
% 1.61/2.01 ($true = $false)),
% 1.61/2.01 inference(superposition,[status(thm)],[f178,f166])).
% 1.61/2.01 thf(f166,plain,(
% 1.61/2.01 ($true = (bigcity @ portland @ mactual))),
% 1.61/2.01 inference(trivial_inequality_removal,[status(thm)],[f163])).
% 1.61/2.01 thf(f163,plain,(
% 1.61/2.01 ($true = (bigcity @ portland @ mactual)) | ($true = $false)),
% 1.61/2.01 inference(superposition,[status(thm)],[f162,f82])).
% 1.61/2.01 thf(f82,plain,(
% 1.61/2.01 ( ! [X0 : mworld] : (($true = (mrel @ '#b_alice' @ X0 @ X0))) )),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f56])).
% 1.61/2.01 thf(f56,plain,(
% 1.61/2.01 ! [X0 : mworld] : ($true = (mrel @ '#b_alice' @ X0 @ X0))),
% 1.61/2.01 inference(fool_elimination,[status(thm)],[f55])).
% 1.61/2.01 thf(f55,plain,(
% 1.61/2.01 ! [X0 : mworld] : (mrel @ '#b_alice' @ X0 @ X0)),
% 1.61/2.01 inference(rectify,[status(thm)],[f13])).
% 1.61/2.01 thf(f13,axiom,(
% 1.61/2.01 ! [X2 : mworld] : (mrel @ '#b_alice' @ X2 @ X2)),
% 1.61/2.01 file('/export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2THF_4642.p','mrel_#b_alice_reflexive')).
% 1.61/2.01 thf(f162,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : (((mrel @ '#b_alice' @ mactual @ X1) = $false) | ($true = (bigcity @ portland @ X1))) )),
% 1.61/2.01 inference(binary_proxy_clausification,[status(thm)],[f161])).
% 1.61/2.01 thf(f161,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : (($true = ((mrel @ '#b_alice' @ mactual @ X1) => (bigcity @ portland @ X1)))) )),
% 1.61/2.01 inference(beta_eta_normalization,[status(thm)],[f160])).
% 1.61/2.01 thf(f160,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ '#b_alice' @ mactual @ Y0) => (bigcity @ portland @ Y0))) @ X1))) )),
% 1.61/2.01 inference(pi_clausification,[status(thm)],[f159])).
% 1.61/2.01 thf(f159,plain,(
% 1.61/2.01 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#b_alice' @ mactual @ Y0) => (bigcity @ portland @ Y0)))))),
% 1.61/2.01 inference(beta_eta_normalization,[status(thm)],[f97])).
% 1.61/2.01 thf(f97,plain,(
% 1.61/2.01 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ '#b_alice' @ (bigcity @ portland))))),
% 1.61/2.01 inference(definition_unfolding,[status(thm)],[f84,f78,f74])).
% 1.61/2.01 thf(f74,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)],[f54])).
% 1.61/2.01 thf(f54,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)],[f53])).
% 1.61/2.01 thf(f53,plain,(
% 1.61/2.01 ((^[X0 : mindex, X1 : mworld > $o, X2 : mworld] : (! [X3 : mworld] : ((mrel @ X0 @ X2 @ X3) => (X1 @ X3)))) = mbox)),
% 1.61/2.01 inference(rectify,[status(thm)],[f7])).
% 1.61/2.01 thf(f7,axiom,(
% 1.61/2.01 ((^[X4 : mindex, X0 : mworld > $o, X2 : mworld] : (! [X5 : mworld] : ((mrel @ X4 @ X2 @ X5) => (X0 @ X5)))) = mbox)),
% 1.61/2.01 file('/export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2THF_4642.p',mbox_def)).
% 1.61/2.01 thf(f78,plain,(
% 1.61/2.01 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f26])).
% 1.61/2.01 thf(f26,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 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.61/2.01 file('/export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2THF_4642.p',mlocal_def)).
% 1.61/2.01 thf(f84,plain,(
% 1.61/2.01 ((mlocal @ (mbox @ '#b_alice' @ (bigcity @ portland))) = $true)),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f58])).
% 1.61/2.01 thf(f58,plain,(
% 1.61/2.01 ((mlocal @ (mbox @ '#b_alice' @ (bigcity @ portland))) = $true)),
% 1.61/2.01 inference(fool_elimination,[status(thm)],[f57])).
% 1.61/2.01 thf(f57,plain,(
% 1.61/2.01 (mlocal @ (mbox @ '#b_alice' @ (bigcity @ portland)))),
% 1.61/2.01 inference(rectify,[status(thm)],[f19])).
% 1.61/2.01 thf(f19,axiom,(
% 1.61/2.01 (mlocal @ (mbox @ '#b_alice' @ (bigcity @ portland)))),
% 1.61/2.01 file('/export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2THF_4642.p',axiom_2)).
% 1.61/2.01 thf(f178,plain,(
% 1.61/2.01 ((bigcity @ portland @ mactual) = $false)),
% 1.61/2.01 inference(trivial_inequality_removal,[status(thm)],[f175])).
% 1.61/2.01 thf(f175,plain,(
% 1.61/2.01 ($true = $false) | ((bigcity @ portland @ mactual) = $false)),
% 1.61/2.01 inference(superposition,[status(thm)],[f172,f82])).
% 1.61/2.01 thf(f172,plain,(
% 1.61/2.01 ( ! [X0 : mworld] : (((mrel @ '#b_alice' @ mactual @ X0) = $false) | ((bigcity @ portland @ X0) = $false)) )),
% 1.61/2.01 inference(trivial_inequality_removal,[status(thm)],[f167])).
% 1.61/2.01 thf(f167,plain,(
% 1.61/2.01 ( ! [X0 : mworld] : (((mrel @ '#b_alice' @ mactual @ X0) = $false) | ((bigcity @ portland @ X0) = $false) | ($true = $false)) )),
% 1.61/2.01 inference(superposition,[status(thm)],[f137,f87])).
% 1.61/2.01 thf(f87,plain,(
% 1.61/2.01 ( ! [X0 : mworld] : (((mrel @ '#b_bob' @ X0 @ X0) = $true)) )),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f62])).
% 1.61/2.01 thf(f62,plain,(
% 1.61/2.01 ! [X0 : mworld] : ((mrel @ '#b_bob' @ X0 @ X0) = $true)),
% 1.61/2.01 inference(fool_elimination,[status(thm)],[f61])).
% 1.61/2.01 thf(f61,plain,(
% 1.61/2.01 ! [X0 : mworld] : (mrel @ '#b_bob' @ X0 @ X0)),
% 1.61/2.01 inference(rectify,[status(thm)],[f15])).
% 1.61/2.01 thf(f15,axiom,(
% 1.61/2.01 ! [X2 : mworld] : (mrel @ '#b_bob' @ X2 @ X2)),
% 1.61/2.01 file('/export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2THF_4642.p','mrel_#b_bob_reflexive')).
% 1.61/2.01 thf(f137,plain,(
% 1.61/2.01 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ '#b_bob' @ X1 @ X2) = $false) | ((bigcity @ portland @ X2) = $false) | ((mrel @ '#b_alice' @ mactual @ X1) = $false)) )),
% 1.61/2.01 inference(not_proxy_clausification,[status(thm)],[f136])).
% 1.61/2.01 thf(f136,plain,(
% 1.61/2.01 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ '#b_alice' @ mactual @ X1) = $false) | ((mrel @ '#b_bob' @ X1 @ X2) = $false) | ((~ (bigcity @ portland @ X2)) = $true)) )),
% 1.61/2.01 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 1.61/2.01 thf(f135,plain,(
% 1.61/2.01 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ '#b_alice' @ mactual @ X1) = $false) | (((mrel @ '#b_bob' @ X1 @ X2) => (~ (bigcity @ portland @ X2))) = $true)) )),
% 1.61/2.01 inference(beta_eta_normalization,[status(thm)],[f134])).
% 1.61/2.01 thf(f134,plain,(
% 1.61/2.01 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ '#b_alice' @ mactual @ X1) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ '#b_bob' @ X1 @ Y0) => (~ (bigcity @ portland @ Y0)))) @ X2))) )),
% 1.61/2.01 inference(pi_clausification,[status(thm)],[f133])).
% 1.61/2.01 thf(f133,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#b_bob' @ X1 @ Y0) => (~ (bigcity @ portland @ Y0)))))) | ((mrel @ '#b_alice' @ mactual @ X1) = $false)) )),
% 1.61/2.01 inference(binary_proxy_clausification,[status(thm)],[f132])).
% 1.61/2.01 thf(f132,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : ((((mrel @ '#b_alice' @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#b_bob' @ X1 @ Y0) => (~ (bigcity @ portland @ Y0)))))) = $true)) )),
% 1.61/2.01 inference(beta_eta_normalization,[status(thm)],[f131])).
% 1.61/2.01 thf(f131,plain,(
% 1.61/2.01 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ '#b_alice' @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#b_bob' @ Y0 @ Y1) => (~ (bigcity @ portland @ Y1))))))) @ X1) = $true)) )),
% 1.61/2.01 inference(pi_clausification,[status(thm)],[f130])).
% 1.61/2.01 thf(f130,plain,(
% 1.61/2.01 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#b_alice' @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#b_bob' @ Y0 @ Y1) => (~ (bigcity @ portland @ Y1)))))))))),
% 1.61/2.01 inference(beta_eta_normalization,[status(thm)],[f96])).
% 1.61/2.01 thf(f96,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_alice' @ ((^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ '#b_bob' @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ (bigcity @ portland))))))),
% 1.61/2.01 inference(definition_unfolding,[status(thm)],[f80,f78,f74,f74,f89])).
% 1.61/2.01 thf(f89,plain,(
% 1.61/2.01 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f48])).
% 1.61/2.01 thf(f48,plain,(
% 1.61/2.01 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.61/2.01 inference(fool_elimination,[status(thm)],[f47])).
% 1.61/2.01 thf(f47,plain,(
% 1.61/2.01 (mnot = (^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))))),
% 1.61/2.01 inference(rectify,[status(thm)],[f2])).
% 1.61/2.01 thf(f2,axiom,(
% 1.61/2.01 (mnot = (^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))))),
% 1.61/2.01 file('/export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2THF_4642.p',mnot_def)).
% 1.61/2.01 thf(f80,plain,(
% 1.61/2.01 ((mlocal @ (mbox @ '#b_alice' @ (mbox @ '#b_bob' @ (mnot @ (bigcity @ portland))))) = $true)),
% 1.61/2.01 inference(cnf_transformation,[status(thm)],[f30])).
% 1.61/2.01 thf(f30,plain,(
% 1.61/2.01 ((mlocal @ (mbox @ '#b_alice' @ (mbox @ '#b_bob' @ (mnot @ (bigcity @ portland))))) = $true)),
% 1.61/2.01 inference(fool_elimination,[status(thm)],[f29])).
% 1.61/2.01 thf(f29,plain,(
% 1.61/2.01 (mlocal @ (mbox @ '#b_alice' @ (mbox @ '#b_bob' @ (mnot @ (bigcity @ portland)))))),
% 1.61/2.01 inference(rectify,[status(thm)],[f20])).
% 1.61/2.01 thf(f20,axiom,(
% 1.61/2.01 (mlocal @ (mbox @ '#b_alice' @ (mbox @ '#b_bob' @ (mnot @ (bigcity @ portland)))))),
% 1.61/2.01 file('/export/starexec/sandbox/tmp/tmp.LoG54obBQa/DTF2THF_4642.p',axiom_3)).
% 1.61/2.01 % SZS output end Proof for DTF2THF_4642
% 1.61/2.01 % (4954)------------------------------
% 1.61/2.01 % (4954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/2.01 % (4954)Termination reason: Refutation
% 1.61/2.01
% 1.61/2.01 % (4954)Memory used [KB]: 5628
% 1.61/2.01 % (4954)Time elapsed: 0.008 s
% 1.61/2.01 % (4954)Instructions burned: 18 (million)
% 1.61/2.01 % (4954)------------------------------
% 1.61/2.01 % (4954)------------------------------
% 1.61/2.01 % (4953)Success in time 0.011 s
%------------------------------------------------------------------------------