%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA092^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 08:38:51 AM UTC 2026
% Result : Theorem 1.68s 1.34s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 108 ( 1 unt; 0 typ; 10 def)
% Number of atoms : 1139 ( 308 equ; 0 cnn)
% Maximal formula atoms : 20 ( 10 avg)
% Number of connectives : 1410 ( 191 ~; 215 |; 60 &; 892 @)
% ( 12 <=>; 38 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 16 con; 0-3 aty)
% Number of variables : 205 ( 0 ^; 163 !; 42 ?; 205 :)
% 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' ).
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(f263,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f49,f54,f59,f104,f109,f122,f128,f130,f136,f149,f168,f235,f262]) ).
thf(f262,plain,
( spl6_15
| ~ spl6_1
| ~ spl6_14 ),
inference(avatar_split_clause,[status(thm)],[f260,f120,f43,f166]) ).
thf(f166,definition,
( spl6_15
<=> ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_15])],[avatar_definition]) ).
thf(f43,definition,
( spl6_1
<=> ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ X3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f120,definition,
( spl6_14
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_14])],[avatar_definition]) ).
thf(f260,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) ) )
| ~ spl6_1
| ~ spl6_14 ),
inference(trivial_inequality_removal,[status(thm)],[f257]) ).
thf(f257,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true != $true ) )
| ~ spl6_1
| ~ spl6_14 ),
inference(superposition,[status(thm)],[f44,f121]) ).
thf(f121,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) ) )
| ~ spl6_14 ),
inference(avatar_component_clause,[status(thm)],[f120]) ).
thf(f44,plain,
( ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ X3 ) ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f235,plain,
( spl6_2
| ~ spl6_11
| ~ spl6_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f234]) ).
thf(f234,plain,
( $false
| spl6_2
| ~ spl6_11
| ~ spl6_15 ),
inference(subsumption_resolution,[status(thm)],[f231,f47]) ).
thf(f47,plain,
( ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
!= $true )
| spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl6_2
<=> ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f231,plain,
( ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ~ spl6_11
| ~ spl6_15 ),
inference(trivial_inequality_removal,[status(thm)],[f230]) ).
thf(f230,plain,
( ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( $true != $true )
| ~ spl6_11
| ~ spl6_15 ),
inference(duplicate_literal_removal,[status(thm)],[f227]) ).
thf(f227,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ~ spl6_11
| ~ spl6_15 ),
inference(superposition,[status(thm)],[f108,f167]) ).
thf(f167,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true ) )
| ~ spl6_15 ),
inference(avatar_component_clause,[status(thm)],[f166]) ).
thf(f108,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK1 ) )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) ) )
| ~ spl6_11 ),
inference(avatar_component_clause,[status(thm)],[f107]) ).
thf(f107,definition,
( spl6_11
<=> ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK1 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_11])],[avatar_definition]) ).
thf(f168,plain,
( spl6_15
| spl6_12
| ~ spl6_1 ),
inference(avatar_split_clause,[status(thm)],[f164,f43,f112,f166]) ).
thf(f112,definition,
( spl6_12
<=> ! [X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_12])],[avatar_definition]) ).
thf(f164,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) )
!= $true ) )
| ~ spl6_1 ),
inference(subsumption_resolution,[status(thm)],[f159,f34]) ).
thf(f34,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ) )
& ( ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
!= $true )
| ( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 )
= $true )
& ( ( 'const/realax/real_le' @ sK0 @ sK2 )
!= $true ) ) )
& ( ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ X3 ) ) ) )
& ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ X5 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f24,f23,f22]) ).
thf(f22,plain,
( ? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) )
!= $true )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
= $true )
& ( ( 'const/realax/real_le' @ X0 @ X2 )
!= $true ) ) )
& ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) )
= $true )
| ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X0 @ X3 ) ) ) )
& ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X1 ) )
| ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) ) )
=> ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ) )
& ( ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
!= $true )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK1 )
= $true )
& ( ( 'const/realax/real_le' @ sK0 @ X2 )
!= $true ) ) )
& ( ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ X3 ) ) ) )
& ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK1 )
= $true )
& ( ( 'const/realax/real_le' @ sK0 @ X2 )
!= $true ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 )
= $true )
& ( ( 'const/realax/real_le' @ sK0 @ sK2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) )
=> ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ X5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) )
!= $true )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
= $true )
& ( ( 'const/realax/real_le' @ X0 @ X2 )
!= $true ) ) )
& ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) )
= $true )
| ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X0 @ X3 ) ) ) )
& ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X1 ) )
| ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) )
!= $true )
| ? [X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
& ( $true
!= ( 'const/realax/real_le' @ X0 @ X4 ) ) ) )
& ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) )
= $true )
| ! [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ X4 ) ) ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X2 @ X3 ) ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) )
!= $true )
| ? [X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
& ( $true
!= ( 'const/realax/real_le' @ X0 @ X4 ) ) ) )
& ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) )
= $true )
| ! [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ X4 ) ) ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X2 @ X3 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ( ! [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ X4 ) ) )
<~> ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) )
= $true ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X2 @ X3 ) ) ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ! [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ X4 ) ) )
<~> ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X2 @ X3 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ! [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
= $true )
=> ( $true
= ( 'const/realax/real_le' @ X2 @ X3 ) ) ) )
=> ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) )
= $true )
<=> ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
=> ( $true
= ( 'const/realax/real_le' @ X0 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X1: 'type/realax/real',X2: 'type/realax/real' > $o] :
( ( ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X2 )
= $true )
=> ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X2 ) ) )
=> ( ! [X6: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X6 @ X2 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ X6 )
= $true ) )
<=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X2 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X1: 'type/realax/real',X2: 'type/realax/real' > $o] :
( ( ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X2 )
=> ( 'const/realax/real_le' @ X4 @ X5 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X2 ) ) )
=> ! [X6: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X6 @ X2 )
=> ( 'const/realax/real_le' @ X1 @ X6 ) )
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: 'type/realax/real',X2: 'type/realax/real' > $o,X3: X0] :
( ( ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X2 )
=> ( 'const/realax/real_le' @ X4 @ X5 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X2 ) ) )
=> ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X2 )
=> ( 'const/realax/real_le' @ X1 @ X4 ) )
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: 'type/realax/real',X2: 'type/realax/real' > $o,X3: X0] :
( ( ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X2 )
=> ( 'const/realax/real_le' @ X4 @ X5 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X2 ) ) )
=> ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X2 )
=> ( 'const/realax/real_le' @ X1 @ X4 ) )
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ASb0gG0Q01/DTF2THF_21590.p','thm/sets/REAL_LE_INF_EQ_') ).
thf(f159,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) )
!= $true ) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f155]) ).
thf(f155,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) )
!= $true ) )
| ~ spl6_1 ),
inference(superposition,[status(thm)],[f44,f36]) ).
thf(f36,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) )
& ! [X2: 'type/realax/real'] :
( ( ( $true
!= ( 'const/realax/real_le' @ X2 @ ( sK4 @ X2 @ X0 ) ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 ) ) )
| ( ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 ) )
& ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f26,f28,f27]) ).
thf(f27,plain,
! [X0: 'type/realax/real' > $o,X2: 'type/realax/real'] :
( ? [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X2 @ X3 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) ) )
=> ( ( $true
!= ( 'const/realax/real_le' @ X2 @ ( sK4 @ X2 @ X0 ) ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
! [X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true ) )
=> ( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 ) )
& ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) )
& ! [X2: 'type/realax/real'] :
( ? [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X2 @ X3 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) ) )
| ( ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X4: 'type/realax/real'] :
? [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) ) )
& ! [X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true ) )
| ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ) )
| ( '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' @ X1 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) ) )
& ! [X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true ) )
| ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ) )
| ( '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' @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,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' @ X1 @ X2 )
= $true ) ) )
=> ( ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) )
=> ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true ) )
& ! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,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)],[f2]) ).
thf(f2,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/sandbox/tmp/tmp.ASb0gG0Q01/DTF2THF_21590.p','thm/sets/INF_') ).
thf(f149,plain,
( ~ spl6_2
| spl6_3
| ~ spl6_4
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f148]) ).
thf(f148,plain,
( $false
| ~ spl6_2
| spl6_3
| ~ spl6_4
| ~ spl6_10 ),
inference(subsumption_resolution,[status(thm)],[f145,f58]) ).
thf(f58,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 )
= $true )
| ~ spl6_4 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl6_4
<=> ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition]) ).
thf(f145,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 )
!= $true )
| ~ spl6_2
| spl6_3
| ~ spl6_10 ),
inference(trivial_inequality_removal,[status(thm)],[f140]) ).
thf(f140,plain,
( ( $true != $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 )
!= $true )
| ~ spl6_2
| spl6_3
| ~ spl6_10 ),
inference(superposition,[status(thm)],[f86,f103]) ).
thf(f103,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true ) )
| ~ spl6_10 ),
inference(avatar_component_clause,[status(thm)],[f102]) ).
thf(f102,definition,
( spl6_10
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_10])],[avatar_definition]) ).
thf(f86,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
!= $true )
| ~ spl6_2
| spl6_3 ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
!= $true )
| ~ spl6_2
| spl6_3 ),
inference(superposition,[status(thm)],[f82,f48]) ).
thf(f48,plain,
( ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ~ spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f82,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK0 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ sK2 )
!= $true ) )
| spl6_3 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ sK0 @ X0 )
!= $true )
| ( $true != $true ) )
| spl6_3 ),
inference(superposition,[status(thm)],[f53,f35]) ).
thf(f35,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)],[f16]) ).
thf(f16,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(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: '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(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) )
=> ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,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/sandbox/tmp/tmp.ASb0gG0Q01/DTF2THF_21590.p','thm/realax/REAL_LE_TRANS_') ).
thf(f53,plain,
( ( ( 'const/realax/real_le' @ sK0 @ sK2 )
!= $true )
| spl6_3 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl6_3
<=> ( ( 'const/realax/real_le' @ sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition]) ).
thf(f136,plain,
( ~ spl6_9
| ~ spl6_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f135]) ).
thf(f135,plain,
( $false
| ~ spl6_9
| ~ spl6_12 ),
inference(trivial_inequality_removal,[status(thm)],[f133]) ).
thf(f133,plain,
( ( $true != $true )
| ~ spl6_9
| ~ spl6_12 ),
inference(superposition,[status(thm)],[f113,f100]) ).
thf(f100,plain,
( ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) ) )
| ~ spl6_9 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f99,definition,
( spl6_9
<=> ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition]) ).
thf(f113,plain,
( ! [X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) )
!= $true )
| ~ spl6_12 ),
inference(avatar_component_clause,[status(thm)],[f112]) ).
thf(f130,plain,
( spl6_10
| ~ spl6_9 ),
inference(avatar_split_clause,[status(thm)],[f129,f99,f102]) ).
thf(f129,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 )
= $true ) )
| ~ spl6_9 ),
inference(subsumption_resolution,[status(thm)],[f125,f34]) ).
thf(f125,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 )
= $true ) )
| ~ spl6_9 ),
inference(trivial_inequality_removal,[status(thm)],[f124]) ).
thf(f124,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 )
!= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 )
= $true ) )
| ~ spl6_9 ),
inference(superposition,[status(thm)],[f40,f100]) ).
thf(f40,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 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f128,plain,
( spl6_11
| ~ spl6_9 ),
inference(avatar_split_clause,[status(thm)],[f127,f99,f107]) ).
thf(f127,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK4 @ X0 @ sK1 ) ) ) )
| ~ spl6_9 ),
inference(subsumption_resolution,[status(thm)],[f126,f34]) ).
thf(f126,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK4 @ X0 @ sK1 ) ) ) )
| ~ spl6_9 ),
inference(trivial_inequality_removal,[status(thm)],[f123]) ).
thf(f123,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true ) )
| ~ spl6_9 ),
inference(superposition,[status(thm)],[f38,f100]) ).
thf(f38,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,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' @ X2 @ ( sK4 @ X2 @ X0 ) ) )
| ( ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f122,plain,
( spl6_14
| spl6_9 ),
inference(avatar_split_clause,[status(thm)],[f118,f99,f120]) ).
thf(f118,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f93,f34]) ).
thf(f93,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) ) )
| ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f30,f37]) ).
thf(f37,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 ) )
| ( ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f30,plain,
! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f109,plain,
( spl6_9
| spl6_11 ),
inference(avatar_split_clause,[status(thm)],[f105,f107,f99]) ).
thf(f105,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK1 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f95,f34]) ).
thf(f95,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK1 ) )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK1 ) )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) ) ),
inference(superposition,[status(thm)],[f30,f39]) ).
thf(f39,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 ) )
| ( ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X2 @ ( sK4 @ X2 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f104,plain,
( spl6_9
| spl6_10 ),
inference(avatar_split_clause,[status(thm)],[f97,f102,f99]) ).
thf(f97,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f96,f34]) ).
thf(f96,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f30,f41]) ).
thf(f41,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/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f59,plain,
( ~ spl6_2
| spl6_4 ),
inference(avatar_split_clause,[status(thm)],[f33,f56,f46]) ).
thf(f33,plain,
( ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f54,plain,
( ~ spl6_3
| ~ spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f32,f46,f51]) ).
thf(f32,plain,
( ( ( 'const/realax/real_le' @ sK0 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f49,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f31,f46,f43]) ).
thf(f31,plain,
! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 ) )
| ( ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA092^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 03:50:57 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.47 ---- Original DTF file ---
% 0.32/0.47 thf(spec,logic,$$dhol).
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 % File : ANA092^1 : TPTP v9.2.1. Released v7.0.0.
% 0.32/0.47 % Domain : Analysis
% 0.32/0.47 % Problem : REAL_LE_INF_EQ
% 0.32/0.47 % Version : Especial.
% 0.32/0.47 % English :
% 0.32/0.47
% 0.32/0.47 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.32/0.47 % Source : [Kal16]
% 0.32/0.47 % Names : REAL_LE_INF_EQ_.p [Kal16]
% 0.32/0.47
% 0.32/0.47 % Status : Theorem
% 0.32/0.47 % Rating : 0.00 v7.1.0
% 0.32/0.47 % Syntax : Number of formulae : 8 ( 0 unt; 5 typ; 0 def)
% 0.32/0.47 % Number of atoms : 20 ( 3 equ; 0 cnn)
% 0.32/0.47 % Maximal formula atoms : 8 ( 6 avg)
% 0.32/0.47 % Number of connectives : 55 ( 2 ~; 0 |; 4 &; 40 @)
% 0.32/0.47 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.32/0.47 % Maximal formula depth : 13 ( 11 avg)
% 0.32/0.47 % Number of types : 2 ( 1 usr)
% 0.32/0.47 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.32/0.47 % Number of symbols : 5 ( 4 usr; 0 con; 1-3 aty)
% 0.32/0.47 % Number of variables : 18 ( 0 ^; 14 !; 2 ?; 18 :)
% 0.32/0.47 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.32/0.47 % SPC : TH1_THM_EQU_NAR
% 0.32/0.47
% 0.32/0.47 % Comments : Exported from core HOL Light.
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 thf('thf_type_type/realax/real',type,
% 0.32/0.47 'type/realax/real': $tType ).
% 0.32/0.47
% 0.32/0.47 thf('thf_const_const/sets/inf',type,
% 0.32/0.47 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.32/0.47
% 0.32/0.47 thf('thf_const_const/sets/IN',type,
% 0.32/0.47 'const/sets/IN':
% 0.32/0.47 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.32/0.47
% 0.32/0.47 thf('thf_const_const/sets/EMPTY',type,
% 0.32/0.47 'const/sets/EMPTY':
% 0.32/0.47 !>[A: $tType] : ( A > $o ) ).
% 0.32/0.47
% 0.32/0.47 thf('thf_const_const/realax/real_le',type,
% 0.32/0.47 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.32/0.47
% 0.32/0.47 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 0.32/0.47 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.32/0.47 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 0.32/0.47 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.32/0.47 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 0.32/0.47
% 0.32/0.47 thf('thm/sets/INF_',axiom,
% 0.32/0.47 ! [A: 'type/realax/real' > $o] :
% 0.32/0.47 ( ( ( A
% 0.32/0.47 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.32/0.47 & ? [A0: 'type/realax/real'] :
% 0.32/0.47 ! [A1: 'type/realax/real'] :
% 0.32/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.32/0.47 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 0.32/0.47 => ( ! [A0: 'type/realax/real'] :
% 0.32/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.32/0.47 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
% 0.32/0.47 & ! [A0: 'type/realax/real'] :
% 0.32/0.47 ( ! [A1: 'type/realax/real'] :
% 0.32/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.32/0.47 => ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.32/0.47 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf('thm/sets/REAL_LE_INF_EQ_',conjecture,
% 0.32/0.47 ! [A: $tType,A0: 'type/realax/real',A1: 'type/realax/real' > $o,A2: A] :
% 0.32/0.47 ( ( ( A1
% 0.32/0.47 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.32/0.47 & ? [A3: 'type/realax/real'] :
% 0.32/0.47 ! [A4: 'type/realax/real'] :
% 0.32/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A4 @ A1 )
% 0.32/0.47 => ( 'const/realax/real_le' @ A3 @ A4 ) ) )
% 0.32/0.47 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A1 ) )
% 0.32/0.47 = ( ! [A3: 'type/realax/real'] :
% 0.32/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A3 @ A1 )
% 0.32/0.47 => ( 'const/realax/real_le' @ A0 @ A3 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 1.48/1.29 ---- Embedded in THF ---
% 1.48/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.29 %%% Generated on Tue Feb 24 03:50:58 EST 2026
% 1.48/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.29 %%% Logic specification used:
% 1.48/1.29 %%% thf(spec, logic, $$dhol).
% 1.48/1.29
% 1.48/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ASb0gG0Q01/DTF2DTF21590.p
% See solution above
% 1.48/1.29 ------------------------
% 1.68/1.30 ---- Cleaned THF ---
% 1.68/1.31 thf('thf_type_type/realax/real',type,
% 1.68/1.31 'type/realax/real': $tType ).
% 1.68/1.31
% 1.68/1.31 thf('thf_const_const/sets/inf',type,
% 1.68/1.31 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 1.68/1.31
% 1.68/1.31 thf('thf_const_const/sets/IN',type,
% 1.68/1.31 'const/sets/IN':
% 1.68/1.31 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.68/1.31
% 1.68/1.31 thf('thf_const_const/sets/EMPTY',type,
% 1.68/1.31 'const/sets/EMPTY':
% 1.68/1.31 !>[A: $tType] : ( A > $o ) ).
% 1.68/1.31
% 1.68/1.31 thf('thf_const_const/realax/real_le',type,
% 1.68/1.31 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.68/1.31
% 1.68/1.31 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 1.68/1.31 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 1.68/1.31 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 1.68/1.31 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 1.68/1.31 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 1.68/1.31
% 1.68/1.31 thf('thm/sets/INF_',axiom,
% 1.68/1.31 ! [A: 'type/realax/real' > $o] :
% 1.68/1.31 ( ( ( A
% 1.68/1.31 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.68/1.31 & ? [A0: 'type/realax/real'] :
% 1.68/1.31 ! [A1: 'type/realax/real'] :
% 1.68/1.31 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.68/1.31 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 1.68/1.31 => ( ! [A0: 'type/realax/real'] :
% 1.68/1.31 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 1.68/1.31 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
% 1.68/1.31 & ! [A0: 'type/realax/real'] :
% 1.68/1.31 ( ! [A1: 'type/realax/real'] :
% 1.68/1.31 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.68/1.31 => ( 'const/realax/real_le' @ A0 @ A1 ) )
% 1.68/1.31 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
% 1.68/1.31
% 1.68/1.31 thf('thm/sets/REAL_LE_INF_EQ_',conjecture,
% 1.68/1.31 ! [A: $tType,A0: 'type/realax/real',A1: 'type/realax/real' > $o,A2: A] :
% 1.68/1.31 ( ( ( A1
% 1.68/1.31 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.68/1.31 & ? [A3: 'type/realax/real'] :
% 1.68/1.31 ! [A4: 'type/realax/real'] :
% 1.68/1.31 ( ( 'const/sets/IN' @ 'type/realax/real' @ A4 @ A1 )
% 1.68/1.31 => ( 'const/realax/real_le' @ A3 @ A4 ) ) )
% 1.68/1.31 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A1 ) )
% 1.68/1.31 = ( ! [A3: 'type/realax/real'] :
% 1.68/1.31 ( ( 'const/sets/IN' @ 'type/realax/real' @ A3 @ A1 )
% 1.68/1.31 => ( 'const/realax/real_le' @ A0 @ A3 ) ) ) ) ) ).
% 1.68/1.31 ------------------------
% 1.68/1.32 % (21924)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_21590 for (2999ds/275Mi)
% 1.68/1.32 % (21922)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21590 for (2999ds/2Mi)
% 1.68/1.32 % (21922)Instruction limit reached!
% 1.68/1.32 % (21922)------------------------------
% 1.68/1.32 % (21922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (21922)Termination reason: Unknown
% 1.68/1.32 % (21922)Termination phase: Property scanning
% 1.68/1.32
% 1.68/1.32 % (21922)Memory used [KB]: 1023
% 1.68/1.32 % (21922)Time elapsed: 0.002 s
% 1.68/1.32 % (21922)Instructions burned: 3 (million)
% 1.68/1.32 % (21922)------------------------------
% 1.68/1.32 % (21922)------------------------------
% 1.68/1.33 % (21920)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_21590 for (2999ds/4Mi)
% 1.68/1.33 % (21919)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21590 for (2999ds/183Mi)
% 1.68/1.33 % (21921)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_21590 for (2999ds/27Mi)
% 1.68/1.33 % (21923)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_21590 for (2999ds/2Mi)
% 1.68/1.33 % (21925)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21590 for (2999ds/18Mi)
% 1.68/1.33 % (21923)Instruction limit reached!
% 1.68/1.33 % (21923)------------------------------
% 1.68/1.33 % (21923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (21923)Termination reason: Unknown
% 1.68/1.33 % (21923)Termination phase: shuffling
% 1.68/1.33
% 1.68/1.33 % (21923)Memory used [KB]: 895
% 1.68/1.33 % (21923)Time elapsed: 0.003 s
% 1.68/1.33 % (21923)Instructions burned: 2 (million)
% 1.68/1.33 % (21923)------------------------------
% 1.68/1.33 % (21923)------------------------------
% 1.68/1.33 % (21920)Instruction limit reached!
% 1.68/1.33 % (21920)------------------------------
% 1.68/1.33 % (21920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (21920)Termination reason: Unknown
% 1.68/1.33 % (21920)Termination phase: Saturation
% 1.68/1.33
% 1.68/1.33 % (21920)Memory used [KB]: 5500
% 1.68/1.33 % (21920)Time elapsed: 0.005 s
% 1.68/1.33 % (21920)Instructions burned: 4 (million)
% 1.68/1.33 % (21920)------------------------------
% 1.68/1.33 % (21920)------------------------------
% 1.68/1.33 % (21926)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21590 for (2999ds/3Mi)
% 1.68/1.33 % (21924)First to succeed.
% 1.68/1.33 % (21926)Instruction limit reached!
% 1.68/1.33 % (21926)------------------------------
% 1.68/1.33 % (21926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (21926)Termination reason: Unknown
% 1.68/1.33 % (21926)Termination phase: Saturation
% 1.68/1.33
% 1.68/1.33 % (21926)Memory used [KB]: 5500
% 1.68/1.33 % (21926)Time elapsed: 0.003 s
% 1.68/1.33 % (21926)Instructions burned: 3 (million)
% 1.68/1.33 % (21926)------------------------------
% 1.68/1.33 % (21926)------------------------------
% 1.68/1.34 % (21924)Refutation found. Thanks to Tanya!
% 1.68/1.34 % SZS status Theorem for DTF2THF_21590
% 1.68/1.34 % SZS output start Proof for DTF2THF_21590
% 1.68/1.34 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.68/1.34 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.68/1.34 thf(func_def_1, type, 'const/sets/inf': ('type/realax/real' > $o) > 'type/realax/real').
% 1.68/1.34 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.68/1.34 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.68/1.34 thf(func_def_4, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.68/1.34 thf(func_def_8, type, sK0: 'type/realax/real').
% 1.68/1.34 thf(func_def_9, type, sK1: 'type/realax/real' > $o).
% 1.68/1.34 thf(func_def_10, type, sK2: 'type/realax/real').
% 1.68/1.34 thf(func_def_11, type, sK3: 'type/realax/real').
% 1.68/1.34 thf(func_def_12, type, sK4: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.68/1.34 thf(func_def_13, type, sK5: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.68/1.34 thf(func_def_15, type, ph7: !>[X0: $tType]:(X0)).
% 1.68/1.34 thf(func_def_16, type, sK8: 'type/realax/real').
% 1.68/1.34 thf(f263,plain,(
% 1.68/1.34 $false),
% 1.68/1.34 inference(avatar_sat_refutation,[status(thm)],[f49,f54,f59,f104,f109,f122,f128,f130,f136,f149,f168,f235,f262])).
% 1.68/1.34 thf(f262,plain,(
% 1.68/1.34 spl6_15 | ~spl6_1 | ~spl6_14),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f260,f120,f43,f166])).
% 1.68/1.34 thf(f166,definition,(
% 1.68/1.34 spl6_15 <=> ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK0 @ (sK4 @ X0 @ sK1))) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true))),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl6_15])],[avatar_definition])).
% 1.68/1.34 thf(f43,definition,(
% 1.68/1.34 spl6_1 <=> ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1)) | ($true = ('const/realax/real_le' @ sK0 @ X3)))),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.68/1.34 thf(f120,definition,(
% 1.68/1.34 spl6_14 <=> ! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1) = $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1))))),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl6_14])],[avatar_definition])).
% 1.68/1.34 thf(f260,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true) | ($true = ('const/realax/real_le' @ sK0 @ (sK4 @ X0 @ sK1)))) ) | (~spl6_1 | ~spl6_14)),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f257])).
% 1.68/1.34 thf(f257,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true) | ($true = ('const/realax/real_le' @ sK0 @ (sK4 @ X0 @ sK1))) | ($true != $true)) ) | (~spl6_1 | ~spl6_14)),
% 1.68/1.34 inference(superposition,[status(thm)],[f44,f121])).
% 1.68/1.34 thf(f121,plain,(
% 1.68/1.34 ( ! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1) = $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)))) ) | ~spl6_14),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f120])).
% 1.68/1.34 thf(f44,plain,(
% 1.68/1.34 ( ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1)) | ($true = ('const/realax/real_le' @ sK0 @ X3))) ) | ~spl6_1),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.68/1.34 thf(f235,plain,(
% 1.68/1.34 spl6_2 | ~spl6_11 | ~spl6_15),
% 1.68/1.34 inference(avatar_contradiction_clause,[status(thm)],[f234])).
% 1.68/1.34 thf(f234,plain,(
% 1.68/1.34 $false | (spl6_2 | ~spl6_11 | ~spl6_15)),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f231,f47])).
% 1.68/1.34 thf(f47,plain,(
% 1.68/1.34 (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) != $true) | spl6_2),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.68/1.34 thf(f46,definition,(
% 1.68/1.34 spl6_2 <=> (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) = $true)),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.68/1.34 thf(f231,plain,(
% 1.68/1.34 (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) = $true) | (~spl6_11 | ~spl6_15)),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f230])).
% 1.68/1.34 thf(f230,plain,(
% 1.68/1.34 (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) = $true) | ($true != $true) | (~spl6_11 | ~spl6_15)),
% 1.68/1.34 inference(duplicate_literal_removal,[status(thm)],[f227])).
% 1.68/1.34 thf(f227,plain,(
% 1.68/1.34 ($true != $true) | (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) = $true) | (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) = $true) | (~spl6_11 | ~spl6_15)),
% 1.68/1.34 inference(superposition,[status(thm)],[f108,f167])).
% 1.68/1.34 thf(f167,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK0 @ (sK4 @ X0 @ sK1))) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true)) ) | ~spl6_15),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f166])).
% 1.68/1.34 thf(f108,plain,(
% 1.68/1.34 ( ! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ (sK4 @ X1 @ sK1)) != $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)))) ) | ~spl6_11),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f107])).
% 1.68/1.34 thf(f107,definition,(
% 1.68/1.34 spl6_11 <=> ! [X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1))) | (('const/realax/real_le' @ X1 @ (sK4 @ X1 @ sK1)) != $true))),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl6_11])],[avatar_definition])).
% 1.68/1.34 thf(f168,plain,(
% 1.68/1.34 spl6_15 | spl6_12 | ~spl6_1),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f164,f43,f112,f166])).
% 1.68/1.34 thf(f112,definition,(
% 1.68/1.34 spl6_12 <=> ! [X1 : 'type/realax/real'] : (('const/realax/real_le' @ X1 @ (sK5 @ X1 @ sK1)) != $true)),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl6_12])],[avatar_definition])).
% 1.68/1.34 thf(f164,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK0 @ (sK4 @ X0 @ sK1))) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true) | (('const/realax/real_le' @ X1 @ (sK5 @ X1 @ sK1)) != $true)) ) | ~spl6_1),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f159,f34])).
% 1.68/1.34 thf(f34,plain,(
% 1.68/1.34 ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f25])).
% 1.68/1.34 thf(f25,plain,(
% 1.68/1.34 ('const/sets/EMPTY' @ 'type/realax/real' != sK1) & ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) != $true) | ((('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1) = $true) & (('const/realax/real_le' @ sK0 @ sK2) != $true))) & ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) = $true) | ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1)) | ($true = ('const/realax/real_le' @ sK0 @ X3)))) & ! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ sK1) != $true) | ($true = ('const/realax/real_le' @ sK3 @ X5)))),
% 1.68/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f24,f23,f22])).
% 1.68/1.34 thf(f22,plain,(
% 1.68/1.34 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' != X1) & ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)) != $true) | ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) = $true) & (('const/realax/real_le' @ X0 @ X2) != $true))) & ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)) = $true) | ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) != $true) | ($true = ('const/realax/real_le' @ X0 @ X3)))) & ? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X1)) | (('const/realax/real_le' @ X4 @ X5) = $true))) => (('const/sets/EMPTY' @ 'type/realax/real' != sK1) & ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) != $true) | ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1) = $true) & (('const/realax/real_le' @ sK0 @ X2) != $true))) & ((('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) = $true) | ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1)) | ($true = ('const/realax/real_le' @ sK0 @ X3)))) & ? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ sK1) != $true) | (('const/realax/real_le' @ X4 @ X5) = $true)))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f23,plain,(
% 1.68/1.34 ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1) = $true) & (('const/realax/real_le' @ sK0 @ X2) != $true)) => ((('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1) = $true) & (('const/realax/real_le' @ sK0 @ sK2) != $true))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f24,plain,(
% 1.68/1.34 ? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ sK1) != $true) | (('const/realax/real_le' @ X4 @ X5) = $true)) => ! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ sK1) != $true) | ($true = ('const/realax/real_le' @ sK3 @ X5)))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f21,plain,(
% 1.68/1.34 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' != X1) & ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)) != $true) | ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) = $true) & (('const/realax/real_le' @ X0 @ X2) != $true))) & ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)) = $true) | ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) != $true) | ($true = ('const/realax/real_le' @ X0 @ X3)))) & ? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X1)) | (('const/realax/real_le' @ X4 @ X5) = $true)))),
% 1.68/1.34 inference(rectify,[status(thm)],[f20])).
% 1.68/1.34 thf(f20,plain,(
% 1.68/1.34 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' != X1) & ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)) != $true) | ? [X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ X4 @ X1)) & ($true != ('const/realax/real_le' @ X0 @ X4)))) & ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)) = $true) | ! [X4 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X4 @ X1)) | ($true = ('const/realax/real_le' @ X0 @ X4)))) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) != $true) | ($true = ('const/realax/real_le' @ X2 @ X3))))),
% 1.68/1.34 inference(flattening,[status(thm)],[f19])).
% 1.68/1.34 thf(f19,plain,(
% 1.68/1.34 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' != X1) & (((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)) != $true) | ? [X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ X4 @ X1)) & ($true != ('const/realax/real_le' @ X0 @ X4)))) & ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)) = $true) | ! [X4 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X4 @ X1)) | ($true = ('const/realax/real_le' @ X0 @ X4))))) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) != $true) | ($true = ('const/realax/real_le' @ X2 @ X3))))),
% 1.68/1.34 inference(nnf_transformation,[status(thm)],[f18])).
% 1.68/1.34 thf(f18,plain,(
% 1.68/1.34 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' != X1) & (! [X4 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X4 @ X1)) | ($true = ('const/realax/real_le' @ X0 @ X4))) <~> (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)) = $true)) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) != $true) | ($true = ('const/realax/real_le' @ X2 @ X3))))),
% 1.68/1.34 inference(flattening,[status(thm)],[f17])).
% 1.68/1.34 thf(f17,plain,(
% 1.68/1.34 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : ((! [X4 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X4 @ X1)) | ($true = ('const/realax/real_le' @ X0 @ X4))) <~> (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)) = $true)) & (('const/sets/EMPTY' @ 'type/realax/real' != X1) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) != $true) | ($true = ('const/realax/real_le' @ X2 @ X3)))))),
% 1.68/1.34 inference(ennf_transformation,[status(thm)],[f12])).
% 1.68/1.34 thf(f12,plain,(
% 1.68/1.34 ~! [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X1) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) = $true) => ($true = ('const/realax/real_le' @ X2 @ X3)))) => ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ X1)) = $true) <=> ! [X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ X4 @ X1)) => ($true = ('const/realax/real_le' @ X0 @ X4)))))),
% 1.68/1.34 inference(rectify,[status(thm)],[f7])).
% 1.68/1.34 thf(f7,plain,(
% 1.68/1.34 ~! [X1 : 'type/realax/real',X2 : 'type/realax/real' > $o] : ((? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X2) = $true) => (('const/realax/real_le' @ X4 @ X5) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X2)) => (! [X6 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X6 @ X2) = $true) => (('const/realax/real_le' @ X1 @ X6) = $true)) <=> (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X2)) = $true)))),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f6])).
% 1.68/1.34 thf(f6,plain,(
% 1.68/1.34 ~! [X1 : 'type/realax/real',X2 : 'type/realax/real' > $o] : ((? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X2) => ('const/realax/real_le' @ X4 @ X5)) & ('const/sets/EMPTY' @ 'type/realax/real' != X2)) => (! [X6 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X6 @ X2) => ('const/realax/real_le' @ X1 @ X6)) = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X2))))),
% 1.68/1.34 inference(rectify,[status(thm)],[f4])).
% 1.68/1.34 thf(f4,negated_conjecture,(
% 1.68/1.34 ~! [X0 : $tType,X1 : 'type/realax/real',X2 : 'type/realax/real' > $o,X3 : X0] : ((? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X2) => ('const/realax/real_le' @ X4 @ X5)) & ('const/sets/EMPTY' @ 'type/realax/real' != X2)) => (! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X2) => ('const/realax/real_le' @ X1 @ X4)) = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X2))))),
% 1.68/1.34 inference(negated_conjecture,[status(cth)],[f3])).
% 1.68/1.34 thf(f3,conjecture,(
% 1.68/1.34 ! [X0 : $tType,X1 : 'type/realax/real',X2 : 'type/realax/real' > $o,X3 : X0] : ((? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X2) => ('const/realax/real_le' @ X4 @ X5)) & ('const/sets/EMPTY' @ 'type/realax/real' != X2)) => (! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X2) => ('const/realax/real_le' @ X1 @ X4)) = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X2))))),
% 1.68/1.34 file('/export/starexec/sandbox/tmp/tmp.ASb0gG0Q01/DTF2THF_21590.p','thm/sets/REAL_LE_INF_EQ_')).
% 1.68/1.34 thf(f159,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = ('const/realax/real_le' @ sK0 @ (sK4 @ X0 @ sK1))) | (('const/realax/real_le' @ X1 @ (sK5 @ X1 @ sK1)) != $true)) ) | ~spl6_1),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f155])).
% 1.68/1.34 thf(f155,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = ('const/realax/real_le' @ sK0 @ (sK4 @ X0 @ sK1))) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true) | ($true != $true) | (('const/realax/real_le' @ X1 @ (sK5 @ X1 @ sK1)) != $true)) ) | ~spl6_1),
% 1.68/1.34 inference(superposition,[status(thm)],[f44,f36])).
% 1.68/1.34 thf(f36,plain,(
% 1.68/1.34 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X2 @ X0) @ X0)) | ($true != ('const/realax/real_le' @ X4 @ (sK5 @ X4 @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)) = $true)) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.68/1.34 thf(f29,plain,(
% 1.68/1.34 ! [X0 : 'type/realax/real' > $o] : ((! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true)) & ! [X2 : 'type/realax/real'] : ((($true != ('const/realax/real_le' @ X2 @ (sK4 @ X2 @ X0))) & ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X2 @ X0) @ X0))) | (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)) = $true))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0)) & ($true != ('const/realax/real_le' @ X4 @ (sK5 @ X4 @ X0)))))),
% 1.68/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f26,f28,f27])).
% 1.68/1.34 thf(f27,plain,(
% 1.68/1.34 ! [X0 : 'type/realax/real' > $o,X2 : 'type/realax/real'] : (? [X3 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X2 @ X3)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) => (($true != ('const/realax/real_le' @ X2 @ (sK4 @ X2 @ X0))) & ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X2 @ X0) @ X0))))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f28,plain,(
% 1.68/1.34 ! [X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) & (('const/realax/real_le' @ X4 @ X5) != $true)) => (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0)) & ($true != ('const/realax/real_le' @ X4 @ (sK5 @ X4 @ X0)))))),
% 1.68/1.34 introduced(definition,[],[choice_axiom])).
% 1.68/1.34 thf(f26,plain,(
% 1.68/1.34 ! [X0 : 'type/realax/real' > $o] : ((! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true)) & ! [X2 : 'type/realax/real'] : (? [X3 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X2 @ X3)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) | (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)) = $true))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X4 : 'type/realax/real'] : ? [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) & (('const/realax/real_le' @ X4 @ X5) != $true)))),
% 1.68/1.34 inference(rectify,[status(thm)],[f14])).
% 1.68/1.34 thf(f14,plain,(
% 1.68/1.34 ! [X0 : 'type/realax/real' > $o] : ((! [X3 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3) = $true) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) & ! [X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ X5) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true)) | (('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)) = $true))) | ('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' @ X1 @ X2) != $true)))),
% 1.68/1.34 inference(flattening,[status(thm)],[f13])).
% 1.68/1.34 thf(f13,plain,(
% 1.68/1.34 ! [X0 : 'type/realax/real' > $o] : ((! [X3 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3) = $true) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) & ! [X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ X5) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true)) | (('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)) = $true))) | (('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' @ X1 @ X2) != $true))))),
% 1.68/1.34 inference(ennf_transformation,[status(thm)],[f11])).
% 1.68/1.34 thf(f11,plain,(
% 1.68/1.34 ! [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' @ X1 @ X2) = $true))) => (! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) => (('const/realax/real_le' @ X4 @ X5) = $true)) => (('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)) = $true)) & ! [X3 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) => (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3) = $true))))),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f10])).
% 1.68/1.34 thf(f10,plain,(
% 1.68/1.34 ! [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)))))),
% 1.68/1.34 inference(rectify,[status(thm)],[f2])).
% 1.68/1.34 thf(f2,axiom,(
% 1.68/1.34 ! [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)))))),
% 1.68/1.34 file('/export/starexec/sandbox/tmp/tmp.ASb0gG0Q01/DTF2THF_21590.p','thm/sets/INF_')).
% 1.68/1.34 thf(f149,plain,(
% 1.68/1.34 ~spl6_2 | spl6_3 | ~spl6_4 | ~spl6_10),
% 1.68/1.34 inference(avatar_contradiction_clause,[status(thm)],[f148])).
% 1.68/1.34 thf(f148,plain,(
% 1.68/1.34 $false | (~spl6_2 | spl6_3 | ~spl6_4 | ~spl6_10)),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f145,f58])).
% 1.68/1.34 thf(f58,plain,(
% 1.68/1.34 (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1) = $true) | ~spl6_4),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.68/1.34 thf(f56,definition,(
% 1.68/1.34 spl6_4 <=> (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1) = $true)),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition])).
% 1.68/1.34 thf(f145,plain,(
% 1.68/1.34 (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1) != $true) | (~spl6_2 | spl6_3 | ~spl6_10)),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f140])).
% 1.68/1.34 thf(f140,plain,(
% 1.68/1.34 ($true != $true) | (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1) != $true) | (~spl6_2 | spl6_3 | ~spl6_10)),
% 1.68/1.34 inference(superposition,[status(thm)],[f86,f103])).
% 1.68/1.34 thf(f103,plain,(
% 1.68/1.34 ( ! [X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X1)) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1) != $true)) ) | ~spl6_10),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f102])).
% 1.68/1.34 thf(f102,definition,(
% 1.68/1.34 spl6_10 <=> ! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1) != $true) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X1)))),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl6_10])],[avatar_definition])).
% 1.68/1.34 thf(f86,plain,(
% 1.68/1.34 (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) != $true) | (~spl6_2 | spl6_3)),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.68/1.34 thf(f84,plain,(
% 1.68/1.34 ($true != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) != $true) | (~spl6_2 | spl6_3)),
% 1.68/1.34 inference(superposition,[status(thm)],[f82,f48])).
% 1.68/1.34 thf(f48,plain,(
% 1.68/1.34 (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) = $true) | ~spl6_2),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.68/1.34 thf(f82,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ sK0 @ X0) != $true) | (('const/realax/real_le' @ X0 @ sK2) != $true)) ) | spl6_3),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.68/1.34 thf(f81,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ sK2) != $true) | (('const/realax/real_le' @ sK0 @ X0) != $true) | ($true != $true)) ) | spl6_3),
% 1.68/1.34 inference(superposition,[status(thm)],[f53,f35])).
% 1.68/1.34 thf(f35,plain,(
% 1.68/1.34 ( ! [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)) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f16])).
% 1.68/1.34 thf(f16,plain,(
% 1.68/1.34 ! [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))),
% 1.68/1.34 inference(flattening,[status(thm)],[f15])).
% 1.68/1.34 thf(f15,plain,(
% 1.68/1.34 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X2) = $true) | ((('const/realax/real_le' @ X0 @ X1) != $true) | (('const/realax/real_le' @ X1 @ X2) != $true)))),
% 1.68/1.34 inference(ennf_transformation,[status(thm)],[f9])).
% 1.68/1.34 thf(f9,plain,(
% 1.68/1.34 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X1) = $true) & (('const/realax/real_le' @ X1 @ X2) = $true)) => (('const/realax/real_le' @ X0 @ X2) = $true))),
% 1.68/1.34 inference(fool_elimination,[status(thm)],[f8])).
% 1.68/1.34 thf(f8,plain,(
% 1.68/1.34 ! [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))),
% 1.68/1.34 inference(rectify,[status(thm)],[f1])).
% 1.68/1.34 thf(f1,axiom,(
% 1.68/1.34 ! [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))),
% 1.68/1.34 file('/export/starexec/sandbox/tmp/tmp.ASb0gG0Q01/DTF2THF_21590.p','thm/realax/REAL_LE_TRANS_')).
% 1.68/1.34 thf(f53,plain,(
% 1.68/1.34 (('const/realax/real_le' @ sK0 @ sK2) != $true) | spl6_3),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.68/1.34 thf(f51,definition,(
% 1.68/1.34 spl6_3 <=> (('const/realax/real_le' @ sK0 @ sK2) = $true)),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition])).
% 1.68/1.34 thf(f136,plain,(
% 1.68/1.34 ~spl6_9 | ~spl6_12),
% 1.68/1.34 inference(avatar_contradiction_clause,[status(thm)],[f135])).
% 1.68/1.34 thf(f135,plain,(
% 1.68/1.34 $false | (~spl6_9 | ~spl6_12)),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f133])).
% 1.68/1.34 thf(f133,plain,(
% 1.68/1.34 ($true != $true) | (~spl6_9 | ~spl6_12)),
% 1.68/1.34 inference(superposition,[status(thm)],[f113,f100])).
% 1.68/1.34 thf(f100,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK3 @ (sK5 @ X0 @ sK1)))) ) | ~spl6_9),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f99])).
% 1.68/1.34 thf(f99,definition,(
% 1.68/1.34 spl6_9 <=> ! [X0 : 'type/realax/real'] : ($true = ('const/realax/real_le' @ sK3 @ (sK5 @ X0 @ sK1)))),
% 1.68/1.34 introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition])).
% 1.68/1.34 thf(f113,plain,(
% 1.68/1.34 ( ! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ (sK5 @ X1 @ sK1)) != $true)) ) | ~spl6_12),
% 1.68/1.34 inference(avatar_component_clause,[status(thm)],[f112])).
% 1.68/1.34 thf(f130,plain,(
% 1.68/1.34 spl6_10 | ~spl6_9),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f129,f99,f102])).
% 1.68/1.34 thf(f129,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0) = $true)) ) | ~spl6_9),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f125,f34])).
% 1.68/1.34 thf(f125,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0) = $true)) ) | ~spl6_9),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f124])).
% 1.68/1.34 thf(f124,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1) != $true) | ($true != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0) = $true)) ) | ~spl6_9),
% 1.68/1.34 inference(superposition,[status(thm)],[f40,f100])).
% 1.68/1.34 thf(f40,plain,(
% 1.68/1.34 ( ! [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) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1) = $true)) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.68/1.34 thf(f128,plain,(
% 1.68/1.34 spl6_11 | ~spl6_9),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f127,f99,f107])).
% 1.68/1.34 thf(f127,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true) | ($true != ('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1)))) ) | ~spl6_9),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f126,f34])).
% 1.68/1.34 thf(f126,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true) | ($true != ('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1)))) ) | ~spl6_9),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f123])).
% 1.68/1.34 thf(f123,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != $true) | ($true != ('const/realax/real_le' @ X0 @ (sK4 @ X0 @ sK1))) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true)) ) | ~spl6_9),
% 1.68/1.34 inference(superposition,[status(thm)],[f38,f100])).
% 1.68/1.34 thf(f38,plain,(
% 1.68/1.34 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X4 @ (sK5 @ X4 @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != ('const/realax/real_le' @ X2 @ (sK4 @ X2 @ X0))) | (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)) = $true)) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.68/1.34 thf(f122,plain,(
% 1.68/1.34 spl6_14 | spl6_9),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f118,f99,f120])).
% 1.68/1.34 thf(f118,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1) = $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1))) | ($true = ('const/realax/real_le' @ sK3 @ (sK5 @ X0 @ sK1)))) )),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f93,f34])).
% 1.68/1.34 thf(f93,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1))) | (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = ('const/realax/real_le' @ sK3 @ (sK5 @ X0 @ sK1)))) )),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.68/1.34 thf(f88,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = ('const/realax/real_le' @ sK3 @ (sK5 @ X0 @ sK1))) | ($true != $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1))) | (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK1) @ sK1) = $true)) )),
% 1.68/1.34 inference(superposition,[status(thm)],[f30,f37])).
% 1.68/1.34 thf(f37,plain,(
% 1.68/1.34 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0)) | (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)) = $true) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X2 @ X0) @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.68/1.34 thf(f30,plain,(
% 1.68/1.34 ( ! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ sK1) != $true) | ($true = ('const/realax/real_le' @ sK3 @ X5))) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f25])).
% 1.68/1.34 thf(f109,plain,(
% 1.68/1.34 spl6_9 | spl6_11),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f105,f107,f99])).
% 1.68/1.34 thf(f105,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK3 @ (sK5 @ X0 @ sK1))) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1))) | (('const/realax/real_le' @ X1 @ (sK4 @ X1 @ sK1)) != $true)) )),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f95,f34])).
% 1.68/1.34 thf(f95,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ (sK4 @ X1 @ sK1)) != $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = ('const/realax/real_le' @ sK3 @ (sK5 @ X0 @ sK1)))) )),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.68/1.34 thf(f89,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = ('const/realax/real_le' @ sK3 @ (sK5 @ X0 @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ X1 @ (sK4 @ X1 @ sK1)) != $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)))) )),
% 1.68/1.34 inference(superposition,[status(thm)],[f30,f39])).
% 1.68/1.34 thf(f39,plain,(
% 1.68/1.34 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X4 @ X0) @ X0)) | (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != ('const/realax/real_le' @ X2 @ (sK4 @ X2 @ X0)))) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.68/1.34 thf(f104,plain,(
% 1.68/1.34 spl6_9 | spl6_10),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f97,f102,f99])).
% 1.68/1.34 thf(f97,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1) != $true) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X1)) | ($true = ('const/realax/real_le' @ sK3 @ (sK5 @ X0 @ sK1)))) )),
% 1.68/1.34 inference(subsumption_resolution,[status(thm)],[f96,f34])).
% 1.68/1.34 thf(f96,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ sK3 @ (sK5 @ X0 @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X1)) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1) != $true)) )),
% 1.68/1.34 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.68/1.34 thf(f87,plain,(
% 1.68/1.34 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X1)) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1) != $true) | ($true = ('const/realax/real_le' @ sK3 @ (sK5 @ X0 @ sK1))) | ($true != $true)) )),
% 1.68/1.34 inference(superposition,[status(thm)],[f30,f41])).
% 1.68/1.34 thf(f41,plain,(
% 1.68/1.34 ( ! [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/realax/real_le' @ ('const/sets/inf' @ X0) @ X1) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true)) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f29])).
% 1.68/1.34 thf(f59,plain,(
% 1.68/1.34 ~spl6_2 | spl6_4),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f33,f56,f46])).
% 1.68/1.34 thf(f33,plain,(
% 1.68/1.34 (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) != $true) | (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1) = $true)),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f25])).
% 1.68/1.34 thf(f54,plain,(
% 1.68/1.34 ~spl6_3 | ~spl6_2),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f32,f46,f51])).
% 1.68/1.34 thf(f32,plain,(
% 1.68/1.34 (('const/realax/real_le' @ sK0 @ sK2) != $true) | (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) != $true)),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f25])).
% 1.68/1.34 thf(f49,plain,(
% 1.68/1.34 spl6_1 | spl6_2),
% 1.68/1.34 inference(avatar_split_clause,[status(thm)],[f31,f46,f43])).
% 1.68/1.34 thf(f31,plain,(
% 1.68/1.34 ( ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1)) | (('const/realax/real_le' @ sK0 @ ('const/sets/inf' @ sK1)) = $true) | ($true = ('const/realax/real_le' @ sK0 @ X3))) )),
% 1.68/1.34 inference(cnf_transformation,[status(thm)],[f25])).
% 1.68/1.34 % SZS output end Proof for DTF2THF_21590
% 1.68/1.34 % (21924)------------------------------
% 1.68/1.34 % (21924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (21924)Termination reason: Refutation
% 1.68/1.34
% 1.68/1.34 % (21924)Memory used [KB]: 5756
% 1.68/1.34 % (21924)Time elapsed: 0.016 s
% 1.68/1.34 % (21924)Instructions burned: 35 (million)
% 1.68/1.34 % (21924)------------------------------
% 1.68/1.34 % (21924)------------------------------
% 1.68/1.34 % (21918)Success in time 0.024 s
%------------------------------------------------------------------------------