%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO382^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 09:54:05 AM UTC 2026
% Result : Theorem 1.63s 1.30s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 7 unt; 0 typ; 5 def)
% Number of atoms : 469 ( 120 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 500 ( 90 ~; 49 |; 48 &; 267 @)
% ( 5 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 147 ( 0 ^; 89 !; 58 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cS: $i > $o ).
thf(func_def_1,type,
cQ: $i > $i > $o ).
thf(func_def_2,type,
cP: $i > $i > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_9,type,
sK2: $i > $i ).
thf(func_def_13,type,
sK6: $i > $i ).
thf(f67,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f39,f44,f53,f58,f61,f66]) ).
thf(f66,plain,
( ~ spl7_1
| ~ spl7_5 ),
inference(avatar_split_clause,[status(thm)],[f64,f41,f26]) ).
thf(f26,definition,
( spl7_1
<=> ( ( cQ @ sK3 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition]) ).
thf(f41,definition,
( spl7_5
<=> ( ( cP @ sK3 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_5])],[avatar_definition]) ).
thf(f64,plain,
( ( ( cQ @ sK3 @ sK4 )
!= $true )
| ~ spl7_5 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( cQ @ sK3 @ sK4 )
!= $true )
| ( $true != $true )
| ~ spl7_5 ),
inference(superposition,[status(thm)],[f24,f43]) ).
thf(f43,plain,
( ( ( cP @ sK3 @ sK4 )
= $true )
| ~ spl7_5 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f24,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cP @ X0 @ X1 ) )
| ( $true
!= ( cQ @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( cQ @ X0 @ X1 ) )
| ( $true
!= ( cP @ X0 @ X1 ) ) )
& ! [X3: $i] :
( ( cP @ X3 @ sK0 )
= $true )
& ( ( ! [X5: $i] :
( ( cQ @ X5 @ sK1 )
!= $true )
& ( ( cS @ sK1 )
= $true ) )
| ! [X6: $i] :
( ( cP @ ( sK2 @ X6 ) @ X6 )
!= $true )
| ( ( ( cP @ sK3 @ sK4 )
= $true )
& ( ( cQ @ sK3 @ sK4 )
= $true ) )
| ( ( cS @ sK5 )
!= $true ) )
& ! [X11: $i] :
( ( cS @ X11 )
= $true )
& ! [X12: $i] :
( ( $true
!= ( cS @ X12 ) )
| ( ( cQ @ ( sK6 @ X12 ) @ X12 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f9,f15,f14,f13,f12,f11,f10]) ).
thf(f10,plain,
( ? [X2: $i] :
! [X3: $i] :
( ( cP @ X3 @ X2 )
= $true )
=> ! [X3: $i] :
( ( cP @ X3 @ sK0 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X4: $i] :
( ! [X5: $i] :
( ( cQ @ X5 @ X4 )
!= $true )
& ( ( cS @ X4 )
= $true ) )
=> ( ! [X5: $i] :
( ( cQ @ X5 @ sK1 )
!= $true )
& ( ( cS @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X6: $i] :
( ? [X7: $i] :
( ( cP @ X7 @ X6 )
!= $true )
=> ( ( cP @ ( sK2 @ X6 ) @ X6 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X8: $i,X9: $i] :
( ( ( cP @ X8 @ X9 )
= $true )
& ( ( cQ @ X8 @ X9 )
= $true ) )
=> ( ( ( cP @ sK3 @ sK4 )
= $true )
& ( ( cQ @ sK3 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X10: $i] :
( ( cS @ X10 )
!= $true )
=> ( ( cS @ sK5 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X12: $i] :
( ? [X13: $i] :
( ( cQ @ X13 @ X12 )
= $true )
=> ( ( cQ @ ( sK6 @ X12 ) @ X12 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( cQ @ X0 @ X1 ) )
| ( $true
!= ( cP @ X0 @ X1 ) ) )
& ? [X2: $i] :
! [X3: $i] :
( ( cP @ X3 @ X2 )
= $true )
& ( ? [X4: $i] :
( ! [X5: $i] :
( ( cQ @ X5 @ X4 )
!= $true )
& ( ( cS @ X4 )
= $true ) )
| ! [X6: $i] :
? [X7: $i] :
( ( cP @ X7 @ X6 )
!= $true )
| ? [X8: $i,X9: $i] :
( ( ( cP @ X8 @ X9 )
= $true )
& ( ( cQ @ X8 @ X9 )
= $true ) )
| ? [X10: $i] :
( ( cS @ X10 )
!= $true ) )
& ! [X11: $i] :
( ( cS @ X11 )
= $true )
& ! [X12: $i] :
( ( $true
!= ( cS @ X12 ) )
| ? [X13: $i] :
( ( cQ @ X13 @ X12 )
= $true ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X8: $i,X7: $i] :
( ( ( cQ @ X8 @ X7 )
!= $true )
| ( ( cP @ X8 @ X7 )
!= $true ) )
& ? [X11: $i] :
! [X12: $i] :
( $true
= ( cP @ X12 @ X11 ) )
& ( ? [X0: $i] :
( ! [X1: $i] :
( ( cQ @ X1 @ X0 )
!= $true )
& ( ( cS @ X0 )
= $true ) )
| ! [X4: $i] :
? [X5: $i] :
( ( cP @ X5 @ X4 )
!= $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( cP @ X2 @ X3 ) )
& ( $true
= ( cQ @ X2 @ X3 ) ) )
| ? [X6: $i] :
( ( cS @ X6 )
!= $true ) )
& ! [X13: $i] :
( $true
= ( cS @ X13 ) )
& ! [X9: $i] :
( ( ( cS @ X9 )
!= $true )
| ? [X10: $i] :
( $true
= ( cQ @ X10 @ X9 ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X13: $i] :
( $true
= ( cS @ X13 ) )
& ! [X8: $i,X7: $i] :
( ( ( cQ @ X8 @ X7 )
!= $true )
| ( ( cP @ X8 @ X7 )
!= $true ) )
& ! [X9: $i] :
( ( ( cS @ X9 )
!= $true )
| ? [X10: $i] :
( $true
= ( cQ @ X10 @ X9 ) ) )
& ? [X11: $i] :
! [X12: $i] :
( $true
= ( cP @ X12 @ X11 ) )
& ( ? [X6: $i] :
( ( cS @ X6 )
!= $true )
| ? [X0: $i] :
( ! [X1: $i] :
( ( cQ @ X1 @ X0 )
!= $true )
& ( ( cS @ X0 )
= $true ) )
| ? [X2: $i,X3: $i] :
( ( $true
= ( cP @ X2 @ X3 ) )
& ( $true
= ( cQ @ X2 @ X3 ) ) )
| ! [X4: $i] :
? [X5: $i] :
( ( cP @ X5 @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ( ! [X0: $i] :
( ( ( cS @ X0 )
= $true )
=> ? [X1: $i] :
( ( cQ @ X1 @ X0 )
= $true ) )
& ! [X2: $i,X3: $i] :
( ( $true
= ( cP @ X2 @ X3 ) )
=> ( $true
!= ( cQ @ X2 @ X3 ) ) )
& ? [X4: $i] :
! [X5: $i] :
( ( cP @ X5 @ X4 )
= $true ) )
=> ? [X6: $i] :
( ( cS @ X6 )
!= $true ) )
=> ( ( ! [X8: $i,X7: $i] :
( ( ( cP @ X8 @ X7 )
= $true )
=> ( ( cQ @ X8 @ X7 )
!= $true ) )
& ! [X9: $i] :
( ( ( cS @ X9 )
= $true )
=> ? [X10: $i] :
( $true
= ( cQ @ X10 @ X9 ) ) )
& ? [X11: $i] :
! [X12: $i] :
( $true
= ( cP @ X12 @ X11 ) ) )
=> ? [X13: $i] :
( $true
!= ( cS @ X13 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ! [X0: $i] :
( ( ( cS @ X0 )
= $true )
=> ? [X1: $i] :
( ( cQ @ X1 @ X0 )
= $true ) )
& ! [X2: $i,X3: $i] :
( ( $true
= ( cP @ X2 @ X3 ) )
=> ( $true
!= ( cQ @ X2 @ X3 ) ) )
& ? [X4: $i] :
! [X5: $i] :
( ( cP @ X5 @ X4 )
= $true ) )
=> ? [X6: $i] :
( ( cS @ X6 )
!= $true ) )
=> ( ( ! [X7: $i,X8: $i] :
( ( ( cP @ X8 @ X7 )
= $true )
=> ( ( cQ @ X8 @ X7 )
!= $true ) )
& ! [X9: $i] :
( ( ( cS @ X9 )
= $true )
=> ? [X10: $i] :
( $true
= ( cQ @ X10 @ X9 ) ) )
& ? [X11: $i] :
! [X12: $i] :
( $true
= ( cP @ X12 @ X11 ) ) )
=> ? [X13: $i] :
( $true
!= ( cS @ X13 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ! [X0: $i] :
( ( cS @ X0 )
=> ? [X1: $i] : ( cQ @ X1 @ X0 ) )
& ! [X2: $i,X3: $i] :
( ( cP @ X2 @ X3 )
=> ~ ( cQ @ X2 @ X3 ) )
& ? [X4: $i] :
! [X5: $i] : ( cP @ X5 @ X4 ) )
=> ? [X6: $i] :
~ ( cS @ X6 ) )
=> ( ( ! [X7: $i,X8: $i] :
( ( cP @ X8 @ X7 )
=> ~ ( cQ @ X8 @ X7 ) )
& ! [X9: $i] :
( ( cS @ X9 )
=> ? [X10: $i] : ( cQ @ X10 @ X9 ) )
& ? [X11: $i] :
! [X12: $i] : ( cP @ X12 @ X11 ) )
=> ? [X13: $i] :
~ ( cS @ X13 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ! [X1: $i] :
( ( cS @ X1 )
=> ? [X2: $i] : ( cQ @ X2 @ X1 ) )
& ! [X1: $i,X2: $i] :
( ( cP @ X1 @ X2 )
=> ~ ( cQ @ X1 @ X2 ) )
& ? [X0: $i] :
! [X1: $i] : ( cP @ X1 @ X0 ) )
=> ? [X3: $i] :
~ ( cS @ X3 ) )
=> ( ( ! [X2: $i,X1: $i] :
( ( cP @ X1 @ X2 )
=> ~ ( cQ @ X1 @ X2 ) )
& ! [X1: $i] :
( ( cS @ X1 )
=> ? [X2: $i] : ( cQ @ X2 @ X1 ) )
& ? [X0: $i] :
! [X1: $i] : ( cP @ X1 @ X0 ) )
=> ? [X3: $i] :
~ ( cS @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ! [X1: $i] :
( ( cS @ X1 )
=> ? [X2: $i] : ( cQ @ X2 @ X1 ) )
& ! [X1: $i,X2: $i] :
( ( cP @ X1 @ X2 )
=> ~ ( cQ @ X1 @ X2 ) )
& ? [X0: $i] :
! [X1: $i] : ( cP @ X1 @ X0 ) )
=> ? [X3: $i] :
~ ( cS @ X3 ) )
=> ( ( ! [X2: $i,X1: $i] :
( ( cP @ X1 @ X2 )
=> ~ ( cQ @ X1 @ X2 ) )
& ! [X1: $i] :
( ( cS @ X1 )
=> ? [X2: $i] : ( cQ @ X2 @ X1 ) )
& ? [X0: $i] :
! [X1: $i] : ( cP @ X1 @ X0 ) )
=> ? [X3: $i] :
~ ( cS @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lyhgI8XMjN/DTF2THF_12888.p',cTHM407) ).
thf(f61,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[status(thm)],[f60]) ).
thf(f60,plain,
( $false
| ~ spl7_2 ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true != $true )
| ~ spl7_2 ),
inference(superposition,[status(thm)],[f31,f23]) ).
thf(f23,plain,
! [X3: $i] :
( ( cP @ X3 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f31,plain,
( ! [X6: $i] :
( ( cP @ ( sK2 @ X6 ) @ X6 )
!= $true )
| ~ spl7_2 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl7_2
<=> ! [X6: $i] :
( ( cP @ ( sK2 @ X6 ) @ X6 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition]) ).
thf(f58,plain,
~ spl7_3,
inference(avatar_contradiction_clause,[status(thm)],[f57]) ).
thf(f57,plain,
( $false
| ~ spl7_3 ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true != $true )
| ~ spl7_3 ),
inference(superposition,[status(thm)],[f34,f55]) ).
thf(f55,plain,
! [X12: $i] :
( ( cQ @ ( sK6 @ X12 ) @ X12 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
! [X12: $i] :
( ( $true != $true )
| ( ( cQ @ ( sK6 @ X12 ) @ X12 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f17,f18]) ).
thf(f18,plain,
! [X11: $i] :
( ( cS @ X11 )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f17,plain,
! [X12: $i] :
( ( ( cQ @ ( sK6 @ X12 ) @ X12 )
= $true )
| ( $true
!= ( cS @ X12 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f34,plain,
( ! [X5: $i] :
( ( cQ @ X5 @ sK1 )
!= $true )
| ~ spl7_3 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl7_3
<=> ! [X5: $i] :
( ( cQ @ X5 @ sK1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_3])],[avatar_definition]) ).
thf(f53,plain,
spl7_4,
inference(avatar_contradiction_clause,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
| spl7_4 ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true != $true )
| spl7_4 ),
inference(superposition,[status(thm)],[f38,f18]) ).
thf(f38,plain,
( ( ( cS @ sK5 )
!= $true )
| spl7_4 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl7_4
<=> ( ( cS @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_4])],[avatar_definition]) ).
thf(f44,plain,
( spl7_5
| spl7_2
| ~ spl7_4
| spl7_3 ),
inference(avatar_split_clause,[status(thm)],[f22,f33,f36,f30,f41]) ).
thf(f22,plain,
! [X6: $i,X5: $i] :
( ( ( cS @ sK5 )
!= $true )
| ( ( cQ @ X5 @ sK1 )
!= $true )
| ( ( cP @ ( sK2 @ X6 ) @ X6 )
!= $true )
| ( ( cP @ sK3 @ sK4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f39,plain,
( spl7_1
| spl7_2
| spl7_3
| ~ spl7_4 ),
inference(avatar_split_clause,[status(thm)],[f21,f36,f33,f30,f26]) ).
thf(f21,plain,
! [X6: $i,X5: $i] :
( ( ( cQ @ sK3 @ sK4 )
= $true )
| ( ( cP @ ( sK2 @ X6 ) @ X6 )
!= $true )
| ( ( cS @ sK5 )
!= $true )
| ( ( cQ @ X5 @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO382^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n003.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:28:56 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO382^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : TPS problem THM407
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0165 [Bro09]
% 0.30/0.46 % : THM407 [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.30/0.46 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 12 ( 12 avg)
% 0.30/0.46 % Number of connectives : 35 ( 4 ~; 0 |; 4 &; 20 @)
% 0.30/0.46 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 11 ( 11 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.30/0.46 % Number of variables : 14 ( 0 ^; 8 !; 6 ?; 14 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(cS,type,
% 0.30/0.46 cS: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cQ,type,
% 0.30/0.46 cQ: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cP,type,
% 0.30/0.46 cP: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cTHM407,conjecture,
% 0.30/0.46 ( ( ( ? [Xv: $i] :
% 0.30/0.46 ! [Xx: $i] : ( cP @ Xx @ Xv )
% 0.30/0.46 & ! [Xx: $i] :
% 0.30/0.46 ( ( cS @ Xx )
% 0.30/0.46 => ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
% 0.30/0.46 & ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( cP @ Xx @ Xy )
% 0.30/0.46 => ~ ( cQ @ Xx @ Xy ) ) )
% 0.30/0.46 => ? [Xu: $i] :
% 0.30/0.46 ~ ( cS @ Xu ) )
% 0.30/0.46 => ( ( ? [Xv: $i] :
% 0.30/0.46 ! [Xx: $i] : ( cP @ Xx @ Xv )
% 0.30/0.46 & ! [Xx: $i] :
% 0.30/0.46 ( ( cS @ Xx )
% 0.30/0.46 => ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
% 0.30/0.46 & ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( cP @ Xx @ Xy )
% 0.30/0.46 => ~ ( cQ @ Xx @ Xy ) ) )
% 0.30/0.46 => ? [Xu: $i] :
% 0.30/0.46 ~ ( cS @ Xu ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.47/1.27 ---- Embedded in THF ---
% 1.47/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.27 %%% Generated on Tue Feb 24 14:28:56 EST 2026
% 1.47/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.27 %%% Logic specification used:
% 1.47/1.27 %%% thf(spec, logic, $$dhol).
% 1.47/1.27
% 1.47/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.lyhgI8XMjN/DTF2DTF12888.p
% See solution above
% 1.47/1.27 ------------------------
% 1.47/1.28 ---- Cleaned THF ---
% 1.47/1.28 thf(cS,type,
% 1.47/1.28 cS: $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(cQ,type,
% 1.47/1.28 cQ: $i > $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(cP,type,
% 1.47/1.28 cP: $i > $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(cTHM407,conjecture,
% 1.47/1.28 ( ( ( ? [Xv: $i] :
% 1.47/1.28 ! [Xx: $i] : ( cP @ Xx @ Xv )
% 1.47/1.28 & ! [Xx: $i] :
% 1.47/1.28 ( ( cS @ Xx )
% 1.47/1.28 => ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
% 1.47/1.28 & ! [Xx: $i,Xy: $i] :
% 1.47/1.28 ( ( cP @ Xx @ Xy )
% 1.47/1.28 => ~ ( cQ @ Xx @ Xy ) ) )
% 1.47/1.28 => ? [Xu: $i] :
% 1.47/1.28 ~ ( cS @ Xu ) )
% 1.47/1.28 => ( ( ? [Xv: $i] :
% 1.47/1.28 ! [Xx: $i] : ( cP @ Xx @ Xv )
% 1.47/1.28 & ! [Xx: $i] :
% 1.47/1.28 ( ( cS @ Xx )
% 1.47/1.28 => ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
% 1.47/1.28 & ! [Xx: $i,Xy: $i] :
% 1.47/1.28 ( ( cP @ Xx @ Xy )
% 1.47/1.28 => ~ ( cQ @ Xx @ Xy ) ) )
% 1.47/1.28 => ? [Xu: $i] :
% 1.47/1.28 ~ ( cS @ Xu ) ) ) ).
% 1.47/1.28 ------------------------
% 1.47/1.30 % (13107)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_12888 for (2999ds/27Mi)
% 1.47/1.30 % (13105)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12888 for (2999ds/183Mi)
% 1.63/1.30 % (13107)First to succeed.
% 1.63/1.30 % (13105)Also succeeded, but the first one will report.
% 1.63/1.30 % (13107)Refutation found. Thanks to Tanya!
% 1.63/1.30 % SZS status Theorem for DTF2THF_12888
% 1.63/1.30 % SZS output start Proof for DTF2THF_12888
% 1.63/1.30 thf(func_def_0, type, cS: $i > $o).
% 1.63/1.30 thf(func_def_1, type, cQ: $i > $i > $o).
% 1.63/1.30 thf(func_def_2, type, cP: $i > $i > $o).
% 1.63/1.30 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.63/1.30 thf(func_def_9, type, sK2: $i > $i).
% 1.63/1.30 thf(func_def_13, type, sK6: $i > $i).
% 1.63/1.30 thf(f67,plain,(
% 1.63/1.30 $false),
% 1.63/1.30 inference(avatar_sat_refutation,[status(thm)],[f39,f44,f53,f58,f61,f66])).
% 1.63/1.30 thf(f66,plain,(
% 1.63/1.30 ~spl7_1 | ~spl7_5),
% 1.63/1.30 inference(avatar_split_clause,[status(thm)],[f64,f41,f26])).
% 1.63/1.30 thf(f26,definition,(
% 1.63/1.30 spl7_1 <=> ((cQ @ sK3 @ sK4) = $true)),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition])).
% 1.63/1.30 thf(f41,definition,(
% 1.63/1.30 spl7_5 <=> ((cP @ sK3 @ sK4) = $true)),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl7_5])],[avatar_definition])).
% 1.63/1.30 thf(f64,plain,(
% 1.63/1.30 ((cQ @ sK3 @ sK4) != $true) | ~spl7_5),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.63/1.30 thf(f63,plain,(
% 1.63/1.30 ((cQ @ sK3 @ sK4) != $true) | ($true != $true) | ~spl7_5),
% 1.63/1.30 inference(superposition,[status(thm)],[f24,f43])).
% 1.63/1.30 thf(f43,plain,(
% 1.63/1.30 ((cP @ sK3 @ sK4) = $true) | ~spl7_5),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.63/1.30 thf(f24,plain,(
% 1.63/1.30 ( ! [X0 : $i,X1 : $i] : (($true != (cP @ X0 @ X1)) | ($true != (cQ @ X0 @ X1))) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.30 thf(f16,plain,(
% 1.63/1.30 ! [X0 : $i,X1 : $i] : (($true != (cQ @ X0 @ X1)) | ($true != (cP @ X0 @ X1))) & ! [X3 : $i] : ((cP @ X3 @ sK0) = $true) & ((! [X5 : $i] : ((cQ @ X5 @ sK1) != $true) & ((cS @ sK1) = $true)) | ! [X6 : $i] : ((cP @ (sK2 @ X6) @ X6) != $true) | (((cP @ sK3 @ sK4) = $true) & ((cQ @ sK3 @ sK4) = $true)) | ((cS @ sK5) != $true)) & ! [X11 : $i] : ((cS @ X11) = $true) & ! [X12 : $i] : (($true != (cS @ X12)) | ((cQ @ (sK6 @ X12) @ X12) = $true))),
% 1.63/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f9,f15,f14,f13,f12,f11,f10])).
% 1.63/1.30 thf(f10,plain,(
% 1.63/1.30 ? [X2 : $i] : ! [X3 : $i] : ((cP @ X3 @ X2) = $true) => ! [X3 : $i] : ((cP @ X3 @ sK0) = $true)),
% 1.63/1.30 introduced(definition,[],[choice_axiom])).
% 1.63/1.30 thf(f11,plain,(
% 1.63/1.30 ? [X4 : $i] : (! [X5 : $i] : ((cQ @ X5 @ X4) != $true) & ((cS @ X4) = $true)) => (! [X5 : $i] : ((cQ @ X5 @ sK1) != $true) & ((cS @ sK1) = $true))),
% 1.63/1.30 introduced(definition,[],[choice_axiom])).
% 1.63/1.30 thf(f12,plain,(
% 1.63/1.30 ! [X6 : $i] : (? [X7 : $i] : ((cP @ X7 @ X6) != $true) => ((cP @ (sK2 @ X6) @ X6) != $true))),
% 1.63/1.30 introduced(definition,[],[choice_axiom])).
% 1.63/1.30 thf(f13,plain,(
% 1.63/1.30 ? [X8 : $i,X9 : $i] : (((cP @ X8 @ X9) = $true) & ((cQ @ X8 @ X9) = $true)) => (((cP @ sK3 @ sK4) = $true) & ((cQ @ sK3 @ sK4) = $true))),
% 1.63/1.30 introduced(definition,[],[choice_axiom])).
% 1.63/1.30 thf(f14,plain,(
% 1.63/1.30 ? [X10 : $i] : ((cS @ X10) != $true) => ((cS @ sK5) != $true)),
% 1.63/1.30 introduced(definition,[],[choice_axiom])).
% 1.63/1.30 thf(f15,plain,(
% 1.63/1.30 ! [X12 : $i] : (? [X13 : $i] : ((cQ @ X13 @ X12) = $true) => ((cQ @ (sK6 @ X12) @ X12) = $true))),
% 1.63/1.30 introduced(definition,[],[choice_axiom])).
% 1.63/1.30 thf(f9,plain,(
% 1.63/1.30 ! [X0 : $i,X1 : $i] : (($true != (cQ @ X0 @ X1)) | ($true != (cP @ X0 @ X1))) & ? [X2 : $i] : ! [X3 : $i] : ((cP @ X3 @ X2) = $true) & (? [X4 : $i] : (! [X5 : $i] : ((cQ @ X5 @ X4) != $true) & ((cS @ X4) = $true)) | ! [X6 : $i] : ? [X7 : $i] : ((cP @ X7 @ X6) != $true) | ? [X8 : $i,X9 : $i] : (((cP @ X8 @ X9) = $true) & ((cQ @ X8 @ X9) = $true)) | ? [X10 : $i] : ((cS @ X10) != $true)) & ! [X11 : $i] : ((cS @ X11) = $true) & ! [X12 : $i] : (($true != (cS @ X12)) | ? [X13 : $i] : ((cQ @ X13 @ X12) = $true))),
% 1.63/1.30 inference(rectify,[status(thm)],[f8])).
% 1.63/1.30 thf(f8,plain,(
% 1.63/1.30 ! [X8 : $i,X7 : $i] : (((cQ @ X8 @ X7) != $true) | ((cP @ X8 @ X7) != $true)) & ? [X11 : $i] : ! [X12 : $i] : ($true = (cP @ X12 @ X11)) & (? [X0 : $i] : (! [X1 : $i] : ((cQ @ X1 @ X0) != $true) & ((cS @ X0) = $true)) | ! [X4 : $i] : ? [X5 : $i] : ((cP @ X5 @ X4) != $true) | ? [X2 : $i,X3 : $i] : (($true = (cP @ X2 @ X3)) & ($true = (cQ @ X2 @ X3))) | ? [X6 : $i] : ((cS @ X6) != $true)) & ! [X13 : $i] : ($true = (cS @ X13)) & ! [X9 : $i] : (((cS @ X9) != $true) | ? [X10 : $i] : ($true = (cQ @ X10 @ X9)))),
% 1.63/1.30 inference(flattening,[status(thm)],[f7])).
% 1.63/1.30 thf(f7,plain,(
% 1.63/1.30 (! [X13 : $i] : ($true = (cS @ X13)) & (! [X8 : $i,X7 : $i] : (((cQ @ X8 @ X7) != $true) | ((cP @ X8 @ X7) != $true)) & ! [X9 : $i] : (((cS @ X9) != $true) | ? [X10 : $i] : ($true = (cQ @ X10 @ X9))) & ? [X11 : $i] : ! [X12 : $i] : ($true = (cP @ X12 @ X11)))) & (? [X6 : $i] : ((cS @ X6) != $true) | (? [X0 : $i] : (! [X1 : $i] : ((cQ @ X1 @ X0) != $true) & ((cS @ X0) = $true)) | ? [X2 : $i,X3 : $i] : (($true = (cP @ X2 @ X3)) & ($true = (cQ @ X2 @ X3))) | ! [X4 : $i] : ? [X5 : $i] : ((cP @ X5 @ X4) != $true)))),
% 1.63/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.63/1.30 thf(f6,plain,(
% 1.63/1.30 ~(((! [X0 : $i] : (((cS @ X0) = $true) => ? [X1 : $i] : ((cQ @ X1 @ X0) = $true)) & ! [X2 : $i,X3 : $i] : (($true = (cP @ X2 @ X3)) => ($true != (cQ @ X2 @ X3))) & ? [X4 : $i] : ! [X5 : $i] : ((cP @ X5 @ X4) = $true)) => ? [X6 : $i] : ((cS @ X6) != $true)) => ((! [X8 : $i,X7 : $i] : (((cP @ X8 @ X7) = $true) => ((cQ @ X8 @ X7) != $true)) & ! [X9 : $i] : (((cS @ X9) = $true) => ? [X10 : $i] : ($true = (cQ @ X10 @ X9))) & ? [X11 : $i] : ! [X12 : $i] : ($true = (cP @ X12 @ X11))) => ? [X13 : $i] : ($true != (cS @ X13))))),
% 1.63/1.30 inference(flattening,[status(thm)],[f5])).
% 1.63/1.30 thf(f5,plain,(
% 1.63/1.30 ~(((! [X0 : $i] : (((cS @ X0) = $true) => ? [X1 : $i] : ((cQ @ X1 @ X0) = $true)) & ! [X2 : $i,X3 : $i] : (($true = (cP @ X2 @ X3)) => ~($true = (cQ @ X2 @ X3))) & ? [X4 : $i] : ! [X5 : $i] : ((cP @ X5 @ X4) = $true)) => ? [X6 : $i] : ~((cS @ X6) = $true)) => ((! [X7 : $i,X8 : $i] : (((cP @ X8 @ X7) = $true) => ~((cQ @ X8 @ X7) = $true)) & ! [X9 : $i] : (((cS @ X9) = $true) => ? [X10 : $i] : ($true = (cQ @ X10 @ X9))) & ? [X11 : $i] : ! [X12 : $i] : ($true = (cP @ X12 @ X11))) => ? [X13 : $i] : ~($true = (cS @ X13))))),
% 1.63/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.30 thf(f4,plain,(
% 1.63/1.30 ~(((! [X0 : $i] : ((cS @ X0) => ? [X1 : $i] : (cQ @ X1 @ X0)) & ! [X2 : $i,X3 : $i] : ((cP @ X2 @ X3) => ~(cQ @ X2 @ X3)) & ? [X4 : $i] : ! [X5 : $i] : (cP @ X5 @ X4)) => ? [X6 : $i] : ~(cS @ X6)) => ((! [X7 : $i,X8 : $i] : ((cP @ X8 @ X7) => ~(cQ @ X8 @ X7)) & ! [X9 : $i] : ((cS @ X9) => ? [X10 : $i] : (cQ @ X10 @ X9)) & ? [X11 : $i] : ! [X12 : $i] : (cP @ X12 @ X11)) => ? [X13 : $i] : ~(cS @ X13)))),
% 1.63/1.30 inference(rectify,[status(thm)],[f2])).
% 1.63/1.30 thf(f2,negated_conjecture,(
% 1.63/1.30 ~(((! [X1 : $i] : ((cS @ X1) => ? [X2 : $i] : (cQ @ X2 @ X1)) & ! [X1 : $i,X2 : $i] : ((cP @ X1 @ X2) => ~(cQ @ X1 @ X2)) & ? [X0 : $i] : ! [X1 : $i] : (cP @ X1 @ X0)) => ? [X3 : $i] : ~(cS @ X3)) => ((! [X2 : $i,X1 : $i] : ((cP @ X1 @ X2) => ~(cQ @ X1 @ X2)) & ! [X1 : $i] : ((cS @ X1) => ? [X2 : $i] : (cQ @ X2 @ X1)) & ? [X0 : $i] : ! [X1 : $i] : (cP @ X1 @ X0)) => ? [X3 : $i] : ~(cS @ X3)))),
% 1.63/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.30 thf(f1,conjecture,(
% 1.63/1.30 ((! [X1 : $i] : ((cS @ X1) => ? [X2 : $i] : (cQ @ X2 @ X1)) & ! [X1 : $i,X2 : $i] : ((cP @ X1 @ X2) => ~(cQ @ X1 @ X2)) & ? [X0 : $i] : ! [X1 : $i] : (cP @ X1 @ X0)) => ? [X3 : $i] : ~(cS @ X3)) => ((! [X2 : $i,X1 : $i] : ((cP @ X1 @ X2) => ~(cQ @ X1 @ X2)) & ! [X1 : $i] : ((cS @ X1) => ? [X2 : $i] : (cQ @ X2 @ X1)) & ? [X0 : $i] : ! [X1 : $i] : (cP @ X1 @ X0)) => ? [X3 : $i] : ~(cS @ X3))),
% 1.63/1.30 file('/export/starexec/sandbox2/tmp/tmp.lyhgI8XMjN/DTF2THF_12888.p',cTHM407)).
% 1.63/1.30 thf(f61,plain,(
% 1.63/1.30 ~spl7_2),
% 1.63/1.30 inference(avatar_contradiction_clause,[status(thm)],[f60])).
% 1.63/1.30 thf(f60,plain,(
% 1.63/1.30 $false | ~spl7_2),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.63/1.30 thf(f59,plain,(
% 1.63/1.30 ($true != $true) | ~spl7_2),
% 1.63/1.30 inference(superposition,[status(thm)],[f31,f23])).
% 1.63/1.30 thf(f23,plain,(
% 1.63/1.30 ( ! [X3 : $i] : (((cP @ X3 @ sK0) = $true)) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.30 thf(f31,plain,(
% 1.63/1.30 ( ! [X6 : $i] : (((cP @ (sK2 @ X6) @ X6) != $true)) ) | ~spl7_2),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.63/1.30 thf(f30,definition,(
% 1.63/1.30 spl7_2 <=> ! [X6 : $i] : ((cP @ (sK2 @ X6) @ X6) != $true)),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition])).
% 1.63/1.30 thf(f58,plain,(
% 1.63/1.30 ~spl7_3),
% 1.63/1.30 inference(avatar_contradiction_clause,[status(thm)],[f57])).
% 1.63/1.30 thf(f57,plain,(
% 1.63/1.30 $false | ~spl7_3),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.63/1.30 thf(f56,plain,(
% 1.63/1.30 ($true != $true) | ~spl7_3),
% 1.63/1.30 inference(superposition,[status(thm)],[f34,f55])).
% 1.63/1.30 thf(f55,plain,(
% 1.63/1.30 ( ! [X12 : $i] : (((cQ @ (sK6 @ X12) @ X12) = $true)) )),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.63/1.30 thf(f54,plain,(
% 1.63/1.30 ( ! [X12 : $i] : (($true != $true) | ((cQ @ (sK6 @ X12) @ X12) = $true)) )),
% 1.63/1.30 inference(forward_demodulation,[status(thm)],[f17,f18])).
% 1.63/1.30 thf(f18,plain,(
% 1.63/1.30 ( ! [X11 : $i] : (((cS @ X11) = $true)) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.30 thf(f17,plain,(
% 1.63/1.30 ( ! [X12 : $i] : (((cQ @ (sK6 @ X12) @ X12) = $true) | ($true != (cS @ X12))) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.30 thf(f34,plain,(
% 1.63/1.30 ( ! [X5 : $i] : (((cQ @ X5 @ sK1) != $true)) ) | ~spl7_3),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.63/1.30 thf(f33,definition,(
% 1.63/1.30 spl7_3 <=> ! [X5 : $i] : ((cQ @ X5 @ sK1) != $true)),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl7_3])],[avatar_definition])).
% 1.63/1.30 thf(f53,plain,(
% 1.63/1.30 spl7_4),
% 1.63/1.30 inference(avatar_contradiction_clause,[status(thm)],[f52])).
% 1.63/1.30 thf(f52,plain,(
% 1.63/1.30 $false | spl7_4),
% 1.63/1.30 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.63/1.30 thf(f51,plain,(
% 1.63/1.30 ($true != $true) | spl7_4),
% 1.63/1.30 inference(superposition,[status(thm)],[f38,f18])).
% 1.63/1.30 thf(f38,plain,(
% 1.63/1.30 ((cS @ sK5) != $true) | spl7_4),
% 1.63/1.30 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.63/1.30 thf(f36,definition,(
% 1.63/1.30 spl7_4 <=> ((cS @ sK5) = $true)),
% 1.63/1.30 introduced(definition,[new_symbols(naming,[spl7_4])],[avatar_definition])).
% 1.63/1.30 thf(f44,plain,(
% 1.63/1.30 spl7_5 | spl7_2 | ~spl7_4 | spl7_3),
% 1.63/1.30 inference(avatar_split_clause,[status(thm)],[f22,f33,f36,f30,f41])).
% 1.63/1.30 thf(f22,plain,(
% 1.63/1.30 ( ! [X6 : $i,X5 : $i] : (((cS @ sK5) != $true) | ((cQ @ X5 @ sK1) != $true) | ((cP @ (sK2 @ X6) @ X6) != $true) | ((cP @ sK3 @ sK4) = $true)) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.30 thf(f39,plain,(
% 1.63/1.30 spl7_1 | spl7_2 | spl7_3 | ~spl7_4),
% 1.63/1.30 inference(avatar_split_clause,[status(thm)],[f21,f36,f33,f30,f26])).
% 1.63/1.30 thf(f21,plain,(
% 1.63/1.30 ( ! [X6 : $i,X5 : $i] : (((cQ @ sK3 @ sK4) = $true) | ((cP @ (sK2 @ X6) @ X6) != $true) | ((cS @ sK5) != $true) | ((cQ @ X5 @ sK1) != $true)) )),
% 1.63/1.30 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.30 % SZS output end Proof for DTF2THF_12888
% 1.63/1.30 % (13107)------------------------------
% 1.63/1.30 % (13107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (13107)Termination reason: Refutation
% 1.63/1.30
% 1.63/1.30 % (13107)Memory used [KB]: 5500
% 1.63/1.30 % (13107)Time elapsed: 0.004 s
% 1.63/1.30 % (13107)Instructions burned: 4 (million)
% 1.63/1.30 % (13107)------------------------------
% 1.63/1.30 % (13107)------------------------------
% 1.63/1.30 % (13104)Success in time 0.014 s
%------------------------------------------------------------------------------