%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV492^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n029.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 09:41:22 AM UTC 2026
% Result : Theorem 1.74s 1.44s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 14
% Syntax : Number of formulae : 120 ( 7 unt; 0 typ; 5 def)
% Number of atoms : 1304 ( 399 equ; 0 cnn)
% Maximal formula atoms : 22 ( 10 avg)
% Number of connectives : 1574 ( 261 ~; 278 |; 80 &; 919 @)
% ( 13 <=>; 21 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 10 con; 0-3 aty)
% Number of variables : 159 ( 0 ^; 130 !; 29 ?; 159 :)
% 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/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_5,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_9,type,
sK0: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_10,type,
sK1: 'type/realax/real' ).
thf(func_def_11,type,
sK2: 'type/realax/real' > $o ).
thf(func_def_12,type,
sK3: 'type/realax/real' ).
thf(func_def_13,type,
sK4: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_15,type,
ph6:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK7: 'type/realax/real' ).
thf(f322,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f76,f77,f81,f86,f208,f243,f321]) ).
thf(f321,plain,
( spl5_2
| ~ spl5_3
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f320]) ).
thf(f320,plain,
( $false
| spl5_2
| ~ spl5_3
| ~ spl5_4 ),
inference(subsumption_resolution,[status(thm)],[f313,f63]) ).
thf(f63,plain,
! [X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X1 @ X1 )
= $true ),
inference(equality_resolution,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X0 )
= $true )
| ( X0 != X1 ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X0 )
= $true ) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X0 )
= $true ) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X0 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X0 )
= $true ) )
<=> ( X0 = X1 ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X0 @ X1 )
& ( ( 'const/realax/real_le' @ X1 @ X0 )
= ( X0 = X1 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X0 @ X1 )
& ( ( 'const/realax/real_le' @ X1 @ X0 )
= ( X0 = X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Jhzb8yfRKP/DTF2THF_7245.p','thm/realax/REAL_LE_ANTISYM_') ).
thf(f313,plain,
( ( ( 'const/realax/real_le' @ sK1 @ sK1 )
!= $true )
| spl5_2
| ~ spl5_3
| ~ spl5_4 ),
inference(trivial_inequality_removal,[status(thm)],[f312]) ).
thf(f312,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ sK1 @ sK1 )
!= $true )
| spl5_2
| ~ spl5_3
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f296,f74]) ).
thf(f74,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f73]) ).
thf(f73,definition,
( spl5_3
<=> ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f296,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ sK1 @ X0 )
!= $true ) )
| spl5_2
| ~ spl5_4 ),
inference(subsumption_resolution,[status(thm)],[f295,f53]) ).
thf(f53,plain,
( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
= $true )
& ( ( ( 'const/sets/sup' @ sK2 )
!= sK1 )
| ( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK2 )
= $true )
& ( ( 'const/realax/real_le' @ sK3 @ sK1 )
!= $true ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) ) )
& ( ( ( 'const/sets/sup' @ sK2 )
= sK1 )
| ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ sK1 )
= $true ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f35,f37,f36]) ).
thf(f36,plain,
( ? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 )
= $true )
& ( ( ( 'const/sets/sup' @ X1 )
!= X0 )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X0 )
!= $true ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 )
!= $true ) )
& ( ( ( 'const/sets/sup' @ X1 )
= X0 )
| ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ X0 )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 )
= $true ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) )
=> ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
= $true )
& ( ( ( 'const/sets/sup' @ sK2 )
!= sK1 )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK2 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ sK1 )
!= $true ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) ) )
& ( ( ( 'const/sets/sup' @ sK2 )
= sK1 )
| ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ sK1 )
= $true ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK2 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ sK1 )
!= $true ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK2 )
= $true )
& ( ( 'const/realax/real_le' @ sK3 @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 )
= $true )
& ( ( ( 'const/sets/sup' @ X1 )
!= X0 )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X0 )
!= $true ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 )
!= $true ) )
& ( ( ( 'const/sets/sup' @ X1 )
= X0 )
| ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ X0 )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 )
= $true ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 )
= $true )
& ( ( ( 'const/sets/sup' @ X1 )
!= X0 )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X0 )
!= $true ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 )
!= $true ) )
& ( ( ( 'const/sets/sup' @ X1 )
= X0 )
| ( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X2 @ X0 )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 )
= $true ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(flattening,[status(thm)],[f33]) ).
thf(f33,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 )
= $true )
& ( ( ( 'const/sets/sup' @ X1 )
!= X0 )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X0 )
!= $true ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 )
!= $true ) )
& ( ( ( 'const/sets/sup' @ X1 )
= X0 )
| ( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X2 @ X0 )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 )
= $true ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 )
= $true )
& ( ( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X2 @ X0 )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 )
= $true ) )
<~> ( ( 'const/sets/sup' @ X1 )
= X0 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X2 @ X0 )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 )
= $true ) )
<~> ( ( 'const/sets/sup' @ X1 )
= X0 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
~ ! [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 )
= $true ) )
=> ( ( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
= $true )
=> ( ( 'const/realax/real_le' @ X2 @ X0 )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 )
= $true ) )
<=> ( ( 'const/sets/sup' @ X1 )
= X0 ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
~ ! [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 ) )
=> ( ( ( ( 'const/sets/sup' @ X1 )
= X0 )
= ( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
=> ( 'const/realax/real_le' @ X2 @ X0 ) ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ! [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 ) )
=> ( ( ( ( 'const/sets/sup' @ X1 )
= X0 )
= ( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
=> ( 'const/realax/real_le' @ X2 @ X0 ) ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
! [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 ) )
=> ( ( ( ( 'const/sets/sup' @ X1 )
= X0 )
= ( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 )
=> ( 'const/realax/real_le' @ X2 @ X0 ) ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Jhzb8yfRKP/DTF2THF_7245.p','thm/sets/SUP_UNIQUE_FINITE_') ).
thf(f295,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ sK1 @ X0 )
!= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true ) )
| spl5_2
| ~ spl5_4 ),
inference(subsumption_resolution,[status(thm)],[f294,f48]) ).
thf(f48,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f294,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK1 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 )
!= $true ) )
| spl5_2
| ~ spl5_4 ),
inference(trivial_inequality_removal,[status(thm)],[f291]) ).
thf(f291,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 )
!= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ sK1 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true ) )
| spl5_2
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f283,f45]) ).
thf(f45,plain,
! [X3: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X3 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 ) )
& ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
= $true ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true ) )
& ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X3 )
!= $true ) ) ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f30,f31]) ).
thf(f31,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) )
=> ( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 ) )
& ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true ) )
& ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X3 )
!= $true ) ) ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true ) )
& ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ) ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) )
<=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) )
<=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true ) )
=> ( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) )
<=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Jhzb8yfRKP/DTF2THF_7245.p','thm/sets/REAL_LE_SUP_FINITE_') ).
thf(f283,plain,
( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| spl5_2
| ~ spl5_4 ),
inference(subsumption_resolution,[status(thm)],[f282,f71]) ).
thf(f71,plain,
( ( ( 'const/sets/sup' @ sK2 )
!= sK1 )
| spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f69]) ).
thf(f69,definition,
( spl5_2
<=> ( ( 'const/sets/sup' @ sK2 )
= sK1 ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f282,plain,
( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ( ( 'const/sets/sup' @ sK2 )
= sK1 )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[status(thm)],[f280]) ).
thf(f280,plain,
( ( ( 'const/sets/sup' @ sK2 )
= sK1 )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ( $true != $true )
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f59,f278]) ).
thf(f278,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK1 )
= $true )
| ~ spl5_4 ),
inference(subsumption_resolution,[status(thm)],[f277,f48]) ).
thf(f277,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK1 )
= $true )
| ~ spl5_4 ),
inference(subsumption_resolution,[status(thm)],[f276,f53]) ).
thf(f276,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK1 )
= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[status(thm)],[f275]) ).
thf(f275,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK1 )
= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ~ spl5_4 ),
inference(duplicate_literal_removal,[status(thm)],[f272]) ).
thf(f272,plain,
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK1 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK1 )
= $true )
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f57,f257]) ).
thf(f257,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK2 ) @ sK1 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true ) )
| ~ spl5_4 ),
inference(subsumption_resolution,[status(thm)],[f256,f48]) ).
thf(f256,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK2 ) @ sK1 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true ) )
| ~ spl5_4 ),
inference(subsumption_resolution,[status(thm)],[f248,f53]) ).
thf(f248,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK2 ) @ sK1 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[status(thm)],[f245]) ).
thf(f245,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( sK4 @ X0 @ sK2 ) @ sK1 )
= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f80,f56]) ).
thf(f56,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
| ( ( ( 'const/realax/real_le' @ ( sK4 @ X1 @ X0 ) @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true ) ) )
& ( ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X3 @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
!= $true ) ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f40,f41]) ).
thf(f41,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
=> ( ( ( 'const/realax/real_le' @ ( sK4 @ X1 @ X0 ) @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) ) )
& ( ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X3 @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
!= $true ) ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) ) )
& ( ! [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 ) ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
<=> ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
<=> ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
<=> ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ! [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(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ! [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/sandbox2/tmp/tmp.Jhzb8yfRKP/DTF2THF_7245.p','thm/sets/REAL_SUP_LE_FINITE_') ).
thf(f80,plain,
( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ sK1 )
= $true ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f79]) ).
thf(f79,definition,
( spl5_4
<=> ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ sK1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f57,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK4 @ X1 @ X0 ) @ X1 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f59,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X0 )
!= $true )
| ( X0 = X1 )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f243,plain,
( ~ spl5_1
| ~ spl5_2
| spl5_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f242]) ).
thf(f242,plain,
( $false
| ~ spl5_1
| ~ spl5_2
| spl5_5 ),
inference(subsumption_resolution,[status(thm)],[f235,f63]) ).
thf(f235,plain,
( ( ( 'const/realax/real_le' @ sK3 @ sK3 )
!= $true )
| ~ spl5_1
| ~ spl5_2
| spl5_5 ),
inference(trivial_inequality_removal,[status(thm)],[f232]) ).
thf(f232,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ sK3 @ sK3 )
!= $true )
| ~ spl5_1
| ~ spl5_2
| spl5_5 ),
inference(superposition,[status(thm)],[f85,f213]) ).
thf(f213,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ sK1 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ sK3 )
!= $true ) )
| ~ spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f212]) ).
thf(f212,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ sK3 )
!= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ X0 @ sK1 )
= $true ) )
| ~ spl5_1
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f111,f67]) ).
thf(f67,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK2 )
= $true )
| ~ spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f65,definition,
( spl5_1
<=> ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f111,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ sK1 )
= $true ) )
| ~ spl5_2 ),
inference(subsumption_resolution,[status(thm)],[f110,f48]) ).
thf(f110,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ sK1 )
= $true ) )
| ~ spl5_2 ),
inference(subsumption_resolution,[status(thm)],[f108,f53]) ).
thf(f108,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ sK1 )
= $true ) )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f45,f70]) ).
thf(f70,plain,
( ( ( 'const/sets/sup' @ sK2 )
= sK1 )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f69]) ).
thf(f85,plain,
( ( ( 'const/realax/real_le' @ sK3 @ sK1 )
!= $true )
| spl5_5 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f83,definition,
( spl5_5
<=> ( ( 'const/realax/real_le' @ sK3 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition]) ).
thf(f208,plain,
( spl5_3
| ~ spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f207,f69,f73]) ).
thf(f207,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) )
| ~ spl5_2 ),
inference(subsumption_resolution,[status(thm)],[f206,f63]) ).
thf(f206,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) )
| ( ( 'const/realax/real_le' @ sK1 @ sK1 )
!= $true )
| ~ spl5_2 ),
inference(forward_demodulation,[status(thm)],[f201,f70]) ).
thf(f201,plain,
( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) )
| ~ spl5_2 ),
inference(subsumption_resolution,[status(thm)],[f200,f48]) ).
thf(f200,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) )
| ~ spl5_2 ),
inference(subsumption_resolution,[status(thm)],[f194,f53]) ).
thf(f194,plain,
( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f47,f178]) ).
thf(f178,plain,
( ( sK1
= ( sK0 @ sK1 @ sK2 ) )
| ~ spl5_2 ),
inference(subsumption_resolution,[status(thm)],[f177,f63]) ).
thf(f177,plain,
( ( ( 'const/realax/real_le' @ sK1 @ sK1 )
!= $true )
| ( sK1
= ( sK0 @ sK1 @ sK2 ) )
| ~ spl5_2 ),
inference(forward_demodulation,[status(thm)],[f176,f70]) ).
thf(f176,plain,
( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ( sK1
= ( sK0 @ sK1 @ sK2 ) )
| ~ spl5_2 ),
inference(subsumption_resolution,[status(thm)],[f175,f53]) ).
thf(f175,plain,
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ( sK1
= ( sK0 @ sK1 @ sK2 ) )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ~ spl5_2 ),
inference(subsumption_resolution,[status(thm)],[f174,f48]) ).
thf(f174,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ( sK1
= ( sK0 @ sK1 @ sK2 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ~ spl5_2 ),
inference(subsumption_resolution,[status(thm)],[f172,f63]) ).
thf(f172,plain,
( ( ( 'const/realax/real_le' @ sK1 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( sK1
= ( sK0 @ sK1 @ sK2 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f170]) ).
thf(f170,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ( $true != $true )
| ( sK1
= ( sK0 @ sK1 @ sK2 ) )
| ( ( 'const/realax/real_le' @ sK1 @ sK1 )
!= $true )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f152,f46]) ).
thf(f46,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f152,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK1 @ ( sK0 @ X0 @ sK2 ) )
!= $true )
| ( ( sK0 @ X0 @ sK2 )
= sK1 )
| ( ( 'const/realax/real_le' @ X0 @ sK1 )
!= $true ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f151]) ).
thf(f151,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ sK1 )
!= $true )
| ( ( sK0 @ X0 @ sK2 )
= sK1 )
| ( ( 'const/realax/real_le' @ sK1 @ ( sK0 @ X0 @ sK2 ) )
!= $true )
| ( $true != $true ) )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f59,f142]) ).
thf(f142,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ sK1 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ sK1 )
!= $true ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f136]) ).
thf(f136,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ X0 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ sK1 )
= $true ) )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f120,f58]) ).
thf(f58,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X0 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: 'type/realax/real'] : ( 'const/realax/real_le' @ X0 @ X0 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: 'type/realax/real'] : ( 'const/realax/real_le' @ X0 @ X0 ),
file('/export/starexec/sandbox2/tmp/tmp.Jhzb8yfRKP/DTF2THF_7245.p','thm/realax/REAL_LE_REFL_') ).
thf(f120,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X0 @ sK2 ) )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ sK1 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ sK1 )
!= $true ) )
| ~ spl5_2 ),
inference(forward_demodulation,[status(thm)],[f119,f70]) ).
thf(f119,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ sK1 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X0 @ sK2 ) )
!= $true ) )
| ~ spl5_2 ),
inference(subsumption_resolution,[status(thm)],[f118,f53]) ).
thf(f118,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X0 @ sK2 ) )
!= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ sK1 )
= $true ) )
| ~ spl5_2 ),
inference(subsumption_resolution,[status(thm)],[f117,f48]) ).
thf(f117,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ sK1 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X0 @ sK2 ) )
!= $true ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f114]) ).
thf(f114,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X0 @ sK2 ) )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ sK1 )
= $true ) )
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f111,f47]) ).
thf(f47,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f86,plain,
( ~ spl5_2
| ~ spl5_3
| ~ spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f51,f83,f73,f69]) ).
thf(f51,plain,
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) )
| ( ( 'const/realax/real_le' @ sK3 @ sK1 )
!= $true )
| ( ( 'const/sets/sup' @ sK2 )
!= sK1 ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f81,plain,
( spl5_2
| spl5_4 ),
inference(avatar_split_clause,[status(thm)],[f50,f79,f69]) ).
thf(f50,plain,
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/sup' @ sK2 )
= sK1 )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f77,plain,
( spl5_2
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f49,f73,f69]) ).
thf(f49,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) )
| ( ( 'const/sets/sup' @ sK2 )
= sK1 ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f76,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f52,f73,f69,f65]) ).
thf(f52,plain,
( ( ( 'const/sets/sup' @ sK2 )
!= sK1 )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV492^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n029.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 12:48:14 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.40 ---- Original DTF file ---
% 0.18/0.40 thf(spec,logic,$$dhol).
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 % File : SEV492^1 : TPTP v9.2.1. Released v7.0.0.
% 0.18/0.40 % Domain : Analysis
% 0.18/0.40 % Problem : SUP_UNIQUE_FINITE
% 0.18/0.40 % Version : Especial.
% 0.18/0.40 % English :
% 0.18/0.40
% 0.18/0.40 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.18/0.40 % Source : [Kal16]
% 0.18/0.40 % Names : SUP_UNIQUE_FINITE_.p [Kal16]
% 0.18/0.40
% 0.18/0.40 % Status : Theorem
% 0.18/0.40 % Rating : 0.00 v7.1.0
% 0.18/0.40 % Syntax : Number of formulae : 12 ( 2 unt; 6 typ; 0 def)
% 0.18/0.40 % Number of atoms : 30 ( 9 equ; 0 cnn)
% 0.18/0.40 % Maximal formula atoms : 3 ( 5 avg)
% 0.18/0.40 % Number of connectives : 62 ( 3 ~; 0 |; 7 &; 46 @)
% 0.18/0.40 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.18/0.40 % Maximal formula depth : 8 ( 6 avg)
% 0.18/0.40 % Number of types : 2 ( 1 usr)
% 0.18/0.40 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.18/0.40 % Number of symbols : 6 ( 5 usr; 0 con; 1-3 aty)
% 0.18/0.40 % Number of variables : 18 ( 0 ^; 14 !; 1 ?; 18 :)
% 0.18/0.40 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.40 % SPC : TH1_THM_EQU_NAR
% 0.18/0.40
% 0.18/0.40 % Comments : Exported from core HOL Light.
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 thf('thf_type_type/realax/real',type,
% 0.18/0.40 'type/realax/real': $tType ).
% 0.18/0.40
% 0.18/0.40 thf('thf_const_const/sets/sup',type,
% 0.18/0.40 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.18/0.40
% 0.18/0.40 thf('thf_const_const/sets/IN',type,
% 0.18/0.40 'const/sets/IN':
% 0.18/0.40 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.18/0.40
% 0.18/0.40 thf('thf_const_const/sets/FINITE',type,
% 0.18/0.40 'const/sets/FINITE':
% 0.18/0.40 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.18/0.40
% 0.18/0.40 thf('thf_const_const/sets/EMPTY',type,
% 0.18/0.40 'const/sets/EMPTY':
% 0.18/0.40 !>[A: $tType] : ( A > $o ) ).
% 0.18/0.40
% 0.18/0.40 thf('thf_const_const/realax/real_le',type,
% 0.18/0.40 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.18/0.40
% 0.18/0.40 thf('thm/realax/REAL_LE_ANTISYM_',axiom,
% 0.18/0.40 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.18/0.40 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 0.18/0.40 & ( 'const/realax/real_le' @ A0 @ A ) )
% 0.18/0.40 = ( A = A0 ) ) ).
% 0.18/0.40
% 0.18/0.40 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 0.18/0.40 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.18/0.40 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 0.18/0.40 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.18/0.40 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 0.18/0.40
% 0.18/0.40 thf('thm/realax/REAL_LE_REFL_',axiom,
% 0.18/0.40 ! [A: 'type/realax/real'] : ( 'const/realax/real_le' @ A @ A ) ).
% 0.18/0.40
% 0.18/0.40 thf('thm/sets/REAL_LE_SUP_FINITE_',axiom,
% 0.18/0.40 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.18/0.40 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.18/0.40 & ( A
% 0.18/0.40 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.18/0.40 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) )
% 0.18/0.40 = ( ? [A1: 'type/realax/real'] :
% 0.18/0.40 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.18/0.40 & ( 'const/realax/real_le' @ A0 @ A1 ) ) ) ) ) ).
% 0.18/0.40
% 0.18/0.40 thf('thm/sets/REAL_SUP_LE_FINITE_',axiom,
% 0.18/0.40 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.18/0.40 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.18/0.40 & ( A
% 0.18/0.40 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.18/0.40 => ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 )
% 0.18/0.40 = ( ! [A1: 'type/realax/real'] :
% 0.18/0.40 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.18/0.40 => ( 'const/realax/real_le' @ A1 @ A0 ) ) ) ) ) ).
% 0.18/0.40
% 0.18/0.40 thf('thm/sets/SUP_UNIQUE_FINITE_',conjecture,
% 0.18/0.40 ! [A: 'type/realax/real',A0: 'type/realax/real' > $o] :
% 0.18/0.40 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A0 )
% 0.18/0.40 & ( A0
% 0.18/0.40 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.18/0.40 => ( ( ( 'const/sets/sup' @ A0 )
% 0.18/0.40 = A )
% 0.18/0.40 = ( ( 'const/sets/IN' @ 'type/realax/real' @ A @ A0 )
% 0.18/0.40 & ! [A1: 'type/realax/real'] :
% 0.18/0.40 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A0 )
% 0.18/0.40 => ( 'const/realax/real_le' @ A1 @ A ) ) ) ) ) ).
% 0.18/0.40
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 ------------------------
% 1.55/1.38 ---- Embedded in THF ---
% 1.55/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.38 %%% Generated on Tue Feb 24 12:48:15 EST 2026
% 1.55/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.38 %%% Logic specification used:
% 1.55/1.38 %%% thf(spec, logic, $$dhol).
% 1.55/1.38
% 1.55/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Jhzb8yfRKP/DTF2DTF7245.p
% See solution above
% 1.55/1.38 ------------------------
% 1.55/1.39 ---- Cleaned THF ---
% 1.55/1.39 thf('thf_type_type/realax/real',type,
% 1.55/1.39 'type/realax/real': $tType ).
% 1.55/1.39
% 1.55/1.39 thf('thf_const_const/sets/sup',type,
% 1.55/1.39 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 1.55/1.39
% 1.55/1.39 thf('thf_const_const/sets/IN',type,
% 1.55/1.39 'const/sets/IN':
% 1.55/1.39 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.55/1.39
% 1.55/1.39 thf('thf_const_const/sets/FINITE',type,
% 1.55/1.39 'const/sets/FINITE':
% 1.55/1.39 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.55/1.39
% 1.55/1.39 thf('thf_const_const/sets/EMPTY',type,
% 1.55/1.39 'const/sets/EMPTY':
% 1.55/1.39 !>[A: $tType] : ( A > $o ) ).
% 1.55/1.39
% 1.55/1.39 thf('thf_const_const/realax/real_le',type,
% 1.55/1.39 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.55/1.39
% 1.55/1.39 thf('thm/realax/REAL_LE_ANTISYM_',axiom,
% 1.55/1.39 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 1.55/1.39 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 1.55/1.39 & ( 'const/realax/real_le' @ A0 @ A ) )
% 1.55/1.39 = ( A = A0 ) ) ).
% 1.55/1.39
% 1.55/1.39 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 1.55/1.39 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 1.55/1.39 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 1.55/1.39 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 1.55/1.39 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 1.55/1.39
% 1.55/1.39 thf('thm/realax/REAL_LE_REFL_',axiom,
% 1.55/1.39 ! [A: 'type/realax/real'] : ( 'const/realax/real_le' @ A @ A ) ).
% 1.55/1.39
% 1.55/1.39 thf('thm/sets/REAL_LE_SUP_FINITE_',axiom,
% 1.55/1.39 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 1.55/1.39 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 1.55/1.39 & ( A
% 1.55/1.39 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 1.55/1.39 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) )
% 1.55/1.39 = ( ? [A1: 'type/realax/real'] :
% 1.55/1.39 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.55/1.39 & ( 'const/realax/real_le' @ A0 @ A1 ) ) ) ) ) ).
% 1.55/1.39
% 1.55/1.39 thf('thm/sets/REAL_SUP_LE_FINITE_',axiom,
% 1.55/1.39 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 1.55/1.39 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 1.55/1.39 & ( A
% 1.55/1.39 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 1.55/1.39 => ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ A0 )
% 1.55/1.39 = ( ! [A1: 'type/realax/real'] :
% 1.55/1.39 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.55/1.39 => ( 'const/realax/real_le' @ A1 @ A0 ) ) ) ) ) ).
% 1.55/1.39
% 1.55/1.39 thf('thm/sets/SUP_UNIQUE_FINITE_',conjecture,
% 1.55/1.39 ! [A: 'type/realax/real',A0: 'type/realax/real' > $o] :
% 1.55/1.39 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A0 )
% 1.55/1.39 & ( A0
% 1.55/1.39 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 1.55/1.39 => ( ( ( 'const/sets/sup' @ A0 )
% 1.55/1.39 = A )
% 1.55/1.39 = ( ( 'const/sets/IN' @ 'type/realax/real' @ A @ A0 )
% 1.55/1.39 & ! [A1: 'type/realax/real'] :
% 1.55/1.39 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A0 )
% 1.55/1.39 => ( 'const/realax/real_le' @ A1 @ A ) ) ) ) ) ).
% 1.55/1.39 ------------------------
% 1.74/1.41 % (7347)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_7245 for (2999ds/2Mi)
% 1.74/1.41 % (7345)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_7245 for (2999ds/27Mi)
% 1.74/1.41 % (7349)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7245 for (2999ds/18Mi)
% 1.74/1.41 % (7343)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7245 for (2999ds/183Mi)
% 1.74/1.41 % (7348)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_7245 for (2999ds/275Mi)
% 1.74/1.41 % (7347)Instruction limit reached!
% 1.74/1.41 % (7347)------------------------------
% 1.74/1.41 % (7347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.41 % (7347)Termination reason: Unknown
% 1.74/1.41 % (7347)Termination phase: Property scanning
% 1.74/1.41
% 1.74/1.41 % (7347)Memory used [KB]: 1023
% 1.74/1.41 % (7347)Time elapsed: 0.003 s
% 1.74/1.41 % (7347)Instructions burned: 2 (million)
% 1.74/1.41 % (7347)------------------------------
% 1.74/1.41 % (7347)------------------------------
% 1.74/1.41 % (7346)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7245 for (2999ds/2Mi)
% 1.74/1.41 % (7346)Instruction limit reached!
% 1.74/1.41 % (7346)------------------------------
% 1.74/1.41 % (7346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.41 % (7346)Termination reason: Unknown
% 1.74/1.41 % (7346)Termination phase: Preprocessing 3
% 1.74/1.41
% 1.74/1.41 % (7346)Memory used [KB]: 895
% 1.74/1.41 % (7346)Time elapsed: 0.002 s
% 1.74/1.41 % (7346)Instructions burned: 2 (million)
% 1.74/1.41 % (7346)------------------------------
% 1.74/1.41 % (7346)------------------------------
% 1.74/1.41 % (7344)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_7245 for (2999ds/4Mi)
% 1.74/1.42 % (7344)Instruction limit reached!
% 1.74/1.42 % (7344)------------------------------
% 1.74/1.42 % (7344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.42 % (7344)Termination reason: Unknown
% 1.74/1.42 % (7344)Termination phase: Saturation
% 1.74/1.42
% 1.74/1.42 % (7344)Memory used [KB]: 5500
% 1.74/1.42 % (7344)Time elapsed: 0.004 s
% 1.74/1.42 % (7344)Instructions burned: 4 (million)
% 1.74/1.42 % (7344)------------------------------
% 1.74/1.42 % (7344)------------------------------
% 1.74/1.42 % (7349)Instruction limit reached!
% 1.74/1.42 % (7349)------------------------------
% 1.74/1.42 % (7349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.42 % (7349)Termination reason: Unknown
% 1.74/1.42 % (7349)Termination phase: Saturation
% 1.74/1.42
% 1.74/1.42 % (7349)Memory used [KB]: 5628
% 1.74/1.42 % (7349)Time elapsed: 0.012 s
% 1.74/1.42 % (7349)Instructions burned: 19 (million)
% 1.74/1.42 % (7349)------------------------------
% 1.74/1.42 % (7349)------------------------------
% 1.74/1.43 % (7345)Instruction limit reached!
% 1.74/1.43 % (7345)------------------------------
% 1.74/1.43 % (7345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.43 % (7345)Termination reason: Unknown
% 1.74/1.43 % (7345)Termination phase: Saturation
% 1.74/1.43
% 1.74/1.43 % (7345)Memory used [KB]: 5628
% 1.74/1.43 % (7345)Time elapsed: 0.016 s
% 1.74/1.43 % (7345)Instructions burned: 27 (million)
% 1.74/1.43 % (7345)------------------------------
% 1.74/1.43 % (7345)------------------------------
% 1.74/1.43 % (7351)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_7245 for (2999ds/37Mi)
% 1.74/1.43 % (7350)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7245 for (2999ds/3Mi)
% 1.74/1.43 % (7350)Instruction limit reached!
% 1.74/1.43 % (7350)------------------------------
% 1.74/1.43 % (7350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.43 % (7350)Termination reason: Unknown
% 1.74/1.43 % (7350)Termination phase: Saturation
% 1.74/1.43
% 1.74/1.43 % (7350)Memory used [KB]: 1023
% 1.74/1.43 % (7350)Time elapsed: 0.003 s
% 1.74/1.43 % (7350)Instructions burned: 3 (million)
% 1.74/1.43 % (7350)------------------------------
% 1.74/1.43 % (7350)------------------------------
% 1.74/1.44 % (7353)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7245 for (2999ds/3Mi)
% 1.74/1.44 % (7352)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_7245 for (2999ds/15Mi)
% 1.74/1.44 % (7353)Instruction limit reached!
% 1.74/1.44 % (7353)------------------------------
% 1.74/1.44 % (7353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.44 % (7353)Termination reason: Unknown
% 1.74/1.44 % (7353)Termination phase: Saturation
% 1.74/1.44
% 1.74/1.44 % (7353)Memory used [KB]: 5500
% 1.74/1.44 % (7353)Time elapsed: 0.003 s
% 1.74/1.44 % (7353)Instructions burned: 3 (million)
% 1.74/1.44 % (7353)------------------------------
% 1.74/1.44 % (7353)------------------------------
% 1.74/1.44 % (7348)First to succeed.
% 1.74/1.44 % (7354)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_7245 for (2999ds/1041Mi)
% 1.74/1.44 % (7348)Refutation found. Thanks to Tanya!
% 1.74/1.44 % SZS status Theorem for DTF2THF_7245
% 1.74/1.44 % SZS output start Proof for DTF2THF_7245
% 1.74/1.44 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.74/1.44 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.74/1.44 thf(func_def_1, type, 'const/sets/sup': ('type/realax/real' > $o) > 'type/realax/real').
% 1.74/1.44 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.74/1.44 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.74/1.44 thf(func_def_4, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.74/1.44 thf(func_def_5, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.74/1.44 thf(func_def_9, type, sK0: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.74/1.44 thf(func_def_10, type, sK1: 'type/realax/real').
% 1.74/1.44 thf(func_def_11, type, sK2: 'type/realax/real' > $o).
% 1.74/1.44 thf(func_def_12, type, sK3: 'type/realax/real').
% 1.74/1.44 thf(func_def_13, type, sK4: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.74/1.44 thf(func_def_15, type, ph6: !>[X0: $tType]:(X0)).
% 1.74/1.44 thf(func_def_16, type, sK7: 'type/realax/real').
% 1.74/1.44 thf(f322,plain,(
% 1.74/1.44 $false),
% 1.74/1.44 inference(avatar_sat_refutation,[status(thm)],[f76,f77,f81,f86,f208,f243,f321])).
% 1.74/1.44 thf(f321,plain,(
% 1.74/1.44 spl5_2 | ~spl5_3 | ~spl5_4),
% 1.74/1.44 inference(avatar_contradiction_clause,[status(thm)],[f320])).
% 1.74/1.44 thf(f320,plain,(
% 1.74/1.44 $false | (spl5_2 | ~spl5_3 | ~spl5_4)),
% 1.74/1.44 inference(subsumption_resolution,[status(thm)],[f313,f63])).
% 1.74/1.44 thf(f63,plain,(
% 1.74/1.44 ( ! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X1) = $true)) )),
% 1.74/1.44 inference(equality_resolution,[status(thm)],[f60])).
% 1.74/1.44 thf(f60,plain,(
% 1.74/1.44 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X0) = $true) | (X0 != X1)) )),
% 1.74/1.44 inference(cnf_transformation,[status(thm)],[f44])).
% 1.74/1.44 thf(f44,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X1) = $true) & (('const/realax/real_le' @ X1 @ X0) = $true)) | (X0 != X1)) & ((X0 = X1) | (('const/realax/real_le' @ X0 @ X1) != $true) | (('const/realax/real_le' @ X1 @ X0) != $true)))),
% 1.74/1.44 inference(flattening,[status(thm)],[f43])).
% 1.74/1.44 thf(f43,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ X0 @ X1) = $true) & (('const/realax/real_le' @ X1 @ X0) = $true)) | (X0 != X1)) & ((X0 = X1) | ((('const/realax/real_le' @ X0 @ X1) != $true) | (('const/realax/real_le' @ X1 @ X0) != $true))))),
% 1.74/1.44 inference(nnf_transformation,[status(thm)],[f10])).
% 1.74/1.44 thf(f10,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X1) = $true) & (('const/realax/real_le' @ X1 @ X0) = $true)) <=> (X0 = X1))),
% 1.74/1.44 inference(fool_elimination,[status(thm)],[f9])).
% 1.74/1.44 thf(f9,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X0) = (X0 = X1))),
% 1.74/1.44 inference(rectify,[status(thm)],[f1])).
% 1.74/1.44 thf(f1,axiom,(
% 1.74/1.44 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ X1 @ X0) = (X0 = X1))),
% 1.74/1.44 file('/export/starexec/sandbox2/tmp/tmp.Jhzb8yfRKP/DTF2THF_7245.p','thm/realax/REAL_LE_ANTISYM_')).
% 1.74/1.44 thf(f313,plain,(
% 1.74/1.44 (('const/realax/real_le' @ sK1 @ sK1) != $true) | (spl5_2 | ~spl5_3 | ~spl5_4)),
% 1.74/1.44 inference(trivial_inequality_removal,[status(thm)],[f312])).
% 1.74/1.44 thf(f312,plain,(
% 1.74/1.44 ($true != $true) | (('const/realax/real_le' @ sK1 @ sK1) != $true) | (spl5_2 | ~spl5_3 | ~spl5_4)),
% 1.74/1.44 inference(superposition,[status(thm)],[f296,f74])).
% 1.74/1.44 thf(f74,plain,(
% 1.74/1.44 ($true = ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2)) | ~spl5_3),
% 1.74/1.44 inference(avatar_component_clause,[status(thm)],[f73])).
% 1.74/1.44 thf(f73,definition,(
% 1.74/1.44 spl5_3 <=> ($true = ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2))),
% 1.74/1.44 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.74/1.44 thf(f296,plain,(
% 1.74/1.44 ( ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2) != $true) | (('const/realax/real_le' @ sK1 @ X0) != $true)) ) | (spl5_2 | ~spl5_4)),
% 1.74/1.44 inference(subsumption_resolution,[status(thm)],[f295,f53])).
% 1.74/1.44 thf(f53,plain,(
% 1.74/1.44 (('const/sets/FINITE' @ 'type/realax/real' @ sK2) = $true)),
% 1.74/1.44 inference(cnf_transformation,[status(thm)],[f38])).
% 1.74/1.44 thf(f38,plain,(
% 1.74/1.44 (('const/sets/FINITE' @ 'type/realax/real' @ sK2) = $true) & ((('const/sets/sup' @ sK2) != sK1) | ((('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK2) = $true) & (('const/realax/real_le' @ sK3 @ sK1) != $true)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2))) & ((('const/sets/sup' @ sK2) = sK1) | (! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2) != $true) | (('const/realax/real_le' @ X3 @ sK1) = $true)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2)))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 1.74/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f35,f37,f36])).
% 1.74/1.44 thf(f36,plain,(
% 1.74/1.44 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X1) = $true) & ((('const/sets/sup' @ X1) != X0) | ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) = $true) & (('const/realax/real_le' @ X2 @ X0) != $true)) | (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) != $true)) & ((('const/sets/sup' @ X1) = X0) | (! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) != $true) | (('const/realax/real_le' @ X3 @ X0) = $true)) & (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) = $true))) & ('const/sets/EMPTY' @ 'type/realax/real' != X1)) => ((('const/sets/FINITE' @ 'type/realax/real' @ sK2) = $true) & ((('const/sets/sup' @ sK2) != sK1) | ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ sK2) = $true) & (('const/realax/real_le' @ X2 @ sK1) != $true)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2))) & ((('const/sets/sup' @ sK2) = sK1) | (! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2) != $true) | (('const/realax/real_le' @ X3 @ sK1) = $true)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2)))) & ('const/sets/EMPTY' @ 'type/realax/real' != sK2))),
% 1.74/1.44 introduced(definition,[],[choice_axiom])).
% 1.74/1.44 thf(f37,plain,(
% 1.74/1.44 ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ sK2) = $true) & (('const/realax/real_le' @ X2 @ sK1) != $true)) => ((('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK2) = $true) & (('const/realax/real_le' @ sK3 @ sK1) != $true))),
% 1.74/1.44 introduced(definition,[],[choice_axiom])).
% 1.74/1.44 thf(f35,plain,(
% 1.74/1.44 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X1) = $true) & ((('const/sets/sup' @ X1) != X0) | ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) = $true) & (('const/realax/real_le' @ X2 @ X0) != $true)) | (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) != $true)) & ((('const/sets/sup' @ X1) = X0) | (! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X1) != $true) | (('const/realax/real_le' @ X3 @ X0) = $true)) & (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) = $true))) & ('const/sets/EMPTY' @ 'type/realax/real' != X1))),
% 1.74/1.44 inference(rectify,[status(thm)],[f34])).
% 1.74/1.44 thf(f34,plain,(
% 1.74/1.44 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X1) = $true) & ((('const/sets/sup' @ X1) != X0) | ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) = $true) & (('const/realax/real_le' @ X2 @ X0) != $true)) | (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) != $true)) & ((('const/sets/sup' @ X1) = X0) | (! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) != $true) | (('const/realax/real_le' @ X2 @ X0) = $true)) & (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) = $true))) & ('const/sets/EMPTY' @ 'type/realax/real' != X1))),
% 1.74/1.44 inference(flattening,[status(thm)],[f33])).
% 1.74/1.44 thf(f33,plain,(
% 1.74/1.44 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X1) = $true) & (((('const/sets/sup' @ X1) != X0) | (? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) = $true) & (('const/realax/real_le' @ X2 @ X0) != $true)) | (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) != $true))) & ((('const/sets/sup' @ X1) = X0) | (! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) != $true) | (('const/realax/real_le' @ X2 @ X0) = $true)) & (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) = $true)))) & ('const/sets/EMPTY' @ 'type/realax/real' != X1))),
% 1.74/1.44 inference(nnf_transformation,[status(thm)],[f22])).
% 1.74/1.44 thf(f22,plain,(
% 1.74/1.44 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X1) = $true) & ((! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) != $true) | (('const/realax/real_le' @ X2 @ X0) = $true)) & (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) = $true)) <~> (('const/sets/sup' @ X1) = X0)) & ('const/sets/EMPTY' @ 'type/realax/real' != X1))),
% 1.74/1.44 inference(flattening,[status(thm)],[f21])).
% 1.74/1.44 thf(f21,plain,(
% 1.74/1.44 ? [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : (((! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) != $true) | (('const/realax/real_le' @ X2 @ X0) = $true)) & (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) = $true)) <~> (('const/sets/sup' @ X1) = X0)) & (('const/sets/EMPTY' @ 'type/realax/real' != X1) & (('const/sets/FINITE' @ 'type/realax/real' @ X1) = $true)))),
% 1.74/1.44 inference(ennf_transformation,[status(thm)],[f16])).
% 1.74/1.44 thf(f16,plain,(
% 1.74/1.44 ~! [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X1) & (('const/sets/FINITE' @ 'type/realax/real' @ X1) = $true)) => ((! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) = $true) => (('const/realax/real_le' @ X2 @ X0) = $true)) & (('const/sets/IN' @ 'type/realax/real' @ X0 @ X1) = $true)) <=> (('const/sets/sup' @ X1) = X0)))),
% 1.74/1.44 inference(fool_elimination,[status(thm)],[f15])).
% 1.74/1.44 thf(f15,plain,(
% 1.74/1.44 ~! [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X1) & ('const/sets/FINITE' @ 'type/realax/real' @ X1)) => ((('const/sets/sup' @ X1) = X0) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) => ('const/realax/real_le' @ X2 @ X0)) & ('const/sets/IN' @ 'type/realax/real' @ X0 @ X1)))),
% 1.74/1.44 inference(rectify,[status(thm)],[f7])).
% 1.74/1.44 thf(f7,negated_conjecture,(
% 1.74/1.44 ~! [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X1) & ('const/sets/FINITE' @ 'type/realax/real' @ X1)) => ((('const/sets/sup' @ X1) = X0) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) => ('const/realax/real_le' @ X2 @ X0)) & ('const/sets/IN' @ 'type/realax/real' @ X0 @ X1)))),
% 1.74/1.44 inference(negated_conjecture,[status(cth)],[f6])).
% 1.74/1.44 thf(f6,conjecture,(
% 1.74/1.44 ! [X0 : 'type/realax/real',X1 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X1) & ('const/sets/FINITE' @ 'type/realax/real' @ X1)) => ((('const/sets/sup' @ X1) = X0) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X1) => ('const/realax/real_le' @ X2 @ X0)) & ('const/sets/IN' @ 'type/realax/real' @ X0 @ X1)))),
% 1.74/1.44 file('/export/starexec/sandbox2/tmp/tmp.Jhzb8yfRKP/DTF2THF_7245.p','thm/sets/SUP_UNIQUE_FINITE_')).
% 1.74/1.44 thf(f295,plain,(
% 1.74/1.44 ( ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2) != $true) | (('const/realax/real_le' @ sK1 @ X0) != $true) | (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true)) ) | (spl5_2 | ~spl5_4)),
% 1.74/1.44 inference(subsumption_resolution,[status(thm)],[f294,f48])).
% 1.74/1.44 thf(f48,plain,(
% 1.74/1.44 ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 1.74/1.44 inference(cnf_transformation,[status(thm)],[f38])).
% 1.74/1.44 thf(f294,plain,(
% 1.74/1.44 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ sK1 @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2) != $true)) ) | (spl5_2 | ~spl5_4)),
% 1.74/1.44 inference(trivial_inequality_removal,[status(thm)],[f291])).
% 1.74/1.44 thf(f291,plain,(
% 1.74/1.44 ( ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2) != $true) | ($true != $true) | (('const/realax/real_le' @ sK1 @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true)) ) | (spl5_2 | ~spl5_4)),
% 1.74/1.44 inference(superposition,[status(thm)],[f283,f45])).
% 1.74/1.44 thf(f45,plain,(
% 1.74/1.44 ( ! [X3 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | (('const/realax/real_le' @ X1 @ X3) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.74/1.44 inference(cnf_transformation,[status(thm)],[f32])).
% 1.74/1.44 thf(f32,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((((($true = ('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0)) & (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)) = $true)) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) != $true)) & ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true) | ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | (('const/realax/real_le' @ X1 @ X3) != $true)))) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.74/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f30,f31])).
% 1.74/1.44 thf(f31,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) = $true)) => (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0)) & (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)) = $true)))),
% 1.74/1.44 introduced(definition,[],[choice_axiom])).
% 1.74/1.44 thf(f30,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (((? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) = $true)) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) != $true)) & ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true) | ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | (('const/realax/real_le' @ X1 @ X3) != $true)))) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.74/1.44 inference(rectify,[status(thm)],[f29])).
% 1.74/1.44 thf(f29,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (((? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) = $true)) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) != $true)) & ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true) | ! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true) | (('const/realax/real_le' @ X1 @ X2) != $true)))) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.74/1.44 inference(nnf_transformation,[status(thm)],[f24])).
% 1.74/1.44 thf(f24,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) = $true)) <=> (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true)) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.74/1.44 inference(flattening,[status(thm)],[f23])).
% 1.74/1.44 thf(f23,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) = $true)) <=> (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true)) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true)))),
% 1.74/1.44 inference(ennf_transformation,[status(thm)],[f14])).
% 1.74/1.44 thf(f14,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true)) => (? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) = $true)) <=> (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true)))),
% 1.74/1.44 inference(fool_elimination,[status(thm)],[f13])).
% 1.74/1.44 thf(f13,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = ? [X2 : 'type/realax/real'] : (('const/realax/real_le' @ X1 @ X2) & ('const/sets/IN' @ 'type/realax/real' @ X2 @ X0))))),
% 1.74/1.44 inference(rectify,[status(thm)],[f4])).
% 1.74/1.44 thf(f4,axiom,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = ? [X2 : 'type/realax/real'] : (('const/realax/real_le' @ X1 @ X2) & ('const/sets/IN' @ 'type/realax/real' @ X2 @ X0))))),
% 1.74/1.44 file('/export/starexec/sandbox2/tmp/tmp.Jhzb8yfRKP/DTF2THF_7245.p','thm/sets/REAL_LE_SUP_FINITE_')).
% 1.74/1.44 thf(f283,plain,(
% 1.74/1.44 (('const/realax/real_le' @ sK1 @ ('const/sets/sup' @ sK2)) != $true) | (spl5_2 | ~spl5_4)),
% 1.74/1.44 inference(subsumption_resolution,[status(thm)],[f282,f71])).
% 1.74/1.44 thf(f71,plain,(
% 1.74/1.44 (('const/sets/sup' @ sK2) != sK1) | spl5_2),
% 1.74/1.44 inference(avatar_component_clause,[status(thm)],[f69])).
% 1.74/1.44 thf(f69,definition,(
% 1.74/1.44 spl5_2 <=> (('const/sets/sup' @ sK2) = sK1)),
% 1.74/1.44 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.74/1.44 thf(f282,plain,(
% 1.74/1.44 (('const/realax/real_le' @ sK1 @ ('const/sets/sup' @ sK2)) != $true) | (('const/sets/sup' @ sK2) = sK1) | ~spl5_4),
% 1.74/1.44 inference(trivial_inequality_removal,[status(thm)],[f280])).
% 1.74/1.44 thf(f280,plain,(
% 1.74/1.44 (('const/sets/sup' @ sK2) = sK1) | (('const/realax/real_le' @ sK1 @ ('const/sets/sup' @ sK2)) != $true) | ($true != $true) | ~spl5_4),
% 1.74/1.44 inference(superposition,[status(thm)],[f59,f278])).
% 1.74/1.44 thf(f278,plain,(
% 1.74/1.44 (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK1) = $true) | ~spl5_4),
% 1.74/1.44 inference(subsumption_resolution,[status(thm)],[f277,f48])).
% 1.74/1.44 thf(f277,plain,(
% 1.74/1.44 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK1) = $true) | ~spl5_4),
% 1.74/1.44 inference(subsumption_resolution,[status(thm)],[f276,f53])).
% 1.74/1.44 thf(f276,plain,(
% 1.74/1.44 (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK1) = $true) | (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ~spl5_4),
% 1.74/1.44 inference(trivial_inequality_removal,[status(thm)],[f275])).
% 1.74/1.44 thf(f275,plain,(
% 1.74/1.44 ($true != $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK1) = $true) | (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ~spl5_4),
% 1.74/1.44 inference(duplicate_literal_removal,[status(thm)],[f272])).
% 1.74/1.44 thf(f272,plain,(
% 1.74/1.44 (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK1) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ sK1) = $true) | ~spl5_4),
% 1.74/1.44 inference(superposition,[status(thm)],[f57,f257])).
% 1.74/1.44 thf(f257,plain,(
% 1.74/1.44 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK4 @ X0 @ sK2) @ sK1) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0) = $true)) ) | ~spl5_4),
% 1.74/1.44 inference(subsumption_resolution,[status(thm)],[f256,f48])).
% 1.74/1.44 thf(f256,plain,(
% 1.74/1.44 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/realax/real_le' @ (sK4 @ X0 @ sK2) @ sK1) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0) = $true)) ) | ~spl5_4),
% 1.74/1.44 inference(subsumption_resolution,[status(thm)],[f248,f53])).
% 1.74/1.44 thf(f248,plain,(
% 1.74/1.44 ( ! [X0 : 'type/realax/real'] : ((('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | (('const/realax/real_le' @ (sK4 @ X0 @ sK2) @ sK1) = $true) | (('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_4),
% 1.74/1.44 inference(trivial_inequality_removal,[status(thm)],[f245])).
% 1.74/1.44 thf(f245,plain,(
% 1.74/1.44 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/sup' @ sK2) @ X0) = $true) | (('const/realax/real_le' @ (sK4 @ X0 @ sK2) @ sK1) = $true) | (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl5_4),
% 1.74/1.44 inference(superposition,[status(thm)],[f80,f56])).
% 1.74/1.44 thf(f56,plain,(
% 1.74/1.44 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true)) )),
% 1.74/1.44 inference(cnf_transformation,[status(thm)],[f42])).
% 1.74/1.44 thf(f42,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true) | ((('const/realax/real_le' @ (sK4 @ X1 @ X0) @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0) = $true))) & (! [X3 : 'type/realax/real'] : ((('const/realax/real_le' @ X3 @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true)) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) != $true))) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.74/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f40,f41])).
% 1.74/1.44 thf(f41,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) => ((('const/realax/real_le' @ (sK4 @ X1 @ X0) @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ (sK4 @ X1 @ X0) @ X0) = $true)))),
% 1.74/1.44 introduced(definition,[],[choice_axiom])).
% 1.74/1.44 thf(f40,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true) | ? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true))) & (! [X3 : 'type/realax/real'] : ((('const/realax/real_le' @ X3 @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true)) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) != $true))) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.74/1.44 inference(rectify,[status(thm)],[f39])).
% 1.74/1.44 thf(f39,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true) | ? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true))) & (! [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))) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.74/1.44 inference(nnf_transformation,[status(thm)],[f28])).
% 1.74/1.44 thf(f28,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true) <=> ! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true))) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.74/1.44 inference(flattening,[status(thm)],[f27])).
% 1.74/1.44 thf(f27,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true) <=> ! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true))) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 1.74/1.44 inference(ennf_transformation,[status(thm)],[f18])).
% 1.74/1.44 thf(f18,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ((('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true) <=> ! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) => (('const/realax/real_le' @ X2 @ X1) = $true))))),
% 1.74/1.44 inference(fool_elimination,[status(thm)],[f17])).
% 1.74/1.44 thf(f17,plain,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [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)))),
% 1.74/1.44 inference(rectify,[status(thm)],[f5])).
% 1.74/1.44 thf(f5,axiom,(
% 1.74/1.44 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [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)))),
% 1.74/1.44 file('/export/starexec/sandbox2/tmp/tmp.Jhzb8yfRKP/DTF2THF_7245.p','thm/sets/REAL_SUP_LE_FINITE_')).
% 1.74/1.44 thf(f80,plain,(
% 1.74/1.44 ( ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2) != $true) | (('const/realax/real_le' @ X3 @ sK1) = $true)) ) | ~spl5_4),
% 1.74/1.44 inference(avatar_component_clause,[status(thm)],[f79])).
% 1.74/1.44 thf(f79,definition,(
% 1.74/1.44 spl5_4 <=> ! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2) != $true) | (('const/realax/real_le' @ X3 @ sK1) = $true))),
% 1.74/1.45 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.74/1.45 thf(f57,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK4 @ X1 @ X0) @ X1) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ ('const/sets/sup' @ X0) @ X1) = $true) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true)) )),
% 1.74/1.45 inference(cnf_transformation,[status(thm)],[f42])).
% 1.74/1.45 thf(f59,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X0) != $true) | (X0 = X1) | (('const/realax/real_le' @ X0 @ X1) != $true)) )),
% 1.74/1.45 inference(cnf_transformation,[status(thm)],[f44])).
% 1.74/1.45 thf(f243,plain,(
% 1.74/1.45 ~spl5_1 | ~spl5_2 | spl5_5),
% 1.74/1.45 inference(avatar_contradiction_clause,[status(thm)],[f242])).
% 1.74/1.45 thf(f242,plain,(
% 1.74/1.45 $false | (~spl5_1 | ~spl5_2 | spl5_5)),
% 1.74/1.45 inference(subsumption_resolution,[status(thm)],[f235,f63])).
% 1.74/1.45 thf(f235,plain,(
% 1.74/1.45 (('const/realax/real_le' @ sK3 @ sK3) != $true) | (~spl5_1 | ~spl5_2 | spl5_5)),
% 1.74/1.45 inference(trivial_inequality_removal,[status(thm)],[f232])).
% 1.74/1.45 thf(f232,plain,(
% 1.74/1.45 ($true != $true) | (('const/realax/real_le' @ sK3 @ sK3) != $true) | (~spl5_1 | ~spl5_2 | spl5_5)),
% 1.74/1.45 inference(superposition,[status(thm)],[f85,f213])).
% 1.74/1.45 thf(f213,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ sK1) = $true) | (('const/realax/real_le' @ X0 @ sK3) != $true)) ) | (~spl5_1 | ~spl5_2)),
% 1.74/1.45 inference(trivial_inequality_removal,[status(thm)],[f212])).
% 1.74/1.45 thf(f212,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ sK3) != $true) | ($true != $true) | (('const/realax/real_le' @ X0 @ sK1) = $true)) ) | (~spl5_1 | ~spl5_2)),
% 1.74/1.45 inference(superposition,[status(thm)],[f111,f67])).
% 1.74/1.45 thf(f67,plain,(
% 1.74/1.45 (('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK2) = $true) | ~spl5_1),
% 1.74/1.45 inference(avatar_component_clause,[status(thm)],[f65])).
% 1.74/1.45 thf(f65,definition,(
% 1.74/1.45 spl5_1 <=> (('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK2) = $true)),
% 1.74/1.45 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.74/1.45 thf(f111,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2) != $true) | (('const/realax/real_le' @ X0 @ X1) != $true) | (('const/realax/real_le' @ X0 @ sK1) = $true)) ) | ~spl5_2),
% 1.74/1.45 inference(subsumption_resolution,[status(thm)],[f110,f48])).
% 1.74/1.45 thf(f110,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2) != $true) | (('const/realax/real_le' @ X0 @ X1) != $true) | (('const/realax/real_le' @ X0 @ sK1) = $true)) ) | ~spl5_2),
% 1.74/1.45 inference(subsumption_resolution,[status(thm)],[f108,f53])).
% 1.74/1.45 thf(f108,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | (('const/realax/real_le' @ X0 @ X1) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2) != $true) | (('const/realax/real_le' @ X0 @ sK1) = $true)) ) | ~spl5_2),
% 1.74/1.45 inference(superposition,[status(thm)],[f45,f70])).
% 1.74/1.45 thf(f70,plain,(
% 1.74/1.45 (('const/sets/sup' @ sK2) = sK1) | ~spl5_2),
% 1.74/1.45 inference(avatar_component_clause,[status(thm)],[f69])).
% 1.74/1.45 thf(f85,plain,(
% 1.74/1.45 (('const/realax/real_le' @ sK3 @ sK1) != $true) | spl5_5),
% 1.74/1.45 inference(avatar_component_clause,[status(thm)],[f83])).
% 1.74/1.45 thf(f83,definition,(
% 1.74/1.45 spl5_5 <=> (('const/realax/real_le' @ sK3 @ sK1) = $true)),
% 1.74/1.45 introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition])).
% 1.74/1.45 thf(f208,plain,(
% 1.74/1.45 spl5_3 | ~spl5_2),
% 1.74/1.45 inference(avatar_split_clause,[status(thm)],[f207,f69,f73])).
% 1.74/1.45 thf(f207,plain,(
% 1.74/1.45 ($true = ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2)) | ~spl5_2),
% 1.74/1.45 inference(subsumption_resolution,[status(thm)],[f206,f63])).
% 1.74/1.45 thf(f206,plain,(
% 1.74/1.45 ($true = ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2)) | (('const/realax/real_le' @ sK1 @ sK1) != $true) | ~spl5_2),
% 1.74/1.45 inference(forward_demodulation,[status(thm)],[f201,f70])).
% 1.74/1.45 thf(f201,plain,(
% 1.74/1.45 (('const/realax/real_le' @ sK1 @ ('const/sets/sup' @ sK2)) != $true) | ($true = ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2)) | ~spl5_2),
% 1.74/1.45 inference(subsumption_resolution,[status(thm)],[f200,f48])).
% 1.74/1.45 thf(f200,plain,(
% 1.74/1.45 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/realax/real_le' @ sK1 @ ('const/sets/sup' @ sK2)) != $true) | ($true = ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2)) | ~spl5_2),
% 1.74/1.45 inference(subsumption_resolution,[status(thm)],[f194,f53])).
% 1.74/1.45 thf(f194,plain,(
% 1.74/1.45 (('const/realax/real_le' @ sK1 @ ('const/sets/sup' @ sK2)) != $true) | (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true = ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2)) | ~spl5_2),
% 1.74/1.45 inference(superposition,[status(thm)],[f47,f178])).
% 1.74/1.45 thf(f178,plain,(
% 1.74/1.45 (sK1 = (sK0 @ sK1 @ sK2)) | ~spl5_2),
% 1.74/1.45 inference(subsumption_resolution,[status(thm)],[f177,f63])).
% 1.74/1.45 thf(f177,plain,(
% 1.74/1.45 (('const/realax/real_le' @ sK1 @ sK1) != $true) | (sK1 = (sK0 @ sK1 @ sK2)) | ~spl5_2),
% 1.74/1.45 inference(forward_demodulation,[status(thm)],[f176,f70])).
% 1.74/1.45 thf(f176,plain,(
% 1.74/1.45 (('const/realax/real_le' @ sK1 @ ('const/sets/sup' @ sK2)) != $true) | (sK1 = (sK0 @ sK1 @ sK2)) | ~spl5_2),
% 1.74/1.45 inference(subsumption_resolution,[status(thm)],[f175,f53])).
% 1.74/1.45 thf(f175,plain,(
% 1.74/1.45 (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | (sK1 = (sK0 @ sK1 @ sK2)) | (('const/realax/real_le' @ sK1 @ ('const/sets/sup' @ sK2)) != $true) | ~spl5_2),
% 1.74/1.45 inference(subsumption_resolution,[status(thm)],[f174,f48])).
% 1.74/1.45 thf(f174,plain,(
% 1.74/1.45 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/realax/real_le' @ sK1 @ ('const/sets/sup' @ sK2)) != $true) | (sK1 = (sK0 @ sK1 @ sK2)) | (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | ~spl5_2),
% 1.74/1.45 inference(subsumption_resolution,[status(thm)],[f172,f63])).
% 1.74/1.45 thf(f172,plain,(
% 1.74/1.45 (('const/realax/real_le' @ sK1 @ sK1) != $true) | (('const/realax/real_le' @ sK1 @ ('const/sets/sup' @ sK2)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (sK1 = (sK0 @ sK1 @ sK2)) | (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | ~spl5_2),
% 1.74/1.45 inference(trivial_inequality_removal,[status(thm)],[f170])).
% 1.74/1.45 thf(f170,plain,(
% 1.74/1.45 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | (('const/realax/real_le' @ sK1 @ ('const/sets/sup' @ sK2)) != $true) | ($true != $true) | (sK1 = (sK0 @ sK1 @ sK2)) | (('const/realax/real_le' @ sK1 @ sK1) != $true) | ~spl5_2),
% 1.74/1.45 inference(superposition,[status(thm)],[f152,f46])).
% 1.74/1.45 thf(f46,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)) = $true) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) != $true)) )),
% 1.74/1.45 inference(cnf_transformation,[status(thm)],[f32])).
% 1.74/1.45 thf(f152,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ sK1 @ (sK0 @ X0 @ sK2)) != $true) | ((sK0 @ X0 @ sK2) = sK1) | (('const/realax/real_le' @ X0 @ sK1) != $true)) ) | ~spl5_2),
% 1.74/1.45 inference(trivial_inequality_removal,[status(thm)],[f151])).
% 1.74/1.45 thf(f151,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ sK1) != $true) | ((sK0 @ X0 @ sK2) = sK1) | (('const/realax/real_le' @ sK1 @ (sK0 @ X0 @ sK2)) != $true) | ($true != $true)) ) | ~spl5_2),
% 1.74/1.45 inference(superposition,[status(thm)],[f59,f142])).
% 1.74/1.45 thf(f142,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK1) = $true) | (('const/realax/real_le' @ X0 @ sK1) != $true)) ) | ~spl5_2),
% 1.74/1.45 inference(trivial_inequality_removal,[status(thm)],[f136])).
% 1.74/1.45 thf(f136,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real'] : (($true != $true) | (('const/realax/real_le' @ X0 @ sK1) != $true) | (('const/realax/real_le' @ (sK0 @ X0 @ sK2) @ sK1) = $true)) ) | ~spl5_2),
% 1.74/1.45 inference(superposition,[status(thm)],[f120,f58])).
% 1.74/1.45 thf(f58,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X0) = $true)) )),
% 1.74/1.45 inference(cnf_transformation,[status(thm)],[f12])).
% 1.74/1.45 thf(f12,plain,(
% 1.74/1.45 ! [X0 : 'type/realax/real'] : (('const/realax/real_le' @ X0 @ X0) = $true)),
% 1.74/1.45 inference(fool_elimination,[status(thm)],[f11])).
% 1.74/1.45 thf(f11,plain,(
% 1.74/1.45 ! [X0 : 'type/realax/real'] : ('const/realax/real_le' @ X0 @ X0)),
% 1.74/1.45 inference(rectify,[status(thm)],[f3])).
% 1.74/1.45 thf(f3,axiom,(
% 1.74/1.45 ! [X0 : 'type/realax/real'] : ('const/realax/real_le' @ X0 @ X0)),
% 1.74/1.45 file('/export/starexec/sandbox2/tmp/tmp.Jhzb8yfRKP/DTF2THF_7245.p','thm/realax/REAL_LE_REFL_')).
% 1.74/1.45 thf(f120,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ (sK0 @ X0 @ sK2)) != $true) | (('const/realax/real_le' @ X1 @ sK1) = $true) | (('const/realax/real_le' @ X0 @ sK1) != $true)) ) | ~spl5_2),
% 1.74/1.45 inference(forward_demodulation,[status(thm)],[f119,f70])).
% 1.74/1.45 thf(f119,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ sK1) = $true) | (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK2)) != $true) | (('const/realax/real_le' @ X1 @ (sK0 @ X0 @ sK2)) != $true)) ) | ~spl5_2),
% 1.74/1.45 inference(subsumption_resolution,[status(thm)],[f118,f53])).
% 1.74/1.45 thf(f118,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ (sK0 @ X0 @ sK2)) != $true) | (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK2)) != $true) | (('const/realax/real_le' @ X1 @ sK1) = $true)) ) | ~spl5_2),
% 1.74/1.45 inference(subsumption_resolution,[status(thm)],[f117,f48])).
% 1.74/1.45 thf(f117,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ sK1) = $true) | (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK2)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | (('const/realax/real_le' @ X1 @ (sK0 @ X0 @ sK2)) != $true)) ) | ~spl5_2),
% 1.74/1.45 inference(trivial_inequality_removal,[status(thm)],[f114])).
% 1.74/1.45 thf(f114,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK2)) != $true) | (('const/sets/FINITE' @ 'type/realax/real' @ sK2) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ($true != $true) | (('const/realax/real_le' @ X1 @ (sK0 @ X0 @ sK2)) != $true) | (('const/realax/real_le' @ X1 @ sK1) = $true)) ) | ~spl5_2),
% 1.74/1.45 inference(superposition,[status(thm)],[f111,f47])).
% 1.74/1.45 thf(f47,plain,(
% 1.74/1.45 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0)) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.74/1.45 inference(cnf_transformation,[status(thm)],[f32])).
% 1.74/1.45 thf(f86,plain,(
% 1.74/1.45 ~spl5_2 | ~spl5_3 | ~spl5_5),
% 1.74/1.45 inference(avatar_split_clause,[status(thm)],[f51,f83,f73,f69])).
% 1.74/1.45 thf(f51,plain,(
% 1.74/1.45 ($true != ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2)) | (('const/realax/real_le' @ sK3 @ sK1) != $true) | (('const/sets/sup' @ sK2) != sK1)),
% 1.74/1.45 inference(cnf_transformation,[status(thm)],[f38])).
% 1.74/1.45 thf(f81,plain,(
% 1.74/1.45 spl5_2 | spl5_4),
% 1.74/1.45 inference(avatar_split_clause,[status(thm)],[f50,f79,f69])).
% 1.74/1.45 thf(f50,plain,(
% 1.74/1.45 ( ! [X3 : 'type/realax/real'] : ((('const/sets/sup' @ sK2) = sK1) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK2) != $true) | (('const/realax/real_le' @ X3 @ sK1) = $true)) )),
% 1.74/1.45 inference(cnf_transformation,[status(thm)],[f38])).
% 1.74/1.45 thf(f77,plain,(
% 1.74/1.45 spl5_2 | spl5_3),
% 1.74/1.45 inference(avatar_split_clause,[status(thm)],[f49,f73,f69])).
% 1.74/1.45 thf(f49,plain,(
% 1.74/1.45 ($true = ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2)) | (('const/sets/sup' @ sK2) = sK1)),
% 1.74/1.45 inference(cnf_transformation,[status(thm)],[f38])).
% 1.74/1.45 thf(f76,plain,(
% 1.74/1.45 spl5_1 | ~spl5_2 | ~spl5_3),
% 1.74/1.45 inference(avatar_split_clause,[status(thm)],[f52,f73,f69,f65])).
% 1.74/1.45 thf(f52,plain,(
% 1.74/1.45 (('const/sets/sup' @ sK2) != sK1) | ($true != ('const/sets/IN' @ 'type/realax/real' @ sK1 @ sK2)) | (('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK2) = $true)),
% 1.74/1.45 inference(cnf_transformation,[status(thm)],[f38])).
% 1.74/1.45 % SZS output end Proof for DTF2THF_7245
% 1.74/1.45 % (7348)------------------------------
% 1.74/1.45 % (7348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.45 % (7348)Termination reason: Refutation
% 1.74/1.45
% 1.74/1.45 % (7348)Memory used [KB]: 5756
% 1.74/1.45 % (7348)Time elapsed: 0.034 s
% 1.74/1.45 % (7348)Instructions burned: 55 (million)
% 1.74/1.45 % (7348)------------------------------
% 1.74/1.45 % (7348)------------------------------
% 1.74/1.45 % (7342)Success in time 0.041 s
%------------------------------------------------------------------------------