%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA076^1 : 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 : n011.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 1.62s 1.46s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 101 ( 3 unt; 0 typ; 8 def)
% Number of atoms : 982 ( 269 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 1228 ( 157 ~; 180 |; 55 &; 797 @)
% ( 9 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 13 con; 0-3 aty)
% Number of variables : 188 ( 0 ^; 162 !; 26 ?; 188 :)
% 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_8,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_9,type,
sK1: 'type/realax/real' > $o ).
thf(func_def_10,type,
sK2: 'type/realax/real' ).
thf(func_def_11,type,
sK3: 'type/realax/real' ).
thf(func_def_12,type,
sK4: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_13,type,
sK5: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_15,type,
ph7:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK8: 'type/realax/real' ).
thf(f223,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f53,f94,f102,f107,f113,f142,f170,f182,f188,f190,f222]) ).
thf(f222,plain,
( spl6_8
| ~ spl6_9 ),
inference(avatar_split_clause,[status(thm)],[f221,f97,f92]) ).
thf(f92,definition,
( spl6_8
<=> ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK1 ) @ sK3 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_8])],[avatar_definition]) ).
thf(f97,definition,
( spl6_9
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition]) ).
thf(f221,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK1 ) @ sK3 )
= $true ) )
| ~ spl6_9 ),
inference(trivial_inequality_removal,[status(thm)],[f219]) ).
thf(f219,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK1 ) @ sK3 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X0 )
= $true ) )
| ~ spl6_9 ),
inference(superposition,[status(thm)],[f34,f98]) ).
thf(f98,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X1 )
= $true ) )
| ~ spl6_9 ),
inference(avatar_component_clause,[status(thm)],[f97]) ).
thf(f34,plain,
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ) )
& ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ sK3 )
!= $true )
| ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/sup' @ sK1 ) )
!= $true ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 )
!= $true )
| ( ( ( 'const/realax/real_le' @ sK2 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ X3 @ sK3 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f16,f25]) ).
thf(f25,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( '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 ) )
& ! [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' != sK1 ) )
& ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ sK3 )
!= $true )
| ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/sup' @ sK1 ) )
!= $true ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 )
!= $true )
| ( ( ( 'const/realax/real_le' @ sK2 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ X3 @ sK3 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( '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 ) )
& ! [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 ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,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' @ X1 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,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)],[f9]) ).
thf(f9,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 )
=> ( ( 'const/realax/real_le' @ X1 @ X3 )
& ( 'const/realax/real_le' @ X3 @ X2 ) ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
& ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [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 )
=> ( ( 'const/realax/real_le' @ X1 @ X3 )
& ( 'const/realax/real_le' @ X3 @ X2 ) ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
& ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [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 )
=> ( ( 'const/realax/real_le' @ X1 @ X3 )
& ( 'const/realax/real_le' @ X3 @ X2 ) ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
& ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1jBW8UPP0L/DTF2THF_16287.p','thm/sets/REAL_SUP_BOUNDS_') ).
thf(f190,plain,
( spl6_12
| ~ spl6_10 ),
inference(avatar_split_clause,[status(thm)],[f189,f100,f111]) ).
thf(f111,definition,
( spl6_12
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X1 )
= $true )
| ( ( 'const/realax/real_le' @ ( sK4 @ X1 @ sK1 ) @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_12])],[avatar_definition]) ).
thf(f100,definition,
( spl6_10
<=> ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK1 ) @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_10])],[avatar_definition]) ).
thf(f189,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK1 ) @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X0 )
= $true ) )
| ~ spl6_10 ),
inference(subsumption_resolution,[status(thm)],[f185,f37]) ).
thf(f37,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f185,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK1 ) @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) )
| ~ spl6_10 ),
inference(trivial_inequality_removal,[status(thm)],[f183]) ).
thf(f183,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK1 ) @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl6_10 ),
inference(superposition,[status(thm)],[f39,f101]) ).
thf(f101,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK1 ) @ sK3 )
= $true )
| ~ spl6_10 ),
inference(avatar_component_clause,[status(thm)],[f100]) ).
thf(f39,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK5 @ X4 @ X0 ) @ X4 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( sK4 @ X2 @ X0 ) @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ! [X2: 'type/realax/real'] :
( ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ ( sK4 @ X2 @ X0 ) @ X2 )
!= $true ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK5 @ X4 @ X0 ) @ X4 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f27,f29,f28]) ).
thf(f28,plain,
! [X0: 'type/realax/real' > $o,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/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ ( sK4 @ X2 @ X0 ) @ X2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
! [X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true ) )
=> ( ( ( 'const/realax/real_le' @ ( sK5 @ X4 @ X0 ) @ X4 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ! [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' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X4: 'type/realax/real'] :
? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X5 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ! [X3: 'type/realax/real'] :
( ? [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X4 @ X3 )
!= $true ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X3 )
= $true ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = 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 ) ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X5 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ! [X3: 'type/realax/real'] :
( ? [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X4 @ X3 )
!= $true ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X3 )
= $true ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = 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 ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,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 )
= $true )
=> ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true ) ) )
=> ( ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X5 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ! [X3: 'type/realax/real'] :
( ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X4 @ X3 )
= $true ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,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)],[f3]) ).
thf(f3,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/sandbox2/tmp/tmp.1jBW8UPP0L/DTF2THF_16287.p','thm/sets/SUP_') ).
thf(f188,plain,
( spl6_11
| ~ spl6_10 ),
inference(avatar_split_clause,[status(thm)],[f187,f100,f105]) ).
thf(f105,definition,
( spl6_11
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK1 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_11])],[avatar_definition]) ).
thf(f187,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK1 ) )
= $true ) )
| ~ spl6_10 ),
inference(subsumption_resolution,[status(thm)],[f186,f37]) ).
thf(f186,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK1 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 )
!= $true ) )
| ~ spl6_10 ),
inference(trivial_inequality_removal,[status(thm)],[f184]) ).
thf(f184,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK1 ) )
= $true ) )
| ~ spl6_10 ),
inference(superposition,[status(thm)],[f43,f101]) ).
thf(f43,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK5 @ X4 @ X0 ) @ X4 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f182,plain,
( spl6_1
| ~ spl6_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f181]) ).
thf(f181,plain,
( $false
| spl6_1
| ~ spl6_11 ),
inference(subsumption_resolution,[status(thm)],[f180,f37]) ).
thf(f180,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| spl6_1
| ~ spl6_11 ),
inference(trivial_inequality_removal,[status(thm)],[f175]) ).
thf(f175,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true != $true )
| spl6_1
| ~ spl6_11 ),
inference(superposition,[status(thm)],[f162,f32]) ).
thf(f32,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X1 ) @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X1 ) @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
& ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f23]) ).
thf(f23,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
=> ( ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X1 ) @ X1 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
& ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
& ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
<=> ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
= ( ? [X2: X0] : ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
= ( ? [X2: X0] : ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1jBW8UPP0L/DTF2THF_16287.p','thm/sets/MEMBER_NOT_EMPTY_') ).
thf(f162,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 )
!= $true )
| spl6_1
| ~ spl6_11 ),
inference(subsumption_resolution,[status(thm)],[f158,f35]) ).
thf(f35,plain,
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ sK2 @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f158,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK2 @ X0 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 )
!= $true ) )
| spl6_1
| ~ spl6_11 ),
inference(trivial_inequality_removal,[status(thm)],[f153]) ).
thf(f153,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK2 @ X0 )
!= $true )
| ( $true != $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 )
!= $true ) )
| spl6_1
| ~ spl6_11 ),
inference(superposition,[status(thm)],[f76,f106]) ).
thf(f106,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK1 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true ) )
| ~ spl6_11 ),
inference(avatar_component_clause,[status(thm)],[f105]) ).
thf(f76,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK1 ) )
!= $true )
| ( ( 'const/realax/real_le' @ sK2 @ X0 )
!= $true ) )
| spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK1 ) )
!= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ sK2 @ X0 )
!= $true ) )
| spl6_1 ),
inference(superposition,[status(thm)],[f48,f33]) ).
thf(f33,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true ) )
=> ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X1 )
& ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X1 )
& ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1jBW8UPP0L/DTF2THF_16287.p','thm/realax/REAL_LE_TRANS_') ).
thf(f48,plain,
( ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/sup' @ sK1 ) )
!= $true )
| spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl6_1
<=> ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/sup' @ sK1 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f170,plain,
( spl6_2
| ~ spl6_8
| ~ spl6_12 ),
inference(avatar_split_clause,[status(thm)],[f167,f111,f92,f50]) ).
thf(f50,definition,
( spl6_2
<=> ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f167,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ sK3 )
= $true )
| ~ spl6_8
| ~ spl6_12 ),
inference(trivial_inequality_removal,[status(thm)],[f166]) ).
thf(f166,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ sK3 )
= $true )
| ~ spl6_8
| ~ spl6_12 ),
inference(duplicate_literal_removal,[status(thm)],[f164]) ).
thf(f164,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ sK3 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ sK3 )
= $true )
| ~ spl6_8
| ~ spl6_12 ),
inference(superposition,[status(thm)],[f112,f93]) ).
thf(f93,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK1 ) @ sK3 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X0 )
= $true ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f112,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK4 @ X1 @ sK1 ) @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X1 )
= $true ) )
| ~ spl6_12 ),
inference(avatar_component_clause,[status(thm)],[f111]) ).
thf(f142,plain,
( ~ spl6_7
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f141]) ).
thf(f141,plain,
( $false
| ~ spl6_7
| ~ spl6_10 ),
inference(trivial_inequality_removal,[status(thm)],[f138]) ).
thf(f138,plain,
( ( $true != $true )
| ~ spl6_7
| ~ spl6_10 ),
inference(superposition,[status(thm)],[f90,f101]) ).
thf(f90,plain,
( ! [X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( sK5 @ X1 @ sK1 ) @ X1 )
!= $true )
| ~ spl6_7 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f89,definition,
( spl6_7
<=> ! [X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( sK5 @ X1 @ sK1 ) @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_7])],[avatar_definition]) ).
thf(f113,plain,
( spl6_12
| spl6_10 ),
inference(avatar_split_clause,[status(thm)],[f109,f100,f111]) ).
thf(f109,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X1 )
= $true )
| ( ( 'const/realax/real_le' @ ( sK4 @ X1 @ sK1 ) @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK1 ) @ sK3 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f82,f37]) ).
thf(f82,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK4 @ X1 @ sK1 ) @ X1 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK1 ) @ sK3 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X1 )
= $true )
| ( ( 'const/realax/real_le' @ ( sK4 @ X1 @ sK1 ) @ X1 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK1 ) @ sK3 )
= $true ) ),
inference(superposition,[status(thm)],[f34,f38]) ).
thf(f38,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( sK4 @ X2 @ X0 ) @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f107,plain,
( spl6_10
| spl6_11 ),
inference(avatar_split_clause,[status(thm)],[f103,f105,f100]) ).
thf(f103,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK1 ) @ sK3 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK1 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f84,f37]) ).
thf(f84,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK1 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK1 ) @ sK3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK1 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true ) ),
inference(superposition,[status(thm)],[f34,f42]) ).
thf(f42,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f102,plain,
( spl6_9
| spl6_10 ),
inference(avatar_split_clause,[status(thm)],[f95,f100,f97]) ).
thf(f95,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X1 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f85,f37]) ).
thf(f85,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X1 )
= $true )
| ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK1 ) @ sK3 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f34,f40]) ).
thf(f40,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f94,plain,
( spl6_7
| spl6_8 ),
inference(avatar_split_clause,[status(thm)],[f87,f92,f89]) ).
thf(f87,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK5 @ X1 @ sK1 ) @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK1 ) @ sK3 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f86,f37]) ).
thf(f86,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK1 ) @ sK3 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ ( sK5 @ X1 @ sK1 ) @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK1 ) @ sK3 )
= $true )
| ( ( 'const/realax/real_le' @ ( sK5 @ X1 @ sK1 ) @ X1 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f34,f41]) ).
thf(f41,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( sK5 @ X4 @ X0 ) @ X4 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f53,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f36,f50,f46]) ).
thf(f36,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK1 ) @ sK3 )
!= $true )
| ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/sup' @ sK1 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ANA076^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n011.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 03:49:32 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.42 ---- Original DTF file ---
% 0.17/0.42 thf(spec,logic,$$dhol).
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 % File : ANA076^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.42 % Domain : Analysis
% 0.17/0.42 % Problem : REAL_SUP_BOUNDS
% 0.17/0.42 % Version : Especial.
% 0.17/0.42 % English :
% 0.17/0.42
% 0.17/0.42 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.17/0.42 % Source : [Kal16]
% 0.17/0.42 % Names : REAL_SUP_BOUNDS_.p [Kal16]
% 0.17/0.42
% 0.17/0.42 % Status : Theorem
% 0.17/0.42 % Rating : 0.00 v7.1.0
% 0.17/0.42 % Syntax : Number of formulae : 9 ( 1 unt; 5 typ; 0 def)
% 0.17/0.42 % Number of atoms : 23 ( 4 equ; 0 cnn)
% 0.17/0.42 % Maximal formula atoms : 8 ( 5 avg)
% 0.17/0.42 % Number of connectives : 61 ( 3 ~; 0 |; 6 &; 44 @)
% 0.17/0.42 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.17/0.42 % Maximal formula depth : 11 ( 8 avg)
% 0.17/0.42 % Number of types : 2 ( 1 usr)
% 0.17/0.42 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.17/0.42 % Number of symbols : 5 ( 4 usr; 0 con; 1-3 aty)
% 0.17/0.42 % Number of variables : 18 ( 0 ^; 14 !; 2 ?; 18 :)
% 0.17/0.42 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.42 % SPC : TH1_THM_EQU_NAR
% 0.17/0.42
% 0.17/0.42 % Comments : Exported from core HOL Light.
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 thf('thf_type_type/realax/real',type,
% 0.17/0.42 'type/realax/real': $tType ).
% 0.17/0.42
% 0.17/0.42 thf('thf_const_const/sets/sup',type,
% 0.17/0.42 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.17/0.42
% 0.17/0.42 thf('thf_const_const/sets/IN',type,
% 0.17/0.42 'const/sets/IN':
% 0.17/0.42 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.17/0.42
% 0.17/0.42 thf('thf_const_const/sets/EMPTY',type,
% 0.17/0.42 'const/sets/EMPTY':
% 0.17/0.42 !>[A: $tType] : ( A > $o ) ).
% 0.17/0.42
% 0.17/0.42 thf('thf_const_const/realax/real_le',type,
% 0.17/0.42 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.17/0.42
% 0.17/0.42 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 0.17/0.42 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.17/0.42 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 0.17/0.42 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.17/0.42 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 0.17/0.42
% 0.17/0.42 thf('thm/sets/MEMBER_NOT_EMPTY_',axiom,
% 0.17/0.42 ! [A: $tType,A0: A > $o] :
% 0.17/0.42 ( ( ? [A1: A] : ( 'const/sets/IN' @ A @ A1 @ A0 ) )
% 0.17/0.42 = ( A0
% 0.17/0.42 != ( 'const/sets/EMPTY' @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf('thm/sets/SUP_',axiom,
% 0.17/0.42 ! [A: 'type/realax/real' > $o] :
% 0.17/0.42 ( ( ( A
% 0.17/0.42 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.17/0.42 & ? [A0: 'type/realax/real'] :
% 0.17/0.42 ! [A1: 'type/realax/real'] :
% 0.17/0.42 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.17/0.42 => ( 'const/realax/real_le' @ A1 @ A0 ) ) )
% 0.17/0.42 => ( ! [A0: 'type/realax/real'] :
% 0.17/0.42 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.17/0.42 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) ) )
% 0.17/0.42 & ! [A0: 'type/realax/real'] :
% 0.17/0.42 ( ! [A1: 'type/realax/real'] :
% 0.17/0.42 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.17/0.42 => ( 'const/realax/real_le' @ A1 @ A0 ) )
% 0.17/0.42 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf('thm/sets/REAL_SUP_BOUNDS_',conjecture,
% 0.17/0.42 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.17/0.42 ( ( ( A
% 0.17/0.42 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.17/0.42 & ! [A2: 'type/realax/real'] :
% 0.17/0.42 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 0.17/0.42 => ( ( 'const/realax/real_le' @ A0 @ A2 )
% 0.17/0.42 & ( 'const/realax/real_le' @ A2 @ A1 ) ) ) )
% 0.17/0.42 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) )
% 0.17/0.42 & ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A1 ) ) ) ).
% 0.17/0.42
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 ------------------------
% 1.62/1.40 ---- Embedded in THF ---
% 1.62/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.62/1.40 %%% Generated on Tue Feb 24 03:49:33 EST 2026
% 1.62/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 1.62/1.40 %%% Logic specification used:
% 1.62/1.40 %%% thf(spec, logic, $$dhol).
% 1.62/1.40
% 1.62/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.1jBW8UPP0L/DTF2DTF16287.p
% See solution above
% 1.62/1.40 ------------------------
% 1.62/1.41 ---- Cleaned THF ---
% 1.62/1.41 thf('thf_type_type/realax/real',type,
% 1.62/1.41 'type/realax/real': $tType ).
% 1.62/1.41
% 1.62/1.41 thf('thf_const_const/sets/sup',type,
% 1.62/1.41 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 1.62/1.41
% 1.62/1.41 thf('thf_const_const/sets/IN',type,
% 1.62/1.41 'const/sets/IN':
% 1.62/1.41 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.62/1.41
% 1.62/1.41 thf('thf_const_const/sets/EMPTY',type,
% 1.62/1.41 'const/sets/EMPTY':
% 1.62/1.41 !>[A: $tType] : ( A > $o ) ).
% 1.62/1.41
% 1.62/1.41 thf('thf_const_const/realax/real_le',type,
% 1.62/1.41 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.62/1.41
% 1.62/1.41 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 1.62/1.41 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 1.62/1.41 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 1.62/1.41 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 1.62/1.41 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 1.62/1.41
% 1.62/1.41 thf('thm/sets/MEMBER_NOT_EMPTY_',axiom,
% 1.62/1.41 ! [A: $tType,A0: A > $o] :
% 1.62/1.41 ( ( ? [A1: A] : ( 'const/sets/IN' @ A @ A1 @ A0 ) )
% 1.62/1.41 = ( A0
% 1.62/1.41 != ( 'const/sets/EMPTY' @ A ) ) ) ).
% 1.62/1.41
% 1.62/1.41 thf('thm/sets/SUP_',axiom,
% 1.62/1.41 ! [A: 'type/realax/real' > $o] :
% 1.62/1.41 ( ( ( A
% 1.62/1.41 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.62/1.41 & ? [A0: 'type/realax/real'] :
% 1.62/1.41 ! [A1: 'type/realax/real'] :
% 1.62/1.41 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.62/1.41 => ( 'const/realax/real_le' @ A1 @ A0 ) ) )
% 1.62/1.41 => ( ! [A0: 'type/realax/real'] :
% 1.62/1.41 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 1.62/1.41 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) ) )
% 1.62/1.41 & ! [A0: 'type/realax/real'] :
% 1.62/1.41 ( ! [A1: 'type/realax/real'] :
% 1.62/1.41 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.62/1.41 => ( 'const/realax/real_le' @ A1 @ A0 ) )
% 1.62/1.41 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ) ) ).
% 1.62/1.41
% 1.62/1.41 thf('thm/sets/REAL_SUP_BOUNDS_',conjecture,
% 1.62/1.41 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real',A1: 'type/realax/real'] :
% 1.62/1.41 ( ( ( A
% 1.62/1.41 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.62/1.41 & ! [A2: 'type/realax/real'] :
% 1.62/1.41 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 1.62/1.41 => ( ( 'const/realax/real_le' @ A0 @ A2 )
% 1.62/1.41 & ( 'const/realax/real_le' @ A2 @ A1 ) ) ) )
% 1.62/1.41 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) )
% 1.62/1.41 & ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A1 ) ) ) ).
% 1.62/1.41 ------------------------
% 1.62/1.44 % (16389)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_16287 for (2999ds/275Mi)
% 1.62/1.44 % (16385)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_16287 for (2999ds/4Mi)
% 1.62/1.44 % (16390)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16287 for (2999ds/18Mi)
% 1.62/1.44 % (16384)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16287 for (2999ds/183Mi)
% 1.62/1.44 % (16388)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_16287 for (2999ds/2Mi)
% 1.62/1.44 % (16386)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_16287 for (2999ds/27Mi)
% 1.62/1.44 % (16387)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16287 for (2999ds/2Mi)
% 1.62/1.44 % (16387)Instruction limit reached!
% 1.62/1.44 % (16387)------------------------------
% 1.62/1.44 % (16387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.44 % (16387)Termination reason: Unknown
% 1.62/1.44 % (16387)Termination phase: Preprocessing 3
% 1.62/1.44 % (16388)Instruction limit reached!
% 1.62/1.44 % (16388)------------------------------
% 1.62/1.44 % (16388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.44 % (16388)Termination reason: Unknown
% 1.62/1.44 % (16388)Termination phase: Property scanning
% 1.62/1.44
% 1.62/1.44 % (16388)Memory used [KB]: 1023
% 1.62/1.44 % (16388)Time elapsed: 0.003 s
% 1.62/1.44 % (16388)Instructions burned: 2 (million)
% 1.62/1.44 % (16388)------------------------------
% 1.62/1.44 % (16388)------------------------------
% 1.62/1.44
% 1.62/1.44 % (16387)Memory used [KB]: 895
% 1.62/1.44 % (16387)Time elapsed: 0.003 s
% 1.62/1.44 % (16387)Instructions burned: 2 (million)
% 1.62/1.44 % (16387)------------------------------
% 1.62/1.44 % (16387)------------------------------
% 1.62/1.44 % (16385)Instruction limit reached!
% 1.62/1.44 % (16385)------------------------------
% 1.62/1.44 % (16385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.44 % (16385)Termination reason: Unknown
% 1.62/1.44 % (16385)Termination phase: Saturation
% 1.62/1.44
% 1.62/1.44 % (16385)Memory used [KB]: 5500
% 1.62/1.44 % (16385)Time elapsed: 0.005 s
% 1.62/1.44 % (16385)Instructions burned: 5 (million)
% 1.62/1.44 % (16385)------------------------------
% 1.62/1.44 % (16385)------------------------------
% 1.62/1.45 % (16390)Instruction limit reached!
% 1.62/1.45 % (16390)------------------------------
% 1.62/1.45 % (16390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.45 % (16390)Termination reason: Unknown
% 1.62/1.45 % (16390)Termination phase: Saturation
% 1.62/1.45
% 1.62/1.45 % (16390)Memory used [KB]: 5628
% 1.62/1.45 % (16390)Time elapsed: 0.012 s
% 1.62/1.45 % (16390)Instructions burned: 18 (million)
% 1.62/1.45 % (16390)------------------------------
% 1.62/1.45 % (16390)------------------------------
% 1.62/1.45 % (16386)Instruction limit reached!
% 1.62/1.45 % (16386)------------------------------
% 1.62/1.45 % (16386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.45 % (16386)Termination reason: Unknown
% 1.62/1.45 % (16386)Termination phase: Saturation
% 1.62/1.45
% 1.62/1.45 % (16386)Memory used [KB]: 5756
% 1.62/1.45 % (16386)Time elapsed: 0.017 s
% 1.62/1.45 % (16386)Instructions burned: 27 (million)
% 1.62/1.45 % (16386)------------------------------
% 1.62/1.45 % (16386)------------------------------
% 1.62/1.45 % (16392)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_16287 for (2999ds/37Mi)
% 1.62/1.45 % (16391)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16287 for (2999ds/3Mi)
% 1.62/1.45 % (16391)Instruction limit reached!
% 1.62/1.45 % (16391)------------------------------
% 1.62/1.45 % (16391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.45 % (16391)Termination reason: Unknown
% 1.62/1.45 % (16391)Termination phase: Saturation
% 1.62/1.45
% 1.62/1.45 % (16391)Memory used [KB]: 1023
% 1.62/1.45 % (16391)Time elapsed: 0.003 s
% 1.62/1.45 % (16391)Instructions burned: 3 (million)
% 1.62/1.45 % (16391)------------------------------
% 1.62/1.45 % (16391)------------------------------
% 1.62/1.45 % (16393)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_16287 for (2999ds/15Mi)
% 1.62/1.45 % (16389)First to succeed.
% 1.62/1.46 % (16389)Refutation found. Thanks to Tanya!
% 1.62/1.46 % SZS status Theorem for DTF2THF_16287
% 1.62/1.46 % SZS output start Proof for DTF2THF_16287
% 1.62/1.46 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.62/1.46 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.62/1.46 thf(func_def_1, type, 'const/sets/sup': ('type/realax/real' > $o) > 'type/realax/real').
% 1.62/1.46 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.62/1.46 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.62/1.46 thf(func_def_4, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.62/1.46 thf(func_def_8, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.62/1.46 thf(func_def_9, type, sK1: 'type/realax/real' > $o).
% 1.62/1.46 thf(func_def_10, type, sK2: 'type/realax/real').
% 1.62/1.46 thf(func_def_11, type, sK3: 'type/realax/real').
% 1.62/1.46 thf(func_def_12, type, sK4: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.62/1.46 thf(func_def_13, type, sK5: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.62/1.46 thf(func_def_15, type, ph7: !>[X0: $tType]:(X0)).
% 1.62/1.46 thf(func_def_16, type, sK8: 'type/realax/real').
% 1.62/1.46 thf(f223,plain,(
% 1.62/1.46 $false),
% 1.62/1.46 inference(avatar_sat_refutation,[status(thm)],[f53,f94,f102,f107,f113,f142,f170,f182,f188,f190,f222])).
% 1.62/1.46 thf(f222,plain,(
% 1.62/1.46 spl6_8 | ~spl6_9),
% 1.62/1.46 inference(avatar_split_clause,[status(thm)],[f221,f97,f92])).
% 1.62/1.46 thf(f92,definition,(
% 1.62/1.46 spl6_8 <=> ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK3) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0) = $true))),
% 1.62/1.46 introduced(definition,[new_symbols(naming,[spl6_8])],[avatar_definition])).
% 1.62/1.46 thf(f97,definition,(
% 1.62/1.46 spl6_9 <=> ! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1) = $true))),
% 1.62/1.46 introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition])).
% 1.62/1.46 thf(f221,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0) = $true) | (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK3) = $true)) ) | ~spl6_9),
% 1.62/1.46 inference(trivial_inequality_removal,[status(thm)],[f219])).
% 1.62/1.46 thf(f219,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : (($true != $true) | (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK3) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0) = $true)) ) | ~spl6_9),
% 1.62/1.46 inference(superposition,[status(thm)],[f34,f98])).
% 1.62/1.46 thf(f98,plain,(
% 1.62/1.46 ( ! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1) = $true)) ) | ~spl6_9),
% 1.62/1.46 inference(avatar_component_clause,[status(thm)],[f97])).
% 1.62/1.46 thf(f34,plain,(
% 1.62/1.46 ( ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1) != $true) | (('const/realax/real_le' @ X3 @ sK3) = $true)) )),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f26])).
% 1.62/1.46 thf(f26,plain,(
% 1.62/1.46 ('const/sets/EMPTY' @ 'type/realax/real' != sK1) & ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK3) != $true) | (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK1)) != $true)) & ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1) != $true) | ((('const/realax/real_le' @ sK2 @ X3) = $true) & (('const/realax/real_le' @ X3 @ sK3) = $true)))),
% 1.62/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f16,f25])).
% 1.62/1.46 thf(f25,plain,(
% 1.62/1.46 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : (('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)) & ! [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' != sK1) & ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK3) != $true) | (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK1)) != $true)) & ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1) != $true) | ((('const/realax/real_le' @ sK2 @ X3) = $true) & (('const/realax/real_le' @ X3 @ sK3) = $true))))),
% 1.62/1.46 introduced(definition,[],[choice_axiom])).
% 1.62/1.46 thf(f16,plain,(
% 1.62/1.46 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : (('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)) & ! [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))))),
% 1.62/1.46 inference(flattening,[status(thm)],[f15])).
% 1.62/1.46 thf(f15,plain,(
% 1.62/1.46 ? [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' @ X1 @ X3) = $true) & (('const/realax/real_le' @ X3 @ X2) = $true))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)))),
% 1.62/1.46 inference(ennf_transformation,[status(thm)],[f10])).
% 1.62/1.46 thf(f10,plain,(
% 1.62/1.46 ~! [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)))),
% 1.62/1.46 inference(fool_elimination,[status(thm)],[f9])).
% 1.62/1.46 thf(f9,plain,(
% 1.62/1.46 ~! [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) => (('const/realax/real_le' @ X1 @ X3) & ('const/realax/real_le' @ X3 @ X2)))) => (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))))),
% 1.62/1.46 inference(rectify,[status(thm)],[f5])).
% 1.62/1.46 thf(f5,negated_conjecture,(
% 1.62/1.46 ~! [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) => (('const/realax/real_le' @ X1 @ X3) & ('const/realax/real_le' @ X3 @ X2)))) => (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))))),
% 1.62/1.46 inference(negated_conjecture,[status(cth)],[f4])).
% 1.62/1.46 thf(f4,conjecture,(
% 1.62/1.46 ! [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) => (('const/realax/real_le' @ X1 @ X3) & ('const/realax/real_le' @ X3 @ X2)))) => (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))))),
% 1.62/1.46 file('/export/starexec/sandbox2/tmp/tmp.1jBW8UPP0L/DTF2THF_16287.p','thm/sets/REAL_SUP_BOUNDS_')).
% 1.62/1.46 thf(f190,plain,(
% 1.62/1.46 spl6_12 | ~spl6_10),
% 1.62/1.46 inference(avatar_split_clause,[status(thm)],[f189,f100,f111])).
% 1.62/1.46 thf(f111,definition,(
% 1.62/1.46 spl6_12 <=> ! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1) = $true) | (('const/realax/real_le' @ (sK4 @ X1 @ sK1) @ X1) != $true))),
% 1.62/1.46 introduced(definition,[new_symbols(naming,[spl6_12])],[avatar_definition])).
% 1.62/1.46 thf(f100,definition,(
% 1.62/1.46 spl6_10 <=> ! [X0 : 'type/realax/real'] : (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK3) = $true)),
% 1.62/1.46 introduced(definition,[new_symbols(naming,[spl6_10])],[avatar_definition])).
% 1.62/1.46 thf(f189,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ X0) != $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0) = $true)) ) | ~spl6_10),
% 1.62/1.46 inference(subsumption_resolution,[status(thm)],[f185,f37])).
% 1.62/1.46 thf(f37,plain,(
% 1.62/1.46 ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f26])).
% 1.62/1.46 thf(f185,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0) = $true) | (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | ~spl6_10),
% 1.62/1.46 inference(trivial_inequality_removal,[status(thm)],[f183])).
% 1.62/1.46 thf(f183,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ X0) != $true) | ($true != $true)) ) | ~spl6_10),
% 1.62/1.46 inference(superposition,[status(thm)],[f39,f101])).
% 1.62/1.46 thf(f101,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK3) = $true)) ) | ~spl6_10),
% 1.62/1.46 inference(avatar_component_clause,[status(thm)],[f100])).
% 1.62/1.46 thf(f39,plain,(
% 1.62/1.46 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK5 @ X4 @ X0) @ X4) != $true) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ (sK4 @ X2 @ X0) @ X2) != $true)) )),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f30])).
% 1.62/1.46 thf(f30,plain,(
% 1.62/1.46 ! [X0 : 'type/realax/real' > $o] : ((! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true)) & ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X2 @ X0) @ X0) = $true) & (('const/realax/real_le' @ (sK4 @ X2 @ X0) @ X2) != $true)) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) = $true))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X4 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK5 @ X4 @ X0) @ X4) != $true) & (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0) = $true)))),
% 1.62/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f27,f29,f28])).
% 1.62/1.46 thf(f28,plain,(
% 1.62/1.46 ! [X0 : 'type/realax/real' > $o,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/sets/IN' @ 'type/realax/real' @ (sK4 @ X2 @ X0) @ X0) = $true) & (('const/realax/real_le' @ (sK4 @ X2 @ X0) @ X2) != $true)))),
% 1.62/1.46 introduced(definition,[],[choice_axiom])).
% 1.62/1.46 thf(f29,plain,(
% 1.62/1.46 ! [X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : ((('const/realax/real_le' @ X5 @ X4) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true)) => ((('const/realax/real_le' @ (sK5 @ X4 @ X0) @ X4) != $true) & (('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0) = $true)))),
% 1.62/1.46 introduced(definition,[],[choice_axiom])).
% 1.62/1.46 thf(f27,plain,(
% 1.62/1.46 ! [X0 : 'type/realax/real' > $o] : ((! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true)) & ! [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' @ ('const/sets/sup' @ X0) @ X2) = $true))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X4 : 'type/realax/real'] : ? [X5 : 'type/realax/real'] : ((('const/realax/real_le' @ X5 @ X4) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true)))),
% 1.62/1.46 inference(rectify,[status(thm)],[f18])).
% 1.62/1.46 thf(f18,plain,(
% 1.62/1.46 ! [X0 : 'type/realax/real' > $o] : ((! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) != $true) | (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)) = $true)) & ! [X3 : 'type/realax/real'] : (? [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) = $true) & (('const/realax/real_le' @ X4 @ X3) != $true)) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3) = $true))) | ('const/sets/EMPTY' @ 'type/realax/real' = 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)))),
% 1.62/1.46 inference(flattening,[status(thm)],[f17])).
% 1.62/1.46 thf(f17,plain,(
% 1.62/1.46 ! [X0 : 'type/realax/real' > $o] : ((! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) != $true) | (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)) = $true)) & ! [X3 : 'type/realax/real'] : (? [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) = $true) & (('const/realax/real_le' @ X4 @ X3) != $true)) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3) = $true))) | (('const/sets/EMPTY' @ 'type/realax/real' = 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))))),
% 1.62/1.46 inference(ennf_transformation,[status(thm)],[f8])).
% 1.62/1.46 thf(f8,plain,(
% 1.62/1.46 ! [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) = $true) => (('const/realax/real_le' @ X2 @ X1) = $true))) => (! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) => (('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0)) = $true)) & ! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) = $true) => (('const/realax/real_le' @ X4 @ X3) = $true)) => (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3) = $true))))),
% 1.62/1.46 inference(fool_elimination,[status(thm)],[f7])).
% 1.62/1.46 thf(f7,plain,(
% 1.62/1.46 ! [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)))))),
% 1.62/1.46 inference(rectify,[status(thm)],[f3])).
% 1.62/1.46 thf(f3,axiom,(
% 1.62/1.46 ! [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)))))),
% 1.62/1.46 file('/export/starexec/sandbox2/tmp/tmp.1jBW8UPP0L/DTF2THF_16287.p','thm/sets/SUP_')).
% 1.62/1.46 thf(f188,plain,(
% 1.62/1.46 spl6_11 | ~spl6_10),
% 1.62/1.46 inference(avatar_split_clause,[status(thm)],[f187,f100,f105])).
% 1.62/1.46 thf(f105,definition,(
% 1.62/1.46 spl6_11 <=> ! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1)) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1) != $true))),
% 1.62/1.46 introduced(definition,[new_symbols(naming,[spl6_11])],[avatar_definition])).
% 1.62/1.46 thf(f187,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1) != $true) | (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1)) = $true)) ) | ~spl6_10),
% 1.62/1.46 inference(subsumption_resolution,[status(thm)],[f186,f37])).
% 1.62/1.46 thf(f186,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1)) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1) != $true)) ) | ~spl6_10),
% 1.62/1.46 inference(trivial_inequality_removal,[status(thm)],[f184])).
% 1.62/1.46 thf(f184,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : (($true != $true) | (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1)) = $true)) ) | ~spl6_10),
% 1.62/1.46 inference(superposition,[status(thm)],[f43,f101])).
% 1.62/1.46 thf(f43,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X4 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK5 @ X4 @ X0) @ X4) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true)) )),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f30])).
% 1.62/1.46 thf(f182,plain,(
% 1.62/1.46 spl6_1 | ~spl6_11),
% 1.62/1.46 inference(avatar_contradiction_clause,[status(thm)],[f181])).
% 1.62/1.46 thf(f181,plain,(
% 1.62/1.46 $false | (spl6_1 | ~spl6_11)),
% 1.62/1.46 inference(subsumption_resolution,[status(thm)],[f180,f37])).
% 1.62/1.46 thf(f180,plain,(
% 1.62/1.46 ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (spl6_1 | ~spl6_11)),
% 1.62/1.46 inference(trivial_inequality_removal,[status(thm)],[f175])).
% 1.62/1.46 thf(f175,plain,(
% 1.62/1.46 ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != $true) | (spl6_1 | ~spl6_11)),
% 1.62/1.46 inference(superposition,[status(thm)],[f162,f32])).
% 1.62/1.46 thf(f32,plain,(
% 1.62/1.46 ( ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ (sK0 @ X0 @ X1) @ X1) = $true) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f24])).
% 1.62/1.46 thf(f24,plain,(
% 1.62/1.46 ! [X0 : $tType,X1 : X0 > $o] : (((('const/sets/IN' @ X0 @ (sK0 @ X0 @ X1) @ X1) = $true) | ('const/sets/EMPTY' @ X0 = X1)) & (('const/sets/EMPTY' @ X0 != X1) | ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) != $true)))),
% 1.62/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f23])).
% 1.62/1.46 thf(f23,plain,(
% 1.62/1.46 ! [X0 : $tType,X1 : X0 > $o] : (? [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = $true) => (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X1) @ X1) = $true))),
% 1.62/1.46 introduced(definition,[],[choice_axiom])).
% 1.62/1.46 thf(f22,plain,(
% 1.62/1.46 ! [X0 : $tType,X1 : X0 > $o] : ((? [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = $true) | ('const/sets/EMPTY' @ X0 = X1)) & (('const/sets/EMPTY' @ X0 != X1) | ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) != $true)))),
% 1.62/1.46 inference(rectify,[status(thm)],[f21])).
% 1.62/1.46 thf(f21,plain,(
% 1.62/1.46 ! [X0 : $tType,X1 : X0 > $o] : ((? [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = $true) | ('const/sets/EMPTY' @ X0 = X1)) & (('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) != $true)))),
% 1.62/1.46 inference(nnf_transformation,[status(thm)],[f12])).
% 1.62/1.46 thf(f12,plain,(
% 1.62/1.46 ! [X0 : $tType,X1 : X0 > $o] : (? [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = $true) <=> ('const/sets/EMPTY' @ X0 != X1))),
% 1.62/1.46 inference(fool_elimination,[status(thm)],[f11])).
% 1.62/1.46 thf(f11,plain,(
% 1.62/1.46 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/EMPTY' @ X0 != X1) = ? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1))),
% 1.62/1.46 inference(rectify,[status(thm)],[f2])).
% 1.62/1.46 thf(f2,axiom,(
% 1.62/1.46 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/EMPTY' @ X0 != X1) = ? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1))),
% 1.62/1.46 file('/export/starexec/sandbox2/tmp/tmp.1jBW8UPP0L/DTF2THF_16287.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 1.62/1.46 thf(f162,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1) != $true)) ) | (spl6_1 | ~spl6_11)),
% 1.62/1.46 inference(subsumption_resolution,[status(thm)],[f158,f35])).
% 1.62/1.46 thf(f35,plain,(
% 1.62/1.46 ( ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1) != $true) | (('const/realax/real_le' @ sK2 @ X3) = $true)) )),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f26])).
% 1.62/1.46 thf(f158,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ sK2 @ X0) != $true) | (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1) != $true)) ) | (spl6_1 | ~spl6_11)),
% 1.62/1.46 inference(trivial_inequality_removal,[status(thm)],[f153])).
% 1.62/1.46 thf(f153,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ sK2 @ X0) != $true) | ($true != $true) | (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1) != $true)) ) | (spl6_1 | ~spl6_11)),
% 1.62/1.46 inference(superposition,[status(thm)],[f76,f106])).
% 1.62/1.46 thf(f106,plain,(
% 1.62/1.46 ( ! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1)) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1) != $true)) ) | ~spl6_11),
% 1.62/1.46 inference(avatar_component_clause,[status(thm)],[f105])).
% 1.62/1.46 thf(f76,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1)) != $true) | (('const/realax/real_le' @ sK2 @ X0) != $true)) ) | spl6_1),
% 1.62/1.46 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.62/1.46 thf(f75,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK1)) != $true) | ($true != $true) | (('const/realax/real_le' @ sK2 @ X0) != $true)) ) | spl6_1),
% 1.62/1.46 inference(superposition,[status(thm)],[f48,f33])).
% 1.62/1.46 thf(f33,plain,(
% 1.62/1.46 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X2) = $true) | (('const/realax/real_le' @ X1 @ X2) != $true) | (('const/realax/real_le' @ X0 @ X1) != $true)) )),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f20])).
% 1.62/1.46 thf(f20,plain,(
% 1.62/1.46 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) != $true) | (('const/realax/real_le' @ X0 @ X2) = $true) | (('const/realax/real_le' @ X0 @ X1) != $true))),
% 1.62/1.46 inference(flattening,[status(thm)],[f19])).
% 1.62/1.46 thf(f19,plain,(
% 1.62/1.46 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X2) = $true) | ((('const/realax/real_le' @ X1 @ X2) != $true) | (('const/realax/real_le' @ X0 @ X1) != $true)))),
% 1.62/1.46 inference(ennf_transformation,[status(thm)],[f14])).
% 1.62/1.46 thf(f14,plain,(
% 1.62/1.46 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2) = $true) & (('const/realax/real_le' @ X0 @ X1) = $true)) => (('const/realax/real_le' @ X0 @ X2) = $true))),
% 1.62/1.46 inference(fool_elimination,[status(thm)],[f13])).
% 1.62/1.46 thf(f13,plain,(
% 1.62/1.46 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X0 @ X2))),
% 1.62/1.46 inference(rectify,[status(thm)],[f1])).
% 1.62/1.46 thf(f1,axiom,(
% 1.62/1.46 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X0 @ X2))),
% 1.62/1.46 file('/export/starexec/sandbox2/tmp/tmp.1jBW8UPP0L/DTF2THF_16287.p','thm/realax/REAL_LE_TRANS_')).
% 1.62/1.46 thf(f48,plain,(
% 1.62/1.46 (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK1)) != $true) | spl6_1),
% 1.62/1.46 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.62/1.46 thf(f46,definition,(
% 1.62/1.46 spl6_1 <=> (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK1)) = $true)),
% 1.62/1.46 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.62/1.46 thf(f170,plain,(
% 1.62/1.46 spl6_2 | ~spl6_8 | ~spl6_12),
% 1.62/1.46 inference(avatar_split_clause,[status(thm)],[f167,f111,f92,f50])).
% 1.62/1.46 thf(f50,definition,(
% 1.62/1.46 spl6_2 <=> (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK3) = $true)),
% 1.62/1.46 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.62/1.46 thf(f167,plain,(
% 1.62/1.46 (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK3) = $true) | (~spl6_8 | ~spl6_12)),
% 1.62/1.46 inference(trivial_inequality_removal,[status(thm)],[f166])).
% 1.62/1.46 thf(f166,plain,(
% 1.62/1.46 ($true != $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK3) = $true) | (~spl6_8 | ~spl6_12)),
% 1.62/1.46 inference(duplicate_literal_removal,[status(thm)],[f164])).
% 1.62/1.46 thf(f164,plain,(
% 1.62/1.46 ($true != $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK3) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK3) = $true) | (~spl6_8 | ~spl6_12)),
% 1.62/1.46 inference(superposition,[status(thm)],[f112,f93])).
% 1.62/1.46 thf(f93,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK3) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0) = $true)) ) | ~spl6_8),
% 1.62/1.46 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.62/1.46 thf(f112,plain,(
% 1.62/1.46 ( ! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK4 @ X1 @ sK1) @ X1) != $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1) = $true)) ) | ~spl6_12),
% 1.62/1.46 inference(avatar_component_clause,[status(thm)],[f111])).
% 1.62/1.46 thf(f142,plain,(
% 1.62/1.46 ~spl6_7 | ~spl6_10),
% 1.62/1.46 inference(avatar_contradiction_clause,[status(thm)],[f141])).
% 1.62/1.46 thf(f141,plain,(
% 1.62/1.46 $false | (~spl6_7 | ~spl6_10)),
% 1.62/1.46 inference(trivial_inequality_removal,[status(thm)],[f138])).
% 1.62/1.46 thf(f138,plain,(
% 1.62/1.46 ($true != $true) | (~spl6_7 | ~spl6_10)),
% 1.62/1.46 inference(superposition,[status(thm)],[f90,f101])).
% 1.62/1.46 thf(f90,plain,(
% 1.62/1.46 ( ! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK5 @ X1 @ sK1) @ X1) != $true)) ) | ~spl6_7),
% 1.62/1.46 inference(avatar_component_clause,[status(thm)],[f89])).
% 1.62/1.46 thf(f89,definition,(
% 1.62/1.46 spl6_7 <=> ! [X1 : 'type/realax/real'] : (('const/realax/real_le' @ (sK5 @ X1 @ sK1) @ X1) != $true)),
% 1.62/1.46 introduced(definition,[new_symbols(naming,[spl6_7])],[avatar_definition])).
% 1.62/1.46 thf(f113,plain,(
% 1.62/1.46 spl6_12 | spl6_10),
% 1.62/1.46 inference(avatar_split_clause,[status(thm)],[f109,f100,f111])).
% 1.62/1.46 thf(f109,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1) = $true) | (('const/realax/real_le' @ (sK4 @ X1 @ sK1) @ X1) != $true) | (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK3) = $true)) )),
% 1.62/1.46 inference(subsumption_resolution,[status(thm)],[f82,f37])).
% 1.62/1.46 thf(f82,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK4 @ X1 @ sK1) @ X1) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK3) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1) = $true)) )),
% 1.62/1.46 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.62/1.46 thf(f77,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1) = $true) | (('const/realax/real_le' @ (sK4 @ X1 @ sK1) @ X1) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != $true) | (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK3) = $true)) )),
% 1.62/1.46 inference(superposition,[status(thm)],[f34,f38])).
% 1.62/1.46 thf(f38,plain,(
% 1.62/1.46 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ (sK4 @ X2 @ X0) @ X2) != $true) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) = $true)) )),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f30])).
% 1.62/1.46 thf(f107,plain,(
% 1.62/1.46 spl6_10 | spl6_11),
% 1.62/1.46 inference(avatar_split_clause,[status(thm)],[f103,f105,f100])).
% 1.62/1.46 thf(f103,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK3) = $true) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1)) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1) != $true)) )),
% 1.62/1.46 inference(subsumption_resolution,[status(thm)],[f84,f37])).
% 1.62/1.46 thf(f84,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1) != $true) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK3) = $true)) )),
% 1.62/1.46 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.62/1.46 thf(f78,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK3) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1) != $true)) )),
% 1.62/1.46 inference(superposition,[status(thm)],[f34,f42])).
% 1.62/1.46 thf(f42,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true)) )),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f30])).
% 1.62/1.46 thf(f102,plain,(
% 1.62/1.46 spl6_9 | spl6_10),
% 1.62/1.46 inference(avatar_split_clause,[status(thm)],[f95,f100,f97])).
% 1.62/1.46 thf(f95,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK3) = $true) | (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1) = $true)) )),
% 1.62/1.46 inference(subsumption_resolution,[status(thm)],[f85,f37])).
% 1.62/1.46 thf(f85,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1) = $true) | (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK3) = $true) | (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 1.62/1.46 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.62/1.46 thf(f79,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ (sK5 @ X0 @ sK1) @ sK3) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1) = $true) | ($true != $true)) )),
% 1.62/1.46 inference(superposition,[status(thm)],[f34,f40])).
% 1.62/1.46 thf(f40,plain,(
% 1.62/1.46 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X2 @ X0) @ X0) = $true)) )),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f30])).
% 1.62/1.46 thf(f94,plain,(
% 1.62/1.46 spl6_7 | spl6_8),
% 1.62/1.46 inference(avatar_split_clause,[status(thm)],[f87,f92,f89])).
% 1.62/1.46 thf(f87,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK5 @ X1 @ sK1) @ X1) != $true) | (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK3) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0) = $true)) )),
% 1.62/1.46 inference(subsumption_resolution,[status(thm)],[f86,f37])).
% 1.62/1.46 thf(f86,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0) = $true) | (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK3) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ (sK5 @ X1 @ sK1) @ X1) != $true)) )),
% 1.62/1.46 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.62/1.46 thf(f80,plain,(
% 1.62/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | (('const/realax/real_le' @ (sK4 @ X0 @ sK1) @ sK3) = $true) | (('const/realax/real_le' @ (sK5 @ X1 @ sK1) @ X1) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ X0) = $true)) )),
% 1.62/1.46 inference(superposition,[status(thm)],[f34,f41])).
% 1.62/1.46 thf(f41,plain,(
% 1.62/1.46 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X2 @ X0) @ X0) = $true) | (('const/realax/real_le' @ (sK5 @ X4 @ X0) @ X4) != $true) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X2) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f30])).
% 1.62/1.46 thf(f53,plain,(
% 1.62/1.46 ~spl6_1 | ~spl6_2),
% 1.62/1.46 inference(avatar_split_clause,[status(thm)],[f36,f50,f46])).
% 1.62/1.46 thf(f36,plain,(
% 1.62/1.46 (('const/realax/real_le' @ ('const/sets/sup' @ sK1) @ sK3) != $true) | (('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK1)) != $true)),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f26])).
% 1.62/1.46 % SZS output end Proof for DTF2THF_16287
% 1.62/1.46 % (16389)------------------------------
% 1.62/1.46 % (16389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.46 % (16389)Termination reason: Refutation
% 1.62/1.46
% 1.62/1.46 % (16389)Memory used [KB]: 5756
% 1.62/1.46 % (16389)Time elapsed: 0.024 s
% 1.62/1.46 % (16389)Instructions burned: 36 (million)
% 1.62/1.46 % (16389)------------------------------
% 1.62/1.46 % (16389)------------------------------
% 1.62/1.46 % (16383)Success in time 0.037 s
%------------------------------------------------------------------------------