%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO886^6 : 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 : 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 09:55:06 AM UTC 2026
% Result : Theorem 1.87s 1.50s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 186 ( 38 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 261 ( 7 ~; 2 |; 0 &; 209 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 6 con; 0-3 aty)
% ( 21 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 94 ( 82 ^; 12 !; 0 ?; 94 :)
% 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_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
f: $i > mworld > $o ).
thf(func_def_28,type,
sK0: mworld > mworld ).
thf(func_def_30,type,
sK2: mworld ).
thf(f74,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
$true = $false,
inference(superposition,[status(thm)],[f65,f71]) ).
thf(f71,plain,
( ( mrel @ mactual @ sK2 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( mrel @ mactual @ sK2 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f61,f67]) ).
thf(f67,plain,
( $false
= ( f @ sK3 @ sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
( $false
= ( ^ [Y0: $i] : ( f @ Y0 @ sK2 )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] : ( f @ Y0 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( mrel @ mactual @ sK2 )
=> ( !! @ $i
@ ^ [Y0: $i] : ( f @ Y0 @ sK2 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] : ( f @ Y1 @ Y0 ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] : ( f @ Y1 @ Y0 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( $true
!= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] : ( f @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( f @ Y0 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f52,f50,f51,f48,f43,f43,f48]) ).
thf(f43,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) )
= mbox ),
file('/export/starexec/sandbox/tmp/tmp.TLHfdOgAAR/DTF2THF_11329.p',mbox_def) ).
thf(f48,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) )
= mforall_di ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X5: $i] : ( X1 @ X5 @ X2 ) )
= mforall_di ),
file('/export/starexec/sandbox/tmp/tmp.TLHfdOgAAR/DTF2THF_11329.p',mforall_di_def) ).
thf(f51,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( mimplies
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TLHfdOgAAR/DTF2THF_11329.p',mimplies_def) ).
thf(f50,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,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/sandbox/tmp/tmp.TLHfdOgAAR/DTF2THF_11329.p',mlocal_def) ).
thf(f52,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
~ ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X0: $i] : ( mbox @ ( f @ X0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( f @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X5: $i] : ( mbox @ ( f @ X5 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X5: $i] : ( f @ X5 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
thf(f12,conjecture,
( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X5: $i] : ( mbox @ ( f @ X5 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X5: $i] : ( f @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TLHfdOgAAR/DTF2THF_11329.p',con) ).
thf(f61,plain,
! [X2: mworld,X1: $i] :
( ( $true
= ( f @ X1 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: mworld,X1: $i] :
( $true
= ( ( mrel @ mactual @ X2 )
=> ( f @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: mworld,X1: $i] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( f @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: $i] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( f @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( f @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f65,plain,
( $true
= ( mrel @ mactual @ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO886^6 : TPTP v9.2.1. Released v8.1.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n013.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:52:38 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.49 ---- Original DTF file ---
% 0.33/0.49 thf(spec,logic,$$dhol).
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 % File : SYO886^6 : TPTP v9.2.1. Released v8.1.0.
% 0.33/0.49 % Domain : Syntactic
% 0.33/0.49 % Problem : Barcan scheme instance. (Ted Sider's qml wwf 1)
% 0.33/0.49 % Version : [BP13] axioms.
% 0.33/0.49 % English :
% 0.33/0.49
% 0.33/0.49 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.33/0.49 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.33/0.49 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.33/0.49 % Source : [TPTP]
% 0.33/0.49 % Names : SYM001+1 [QMLTP]
% 0.33/0.49
% 0.33/0.49 % Status : Theorem
% 0.33/0.49 % Rating : 0.00 v8.2.0, 0.15 v8.1.0
% 0.33/0.49 % Syntax : Number of formulae : 26 ( 11 unt; 14 typ; 10 def)
% 0.33/0.49 % Number of atoms : 31 ( 10 equ; 0 cnn)
% 0.33/0.49 % Maximal formula atoms : 8 ( 2 avg)
% 0.33/0.49 % Number of connectives : 38 ( 1 ~; 1 |; 2 &; 31 @)
% 0.33/0.49 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.33/0.49 % Maximal formula depth : 8 ( 2 avg)
% 0.33/0.49 % Number of types : 3 ( 1 usr)
% 0.33/0.49 % Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% 0.33/0.49 % Number of symbols : 14 ( 13 usr; 1 con; 0-3 aty)
% 0.33/0.49 % Number of variables : 31 ( 25 ^; 3 !; 3 ?; 31 :)
% 0.33/0.49 % SPC : TH0_THM_EQU_NAR
% 0.33/0.49
% 0.33/0.49 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.33/0.49 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.33/0.49 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.33/0.49 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.33/0.49 % $modalities == $modal_system_D].
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 thf(mworld,type,
% 0.33/0.49 mworld: $tType ).
% 0.33/0.49
% 0.33/0.49 thf(mrel_type,type,
% 0.33/0.49 mrel: mworld > mworld > $o ).
% 0.33/0.49
% 0.33/0.49 thf(mactual_type,type,
% 0.33/0.49 mactual: mworld ).
% 0.33/0.49
% 0.33/0.49 thf(mlocal_type,type,
% 0.33/0.49 mlocal: ( mworld > $o ) > $o ).
% 0.33/0.49
% 0.33/0.49 thf(mlocal_def,definition,
% 0.33/0.49 ( mlocal
% 0.33/0.49 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(mnot_type,type,
% 0.33/0.49 mnot: ( mworld > $o ) > mworld > $o ).
% 0.33/0.49
% 0.33/0.49 thf(mand_type,type,
% 0.33/0.49 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.33/0.49
% 0.33/0.49 thf(mor_type,type,
% 0.33/0.49 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.33/0.49
% 0.33/0.49 thf(mimplies_type,type,
% 0.33/0.49 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.33/0.49
% 0.33/0.49 thf(mequiv_type,type,
% 0.33/0.49 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.33/0.49
% 0.33/0.49 thf(mnot_def,definition,
% 0.33/0.49 ( mnot
% 0.33/0.49 = ( ^ [A: mworld > $o,W: mworld] :
% 0.33/0.49 ~ ( A @ W ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(mand_def,definition,
% 0.33/0.49 ( mand
% 0.33/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.33/0.49 ( ( A @ W )
% 0.33/0.49 & ( B @ W ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(mor_def,definition,
% 0.33/0.49 ( mor
% 0.33/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.33/0.49 ( ( A @ W )
% 0.33/0.49 | ( B @ W ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(mimplies_def,definition,
% 0.33/0.49 ( mimplies
% 0.33/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.33/0.49 ( ( A @ W )
% 0.33/0.49 => ( B @ W ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(mequiv_def,definition,
% 0.33/0.49 ( mequiv
% 0.33/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.33/0.49 ( ( A @ W )
% 0.33/0.49 <=> ( B @ W ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(mbox_type,type,
% 0.33/0.49 mbox: ( mworld > $o ) > mworld > $o ).
% 0.33/0.49
% 0.33/0.49 thf(mbox_def,definition,
% 0.33/0.49 ( mbox
% 0.33/0.49 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.33/0.49 ! [V: mworld] :
% 0.33/0.49 ( ( mrel @ W @ V )
% 0.33/0.49 => ( Phi @ V ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(mdia_type,type,
% 0.33/0.49 mdia: ( mworld > $o ) > mworld > $o ).
% 0.33/0.49
% 0.33/0.49 thf(mdia_def,definition,
% 0.33/0.49 ( mdia
% 0.33/0.49 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.33/0.49 ? [V: mworld] :
% 0.33/0.49 ( ( mrel @ W @ V )
% 0.33/0.49 & ( Phi @ V ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(mrel_serial,axiom,
% 0.33/0.49 ! [W: mworld] :
% 0.33/0.49 ? [V: mworld] : ( mrel @ W @ V ) ).
% 0.33/0.49
% 0.33/0.49 thf(mforall_di_type,type,
% 0.33/0.49 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.33/0.49
% 0.33/0.49 thf(mforall_di_def,definition,
% 0.33/0.49 ( mforall_di
% 0.33/0.49 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.33/0.49 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(mexists_di_type,type,
% 0.33/0.49 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.33/0.49
% 0.33/0.49 thf(mexists_di_def,definition,
% 0.33/0.49 ( mexists_di
% 0.33/0.49 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.33/0.49 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(f_decl,type,
% 0.33/0.49 f: $i > mworld > $o ).
% 0.33/0.49
% 0.33/0.49 thf(con,conjecture,
% 0.33/0.49 ( mlocal
% 0.33/0.49 @ ( mimplies
% 0.33/0.49 @ ( mforall_di
% 0.33/0.49 @ ^ [X: $i] : ( mbox @ ( f @ X ) ) )
% 0.33/0.49 @ ( mbox
% 0.33/0.49 @ ( mforall_di
% 0.33/0.49 @ ^ [X: $i] : ( f @ X ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 1.72/1.46 ---- Embedded in THF ---
% 1.72/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.72/1.46 %%% Generated on Tue Feb 24 14:52:39 EST 2026
% 1.72/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.72/1.46 %%% Logic specification used:
% 1.72/1.46 %%% thf(spec, logic, $$dhol).
% 1.72/1.46
% 1.72/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.TLHfdOgAAR/DTF2DTF11329.p
% See solution above
% 1.72/1.46 ------------------------
% 1.72/1.47 ---- Cleaned THF ---
% 1.72/1.47 thf(mworld,type,
% 1.72/1.47 mworld: $tType ).
% 1.72/1.47
% 1.72/1.47 thf(mrel_type,type,
% 1.72/1.47 mrel: mworld > mworld > $o ).
% 1.72/1.47
% 1.72/1.47 thf(mactual_type,type,
% 1.72/1.47 mactual: mworld ).
% 1.72/1.47
% 1.72/1.47 thf(mlocal_type,type,
% 1.72/1.47 mlocal: ( mworld > $o ) > $o ).
% 1.72/1.47
% 1.72/1.47 thf(mlocal_def,definition,
% 1.72/1.47 ( mlocal
% 1.72/1.47 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.72/1.47
% 1.72/1.47 thf(mnot_type,type,
% 1.72/1.47 mnot: ( mworld > $o ) > mworld > $o ).
% 1.72/1.47
% 1.72/1.47 thf(mand_type,type,
% 1.72/1.47 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.72/1.47
% 1.72/1.47 thf(mor_type,type,
% 1.72/1.47 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.72/1.47
% 1.72/1.47 thf(mimplies_type,type,
% 1.72/1.47 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.72/1.47
% 1.72/1.47 thf(mequiv_type,type,
% 1.72/1.47 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.72/1.47
% 1.72/1.47 thf(mnot_def,definition,
% 1.72/1.47 ( mnot
% 1.72/1.47 = ( ^ [A: mworld > $o,W: mworld] :
% 1.72/1.47 ~ ( A @ W ) ) ) ).
% 1.72/1.47
% 1.72/1.47 thf(mand_def,definition,
% 1.72/1.47 ( mand
% 1.72/1.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.72/1.47 ( ( A @ W )
% 1.72/1.47 & ( B @ W ) ) ) ) ).
% 1.72/1.47
% 1.72/1.47 thf(mor_def,definition,
% 1.72/1.47 ( mor
% 1.72/1.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.72/1.47 ( ( A @ W )
% 1.72/1.47 | ( B @ W ) ) ) ) ).
% 1.72/1.47
% 1.72/1.47 thf(mimplies_def,definition,
% 1.72/1.47 ( mimplies
% 1.72/1.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.72/1.47 ( ( A @ W )
% 1.72/1.47 => ( B @ W ) ) ) ) ).
% 1.72/1.47
% 1.72/1.47 thf(mequiv_def,definition,
% 1.72/1.47 ( mequiv
% 1.72/1.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.72/1.47 ( ( A @ W )
% 1.72/1.47 <=> ( B @ W ) ) ) ) ).
% 1.72/1.47
% 1.72/1.47 thf(mbox_type,type,
% 1.72/1.47 mbox: ( mworld > $o ) > mworld > $o ).
% 1.72/1.47
% 1.72/1.47 thf(mbox_def,definition,
% 1.72/1.47 ( mbox
% 1.72/1.47 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.72/1.47 ! [V: mworld] :
% 1.72/1.47 ( ( mrel @ W @ V )
% 1.72/1.47 => ( Phi @ V ) ) ) ) ).
% 1.72/1.47
% 1.72/1.47 thf(mdia_type,type,
% 1.72/1.47 mdia: ( mworld > $o ) > mworld > $o ).
% 1.72/1.47
% 1.72/1.47 thf(mdia_def,definition,
% 1.72/1.47 ( mdia
% 1.72/1.47 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.72/1.47 ? [V: mworld] :
% 1.72/1.47 ( ( mrel @ W @ V )
% 1.72/1.47 & ( Phi @ V ) ) ) ) ).
% 1.72/1.47
% 1.72/1.47 thf(mrel_serial,axiom,
% 1.72/1.47 ! [W: mworld] :
% 1.72/1.47 ? [V: mworld] : ( mrel @ W @ V ) ).
% 1.72/1.47
% 1.72/1.47 thf(mforall_di_type,type,
% 1.72/1.47 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.72/1.47
% 1.72/1.47 thf(mforall_di_def,definition,
% 1.72/1.47 ( mforall_di
% 1.72/1.47 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.72/1.47 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 1.72/1.47
% 1.72/1.47 thf(mexists_di_type,type,
% 1.72/1.47 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.72/1.47
% 1.72/1.47 thf(mexists_di_def,definition,
% 1.72/1.47 ( mexists_di
% 1.72/1.47 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.72/1.47 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 1.72/1.47
% 1.72/1.47 thf(f_decl,type,
% 1.72/1.47 f: $i > mworld > $o ).
% 1.72/1.47
% 1.72/1.47 thf(con,conjecture,
% 1.72/1.47 ( mlocal
% 1.72/1.47 @ ( mimplies
% 1.72/1.47 @ ( mforall_di
% 1.72/1.47 @ ^ [X: $i] : ( mbox @ ( f @ X ) ) )
% 1.72/1.47 @ ( mbox
% 1.72/1.47 @ ( mforall_di
% 1.72/1.47 @ ^ [X: $i] : ( f @ X ) ) ) ) ) ).
% 1.72/1.47 ------------------------
% 1.72/1.49 % (11451)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_11329 for (2999ds/275Mi)
% 1.72/1.49 % (11446)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11329 for (2999ds/183Mi)
% 1.72/1.49 % (11447)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_11329 for (2999ds/4Mi)
% 1.72/1.49 % (11450)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_11329 for (2999ds/2Mi)
% 1.72/1.49 % (11449)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11329 for (2999ds/2Mi)
% 1.72/1.49 % (11448)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_11329 for (2999ds/27Mi)
% 1.72/1.49 % (11452)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11329 for (2999ds/18Mi)
% 1.72/1.49 % (11449)Instruction limit reached!
% 1.72/1.49 % (11449)------------------------------
% 1.72/1.49 % (11449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (11449)Termination reason: Unknown
% 1.72/1.49 % (11449)Termination phase: Naming
% 1.72/1.49 % (11450)Instruction limit reached!
% 1.72/1.49 % (11450)------------------------------
% 1.72/1.49 % (11450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (11450)Termination reason: Unknown
% 1.72/1.49 % (11450)Termination phase: Property scanning
% 1.72/1.49
% 1.72/1.49 % (11450)Memory used [KB]: 1023
% 1.72/1.49 % (11450)Time elapsed: 0.003 s
% 1.72/1.49 % (11450)Instructions burned: 2 (million)
% 1.72/1.49 % (11450)------------------------------
% 1.72/1.49 % (11450)------------------------------
% 1.72/1.49
% 1.72/1.49 % (11449)Memory used [KB]: 1023
% 1.72/1.49 % (11449)Time elapsed: 0.003 s
% 1.72/1.49 % (11449)Instructions burned: 2 (million)
% 1.72/1.49 % (11449)------------------------------
% 1.72/1.49 % (11449)------------------------------
% 1.72/1.49 % (11447)Instruction limit reached!
% 1.72/1.49 % (11447)------------------------------
% 1.72/1.49 % (11447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (11447)Termination reason: Unknown
% 1.72/1.49 % (11447)Termination phase: Saturation
% 1.72/1.49
% 1.72/1.49 % (11447)Memory used [KB]: 5500
% 1.72/1.49 % (11447)Time elapsed: 0.004 s
% 1.72/1.49 % (11447)Instructions burned: 4 (million)
% 1.72/1.49 % (11447)------------------------------
% 1.72/1.49 % (11447)------------------------------
% 1.72/1.49 % (11451)Refutation not found, incomplete strategy
% 1.72/1.49 % (11451)------------------------------
% 1.72/1.49 % (11451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (11451)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.49
% 1.72/1.49
% 1.72/1.49 % (11451)Memory used [KB]: 5500
% 1.72/1.49 % (11451)Time elapsed: 0.004 s
% 1.72/1.49 % (11451)Instructions burned: 4 (million)
% 1.72/1.49 % (11451)------------------------------
% 1.72/1.49 % (11451)------------------------------
% 1.72/1.49 % (11446)First to succeed.
% 1.72/1.50 % (11448)Also succeeded, but the first one will report.
% 1.87/1.50 % (11446)Refutation found. Thanks to Tanya!
% 1.87/1.50 % SZS status Theorem for DTF2THF_11329
% 1.87/1.50 % SZS output start Proof for DTF2THF_11329
% 1.87/1.50 thf(type_def_5, type, mworld: $tType).
% 1.87/1.50 thf(func_def_0, type, mworld: $tType).
% 1.87/1.50 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.87/1.50 thf(func_def_2, type, mactual: mworld).
% 1.87/1.50 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.87/1.50 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.87/1.50 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.87/1.50 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.87/1.50 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.87/1.50 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.87/1.50 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.87/1.50 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.87/1.50 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.87/1.50 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.87/1.50 thf(func_def_14, type, f: $i > mworld > $o).
% 1.87/1.50 thf(func_def_28, type, sK0: mworld > mworld).
% 1.87/1.50 thf(func_def_30, type, sK2: mworld).
% 1.87/1.50 thf(f74,plain,(
% 1.87/1.50 $false),
% 1.87/1.50 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.87/1.50 thf(f73,plain,(
% 1.87/1.50 ($true = $false)),
% 1.87/1.50 inference(superposition,[status(thm)],[f65,f71])).
% 1.87/1.50 thf(f71,plain,(
% 1.87/1.50 ((mrel @ mactual @ sK2) = $false)),
% 1.87/1.50 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.87/1.50 thf(f68,plain,(
% 1.87/1.50 ((mrel @ mactual @ sK2) = $false) | ($true = $false)),
% 1.87/1.50 inference(superposition,[status(thm)],[f61,f67])).
% 1.87/1.50 thf(f67,plain,(
% 1.87/1.50 ($false = (f @ sK3 @ sK2))),
% 1.87/1.50 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.87/1.50 thf(f66,plain,(
% 1.87/1.50 ($false = ((^[Y0 : $i]: (f @ Y0 @ sK2)) @ sK3))),
% 1.87/1.50 inference(sigma_clausification,[status(thm)],[f64])).
% 1.87/1.50 thf(f64,plain,(
% 1.87/1.50 ($false = (!! @ $i @ (^[Y0 : $i]: (f @ Y0 @ sK2))))),
% 1.87/1.50 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.87/1.50 thf(f63,plain,(
% 1.87/1.50 (((mrel @ mactual @ sK2) => (!! @ $i @ (^[Y0 : $i]: (f @ Y0 @ sK2)))) = $false)),
% 1.87/1.50 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.87/1.50 thf(f62,plain,(
% 1.87/1.50 (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (f @ Y1 @ Y0))))) @ sK2) = $false)),
% 1.87/1.50 inference(sigma_clausification,[status(thm)],[f55])).
% 1.87/1.50 thf(f55,plain,(
% 1.87/1.50 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (f @ Y1 @ Y0)))))) = $false)),
% 1.87/1.50 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.87/1.50 thf(f54,plain,(
% 1.87/1.50 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (f @ Y0 @ Y1)))))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (f @ Y1 @ Y0))))))))),
% 1.87/1.50 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.87/1.50 thf(f53,plain,(
% 1.87/1.50 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ (f @ Y0)))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: (f @ Y0)))))))),
% 1.87/1.50 inference(definition_unfolding,[status(thm)],[f52,f50,f51,f48,f43,f43,f48])).
% 1.87/1.50 thf(f43,plain,(
% 1.87/1.50 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.87/1.50 inference(cnf_transformation,[status(thm)],[f22])).
% 1.87/1.50 thf(f22,plain,(
% 1.87/1.50 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.87/1.50 inference(fool_elimination,[status(thm)],[f21])).
% 1.87/1.50 thf(f21,plain,(
% 1.87/1.50 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 1.87/1.50 inference(rectify,[status(thm)],[f7])).
% 1.87/1.50 thf(f7,axiom,(
% 1.87/1.50 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 1.87/1.50 file('/export/starexec/sandbox/tmp/tmp.TLHfdOgAAR/DTF2THF_11329.p',mbox_def)).
% 1.87/1.50 thf(f48,plain,(
% 1.87/1.50 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.87/1.50 inference(cnf_transformation,[status(thm)],[f16])).
% 1.87/1.50 thf(f16,plain,(
% 1.87/1.50 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.87/1.50 inference(fool_elimination,[status(thm)],[f15])).
% 1.87/1.50 thf(f15,plain,(
% 1.87/1.50 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))) = mforall_di)),
% 1.87/1.50 inference(rectify,[status(thm)],[f10])).
% 1.87/1.50 thf(f10,axiom,(
% 1.87/1.50 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5 : $i] : (X1 @ X5 @ X2))) = mforall_di)),
% 1.87/1.50 file('/export/starexec/sandbox/tmp/tmp.TLHfdOgAAR/DTF2THF_11329.p',mforall_di_def)).
% 1.87/1.50 thf(f51,plain,(
% 1.87/1.50 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.87/1.50 inference(cnf_transformation,[status(thm)],[f26])).
% 1.87/1.50 thf(f26,plain,(
% 1.87/1.50 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.87/1.50 inference(fool_elimination,[status(thm)],[f25])).
% 1.87/1.50 thf(f25,plain,(
% 1.87/1.50 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.87/1.50 inference(rectify,[status(thm)],[f5])).
% 1.87/1.50 thf(f5,axiom,(
% 1.87/1.50 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.87/1.50 file('/export/starexec/sandbox/tmp/tmp.TLHfdOgAAR/DTF2THF_11329.p',mimplies_def)).
% 1.87/1.50 thf(f50,plain,(
% 1.87/1.50 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.87/1.50 inference(cnf_transformation,[status(thm)],[f35])).
% 1.87/1.50 thf(f35,plain,(
% 1.87/1.50 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.87/1.50 inference(fool_elimination,[status(thm)],[f1])).
% 1.87/1.50 thf(f1,axiom,(
% 1.87/1.50 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.87/1.50 file('/export/starexec/sandbox/tmp/tmp.TLHfdOgAAR/DTF2THF_11329.p',mlocal_def)).
% 1.87/1.50 thf(f52,plain,(
% 1.87/1.50 ($true != (mlocal @ (mimplies @ (mforall_di @ (^[Y0 : $i]: (mbox @ (f @ Y0)))) @ (mbox @ (mforall_di @ (^[Y0 : $i]: (f @ Y0)))))))),
% 1.87/1.50 inference(cnf_transformation,[status(thm)],[f38])).
% 1.87/1.50 thf(f38,plain,(
% 1.87/1.50 ($true != (mlocal @ (mimplies @ (mforall_di @ (^[Y0 : $i]: (mbox @ (f @ Y0)))) @ (mbox @ (mforall_di @ (^[Y0 : $i]: (f @ Y0)))))))),
% 1.87/1.50 inference(flattening,[status(thm)],[f20])).
% 1.87/1.50 thf(f20,plain,(
% 1.87/1.50 ~($true = (mlocal @ (mimplies @ (mforall_di @ (^[Y0 : $i]: (mbox @ (f @ Y0)))) @ (mbox @ (mforall_di @ (^[Y0 : $i]: (f @ Y0)))))))),
% 1.87/1.50 inference(fool_elimination,[status(thm)],[f19])).
% 1.87/1.50 thf(f19,plain,(
% 1.87/1.50 ~(mlocal @ (mimplies @ (mforall_di @ (^[X0 : $i] : (mbox @ (f @ X0)))) @ (mbox @ (mforall_di @ (^[X1 : $i] : (f @ X1))))))),
% 1.87/1.50 inference(rectify,[status(thm)],[f13])).
% 1.87/1.50 thf(f13,negated_conjecture,(
% 1.87/1.50 ~(mlocal @ (mimplies @ (mforall_di @ (^[X5 : $i] : (mbox @ (f @ X5)))) @ (mbox @ (mforall_di @ (^[X5 : $i] : (f @ X5))))))),
% 1.87/1.50 inference(negated_conjecture,[status(cth)],[f12])).
% 1.87/1.50 thf(f12,conjecture,(
% 1.87/1.50 (mlocal @ (mimplies @ (mforall_di @ (^[X5 : $i] : (mbox @ (f @ X5)))) @ (mbox @ (mforall_di @ (^[X5 : $i] : (f @ X5))))))),
% 1.87/1.50 file('/export/starexec/sandbox/tmp/tmp.TLHfdOgAAR/DTF2THF_11329.p',con)).
% 1.87/1.50 thf(f61,plain,(
% 1.87/1.50 ( ! [X2 : mworld,X1 : $i] : (($true = (f @ X1 @ X2)) | ($false = (mrel @ mactual @ X2))) )),
% 1.87/1.50 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.87/1.50 thf(f60,plain,(
% 1.87/1.50 ( ! [X2 : mworld,X1 : $i] : (($true = ((mrel @ mactual @ X2) => (f @ X1 @ X2)))) )),
% 1.87/1.50 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.87/1.50 thf(f59,plain,(
% 1.87/1.50 ( ! [X2 : mworld,X1 : $i] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (f @ X1 @ Y0))) @ X2))) )),
% 1.87/1.50 inference(pi_clausification,[status(thm)],[f58])).
% 1.87/1.50 thf(f58,plain,(
% 1.87/1.50 ( ! [X1 : $i] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (f @ X1 @ Y0)))))) )),
% 1.87/1.50 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.87/1.50 thf(f57,plain,(
% 1.87/1.50 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (f @ Y0 @ Y1))))) @ X1))) )),
% 1.87/1.50 inference(pi_clausification,[status(thm)],[f56])).
% 1.87/1.50 thf(f56,plain,(
% 1.87/1.50 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (f @ Y0 @ Y1)))))))),
% 1.87/1.50 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.87/1.50 thf(f65,plain,(
% 1.87/1.50 ($true = (mrel @ mactual @ sK2))),
% 1.87/1.50 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.87/1.50 % SZS output end Proof for DTF2THF_11329
% 1.87/1.50 % (11446)------------------------------
% 1.87/1.50 % (11446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.87/1.50 % (11446)Termination reason: Refutation
% 1.87/1.50
% 1.87/1.50 % (11446)Memory used [KB]: 5500
% 1.87/1.50 % (11446)Time elapsed: 0.006 s
% 1.87/1.50 % (11446)Instructions burned: 5 (million)
% 1.87/1.50 % (11446)------------------------------
% 1.87/1.50 % (11446)------------------------------
% 1.87/1.50 % (11445)Success in time 0.02 s
%------------------------------------------------------------------------------