%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA077^1 : 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 : n026.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 1.58s 1.46s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 78 ( 6 unt; 0 typ; 4 def)
% Number of atoms : 652 ( 182 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 844 ( 78 ~; 100 |; 37 &; 609 @)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 119 ( 0 ^; 110 !; 9 ?; 119 :)
% 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_neg': 'type/realax/real' > 'type/realax/real' ).
thf(func_def_5,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_6,type,
'const/realax/real_abs': 'type/realax/real' > 'type/realax/real' ).
thf(func_def_11,type,
sK0: 'type/realax/real' > $o ).
thf(func_def_12,type,
sK1: 'type/realax/real' ).
thf(func_def_13,type,
sK2: 'type/realax/real' > 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_15,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK5: 'type/realax/real' ).
thf(f174,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f74,f145,f157,f163,f173]) ).
thf(f173,plain,
~ spl3_6,
inference(avatar_contradiction_clause,[status(thm)],[f172]) ).
thf(f172,plain,
( $false
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f167]) ).
thf(f167,plain,
( ( $false = $true )
| ~ spl3_6 ),
inference(superposition,[status(thm)],[f121,f73]) ).
thf(f73,plain,
( ( $false
= ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK1 ) @ ( 'const/sets/sup' @ sK0 ) ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f71]) ).
thf(f71,definition,
( spl3_6
<=> ( $false
= ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK1 ) @ ( 'const/sets/sup' @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f121,plain,
( $true
= ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK1 ) @ ( 'const/sets/sup' @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK1 ) @ ( 'const/sets/sup' @ sK0 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f112]) ).
thf(f112,plain,
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK1 ) @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK1 ) @ ( 'const/sets/sup' @ sK0 ) ) ) ),
inference(superposition,[status(thm)],[f111,f90]) ).
thf(f90,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK1 ) @ ( sK2 @ X0 @ X1 @ sK0 ) )
= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $false = $true )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK1 ) @ ( sK2 @ X0 @ X1 @ sK0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f77,f31]) ).
thf(f31,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= $false )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 )
& ( 'const/realax/real_le' @ X0 @ X1 ) ) )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 )
& ( 'const/realax/real_le' @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 )
& ( 'const/realax/real_le' @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X0 @ X1 )
& ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 )
= ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X0 @ X1 )
& ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 )
= ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.brR7XCUkcK/DTF2THF_17657.p','thm/real/REAL_ABS_BOUNDS_') ).
thf(f77,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( sK2 @ X0 @ X1 @ sK0 ) ) @ sK1 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f76,f23]) ).
thf(f23,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ! [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X2 ) @ sK1 )
= $true ) )
& ( $true
!= ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/sup' @ sK0 ) ) @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16]) ).
thf(f16,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' @ ( 'const/realax/real_abs' @ X2 ) @ X1 )
= $true ) )
& ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/sup' @ X0 ) ) @ X1 )
!= $true ) )
=> ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ! [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X2 ) @ sK1 )
= $true ) )
& ( $true
!= ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/sup' @ sK0 ) ) @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,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' @ ( 'const/realax/real_abs' @ X2 ) @ X1 )
= $true ) )
& ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/sup' @ X0 ) ) @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/sup' @ X0 ) ) @ X1 )
!= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X2 ) @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,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' @ ( 'const/realax/real_abs' @ X2 ) @ X1 )
= $true ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/sup' @ X0 ) ) @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,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' @ ( 'const/realax/real_abs' @ X2 ) @ X1 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/sup' @ X0 ) ) @ X1 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,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' @ ( 'const/realax/real_abs' @ X2 ) @ X1 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/sup' @ X0 ) ) @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,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' @ ( 'const/realax/real_abs' @ X2 ) @ X1 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/sup' @ X0 ) ) @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.brR7XCUkcK/DTF2THF_17657.p','thm/sets/REAL_ABS_SUP_LE_') ).
thf(f76,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( sK2 @ X0 @ X1 @ sK0 ) ) @ sK1 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( sK2 @ X0 @ X1 @ sK0 ) ) @ sK1 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(superposition,[status(thm)],[f22,f26]) ).
thf(f26,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( $true
!= ( 'const/realax/real_le' @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK2 @ X2 @ X1 @ X0 ) ) ) ) )
| ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f13,f18]) ).
thf(f18,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ? [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( ( 'const/realax/real_le' @ X3 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X3 )
!= $true ) ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( $true
!= ( 'const/realax/real_le' @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK2 @ X2 @ X1 @ X0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ? [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( ( 'const/realax/real_le' @ X3 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X3 )
!= $true ) ) )
| ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
| ? [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( ( 'const/realax/real_le' @ X3 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X3 )
!= $true ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
=> ( ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( ( 'const/realax/real_le' @ X1 @ X3 )
& ( 'const/realax/real_le' @ X3 @ X2 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
& ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( ( 'const/realax/real_le' @ X1 @ X3 )
& ( 'const/realax/real_le' @ X3 @ X2 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
& ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.brR7XCUkcK/DTF2THF_17657.p','thm/sets/REAL_SUP_BOUNDS_') ).
thf(f22,plain,
! [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X2 ) @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f111,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK2 @ sK1 @ X0 @ sK0 ) ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f110,f23]) ).
thf(f110,plain,
! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK2 @ sK1 @ X0 @ sK0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f109]) ).
thf(f109,plain,
! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK2 @ sK1 @ X0 @ sK0 ) ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f107]) ).
thf(f107,plain,
! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK2 @ sK1 @ X0 @ sK0 ) ) )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f24,f89]) ).
thf(f89,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK2 @ X0 @ X1 @ sK0 ) @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $false = $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK2 @ X0 @ X1 @ sK0 ) @ sK1 ) ) ),
inference(superposition,[status(thm)],[f30,f77]) ).
thf(f30,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= $false )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f24,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK2 @ X2 @ X1 @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f163,plain,
( ~ spl3_5
| ~ spl3_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f162]) ).
thf(f162,plain,
( $false
| ~ spl3_5
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f158]) ).
thf(f158,plain,
( ( $false = $true )
| ~ spl3_5
| ~ spl3_8 ),
inference(superposition,[status(thm)],[f144,f69]) ).
thf(f69,plain,
( ( $false
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f67,definition,
( spl3_5
<=> ( $false
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f144,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ~ spl3_8 ),
inference(avatar_component_clause,[status(thm)],[f142]) ).
thf(f142,definition,
( spl3_8
<=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition]) ).
thf(f157,plain,
( spl3_8
| ~ spl3_7 ),
inference(avatar_split_clause,[status(thm)],[f155,f139,f142]) ).
thf(f139,definition,
( spl3_7
<=> ! [X0: 'type/realax/real'] :
( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK2 @ sK1 @ X0 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition]) ).
thf(f155,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ~ spl3_7 ),
inference(trivial_inequality_removal,[status(thm)],[f146]) ).
thf(f146,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( $true != $true )
| ~ spl3_7 ),
inference(superposition,[status(thm)],[f140,f104]) ).
thf(f104,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK1 ) @ ( sK2 @ X0 @ X1 @ sK0 ) )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $false = $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK1 ) @ ( sK2 @ X0 @ X1 @ sK0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f97,f31]) ).
thf(f97,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( sK2 @ X0 @ X1 @ sK0 ) ) @ sK1 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f96,f23]) ).
thf(f96,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( sK2 @ X0 @ X1 @ sK0 ) ) @ sK1 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( sK2 @ X0 @ X1 @ sK0 ) ) @ sK1 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(superposition,[status(thm)],[f22,f27]) ).
thf(f27,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f140,plain,
( ! [X0: 'type/realax/real'] :
( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK2 @ sK1 @ X0 @ sK0 ) ) )
| ~ spl3_7 ),
inference(avatar_component_clause,[status(thm)],[f139]) ).
thf(f145,plain,
( spl3_7
| spl3_8 ),
inference(avatar_split_clause,[status(thm)],[f137,f142,f139]) ).
thf(f137,plain,
! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK2 @ sK1 @ X0 @ sK0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f135,f23]) ).
thf(f135,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK2 @ sK1 @ X0 @ sK0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f134]) ).
thf(f134,plain,
! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK2 @ sK1 @ X0 @ sK0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f132]) ).
thf(f132,plain,
! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK2 @ sK1 @ X0 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f25,f105]) ).
thf(f105,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK2 @ X0 @ X1 @ sK0 ) @ sK1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $false = $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK2 @ X0 @ X1 @ sK0 ) @ sK1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f97,f30]) ).
thf(f25,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK2 @ X2 @ X1 @ X0 ) @ X2 ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK2 @ X2 @ X1 @ X0 ) ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f74,plain,
( spl3_5
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f64,f71,f67]) ).
thf(f64,plain,
( ( $false
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( $false
= ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK1 ) @ ( 'const/sets/sup' @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $true != $true )
| ( $false
= ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK1 ) @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $false
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) ),
inference(superposition,[status(thm)],[f21,f32]) ).
thf(f32,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
= $false )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $false
= ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 )
& ( 'const/realax/real_le' @ X0 @ X1 ) ) )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f21,plain,
( $true
!= ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/sup' @ sK0 ) ) @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ANA077^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n026.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 03:50:10 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.40 ---- Original DTF file ---
% 0.18/0.40 thf(spec,logic,$$dhol).
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 % File : ANA077^1 : TPTP v9.2.1. Released v7.0.0.
% 0.18/0.40 % Domain : Analysis
% 0.18/0.40 % Problem : REAL_ABS_SUP_LE
% 0.18/0.40 % Version : Especial.
% 0.18/0.40 % English :
% 0.18/0.40
% 0.18/0.40 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.18/0.40 % Source : [Kal16]
% 0.18/0.40 % Names : REAL_ABS_SUP_LE_.p [Kal16]
% 0.18/0.40
% 0.18/0.40 % Status : Theorem
% 0.18/0.40 % Rating : 0.00 v7.1.0
% 0.18/0.40 % Syntax : Number of formulae : 10 ( 1 unt; 7 typ; 0 def)
% 0.18/0.40 % Number of atoms : 16 ( 3 equ; 0 cnn)
% 0.18/0.40 % Maximal formula atoms : 6 ( 5 avg)
% 0.18/0.40 % Number of connectives : 44 ( 2 ~; 0 |; 5 &; 33 @)
% 0.18/0.40 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.18/0.40 % Maximal formula depth : 11 ( 8 avg)
% 0.18/0.40 % Number of types : 2 ( 1 usr)
% 0.18/0.40 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.18/0.40 % Number of symbols : 7 ( 6 usr; 0 con; 1-3 aty)
% 0.18/0.40 % Number of variables : 11 ( 0 ^; 9 !; 0 ?; 11 :)
% 0.18/0.40 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.40 % SPC : TH1_THM_EQU_NAR
% 0.18/0.40
% 0.18/0.40 % Comments : Exported from core HOL Light.
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 thf('thf_type_type/realax/real',type,
% 0.18/0.40 'type/realax/real': $tType ).
% 0.18/0.40
% 0.18/0.40 thf('thf_const_const/sets/sup',type,
% 0.18/0.40 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.18/0.40
% 0.18/0.40 thf('thf_const_const/sets/IN',type,
% 0.18/0.40 'const/sets/IN':
% 0.18/0.40 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.18/0.40
% 0.18/0.40 thf('thf_const_const/sets/EMPTY',type,
% 0.18/0.40 'const/sets/EMPTY':
% 0.18/0.40 !>[A: $tType] : ( A > $o ) ).
% 0.18/0.40
% 0.18/0.40 thf('thf_const_const/realax/real_neg',type,
% 0.18/0.40 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
% 0.18/0.40
% 0.18/0.40 thf('thf_const_const/realax/real_le',type,
% 0.18/0.40 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.18/0.40
% 0.18/0.40 thf('thf_const_const/realax/real_abs',type,
% 0.18/0.40 'const/realax/real_abs': 'type/realax/real' > 'type/realax/real' ).
% 0.18/0.40
% 0.18/0.40 thf('thm/sets/REAL_SUP_BOUNDS_',axiom,
% 0.18/0.40 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.18/0.40 ( ( ( A
% 0.18/0.40 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.18/0.40 & ! [A2: 'type/realax/real'] :
% 0.18/0.40 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 0.18/0.40 => ( ( 'const/realax/real_le' @ A0 @ A2 )
% 0.18/0.40 & ( 'const/realax/real_le' @ A2 @ A1 ) ) ) )
% 0.18/0.40 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) )
% 0.18/0.40 & ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A1 ) ) ) ).
% 0.18/0.40
% 0.18/0.40 thf('thm/real/REAL_ABS_BOUNDS_',axiom,
% 0.18/0.40 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.18/0.40 ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ A ) @ A0 )
% 0.18/0.40 = ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ A0 ) @ A )
% 0.18/0.40 & ( 'const/realax/real_le' @ A @ A0 ) ) ) ).
% 0.18/0.40
% 0.18/0.40 thf('thm/sets/REAL_ABS_SUP_LE_',conjecture,
% 0.18/0.40 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.18/0.40 ( ( ( A
% 0.18/0.40 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.18/0.40 & ! [A1: 'type/realax/real'] :
% 0.18/0.40 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.18/0.40 => ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ A1 ) @ A0 ) ) )
% 0.18/0.40 => ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/sup' @ A ) ) @ A0 ) ) ).
% 0.18/0.40
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 ------------------------
% 1.58/1.41 ---- Embedded in THF ---
% 1.58/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.58/1.41 %%% Generated on Tue Feb 24 03:50:11 EST 2026
% 1.58/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.58/1.41 %%% Logic specification used:
% 1.58/1.41 %%% thf(spec, logic, $$dhol).
% 1.58/1.41
% 1.58/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.brR7XCUkcK/DTF2DTF17657.p
% See solution above
% 1.58/1.41 ------------------------
% 1.58/1.42 ---- Cleaned THF ---
% 1.58/1.42 thf('thf_type_type/realax/real',type,
% 1.58/1.42 'type/realax/real': $tType ).
% 1.58/1.42
% 1.58/1.42 thf('thf_const_const/sets/sup',type,
% 1.58/1.42 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 1.58/1.42
% 1.58/1.42 thf('thf_const_const/sets/IN',type,
% 1.58/1.42 'const/sets/IN':
% 1.58/1.42 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.58/1.42
% 1.58/1.42 thf('thf_const_const/sets/EMPTY',type,
% 1.58/1.42 'const/sets/EMPTY':
% 1.58/1.42 !>[A: $tType] : ( A > $o ) ).
% 1.58/1.42
% 1.58/1.42 thf('thf_const_const/realax/real_neg',type,
% 1.58/1.42 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
% 1.58/1.42
% 1.58/1.42 thf('thf_const_const/realax/real_le',type,
% 1.58/1.42 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.58/1.42
% 1.58/1.42 thf('thf_const_const/realax/real_abs',type,
% 1.58/1.42 'const/realax/real_abs': 'type/realax/real' > 'type/realax/real' ).
% 1.58/1.42
% 1.58/1.42 thf('thm/sets/REAL_SUP_BOUNDS_',axiom,
% 1.58/1.42 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real',A1: 'type/realax/real'] :
% 1.58/1.42 ( ( ( A
% 1.58/1.42 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.58/1.42 & ! [A2: 'type/realax/real'] :
% 1.58/1.42 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 1.58/1.42 => ( ( 'const/realax/real_le' @ A0 @ A2 )
% 1.58/1.42 & ( 'const/realax/real_le' @ A2 @ A1 ) ) ) )
% 1.58/1.42 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) )
% 1.58/1.42 & ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A1 ) ) ) ).
% 1.58/1.42
% 1.58/1.42 thf('thm/real/REAL_ABS_BOUNDS_',axiom,
% 1.58/1.42 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 1.58/1.42 ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ A ) @ A0 )
% 1.58/1.42 = ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ A0 ) @ A )
% 1.58/1.42 & ( 'const/realax/real_le' @ A @ A0 ) ) ) ).
% 1.58/1.42
% 1.58/1.42 thf('thm/sets/REAL_ABS_SUP_LE_',conjecture,
% 1.58/1.42 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 1.58/1.42 ( ( ( A
% 1.58/1.42 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.58/1.42 & ! [A1: 'type/realax/real'] :
% 1.58/1.42 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.58/1.42 => ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ A1 ) @ A0 ) ) )
% 1.58/1.42 => ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/sup' @ A ) ) @ A0 ) ) ).
% 1.58/1.42 ------------------------
% 1.58/1.44 % (17758)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_17657 for (2999ds/2Mi)
% 1.58/1.44 % (17757)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17657 for (2999ds/2Mi)
% 1.58/1.44 % (17755)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_17657 for (2999ds/4Mi)
% 1.58/1.44 % (17760)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17657 for (2999ds/18Mi)
% 1.58/1.44 % (17756)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_17657 for (2999ds/27Mi)
% 1.58/1.44 % (17754)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17657 for (2999ds/183Mi)
% 1.58/1.44 % (17759)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_17657 for (2999ds/275Mi)
% 1.58/1.44 % (17757)Instruction limit reached!
% 1.58/1.44 % (17757)------------------------------
% 1.58/1.44 % (17757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.44 % (17757)Termination reason: Unknown
% 1.58/1.44 % (17757)Termination phase: Saturation
% 1.58/1.44 % (17758)Instruction limit reached!
% 1.58/1.44 % (17758)------------------------------
% 1.58/1.44 % (17758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.44 % (17758)Termination reason: Unknown
% 1.58/1.44 % (17758)Termination phase: Saturation
% 1.58/1.44
% 1.58/1.44 % (17758)Memory used [KB]: 1023
% 1.58/1.44 % (17758)Time elapsed: 0.003 s
% 1.58/1.44 % (17758)Instructions burned: 3 (million)
% 1.58/1.44 % (17758)------------------------------
% 1.58/1.44 % (17758)------------------------------
% 1.58/1.44
% 1.58/1.44 % (17757)Memory used [KB]: 1023
% 1.58/1.44 % (17757)Time elapsed: 0.003 s
% 1.58/1.44 % (17757)Instructions burned: 2 (million)
% 1.58/1.44 % (17757)------------------------------
% 1.58/1.44 % (17757)------------------------------
% 1.58/1.44 % (17755)Instruction limit reached!
% 1.58/1.44 % (17755)------------------------------
% 1.58/1.44 % (17755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.44 % (17755)Termination reason: Unknown
% 1.58/1.44 % (17755)Termination phase: Saturation
% 1.58/1.44
% 1.58/1.44 % (17755)Memory used [KB]: 5500
% 1.58/1.44 % (17755)Time elapsed: 0.004 s
% 1.58/1.44 % (17755)Instructions burned: 4 (million)
% 1.58/1.44 % (17755)------------------------------
% 1.58/1.44 % (17755)------------------------------
% 1.58/1.44 % (17759)Refutation not found, incomplete strategy
% 1.58/1.44 % (17759)------------------------------
% 1.58/1.44 % (17759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.44 % (17759)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.44
% 1.58/1.44
% 1.58/1.44 % (17759)Memory used [KB]: 5500
% 1.58/1.44 % (17759)Time elapsed: 0.005 s
% 1.58/1.44 % (17759)Instructions burned: 5 (million)
% 1.58/1.44 % (17759)------------------------------
% 1.58/1.44 % (17759)------------------------------
% 1.58/1.45 % (17760)Instruction limit reached!
% 1.58/1.45 % (17760)------------------------------
% 1.58/1.45 % (17760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.45 % (17760)Termination reason: Unknown
% 1.58/1.45 % (17760)Termination phase: Saturation
% 1.58/1.45
% 1.58/1.45 % (17760)Memory used [KB]: 5628
% 1.58/1.45 % (17760)Time elapsed: 0.012 s
% 1.58/1.45 % (17760)Instructions burned: 19 (million)
% 1.58/1.45 % (17760)------------------------------
% 1.58/1.45 % (17760)------------------------------
% 1.58/1.45 % (17754)First to succeed.
% 1.58/1.46 % (17756)Instruction limit reached!
% 1.58/1.46 % (17756)------------------------------
% 1.58/1.46 % (17756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.46 % (17756)Termination reason: Unknown
% 1.58/1.46 % (17756)Termination phase: Saturation
% 1.58/1.46
% 1.58/1.46 % (17756)Memory used [KB]: 5628
% 1.58/1.46 % (17756)Time elapsed: 0.017 s
% 1.58/1.46 % (17756)Instructions burned: 27 (million)
% 1.58/1.46 % (17756)------------------------------
% 1.58/1.46 % (17756)------------------------------
% 1.58/1.46 % (17754)Refutation found. Thanks to Tanya!
% 1.58/1.46 % SZS status Theorem for DTF2THF_17657
% 1.58/1.46 % SZS output start Proof for DTF2THF_17657
% 1.58/1.46 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.58/1.46 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.58/1.46 thf(func_def_1, type, 'const/sets/sup': ('type/realax/real' > $o) > 'type/realax/real').
% 1.58/1.46 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.58/1.46 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.58/1.46 thf(func_def_4, type, 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real').
% 1.58/1.46 thf(func_def_5, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.58/1.46 thf(func_def_6, type, 'const/realax/real_abs': 'type/realax/real' > 'type/realax/real').
% 1.58/1.46 thf(func_def_11, type, sK0: 'type/realax/real' > $o).
% 1.58/1.46 thf(func_def_12, type, sK1: 'type/realax/real').
% 1.58/1.46 thf(func_def_13, type, sK2: 'type/realax/real' > 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.58/1.46 thf(func_def_15, type, ph4: !>[X0: $tType]:(X0)).
% 1.58/1.46 thf(func_def_16, type, sK5: 'type/realax/real').
% 1.58/1.46 thf(f174,plain,(
% 1.58/1.46 $false),
% 1.58/1.46 inference(avatar_sat_refutation,[status(thm)],[f74,f145,f157,f163,f173])).
% 1.58/1.46 thf(f173,plain,(
% 1.58/1.46 ~spl3_6),
% 1.58/1.46 inference(avatar_contradiction_clause,[status(thm)],[f172])).
% 1.58/1.46 thf(f172,plain,(
% 1.58/1.46 $false | ~spl3_6),
% 1.58/1.46 inference(trivial_inequality_removal,[status(thm)],[f167])).
% 1.58/1.46 thf(f167,plain,(
% 1.58/1.46 ($false = $true) | ~spl3_6),
% 1.58/1.46 inference(superposition,[status(thm)],[f121,f73])).
% 1.58/1.46 thf(f73,plain,(
% 1.58/1.46 ($false = ('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ ('const/sets/sup' @ sK0))) | ~spl3_6),
% 1.58/1.46 inference(avatar_component_clause,[status(thm)],[f71])).
% 1.58/1.46 thf(f71,definition,(
% 1.58/1.46 spl3_6 <=> ($false = ('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ ('const/sets/sup' @ sK0)))),
% 1.58/1.46 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.58/1.46 thf(f121,plain,(
% 1.58/1.46 ($true = ('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ ('const/sets/sup' @ sK0)))),
% 1.58/1.46 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.58/1.46 thf(f120,plain,(
% 1.58/1.46 ($true != $true) | ($true = ('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ ('const/sets/sup' @ sK0)))),
% 1.58/1.46 inference(duplicate_literal_removal,[status(thm)],[f112])).
% 1.58/1.46 thf(f112,plain,(
% 1.58/1.46 ($true != $true) | ($true = ('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ ('const/sets/sup' @ sK0))) | ($true = ('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ ('const/sets/sup' @ sK0)))),
% 1.58/1.46 inference(superposition,[status(thm)],[f111,f90])).
% 1.58/1.46 thf(f90,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ (sK2 @ X0 @ X1 @ sK0)) = $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK0)))) )),
% 1.58/1.46 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.58/1.46 thf(f83,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK0))) | ($false = $true) | (('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ (sK2 @ X0 @ X1 @ sK0)) = $true)) )),
% 1.58/1.46 inference(superposition,[status(thm)],[f77,f31])).
% 1.58/1.46 thf(f31,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = $false) | (('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) = $true)) )),
% 1.58/1.46 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.58/1.46 thf(f29,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) & ('const/realax/real_le' @ X0 @ X1))) | (('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = $false)) )),
% 1.58/1.46 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.58/1.46 thf(f20,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = (('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) & ('const/realax/real_le' @ X0 @ X1)))) )),
% 1.58/1.46 inference(cnf_transformation,[status(thm)],[f9])).
% 1.58/1.46 thf(f9,plain,(
% 1.58/1.46 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = (('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) & ('const/realax/real_le' @ X0 @ X1)))),
% 1.58/1.46 inference(fool_elimination,[status(thm)],[f8])).
% 1.58/1.46 thf(f8,plain,(
% 1.58/1.46 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) = ('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1))),
% 1.58/1.46 inference(rectify,[status(thm)],[f2])).
% 1.58/1.46 thf(f2,axiom,(
% 1.58/1.46 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) = ('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1))),
% 1.58/1.46 file('/export/starexec/sandbox2/tmp/tmp.brR7XCUkcK/DTF2THF_17657.p','thm/real/REAL_ABS_BOUNDS_')).
% 1.58/1.46 thf(f77,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ (sK2 @ X0 @ X1 @ sK0)) @ sK1) = $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK0)))) )),
% 1.58/1.46 inference(subsumption_resolution,[status(thm)],[f76,f23])).
% 1.58/1.46 thf(f23,plain,(
% 1.58/1.46 ('const/sets/EMPTY' @ 'type/realax/real' != sK0)),
% 1.58/1.46 inference(cnf_transformation,[status(thm)],[f17])).
% 1.58/1.46 thf(f17,plain,(
% 1.58/1.46 ('const/sets/EMPTY' @ 'type/realax/real' != sK0) & ! [X2 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0)) | (('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ sK1) = $true)) & ($true != ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ sK0)) @ sK1))),
% 1.58/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16])).
% 1.58/1.46 thf(f16,plain,(
% 1.58/1.46 ? [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' @ ('const/realax/real_abs' @ X2) @ X1) = $true)) & (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1) != $true)) => (('const/sets/EMPTY' @ 'type/realax/real' != sK0) & ! [X2 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0)) | (('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ sK1) = $true)) & ($true != ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ sK0)) @ sK1)))),
% 1.58/1.46 introduced(definition,[],[choice_axiom])).
% 1.58/1.46 thf(f15,plain,(
% 1.58/1.46 ? [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' @ ('const/realax/real_abs' @ X2) @ X1) = $true)) & (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1) != $true))),
% 1.58/1.46 inference(flattening,[status(thm)],[f14])).
% 1.58/1.46 thf(f14,plain,(
% 1.58/1.46 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1) != $true) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true) | (('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1) = $true))))),
% 1.58/1.46 inference(ennf_transformation,[status(thm)],[f11])).
% 1.58/1.46 thf(f11,plain,(
% 1.58/1.46 ~! [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' @ ('const/realax/real_abs' @ X2) @ X1) = $true))) => (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1) = $true))),
% 1.58/1.46 inference(fool_elimination,[status(thm)],[f10])).
% 1.58/1.46 thf(f10,plain,(
% 1.58/1.46 ~! [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' @ ('const/realax/real_abs' @ X2) @ X1))) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1))),
% 1.58/1.46 inference(rectify,[status(thm)],[f4])).
% 1.58/1.46 thf(f4,negated_conjecture,(
% 1.58/1.46 ~! [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' @ ('const/realax/real_abs' @ X2) @ X1))) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1))),
% 1.58/1.46 inference(negated_conjecture,[status(cth)],[f3])).
% 1.58/1.46 thf(f3,conjecture,(
% 1.58/1.46 ! [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' @ ('const/realax/real_abs' @ X2) @ X1))) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ X0)) @ X1))),
% 1.58/1.46 file('/export/starexec/sandbox2/tmp/tmp.brR7XCUkcK/DTF2THF_17657.p','thm/sets/REAL_ABS_SUP_LE_')).
% 1.58/1.46 thf(f76,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK2 @ X0 @ X1 @ sK0)) @ sK1) = $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK0)))) )),
% 1.58/1.46 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.58/1.46 thf(f75,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK0))) | (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK2 @ X0 @ X1 @ sK0)) @ sK1) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) )),
% 1.58/1.46 inference(superposition,[status(thm)],[f22,f26])).
% 1.58/1.46 thf(f26,plain,(
% 1.58/1.46 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X2 @ X1 @ X0) @ X0) = $true) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.58/1.46 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.46 thf(f19,plain,(
% 1.58/1.46 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X2 @ X1 @ X0) @ X0) = $true) & (($true != ('const/realax/real_le' @ (sK2 @ X2 @ X1 @ X0) @ X2)) | ($true != ('const/realax/real_le' @ X1 @ (sK2 @ X2 @ X1 @ X0))))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) = $true) & (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true)))),
% 1.58/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f13,f18])).
% 1.58/1.46 thf(f18,plain,(
% 1.58/1.46 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : (? [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) & ((('const/realax/real_le' @ X3 @ X2) != $true) | (('const/realax/real_le' @ X1 @ X3) != $true))) => ((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X2 @ X1 @ X0) @ X0) = $true) & (($true != ('const/realax/real_le' @ (sK2 @ X2 @ X1 @ X0) @ X2)) | ($true != ('const/realax/real_le' @ X1 @ (sK2 @ X2 @ X1 @ X0))))))),
% 1.58/1.46 introduced(definition,[],[choice_axiom])).
% 1.58/1.46 thf(f13,plain,(
% 1.58/1.46 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ? [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) & ((('const/realax/real_le' @ X3 @ X2) != $true) | (('const/realax/real_le' @ X1 @ X3) != $true))) | ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) = $true) & (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true)))),
% 1.58/1.46 inference(flattening,[status(thm)],[f12])).
% 1.58/1.46 thf(f12,plain,(
% 1.58/1.46 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) = $true) & (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true)) | (? [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) & ((('const/realax/real_le' @ X3 @ X2) != $true) | (('const/realax/real_le' @ X1 @ X3) != $true))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 1.58/1.46 inference(ennf_transformation,[status(thm)],[f7])).
% 1.58/1.46 thf(f7,plain,(
% 1.58/1.46 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) => ((('const/realax/real_le' @ X1 @ X3) = $true) & (('const/realax/real_le' @ X3 @ X2) = $true))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) = $true) & (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true)))),
% 1.58/1.46 inference(fool_elimination,[status(thm)],[f6])).
% 1.58/1.46 thf(f6,plain,(
% 1.58/1.46 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X1 @ X3) & ('const/realax/real_le' @ X3 @ X2))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))))),
% 1.58/1.46 inference(rectify,[status(thm)],[f1])).
% 1.58/1.46 thf(f1,axiom,(
% 1.58/1.46 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X1 @ X3) & ('const/realax/real_le' @ X3 @ X2))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))))),
% 1.58/1.46 file('/export/starexec/sandbox2/tmp/tmp.brR7XCUkcK/DTF2THF_17657.p','thm/sets/REAL_SUP_BOUNDS_')).
% 1.58/1.46 thf(f22,plain,(
% 1.58/1.46 ( ! [X2 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0)) | (('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ sK1) = $true)) )),
% 1.58/1.46 inference(cnf_transformation,[status(thm)],[f17])).
% 1.58/1.46 thf(f111,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X0 @ (sK2 @ sK1 @ X0 @ sK0))) | (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK0)) = $true)) )),
% 1.58/1.46 inference(subsumption_resolution,[status(thm)],[f110,f23])).
% 1.58/1.46 thf(f110,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK0)) = $true) | ($true != ('const/realax/real_le' @ X0 @ (sK2 @ sK1 @ X0 @ sK0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) )),
% 1.58/1.46 inference(trivial_inequality_removal,[status(thm)],[f109])).
% 1.58/1.46 thf(f109,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK0)) = $true) | ($true != ('const/realax/real_le' @ X0 @ (sK2 @ sK1 @ X0 @ sK0))) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) )),
% 1.58/1.46 inference(duplicate_literal_removal,[status(thm)],[f107])).
% 1.58/1.46 thf(f107,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK0)) = $true) | ($true != ('const/realax/real_le' @ X0 @ (sK2 @ sK1 @ X0 @ sK0))) | ($true != $true) | (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK0)) = $true)) )),
% 1.58/1.46 inference(superposition,[status(thm)],[f24,f89])).
% 1.58/1.46 thf(f89,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK2 @ X0 @ X1 @ sK0) @ sK1)) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK0)))) )),
% 1.58/1.46 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.58/1.46 thf(f86,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK0))) | ($false = $true) | ($true = ('const/realax/real_le' @ (sK2 @ X0 @ X1 @ sK0) @ sK1))) )),
% 1.58/1.46 inference(superposition,[status(thm)],[f30,f77])).
% 1.58/1.46 thf(f30,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = $false) | (('const/realax/real_le' @ X0 @ X1) = $true)) )),
% 1.58/1.46 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.58/1.46 thf(f24,plain,(
% 1.58/1.46 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK2 @ X2 @ X1 @ X0) @ X2)) | ($true != ('const/realax/real_le' @ X1 @ (sK2 @ X2 @ X1 @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true)) )),
% 1.58/1.46 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.46 thf(f163,plain,(
% 1.58/1.46 ~spl3_5 | ~spl3_8),
% 1.58/1.46 inference(avatar_contradiction_clause,[status(thm)],[f162])).
% 1.58/1.46 thf(f162,plain,(
% 1.58/1.46 $false | (~spl3_5 | ~spl3_8)),
% 1.58/1.46 inference(trivial_inequality_removal,[status(thm)],[f158])).
% 1.58/1.46 thf(f158,plain,(
% 1.58/1.46 ($false = $true) | (~spl3_5 | ~spl3_8)),
% 1.58/1.46 inference(superposition,[status(thm)],[f144,f69])).
% 1.58/1.46 thf(f69,plain,(
% 1.58/1.46 ($false = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ~spl3_5),
% 1.58/1.46 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.58/1.46 thf(f67,definition,(
% 1.58/1.46 spl3_5 <=> ($false = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1))),
% 1.58/1.46 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.58/1.46 thf(f144,plain,(
% 1.58/1.46 ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ~spl3_8),
% 1.58/1.46 inference(avatar_component_clause,[status(thm)],[f142])).
% 1.58/1.46 thf(f142,definition,(
% 1.58/1.46 spl3_8 <=> ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1))),
% 1.58/1.46 introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition])).
% 1.58/1.46 thf(f157,plain,(
% 1.58/1.46 spl3_8 | ~spl3_7),
% 1.58/1.46 inference(avatar_split_clause,[status(thm)],[f155,f139,f142])).
% 1.58/1.46 thf(f139,definition,(
% 1.58/1.46 spl3_7 <=> ! [X0 : 'type/realax/real'] : ($true != ('const/realax/real_le' @ X0 @ (sK2 @ sK1 @ X0 @ sK0)))),
% 1.58/1.46 introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition])).
% 1.58/1.46 thf(f155,plain,(
% 1.58/1.46 ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ~spl3_7),
% 1.58/1.46 inference(trivial_inequality_removal,[status(thm)],[f146])).
% 1.58/1.46 thf(f146,plain,(
% 1.58/1.46 ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ($true != $true) | ~spl3_7),
% 1.58/1.46 inference(superposition,[status(thm)],[f140,f104])).
% 1.58/1.46 thf(f104,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ (sK2 @ X0 @ X1 @ sK0)) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true)) )),
% 1.58/1.46 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.58/1.46 thf(f98,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($false = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true) | (('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ (sK2 @ X0 @ X1 @ sK0)) = $true)) )),
% 1.58/1.46 inference(superposition,[status(thm)],[f97,f31])).
% 1.58/1.46 thf(f97,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ (sK2 @ X0 @ X1 @ sK0)) @ sK1) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true)) )),
% 1.58/1.46 inference(subsumption_resolution,[status(thm)],[f96,f23])).
% 1.58/1.46 thf(f96,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ (sK2 @ X0 @ X1 @ sK0)) @ sK1) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true)) )),
% 1.58/1.46 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.58/1.46 thf(f95,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true) | ($true != $true) | (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK2 @ X0 @ X1 @ sK0)) @ sK1) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) )),
% 1.58/1.46 inference(superposition,[status(thm)],[f22,f27])).
% 1.58/1.46 thf(f27,plain,(
% 1.58/1.46 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X2 @ X1 @ X0) @ X0) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.58/1.46 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.46 thf(f140,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X0 @ (sK2 @ sK1 @ X0 @ sK0)))) ) | ~spl3_7),
% 1.58/1.46 inference(avatar_component_clause,[status(thm)],[f139])).
% 1.58/1.46 thf(f145,plain,(
% 1.58/1.46 spl3_7 | spl3_8),
% 1.58/1.46 inference(avatar_split_clause,[status(thm)],[f137,f142,f139])).
% 1.58/1.46 thf(f137,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ($true != ('const/realax/real_le' @ X0 @ (sK2 @ sK1 @ X0 @ sK0)))) )),
% 1.58/1.46 inference(subsumption_resolution,[status(thm)],[f135,f23])).
% 1.58/1.46 thf(f135,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X0 @ (sK2 @ sK1 @ X0 @ sK0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1))) )),
% 1.58/1.46 inference(trivial_inequality_removal,[status(thm)],[f134])).
% 1.58/1.46 thf(f134,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ($true != ('const/realax/real_le' @ X0 @ (sK2 @ sK1 @ X0 @ sK0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) )),
% 1.58/1.46 inference(duplicate_literal_removal,[status(thm)],[f132])).
% 1.58/1.46 thf(f132,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ($true != ('const/realax/real_le' @ X0 @ (sK2 @ sK1 @ X0 @ sK0))) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != $true)) )),
% 1.58/1.46 inference(superposition,[status(thm)],[f25,f105])).
% 1.58/1.46 thf(f105,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK2 @ X0 @ X1 @ sK0) @ sK1)) | (('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true)) )),
% 1.58/1.46 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.58/1.46 thf(f99,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($false = $true) | ($true = ('const/realax/real_le' @ (sK2 @ X0 @ X1 @ sK0) @ sK1)) | (('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true)) )),
% 1.58/1.46 inference(superposition,[status(thm)],[f97,f30])).
% 1.58/1.46 thf(f25,plain,(
% 1.58/1.46 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK2 @ X2 @ X1 @ X0) @ X2)) | ($true != ('const/realax/real_le' @ X1 @ (sK2 @ X2 @ X1 @ X0))) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.58/1.46 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.46 thf(f74,plain,(
% 1.58/1.46 spl3_5 | spl3_6),
% 1.58/1.46 inference(avatar_split_clause,[status(thm)],[f64,f71,f67])).
% 1.58/1.46 thf(f64,plain,(
% 1.58/1.46 ($false = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ($false = ('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ ('const/sets/sup' @ sK0)))),
% 1.58/1.46 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.58/1.46 thf(f58,plain,(
% 1.58/1.46 ($true != $true) | ($false = ('const/realax/real_le' @ ('const/realax/real_neg' @ sK1) @ ('const/sets/sup' @ sK0))) | ($false = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1))),
% 1.58/1.46 inference(superposition,[status(thm)],[f21,f32])).
% 1.58/1.46 thf(f32,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = $true) | (('const/realax/real_le' @ X0 @ X1) = $false) | (('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) = $false)) )),
% 1.58/1.46 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.58/1.46 thf(f28,plain,(
% 1.58/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($false = (('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) & ('const/realax/real_le' @ X0 @ X1))) | (('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = $true)) )),
% 1.58/1.46 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.58/1.46 thf(f21,plain,(
% 1.58/1.46 ($true != ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/sup' @ sK0)) @ sK1))),
% 1.58/1.46 inference(cnf_transformation,[status(thm)],[f17])).
% 1.58/1.46 % SZS output end Proof for DTF2THF_17657
% 1.58/1.46 % (17754)------------------------------
% 1.58/1.46 % (17754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.46 % (17754)Termination reason: Refutation
% 1.58/1.46
% 1.58/1.46 % (17754)Memory used [KB]: 5628
% 1.58/1.46 % (17754)Time elapsed: 0.018 s
% 1.58/1.46 % (17754)Instructions burned: 24 (million)
% 1.58/1.46 % (17754)------------------------------
% 1.58/1.46 % (17754)------------------------------
% 1.58/1.46 % (17753)Success in time 0.031 s
%------------------------------------------------------------------------------