%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA088^1 : 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 08:38:50 AM UTC 2026
% Result : Theorem 1.67s 1.35s
% Output : Refutation 1.67s
% 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 : 963 ( 262 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 1202 ( 157 ~; 178 |; 52 &; 776 @)
% ( 9 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 13 con; 0-3 aty)
% Number of variables : 183 ( 0 ^; 159 !; 24 ?; 183 :)
% 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/inf': ( '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: 'type/realax/real' > $o ).
thf(func_def_9,type,
sK1: 'type/realax/real' ).
thf(func_def_10,type,
sK2: 'type/realax/real' ).
thf(func_def_11,type,
sK3:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
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(f235,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f52,f132,f134,f139,f141,f150,f175,f214,f226,f228,f234]) ).
thf(f234,plain,
( spl6_11
| ~ spl6_14 ),
inference(avatar_split_clause,[status(thm)],[f233,f137,f109]) ).
thf(f109,definition,
( spl6_11
<=> ! [X1: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_11])],[avatar_definition]) ).
thf(f137,definition,
( spl6_14
<=> ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK4 @ X0 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_14])],[avatar_definition]) ).
thf(f233,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ X0 )
= $true ) )
| ~ spl6_14 ),
inference(subsumption_resolution,[status(thm)],[f232,f33]) ).
thf(f33,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ( ( $true
!= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK2 ) ) )
& ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 ) )
| ( ( $true
= ( 'const/realax/real_le' @ sK1 @ X3 ) )
& ( $true
= ( 'const/realax/real_le' @ X3 @ sK2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f21]) ).
thf(f21,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' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
!= $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' != sK0 ) )
& ( ( $true
!= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK2 ) ) )
& ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 ) )
| ( ( $true
= ( 'const/realax/real_le' @ sK1 @ X3 ) )
& ( $true
= ( 'const/realax/real_le' @ X3 @ sK2 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,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' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
!= $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)],[f19]) ).
thf(f19,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
!= $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)],[f14]) ).
thf(f14,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' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,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' @ X3 @ X2 )
& ( 'const/realax/real_le' @ X1 @ X3 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
& ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [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' @ X3 @ X2 )
& ( 'const/realax/real_le' @ X1 @ X3 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
& ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [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' @ X3 @ X2 )
& ( 'const/realax/real_le' @ X1 @ X3 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
& ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3rFaraA8p9/DTF2THF_19014.p','thm/sets/REAL_INF_BOUNDS_') ).
thf(f232,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ X0 )
= $true ) )
| ~ spl6_14 ),
inference(trivial_inequality_removal,[status(thm)],[f231]) ).
thf(f231,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ X0 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) ) )
| ~ spl6_14 ),
inference(superposition,[status(thm)],[f38,f138]) ).
thf(f138,plain,
( ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK4 @ X0 @ sK0 ) ) )
| ~ spl6_14 ),
inference(avatar_component_clause,[status(thm)],[f137]) ).
thf(f38,plain,
! [X3: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: 'type/realax/real' > $o] :
( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ X0 ) ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) )
& ! [X4: 'type/realax/real'] :
( ( ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f16,f28,f27]) ).
thf(f27,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
! [X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) )
=> ( ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o] :
( ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) )
& ! [X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) )
& ! [X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: 'type/realax/real' > $o] :
( ( ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) ) )
& ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
=> ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) )
=> ( $true
= ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) ) ) ),
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' @ X1 @ X2 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) )
& ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
=> ( 'const/realax/real_le' @ X4 @ X5 ) )
=> ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ 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' @ X1 @ X2 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) )
& ! [X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3rFaraA8p9/DTF2THF_19014.p','thm/sets/INF_') ).
thf(f228,plain,
( spl6_2
| spl6_12
| ~ spl6_13 ),
inference(avatar_split_clause,[status(thm)],[f227,f130,f114,f49]) ).
thf(f49,definition,
( spl6_2
<=> ( $true
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f114,definition,
( spl6_12
<=> ! [X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK0 ) )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_12])],[avatar_definition]) ).
thf(f130,definition,
( spl6_13
<=> ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK5 @ X0 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_13])],[avatar_definition]) ).
thf(f227,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK4 @ X0 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) )
| ~ spl6_13 ),
inference(subsumption_resolution,[status(thm)],[f221,f33]) ).
thf(f221,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK4 @ X0 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) )
| ~ spl6_13 ),
inference(trivial_inequality_removal,[status(thm)],[f220]) ).
thf(f220,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK4 @ X0 @ sK0 ) ) ) )
| ~ spl6_13 ),
inference(duplicate_literal_removal,[status(thm)],[f218]) ).
thf(f218,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK4 @ X0 @ sK0 ) ) ) )
| ~ spl6_13 ),
inference(superposition,[status(thm)],[f37,f131]) ).
thf(f131,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK5 @ X0 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) ) ) )
| ~ spl6_13 ),
inference(avatar_component_clause,[status(thm)],[f130]) ).
thf(f37,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f226,plain,
( spl6_2
| ~ spl6_9
| ~ spl6_13 ),
inference(avatar_split_clause,[status(thm)],[f223,f130,f101,f49]) ).
thf(f101,definition,
( spl6_9
<=> ! [X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition]) ).
thf(f223,plain,
( ( $true
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ~ spl6_9
| ~ spl6_13 ),
inference(trivial_inequality_removal,[status(thm)],[f222]) ).
thf(f222,plain,
( ( $true
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( $true != $true )
| ~ spl6_9
| ~ spl6_13 ),
inference(duplicate_literal_removal,[status(thm)],[f219]) ).
thf(f219,plain,
( ( $true
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ~ spl6_9
| ~ spl6_13 ),
inference(superposition,[status(thm)],[f102,f131]) ).
thf(f102,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) ) )
| ~ spl6_9 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f214,plain,
( ~ spl6_12
| ~ spl6_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f213]) ).
thf(f213,plain,
( $false
| ~ spl6_12
| ~ spl6_14 ),
inference(trivial_inequality_removal,[status(thm)],[f210]) ).
thf(f210,plain,
( ( $true != $true )
| ~ spl6_12
| ~ spl6_14 ),
inference(superposition,[status(thm)],[f115,f138]) ).
thf(f115,plain,
( ! [X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK0 ) )
!= $true )
| ~ spl6_12 ),
inference(avatar_component_clause,[status(thm)],[f114]) ).
thf(f175,plain,
( spl6_1
| ~ spl6_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f174]) ).
thf(f174,plain,
( $false
| spl6_1
| ~ spl6_11 ),
inference(subsumption_resolution,[status(thm)],[f170,f33]) ).
thf(f170,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| spl6_1
| ~ spl6_11 ),
inference(trivial_inequality_removal,[status(thm)],[f166]) ).
thf(f166,plain,
( ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| spl6_1
| ~ spl6_11 ),
inference(superposition,[status(thm)],[f161,f34]) ).
thf(f34,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) )
& ( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f24,f25]) ).
thf(f25,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X3: X0] :
( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
=> ( $true
= ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 ) @ X1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) )
& ( ? [X3: X0] :
( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) )
& ( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
<=> ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o] :
? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o] :
? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3rFaraA8p9/DTF2THF_19014.p','thm/sets/MEMBER_NOT_EMPTY_') ).
thf(f161,plain,
( ! [X0: 'type/realax/real'] :
( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| spl6_1
| ~ spl6_11 ),
inference(subsumption_resolution,[status(thm)],[f159,f30]) ).
thf(f30,plain,
! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X3 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f159,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK2 ) ) )
| spl6_1
| ~ spl6_11 ),
inference(trivial_inequality_removal,[status(thm)],[f152]) ).
thf(f152,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK2 ) ) )
| spl6_1
| ~ spl6_11 ),
inference(superposition,[status(thm)],[f79,f110]) ).
thf(f110,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) ) )
| ~ spl6_11 ),
inference(avatar_component_clause,[status(thm)],[f109]) ).
thf(f79,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ X0 )
!= $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK2 ) ) )
| spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ X0 )
!= $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK2 ) )
| ( $true != $true ) )
| spl6_1 ),
inference(superposition,[status(thm)],[f47,f42]) ).
thf(f42,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,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(flattening,[status(thm)],[f17]) ).
thf(f17,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)],[f10]) ).
thf(f10,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)],[f9]) ).
thf(f9,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.3rFaraA8p9/DTF2THF_19014.p','thm/realax/REAL_LE_TRANS_') ).
thf(f47,plain,
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK2 ) )
| spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl6_1
<=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f150,plain,
( spl6_14
| ~ spl6_8 ),
inference(avatar_split_clause,[status(thm)],[f149,f95,f137]) ).
thf(f95,definition,
( spl6_8
<=> ! [X1: 'type/realax/real'] :
( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK0 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_8])],[avatar_definition]) ).
thf(f149,plain,
( ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK4 @ X0 @ sK0 ) ) )
| ~ spl6_8 ),
inference(trivial_inequality_removal,[status(thm)],[f146]) ).
thf(f146,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK4 @ X0 @ sK0 ) ) ) )
| ~ spl6_8 ),
inference(superposition,[status(thm)],[f31,f96]) ).
thf(f96,plain,
( ! [X1: 'type/realax/real'] :
( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK0 ) @ sK0 ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[status(thm)],[f95]) ).
thf(f31,plain,
! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f141,plain,
( spl6_9
| spl6_14 ),
inference(avatar_split_clause,[status(thm)],[f140,f137,f101]) ).
thf(f140,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK4 @ X0 @ sK0 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f122,f33]) ).
thf(f122,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK4 @ X0 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK4 @ X0 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) ) ),
inference(superposition,[status(thm)],[f31,f40]) ).
thf(f40,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f139,plain,
( spl6_14
| spl6_11 ),
inference(avatar_split_clause,[status(thm)],[f135,f109,f137]) ).
thf(f135,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK4 @ X0 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) ) ),
inference(subsumption_resolution,[status(thm)],[f123,f33]) ).
thf(f123,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK4 @ X0 @ sK0 ) ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK4 @ X0 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ X1 ) ) ),
inference(superposition,[status(thm)],[f31,f41]) ).
thf(f41,plain,
! [X3: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f134,plain,
( spl6_13
| spl6_12 ),
inference(avatar_split_clause,[status(thm)],[f133,f114,f130]) ).
thf(f133,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK0 ) )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK5 @ X0 @ sK0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f124,f33]) ).
thf(f124,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK0 ) )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK5 @ X0 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK5 @ X0 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK0 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(superposition,[status(thm)],[f31,f36]) ).
thf(f36,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f132,plain,
( spl6_13
| spl6_8 ),
inference(avatar_split_clause,[status(thm)],[f128,f95,f130]) ).
thf(f128,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK5 @ X0 @ sK0 ) ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK0 ) @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f125,f33]) ).
thf(f125,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK5 @ X0 @ sK0 ) ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK0 ) @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( $true != $true )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK0 ) @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( sK5 @ X0 @ sK0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(superposition,[status(thm)],[f31,f39]) ).
thf(f39,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f52,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f32,f49,f45]) ).
thf(f32,plain,
( ( $true
!= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA088^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n026.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 03:50:25 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.25/0.47 ---- Original DTF file ---
% 0.25/0.48 thf(spec,logic,$$dhol).
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.48 % File : ANA088^1 : TPTP v9.2.1. Released v7.0.0.
% 0.25/0.48 % Domain : Analysis
% 0.25/0.48 % Problem : REAL_INF_BOUNDS
% 0.25/0.48 % Version : Especial.
% 0.25/0.48 % English :
% 0.25/0.48
% 0.25/0.48 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.25/0.48 % Source : [Kal16]
% 0.25/0.48 % Names : REAL_INF_BOUNDS_.p [Kal16]
% 0.25/0.48
% 0.25/0.48 % Status : Theorem
% 0.25/0.48 % Rating : 0.00 v7.1.0
% 0.25/0.48 % Syntax : Number of formulae : 9 ( 1 unt; 5 typ; 0 def)
% 0.25/0.48 % Number of atoms : 23 ( 4 equ; 0 cnn)
% 0.25/0.48 % Maximal formula atoms : 8 ( 5 avg)
% 0.25/0.48 % Number of connectives : 61 ( 3 ~; 0 |; 6 &; 44 @)
% 0.25/0.48 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.25/0.48 % Maximal formula depth : 11 ( 8 avg)
% 0.25/0.48 % Number of types : 2 ( 1 usr)
% 0.25/0.48 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.25/0.48 % Number of symbols : 5 ( 4 usr; 0 con; 1-3 aty)
% 0.25/0.48 % Number of variables : 18 ( 0 ^; 14 !; 2 ?; 18 :)
% 0.25/0.48 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.25/0.48 % SPC : TH1_THM_EQU_NAR
% 0.25/0.48
% 0.25/0.48 % Comments : Exported from core HOL Light.
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.48 thf('thf_type_type/realax/real',type,
% 0.25/0.48 'type/realax/real': $tType ).
% 0.25/0.48
% 0.25/0.48 thf('thf_const_const/sets/inf',type,
% 0.25/0.48 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.25/0.48
% 0.25/0.48 thf('thf_const_const/sets/IN',type,
% 0.25/0.48 'const/sets/IN':
% 0.25/0.48 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.25/0.48
% 0.25/0.48 thf('thf_const_const/sets/EMPTY',type,
% 0.25/0.48 'const/sets/EMPTY':
% 0.25/0.48 !>[A: $tType] : ( A > $o ) ).
% 0.25/0.48
% 0.25/0.48 thf('thf_const_const/realax/real_le',type,
% 0.25/0.48 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.25/0.48
% 0.25/0.48 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 0.25/0.48 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.25/0.48 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 0.25/0.48 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.25/0.48 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 0.25/0.48
% 0.25/0.48 thf('thm/sets/MEMBER_NOT_EMPTY_',axiom,
% 0.25/0.48 ! [A: $tType,A0: A > $o] :
% 0.25/0.48 ( ( ? [A1: A] : ( 'const/sets/IN' @ A @ A1 @ A0 ) )
% 0.25/0.48 = ( A0
% 0.25/0.48 != ( 'const/sets/EMPTY' @ A ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf('thm/sets/INF_',axiom,
% 0.25/0.48 ! [A: 'type/realax/real' > $o] :
% 0.25/0.48 ( ( ( A
% 0.25/0.48 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.25/0.48 & ? [A0: 'type/realax/real'] :
% 0.25/0.48 ! [A1: 'type/realax/real'] :
% 0.25/0.48 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.25/0.48 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 0.25/0.48 => ( ! [A0: 'type/realax/real'] :
% 0.25/0.48 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.25/0.48 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
% 0.25/0.48 & ! [A0: 'type/realax/real'] :
% 0.25/0.48 ( ! [A1: 'type/realax/real'] :
% 0.25/0.48 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.25/0.48 => ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.25/0.48 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf('thm/sets/REAL_INF_BOUNDS_',conjecture,
% 0.25/0.48 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.25/0.48 ( ( ( A
% 0.25/0.48 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.25/0.48 & ! [A2: 'type/realax/real'] :
% 0.25/0.48 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 0.25/0.48 => ( ( 'const/realax/real_le' @ A0 @ A2 )
% 0.25/0.48 & ( 'const/realax/real_le' @ A2 @ A1 ) ) ) )
% 0.25/0.48 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) )
% 0.25/0.48 & ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A1 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.48 ------------------------
% 1.67/1.31 ---- Embedded in THF ---
% 1.67/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.31 %%% Generated on Tue Feb 24 03:50:26 EST 2026
% 1.67/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.31 %%% Logic specification used:
% 1.67/1.31 %%% thf(spec, logic, $$dhol).
% 1.67/1.31
% 1.67/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.3rFaraA8p9/DTF2DTF19014.p
% See solution above
% 1.67/1.31 ------------------------
% 1.67/1.32 ---- Cleaned THF ---
% 1.67/1.32 thf('thf_type_type/realax/real',type,
% 1.67/1.32 'type/realax/real': $tType ).
% 1.67/1.32
% 1.67/1.32 thf('thf_const_const/sets/inf',type,
% 1.67/1.32 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 1.67/1.32
% 1.67/1.32 thf('thf_const_const/sets/IN',type,
% 1.67/1.32 'const/sets/IN':
% 1.67/1.32 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.67/1.32
% 1.67/1.32 thf('thf_const_const/sets/EMPTY',type,
% 1.67/1.32 'const/sets/EMPTY':
% 1.67/1.32 !>[A: $tType] : ( A > $o ) ).
% 1.67/1.32
% 1.67/1.32 thf('thf_const_const/realax/real_le',type,
% 1.67/1.32 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.67/1.32
% 1.67/1.32 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 1.67/1.32 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 1.67/1.32 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 1.67/1.32 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 1.67/1.32 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 1.67/1.32
% 1.67/1.32 thf('thm/sets/MEMBER_NOT_EMPTY_',axiom,
% 1.67/1.32 ! [A: $tType,A0: A > $o] :
% 1.67/1.32 ( ( ? [A1: A] : ( 'const/sets/IN' @ A @ A1 @ A0 ) )
% 1.67/1.32 = ( A0
% 1.67/1.32 != ( 'const/sets/EMPTY' @ A ) ) ) ).
% 1.67/1.32
% 1.67/1.32 thf('thm/sets/INF_',axiom,
% 1.67/1.32 ! [A: 'type/realax/real' > $o] :
% 1.67/1.32 ( ( ( A
% 1.67/1.32 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.67/1.32 & ? [A0: 'type/realax/real'] :
% 1.67/1.32 ! [A1: 'type/realax/real'] :
% 1.67/1.32 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.67/1.32 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 1.67/1.32 => ( ! [A0: 'type/realax/real'] :
% 1.67/1.32 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 1.67/1.32 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
% 1.67/1.32 & ! [A0: 'type/realax/real'] :
% 1.67/1.32 ( ! [A1: 'type/realax/real'] :
% 1.67/1.32 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.67/1.32 => ( 'const/realax/real_le' @ A0 @ A1 ) )
% 1.67/1.32 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
% 1.67/1.32
% 1.67/1.32 thf('thm/sets/REAL_INF_BOUNDS_',conjecture,
% 1.67/1.32 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real',A1: 'type/realax/real'] :
% 1.67/1.32 ( ( ( A
% 1.67/1.32 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.67/1.32 & ! [A2: 'type/realax/real'] :
% 1.67/1.32 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 1.67/1.32 => ( ( 'const/realax/real_le' @ A0 @ A2 )
% 1.67/1.32 & ( 'const/realax/real_le' @ A2 @ A1 ) ) ) )
% 1.67/1.32 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) )
% 1.67/1.32 & ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A1 ) ) ) ).
% 1.67/1.32 ------------------------
% 1.67/1.34 % (19289)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_19014 for (2999ds/275Mi)
% 1.67/1.34 % (19284)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19014 for (2999ds/183Mi)
% 1.67/1.34 % (19285)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_19014 for (2999ds/4Mi)
% 1.67/1.34 % (19286)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_19014 for (2999ds/27Mi)
% 1.67/1.34 % (19287)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19014 for (2999ds/2Mi)
% 1.67/1.34 % (19288)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_19014 for (2999ds/2Mi)
% 1.67/1.34 % (19290)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19014 for (2999ds/18Mi)
% 1.67/1.34 % (19287)Instruction limit reached!
% 1.67/1.34 % (19287)------------------------------
% 1.67/1.34 % (19287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (19287)Termination reason: Unknown
% 1.67/1.34 % (19287)Termination phase: Preprocessing 1
% 1.67/1.34
% 1.67/1.34 % (19287)Memory used [KB]: 895
% 1.67/1.34 % (19287)Time elapsed: 0.003 s
% 1.67/1.34 % (19287)Instructions burned: 2 (million)
% 1.67/1.34 % (19287)------------------------------
% 1.67/1.34 % (19287)------------------------------
% 1.67/1.34 % (19288)Instruction limit reached!
% 1.67/1.34 % (19288)------------------------------
% 1.67/1.34 % (19288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (19288)Termination reason: Unknown
% 1.67/1.34 % (19288)Termination phase: shuffling
% 1.67/1.34
% 1.67/1.34 % (19288)Memory used [KB]: 895
% 1.67/1.34 % (19288)Time elapsed: 0.003 s
% 1.67/1.34 % (19288)Instructions burned: 2 (million)
% 1.67/1.34 % (19288)------------------------------
% 1.67/1.34 % (19288)------------------------------
% 1.67/1.34 % (19285)Instruction limit reached!
% 1.67/1.34 % (19285)------------------------------
% 1.67/1.34 % (19285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (19285)Termination reason: Unknown
% 1.67/1.35 % (19285)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (19285)Memory used [KB]: 5500
% 1.67/1.35 % (19285)Time elapsed: 0.005 s
% 1.67/1.35 % (19285)Instructions burned: 5 (million)
% 1.67/1.35 % (19285)------------------------------
% 1.67/1.35 % (19285)------------------------------
% 1.67/1.35 % (19289)First to succeed.
% 1.67/1.35 % (19289)Refutation found. Thanks to Tanya!
% 1.67/1.35 % SZS status Theorem for DTF2THF_19014
% 1.67/1.35 % SZS output start Proof for DTF2THF_19014
% 1.67/1.35 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.67/1.35 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.67/1.35 thf(func_def_1, type, 'const/sets/inf': ('type/realax/real' > $o) > 'type/realax/real').
% 1.67/1.35 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.67/1.35 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.67/1.35 thf(func_def_4, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.67/1.35 thf(func_def_8, type, sK0: 'type/realax/real' > $o).
% 1.67/1.35 thf(func_def_9, type, sK1: 'type/realax/real').
% 1.67/1.35 thf(func_def_10, type, sK2: 'type/realax/real').
% 1.67/1.35 thf(func_def_11, type, sK3: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.67/1.35 thf(func_def_12, type, sK4: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.67/1.35 thf(func_def_13, type, sK5: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.67/1.35 thf(func_def_15, type, ph7: !>[X0: $tType]:(X0)).
% 1.67/1.35 thf(func_def_16, type, sK8: 'type/realax/real').
% 1.67/1.35 thf(f235,plain,(
% 1.67/1.35 $false),
% 1.67/1.35 inference(avatar_sat_refutation,[status(thm)],[f52,f132,f134,f139,f141,f150,f175,f214,f226,f228,f234])).
% 1.67/1.35 thf(f234,plain,(
% 1.67/1.35 spl6_11 | ~spl6_14),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f233,f137,f109])).
% 1.67/1.35 thf(f109,definition,(
% 1.67/1.35 spl6_11 <=> ! [X1 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0)) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X1)))),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl6_11])],[avatar_definition])).
% 1.67/1.35 thf(f137,definition,(
% 1.67/1.35 spl6_14 <=> ! [X0 : 'type/realax/real'] : ($true = ('const/realax/real_le' @ sK1 @ (sK4 @ X0 @ sK0)))),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl6_14])],[avatar_definition])).
% 1.67/1.35 thf(f233,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0)) | (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X0) = $true)) ) | ~spl6_14),
% 1.67/1.35 inference(subsumption_resolution,[status(thm)],[f232,f33])).
% 1.67/1.35 thf(f33,plain,(
% 1.67/1.35 ('const/sets/EMPTY' @ 'type/realax/real' != sK0)),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f22])).
% 1.67/1.35 thf(f22,plain,(
% 1.67/1.35 ('const/sets/EMPTY' @ 'type/realax/real' != sK0) & (($true != ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | ($true != ('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2))) & ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0)) | (($true = ('const/realax/real_le' @ sK1 @ X3)) & ($true = ('const/realax/real_le' @ X3 @ sK2))))),
% 1.67/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f21])).
% 1.67/1.35 thf(f21,plain,(
% 1.67/1.35 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) != $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) = $true)))) => (('const/sets/EMPTY' @ 'type/realax/real' != sK0) & (($true != ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | ($true != ('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2))) & ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0)) | (($true = ('const/realax/real_le' @ sK1 @ X3)) & ($true = ('const/realax/real_le' @ X3 @ sK2)))))),
% 1.67/1.35 introduced(definition,[],[choice_axiom])).
% 1.67/1.35 thf(f20,plain,(
% 1.67/1.35 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) != $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))))),
% 1.67/1.35 inference(flattening,[status(thm)],[f19])).
% 1.67/1.35 thf(f19,plain,(
% 1.67/1.35 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) != $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)))),
% 1.67/1.35 inference(ennf_transformation,[status(thm)],[f14])).
% 1.67/1.35 thf(f14,plain,(
% 1.67/1.35 ~! [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' @ X1 @ ('const/sets/inf' @ X0)) = $true) & (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) = $true)))),
% 1.67/1.35 inference(fool_elimination,[status(thm)],[f13])).
% 1.67/1.35 thf(f13,plain,(
% 1.67/1.35 ~! [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' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))))),
% 1.67/1.35 inference(rectify,[status(thm)],[f5])).
% 1.67/1.35 thf(f5,negated_conjecture,(
% 1.67/1.35 ~! [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' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))))),
% 1.67/1.35 inference(negated_conjecture,[status(cth)],[f4])).
% 1.67/1.35 thf(f4,conjecture,(
% 1.67/1.35 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) & ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))))),
% 1.67/1.35 file('/export/starexec/sandbox2/tmp/tmp.3rFaraA8p9/DTF2THF_19014.p','thm/sets/REAL_INF_BOUNDS_')).
% 1.67/1.35 thf(f232,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X0) = $true)) ) | ~spl6_14),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f231])).
% 1.67/1.35 thf(f231,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X0) = $true) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0))) ) | ~spl6_14),
% 1.67/1.35 inference(superposition,[status(thm)],[f38,f138])).
% 1.67/1.35 thf(f138,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK1 @ (sK4 @ X0 @ sK0)))) ) | ~spl6_14),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f137])).
% 1.67/1.35 thf(f38,plain,(
% 1.67/1.35 ( ! [X3 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X1 @ (sK4 @ X1 @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.35 thf(f29,plain,(
% 1.67/1.35 ! [X0 : 'type/realax/real' > $o] : (! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0) = $true) & ($true != ('const/realax/real_le' @ X1 @ (sK4 @ X1 @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X3 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3)) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true)) & ! [X4 : 'type/realax/real'] : ((($true != ('const/realax/real_le' @ X4 @ (sK5 @ X4 @ X0))) & ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0))) | ($true = ('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))))))),
% 1.67/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f16,f28,f27])).
% 1.67/1.35 thf(f27,plain,(
% 1.67/1.35 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) != $true)) => ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0) = $true) & ($true != ('const/realax/real_le' @ X1 @ (sK4 @ X1 @ X0)))))),
% 1.67/1.35 introduced(definition,[],[choice_axiom])).
% 1.67/1.35 thf(f28,plain,(
% 1.67/1.35 ! [X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ X5) != $true) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) => (($true != ('const/realax/real_le' @ X4 @ (sK5 @ X4 @ X0))) & ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0))))),
% 1.67/1.35 introduced(definition,[],[choice_axiom])).
% 1.67/1.35 thf(f16,plain,(
% 1.67/1.35 ! [X0 : 'type/realax/real' > $o] : (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) != $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X3 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3)) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true)) & ! [X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ X5) != $true) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ($true = ('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))))))),
% 1.67/1.35 inference(flattening,[status(thm)],[f15])).
% 1.67/1.35 thf(f15,plain,(
% 1.67/1.35 ! [X0 : 'type/realax/real' > $o] : ((! [X3 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3)) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true)) & ! [X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ X5) != $true) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ($true = ('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))))) | (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) != $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 1.67/1.35 inference(ennf_transformation,[status(thm)],[f8])).
% 1.67/1.35 thf(f8,plain,(
% 1.67/1.35 ! [X0 : 'type/realax/real' > $o] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) => (('const/realax/real_le' @ X1 @ X2) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) => ($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) & ! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) => (('const/realax/real_le' @ X4 @ X5) = $true)) => ($true = ('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))))))),
% 1.67/1.35 inference(fool_elimination,[status(thm)],[f7])).
% 1.67/1.35 thf(f7,plain,(
% 1.67/1.35 ! [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' @ X1 @ X2))) => (! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3)) & ! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ X4 @ X5)) => ('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)))))),
% 1.67/1.35 inference(rectify,[status(thm)],[f3])).
% 1.67/1.35 thf(f3,axiom,(
% 1.67/1.35 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) & ! [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)))))),
% 1.67/1.35 file('/export/starexec/sandbox2/tmp/tmp.3rFaraA8p9/DTF2THF_19014.p','thm/sets/INF_')).
% 1.67/1.35 thf(f228,plain,(
% 1.67/1.35 spl6_2 | spl6_12 | ~spl6_13),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f227,f130,f114,f49])).
% 1.67/1.35 thf(f49,definition,(
% 1.67/1.35 spl6_2 <=> ($true = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)))),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.67/1.35 thf(f114,definition,(
% 1.67/1.35 spl6_12 <=> ! [X1 : 'type/realax/real'] : (('const/realax/real_le' @ X1 @ (sK4 @ X1 @ sK0)) != $true)),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl6_12])],[avatar_definition])).
% 1.67/1.35 thf(f130,definition,(
% 1.67/1.35 spl6_13 <=> ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK1 @ (sK5 @ X0 @ sK0))) | ($true = ('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0))))),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl6_13])],[avatar_definition])).
% 1.67/1.35 thf(f227,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK0))) | ($true = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)))) ) | ~spl6_13),
% 1.67/1.35 inference(subsumption_resolution,[status(thm)],[f221,f33])).
% 1.67/1.35 thf(f221,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK0))) | ($true = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) ) | ~spl6_13),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f220])).
% 1.67/1.35 thf(f220,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | ($true != $true) | ($true != ('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK0)))) ) | ~spl6_13),
% 1.67/1.35 inference(duplicate_literal_removal,[status(thm)],[f218])).
% 1.67/1.35 thf(f218,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | ($true = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | ($true != $true) | ($true != ('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK0)))) ) | ~spl6_13),
% 1.67/1.35 inference(superposition,[status(thm)],[f37,f131])).
% 1.67/1.35 thf(f131,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK1 @ (sK5 @ X0 @ sK0))) | ($true = ('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)))) ) | ~spl6_13),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f130])).
% 1.67/1.35 thf(f37,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X4 @ (sK5 @ X4 @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = ('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))) | ($true != ('const/realax/real_le' @ X1 @ (sK4 @ X1 @ X0)))) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.35 thf(f226,plain,(
% 1.67/1.35 spl6_2 | ~spl6_9 | ~spl6_13),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f223,f130,f101,f49])).
% 1.67/1.35 thf(f101,definition,(
% 1.67/1.35 spl6_9 <=> ! [X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X1 @ (sK5 @ X1 @ sK0))) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0))))),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition])).
% 1.67/1.35 thf(f223,plain,(
% 1.67/1.35 ($true = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | (~spl6_9 | ~spl6_13)),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f222])).
% 1.67/1.35 thf(f222,plain,(
% 1.67/1.35 ($true = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | ($true != $true) | (~spl6_9 | ~spl6_13)),
% 1.67/1.35 inference(duplicate_literal_removal,[status(thm)],[f219])).
% 1.67/1.35 thf(f219,plain,(
% 1.67/1.35 ($true = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | ($true != $true) | ($true = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | (~spl6_9 | ~spl6_13)),
% 1.67/1.35 inference(superposition,[status(thm)],[f102,f131])).
% 1.67/1.35 thf(f102,plain,(
% 1.67/1.35 ( ! [X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X1 @ (sK5 @ X1 @ sK0))) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0)))) ) | ~spl6_9),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.67/1.35 thf(f214,plain,(
% 1.67/1.35 ~spl6_12 | ~spl6_14),
% 1.67/1.35 inference(avatar_contradiction_clause,[status(thm)],[f213])).
% 1.67/1.35 thf(f213,plain,(
% 1.67/1.35 $false | (~spl6_12 | ~spl6_14)),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f210])).
% 1.67/1.35 thf(f210,plain,(
% 1.67/1.35 ($true != $true) | (~spl6_12 | ~spl6_14)),
% 1.67/1.35 inference(superposition,[status(thm)],[f115,f138])).
% 1.67/1.35 thf(f115,plain,(
% 1.67/1.35 ( ! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ (sK4 @ X1 @ sK0)) != $true)) ) | ~spl6_12),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f114])).
% 1.67/1.35 thf(f175,plain,(
% 1.67/1.35 spl6_1 | ~spl6_11),
% 1.67/1.35 inference(avatar_contradiction_clause,[status(thm)],[f174])).
% 1.67/1.35 thf(f174,plain,(
% 1.67/1.35 $false | (spl6_1 | ~spl6_11)),
% 1.67/1.35 inference(subsumption_resolution,[status(thm)],[f170,f33])).
% 1.67/1.35 thf(f170,plain,(
% 1.67/1.35 ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (spl6_1 | ~spl6_11)),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f166])).
% 1.67/1.35 thf(f166,plain,(
% 1.67/1.35 ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (spl6_1 | ~spl6_11)),
% 1.67/1.35 inference(superposition,[status(thm)],[f161,f34])).
% 1.67/1.35 thf(f34,plain,(
% 1.67/1.35 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = ('const/sets/IN' @ X0 @ (sK3 @ X0 @ X1) @ X1)) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f26])).
% 1.67/1.35 thf(f26,plain,(
% 1.67/1.35 ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) != $true)) & (($true = ('const/sets/IN' @ X0 @ (sK3 @ X0 @ X1) @ X1)) | ('const/sets/EMPTY' @ X0 = X1)))),
% 1.67/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f24,f25])).
% 1.67/1.35 thf(f25,plain,(
% 1.67/1.35 ! [X0 : $tType,X1 : X0 > $o] : (? [X3 : X0] : ($true = ('const/sets/IN' @ X0 @ X3 @ X1)) => ($true = ('const/sets/IN' @ X0 @ (sK3 @ X0 @ X1) @ X1)))),
% 1.67/1.35 introduced(definition,[],[choice_axiom])).
% 1.67/1.35 thf(f24,plain,(
% 1.67/1.35 ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) != $true)) & (? [X3 : X0] : ($true = ('const/sets/IN' @ X0 @ X3 @ X1)) | ('const/sets/EMPTY' @ X0 = X1)))),
% 1.67/1.35 inference(rectify,[status(thm)],[f23])).
% 1.67/1.35 thf(f23,plain,(
% 1.67/1.35 ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/EMPTY' @ X0 != X1) | ! [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) != $true)) & (? [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = $true) | ('const/sets/EMPTY' @ X0 = X1)))),
% 1.67/1.35 inference(nnf_transformation,[status(thm)],[f12])).
% 1.67/1.35 thf(f12,plain,(
% 1.67/1.35 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/EMPTY' @ X0 != X1) <=> ? [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = $true))),
% 1.67/1.35 inference(fool_elimination,[status(thm)],[f11])).
% 1.67/1.35 thf(f11,plain,(
% 1.67/1.35 ! [X0 : $tType,X1 : X0 > $o] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = ('const/sets/EMPTY' @ X0 != X1))),
% 1.67/1.35 inference(rectify,[status(thm)],[f2])).
% 1.67/1.35 thf(f2,axiom,(
% 1.67/1.35 ! [X0 : $tType,X1 : X0 > $o] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = ('const/sets/EMPTY' @ X0 != X1))),
% 1.67/1.35 file('/export/starexec/sandbox2/tmp/tmp.3rFaraA8p9/DTF2THF_19014.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 1.67/1.35 thf(f161,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0))) ) | (spl6_1 | ~spl6_11)),
% 1.67/1.35 inference(subsumption_resolution,[status(thm)],[f159,f30])).
% 1.67/1.35 thf(f30,plain,(
% 1.67/1.35 ( ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0)) | ($true = ('const/realax/real_le' @ X3 @ sK2))) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f22])).
% 1.67/1.35 thf(f159,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0)) | ($true != ('const/realax/real_le' @ X0 @ sK2))) ) | (spl6_1 | ~spl6_11)),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f152])).
% 1.67/1.35 thf(f152,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0)) | ($true != $true) | ($true != ('const/realax/real_le' @ X0 @ sK2))) ) | (spl6_1 | ~spl6_11)),
% 1.67/1.35 inference(superposition,[status(thm)],[f79,f110])).
% 1.67/1.35 thf(f110,plain,(
% 1.67/1.35 ( ! [X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X1)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0))) ) | ~spl6_11),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f109])).
% 1.67/1.35 thf(f79,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X0) != $true) | ($true != ('const/realax/real_le' @ X0 @ sK2))) ) | spl6_1),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.67/1.35 thf(f78,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X0) != $true) | ($true != ('const/realax/real_le' @ X0 @ sK2)) | ($true != $true)) ) | spl6_1),
% 1.67/1.35 inference(superposition,[status(thm)],[f47,f42])).
% 1.67/1.35 thf(f42,plain,(
% 1.67/1.35 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X2) = $true) | (('const/realax/real_le' @ X0 @ X1) != $true) | (('const/realax/real_le' @ X1 @ X2) != $true)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.35 thf(f18,plain,(
% 1.67/1.35 ! [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))),
% 1.67/1.35 inference(flattening,[status(thm)],[f17])).
% 1.67/1.35 thf(f17,plain,(
% 1.67/1.35 ! [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)))),
% 1.67/1.35 inference(ennf_transformation,[status(thm)],[f10])).
% 1.67/1.35 thf(f10,plain,(
% 1.67/1.35 ! [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) = $true))),
% 1.67/1.35 inference(fool_elimination,[status(thm)],[f9])).
% 1.67/1.35 thf(f9,plain,(
% 1.67/1.35 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X0 @ X2))),
% 1.67/1.35 inference(rectify,[status(thm)],[f1])).
% 1.67/1.35 thf(f1,axiom,(
% 1.67/1.35 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X0 @ X2))),
% 1.67/1.35 file('/export/starexec/sandbox2/tmp/tmp.3rFaraA8p9/DTF2THF_19014.p','thm/realax/REAL_LE_TRANS_')).
% 1.67/1.35 thf(f47,plain,(
% 1.67/1.35 ($true != ('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2)) | spl6_1),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.67/1.35 thf(f45,definition,(
% 1.67/1.35 spl6_1 <=> ($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2))),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.67/1.35 thf(f150,plain,(
% 1.67/1.35 spl6_14 | ~spl6_8),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f149,f95,f137])).
% 1.67/1.35 thf(f95,definition,(
% 1.67/1.35 spl6_8 <=> ! [X1 : 'type/realax/real'] : ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK0) @ sK0))),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl6_8])],[avatar_definition])).
% 1.67/1.35 thf(f149,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK1 @ (sK4 @ X0 @ sK0)))) ) | ~spl6_8),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f146])).
% 1.67/1.35 thf(f146,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = ('const/realax/real_le' @ sK1 @ (sK4 @ X0 @ sK0)))) ) | ~spl6_8),
% 1.67/1.35 inference(superposition,[status(thm)],[f31,f96])).
% 1.67/1.35 thf(f96,plain,(
% 1.67/1.35 ( ! [X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK0) @ sK0))) ) | ~spl6_8),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f95])).
% 1.67/1.35 thf(f31,plain,(
% 1.67/1.35 ( ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0)) | ($true = ('const/realax/real_le' @ sK1 @ X3))) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f22])).
% 1.67/1.35 thf(f141,plain,(
% 1.67/1.35 spl6_9 | spl6_14),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f140,f137,f101])).
% 1.67/1.35 thf(f140,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0))) | ($true = ('const/realax/real_le' @ sK1 @ (sK4 @ X0 @ sK0))) | ($true != ('const/realax/real_le' @ X1 @ (sK5 @ X1 @ sK0)))) )),
% 1.67/1.35 inference(subsumption_resolution,[status(thm)],[f122,f33])).
% 1.67/1.35 thf(f122,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X1 @ (sK5 @ X1 @ sK0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0))) | ($true = ('const/realax/real_le' @ sK1 @ (sK4 @ X0 @ sK0)))) )),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.67/1.35 thf(f120,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != $true) | ($true != ('const/realax/real_le' @ X1 @ (sK5 @ X1 @ sK0))) | ($true = ('const/realax/real_le' @ sK1 @ (sK4 @ X0 @ sK0))) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0)))) )),
% 1.67/1.35 inference(superposition,[status(thm)],[f31,f40])).
% 1.67/1.35 thf(f40,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0) = $true) | ($true != ('const/realax/real_le' @ X4 @ (sK5 @ X4 @ X0))) | ($true = ('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.35 thf(f139,plain,(
% 1.67/1.35 spl6_14 | spl6_11),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f135,f109,f137])).
% 1.67/1.35 thf(f135,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK1 @ (sK4 @ X0 @ sK0))) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X1)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0))) )),
% 1.67/1.35 inference(subsumption_resolution,[status(thm)],[f123,f33])).
% 1.67/1.35 thf(f123,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK1 @ (sK4 @ X0 @ sK0))) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0)) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X1)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) )),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.67/1.35 thf(f119,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != $true) | ($true = ('const/realax/real_le' @ sK1 @ (sK4 @ X0 @ sK0))) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ X1))) )),
% 1.67/1.35 inference(superposition,[status(thm)],[f31,f41])).
% 1.67/1.35 thf(f41,plain,(
% 1.67/1.35 ( ! [X3 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3)) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.35 thf(f134,plain,(
% 1.67/1.35 spl6_13 | spl6_12),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f133,f114,f130])).
% 1.67/1.35 thf(f133,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0))) | (('const/realax/real_le' @ X1 @ (sK4 @ X1 @ sK0)) != $true) | ($true = ('const/realax/real_le' @ sK1 @ (sK5 @ X0 @ sK0)))) )),
% 1.67/1.35 inference(subsumption_resolution,[status(thm)],[f124,f33])).
% 1.67/1.35 thf(f124,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ (sK4 @ X1 @ sK0)) != $true) | ($true = ('const/realax/real_le' @ sK1 @ (sK5 @ X0 @ sK0))) | ($true = ('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) )),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.67/1.35 thf(f117,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = ('const/realax/real_le' @ sK1 @ (sK5 @ X0 @ sK0))) | ($true = ('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0))) | (('const/realax/real_le' @ X1 @ (sK4 @ X1 @ sK0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) )),
% 1.67/1.35 inference(superposition,[status(thm)],[f31,f36])).
% 1.67/1.35 thf(f36,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0)) | ($true = ('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))) | ($true != ('const/realax/real_le' @ X1 @ (sK4 @ X1 @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.35 thf(f132,plain,(
% 1.67/1.35 spl6_13 | spl6_8),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f128,f95,f130])).
% 1.67/1.35 thf(f128,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK1 @ (sK5 @ X0 @ sK0))) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK0) @ sK0)) | ($true = ('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)))) )),
% 1.67/1.35 inference(subsumption_resolution,[status(thm)],[f125,f33])).
% 1.67/1.35 thf(f125,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = ('const/realax/real_le' @ sK1 @ (sK5 @ X0 @ sK0))) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK0) @ sK0)) | ($true = ('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)))) )),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.67/1.35 thf(f118,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0))) | ($true != $true) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK0) @ sK0)) | ($true = ('const/realax/real_le' @ sK1 @ (sK5 @ X0 @ sK0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) )),
% 1.67/1.35 inference(superposition,[status(thm)],[f31,f39])).
% 1.67/1.35 thf(f39,plain,(
% 1.67/1.35 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true = ('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0))) | (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0) = $true)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.35 thf(f52,plain,(
% 1.67/1.35 ~spl6_1 | ~spl6_2),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f32,f49,f45])).
% 1.67/1.35 thf(f32,plain,(
% 1.67/1.35 ($true != ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | ($true != ('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK2))),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f22])).
% 1.67/1.35 % SZS output end Proof for DTF2THF_19014
% 1.67/1.35 % (19289)------------------------------
% 1.67/1.35 % (19289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (19289)Termination reason: Refutation
% 1.67/1.35
% 1.67/1.35 % (19289)Memory used [KB]: 5756
% 1.67/1.35 % (19289)Time elapsed: 0.016 s
% 1.67/1.35 % (19289)Instructions burned: 34 (million)
% 1.67/1.35 % (19289)------------------------------
% 1.67/1.35 % (19289)------------------------------
% 1.67/1.35 % (19283)Success in time 0.025 s
%------------------------------------------------------------------------------