%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA074^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 08:38:48 AM UTC 2026
% Result : Theorem 1.66s 1.42s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 4 unt; 0 typ; 6 def)
% Number of atoms : 623 ( 166 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 782 ( 98 ~; 112 |; 36 &; 504 @)
% ( 6 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 10 con; 0-3 aty)
% Number of variables : 105 ( 0 ^; 88 !; 17 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_4,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_6,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_9,type,
sK0: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_10,type,
sK1: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_11,type,
sK2: 'type/realax/real' > $o ).
thf(func_def_12,type,
sK3: 'type/realax/real' ).
thf(func_def_14,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK6: 'type/realax/real' ).
thf(f152,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f64,f72,f86,f94,f127,f134,f148,f151]) ).
thf(f151,plain,
~ spl4_8,
inference(avatar_contradiction_clause,[status(thm)],[f150]) ).
thf(f150,plain,
( $false
| ~ spl4_8 ),
inference(trivial_inequality_removal,[status(thm)],[f149]) ).
thf(f149,plain,
( ( $true != $true )
| ~ spl4_8 ),
inference(superposition,[status(thm)],[f25,f71]) ).
thf(f71,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK3 ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[status(thm)],[f69]) ).
thf(f69,definition,
( spl4_8
<=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition]) ).
thf(f25,plain,
( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X2: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X2 @ sK3 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK2 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) )
& ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f12,f17]) ).
thf(f17,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
!= $true ) )
=> ( ! [X2: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X2 @ sK3 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK2 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) )
& ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
!= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.7rtkHPz9iM/DTF2THF_9025.p','thm/sets/REAL_SUP_LE_') ).
thf(f148,plain,
~ spl4_7,
inference(avatar_contradiction_clause,[status(thm)],[f147]) ).
thf(f147,plain,
( $false
| ~ spl4_7 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ( sK2 != sK2 )
| ~ spl4_7 ),
inference(superposition,[status(thm)],[f26,f63]) ).
thf(f63,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl4_7
<=> ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition]) ).
thf(f26,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f134,plain,
( spl4_5
| ~ spl4_11 ),
inference(avatar_split_clause,[status(thm)],[f132,f92,f55]) ).
thf(f55,definition,
( spl4_5
<=> ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK3 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f92,definition,
( spl4_11
<=> ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X0 @ sK2 ) @ sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_11])],[avatar_definition]) ).
thf(f132,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK3 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) ) )
| ~ spl4_11 ),
inference(trivial_inequality_removal,[status(thm)],[f129]) ).
thf(f129,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) )
| ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK3 ) ) )
| ~ spl4_11 ),
inference(superposition,[status(thm)],[f27,f93]) ).
thf(f93,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X0 @ sK2 ) @ sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) ) )
| ~ spl4_11 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f27,plain,
! [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ X2 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f127,plain,
( spl4_8
| ~ spl4_5
| ~ spl4_9 ),
inference(avatar_split_clause,[status(thm)],[f126,f84,f55,f69]) ).
thf(f84,definition,
( spl4_9
<=> ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition]) ).
thf(f126,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK3 ) )
| ~ spl4_5
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK3 ) )
| ~ spl4_5
| ~ spl4_9 ),
inference(duplicate_literal_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK3 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK3 ) )
| ~ spl4_5
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f85,f56]) ).
thf(f56,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK3 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f85,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f94,plain,
( spl4_11
| spl4_7
| ~ spl4_6 ),
inference(avatar_split_clause,[status(thm)],[f80,f58,f61,f92]) ).
thf(f58,definition,
( spl4_6
<=> ! [X1: 'type/realax/real'] :
( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition]) ).
thf(f80,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X0 @ sK2 ) @ sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X0 @ sK2 ) @ sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
| ~ spl4_6 ),
inference(superposition,[status(thm)],[f22,f76]) ).
thf(f76,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ sK3 )
= $true )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ sK3 )
= $true ) )
| ~ spl4_6 ),
inference(superposition,[status(thm)],[f27,f59]) ).
thf(f59,plain,
( ! [X1: 'type/realax/real'] :
( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f22,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK0 @ X1 @ X0 ) @ X1 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o] :
( ! [X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK0 @ X1 @ X0 ) @ X1 ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true ) )
| ( ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) ) )
& ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) )
| ( ( ( 'const/realax/real_le' @ ( sK1 @ X4 @ X0 ) @ X4 )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) ) ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f15,f14]) ).
thf(f14,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
=> ( ( $true
!= ( 'const/realax/real_le' @ ( sK0 @ X1 @ X0 ) @ X1 ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) )
=> ( ( ( 'const/realax/real_le' @ ( sK1 @ X4 @ X0 ) @ X4 )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X0: 'type/realax/real' > $o] :
( ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) ) )
& ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) )
| ? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: 'type/realax/real' > $o] :
( ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( ! [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X5 @ ( 'const/sets/sup' @ X0 ) ) ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X3 )
= $true )
| ? [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ X3 )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) ) ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X5 @ ( 'const/sets/sup' @ X0 ) ) ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X3 )
= $true )
| ? [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ X3 )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) ) ) ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: 'type/realax/real' > $o] :
( ( ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) )
=> ( ( 'const/realax/real_le' @ X4 @ X3 )
= $true ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X3 )
= $true ) )
& ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
=> ( $true
= ( 'const/realax/real_le' @ X5 @ ( 'const/sets/sup' @ X0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X4 @ X3 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X3 ) )
& ! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
=> ( 'const/realax/real_le' @ X5 @ ( 'const/sets/sup' @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) )
& ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7rtkHPz9iM/DTF2THF_9025.p','thm/sets/SUP_') ).
thf(f86,plain,
( spl4_7
| spl4_9
| ~ spl4_6 ),
inference(avatar_split_clause,[status(thm)],[f82,f58,f84,f61]) ).
thf(f82,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ X0 ) ) )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ X0 ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) ) )
| ~ spl4_6 ),
inference(superposition,[status(thm)],[f23,f76]) ).
thf(f23,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK0 @ X1 @ X0 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) )
| ( ( 'const/realax/real_le' @ ( sK1 @ X4 @ X0 ) @ X4 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f72,plain,
( spl4_6
| spl4_8
| spl4_7
| ~ spl4_5 ),
inference(avatar_split_clause,[status(thm)],[f67,f55,f61,f69,f58]) ).
thf(f67,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X0 @ sK2 ) @ sK2 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK3 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
| ~ spl4_5 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK3 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X0 @ sK2 ) @ sK2 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
| ~ spl4_5 ),
inference(duplicate_literal_removal,[status(thm)],[f65]) ).
thf(f65,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X0 @ sK2 ) @ sK2 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK3 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK3 ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
| ~ spl4_5 ),
inference(superposition,[status(thm)],[f20,f56]) ).
thf(f20,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK1 @ X4 @ X0 ) @ X4 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f64,plain,
( spl4_5
| spl4_6
| spl4_7 ),
inference(avatar_split_clause,[status(thm)],[f53,f61,f58,f55]) ).
thf(f53,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) )
| ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK3 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 ) ) ),
inference(superposition,[status(thm)],[f27,f19]) ).
thf(f19,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA074^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n008.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 03:49:54 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : ANA074^1 : TPTP v9.2.1. Released v7.0.0.
% 0.30/0.47 % Domain : Analysis
% 0.30/0.47 % Problem : REAL_SUP_LE
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Kal16]
% 0.30/0.47 % Names : REAL_SUP_LE_.p [Kal16]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.00 v7.1.0
% 0.30/0.47 % Syntax : Number of formulae : 7 ( 0 unt; 5 typ; 0 def)
% 0.30/0.47 % Number of atoms : 14 ( 2 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 8 ( 7 avg)
% 0.30/0.47 % Number of connectives : 41 ( 2 ~; 0 |; 3 &; 29 @)
% 0.30/0.47 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 11 ( 11 avg)
% 0.30/0.47 % Number of types : 2 ( 1 usr)
% 0.30/0.47 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 5 ( 4 usr; 0 con; 1-3 aty)
% 0.30/0.47 % Number of variables : 11 ( 0 ^; 8 !; 1 ?; 11 :)
% 0.30/0.47 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.47 % SPC : TH1_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : Exported from core HOL Light.
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf('thf_type_type/realax/real',type,
% 0.30/0.47 'type/realax/real': $tType ).
% 0.30/0.47
% 0.30/0.47 thf('thf_const_const/sets/sup',type,
% 0.30/0.47 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.30/0.47
% 0.30/0.47 thf('thf_const_const/sets/IN',type,
% 0.30/0.47 'const/sets/IN':
% 0.30/0.47 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf('thf_const_const/sets/EMPTY',type,
% 0.30/0.47 'const/sets/EMPTY':
% 0.30/0.47 !>[A: $tType] : ( A > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf('thf_const_const/realax/real_le',type,
% 0.30/0.47 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.30/0.47
% 0.30/0.47 thf('thm/sets/SUP_',axiom,
% 0.30/0.47 ! [A: 'type/realax/real' > $o] :
% 0.30/0.47 ( ( ( A
% 0.30/0.47 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.30/0.47 & ? [A0: 'type/realax/real'] :
% 0.30/0.47 ! [A1: 'type/realax/real'] :
% 0.30/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.30/0.47 => ( 'const/realax/real_le' @ A1 @ A0 ) ) )
% 0.30/0.47 => ( ! [A0: 'type/realax/real'] :
% 0.30/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.30/0.47 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) ) )
% 0.30/0.47 & ! [A0: 'type/realax/real'] :
% 0.30/0.47 ( ! [A1: 'type/realax/real'] :
% 0.30/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.30/0.47 => ( 'const/realax/real_le' @ A1 @ A0 ) )
% 0.30/0.47 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf('thm/sets/REAL_SUP_LE_',conjecture,
% 0.30/0.47 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.30/0.47 ( ( ( A
% 0.30/0.47 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.30/0.47 & ! [A1: 'type/realax/real'] :
% 0.30/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.30/0.47 => ( 'const/realax/real_le' @ A1 @ A0 ) ) )
% 0.30/0.47 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.48/1.39 ---- Embedded in THF ---
% 1.48/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.39 %%% Generated on Tue Feb 24 03:49:55 EST 2026
% 1.48/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.39 %%% Logic specification used:
% 1.48/1.39 %%% thf(spec, logic, $$dhol).
% 1.48/1.39
% 1.48/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.7rtkHPz9iM/DTF2DTF9025.p
% See solution above
% 1.48/1.39 ------------------------
% 1.48/1.40 ---- Cleaned THF ---
% 1.66/1.40 thf('thf_type_type/realax/real',type,
% 1.66/1.40 'type/realax/real': $tType ).
% 1.66/1.40
% 1.66/1.40 thf('thf_const_const/sets/sup',type,
% 1.66/1.40 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 1.66/1.40
% 1.66/1.40 thf('thf_const_const/sets/IN',type,
% 1.66/1.40 'const/sets/IN':
% 1.66/1.40 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.66/1.40
% 1.66/1.40 thf('thf_const_const/sets/EMPTY',type,
% 1.66/1.40 'const/sets/EMPTY':
% 1.66/1.40 !>[A: $tType] : ( A > $o ) ).
% 1.66/1.40
% 1.66/1.40 thf('thf_const_const/realax/real_le',type,
% 1.66/1.40 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.66/1.40
% 1.66/1.40 thf('thm/sets/SUP_',axiom,
% 1.66/1.40 ! [A: 'type/realax/real' > $o] :
% 1.66/1.40 ( ( ( A
% 1.66/1.40 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.66/1.40 & ? [A0: 'type/realax/real'] :
% 1.66/1.40 ! [A1: 'type/realax/real'] :
% 1.66/1.40 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.66/1.40 => ( 'const/realax/real_le' @ A1 @ A0 ) ) )
% 1.66/1.40 => ( ! [A0: 'type/realax/real'] :
% 1.66/1.40 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 1.66/1.40 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) ) )
% 1.66/1.40 & ! [A0: 'type/realax/real'] :
% 1.66/1.40 ( ! [A1: 'type/realax/real'] :
% 1.66/1.40 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.66/1.40 => ( 'const/realax/real_le' @ A1 @ A0 ) )
% 1.66/1.40 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ) ) ).
% 1.66/1.40
% 1.66/1.40 thf('thm/sets/REAL_SUP_LE_',conjecture,
% 1.66/1.40 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 1.66/1.40 ( ( ( A
% 1.66/1.40 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.66/1.40 & ! [A1: 'type/realax/real'] :
% 1.66/1.40 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.66/1.40 => ( 'const/realax/real_le' @ A1 @ A0 ) ) )
% 1.66/1.40 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ).
% 1.66/1.40 ------------------------
% 1.66/1.41 % (9355)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_9025 for (2999ds/27Mi)
% 1.66/1.41 % (9354)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_9025 for (2999ds/4Mi)
% 1.66/1.41 % (9354)Instruction limit reached!
% 1.66/1.41 % (9354)------------------------------
% 1.66/1.41 % (9354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (9354)Termination reason: Unknown
% 1.66/1.41 % (9354)Termination phase: Saturation
% 1.66/1.41
% 1.66/1.41 % (9354)Memory used [KB]: 5500
% 1.66/1.41 % (9354)Time elapsed: 0.003 s
% 1.66/1.41 % (9354)Instructions burned: 6 (million)
% 1.66/1.41 % (9354)------------------------------
% 1.66/1.41 % (9354)------------------------------
% 1.66/1.42 % (9353)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9025 for (2999ds/183Mi)
% 1.66/1.42 % (9356)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9025 for (2999ds/2Mi)
% 1.66/1.42 % (9357)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_9025 for (2999ds/2Mi)
% 1.66/1.42 % (9358)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_9025 for (2999ds/275Mi)
% 1.66/1.42 % (9359)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9025 for (2999ds/18Mi)
% 1.66/1.42 % (9356)Instruction limit reached!
% 1.66/1.42 % (9356)------------------------------
% 1.66/1.42 % (9356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (9356)Termination reason: Unknown
% 1.66/1.42 % (9356)Termination phase: Preprocessing 3
% 1.66/1.42
% 1.66/1.42 % (9356)Memory used [KB]: 895
% 1.66/1.42 % (9356)Time elapsed: 0.003 s
% 1.66/1.42 % (9356)Instructions burned: 2 (million)
% 1.66/1.42 % (9356)------------------------------
% 1.66/1.42 % (9356)------------------------------
% 1.66/1.42 % (9357)Instruction limit reached!
% 1.66/1.42 % (9357)------------------------------
% 1.66/1.42 % (9357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (9357)Termination reason: Unknown
% 1.66/1.42 % (9357)Termination phase: Property scanning
% 1.66/1.42
% 1.66/1.42 % (9357)Memory used [KB]: 895
% 1.66/1.42 % (9357)Time elapsed: 0.003 s
% 1.66/1.42 % (9357)Instructions burned: 2 (million)
% 1.66/1.42 % (9357)------------------------------
% 1.66/1.42 % (9357)------------------------------
% 1.66/1.42 % (9355)First to succeed.
% 1.66/1.42 % (9355)Refutation found. Thanks to Tanya!
% 1.66/1.42 % SZS status Theorem for DTF2THF_9025
% 1.66/1.42 % SZS output start Proof for DTF2THF_9025
% 1.66/1.42 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.66/1.42 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.66/1.42 thf(func_def_1, type, 'const/sets/sup': ('type/realax/real' > $o) > 'type/realax/real').
% 1.66/1.42 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.66/1.42 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.66/1.42 thf(func_def_4, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.66/1.42 thf(func_def_6, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.66/1.42 thf(func_def_9, type, sK0: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.66/1.42 thf(func_def_10, type, sK1: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.66/1.42 thf(func_def_11, type, sK2: 'type/realax/real' > $o).
% 1.66/1.42 thf(func_def_12, type, sK3: 'type/realax/real').
% 1.66/1.42 thf(func_def_14, type, ph5: !>[X0: $tType]:(X0)).
% 1.66/1.42 thf(func_def_15, type, sK6: 'type/realax/real').
% 1.66/1.42 thf(f152,plain,(
% 1.66/1.42 $false),
% 1.66/1.42 inference(avatar_sat_refutation,[status(thm)],[f64,f72,f86,f94,f127,f134,f148,f151])).
% 1.66/1.42 thf(f151,plain,(
% 1.66/1.42 ~spl4_8),
% 1.66/1.42 inference(avatar_contradiction_clause,[status(thm)],[f150])).
% 1.66/1.42 thf(f150,plain,(
% 1.66/1.42 $false | ~spl4_8),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f149])).
% 1.66/1.42 thf(f149,plain,(
% 1.66/1.42 ($true != $true) | ~spl4_8),
% 1.66/1.42 inference(superposition,[status(thm)],[f25,f71])).
% 1.66/1.42 thf(f71,plain,(
% 1.66/1.42 ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) | ~spl4_8),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f69])).
% 1.66/1.42 thf(f69,definition,(
% 1.66/1.42 spl4_8 <=> ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition])).
% 1.66/1.42 thf(f25,plain,(
% 1.66/1.42 ($true != ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.66/1.42 thf(f18,plain,(
% 1.66/1.42 ! [X2 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X2 @ sK3)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X2 @ sK2))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK2) & ($true != ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3))),
% 1.66/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f12,f17])).
% 1.66/1.42 thf(f17,plain,(
% 1.66/1.42 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) != $true)) => (! [X2 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X2 @ sK3)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X2 @ sK2))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK2) & ($true != ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)))),
% 1.66/1.42 introduced(definition,[],[choice_axiom])).
% 1.66/1.42 thf(f12,plain,(
% 1.66/1.42 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) != $true))),
% 1.66/1.42 inference(flattening,[status(thm)],[f11])).
% 1.66/1.42 thf(f11,plain,(
% 1.66/1.42 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) != $true) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true))))),
% 1.66/1.42 inference(ennf_transformation,[status(thm)],[f8])).
% 1.66/1.42 thf(f8,plain,(
% 1.66/1.42 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) => (('const/realax/real_le' @ X2 @ X1) = $true))) => (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true))),
% 1.66/1.42 inference(fool_elimination,[status(thm)],[f7])).
% 1.66/1.42 thf(f7,plain,(
% 1.66/1.42 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1))),
% 1.66/1.42 inference(rectify,[status(thm)],[f3])).
% 1.66/1.42 thf(f3,negated_conjecture,(
% 1.66/1.42 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1))),
% 1.66/1.42 inference(negated_conjecture,[status(cth)],[f2])).
% 1.66/1.42 thf(f2,conjecture,(
% 1.66/1.42 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1))),
% 1.66/1.42 file('/export/starexec/sandbox/tmp/tmp.7rtkHPz9iM/DTF2THF_9025.p','thm/sets/REAL_SUP_LE_')).
% 1.66/1.42 thf(f148,plain,(
% 1.66/1.42 ~spl4_7),
% 1.66/1.42 inference(avatar_contradiction_clause,[status(thm)],[f147])).
% 1.66/1.42 thf(f147,plain,(
% 1.66/1.42 $false | ~spl4_7),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.66/1.42 thf(f144,plain,(
% 1.66/1.42 (sK2 != sK2) | ~spl4_7),
% 1.66/1.42 inference(superposition,[status(thm)],[f26,f63])).
% 1.66/1.42 thf(f63,plain,(
% 1.66/1.42 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ~spl4_7),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.66/1.42 thf(f61,definition,(
% 1.66/1.42 spl4_7 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK2)),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition])).
% 1.66/1.42 thf(f26,plain,(
% 1.66/1.42 ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.66/1.42 thf(f134,plain,(
% 1.66/1.42 spl4_5 | ~spl4_11),
% 1.66/1.42 inference(avatar_split_clause,[status(thm)],[f132,f92,f55])).
% 1.66/1.42 thf(f55,definition,(
% 1.66/1.42 spl4_5 <=> ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 1.66/1.42 thf(f92,definition,(
% 1.66/1.42 spl4_11 <=> ! [X0 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl4_11])],[avatar_definition])).
% 1.66/1.42 thf(f132,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) ) | ~spl4_11),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f129])).
% 1.66/1.42 thf(f129,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)) | ($true != $true) | ($true = ('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3))) ) | ~spl4_11),
% 1.66/1.42 inference(superposition,[status(thm)],[f27,f93])).
% 1.66/1.42 thf(f93,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) ) | ~spl4_11),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.66/1.42 thf(f27,plain,(
% 1.66/1.42 ( ! [X2 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X2 @ sK2)) | ($true = ('const/realax/real_le' @ X2 @ sK3))) )),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.66/1.42 thf(f127,plain,(
% 1.66/1.42 spl4_8 | ~spl4_5 | ~spl4_9),
% 1.66/1.42 inference(avatar_split_clause,[status(thm)],[f126,f84,f55,f69])).
% 1.66/1.42 thf(f84,definition,(
% 1.66/1.42 spl4_9 <=> ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)) | ($true != ('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition])).
% 1.66/1.42 thf(f126,plain,(
% 1.66/1.42 ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) | (~spl4_5 | ~spl4_9)),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.66/1.42 thf(f125,plain,(
% 1.66/1.42 ($true != $true) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) | (~spl4_5 | ~spl4_9)),
% 1.66/1.42 inference(duplicate_literal_removal,[status(thm)],[f121])).
% 1.66/1.42 thf(f121,plain,(
% 1.66/1.42 ($true != $true) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) | (~spl4_5 | ~spl4_9)),
% 1.66/1.42 inference(superposition,[status(thm)],[f85,f56])).
% 1.66/1.42 thf(f56,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) ) | ~spl4_5),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.66/1.42 thf(f85,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) ) | ~spl4_9),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.66/1.42 thf(f94,plain,(
% 1.66/1.42 spl4_11 | spl4_7 | ~spl4_6),
% 1.66/1.42 inference(avatar_split_clause,[status(thm)],[f80,f58,f61,f92])).
% 1.66/1.42 thf(f58,definition,(
% 1.66/1.42 spl4_6 <=> ! [X1 : 'type/realax/real'] : ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK2) @ sK2))),
% 1.66/1.42 introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
% 1.66/1.42 thf(f80,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl4_6),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.66/1.42 thf(f77,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X0 @ sK2) @ sK2)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl4_6),
% 1.66/1.42 inference(superposition,[status(thm)],[f22,f76])).
% 1.66/1.42 thf(f76,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3) = $true)) ) | ~spl4_6),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.66/1.42 thf(f73,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : (($true != $true) | (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK3) = $true)) ) | ~spl4_6),
% 1.66/1.42 inference(superposition,[status(thm)],[f27,f59])).
% 1.66/1.42 thf(f59,plain,(
% 1.66/1.42 ( ! [X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK2) @ sK2))) ) | ~spl4_6),
% 1.66/1.42 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.66/1.42 thf(f22,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1)) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f16])).
% 1.66/1.42 thf(f16,plain,(
% 1.66/1.42 ! [X0 : 'type/realax/real' > $o] : (! [X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1)) & (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0) = $true)) | (! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) | ($true = ('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))) & ! [X4 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4)) | ((('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4) != $true) & ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.66/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f15,f14])).
% 1.66/1.42 thf(f14,plain,(
% 1.66/1.42 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) => (($true != ('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1)) & (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0) = $true)))),
% 1.66/1.42 introduced(definition,[],[choice_axiom])).
% 1.66/1.42 thf(f15,plain,(
% 1.66/1.42 ! [X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : ((('const/realax/real_le' @ X5 @ X4) != $true) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) => ((('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4) != $true) & ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0))))),
% 1.66/1.42 introduced(definition,[],[choice_axiom])).
% 1.66/1.42 thf(f13,plain,(
% 1.66/1.42 ! [X0 : 'type/realax/real' > $o] : (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) | (! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) | ($true = ('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0)))) & ! [X4 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4)) | ? [X5 : 'type/realax/real'] : ((('const/realax/real_le' @ X5 @ X4) != $true) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.66/1.42 inference(rectify,[status(thm)],[f10])).
% 1.66/1.42 thf(f10,plain,(
% 1.66/1.42 ! [X0 : 'type/realax/real' > $o] : (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) | (! [X5 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) | ($true = ('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))) & ! [X3 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3) = $true) | ? [X4 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ X3) != $true) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.66/1.42 inference(flattening,[status(thm)],[f9])).
% 1.66/1.42 thf(f9,plain,(
% 1.66/1.42 ! [X0 : 'type/realax/real' > $o] : ((! [X5 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) | ($true = ('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))) & ! [X3 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3) = $true) | ? [X4 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ X3) != $true) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))))) | (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 1.66/1.42 inference(ennf_transformation,[status(thm)],[f6])).
% 1.66/1.42 thf(f6,plain,(
% 1.66/1.42 ! [X0 : 'type/realax/real' > $o] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) => (('const/realax/real_le' @ X2 @ X1) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) => (('const/realax/real_le' @ X4 @ X3) = $true)) => (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3) = $true)) & ! [X5 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) => ($true = ('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))))))),
% 1.66/1.42 inference(fool_elimination,[status(thm)],[f5])).
% 1.66/1.42 thf(f5,plain,(
% 1.66/1.42 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X4 @ X3)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3)) & ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)))))),
% 1.66/1.42 inference(rectify,[status(thm)],[f1])).
% 1.66/1.42 thf(f1,axiom,(
% 1.66/1.42 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1))) => (! [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)))))),
% 1.66/1.42 file('/export/starexec/sandbox/tmp/tmp.7rtkHPz9iM/DTF2THF_9025.p','thm/sets/SUP_')).
% 1.66/1.42 thf(f86,plain,(
% 1.66/1.42 spl4_7 | spl4_9 | ~spl4_6),
% 1.66/1.42 inference(avatar_split_clause,[status(thm)],[f82,f58,f84,f61])).
% 1.66/1.42 thf(f82,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0)) | ($true != ('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0))) ) | ~spl4_6),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.66/1.42 thf(f78,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ X0)) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) ) | ~spl4_6),
% 1.66/1.42 inference(superposition,[status(thm)],[f23,f76])).
% 1.66/1.42 thf(f23,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK0 @ X1 @ X0) @ X1)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4)) | (('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f16])).
% 1.66/1.42 thf(f72,plain,(
% 1.66/1.42 spl4_6 | spl4_8 | spl4_7 | ~spl4_5),
% 1.66/1.42 inference(avatar_split_clause,[status(thm)],[f67,f55,f61,f69,f58])).
% 1.66/1.42 thf(f67,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK2) @ sK2) = $true) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl4_5),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.66/1.42 thf(f66,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) | (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK2) @ sK2) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl4_5),
% 1.66/1.42 inference(duplicate_literal_removal,[status(thm)],[f65])).
% 1.66/1.42 thf(f65,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X0 @ sK2) @ sK2) = $true) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK3)) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl4_5),
% 1.66/1.42 inference(superposition,[status(thm)],[f20,f56])).
% 1.66/1.42 thf(f20,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X4 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK1 @ X4 @ X0) @ X4) != $true) | (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4))) )),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f16])).
% 1.66/1.42 thf(f64,plain,(
% 1.66/1.42 spl4_5 | spl4_6 | spl4_7),
% 1.66/1.42 inference(avatar_split_clause,[status(thm)],[f53,f61,f58,f55])).
% 1.66/1.42 thf(f53,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3)) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK2) @ sK2)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) )),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.66/1.42 thf(f49,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ sK2) @ sK2)) | ($true != $true) | ($true = ('const/realax/real_le' @ (sK1 @ X0 @ sK2) @ sK3)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0))) )),
% 1.66/1.42 inference(superposition,[status(thm)],[f27,f19])).
% 1.66/1.42 thf(f19,plain,(
% 1.66/1.42 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0) = $true)) )),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f16])).
% 1.66/1.42 % SZS output end Proof for DTF2THF_9025
% 1.66/1.42 % (9355)------------------------------
% 1.66/1.42 % (9355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (9355)Termination reason: Refutation
% 1.66/1.42
% 1.66/1.42 % (9355)Memory used [KB]: 5628
% 1.66/1.42 % (9355)Time elapsed: 0.011 s
% 1.66/1.42 % (9355)Instructions burned: 25 (million)
% 1.66/1.42 % (9355)------------------------------
% 1.66/1.42 % (9355)------------------------------
% 1.66/1.42 % (9352)Success in time 0.02 s
%------------------------------------------------------------------------------