%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV508^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 09:41:25 AM UTC 2026
% Result : Theorem 1.55s 1.35s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 631 ( 172 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 1069 ( 106 ~; 92 |; 41 &; 806 @)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 6 con; 0-4 aty)
% Number of variables : 137 ( 0 ^; 112 !; 25 ?; 137 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/realax/real': $tType ).
thf(type_def_7,type,
sK2: $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/trivia/I':
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_5,type,
'const/realax/real_lt': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_6,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_7,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_11,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_12,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > ( X0 > 'type/realax/real' ) > X0 ) ).
thf(func_def_13,type,
sK3: sK2 > 'type/realax/real' ).
thf(func_def_14,type,
sK4: sK2 > 'type/realax/real' ).
thf(func_def_15,type,
sK5: sK2 > $o ).
thf(func_def_16,type,
sP6: $o > $o ).
thf(func_def_18,type,
ph8:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
sK9: sK2 ).
thf(f114,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f87,f101,f105,f113]) ).
thf(f113,plain,
~ spl7_7,
inference(avatar_contradiction_clause,[status(thm)],[f112]) ).
thf(f112,plain,
( $false
| ~ spl7_7 ),
inference(subsumption_resolution,[status(thm)],[f109,f35]) ).
thf(f35,plain,
'const/sets/EMPTY' @ ( sK2 != sK5 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ! [X4: sK2] :
( ( $true
= ( 'const/realax/real_lt' @ ( sK3 @ X4 ) @ ( sK4 @ X4 ) ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X4 @ sK5 ) ) )
& ( $true
= ( 'const/sets/FINITE' @ sK2 @ sK5 ) )
& ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) )
!= $true )
& ( 'const/sets/EMPTY' @ ( sK2 != sK5 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f17,f28]) ).
thf(f28,plain,
( ? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ! [X4: X0] :
( ( ( 'const/realax/real_lt' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
!= $true ) )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
!= $true )
& ( 'const/sets/EMPTY' @ ( X0 != X3 ) ) )
=> ( ! [X4: sK2] :
( ( $true
= ( 'const/realax/real_lt' @ ( sK3 @ X4 ) @ ( sK4 @ X4 ) ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X4 @ sK5 ) ) )
& ( $true
= ( 'const/sets/FINITE' @ sK2 @ sK5 ) )
& ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) )
!= $true )
& ( 'const/sets/EMPTY' @ ( sK2 != sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ! [X4: X0] :
( ( ( 'const/realax/real_lt' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
!= $true ) )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
!= $true )
& ( 'const/sets/EMPTY' @ ( X0 != X3 ) ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
!= $true )
& ( 'const/sets/EMPTY' @ ( X0 != X3 ) )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ! [X4: X0] :
( ( ( 'const/realax/real_lt' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/sets/EMPTY' @ ( X0 != X3 ) )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ! [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
= $true )
=> ( ( 'const/realax/real_lt' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
= $true ) ) )
=> ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
=> ( 'const/realax/real_lt' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
& ( 'const/sets/FINITE' @ X0 @ X3 )
& ( 'const/sets/EMPTY' @ ( X0 != X3 ) ) )
=> ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
=> ( 'const/realax/real_lt' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
& ( 'const/sets/FINITE' @ X0 @ X3 )
& ( 'const/sets/EMPTY' @ ( X0 != X3 ) ) )
=> ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
=> ( 'const/realax/real_lt' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
& ( 'const/sets/FINITE' @ X0 @ X3 )
& ( 'const/sets/EMPTY' @ ( X0 != X3 ) ) )
=> ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KpznZEX3Io/DTF2THF_9324.p','thm/iterate/SUM_LT_ALL_') ).
thf(f109,plain,
( ( 'const/sets/EMPTY' @ ( sK2 = sK5 ) )
| ~ spl7_7 ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ( 'const/sets/EMPTY' @ ( sK2 = sK5 ) )
| ( $true != $true )
| ~ spl7_7 ),
inference(superposition,[status(thm)],[f100,f30]) ).
thf(f30,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X1 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) )
& ( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X1 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f23]) ).
thf(f23,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X3: X0] :
( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
=> ( $true
= ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X1 ) @ X1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) )
& ( ? [X3: X0] :
( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) )
& ( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
<=> ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > $o] :
? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: $tType,X1: X0 > $o] :
? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KpznZEX3Io/DTF2THF_9324.p','thm/sets/MEMBER_NOT_EMPTY_') ).
thf(f100,plain,
( ! [X0: sK2] :
( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK5 ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f99,definition,
( spl7_7
<=> ! [X0: sK2] :
( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl7_7])],[avatar_definition]) ).
thf(f105,plain,
~ spl7_6,
inference(avatar_contradiction_clause,[status(thm)],[f104]) ).
thf(f104,plain,
( $false
| ~ spl7_6 ),
inference(trivial_inequality_removal,[status(thm)],[f103]) ).
thf(f103,plain,
( ( $true = $false )
| ~ spl7_6 ),
inference(backward_demodulation,[status(thm)],[f40,f102]) ).
thf(f102,plain,
( ( ( sP6 @ $true )
= $false )
| ~ spl7_6 ),
inference(backward_demodulation,[status(thm)],[f39,f86]) ).
thf(f86,plain,
( ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) )
= $true )
| ~ spl7_6 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f84,definition,
( spl7_6
<=> ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_6])],[avatar_definition]) ).
thf(f39,plain,
( ( sP6 @ ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) ) )
= $false ),
introduced(definition,[new_symbols(naming,[sP6])],[inequality_splitting_name_introduction]) ).
thf(f40,plain,
( $true
= ( sP6 @ $true ) ),
inference(inequality_splitting,[status(thm)],[f36,f39]) ).
thf(f36,plain,
( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f101,plain,
( spl7_6
| spl7_7
| ~ spl7_5 ),
inference(avatar_split_clause,[status(thm)],[f97,f80,f99,f84]) ).
thf(f80,definition,
( spl7_5
<=> ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl7_5])],[avatar_definition]) ).
thf(f97,plain,
( ! [X0: sK2] :
( ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) )
= $true )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK5 ) ) )
| ~ spl7_5 ),
inference(subsumption_resolution,[status(thm)],[f96,f38]) ).
thf(f38,plain,
! [X4: sK2] :
( ( $true
!= ( 'const/sets/IN' @ sK2 @ X4 @ sK5 ) )
| ( $true
= ( 'const/realax/real_lt' @ ( sK3 @ X4 ) @ ( sK4 @ X4 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f96,plain,
( ! [X0: sK2] :
( ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) )
= $true )
| ( ( 'const/realax/real_lt' @ ( sK3 @ X0 ) @ ( sK4 @ X0 ) )
!= $true )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK5 ) ) )
| ~ spl7_5 ),
inference(subsumption_resolution,[status(thm)],[f95,f37]) ).
thf(f37,plain,
( $true
= ( 'const/sets/FINITE' @ sK2 @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f95,plain,
( ! [X0: sK2] :
( ( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK5 ) )
| ( ( 'const/realax/real_lt' @ ( sK3 @ X0 ) @ ( sK4 @ X0 ) )
!= $true )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK5 ) )
| ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) )
= $true ) )
| ~ spl7_5 ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ! [X0: sK2] :
( ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) )
= $true )
| ( $true != $true )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK5 ) )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ X0 @ sK5 ) )
| ( ( 'const/realax/real_lt' @ ( sK3 @ X0 ) @ ( sK4 @ X0 ) )
!= $true ) )
| ~ spl7_5 ),
inference(superposition,[status(thm)],[f32,f93]) ).
thf(f93,plain,
( ( $true
= ( 'const/realax/real_le' @ ( sK3 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) ) @ ( sK4 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) ) ) )
| ~ spl7_5 ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK3 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) ) @ ( sK4 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) ) ) )
| ~ spl7_5 ),
inference(superposition,[status(thm)],[f34,f89]) ).
thf(f89,plain,
( ( $true
= ( 'const/realax/real_lt' @ ( sK3 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) ) @ ( sK4 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) ) ) )
| ~ spl7_5 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $true != $true )
| ( $true
= ( 'const/realax/real_lt' @ ( sK3 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) ) @ ( sK4 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) ) ) )
| ~ spl7_5 ),
inference(superposition,[status(thm)],[f38,f82]) ).
thf(f82,plain,
( ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) @ sK5 ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[status(thm)],[f80]) ).
thf(f34,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X0 @ X1 )
= $true )
=> ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ X0 @ X1 )
=> ( 'const/realax/real_le' @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ X0 @ X1 )
=> ( 'const/realax/real_le' @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.KpznZEX3Io/DTF2THF_9324.p','thm/realarith/REAL_LT_IMP_LE_') ).
thf(f32,plain,
! [X0: $tType,X2: X0 > 'type/realax/real',X3: X0 > $o,X1: X0 > 'type/realax/real',X5: X0] :
( ( $true
!= ( 'const/realax/real_le' @ ( X1 @ ( sK1 @ X0 @ X3 @ X2 @ X1 ) ) @ ( X2 @ ( sK1 @ X0 @ X3 @ X2 @ X1 ) ) ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X5 @ X3 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( $true
!= ( 'const/realax/real_lt' @ ( X1 @ X5 ) @ ( X2 @ X5 ) ) )
| ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK1 @ X0 @ X3 @ X2 @ X1 ) @ X3 ) )
& ( $true
!= ( 'const/realax/real_le' @ ( X1 @ ( sK1 @ X0 @ X3 @ X2 @ X1 ) ) @ ( X2 @ ( sK1 @ X0 @ X3 @ X2 @ X1 ) ) ) ) )
| ! [X5: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X5 @ X3 ) )
| ( $true
!= ( 'const/realax/real_lt' @ ( X1 @ X5 ) @ ( X2 @ X5 ) ) ) )
| ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f25,f26]) ).
thf(f26,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
!= $true ) )
=> ( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK1 @ X0 @ X3 @ X2 @ X1 ) @ X3 ) )
& ( $true
!= ( 'const/realax/real_le' @ ( X1 @ ( sK1 @ X0 @ X3 @ X2 @ X1 ) ) @ ( X2 @ ( sK1 @ X0 @ X3 @ X2 @ X1 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
!= $true ) )
| ! [X5: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X5 @ X3 ) )
| ( $true
!= ( 'const/realax/real_lt' @ ( X1 @ X5 ) @ ( X2 @ X5 ) ) ) )
| ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ? [X5: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X5 @ X3 ) )
& ( $true
!= ( 'const/realax/real_le' @ ( X1 @ X5 ) @ ( X2 @ X5 ) ) ) )
| ! [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
!= $true )
| ( ( 'const/realax/real_lt' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
!= $true ) )
| ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ! [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
!= $true )
| ( ( 'const/realax/real_lt' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
!= $true ) )
| ? [X5: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X5 @ X3 ) )
& ( $true
!= ( 'const/realax/real_le' @ ( X1 @ X5 ) @ ( X2 @ X5 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
& ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
= $true )
& ( ( 'const/realax/real_lt' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
= $true ) )
& ! [X5: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X5 @ X3 ) )
=> ( $true
= ( 'const/realax/real_le' @ ( X1 @ X5 ) @ ( X2 @ X5 ) ) ) ) )
=> ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ? [X4: X0] :
( ( 'const/realax/real_lt' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
& ( 'const/sets/IN' @ X0 @ X4 @ X3 ) )
& ( 'const/sets/FINITE' @ X0 @ X3 )
& ! [X5: X0] :
( ( 'const/sets/IN' @ X0 @ X5 @ X3 )
=> ( 'const/realax/real_le' @ ( X1 @ X5 ) @ ( X2 @ X5 ) ) ) )
=> ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ? [X4: X0] :
( ( 'const/realax/real_lt' @ ( X1 @ X4 ) @ ( X2 @ X4 ) )
& ( 'const/sets/IN' @ X0 @ X4 @ X3 ) )
& ( 'const/sets/FINITE' @ X0 @ X3 )
& ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X3 )
=> ( 'const/realax/real_le' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) ) )
=> ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KpznZEX3Io/DTF2THF_9324.p','thm/iterate/SUM_LT_') ).
thf(f87,plain,
( spl7_5
| spl7_6 ),
inference(avatar_split_clause,[status(thm)],[f78,f84,f80]) ).
thf(f78,plain,
( ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) @ sK5 ) ) ),
inference(subsumption_resolution,[status(thm)],[f77,f37]) ).
thf(f77,plain,
( ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) @ sK5 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK5 ) ) ),
inference(subsumption_resolution,[status(thm)],[f76,f35]) ).
thf(f76,plain,
( ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( sK2 = sK5 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK5 ) )
| ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) @ sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $true != $true )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ sK5 ) )
| ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK1 @ sK2 @ sK5 @ sK4 @ sK3 ) @ sK5 ) )
| ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ sK5 @ sK4 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( sK2 = sK5 ) ) ),
inference(superposition,[status(thm)],[f73,f30]) ).
thf(f73,plain,
! [X0: sK2 > $o] :
( ( $true
!= ( 'const/sets/IN' @ sK2 @ ( sK0 @ sK2 @ sK5 ) @ X0 ) )
| ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK1 @ sK2 @ X0 @ sK4 @ sK3 ) @ X0 ) )
| ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ X0 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ X0 @ sK4 ) )
= $true )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
! [X0: sK2 > $o] :
( ( $true != $true )
| ( $true
!= ( 'const/sets/IN' @ sK2 @ ( sK0 @ sK2 @ sK5 ) @ X0 ) )
| ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ sK2 @ X0 @ sK3 ) @ ( 'const/iterate/sum' @ sK2 @ X0 @ sK4 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK2 @ ( sK1 @ sK2 @ X0 @ sK4 @ sK3 ) @ X0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK2 @ X0 ) ) ),
inference(superposition,[status(thm)],[f33,f70]) ).
thf(f70,plain,
( ( 'const/realax/real_lt' @ ( sK3 @ ( sK0 @ sK2 @ sK5 ) ) @ ( sK4 @ ( sK0 @ sK2 @ sK5 ) ) )
= $true ),
inference(subsumption_resolution,[status(thm)],[f69,f35]) ).
thf(f69,plain,
( ( ( 'const/realax/real_lt' @ ( sK3 @ ( sK0 @ sK2 @ sK5 ) ) @ ( sK4 @ ( sK0 @ sK2 @ sK5 ) ) )
= $true )
| ( 'const/sets/EMPTY' @ ( sK2 = sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ( 'const/realax/real_lt' @ ( sK3 @ ( sK0 @ sK2 @ sK5 ) ) @ ( sK4 @ ( sK0 @ sK2 @ sK5 ) ) )
= $true )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( sK2 = sK5 ) ) ),
inference(superposition,[status(thm)],[f38,f30]) ).
thf(f33,plain,
! [X0: $tType,X2: X0 > 'type/realax/real',X3: X0 > $o,X1: X0 > 'type/realax/real',X5: X0] :
( ( $true
!= ( 'const/realax/real_lt' @ ( X1 @ X5 ) @ ( X2 @ X5 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X5 @ X3 ) )
| ( ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ X0 @ ( sK1 @ X0 @ X3 @ X2 @ X1 ) @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV508^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.31 % Computer : n005.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Tue Feb 24 12:48:14 EST 2026
% 0.14/0.31 % CPUTime :
% 0.14/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.43 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SEV508^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.44 % Domain : Analysis
% 0.17/0.44 % Problem : SUM_LT_ALL
% 0.17/0.44 % Version : Especial.
% 0.17/0.44 % English :
% 0.17/0.44
% 0.17/0.44 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.17/0.44 % Source : [Kal16]
% 0.17/0.44 % Names : SUM_LT_ALL_.p [Kal16]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % Rating : 0.00 v7.1.0
% 0.17/0.44 % Syntax : Number of formulae : 13 ( 2 unt; 8 typ; 0 def)
% 0.17/0.44 % Number of atoms : 19 ( 4 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 6 ( 3 avg)
% 0.17/0.44 % Number of connectives : 64 ( 2 ~; 0 |; 5 &; 52 @)
% 0.17/0.44 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 13 ( 8 avg)
% 0.17/0.44 % Number of types : 2 ( 1 usr)
% 0.17/0.44 % Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 8 ( 7 usr; 0 con; 2-3 aty)
% 0.17/0.44 % Number of variables : 23 ( 0 ^; 16 !; 2 ?; 23 :)
% 0.17/0.44 % ( 5 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.44 % SPC : TH1_THM_EQU_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : Exported from core HOL Light.
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf('thf_type_type/realax/real',type,
% 0.17/0.44 'type/realax/real': $tType ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/trivia/I',type,
% 0.17/0.44 'const/trivia/I':
% 0.17/0.44 !>[A: $tType] : ( A > A ) ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/sets/IN',type,
% 0.17/0.44 'const/sets/IN':
% 0.17/0.44 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/sets/FINITE',type,
% 0.17/0.44 'const/sets/FINITE':
% 0.17/0.44 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/sets/EMPTY',type,
% 0.17/0.44 'const/sets/EMPTY':
% 0.17/0.44 !>[A: $tType] : ( A > $o ) ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/realax/real_lt',type,
% 0.17/0.44 'const/realax/real_lt': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/realax/real_le',type,
% 0.17/0.44 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/iterate/sum',type,
% 0.17/0.44 'const/iterate/sum':
% 0.17/0.44 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.17/0.44
% 0.17/0.44 thf('thm/trivia/I_THM_',axiom,
% 0.17/0.44 ! [A: $tType,A0: A] :
% 0.17/0.44 ( ( 'const/trivia/I' @ A @ A0 )
% 0.17/0.44 = A0 ) ).
% 0.17/0.44
% 0.17/0.44 thf('thm/iterate/SUM_LT_',axiom,
% 0.17/0.44 ! [A: $tType,A0: A > 'type/realax/real',A1: A > 'type/realax/real',A2: A > $o] :
% 0.17/0.44 ( ( ( 'const/sets/FINITE' @ A @ A2 )
% 0.17/0.44 & ! [A3: A] :
% 0.17/0.44 ( ( 'const/sets/IN' @ A @ A3 @ A2 )
% 0.17/0.44 => ( 'const/realax/real_le' @ ( A0 @ A3 ) @ ( A1 @ A3 ) ) )
% 0.17/0.44 & ? [A3: A] :
% 0.17/0.44 ( ( 'const/sets/IN' @ A @ A3 @ A2 )
% 0.17/0.44 & ( 'const/realax/real_lt' @ ( A0 @ A3 ) @ ( A1 @ A3 ) ) ) )
% 0.17/0.44 => ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A1 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf('thm/realarith/REAL_LT_IMP_LE_',axiom,
% 0.17/0.44 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.17/0.44 ( ( 'const/realax/real_lt' @ A @ A0 )
% 0.17/0.44 => ( 'const/realax/real_le' @ A @ A0 ) ) ).
% 0.17/0.44
% 0.17/0.44 thf('thm/sets/MEMBER_NOT_EMPTY_',axiom,
% 0.17/0.44 ! [A: $tType,A0: A > $o] :
% 0.17/0.44 ( ( ? [A1: A] : ( 'const/sets/IN' @ A @ A1 @ A0 ) )
% 0.17/0.44 = ( A0
% 0.17/0.44 != ( 'const/sets/EMPTY' @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf('thm/iterate/SUM_LT_ALL_',conjecture,
% 0.17/0.44 ! [A: $tType,A0: A > 'type/realax/real',A1: A > 'type/realax/real',A2: A > $o] :
% 0.17/0.44 ( ( ( 'const/sets/FINITE' @ A @ A2 )
% 0.17/0.44 & ( A2
% 0.17/0.44 != ( 'const/sets/EMPTY' @ A ) )
% 0.17/0.44 & ! [A3: A] :
% 0.17/0.44 ( ( 'const/sets/IN' @ A @ A3 @ A2 )
% 0.17/0.44 => ( 'const/realax/real_lt' @ ( A0 @ A3 ) @ ( A1 @ A3 ) ) ) )
% 0.17/0.44 => ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A1 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 0.30/1.20 ---- Embedded in THF ---
% 0.30/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.30/1.20 %%% Generated on Tue Feb 24 12:48:15 EST 2026
% 0.30/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 0.30/1.20 %%% Logic specification used:
% 0.30/1.20 %%% thf(spec, logic, $$dhol).
% 0.30/1.20
% 0.30/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.KpznZEX3Io/DTF2DTF9324.p
% See solution above
% 0.30/1.20 ------------------------
% 0.30/1.21 ---- Cleaned THF ---
% 0.30/1.21 thf('thf_type_type/realax/real',type,
% 0.30/1.21 'type/realax/real': $tType ).
% 0.30/1.21
% 0.30/1.21 thf('thf_const_const/trivia/I',type,
% 0.30/1.21 'const/trivia/I':
% 0.30/1.21 !>[A: $tType] : ( A > A ) ).
% 0.30/1.21
% 0.30/1.21 thf('thf_const_const/sets/IN',type,
% 0.30/1.21 'const/sets/IN':
% 0.30/1.21 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.30/1.21
% 0.30/1.21 thf('thf_const_const/sets/FINITE',type,
% 0.30/1.21 'const/sets/FINITE':
% 0.30/1.21 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.30/1.21
% 0.30/1.21 thf('thf_const_const/sets/EMPTY',type,
% 0.30/1.21 'const/sets/EMPTY':
% 0.30/1.21 !>[A: $tType] : ( A > $o ) ).
% 0.30/1.21
% 0.30/1.21 thf('thf_const_const/realax/real_lt',type,
% 0.30/1.21 'const/realax/real_lt': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.30/1.21
% 0.30/1.21 thf('thf_const_const/realax/real_le',type,
% 0.30/1.21 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.30/1.21
% 0.30/1.21 thf('thf_const_const/iterate/sum',type,
% 0.30/1.21 'const/iterate/sum':
% 0.30/1.21 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/realax/real' ) > 'type/realax/real' ) ).
% 0.30/1.21
% 0.30/1.21 thf('thm/trivia/I_THM_',axiom,
% 0.30/1.21 ! [A: $tType,A0: A] :
% 0.30/1.21 ( ( 'const/trivia/I' @ A @ A0 )
% 0.30/1.21 = A0 ) ).
% 0.30/1.21
% 0.30/1.21 thf('thm/iterate/SUM_LT_',axiom,
% 0.30/1.21 ! [A: $tType,A0: A > 'type/realax/real',A1: A > 'type/realax/real',A2: A > $o] :
% 0.30/1.21 ( ( ( 'const/sets/FINITE' @ A @ A2 )
% 0.30/1.21 & ! [A3: A] :
% 0.30/1.21 ( ( 'const/sets/IN' @ A @ A3 @ A2 )
% 0.30/1.21 => ( 'const/realax/real_le' @ ( A0 @ A3 ) @ ( A1 @ A3 ) ) )
% 0.30/1.21 & ? [A3: A] :
% 0.30/1.21 ( ( 'const/sets/IN' @ A @ A3 @ A2 )
% 0.30/1.21 & ( 'const/realax/real_lt' @ ( A0 @ A3 ) @ ( A1 @ A3 ) ) ) )
% 0.30/1.21 => ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A1 ) ) ) ).
% 0.30/1.21
% 0.30/1.21 thf('thm/realarith/REAL_LT_IMP_LE_',axiom,
% 0.30/1.21 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.30/1.21 ( ( 'const/realax/real_lt' @ A @ A0 )
% 0.30/1.21 => ( 'const/realax/real_le' @ A @ A0 ) ) ).
% 0.30/1.21
% 0.30/1.21 thf('thm/sets/MEMBER_NOT_EMPTY_',axiom,
% 0.30/1.21 ! [A: $tType,A0: A > $o] :
% 0.30/1.21 ( ( ? [A1: A] : ( 'const/sets/IN' @ A @ A1 @ A0 ) )
% 0.30/1.21 = ( A0
% 0.30/1.21 != ( 'const/sets/EMPTY' @ A ) ) ) ).
% 0.30/1.21
% 0.30/1.21 thf('thm/iterate/SUM_LT_ALL_',conjecture,
% 0.30/1.21 ! [A: $tType,A0: A > 'type/realax/real',A1: A > 'type/realax/real',A2: A > $o] :
% 0.30/1.21 ( ( ( 'const/sets/FINITE' @ A @ A2 )
% 0.30/1.21 & ( A2
% 0.30/1.21 != ( 'const/sets/EMPTY' @ A ) )
% 0.30/1.21 & ! [A3: A] :
% 0.30/1.21 ( ( 'const/sets/IN' @ A @ A3 @ A2 )
% 0.30/1.21 => ( 'const/realax/real_lt' @ ( A0 @ A3 ) @ ( A1 @ A3 ) ) ) )
% 0.30/1.21 => ( 'const/realax/real_lt' @ ( 'const/iterate/sum' @ A @ A2 @ A0 ) @ ( 'const/iterate/sum' @ A @ A2 @ A1 ) ) ) ).
% 0.30/1.21 ------------------------
% 0.30/1.22 % (9423)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_9324 for (2999ds/27Mi)
% 0.30/1.22 % (9426)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_9324 for (2999ds/275Mi)
% 0.30/1.22 % (9426)Refutation not found, incomplete strategy
% 0.30/1.22 % (9426)------------------------------
% 0.30/1.22 % (9426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.22 % (9426)Termination reason: Refutation not found, incomplete strategy
% 0.30/1.22
% 0.30/1.22
% 0.30/1.22 % (9426)Memory used [KB]: 5500
% 0.30/1.22 % (9426)Time elapsed: 0.003 s
% 0.30/1.22 % (9426)Instructions burned: 4 (million)
% 0.30/1.22 % (9426)------------------------------
% 0.30/1.22 % (9426)------------------------------
% 0.30/1.23 % (9422)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_9324 for (2999ds/4Mi)
% 0.30/1.23 % (9427)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/18Mi)
% 0.30/1.23 % (9424)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/2Mi)
% 0.30/1.23 % (9424)Instruction limit reached!
% 0.30/1.23 % (9424)------------------------------
% 0.30/1.23 % (9424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.23 % (9424)Termination reason: Unknown
% 0.30/1.23 % (9424)Termination phase: Saturation
% 0.30/1.23
% 0.30/1.23 % (9424)Memory used [KB]: 5500
% 0.30/1.23 % (9424)Time elapsed: 0.002 s
% 0.30/1.23 % (9424)Instructions burned: 3 (million)
% 0.30/1.23 % (9424)------------------------------
% 0.30/1.23 % (9424)------------------------------
% 0.30/1.23 % (9421)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/183Mi)
% 0.30/1.23 % (9422)Instruction limit reached!
% 0.30/1.23 % (9422)------------------------------
% 0.30/1.23 % (9422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.23 % (9422)Termination reason: Unknown
% 0.30/1.23 % (9422)Termination phase: Saturation
% 0.30/1.23
% 0.30/1.23 % (9422)Memory used [KB]: 5500
% 0.30/1.23 % (9422)Time elapsed: 0.005 s
% 0.30/1.23 % (9422)Instructions burned: 4 (million)
% 0.30/1.23 % (9422)------------------------------
% 0.30/1.23 % (9422)------------------------------
% 0.30/1.24 % (9425)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_9324 for (2999ds/2Mi)
% 0.30/1.24 % Exception at run slice level
% 0.30/1.24 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.30/1.24 % (9428)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/3Mi)
% 0.30/1.24 % (9427)Instruction limit reached!
% 0.30/1.24 % (9427)------------------------------
% 0.30/1.24 % (9427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.24 % (9427)Termination reason: Unknown
% 0.30/1.24 % (9427)Termination phase: Saturation
% 0.30/1.24
% 0.30/1.24 % (9427)Memory used [KB]: 5628
% 0.30/1.24 % (9427)Time elapsed: 0.009 s
% 0.30/1.24 % (9427)Instructions burned: 19 (million)
% 0.30/1.24 % (9423)Instruction limit reached!
% 0.30/1.24 % (9423)------------------------------
% 0.30/1.24 % (9423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.24 % (9423)Termination reason: Unknown
% 0.30/1.24 % (9423)Termination phase: Saturation
% 0.30/1.24
% 0.30/1.24 % (9423)Memory used [KB]: 5628
% 0.30/1.24 % (9423)Time elapsed: 0.012 s
% 0.30/1.24 % (9423)Instructions burned: 28 (million)
% 0.30/1.24 % (9423)------------------------------
% 0.30/1.24 % (9423)------------------------------
% 0.30/1.24 % (9427)------------------------------
% 0.30/1.24 % (9427)------------------------------
% 0.30/1.24 % (9428)Instruction limit reached!
% 0.30/1.24 % (9428)------------------------------
% 0.30/1.24 % (9428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.24 % (9428)Termination reason: Unknown
% 0.30/1.24 % (9428)Termination phase: Saturation
% 0.30/1.24
% 0.30/1.24 % (9428)Memory used [KB]: 5500
% 0.30/1.24 % (9428)Time elapsed: 0.003 s
% 0.30/1.24 % (9428)Instructions burned: 4 (million)
% 0.30/1.24 % (9428)------------------------------
% 0.30/1.24 % (9428)------------------------------
% 0.30/1.25 % (9430)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/15Mi)
% 0.30/1.25 % (9429)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/37Mi)
% 0.30/1.25 % (9432)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/1041Mi)
% 0.30/1.25 % Exception at run slice level
% 0.30/1.25 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.30/1.25 % Exception at run slice level
% 0.30/1.25 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.30/1.25 % (9434)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/16Mi)
% 0.30/1.25 % (9431)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/3Mi)
% 0.30/1.25 % (9431)Instruction limit reached!
% 0.30/1.25 % (9431)------------------------------
% 0.30/1.25 % (9431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.25 % (9431)Termination reason: Unknown
% 0.30/1.25 % (9431)Termination phase: Saturation
% 0.30/1.25
% 0.30/1.25 % (9431)Memory used [KB]: 5500
% 0.30/1.25 % (9431)Time elapsed: 0.004 s
% 0.30/1.25 % (9431)Instructions burned: 4 (million)
% 0.30/1.25 % (9431)------------------------------
% 0.30/1.25 % (9431)------------------------------
% 0.30/1.26 % (9430)Instruction limit reached!
% 0.30/1.26 % (9430)------------------------------
% 0.30/1.26 % (9430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.26 % (9430)Termination reason: Unknown
% 0.30/1.26 % (9430)Termination phase: Saturation
% 0.30/1.26
% 0.30/1.26 % (9430)Memory used [KB]: 5756
% 0.30/1.26 % (9430)Time elapsed: 0.010 s
% 0.30/1.26 % (9430)Instructions burned: 15 (million)
% 0.30/1.26 % (9430)------------------------------
% 0.30/1.26 % (9430)------------------------------
% 0.30/1.26 % (9434)Instruction limit reached!
% 0.30/1.26 % (9434)------------------------------
% 0.30/1.26 % (9434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.26 % (9434)Termination reason: Unknown
% 0.30/1.26 % (9434)Termination phase: Saturation
% 0.30/1.26
% 0.30/1.26 % (9434)Memory used [KB]: 5756
% 0.30/1.26 % (9434)Time elapsed: 0.007 s
% 0.30/1.26 % (9434)Instructions burned: 17 (million)
% 0.30/1.26 % (9434)------------------------------
% 0.30/1.26 % (9434)------------------------------
% 0.30/1.26 % (9436)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/3Mi)
% 0.30/1.26 % (9436)Instruction limit reached!
% 0.30/1.26 % (9436)------------------------------
% 0.30/1.26 % (9436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.26 % (9436)Termination reason: Unknown
% 0.30/1.26 % (9436)Termination phase: Saturation
% 0.30/1.26
% 0.30/1.26 % (9436)Memory used [KB]: 1023
% 0.30/1.26 % (9436)Time elapsed: 0.002 s
% 0.30/1.26 % (9436)Instructions burned: 4 (million)
% 0.30/1.26 % (9436)------------------------------
% 0.30/1.26 % (9436)------------------------------
% 0.30/1.27 % (9439)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/4Mi)
% 0.30/1.27 % (9433)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/7Mi)
% 0.30/1.27 % (9435)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/3Mi)
% 0.30/1.27 % (9439)Instruction limit reached!
% 0.30/1.27 % (9439)------------------------------
% 0.30/1.27 % (9439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.27 % (9439)Termination reason: Unknown
% 0.30/1.27 % (9439)Termination phase: Saturation
% 0.30/1.27
% 0.30/1.27 % (9439)Memory used [KB]: 5500
% 0.30/1.27 % (9439)Time elapsed: 0.003 s
% 0.30/1.27 % (9439)Instructions burned: 5 (million)
% 0.30/1.27 % (9439)------------------------------
% 0.30/1.27 % (9439)------------------------------
% 0.30/1.27 % (9437)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/7Mi)
% 0.30/1.27 % (9435)Instruction limit reached!
% 0.30/1.27 % (9435)------------------------------
% 0.30/1.27 % (9435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.27 % (9435)Termination reason: Unknown
% 0.30/1.27 % (9435)Termination phase: Twee Goal Transformation
% 0.30/1.27
% 0.30/1.27 % (9435)Memory used [KB]: 1023
% 0.30/1.27 % (9435)Time elapsed: 0.004 s
% 0.30/1.27 % (9435)Instructions burned: 3 (million)
% 0.30/1.27 % (9435)------------------------------
% 0.30/1.27 % (9435)------------------------------
% 0.30/1.27 % (9440)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/18Mi)
% 0.30/1.27 % (9433)Instruction limit reached!
% 0.30/1.27 % (9433)------------------------------
% 0.30/1.27 % (9433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.27 % (9433)Termination reason: Unknown
% 0.30/1.27 % (9433)Termination phase: Saturation
% 0.30/1.27
% 0.30/1.27 % (9433)Memory used [KB]: 1023
% 0.30/1.27 % (9433)Time elapsed: 0.005 s
% 0.30/1.27 % (9433)Instructions burned: 7 (million)
% 0.30/1.27 % (9433)------------------------------
% 0.30/1.27 % (9433)------------------------------
% 0.30/1.27 % (9437)Instruction limit reached!
% 0.30/1.27 % (9437)------------------------------
% 0.30/1.27 % (9437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.27 % (9437)Termination reason: Unknown
% 0.30/1.27 % (9437)Termination phase: Saturation
% 0.30/1.27
% 0.30/1.27 % (9437)Memory used [KB]: 5500
% 0.30/1.27 % (9437)Time elapsed: 0.006 s
% 0.30/1.27 % (9437)Instructions burned: 8 (million)
% 0.30/1.27 % (9437)------------------------------
% 0.30/1.27 % (9437)------------------------------
% 0.30/1.28 % (9440)Instruction limit reached!
% 0.30/1.28 % (9440)------------------------------
% 0.30/1.28 % (9440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.28 % (9440)Termination reason: Unknown
% 0.30/1.28 % (9440)Termination phase: Saturation
% 0.30/1.28
% 0.30/1.28 % (9440)Memory used [KB]: 5628
% 0.30/1.28 % (9440)Time elapsed: 0.007 s
% 0.30/1.28 % (9440)Instructions burned: 18 (million)
% 0.30/1.28 % (9440)------------------------------
% 0.30/1.28 % (9440)------------------------------
% 0.30/1.28 % (9441)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/710Mi)
% 0.30/1.28 % (9438)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/3Mi)
% 0.30/1.28 % Exception at run slice level
% 0.30/1.28 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.30/1.29 % (9445)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/5Mi)
% 0.30/1.29 % Exception at run slice level
% 0.30/1.29 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.30/1.29 % (9444)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/21Mi)
% 0.30/1.29 % (9443)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/902Mi)
% 0.30/1.29 % (9442)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/6Mi)
% 0.30/1.29 % (9443)Refutation not found, incomplete strategy
% 0.30/1.29 % (9443)------------------------------
% 0.30/1.29 % (9443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.29 % (9443)Termination reason: Refutation not found, incomplete strategy
% 0.30/1.29
% 0.30/1.29
% 0.30/1.29 % (9443)Memory used [KB]: 5500
% 0.30/1.29 % (9443)Time elapsed: 0.004 s
% 0.30/1.29 % (9443)Instructions burned: 5 (million)
% 0.30/1.29 % (9443)------------------------------
% 0.30/1.29 % (9443)------------------------------
% 0.30/1.29 % (9446)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/6Mi)
% 0.30/1.29 % Exception at run slice level
% 0.30/1.29 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 0.30/1.29 % (9442)Instruction limit reached!
% 0.30/1.29 % (9442)------------------------------
% 0.30/1.29 % (9442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.29 % (9442)Termination reason: Unknown
% 0.30/1.29 % (9442)Termination phase: Saturation
% 0.30/1.29
% 0.30/1.29 % (9442)Memory used [KB]: 5500
% 0.30/1.29 % (9442)Time elapsed: 0.008 s
% 0.30/1.29 % (9442)Instructions burned: 6 (million)
% 0.30/1.29 % (9442)------------------------------
% 0.30/1.29 % (9442)------------------------------
% 0.30/1.30 % (9447)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/377Mi)
% 1.55/1.30 % (9444)Instruction limit reached!
% 1.55/1.30 % (9444)------------------------------
% 1.55/1.30 % (9444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.30 % (9444)Termination reason: Unknown
% 1.55/1.30 % (9444)Termination phase: Saturation
% 1.55/1.30
% 1.55/1.30 % (9444)Memory used [KB]: 5628
% 1.55/1.30 % (9444)Time elapsed: 0.012 s
% 1.55/1.30 % (9444)Instructions burned: 21 (million)
% 1.55/1.30 % (9444)------------------------------
% 1.55/1.30 % (9444)------------------------------
% 1.55/1.30 % (9448)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/779Mi)
% 1.55/1.30 % Exception at run slice level
% 1.55/1.30 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.55/1.30 % (9449)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/19Mi)
% 1.55/1.30 % Exception at run slice level
% 1.55/1.30 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.55/1.31 % (9451)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/17Mi)
% 1.55/1.31 % (9452)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/3Mi)
% 1.55/1.31 % (9450)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/879Mi)
% 1.55/1.31 % (9452)Instruction limit reached!
% 1.55/1.31 % (9452)------------------------------
% 1.55/1.31 % (9452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (9452)Termination reason: Unknown
% 1.55/1.31 % (9452)Termination phase: Saturation
% 1.55/1.31
% 1.55/1.31 % (9452)Memory used [KB]: 1023
% 1.55/1.31 % (9452)Time elapsed: 0.002 s
% 1.55/1.31 % (9452)Instructions burned: 4 (million)
% 1.55/1.31 % (9452)------------------------------
% 1.55/1.31 % (9452)------------------------------
% 1.55/1.31 % (9453)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/30Mi)
% 1.55/1.31 % (9451)Instruction limit reached!
% 1.55/1.31 % (9451)------------------------------
% 1.55/1.31 % (9451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (9451)Termination reason: Unknown
% 1.55/1.31 % (9451)Termination phase: Saturation
% 1.55/1.31
% 1.55/1.31 % (9451)Memory used [KB]: 5628
% 1.55/1.31 % (9451)Time elapsed: 0.008 s
% 1.55/1.31 % (9451)Instructions burned: 19 (million)
% 1.55/1.31 % (9451)------------------------------
% 1.55/1.31 % (9451)------------------------------
% 1.55/1.31 % (9421)Instruction limit reached!
% 1.55/1.31 % (9421)------------------------------
% 1.55/1.31 % (9421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (9421)Termination reason: Unknown
% 1.55/1.31 % (9421)Termination phase: Saturation
% 1.55/1.31
% 1.55/1.31 % (9421)Memory used [KB]: 6268
% 1.55/1.31 % (9421)Time elapsed: 0.075 s
% 1.55/1.31 % (9421)Instructions burned: 184 (million)
% 1.55/1.31 % (9421)------------------------------
% 1.55/1.31 % (9421)------------------------------
% 1.55/1.32 % (9454)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/127Mi)
% 1.55/1.32 % (9455)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/100Mi)
% 1.55/1.32 % (9453)Instruction limit reached!
% 1.55/1.32 % (9453)------------------------------
% 1.55/1.32 % (9453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (9453)Termination reason: Unknown
% 1.55/1.32 % (9453)Termination phase: Saturation
% 1.55/1.32
% 1.55/1.32 % (9453)Memory used [KB]: 5628
% 1.55/1.32 % (9453)Time elapsed: 0.013 s
% 1.55/1.32 % (9453)Instructions burned: 31 (million)
% 1.55/1.32 % (9453)------------------------------
% 1.55/1.32 % (9453)------------------------------
% 1.55/1.34 % (9457)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_9324 for (2999ds/20Mi)
% 1.55/1.34 % (9457)First to succeed.
% 1.55/1.35 % (9457)Refutation found. Thanks to Tanya!
% 1.55/1.35 % SZS status Theorem for DTF2THF_9324
% 1.55/1.35 % SZS output start Proof for DTF2THF_9324
% 1.55/1.35 thf(type_def_6, type, 'type/realax/real': $tType).
% 1.55/1.35 thf(type_def_7, type, sK2: $tType).
% 1.55/1.35 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.55/1.35 thf(func_def_1, type, 'const/trivia/I': !>[X0: $tType]:(X0 > X0)).
% 1.55/1.35 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.55/1.35 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.55/1.35 thf(func_def_4, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.55/1.35 thf(func_def_5, type, 'const/realax/real_lt': 'type/realax/real' > 'type/realax/real' > $o).
% 1.55/1.35 thf(func_def_6, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.55/1.35 thf(func_def_7, type, 'const/iterate/sum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real')).
% 1.55/1.35 thf(func_def_11, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.55/1.35 thf(func_def_12, type, sK1: !>[X0: $tType]:((X0 > $o) > (X0 > 'type/realax/real') > (X0 > 'type/realax/real') > X0)).
% 1.55/1.35 thf(func_def_13, type, sK3: sK2 > 'type/realax/real').
% 1.55/1.35 thf(func_def_14, type, sK4: sK2 > 'type/realax/real').
% 1.55/1.35 thf(func_def_15, type, sK5: sK2 > $o).
% 1.55/1.35 thf(func_def_16, type, sP6: $o > $o).
% 1.55/1.35 thf(func_def_18, type, ph8: !>[X0: $tType]:(X0)).
% 1.55/1.35 thf(func_def_19, type, sK9: sK2).
% 1.55/1.35 thf(f114,plain,(
% 1.55/1.35 $false),
% 1.55/1.35 inference(avatar_sat_refutation,[status(thm)],[f87,f101,f105,f113])).
% 1.55/1.35 thf(f113,plain,(
% 1.55/1.35 ~spl7_7),
% 1.55/1.35 inference(avatar_contradiction_clause,[status(thm)],[f112])).
% 1.55/1.35 thf(f112,plain,(
% 1.55/1.35 $false | ~spl7_7),
% 1.55/1.35 inference(subsumption_resolution,[status(thm)],[f109,f35])).
% 1.55/1.35 thf(f35,plain,(
% 1.55/1.35 ('const/sets/EMPTY' @ sK2 != sK5)),
% 1.55/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.55/1.35 thf(f29,plain,(
% 1.55/1.35 ! [X4 : sK2] : (($true = ('const/realax/real_lt' @ (sK3 @ X4) @ (sK4 @ X4))) | ($true != ('const/sets/IN' @ sK2 @ X4 @ sK5))) & ($true = ('const/sets/FINITE' @ sK2 @ sK5)) & (('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4)) != $true) & ('const/sets/EMPTY' @ sK2 != sK5)),
% 1.55/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f17,f28])).
% 1.55/1.35 thf(f28,plain,(
% 1.55/1.35 ? [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : (! [X4 : X0] : ((('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4)) = $true) | (('const/sets/IN' @ X0 @ X4 @ X3) != $true)) & (('const/sets/FINITE' @ X0 @ X3) = $true) & (('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) != $true) & ('const/sets/EMPTY' @ X0 != X3)) => (! [X4 : sK2] : (($true = ('const/realax/real_lt' @ (sK3 @ X4) @ (sK4 @ X4))) | ($true != ('const/sets/IN' @ sK2 @ X4 @ sK5))) & ($true = ('const/sets/FINITE' @ sK2 @ sK5)) & (('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4)) != $true) & ('const/sets/EMPTY' @ sK2 != sK5))),
% 1.55/1.35 introduced(definition,[],[choice_axiom])).
% 1.55/1.35 thf(f17,plain,(
% 1.55/1.35 ? [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : (! [X4 : X0] : ((('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4)) = $true) | (('const/sets/IN' @ X0 @ X4 @ X3) != $true)) & (('const/sets/FINITE' @ X0 @ X3) = $true) & (('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) != $true) & ('const/sets/EMPTY' @ X0 != X3))),
% 1.55/1.35 inference(flattening,[status(thm)],[f16])).
% 1.55/1.35 thf(f16,plain,(
% 1.55/1.35 ? [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) != $true) & (('const/sets/EMPTY' @ X0 != X3) & (('const/sets/FINITE' @ X0 @ X3) = $true) & ! [X4 : X0] : ((('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4)) = $true) | (('const/sets/IN' @ X0 @ X4 @ X3) != $true))))),
% 1.55/1.35 inference(ennf_transformation,[status(thm)],[f9])).
% 1.55/1.35 thf(f9,plain,(
% 1.55/1.35 ~! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((('const/sets/EMPTY' @ X0 != X3) & (('const/sets/FINITE' @ X0 @ X3) = $true) & ! [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X3) = $true) => (('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4)) = $true))) => (('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true))),
% 1.55/1.35 inference(fool_elimination,[status(thm)],[f8])).
% 1.55/1.35 thf(f8,plain,(
% 1.55/1.35 ~! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) & ('const/sets/FINITE' @ X0 @ X3) & ('const/sets/EMPTY' @ X0 != X3)) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 1.55/1.35 inference(rectify,[status(thm)],[f6])).
% 1.55/1.35 thf(f6,negated_conjecture,(
% 1.55/1.35 ~! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) & ('const/sets/FINITE' @ X0 @ X3) & ('const/sets/EMPTY' @ X0 != X3)) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 1.55/1.35 inference(negated_conjecture,[status(cth)],[f5])).
% 1.55/1.35 thf(f5,conjecture,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) & ('const/sets/FINITE' @ X0 @ X3) & ('const/sets/EMPTY' @ X0 != X3)) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 1.55/1.35 file('/export/starexec/sandbox2/tmp/tmp.KpznZEX3Io/DTF2THF_9324.p','thm/iterate/SUM_LT_ALL_')).
% 1.55/1.35 thf(f109,plain,(
% 1.55/1.35 ('const/sets/EMPTY' @ sK2 = sK5) | ~spl7_7),
% 1.55/1.35 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.55/1.35 thf(f107,plain,(
% 1.55/1.35 ('const/sets/EMPTY' @ sK2 = sK5) | ($true != $true) | ~spl7_7),
% 1.55/1.35 inference(superposition,[status(thm)],[f100,f30])).
% 1.55/1.35 thf(f30,plain,(
% 1.55/1.35 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = ('const/sets/IN' @ X0 @ (sK0 @ X0 @ X1) @ X1)) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 1.55/1.35 inference(cnf_transformation,[status(thm)],[f24])).
% 1.55/1.35 thf(f24,plain,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) != $true)) & (($true = ('const/sets/IN' @ X0 @ (sK0 @ X0 @ X1) @ X1)) | ('const/sets/EMPTY' @ X0 = X1)))),
% 1.55/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f23])).
% 1.55/1.35 thf(f23,plain,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > $o] : (? [X3 : X0] : ($true = ('const/sets/IN' @ X0 @ X3 @ X1)) => ($true = ('const/sets/IN' @ X0 @ (sK0 @ X0 @ X1) @ X1)))),
% 1.55/1.35 introduced(definition,[],[choice_axiom])).
% 1.55/1.35 thf(f22,plain,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) != $true)) & (? [X3 : X0] : ($true = ('const/sets/IN' @ X0 @ X3 @ X1)) | ('const/sets/EMPTY' @ X0 = X1)))),
% 1.55/1.35 inference(rectify,[status(thm)],[f21])).
% 1.55/1.35 thf(f21,plain,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) != $true)) & (? [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = $true) | ('const/sets/EMPTY' @ X0 = X1)))),
% 1.55/1.35 inference(nnf_transformation,[status(thm)],[f13])).
% 1.55/1.35 thf(f13,plain,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/EMPTY' @ X0 != X1) <=> ? [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = $true))),
% 1.55/1.35 inference(fool_elimination,[status(thm)],[f12])).
% 1.55/1.35 thf(f12,plain,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > $o] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = ('const/sets/EMPTY' @ X0 != X1))),
% 1.55/1.35 inference(rectify,[status(thm)],[f4])).
% 1.55/1.35 thf(f4,axiom,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > $o] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = ('const/sets/EMPTY' @ X0 != X1))),
% 1.55/1.35 file('/export/starexec/sandbox2/tmp/tmp.KpznZEX3Io/DTF2THF_9324.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 1.55/1.35 thf(f100,plain,(
% 1.55/1.35 ( ! [X0 : sK2] : (($true != ('const/sets/IN' @ sK2 @ X0 @ sK5))) ) | ~spl7_7),
% 1.55/1.35 inference(avatar_component_clause,[status(thm)],[f99])).
% 1.55/1.35 thf(f99,definition,(
% 1.55/1.35 spl7_7 <=> ! [X0 : sK2] : ($true != ('const/sets/IN' @ sK2 @ X0 @ sK5))),
% 1.55/1.35 introduced(definition,[new_symbols(naming,[spl7_7])],[avatar_definition])).
% 1.55/1.35 thf(f105,plain,(
% 1.55/1.35 ~spl7_6),
% 1.55/1.35 inference(avatar_contradiction_clause,[status(thm)],[f104])).
% 1.55/1.35 thf(f104,plain,(
% 1.55/1.35 $false | ~spl7_6),
% 1.55/1.35 inference(trivial_inequality_removal,[status(thm)],[f103])).
% 1.55/1.35 thf(f103,plain,(
% 1.55/1.35 ($true = $false) | ~spl7_6),
% 1.55/1.35 inference(backward_demodulation,[status(thm)],[f40,f102])).
% 1.55/1.35 thf(f102,plain,(
% 1.55/1.35 ((sP6 @ $true) = $false) | ~spl7_6),
% 1.55/1.35 inference(backward_demodulation,[status(thm)],[f39,f86])).
% 1.55/1.35 thf(f86,plain,(
% 1.55/1.35 (('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4)) = $true) | ~spl7_6),
% 1.55/1.35 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.55/1.35 thf(f84,definition,(
% 1.55/1.35 spl7_6 <=> (('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4)) = $true)),
% 1.55/1.35 introduced(definition,[new_symbols(naming,[spl7_6])],[avatar_definition])).
% 1.55/1.35 thf(f39,plain,(
% 1.55/1.35 ((sP6 @ ('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4))) = $false)),
% 1.55/1.35 introduced(definition,[new_symbols(naming,[sP6])],[inequality_splitting_name_introduction])).
% 1.55/1.35 thf(f40,plain,(
% 1.55/1.35 ($true = (sP6 @ $true))),
% 1.55/1.35 inference(inequality_splitting,[status(thm)],[f36,f39])).
% 1.55/1.35 thf(f36,plain,(
% 1.55/1.35 (('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4)) != $true)),
% 1.55/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.55/1.35 thf(f101,plain,(
% 1.55/1.35 spl7_6 | spl7_7 | ~spl7_5),
% 1.55/1.35 inference(avatar_split_clause,[status(thm)],[f97,f80,f99,f84])).
% 1.55/1.35 thf(f80,definition,(
% 1.55/1.35 spl7_5 <=> ($true = ('const/sets/IN' @ sK2 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3) @ sK5))),
% 1.55/1.35 introduced(definition,[new_symbols(naming,[spl7_5])],[avatar_definition])).
% 1.55/1.35 thf(f97,plain,(
% 1.55/1.35 ( ! [X0 : sK2] : ((('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4)) = $true) | ($true != ('const/sets/IN' @ sK2 @ X0 @ sK5))) ) | ~spl7_5),
% 1.55/1.35 inference(subsumption_resolution,[status(thm)],[f96,f38])).
% 1.55/1.35 thf(f38,plain,(
% 1.55/1.35 ( ! [X4 : sK2] : (($true != ('const/sets/IN' @ sK2 @ X4 @ sK5)) | ($true = ('const/realax/real_lt' @ (sK3 @ X4) @ (sK4 @ X4)))) )),
% 1.55/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.55/1.35 thf(f96,plain,(
% 1.55/1.35 ( ! [X0 : sK2] : ((('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4)) = $true) | (('const/realax/real_lt' @ (sK3 @ X0) @ (sK4 @ X0)) != $true) | ($true != ('const/sets/IN' @ sK2 @ X0 @ sK5))) ) | ~spl7_5),
% 1.55/1.35 inference(subsumption_resolution,[status(thm)],[f95,f37])).
% 1.55/1.35 thf(f37,plain,(
% 1.55/1.35 ($true = ('const/sets/FINITE' @ sK2 @ sK5))),
% 1.55/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.55/1.35 thf(f95,plain,(
% 1.55/1.35 ( ! [X0 : sK2] : (($true != ('const/sets/IN' @ sK2 @ X0 @ sK5)) | (('const/realax/real_lt' @ (sK3 @ X0) @ (sK4 @ X0)) != $true) | ($true != ('const/sets/FINITE' @ sK2 @ sK5)) | (('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4)) = $true)) ) | ~spl7_5),
% 1.55/1.35 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.55/1.35 thf(f94,plain,(
% 1.55/1.35 ( ! [X0 : sK2] : ((('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4)) = $true) | ($true != $true) | ($true != ('const/sets/FINITE' @ sK2 @ sK5)) | ($true != ('const/sets/IN' @ sK2 @ X0 @ sK5)) | (('const/realax/real_lt' @ (sK3 @ X0) @ (sK4 @ X0)) != $true)) ) | ~spl7_5),
% 1.55/1.35 inference(superposition,[status(thm)],[f32,f93])).
% 1.55/1.35 thf(f93,plain,(
% 1.55/1.35 ($true = ('const/realax/real_le' @ (sK3 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3)) @ (sK4 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3)))) | ~spl7_5),
% 1.55/1.35 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.55/1.35 thf(f90,plain,(
% 1.55/1.35 ($true != $true) | ($true = ('const/realax/real_le' @ (sK3 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3)) @ (sK4 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3)))) | ~spl7_5),
% 1.55/1.35 inference(superposition,[status(thm)],[f34,f89])).
% 1.55/1.35 thf(f89,plain,(
% 1.55/1.35 ($true = ('const/realax/real_lt' @ (sK3 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3)) @ (sK4 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3)))) | ~spl7_5),
% 1.55/1.35 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.55/1.35 thf(f88,plain,(
% 1.55/1.35 ($true != $true) | ($true = ('const/realax/real_lt' @ (sK3 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3)) @ (sK4 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3)))) | ~spl7_5),
% 1.55/1.35 inference(superposition,[status(thm)],[f38,f82])).
% 1.55/1.35 thf(f82,plain,(
% 1.55/1.35 ($true = ('const/sets/IN' @ sK2 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3) @ sK5)) | ~spl7_5),
% 1.55/1.35 inference(avatar_component_clause,[status(thm)],[f80])).
% 1.55/1.35 thf(f34,plain,(
% 1.55/1.35 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_lt' @ X0 @ X1) != $true) | (('const/realax/real_le' @ X0 @ X1) = $true)) )),
% 1.55/1.35 inference(cnf_transformation,[status(thm)],[f20])).
% 1.55/1.35 thf(f20,plain,(
% 1.55/1.35 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_lt' @ X0 @ X1) != $true) | (('const/realax/real_le' @ X0 @ X1) = $true))),
% 1.55/1.35 inference(ennf_transformation,[status(thm)],[f15])).
% 1.55/1.35 thf(f15,plain,(
% 1.55/1.35 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_lt' @ X0 @ X1) = $true) => (('const/realax/real_le' @ X0 @ X1) = $true))),
% 1.55/1.35 inference(fool_elimination,[status(thm)],[f14])).
% 1.55/1.35 thf(f14,plain,(
% 1.55/1.35 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_lt' @ X0 @ X1) => ('const/realax/real_le' @ X0 @ X1))),
% 1.55/1.35 inference(rectify,[status(thm)],[f3])).
% 1.55/1.35 thf(f3,axiom,(
% 1.55/1.35 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_lt' @ X0 @ X1) => ('const/realax/real_le' @ X0 @ X1))),
% 1.55/1.35 file('/export/starexec/sandbox2/tmp/tmp.KpznZEX3Io/DTF2THF_9324.p','thm/realarith/REAL_LT_IMP_LE_')).
% 1.55/1.35 thf(f32,plain,(
% 1.55/1.35 ( ! [X0 : $tType,X2 : X0 > 'type/realax/real',X3 : X0 > $o,X1 : X0 > 'type/realax/real',X5 : X0] : (($true != ('const/realax/real_le' @ (X1 @ (sK1 @ X0 @ X3 @ X2 @ X1)) @ (X2 @ (sK1 @ X0 @ X3 @ X2 @ X1)))) | ($true != ('const/sets/IN' @ X0 @ X5 @ X3)) | (('const/sets/FINITE' @ X0 @ X3) != $true) | ($true != ('const/realax/real_lt' @ (X1 @ X5) @ (X2 @ X5))) | (('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true)) )),
% 1.55/1.35 inference(cnf_transformation,[status(thm)],[f27])).
% 1.55/1.35 thf(f27,plain,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((($true = ('const/sets/IN' @ X0 @ (sK1 @ X0 @ X3 @ X2 @ X1) @ X3)) & ($true != ('const/realax/real_le' @ (X1 @ (sK1 @ X0 @ X3 @ X2 @ X1)) @ (X2 @ (sK1 @ X0 @ X3 @ X2 @ X1))))) | ! [X5 : X0] : (($true != ('const/sets/IN' @ X0 @ X5 @ X3)) | ($true != ('const/realax/real_lt' @ (X1 @ X5) @ (X2 @ X5)))) | (('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true) | (('const/sets/FINITE' @ X0 @ X3) != $true))),
% 1.55/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f25,f26])).
% 1.55/1.35 thf(f26,plain,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : (? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X3) = $true) & (('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4)) != $true)) => (($true = ('const/sets/IN' @ X0 @ (sK1 @ X0 @ X3 @ X2 @ X1) @ X3)) & ($true != ('const/realax/real_le' @ (X1 @ (sK1 @ X0 @ X3 @ X2 @ X1)) @ (X2 @ (sK1 @ X0 @ X3 @ X2 @ X1))))))),
% 1.55/1.35 introduced(definition,[],[choice_axiom])).
% 1.55/1.35 thf(f25,plain,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : (? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X3) = $true) & (('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4)) != $true)) | ! [X5 : X0] : (($true != ('const/sets/IN' @ X0 @ X5 @ X3)) | ($true != ('const/realax/real_lt' @ (X1 @ X5) @ (X2 @ X5)))) | (('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true) | (('const/sets/FINITE' @ X0 @ X3) != $true))),
% 1.55/1.35 inference(rectify,[status(thm)],[f19])).
% 1.55/1.35 thf(f19,plain,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : (? [X5 : X0] : (($true = ('const/sets/IN' @ X0 @ X5 @ X3)) & ($true != ('const/realax/real_le' @ (X1 @ X5) @ (X2 @ X5)))) | ! [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X3) != $true) | (('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4)) != $true)) | (('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true) | (('const/sets/FINITE' @ X0 @ X3) != $true))),
% 1.55/1.35 inference(flattening,[status(thm)],[f18])).
% 1.55/1.35 thf(f18,plain,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true) | ((('const/sets/FINITE' @ X0 @ X3) != $true) | ! [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X3) != $true) | (('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4)) != $true)) | ? [X5 : X0] : (($true = ('const/sets/IN' @ X0 @ X5 @ X3)) & ($true != ('const/realax/real_le' @ (X1 @ X5) @ (X2 @ X5))))))),
% 1.55/1.35 inference(ennf_transformation,[status(thm)],[f11])).
% 1.55/1.35 thf(f11,plain,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : (((('const/sets/FINITE' @ X0 @ X3) = $true) & ? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X3) = $true) & (('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4)) = $true)) & ! [X5 : X0] : (($true = ('const/sets/IN' @ X0 @ X5 @ X3)) => ($true = ('const/realax/real_le' @ (X1 @ X5) @ (X2 @ X5))))) => (('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true))),
% 1.55/1.35 inference(fool_elimination,[status(thm)],[f10])).
% 1.55/1.35 thf(f10,plain,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((? [X4 : X0] : (('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4)) & ('const/sets/IN' @ X0 @ X4 @ X3)) & ('const/sets/FINITE' @ X0 @ X3) & ! [X5 : X0] : (('const/sets/IN' @ X0 @ X5 @ X3) => ('const/realax/real_le' @ (X1 @ X5) @ (X2 @ X5)))) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 1.55/1.35 inference(rectify,[status(thm)],[f2])).
% 1.55/1.35 thf(f2,axiom,(
% 1.55/1.35 ! [X0 : $tType,X1 : X0 > 'type/realax/real',X2 : X0 > 'type/realax/real',X3 : X0 > $o] : ((? [X4 : X0] : (('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4)) & ('const/sets/IN' @ X0 @ X4 @ X3)) & ('const/sets/FINITE' @ X0 @ X3) & ! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4)))) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 1.55/1.35 file('/export/starexec/sandbox2/tmp/tmp.KpznZEX3Io/DTF2THF_9324.p','thm/iterate/SUM_LT_')).
% 1.55/1.35 thf(f87,plain,(
% 1.55/1.35 spl7_5 | spl7_6),
% 1.55/1.35 inference(avatar_split_clause,[status(thm)],[f78,f84,f80])).
% 1.55/1.35 thf(f78,plain,(
% 1.55/1.35 (('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4)) = $true) | ($true = ('const/sets/IN' @ sK2 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3) @ sK5))),
% 1.55/1.35 inference(subsumption_resolution,[status(thm)],[f77,f37])).
% 1.55/1.35 thf(f77,plain,(
% 1.55/1.35 (('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4)) = $true) | ($true = ('const/sets/IN' @ sK2 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3) @ sK5)) | ($true != ('const/sets/FINITE' @ sK2 @ sK5))),
% 1.55/1.35 inference(subsumption_resolution,[status(thm)],[f76,f35])).
% 1.55/1.35 thf(f76,plain,(
% 1.55/1.35 (('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4)) = $true) | ('const/sets/EMPTY' @ sK2 = sK5) | ($true != ('const/sets/FINITE' @ sK2 @ sK5)) | ($true = ('const/sets/IN' @ sK2 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3) @ sK5))),
% 1.55/1.35 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.55/1.35 thf(f75,plain,(
% 1.55/1.35 ($true != $true) | ($true != ('const/sets/FINITE' @ sK2 @ sK5)) | ($true = ('const/sets/IN' @ sK2 @ (sK1 @ sK2 @ sK5 @ sK4 @ sK3) @ sK5)) | (('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ sK5 @ sK3) @ ('const/iterate/sum' @ sK2 @ sK5 @ sK4)) = $true) | ('const/sets/EMPTY' @ sK2 = sK5)),
% 1.55/1.35 inference(superposition,[status(thm)],[f73,f30])).
% 1.55/1.35 thf(f73,plain,(
% 1.55/1.35 ( ! [X0 : sK2 > $o] : (($true != ('const/sets/IN' @ sK2 @ (sK0 @ sK2 @ sK5) @ X0)) | ($true = ('const/sets/IN' @ sK2 @ (sK1 @ sK2 @ X0 @ sK4 @ sK3) @ X0)) | (('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ X0 @ sK3) @ ('const/iterate/sum' @ sK2 @ X0 @ sK4)) = $true) | ($true != ('const/sets/FINITE' @ sK2 @ X0))) )),
% 1.55/1.35 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.55/1.35 thf(f72,plain,(
% 1.55/1.35 ( ! [X0 : sK2 > $o] : (($true != $true) | ($true != ('const/sets/IN' @ sK2 @ (sK0 @ sK2 @ sK5) @ X0)) | (('const/realax/real_lt' @ ('const/iterate/sum' @ sK2 @ X0 @ sK3) @ ('const/iterate/sum' @ sK2 @ X0 @ sK4)) = $true) | ($true = ('const/sets/IN' @ sK2 @ (sK1 @ sK2 @ X0 @ sK4 @ sK3) @ X0)) | ($true != ('const/sets/FINITE' @ sK2 @ X0))) )),
% 1.55/1.35 inference(superposition,[status(thm)],[f33,f70])).
% 1.55/1.35 thf(f70,plain,(
% 1.55/1.35 (('const/realax/real_lt' @ (sK3 @ (sK0 @ sK2 @ sK5)) @ (sK4 @ (sK0 @ sK2 @ sK5))) = $true)),
% 1.55/1.35 inference(subsumption_resolution,[status(thm)],[f69,f35])).
% 1.55/1.35 thf(f69,plain,(
% 1.55/1.35 (('const/realax/real_lt' @ (sK3 @ (sK0 @ sK2 @ sK5)) @ (sK4 @ (sK0 @ sK2 @ sK5))) = $true) | ('const/sets/EMPTY' @ sK2 = sK5)),
% 1.55/1.35 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.55/1.35 thf(f67,plain,(
% 1.55/1.35 (('const/realax/real_lt' @ (sK3 @ (sK0 @ sK2 @ sK5)) @ (sK4 @ (sK0 @ sK2 @ sK5))) = $true) | ($true != $true) | ('const/sets/EMPTY' @ sK2 = sK5)),
% 1.55/1.35 inference(superposition,[status(thm)],[f38,f30])).
% 1.55/1.35 thf(f33,plain,(
% 1.55/1.35 ( ! [X0 : $tType,X2 : X0 > 'type/realax/real',X3 : X0 > $o,X1 : X0 > 'type/realax/real',X5 : X0] : (($true != ('const/realax/real_lt' @ (X1 @ X5) @ (X2 @ X5))) | (('const/sets/FINITE' @ X0 @ X3) != $true) | ($true != ('const/sets/IN' @ X0 @ X5 @ X3)) | (('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)) = $true) | ($true = ('const/sets/IN' @ X0 @ (sK1 @ X0 @ X3 @ X2 @ X1) @ X3))) )),
% 1.55/1.35 inference(cnf_transformation,[status(thm)],[f27])).
% 1.55/1.35 % SZS output end Proof for DTF2THF_9324
% 1.55/1.35 % (9457)------------------------------
% 1.55/1.35 % (9457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.35 % (9457)Termination reason: Refutation
% 1.55/1.35
% 1.55/1.35 % (9457)Memory used [KB]: 5628
% 1.55/1.35 % (9457)Time elapsed: 0.031 s
% 1.55/1.35 % (9457)Instructions burned: 17 (million)
% 1.55/1.35 % (9457)------------------------------
% 1.55/1.35 % (9457)------------------------------
% 1.55/1.35 % (9420)Success in time 0.115 s
%------------------------------------------------------------------------------