%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA080^1 : 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 : n012.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 08:38:49 AM UTC 2026
% Result : Theorem 1.55s 1.30s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 109 ( 1 unt; 0 typ; 10 def)
% Number of atoms : 1133 ( 304 equ; 0 cnn)
% Maximal formula atoms : 20 ( 10 avg)
% Number of connectives : 1402 ( 195 ~; 221 |; 59 &; 879 @)
% ( 11 <=>; 35 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 16 con; 0-3 aty)
% Number of variables : 198 ( 0 ^; 157 !; 41 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_4,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_8,type,
sK0: '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: '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(f227,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f49,f53,f58,f105,f115,f128,f130,f144,f152,f193,f202,f222,f226]) ).
thf(f226,plain,
( spl6_14
| ~ spl6_12 ),
inference(avatar_split_clause,[status(thm)],[f225,f103,f113]) ).
thf(f113,definition,
( spl6_14
<=> ! [X1: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_14])],[avatar_definition]) ).
thf(f103,definition,
( spl6_12
<=> ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_12])],[avatar_definition]) ).
thf(f225,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) ) )
| ~ spl6_12 ),
inference(subsumption_resolution,[status(thm)],[f224,f33]) ).
thf(f33,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ( ( ( $true
!= ( 'const/realax/real_le' @ sK2 @ sK1 ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true ) )
| ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) )
& ( ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X3 @ sK1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 )
!= $true ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) )
& ! [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X5 @ sK3 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f23,f22,f21]) ).
thf(f21,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
!= $true ) )
& ( ! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X3 @ X1 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true ) )
& ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X5 @ X4 ) ) ) )
=> ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ( ? [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X2 @ sK1 ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
= $true ) )
| ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) )
& ( ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X3 @ sK1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 )
!= $true ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) )
& ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X5 @ X4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X2 @ sK1 ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
= $true ) )
=> ( ( $true
!= ( 'const/realax/real_le' @ sK2 @ sK1 ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X5 @ X4 ) ) )
=> ! [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X5 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
!= $true ) )
& ( ! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X3 @ X1 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true ) )
& ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X5 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ? [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X4 @ X1 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
!= $true ) )
& ( ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X4 @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ? [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X4 @ X1 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
!= $true ) )
& ( ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X4 @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
<~> ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X4 @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) ) ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
<~> ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X4 @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) ) )
=> ( ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) )
=> ( $true
= ( 'const/realax/real_le' @ X4 @ X1 ) ) )
<=> ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( 'const/realax/real_le' @ X3 @ X2 ) ) )
=> ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X4 @ X1 ) )
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( 'const/realax/real_le' @ X3 @ X2 ) ) )
=> ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) )
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( 'const/realax/real_le' @ X3 @ X2 ) ) )
=> ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) )
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FdEABJUAbk/DTF2THF_28211.p','thm/sets/REAL_SUP_LE_EQ_') ).
thf(f224,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) ) ) )
| ~ spl6_12 ),
inference(trivial_inequality_removal,[status(thm)],[f223]) ).
thf(f223,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) ) ) )
| ~ spl6_12 ),
inference(superposition,[status(thm)],[f34,f104]) ).
thf(f104,plain,
( ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ sK3 ) )
| ~ spl6_12 ),
inference(avatar_component_clause,[status(thm)],[f103]) ).
thf(f34,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X5: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X1 @ X0 ) @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X5 @ ( 'const/sets/sup' @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 ) )
& ( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X1 @ X0 ) @ X1 ) ) )
| ( ! [X3: 'type/realax/real'] :
( ( ( $true
!= ( 'const/realax/real_le' @ ( sK5 @ X3 @ X0 ) @ X3 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X3 @ X0 ) @ X0 ) ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X3 )
= $true ) )
& ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X5 @ ( 'const/sets/sup' @ X0 ) ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f25,f27,f26]) ).
thf(f26,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true ) )
=> ( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 ) )
& ( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X1 @ X0 ) @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
! [X0: 'type/realax/real' > $o,X3: 'type/realax/real'] :
( ? [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X4 @ X3 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) ) )
=> ( ( $true
!= ( 'const/realax/real_le' @ ( sK5 @ X3 @ X0 ) @ X3 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X3 @ X0 ) @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true ) )
| ( ! [X3: 'type/realax/real'] :
( ? [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X4 @ X3 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X3 )
= $true ) )
& ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X5 @ ( 'const/sets/sup' @ X0 ) ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true ) )
| ( ! [X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X5 @ X4 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) ) )
& ! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X5 @ X4 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) ) )
& ! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ 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' @ X2 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true ) ) )
=> ( ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
=> ( $true
= ( 'const/realax/real_le' @ X5 @ X4 ) ) )
=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
=> ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) ) ) ) ),
inference(fool_elimination,[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 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) )
& ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
=> ( 'const/realax/real_le' @ X5 @ X4 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) )
& ! [X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FdEABJUAbk/DTF2THF_28211.p','thm/sets/SUP_') ).
thf(f222,plain,
( spl6_1
| ~ spl6_2
| ~ spl6_4
| ~ spl6_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f221]) ).
thf(f221,plain,
( $false
| spl6_1
| ~ spl6_2
| ~ spl6_4
| ~ spl6_14 ),
inference(subsumption_resolution,[status(thm)],[f220,f57]) ).
thf(f57,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true )
| ~ spl6_4 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl6_4
<=> ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition]) ).
thf(f220,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
!= $true )
| spl6_1
| ~ spl6_2
| ~ spl6_14 ),
inference(trivial_inequality_removal,[status(thm)],[f217]) ).
thf(f217,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
!= $true )
| ( $true != $true )
| spl6_1
| ~ spl6_2
| ~ spl6_14 ),
inference(superposition,[status(thm)],[f215,f114]) ).
thf(f114,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) ) )
| ~ spl6_14 ),
inference(avatar_component_clause,[status(thm)],[f113]) ).
thf(f215,plain,
( ( $true
!= ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/sup' @ sK0 ) ) )
| spl6_1
| ~ spl6_2 ),
inference(trivial_inequality_removal,[status(thm)],[f212]) ).
thf(f212,plain,
( ( $true
!= ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $true != $true )
| spl6_1
| ~ spl6_2 ),
inference(superposition,[status(thm)],[f204,f47]) ).
thf(f47,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl6_2
<=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f204,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ sK1 ) )
| ( ( 'const/realax/real_le' @ sK2 @ X0 )
!= $true ) )
| spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f203]) ).
thf(f203,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK1 ) )
| ( ( 'const/realax/real_le' @ sK2 @ X0 )
!= $true ) )
| spl6_1 ),
inference(superposition,[status(thm)],[f44,f40]) ).
thf(f40,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[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(flattening,[status(thm)],[f16]) ).
thf(f16,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)],[f11]) ).
thf(f11,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)],[f10]) ).
thf(f10,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X0 @ X1 ) )
=> ( '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' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X0 @ X1 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.FdEABJUAbk/DTF2THF_28211.p','thm/realax/REAL_LE_TRANS_') ).
thf(f44,plain,
( ( $true
!= ( 'const/realax/real_le' @ sK2 @ sK1 ) )
| spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f42,definition,
( spl6_1
<=> ( $true
= ( 'const/realax/real_le' @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f202,plain,
( spl6_13
| spl6_2
| ~ spl6_15 ),
inference(avatar_split_clause,[status(thm)],[f201,f126,f46,f108]) ).
thf(f108,definition,
( spl6_13
<=> ! [X1: 'type/realax/real'] :
( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X1 @ sK0 ) @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_13])],[avatar_definition]) ).
thf(f126,definition,
( spl6_15
<=> ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_15])],[avatar_definition]) ).
thf(f201,plain,
( ! [X0: 'type/realax/real'] :
( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ X0 ) )
| spl6_2
| ~ spl6_15 ),
inference(subsumption_resolution,[status(thm)],[f200,f33]) ).
thf(f200,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ X0 ) ) )
| spl6_2
| ~ spl6_15 ),
inference(subsumption_resolution,[status(thm)],[f189,f48]) ).
thf(f48,plain,
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f189,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) )
| ~ spl6_15 ),
inference(trivial_inequality_removal,[status(thm)],[f188]) ).
thf(f188,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ X0 ) )
| ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) )
| ~ spl6_15 ),
inference(duplicate_literal_removal,[status(thm)],[f186]) ).
thf(f186,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) )
| ~ spl6_15 ),
inference(superposition,[status(thm)],[f36,f127]) ).
thf(f127,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true ) )
| ~ spl6_15 ),
inference(avatar_component_clause,[status(thm)],[f126]) ).
thf(f36,plain,
! [X3: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK5 @ X3 @ X0 ) @ X3 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X3 )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X1 @ X0 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f193,plain,
( spl6_2
| ~ spl6_11
| ~ spl6_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f192]) ).
thf(f192,plain,
( $false
| spl6_2
| ~ spl6_11
| ~ spl6_15 ),
inference(subsumption_resolution,[status(thm)],[f191,f48]) ).
thf(f191,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ~ spl6_11
| ~ spl6_15 ),
inference(trivial_inequality_removal,[status(thm)],[f190]) ).
thf(f190,plain,
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ~ spl6_11
| ~ spl6_15 ),
inference(duplicate_literal_removal,[status(thm)],[f187]) ).
thf(f187,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( $true != $true )
| ~ spl6_11
| ~ spl6_15 ),
inference(superposition,[status(thm)],[f101,f127]) ).
thf(f101,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK5 @ X1 @ sK0 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X1 ) ) )
| ~ spl6_11 ),
inference(avatar_component_clause,[status(thm)],[f100]) ).
thf(f100,definition,
( spl6_11
<=> ! [X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK5 @ X1 @ sK0 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_11])],[avatar_definition]) ).
thf(f152,plain,
( spl6_12
| ~ spl6_9 ),
inference(avatar_split_clause,[status(thm)],[f149,f92,f103]) ).
thf(f92,definition,
( spl6_9
<=> ! [X1: 'type/realax/real'] :
( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK0 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition]) ).
thf(f149,plain,
( ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ sK3 ) )
| ~ spl6_9 ),
inference(trivial_inequality_removal,[status(thm)],[f148]) ).
thf(f148,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ sK3 ) )
| ( $true != $true ) )
| ~ spl6_9 ),
inference(superposition,[status(thm)],[f29,f93]) ).
thf(f93,plain,
( ! [X1: 'type/realax/real'] :
( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK0 ) @ sK0 ) )
| ~ spl6_9 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f29,plain,
! [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X5 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f144,plain,
( ~ spl6_12
| ~ spl6_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f143]) ).
thf(f143,plain,
( $false
| ~ spl6_12
| ~ spl6_13 ),
inference(trivial_inequality_removal,[status(thm)],[f141]) ).
thf(f141,plain,
( ( $true != $true )
| ~ spl6_12
| ~ spl6_13 ),
inference(superposition,[status(thm)],[f109,f104]) ).
thf(f109,plain,
( ! [X1: 'type/realax/real'] :
( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X1 @ sK0 ) @ X1 ) )
| ~ spl6_13 ),
inference(avatar_component_clause,[status(thm)],[f108]) ).
thf(f130,plain,
( spl6_9
| spl6_15
| ~ spl6_3 ),
inference(avatar_split_clause,[status(thm)],[f129,f51,f126,f92]) ).
thf(f51,definition,
( spl6_3
<=> ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ sK1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition]) ).
thf(f129,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK1 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK0 ) @ sK0 ) ) )
| ~ spl6_3 ),
inference(subsumption_resolution,[status(thm)],[f122,f33]) ).
thf(f122,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK1 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK0 ) @ sK0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK0 ) @ sK0 ) )
| ( $true != $true ) )
| ~ spl6_3 ),
inference(superposition,[status(thm)],[f52,f38]) ).
thf(f38,plain,
! [X3: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X3 @ X0 ) @ X0 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X3 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f52,plain,
( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ sK1 )
= $true ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f128,plain,
( spl6_15
| spl6_13
| ~ spl6_3 ),
inference(avatar_split_clause,[status(thm)],[f124,f51,f108,f126]) ).
thf(f124,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X1 @ sK0 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK1 ) ) )
| ~ spl6_3 ),
inference(subsumption_resolution,[status(thm)],[f123,f33]) ).
thf(f123,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK1 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X1 @ sK0 ) @ X1 ) ) )
| ~ spl6_3 ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK1 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X1 @ sK0 ) @ X1 ) ) )
| ~ spl6_3 ),
inference(superposition,[status(thm)],[f52,f35]) ).
thf(f35,plain,
! [X3: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X3 @ X0 ) @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( sK4 @ X1 @ X0 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f115,plain,
( spl6_14
| spl6_12 ),
inference(avatar_split_clause,[status(thm)],[f111,f103,f113]) ).
thf(f111,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ sK3 ) ) ),
inference(subsumption_resolution,[status(thm)],[f86,f33]) ).
thf(f86,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ sK3 ) ) ),
inference(superposition,[status(thm)],[f29,f37]) ).
thf(f37,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X5 @ ( 'const/sets/sup' @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f105,plain,
( spl6_11
| spl6_12 ),
inference(avatar_split_clause,[status(thm)],[f98,f103,f100]) ).
thf(f98,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK5 @ X1 @ sK0 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ sK3 ) ) ),
inference(subsumption_resolution,[status(thm)],[f88,f33]) ).
thf(f88,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK5 @ X1 @ sK0 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK0 ) @ sK3 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ X1 ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( sK5 @ X1 @ sK0 ) @ X1 ) ) ),
inference(superposition,[status(thm)],[f29,f39]) ).
thf(f39,plain,
! [X3: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X3 )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ ( sK5 @ X3 @ X0 ) @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f58,plain,
( ~ spl6_2
| spl6_4 ),
inference(avatar_split_clause,[status(thm)],[f31,f55,f46]) ).
thf(f31,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f53,plain,
( spl6_3
| spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f30,f46,f51]) ).
thf(f30,plain,
! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f49,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f32,f46,f42]) ).
thf(f32,plain,
( ( $true
!= ( 'const/realax/real_le' @ sK2 @ sK1 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ANA080^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 03:50:15 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.34 ---- Original DTF file ---
% 0.07/0.34 thf(spec,logic,$$dhol).
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 % File : ANA080^1 : TPTP v9.2.1. Released v7.0.0.
% 0.07/0.34 % Domain : Analysis
% 0.07/0.34 % Problem : REAL_SUP_LE_EQ
% 0.07/0.34 % Version : Especial.
% 0.07/0.34 % English :
% 0.07/0.34
% 0.07/0.34 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.07/0.34 % Source : [Kal16]
% 0.07/0.34 % Names : REAL_SUP_LE_EQ_.p [Kal16]
% 0.07/0.34
% 0.07/0.34 % Status : Theorem
% 0.07/0.34 % Rating : 0.00 v7.1.0
% 0.07/0.34 % Syntax : Number of formulae : 8 ( 0 unt; 5 typ; 0 def)
% 0.07/0.34 % Number of atoms : 20 ( 3 equ; 0 cnn)
% 0.07/0.34 % Maximal formula atoms : 8 ( 6 avg)
% 0.07/0.34 % Number of connectives : 55 ( 2 ~; 0 |; 4 &; 40 @)
% 0.07/0.34 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.07/0.34 % Maximal formula depth : 11 ( 10 avg)
% 0.07/0.34 % Number of types : 2 ( 1 usr)
% 0.07/0.34 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.07/0.34 % Number of symbols : 5 ( 4 usr; 0 con; 1-3 aty)
% 0.07/0.34 % Number of variables : 16 ( 0 ^; 12 !; 2 ?; 16 :)
% 0.07/0.34 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.07/0.34 % SPC : TH1_THM_EQU_NAR
% 0.07/0.34
% 0.07/0.34 % Comments : Exported from core HOL Light.
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 thf('thf_type_type/realax/real',type,
% 0.07/0.34 'type/realax/real': $tType ).
% 0.07/0.34
% 0.07/0.34 thf('thf_const_const/sets/sup',type,
% 0.07/0.34 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.07/0.34
% 0.07/0.34 thf('thf_const_const/sets/IN',type,
% 0.07/0.34 'const/sets/IN':
% 0.07/0.34 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.07/0.34
% 0.07/0.34 thf('thf_const_const/sets/EMPTY',type,
% 0.07/0.34 'const/sets/EMPTY':
% 0.07/0.34 !>[A: $tType] : ( A > $o ) ).
% 0.07/0.34
% 0.07/0.34 thf('thf_const_const/realax/real_le',type,
% 0.07/0.34 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.07/0.34
% 0.07/0.34 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 0.07/0.34 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.07/0.34 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 0.07/0.34 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.07/0.34 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 0.07/0.34
% 0.07/0.34 thf('thm/sets/SUP_',axiom,
% 0.07/0.34 ! [A: 'type/realax/real' > $o] :
% 0.07/0.34 ( ( ( A
% 0.07/0.34 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.07/0.34 & ? [A0: 'type/realax/real'] :
% 0.07/0.34 ! [A1: 'type/realax/real'] :
% 0.07/0.34 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.07/0.34 => ( 'const/realax/real_le' @ A1 @ A0 ) ) )
% 0.07/0.34 => ( ! [A0: 'type/realax/real'] :
% 0.07/0.34 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.07/0.34 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) ) )
% 0.07/0.34 & ! [A0: 'type/realax/real'] :
% 0.07/0.34 ( ! [A1: 'type/realax/real'] :
% 0.07/0.34 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.07/0.34 => ( 'const/realax/real_le' @ A1 @ A0 ) )
% 0.07/0.34 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 thf('thm/sets/REAL_SUP_LE_EQ_',conjecture,
% 0.07/0.34 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.07/0.34 ( ( ( A
% 0.07/0.34 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.07/0.34 & ? [A1: 'type/realax/real'] :
% 0.07/0.34 ! [A2: 'type/realax/real'] :
% 0.07/0.34 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 0.07/0.34 => ( 'const/realax/real_le' @ A2 @ A1 ) ) )
% 0.07/0.34 => ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 )
% 0.07/0.34 = ( ! [A1: 'type/realax/real'] :
% 0.07/0.34 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.07/0.34 => ( 'const/realax/real_le' @ A1 @ A0 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 ------------------------
% 1.45/1.25 ---- Embedded in THF ---
% 1.45/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.25 %%% Generated on Tue Feb 24 03:50:16 EST 2026
% 1.45/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.25 %%% Logic specification used:
% 1.45/1.25 %%% thf(spec, logic, $$dhol).
% 1.45/1.25
% 1.45/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.FdEABJUAbk/DTF2DTF28211.p
% See solution above
% 1.45/1.25 ------------------------
% 1.45/1.26 ---- Cleaned THF ---
% 1.45/1.26 thf('thf_type_type/realax/real',type,
% 1.45/1.26 'type/realax/real': $tType ).
% 1.45/1.26
% 1.45/1.26 thf('thf_const_const/sets/sup',type,
% 1.45/1.26 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 1.45/1.26
% 1.45/1.26 thf('thf_const_const/sets/IN',type,
% 1.45/1.26 'const/sets/IN':
% 1.45/1.26 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.45/1.26
% 1.45/1.26 thf('thf_const_const/sets/EMPTY',type,
% 1.45/1.26 'const/sets/EMPTY':
% 1.45/1.26 !>[A: $tType] : ( A > $o ) ).
% 1.45/1.26
% 1.45/1.26 thf('thf_const_const/realax/real_le',type,
% 1.45/1.26 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.45/1.26
% 1.45/1.26 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 1.45/1.26 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 1.45/1.26 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 1.45/1.26 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 1.45/1.26 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 1.45/1.26
% 1.45/1.26 thf('thm/sets/SUP_',axiom,
% 1.45/1.26 ! [A: 'type/realax/real' > $o] :
% 1.45/1.26 ( ( ( A
% 1.45/1.26 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.45/1.26 & ? [A0: 'type/realax/real'] :
% 1.45/1.26 ! [A1: 'type/realax/real'] :
% 1.45/1.26 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.45/1.26 => ( 'const/realax/real_le' @ A1 @ A0 ) ) )
% 1.45/1.26 => ( ! [A0: 'type/realax/real'] :
% 1.45/1.26 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 1.45/1.26 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) ) )
% 1.45/1.26 & ! [A0: 'type/realax/real'] :
% 1.45/1.26 ( ! [A1: 'type/realax/real'] :
% 1.45/1.26 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.45/1.26 => ( 'const/realax/real_le' @ A1 @ A0 ) )
% 1.45/1.26 => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 ) ) ) ) ).
% 1.45/1.26
% 1.45/1.26 thf('thm/sets/REAL_SUP_LE_EQ_',conjecture,
% 1.45/1.26 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 1.45/1.26 ( ( ( A
% 1.45/1.26 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.45/1.26 & ? [A1: 'type/realax/real'] :
% 1.45/1.26 ! [A2: 'type/realax/real'] :
% 1.45/1.26 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 1.45/1.26 => ( 'const/realax/real_le' @ A2 @ A1 ) ) )
% 1.45/1.26 => ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 )
% 1.45/1.26 = ( ! [A1: 'type/realax/real'] :
% 1.45/1.26 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.45/1.26 => ( 'const/realax/real_le' @ A1 @ A0 ) ) ) ) ) ).
% 1.45/1.26 ------------------------
% 1.45/1.28 % (28311)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/2Mi)
% 1.45/1.28 % (28309)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_28211 for (2999ds/4Mi)
% 1.45/1.28 % (28308)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/183Mi)
% 1.45/1.28 % (28313)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_28211 for (2999ds/275Mi)
% 1.45/1.28 % (28314)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/18Mi)
% 1.45/1.28 % (28312)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_28211 for (2999ds/2Mi)
% 1.45/1.28 % (28310)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_28211 for (2999ds/27Mi)
% 1.45/1.28 % (28311)Instruction limit reached!
% 1.45/1.28 % (28311)------------------------------
% 1.45/1.28 % (28311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (28311)Termination reason: Unknown
% 1.45/1.28 % (28312)Instruction limit reached!
% 1.45/1.28 % (28312)------------------------------
% 1.45/1.28 % (28312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (28311)Termination phase: Property scanning
% 1.45/1.28
% 1.45/1.28 % (28311)Memory used [KB]: 1023
% 1.45/1.28 % (28311)Time elapsed: 0.003 s
% 1.45/1.28 % (28311)Instructions burned: 2 (million)
% 1.45/1.28 % (28311)------------------------------
% 1.45/1.28 % (28311)------------------------------
% 1.45/1.28 % (28312)Termination reason: Unknown
% 1.45/1.28 % (28312)Termination phase: Saturation
% 1.45/1.28
% 1.45/1.28 % (28312)Memory used [KB]: 895
% 1.45/1.28 % (28312)Time elapsed: 0.003 s
% 1.45/1.28 % (28312)Instructions burned: 3 (million)
% 1.45/1.28 % (28312)------------------------------
% 1.45/1.28 % (28312)------------------------------
% 1.45/1.28 % (28309)Instruction limit reached!
% 1.45/1.28 % (28309)------------------------------
% 1.45/1.28 % (28309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (28309)Termination reason: Unknown
% 1.45/1.28 % (28309)Termination phase: Saturation
% 1.45/1.28
% 1.45/1.28 % (28309)Memory used [KB]: 5500
% 1.45/1.28 % (28309)Time elapsed: 0.004 s
% 1.45/1.28 % (28309)Instructions burned: 4 (million)
% 1.45/1.28 % (28309)------------------------------
% 1.45/1.28 % (28309)------------------------------
% 1.45/1.29 % (28314)Instruction limit reached!
% 1.45/1.29 % (28314)------------------------------
% 1.45/1.29 % (28314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (28314)Termination reason: Unknown
% 1.45/1.29 % (28314)Termination phase: Saturation
% 1.45/1.29
% 1.45/1.29 % (28314)Memory used [KB]: 5628
% 1.45/1.29 % (28314)Time elapsed: 0.012 s
% 1.45/1.29 % (28314)Instructions burned: 19 (million)
% 1.45/1.29 % (28314)------------------------------
% 1.45/1.29 % (28314)------------------------------
% 1.45/1.29 % (28310)Instruction limit reached!
% 1.45/1.29 % (28310)------------------------------
% 1.45/1.29 % (28310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (28310)Termination reason: Unknown
% 1.45/1.29 % (28310)Termination phase: Saturation
% 1.45/1.29
% 1.45/1.29 % (28310)Memory used [KB]: 5628
% 1.45/1.29 % (28310)Time elapsed: 0.017 s
% 1.45/1.29 % (28310)Instructions burned: 27 (million)
% 1.45/1.29 % (28310)------------------------------
% 1.45/1.29 % (28310)------------------------------
% 1.45/1.29 % (28313)First to succeed.
% 1.45/1.30 % (28315)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/3Mi)
% 1.45/1.30 % (28316)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/37Mi)
% 1.55/1.30 % (28317)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_28211 for (2999ds/15Mi)
% 1.55/1.30 % (28315)Instruction limit reached!
% 1.55/1.30 % (28315)------------------------------
% 1.55/1.30 % (28315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.30 % (28315)Termination reason: Unknown
% 1.55/1.30 % (28315)Termination phase: Saturation
% 1.55/1.30
% 1.55/1.30 % (28315)Memory used [KB]: 5500
% 1.55/1.30 % (28315)Time elapsed: 0.003 s
% 1.55/1.30 % (28315)Instructions burned: 3 (million)
% 1.55/1.30 % (28315)------------------------------
% 1.55/1.30 % (28315)------------------------------
% 1.55/1.30 % (28313)Refutation found. Thanks to Tanya!
% 1.55/1.30 % SZS status Theorem for DTF2THF_28211
% 1.55/1.30 % SZS output start Proof for DTF2THF_28211
% 1.55/1.30 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.55/1.30 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.55/1.30 thf(func_def_1, type, 'const/sets/sup': ('type/realax/real' > $o) > 'type/realax/real').
% 1.55/1.30 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.55/1.30 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.55/1.30 thf(func_def_4, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.55/1.30 thf(func_def_8, type, sK0: 'type/realax/real' > $o).
% 1.55/1.30 thf(func_def_9, type, sK1: 'type/realax/real').
% 1.55/1.30 thf(func_def_10, type, sK2: 'type/realax/real').
% 1.55/1.30 thf(func_def_11, type, sK3: 'type/realax/real').
% 1.55/1.30 thf(func_def_12, type, sK4: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.55/1.30 thf(func_def_13, type, sK5: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.55/1.30 thf(func_def_15, type, ph7: !>[X0: $tType]:(X0)).
% 1.55/1.30 thf(func_def_16, type, sK8: 'type/realax/real').
% 1.55/1.30 thf(f227,plain,(
% 1.55/1.30 $false),
% 1.55/1.30 inference(avatar_sat_refutation,[status(thm)],[f49,f53,f58,f105,f115,f128,f130,f144,f152,f193,f202,f222,f226])).
% 1.55/1.30 thf(f226,plain,(
% 1.55/1.30 spl6_14 | ~spl6_12),
% 1.55/1.30 inference(avatar_split_clause,[status(thm)],[f225,f103,f113])).
% 1.55/1.30 thf(f113,definition,(
% 1.55/1.30 spl6_14 <=> ! [X1 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0)) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK0))))),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl6_14])],[avatar_definition])).
% 1.55/1.30 thf(f103,definition,(
% 1.55/1.30 spl6_12 <=> ! [X0 : 'type/realax/real'] : ($true = ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ sK3))),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl6_12])],[avatar_definition])).
% 1.55/1.30 thf(f225,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK0))) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0))) ) | ~spl6_12),
% 1.55/1.30 inference(subsumption_resolution,[status(thm)],[f224,f33])).
% 1.55/1.30 thf(f33,plain,(
% 1.55/1.30 ('const/sets/EMPTY' @ 'type/realax/real' != sK0)),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f24])).
% 1.55/1.30 thf(f24,plain,(
% 1.55/1.30 ('const/sets/EMPTY' @ 'type/realax/real' != sK0) & ((($true != ('const/realax/real_le' @ sK2 @ sK1)) & (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) = $true)) | ($true != ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1))) & (! [X3 : 'type/realax/real'] : ((('const/realax/real_le' @ X3 @ sK1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0) != $true)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1))) & ! [X5 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ sK0)) | ($true = ('const/realax/real_le' @ X5 @ sK3)))),
% 1.55/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f23,f22,f21])).
% 1.55/1.30 thf(f21,plain,(
% 1.55/1.30 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) != $true)) & (! [X3 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X3 @ X1)) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true)) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true)) & ? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) | ($true = ('const/realax/real_le' @ X5 @ X4)))) => (('const/sets/EMPTY' @ 'type/realax/real' != sK0) & (? [X2 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X2 @ sK1)) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0) = $true)) | ($true != ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1))) & (! [X3 : 'type/realax/real'] : ((('const/realax/real_le' @ X3 @ sK1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0) != $true)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1))) & ? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ sK0)) | ($true = ('const/realax/real_le' @ X5 @ X4))))),
% 1.55/1.30 introduced(definition,[],[choice_axiom])).
% 1.55/1.30 thf(f22,plain,(
% 1.55/1.30 ? [X2 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X2 @ sK1)) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0) = $true)) => (($true != ('const/realax/real_le' @ sK2 @ sK1)) & (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) = $true))),
% 1.55/1.30 introduced(definition,[],[choice_axiom])).
% 1.55/1.30 thf(f23,plain,(
% 1.55/1.30 ? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ sK0)) | ($true = ('const/realax/real_le' @ X5 @ X4))) => ! [X5 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ sK0)) | ($true = ('const/realax/real_le' @ X5 @ sK3)))),
% 1.55/1.30 introduced(definition,[],[choice_axiom])).
% 1.55/1.30 thf(f20,plain,(
% 1.55/1.30 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) != $true)) & (! [X3 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X3 @ X1)) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true)) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true)) & ? [X4 : 'type/realax/real'] : ! [X5 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) | ($true = ('const/realax/real_le' @ X5 @ X4))))),
% 1.55/1.30 inference(rectify,[status(thm)],[f19])).
% 1.55/1.30 thf(f19,plain,(
% 1.55/1.30 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (? [X4 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X4 @ X1)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) != $true)) & (! [X4 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X4 @ X1)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true)) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | (('const/realax/real_le' @ X3 @ X2) = $true)))),
% 1.55/1.30 inference(flattening,[status(thm)],[f18])).
% 1.55/1.30 thf(f18,plain,(
% 1.55/1.30 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((? [X4 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X4 @ X1)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) != $true)) & (! [X4 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X4 @ X1)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true))) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | (('const/realax/real_le' @ X3 @ X2) = $true)))),
% 1.55/1.30 inference(nnf_transformation,[status(thm)],[f15])).
% 1.55/1.30 thf(f15,plain,(
% 1.55/1.30 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true) <~> ! [X4 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X4 @ X1)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)))) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | (('const/realax/real_le' @ X3 @ X2) = $true)))),
% 1.55/1.30 inference(flattening,[status(thm)],[f14])).
% 1.55/1.30 thf(f14,plain,(
% 1.55/1.30 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true) <~> ! [X4 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X4 @ X1)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)))) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | (('const/realax/real_le' @ X3 @ X2) = $true))))),
% 1.55/1.30 inference(ennf_transformation,[status(thm)],[f7])).
% 1.55/1.30 thf(f7,plain,(
% 1.55/1.30 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) => (('const/realax/real_le' @ X3 @ X2) = $true))) => (! [X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)) => ($true = ('const/realax/real_le' @ X4 @ X1))) <=> (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true)))),
% 1.55/1.30 inference(fool_elimination,[status(thm)],[f6])).
% 1.55/1.30 thf(f6,plain,(
% 1.55/1.30 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ X3 @ X2))) => (! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X4 @ X1)) = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)))),
% 1.55/1.30 inference(rectify,[status(thm)],[f4])).
% 1.55/1.30 thf(f4,negated_conjecture,(
% 1.55/1.30 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ X3 @ X2))) => (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1)) = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)))),
% 1.55/1.30 inference(negated_conjecture,[status(cth)],[f3])).
% 1.55/1.30 thf(f3,conjecture,(
% 1.55/1.30 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ X3 @ X2))) => (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1)) = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1)))),
% 1.55/1.30 file('/export/starexec/sandbox/tmp/tmp.FdEABJUAbk/DTF2THF_28211.p','thm/sets/REAL_SUP_LE_EQ_')).
% 1.55/1.30 thf(f224,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0)) | ($true = ('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK0)))) ) | ~spl6_12),
% 1.55/1.30 inference(trivial_inequality_removal,[status(thm)],[f223])).
% 1.55/1.30 thf(f223,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0)) | ($true = ('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK0)))) ) | ~spl6_12),
% 1.55/1.30 inference(superposition,[status(thm)],[f34,f104])).
% 1.55/1.30 thf(f104,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ sK3))) ) | ~spl6_12),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f103])).
% 1.55/1.30 thf(f34,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X5 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK4 @ X1 @ X0) @ X1)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) | ($true = ('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f28])).
% 1.55/1.30 thf(f28,plain,(
% 1.55/1.30 ! [X0 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0)) & ($true != ('const/realax/real_le' @ (sK4 @ X1 @ X0) @ X1))) | (! [X3 : 'type/realax/real'] : ((($true != ('const/realax/real_le' @ (sK5 @ X3 @ X0) @ X3)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X3 @ X0) @ X0))) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3) = $true)) & ! [X5 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)))))),
% 1.55/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f25,f27,f26])).
% 1.55/1.30 thf(f26,plain,(
% 1.55/1.30 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X2 @ X1) != $true)) => (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0)) & ($true != ('const/realax/real_le' @ (sK4 @ X1 @ X0) @ X1))))),
% 1.55/1.30 introduced(definition,[],[choice_axiom])).
% 1.55/1.30 thf(f27,plain,(
% 1.55/1.30 ! [X0 : 'type/realax/real' > $o,X3 : 'type/realax/real'] : (? [X4 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X4 @ X3)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) => (($true != ('const/realax/real_le' @ (sK5 @ X3 @ X0) @ X3)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X3 @ X0) @ X0))))),
% 1.55/1.30 introduced(definition,[],[choice_axiom])).
% 1.55/1.30 thf(f25,plain,(
% 1.55/1.30 ! [X0 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X2 @ X1) != $true)) | (! [X3 : 'type/realax/real'] : (? [X4 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X4 @ X3)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3) = $true)) & ! [X5 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)))))),
% 1.55/1.30 inference(rectify,[status(thm)],[f13])).
% 1.55/1.30 thf(f13,plain,(
% 1.55/1.30 ! [X0 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X2 @ X1) != $true)) | (! [X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X5 @ X4)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4))) & ! [X3 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true))))),
% 1.55/1.30 inference(flattening,[status(thm)],[f12])).
% 1.55/1.30 thf(f12,plain,(
% 1.55/1.30 ! [X0 : 'type/realax/real' > $o] : ((! [X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X5 @ X4)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0))) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4))) & ! [X3 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ 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' @ X2 @ X1) != $true))))),
% 1.55/1.30 inference(ennf_transformation,[status(thm)],[f9])).
% 1.55/1.30 thf(f9,plain,(
% 1.55/1.30 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) => (('const/realax/real_le' @ X2 @ X1) = $true))) => (! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) => ($true = ('const/realax/real_le' @ X5 @ X4))) => ($true = ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4))) & ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) => ($true = ('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))))))),
% 1.55/1.30 inference(fool_elimination,[status(thm)],[f8])).
% 1.55/1.30 thf(f8,plain,(
% 1.55/1.30 ! [X0 : 'type/realax/real' > $o] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ X3 @ ('const/sets/sup' @ X0))) & ! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ X5 @ X4)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X4))))),
% 1.55/1.30 inference(rectify,[status(thm)],[f2])).
% 1.55/1.30 thf(f2,axiom,(
% 1.55/1.30 ! [X0 : 'type/realax/real' > $o] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) & ! [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X2 @ X1)) => ('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1))))),
% 1.55/1.30 file('/export/starexec/sandbox/tmp/tmp.FdEABJUAbk/DTF2THF_28211.p','thm/sets/SUP_')).
% 1.55/1.30 thf(f222,plain,(
% 1.55/1.30 spl6_1 | ~spl6_2 | ~spl6_4 | ~spl6_14),
% 1.55/1.30 inference(avatar_contradiction_clause,[status(thm)],[f221])).
% 1.55/1.30 thf(f221,plain,(
% 1.55/1.30 $false | (spl6_1 | ~spl6_2 | ~spl6_4 | ~spl6_14)),
% 1.55/1.30 inference(subsumption_resolution,[status(thm)],[f220,f57])).
% 1.55/1.30 thf(f57,plain,(
% 1.55/1.30 (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) = $true) | ~spl6_4),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.55/1.30 thf(f55,definition,(
% 1.55/1.30 spl6_4 <=> (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) = $true)),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition])).
% 1.55/1.30 thf(f220,plain,(
% 1.55/1.30 (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) != $true) | (spl6_1 | ~spl6_2 | ~spl6_14)),
% 1.55/1.30 inference(trivial_inequality_removal,[status(thm)],[f217])).
% 1.55/1.30 thf(f217,plain,(
% 1.55/1.30 (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) != $true) | ($true != $true) | (spl6_1 | ~spl6_2 | ~spl6_14)),
% 1.55/1.30 inference(superposition,[status(thm)],[f215,f114])).
% 1.55/1.30 thf(f114,plain,(
% 1.55/1.30 ( ! [X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK0))) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0))) ) | ~spl6_14),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f113])).
% 1.55/1.30 thf(f215,plain,(
% 1.55/1.30 ($true != ('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK0))) | (spl6_1 | ~spl6_2)),
% 1.55/1.30 inference(trivial_inequality_removal,[status(thm)],[f212])).
% 1.55/1.30 thf(f212,plain,(
% 1.55/1.30 ($true != ('const/realax/real_le' @ sK2 @ ('const/sets/sup' @ sK0))) | ($true != $true) | (spl6_1 | ~spl6_2)),
% 1.55/1.30 inference(superposition,[status(thm)],[f204,f47])).
% 1.55/1.30 thf(f47,plain,(
% 1.55/1.30 ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ~spl6_2),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.55/1.30 thf(f46,definition,(
% 1.55/1.30 spl6_2 <=> ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1))),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.55/1.30 thf(f204,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X0 @ sK1)) | (('const/realax/real_le' @ sK2 @ X0) != $true)) ) | spl6_1),
% 1.55/1.30 inference(trivial_inequality_removal,[status(thm)],[f203])).
% 1.55/1.30 thf(f203,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != ('const/realax/real_le' @ X0 @ sK1)) | (('const/realax/real_le' @ sK2 @ X0) != $true)) ) | spl6_1),
% 1.55/1.30 inference(superposition,[status(thm)],[f44,f40])).
% 1.55/1.30 thf(f40,plain,(
% 1.55/1.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X2) = $true) | (('const/realax/real_le' @ X1 @ X2) != $true) | (('const/realax/real_le' @ X0 @ X1) != $true)) )),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f17])).
% 1.55/1.30 thf(f17,plain,(
% 1.55/1.30 ! [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))),
% 1.55/1.30 inference(flattening,[status(thm)],[f16])).
% 1.55/1.30 thf(f16,plain,(
% 1.55/1.30 ! [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)))),
% 1.55/1.30 inference(ennf_transformation,[status(thm)],[f11])).
% 1.55/1.30 thf(f11,plain,(
% 1.55/1.30 ! [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) = $true))),
% 1.55/1.30 inference(fool_elimination,[status(thm)],[f10])).
% 1.55/1.30 thf(f10,plain,(
% 1.55/1.30 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 1.55/1.30 inference(rectify,[status(thm)],[f1])).
% 1.55/1.30 thf(f1,axiom,(
% 1.55/1.30 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 1.55/1.30 file('/export/starexec/sandbox/tmp/tmp.FdEABJUAbk/DTF2THF_28211.p','thm/realax/REAL_LE_TRANS_')).
% 1.55/1.30 thf(f44,plain,(
% 1.55/1.30 ($true != ('const/realax/real_le' @ sK2 @ sK1)) | spl6_1),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.55/1.30 thf(f42,definition,(
% 1.55/1.30 spl6_1 <=> ($true = ('const/realax/real_le' @ sK2 @ sK1))),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.55/1.30 thf(f202,plain,(
% 1.55/1.30 spl6_13 | spl6_2 | ~spl6_15),
% 1.55/1.30 inference(avatar_split_clause,[status(thm)],[f201,f126,f46,f108])).
% 1.55/1.30 thf(f108,definition,(
% 1.55/1.30 spl6_13 <=> ! [X1 : 'type/realax/real'] : ($true != ('const/realax/real_le' @ (sK4 @ X1 @ sK0) @ X1))),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl6_13])],[avatar_definition])).
% 1.55/1.30 thf(f126,definition,(
% 1.55/1.30 spl6_15 <=> ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true) | ($true = ('const/realax/real_le' @ (sK5 @ X0 @ sK0) @ sK1)))),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl6_15])],[avatar_definition])).
% 1.55/1.30 thf(f201,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ X0))) ) | (spl6_2 | ~spl6_15)),
% 1.55/1.30 inference(subsumption_resolution,[status(thm)],[f200,f33])).
% 1.55/1.30 thf(f200,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ X0))) ) | (spl6_2 | ~spl6_15)),
% 1.55/1.30 inference(subsumption_resolution,[status(thm)],[f189,f48])).
% 1.55/1.30 thf(f48,plain,(
% 1.55/1.30 ($true != ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | spl6_2),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.55/1.30 thf(f189,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1))) ) | ~spl6_15),
% 1.55/1.30 inference(trivial_inequality_removal,[status(thm)],[f188])).
% 1.55/1.30 thf(f188,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ X0)) | ($true != $true) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) ) | ~spl6_15),
% 1.55/1.30 inference(duplicate_literal_removal,[status(thm)],[f186])).
% 1.55/1.30 thf(f186,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ X0)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1))) ) | ~spl6_15),
% 1.55/1.30 inference(superposition,[status(thm)],[f36,f127])).
% 1.55/1.30 thf(f127,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK5 @ X0 @ sK0) @ sK1)) | (('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true)) ) | ~spl6_15),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f126])).
% 1.55/1.30 thf(f36,plain,(
% 1.55/1.30 ( ! [X3 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK5 @ X3 @ X0) @ X3)) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3) = $true) | ($true != ('const/realax/real_le' @ (sK4 @ X1 @ X0) @ X1)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f28])).
% 1.55/1.30 thf(f193,plain,(
% 1.55/1.30 spl6_2 | ~spl6_11 | ~spl6_15),
% 1.55/1.30 inference(avatar_contradiction_clause,[status(thm)],[f192])).
% 1.55/1.30 thf(f192,plain,(
% 1.55/1.30 $false | (spl6_2 | ~spl6_11 | ~spl6_15)),
% 1.55/1.30 inference(subsumption_resolution,[status(thm)],[f191,f48])).
% 1.55/1.30 thf(f191,plain,(
% 1.55/1.30 ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | (~spl6_11 | ~spl6_15)),
% 1.55/1.30 inference(trivial_inequality_removal,[status(thm)],[f190])).
% 1.55/1.30 thf(f190,plain,(
% 1.55/1.30 ($true != $true) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | (~spl6_11 | ~spl6_15)),
% 1.55/1.30 inference(duplicate_literal_removal,[status(thm)],[f187])).
% 1.55/1.30 thf(f187,plain,(
% 1.55/1.30 ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | ($true != $true) | (~spl6_11 | ~spl6_15)),
% 1.55/1.30 inference(superposition,[status(thm)],[f101,f127])).
% 1.55/1.30 thf(f101,plain,(
% 1.55/1.30 ( ! [X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK5 @ X1 @ sK0) @ X1)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X1))) ) | ~spl6_11),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f100])).
% 1.55/1.30 thf(f100,definition,(
% 1.55/1.30 spl6_11 <=> ! [X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK5 @ X1 @ sK0) @ X1)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X1)))),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl6_11])],[avatar_definition])).
% 1.55/1.30 thf(f152,plain,(
% 1.55/1.30 spl6_12 | ~spl6_9),
% 1.55/1.30 inference(avatar_split_clause,[status(thm)],[f149,f92,f103])).
% 1.55/1.30 thf(f92,definition,(
% 1.55/1.30 spl6_9 <=> ! [X1 : 'type/realax/real'] : ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK0) @ sK0))),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition])).
% 1.55/1.30 thf(f149,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ sK3))) ) | ~spl6_9),
% 1.55/1.30 inference(trivial_inequality_removal,[status(thm)],[f148])).
% 1.55/1.30 thf(f148,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ sK3)) | ($true != $true)) ) | ~spl6_9),
% 1.55/1.30 inference(superposition,[status(thm)],[f29,f93])).
% 1.55/1.30 thf(f93,plain,(
% 1.55/1.30 ( ! [X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK0) @ sK0))) ) | ~spl6_9),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.55/1.30 thf(f29,plain,(
% 1.55/1.30 ( ! [X5 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ sK0)) | ($true = ('const/realax/real_le' @ X5 @ sK3))) )),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f24])).
% 1.55/1.30 thf(f144,plain,(
% 1.55/1.30 ~spl6_12 | ~spl6_13),
% 1.55/1.30 inference(avatar_contradiction_clause,[status(thm)],[f143])).
% 1.55/1.30 thf(f143,plain,(
% 1.55/1.30 $false | (~spl6_12 | ~spl6_13)),
% 1.55/1.30 inference(trivial_inequality_removal,[status(thm)],[f141])).
% 1.55/1.30 thf(f141,plain,(
% 1.55/1.30 ($true != $true) | (~spl6_12 | ~spl6_13)),
% 1.55/1.30 inference(superposition,[status(thm)],[f109,f104])).
% 1.55/1.30 thf(f109,plain,(
% 1.55/1.30 ( ! [X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK4 @ X1 @ sK0) @ X1))) ) | ~spl6_13),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f108])).
% 1.55/1.30 thf(f130,plain,(
% 1.55/1.30 spl6_9 | spl6_15 | ~spl6_3),
% 1.55/1.30 inference(avatar_split_clause,[status(thm)],[f129,f51,f126,f92])).
% 1.55/1.30 thf(f51,definition,(
% 1.55/1.30 spl6_3 <=> ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0) != $true) | (('const/realax/real_le' @ X3 @ sK1) = $true))),
% 1.55/1.30 introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition])).
% 1.55/1.30 thf(f129,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true) | ($true = ('const/realax/real_le' @ (sK5 @ X0 @ sK0) @ sK1)) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK0) @ sK0))) ) | ~spl6_3),
% 1.55/1.30 inference(subsumption_resolution,[status(thm)],[f122,f33])).
% 1.55/1.30 thf(f122,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK5 @ X0 @ sK0) @ sK1)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK0) @ sK0)) | (('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true)) ) | ~spl6_3),
% 1.55/1.30 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.55/1.30 thf(f116,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK5 @ X0 @ sK0) @ sK1)) | (('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ sK0) @ sK0)) | ($true != $true)) ) | ~spl6_3),
% 1.55/1.30 inference(superposition,[status(thm)],[f52,f38])).
% 1.55/1.30 thf(f38,plain,(
% 1.55/1.30 ( ! [X3 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X3 @ X0) @ X0)) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0)) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f28])).
% 1.55/1.30 thf(f52,plain,(
% 1.55/1.30 ( ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0) != $true) | (('const/realax/real_le' @ X3 @ sK1) = $true)) ) | ~spl6_3),
% 1.55/1.30 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.55/1.30 thf(f128,plain,(
% 1.55/1.30 spl6_15 | spl6_13 | ~spl6_3),
% 1.55/1.30 inference(avatar_split_clause,[status(thm)],[f124,f51,f108,f126])).
% 1.55/1.30 thf(f124,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true) | ($true != ('const/realax/real_le' @ (sK4 @ X1 @ sK0) @ X1)) | ($true = ('const/realax/real_le' @ (sK5 @ X0 @ sK0) @ sK1))) ) | ~spl6_3),
% 1.55/1.30 inference(subsumption_resolution,[status(thm)],[f123,f33])).
% 1.55/1.30 thf(f123,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true) | ($true = ('const/realax/real_le' @ (sK5 @ X0 @ sK0) @ sK1)) | ($true != ('const/realax/real_le' @ (sK4 @ X1 @ sK0) @ X1))) ) | ~spl6_3),
% 1.55/1.30 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.55/1.30 thf(f117,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK5 @ X0 @ sK0) @ sK1)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X0) = $true) | ($true != ('const/realax/real_le' @ (sK4 @ X1 @ sK0) @ X1))) ) | ~spl6_3),
% 1.55/1.30 inference(superposition,[status(thm)],[f52,f35])).
% 1.55/1.30 thf(f35,plain,(
% 1.55/1.30 ( ! [X3 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X3 @ X0) @ X0)) | ($true != ('const/realax/real_le' @ (sK4 @ X1 @ X0) @ X1)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3) = $true)) )),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f28])).
% 1.55/1.30 thf(f115,plain,(
% 1.55/1.30 spl6_14 | spl6_12),
% 1.55/1.30 inference(avatar_split_clause,[status(thm)],[f111,f103,f113])).
% 1.55/1.30 thf(f111,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0)) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK0))) | ($true = ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ sK3))) )),
% 1.55/1.30 inference(subsumption_resolution,[status(thm)],[f86,f33])).
% 1.55/1.30 thf(f86,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0)) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK0))) | ($true = ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ sK3))) )),
% 1.55/1.30 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.55/1.30 thf(f84,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ sK0))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0)) | ($true = ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ sK3))) )),
% 1.55/1.30 inference(superposition,[status(thm)],[f29,f37])).
% 1.55/1.30 thf(f37,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X5 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) | ($true = ('const/realax/real_le' @ X5 @ ('const/sets/sup' @ X0))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f28])).
% 1.55/1.30 thf(f105,plain,(
% 1.55/1.30 spl6_11 | spl6_12),
% 1.55/1.30 inference(avatar_split_clause,[status(thm)],[f98,f103,f100])).
% 1.55/1.30 thf(f98,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK5 @ X1 @ sK0) @ X1)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X1)) | ($true = ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ sK3))) )),
% 1.55/1.30 inference(subsumption_resolution,[status(thm)],[f88,f33])).
% 1.55/1.30 thf(f88,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ (sK5 @ X1 @ sK0) @ X1)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X1)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ sK3))) )),
% 1.55/1.30 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.55/1.30 thf(f85,plain,(
% 1.55/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ (sK4 @ X0 @ sK0) @ sK3)) | ($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ X1)) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != ('const/realax/real_le' @ (sK5 @ X1 @ sK0) @ X1))) )),
% 1.55/1.30 inference(superposition,[status(thm)],[f29,f39])).
% 1.55/1.30 thf(f39,plain,(
% 1.55/1.30 ( ! [X3 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X3) = $true) | ($true != ('const/realax/real_le' @ (sK5 @ X3 @ X0) @ X3))) )),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f28])).
% 1.55/1.30 thf(f58,plain,(
% 1.55/1.30 ~spl6_2 | spl6_4),
% 1.55/1.30 inference(avatar_split_clause,[status(thm)],[f31,f55,f46])).
% 1.55/1.30 thf(f31,plain,(
% 1.55/1.30 (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) = $true) | ($true != ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1))),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f24])).
% 1.55/1.30 thf(f53,plain,(
% 1.55/1.30 spl6_3 | spl6_2),
% 1.55/1.30 inference(avatar_split_clause,[status(thm)],[f30,f46,f51])).
% 1.55/1.30 thf(f30,plain,(
% 1.55/1.30 ( ! [X3 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1)) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0) != $true) | (('const/realax/real_le' @ X3 @ sK1) = $true)) )),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f24])).
% 1.55/1.30 thf(f49,plain,(
% 1.55/1.30 ~spl6_1 | ~spl6_2),
% 1.55/1.30 inference(avatar_split_clause,[status(thm)],[f32,f46,f42])).
% 1.55/1.30 thf(f32,plain,(
% 1.55/1.30 ($true != ('const/realax/real_le' @ sK2 @ sK1)) | ($true != ('const/realax/real_le' @ ('const/sets/sup' @ sK0) @ sK1))),
% 1.55/1.30 inference(cnf_transformation,[status(thm)],[f24])).
% 1.55/1.30 % SZS output end Proof for DTF2THF_28211
% 1.55/1.30 % (28313)------------------------------
% 1.55/1.30 % (28313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.30 % (28313)Termination reason: Refutation
% 1.55/1.30
% 1.55/1.30 % (28313)Memory used [KB]: 5756
% 1.55/1.30 % (28313)Time elapsed: 0.021 s
% 1.55/1.30 % (28313)Instructions burned: 28 (million)
% 1.55/1.30 % (28313)------------------------------
% 1.55/1.30 % (28313)------------------------------
% 1.55/1.30 % (28307)Success in time 0.034 s
%------------------------------------------------------------------------------