%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA086^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:38:50 AM UTC 2026
% Result : Theorem 1.50s 1.29s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 2 unt; 0 typ; 5 def)
% Number of atoms : 627 ( 170 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 807 ( 97 ~; 108 |; 36 &; 535 @)
% ( 5 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 115 ( 0 ^; 98 !; 17 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_4,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_8,type,
sK0: 'type/realax/real' > $o ).
thf(func_def_9,type,
sK1: 'type/realax/real' ).
thf(func_def_10,type,
sK2: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_11,type,
sK3: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_13,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK6: 'type/realax/real' ).
thf(f140,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f69,f75,f106,f111,f116,f126,f139]) ).
thf(f139,plain,
( spl4_11
| ~ spl4_12 ),
inference(avatar_split_clause,[status(thm)],[f137,f124,f104]) ).
thf(f104,definition,
( spl4_11
<=> ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK1 @ ( sK2 @ X0 @ sK0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl4_11])],[avatar_definition]) ).
thf(f124,definition,
( spl4_12
<=> ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X1 @ sK0 ) @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_12])],[avatar_definition]) ).
thf(f137,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK1 @ ( sK2 @ X0 @ sK0 ) )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) )
= $true ) )
| ~ spl4_12 ),
inference(trivial_inequality_removal,[status(thm)],[f136]) ).
thf(f136,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK1 @ ( sK2 @ X0 @ sK0 ) )
= $true )
| ( $true != $true ) )
| ~ spl4_12 ),
inference(superposition,[status(thm)],[f21,f125]) ).
thf(f125,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X1 @ sK0 ) @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) ) )
| ~ spl4_12 ),
inference(avatar_component_clause,[status(thm)],[f124]) ).
thf(f21,plain,
! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
!= $true )
| ( ( 'const/realax/real_le' @ sK1 @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK1 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
!= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true ) )
=> ( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK1 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
!= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UDLuqFWjwN/DTF2THF_14920.p','thm/sets/REAL_LE_INF_') ).
thf(f126,plain,
( spl4_6
| spl4_12 ),
inference(avatar_split_clause,[status(thm)],[f122,f124,f56]) ).
thf(f56,definition,
( spl4_6
<=> ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sK1 @ ( sK3 @ X0 @ sK0 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition]) ).
thf(f122,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK1 @ ( sK3 @ X0 @ sK0 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X1 @ sK0 ) @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f119,f20]) ).
thf(f20,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f119,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X1 @ sK0 ) @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( ( 'const/realax/real_le' @ sK1 @ ( sK3 @ X0 @ sK0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X1 @ sK0 ) @ sK0 ) )
| ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( ( 'const/realax/real_le' @ sK1 @ ( sK3 @ X0 @ sK0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f21,f24]) ).
thf(f24,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK3 @ X4 @ X0 ) @ X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X2 @ X0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true ) )
& ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X2 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ ( sK2 @ X2 @ X0 ) )
!= $true ) ) ) )
| ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ ( sK3 @ X4 @ X0 ) )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK3 @ X4 @ X0 ) @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f15,f17,f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o,X2: 'type/realax/real'] :
( ? [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X3 )
!= $true ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X2 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ ( sK2 @ X2 @ X0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
! [X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true ) )
=> ( ( ( 'const/realax/real_le' @ X4 @ ( sK3 @ X4 @ X0 ) )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK3 @ X4 @ X0 ) @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true ) )
& ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ? [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X3 )
!= $true ) ) ) )
| ! [X4: 'type/realax/real'] :
? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) ) )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ? [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true ) ) ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) ) )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ? [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true ) ) ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: 'type/realax/real' > $o] :
( ( ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) ) )
& ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) )
=> ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: 'type/realax/real' > $o] :
( ( ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) )
& ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
=> ( 'const/realax/real_le' @ X4 @ X5 ) )
=> ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) )
& ! [X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UDLuqFWjwN/DTF2THF_14920.p','thm/sets/INF_') ).
thf(f116,plain,
( ~ spl4_7
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f115]) ).
thf(f115,plain,
( $false
| ~ spl4_7
| ~ spl4_11 ),
inference(subsumption_resolution,[status(thm)],[f114,f19]) ).
thf(f19,plain,
( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f114,plain,
( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ~ spl4_7
| ~ spl4_11 ),
inference(trivial_inequality_removal,[status(thm)],[f113]) ).
thf(f113,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ~ spl4_7
| ~ spl4_11 ),
inference(duplicate_literal_removal,[status(thm)],[f112]) ).
thf(f112,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ~ spl4_7
| ~ spl4_11 ),
inference(superposition,[status(thm)],[f68,f105]) ).
thf(f105,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK1 @ ( sK2 @ X0 @ sK0 ) )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) )
= $true ) )
| ~ spl4_11 ),
inference(avatar_component_clause,[status(thm)],[f104]) ).
thf(f68,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( sK2 @ X1 @ sK0 ) )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f67,definition,
( spl4_7
<=> ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( ( 'const/realax/real_le' @ X1 @ ( sK2 @ X1 @ sK0 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition]) ).
thf(f111,plain,
( ~ spl4_6
| ~ spl4_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f110]) ).
thf(f110,plain,
( $false
| ~ spl4_6
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ( $true != $true )
| ~ spl4_6
| ~ spl4_10 ),
inference(superposition,[status(thm)],[f100,f57]) ).
thf(f57,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sK1 @ ( sK3 @ X0 @ sK0 ) )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f100,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X0 @ ( sK3 @ X0 @ sK0 ) )
!= $true )
| ~ spl4_10 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f99,definition,
( spl4_10
<=> ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X0 @ ( sK3 @ X0 @ sK0 ) )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition]) ).
thf(f106,plain,
( spl4_10
| spl4_11 ),
inference(avatar_split_clause,[status(thm)],[f102,f104,f99]) ).
thf(f102,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK1 @ ( sK2 @ X0 @ sK0 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK3 @ X1 @ sK0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f95,f20]) ).
thf(f95,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ sK1 @ ( sK2 @ X0 @ sK0 ) )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK3 @ X1 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK1 @ ( sK2 @ X0 @ sK0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK3 @ X1 @ sK0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f21,f25]) ).
thf(f25,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK2 @ X2 @ X0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ X4 @ ( sK3 @ X4 @ X0 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f75,plain,
( spl4_7
| ~ spl4_6 ),
inference(avatar_split_clause,[status(thm)],[f74,f56,f67]) ).
thf(f74,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( sK2 @ X0 @ sK0 ) )
!= $true ) )
| ~ spl4_6 ),
inference(subsumption_resolution,[status(thm)],[f73,f20]) ).
thf(f73,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( sK2 @ X0 @ sK0 ) )
!= $true ) )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( sK2 @ X0 @ sK0 ) )
!= $true ) )
| ~ spl4_6 ),
inference(superposition,[status(thm)],[f23,f57]) ).
thf(f23,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ ( sK3 @ X4 @ X0 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( ( 'const/realax/real_le' @ X2 @ ( sK2 @ X2 @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f69,plain,
( spl4_7
| spl4_6 ),
inference(avatar_split_clause,[status(thm)],[f65,f56,f67]) ).
thf(f65,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( ( 'const/realax/real_le' @ sK1 @ ( sK3 @ X0 @ sK0 ) )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK2 @ X1 @ sK0 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f64,f20]) ).
thf(f64,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( sK2 @ X1 @ sK0 ) )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( ( 'const/realax/real_le' @ sK1 @ ( sK3 @ X0 @ sK0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK2 @ X1 @ sK0 ) )
!= $true )
| ( ( 'const/realax/real_le' @ sK1 @ ( sK3 @ X0 @ sK0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(superposition,[status(thm)],[f21,f22]) ).
thf(f22,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK3 @ X4 @ X0 ) @ X0 ) )
| ( ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( ( 'const/realax/real_le' @ X2 @ ( sK2 @ X2 @ X0 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ANA086^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n005.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 03:49:59 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : ANA086^1 : TPTP v9.2.1. Released v7.0.0.
% 0.31/0.45 % Domain : Analysis
% 0.31/0.45 % Problem : REAL_LE_INF
% 0.31/0.45 % Version : Especial.
% 0.31/0.45 % English :
% 0.31/0.45
% 0.31/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.31/0.45 % Source : [Kal16]
% 0.31/0.45 % Names : REAL_LE_INF_.p [Kal16]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % Rating : 0.00 v7.1.0
% 0.31/0.45 % Syntax : Number of formulae : 7 ( 0 unt; 5 typ; 0 def)
% 0.31/0.45 % Number of atoms : 14 ( 2 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 8 ( 7 avg)
% 0.31/0.45 % Number of connectives : 41 ( 2 ~; 0 |; 3 &; 29 @)
% 0.31/0.45 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.31/0.45 % Maximal formula depth : 11 ( 11 avg)
% 0.31/0.45 % Number of types : 2 ( 1 usr)
% 0.31/0.45 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.31/0.45 % Number of symbols : 5 ( 4 usr; 0 con; 1-3 aty)
% 0.31/0.45 % Number of variables : 11 ( 0 ^; 8 !; 1 ?; 11 :)
% 0.31/0.45 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.45 % SPC : TH1_THM_EQU_NAR
% 0.31/0.45
% 0.31/0.45 % Comments : Exported from core HOL Light.
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 thf('thf_type_type/realax/real',type,
% 0.31/0.45 'type/realax/real': $tType ).
% 0.31/0.45
% 0.31/0.45 thf('thf_const_const/sets/inf',type,
% 0.31/0.45 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.31/0.45
% 0.31/0.45 thf('thf_const_const/sets/IN',type,
% 0.31/0.45 'const/sets/IN':
% 0.31/0.45 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf('thf_const_const/sets/EMPTY',type,
% 0.31/0.45 'const/sets/EMPTY':
% 0.31/0.45 !>[A: $tType] : ( A > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf('thf_const_const/realax/real_le',type,
% 0.31/0.45 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.31/0.45
% 0.31/0.45 thf('thm/sets/INF_',axiom,
% 0.31/0.45 ! [A: 'type/realax/real' > $o] :
% 0.31/0.45 ( ( ( A
% 0.31/0.45 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.31/0.45 & ? [A0: 'type/realax/real'] :
% 0.31/0.45 ! [A1: 'type/realax/real'] :
% 0.31/0.45 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.31/0.45 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 0.31/0.45 => ( ! [A0: 'type/realax/real'] :
% 0.31/0.45 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.31/0.45 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
% 0.31/0.45 & ! [A0: 'type/realax/real'] :
% 0.31/0.45 ( ! [A1: 'type/realax/real'] :
% 0.31/0.45 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.31/0.45 => ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.31/0.45 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf('thm/sets/REAL_LE_INF_',conjecture,
% 0.31/0.45 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.31/0.45 ( ( ( A
% 0.31/0.45 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.31/0.45 & ! [A1: 'type/realax/real'] :
% 0.31/0.45 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.31/0.45 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 0.31/0.45 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ).
% 0.31/0.45
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 ------------------------
% 1.50/1.26 ---- Embedded in THF ---
% 1.50/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.26 %%% Generated on Tue Feb 24 03:50:00 EST 2026
% 1.50/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.26 %%% Logic specification used:
% 1.50/1.26 %%% thf(spec, logic, $$dhol).
% 1.50/1.26
% 1.50/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.UDLuqFWjwN/DTF2DTF14920.p
% See solution above
% 1.50/1.26 ------------------------
% 1.50/1.27 ---- Cleaned THF ---
% 1.50/1.27 thf('thf_type_type/realax/real',type,
% 1.50/1.27 'type/realax/real': $tType ).
% 1.50/1.27
% 1.50/1.27 thf('thf_const_const/sets/inf',type,
% 1.50/1.27 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 1.50/1.27
% 1.50/1.27 thf('thf_const_const/sets/IN',type,
% 1.50/1.27 'const/sets/IN':
% 1.50/1.27 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.50/1.27
% 1.50/1.27 thf('thf_const_const/sets/EMPTY',type,
% 1.50/1.27 'const/sets/EMPTY':
% 1.50/1.27 !>[A: $tType] : ( A > $o ) ).
% 1.50/1.27
% 1.50/1.27 thf('thf_const_const/realax/real_le',type,
% 1.50/1.27 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.50/1.27
% 1.50/1.27 thf('thm/sets/INF_',axiom,
% 1.50/1.27 ! [A: 'type/realax/real' > $o] :
% 1.50/1.27 ( ( ( A
% 1.50/1.27 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.50/1.27 & ? [A0: 'type/realax/real'] :
% 1.50/1.27 ! [A1: 'type/realax/real'] :
% 1.50/1.27 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.50/1.27 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 1.50/1.27 => ( ! [A0: 'type/realax/real'] :
% 1.50/1.27 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 1.50/1.27 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
% 1.50/1.27 & ! [A0: 'type/realax/real'] :
% 1.50/1.27 ( ! [A1: 'type/realax/real'] :
% 1.50/1.27 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.50/1.27 => ( 'const/realax/real_le' @ A0 @ A1 ) )
% 1.50/1.27 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
% 1.50/1.27
% 1.50/1.27 thf('thm/sets/REAL_LE_INF_',conjecture,
% 1.50/1.27 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 1.50/1.27 ( ( ( A
% 1.50/1.27 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.50/1.27 & ! [A1: 'type/realax/real'] :
% 1.50/1.27 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.50/1.27 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 1.50/1.27 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ).
% 1.50/1.27 ------------------------
% 1.50/1.28 % (15129)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14920 for (3000ds/18Mi)
% 1.50/1.28 % (15125)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_14920 for (3000ds/27Mi)
% 1.50/1.28 % (15124)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_14920 for (3000ds/4Mi)
% 1.50/1.28 % (15123)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14920 for (3000ds/183Mi)
% 1.50/1.29 % (15124)Instruction limit reached!
% 1.50/1.29 % (15124)------------------------------
% 1.50/1.29 % (15124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (15124)Termination reason: Unknown
% 1.50/1.29 % (15124)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (15124)Memory used [KB]: 5500
% 1.50/1.29 % (15124)Time elapsed: 0.003 s
% 1.50/1.29 % (15124)Instructions burned: 5 (million)
% 1.50/1.29 % (15124)------------------------------
% 1.50/1.29 % (15124)------------------------------
% 1.50/1.29 % (15129)Instruction limit reached!
% 1.50/1.29 % (15129)------------------------------
% 1.50/1.29 % (15129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (15129)Termination reason: Unknown
% 1.50/1.29 % (15129)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (15129)Memory used [KB]: 5628
% 1.50/1.29 % (15129)Time elapsed: 0.009 s
% 1.50/1.29 % (15129)Instructions burned: 20 (million)
% 1.50/1.29 % (15129)------------------------------
% 1.50/1.29 % (15129)------------------------------
% 1.50/1.29 % (15126)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14920 for (3000ds/2Mi)
% 1.50/1.29 % (15127)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_14920 for (3000ds/2Mi)
% 1.50/1.29 % (15123)First to succeed.
% 1.50/1.29 % (15128)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_14920 for (3000ds/275Mi)
% 1.50/1.29 % (15126)Instruction limit reached!
% 1.50/1.29 % (15126)------------------------------
% 1.50/1.29 % (15126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (15126)Termination reason: Unknown
% 1.50/1.29 % (15126)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (15126)Memory used [KB]: 5500
% 1.50/1.29 % (15126)Time elapsed: 0.004 s
% 1.50/1.29 % (15126)Instructions burned: 3 (million)
% 1.50/1.29 % (15126)------------------------------
% 1.50/1.29 % (15126)------------------------------
% 1.50/1.29 % (15127)Instruction limit reached!
% 1.50/1.29 % (15127)------------------------------
% 1.50/1.29 % (15127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (15127)Termination reason: Unknown
% 1.50/1.29 % (15127)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (15127)Memory used [KB]: 5500
% 1.50/1.29 % (15127)Time elapsed: 0.004 s
% 1.50/1.29 % (15127)Instructions burned: 3 (million)
% 1.50/1.29 % (15127)------------------------------
% 1.50/1.29 % (15127)------------------------------
% 1.50/1.29 % (15125)Also succeeded, but the first one will report.
% 1.50/1.29 % (15123)Refutation found. Thanks to Tanya!
% 1.50/1.29 % SZS status Theorem for DTF2THF_14920
% 1.50/1.29 % SZS output start Proof for DTF2THF_14920
% 1.50/1.29 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.50/1.29 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.50/1.29 thf(func_def_1, type, 'const/sets/inf': ('type/realax/real' > $o) > 'type/realax/real').
% 1.50/1.29 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.50/1.29 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.50/1.29 thf(func_def_4, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.50/1.29 thf(func_def_8, type, sK0: 'type/realax/real' > $o).
% 1.50/1.29 thf(func_def_9, type, sK1: 'type/realax/real').
% 1.50/1.29 thf(func_def_10, type, sK2: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.50/1.29 thf(func_def_11, type, sK3: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.50/1.29 thf(func_def_13, type, ph5: !>[X0: $tType]:(X0)).
% 1.50/1.29 thf(func_def_14, type, sK6: 'type/realax/real').
% 1.50/1.29 thf(f140,plain,(
% 1.50/1.29 $false),
% 1.50/1.29 inference(avatar_sat_refutation,[status(thm)],[f69,f75,f106,f111,f116,f126,f139])).
% 1.50/1.29 thf(f139,plain,(
% 1.50/1.29 spl4_11 | ~spl4_12),
% 1.50/1.29 inference(avatar_split_clause,[status(thm)],[f137,f124,f104])).
% 1.50/1.29 thf(f104,definition,(
% 1.50/1.29 spl4_11 <=> ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)) = $true) | (('const/realax/real_le' @ sK1 @ (sK2 @ X0 @ sK0)) = $true))),
% 1.50/1.29 introduced(definition,[new_symbols(naming,[spl4_11])],[avatar_definition])).
% 1.50/1.29 thf(f124,definition,(
% 1.50/1.29 spl4_12 <=> ! [X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ sK0) @ sK0)) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0))))),
% 1.50/1.29 introduced(definition,[new_symbols(naming,[spl4_12])],[avatar_definition])).
% 1.50/1.29 thf(f137,plain,(
% 1.50/1.29 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ sK1 @ (sK2 @ X0 @ sK0)) = $true) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)) = $true)) ) | ~spl4_12),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f136])).
% 1.50/1.29 thf(f136,plain,(
% 1.50/1.29 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)) = $true) | (('const/realax/real_le' @ sK1 @ (sK2 @ X0 @ sK0)) = $true) | ($true != $true)) ) | ~spl4_12),
% 1.50/1.29 inference(superposition,[status(thm)],[f21,f125])).
% 1.50/1.29 thf(f125,plain,(
% 1.50/1.29 ( ! [X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ sK0) @ sK0)) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0)))) ) | ~spl4_12),
% 1.50/1.29 inference(avatar_component_clause,[status(thm)],[f124])).
% 1.50/1.29 thf(f21,plain,(
% 1.50/1.29 ( ! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0) != $true) | (('const/realax/real_le' @ sK1 @ X2) = $true)) )),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f14])).
% 1.50/1.29 thf(f14,plain,(
% 1.50/1.29 ! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ sK1 @ X2) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != sK0) & (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) != $true)),
% 1.50/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13])).
% 1.50/1.29 thf(f13,plain,(
% 1.50/1.29 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) != $true)) => (! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ sK1 @ X2) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != sK0) & (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) != $true))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f12,plain,(
% 1.50/1.29 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) != $true))),
% 1.50/1.29 inference(flattening,[status(thm)],[f11])).
% 1.50/1.29 thf(f11,plain,(
% 1.50/1.29 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) != $true) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true))))),
% 1.50/1.29 inference(ennf_transformation,[status(thm)],[f6])).
% 1.50/1.29 thf(f6,plain,(
% 1.50/1.29 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [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/inf' @ X0)) = $true))),
% 1.50/1.29 inference(fool_elimination,[status(thm)],[f5])).
% 1.50/1.29 thf(f5,plain,(
% 1.50/1.29 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)))),
% 1.50/1.29 inference(rectify,[status(thm)],[f3])).
% 1.50/1.29 thf(f3,negated_conjecture,(
% 1.50/1.29 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)))),
% 1.50/1.29 inference(negated_conjecture,[status(cth)],[f2])).
% 1.50/1.29 thf(f2,conjecture,(
% 1.50/1.29 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)))),
% 1.50/1.29 file('/export/starexec/sandbox/tmp/tmp.UDLuqFWjwN/DTF2THF_14920.p','thm/sets/REAL_LE_INF_')).
% 1.50/1.29 thf(f126,plain,(
% 1.50/1.29 spl4_6 | spl4_12),
% 1.50/1.29 inference(avatar_split_clause,[status(thm)],[f122,f124,f56])).
% 1.50/1.29 thf(f56,definition,(
% 1.50/1.29 spl4_6 <=> ! [X0 : 'type/realax/real'] : (('const/realax/real_le' @ sK1 @ (sK3 @ X0 @ sK0)) = $true)),
% 1.50/1.29 introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
% 1.50/1.29 thf(f122,plain,(
% 1.50/1.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ sK1 @ (sK3 @ X0 @ sK0)) = $true) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ sK0) @ sK0)) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0)))) )),
% 1.50/1.29 inference(subsumption_resolution,[status(thm)],[f119,f20])).
% 1.50/1.29 thf(f20,plain,(
% 1.50/1.29 ('const/sets/EMPTY' @ 'type/realax/real' != sK0)),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f14])).
% 1.50/1.29 thf(f119,plain,(
% 1.50/1.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ sK0) @ sK0)) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0))) | (('const/realax/real_le' @ sK1 @ (sK3 @ X0 @ sK0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) )),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.50/1.29 thf(f118,plain,(
% 1.50/1.29 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X1 @ sK0) @ sK0)) | ($true != $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0))) | (('const/realax/real_le' @ sK1 @ (sK3 @ X0 @ sK0)) = $true)) )),
% 1.50/1.29 inference(superposition,[status(thm)],[f21,f24])).
% 1.50/1.29 thf(f24,plain,(
% 1.50/1.29 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X4 @ X0) @ X0)) | (('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X2 @ X0) @ X0) = $true) | (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.50/1.29 thf(f18,plain,(
% 1.50/1.29 ! [X0 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1) = $true)) & ! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X2 @ X0) @ X0) = $true) & (('const/realax/real_le' @ X2 @ (sK2 @ X2 @ X0)) != $true)))) | ! [X4 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ (sK3 @ X4 @ X0)) != $true) & ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X4 @ X0) @ X0))))),
% 1.50/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f15,f17,f16])).
% 1.50/1.29 thf(f16,plain,(
% 1.50/1.29 ! [X0 : 'type/realax/real' > $o,X2 : 'type/realax/real'] : (? [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) & (('const/realax/real_le' @ X2 @ X3) != $true)) => ((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X2 @ X0) @ X0) = $true) & (('const/realax/real_le' @ X2 @ (sK2 @ X2 @ X0)) != $true)))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f17,plain,(
% 1.50/1.29 ! [X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ X5) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true)) => ((('const/realax/real_le' @ X4 @ (sK3 @ X4 @ X0)) != $true) & ($true = ('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X4 @ X0) @ X0))))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f15,plain,(
% 1.50/1.29 ! [X0 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1) = $true)) & ! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)) = $true) | ? [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) & (('const/realax/real_le' @ X2 @ X3) != $true)))) | ! [X4 : 'type/realax/real'] : ? [X5 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ X5) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true)))),
% 1.50/1.29 inference(rectify,[status(thm)],[f10])).
% 1.50/1.29 thf(f10,plain,(
% 1.50/1.29 ! [X0 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) & ! [X4 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)) = $true) | ? [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) & (('const/realax/real_le' @ X4 @ X5) != $true)))) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)))),
% 1.50/1.29 inference(flattening,[status(thm)],[f9])).
% 1.50/1.29 thf(f9,plain,(
% 1.50/1.29 ! [X0 : 'type/realax/real' > $o] : ((! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | ($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) & ! [X4 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)) = $true) | ? [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) & (('const/realax/real_le' @ X4 @ X5) != $true)))) | (! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 1.50/1.29 inference(ennf_transformation,[status(thm)],[f8])).
% 1.50/1.29 thf(f8,plain,(
% 1.50/1.29 ! [X0 : 'type/realax/real' > $o] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) => (('const/realax/real_le' @ X1 @ X2) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) => ($true = ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3))) & ! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) => (('const/realax/real_le' @ X4 @ X5) = $true)) => (('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)) = $true))))),
% 1.50/1.29 inference(fool_elimination,[status(thm)],[f7])).
% 1.50/1.29 thf(f7,plain,(
% 1.50/1.29 ! [X0 : 'type/realax/real' > $o] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3)) & ! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ X4 @ X5)) => ('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)))))),
% 1.50/1.29 inference(rectify,[status(thm)],[f1])).
% 1.50/1.29 thf(f1,axiom,(
% 1.50/1.29 ! [X0 : 'type/realax/real' > $o] : ((? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) & ! [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)))))),
% 1.50/1.29 file('/export/starexec/sandbox/tmp/tmp.UDLuqFWjwN/DTF2THF_14920.p','thm/sets/INF_')).
% 1.50/1.29 thf(f116,plain,(
% 1.50/1.29 ~spl4_7 | ~spl4_11),
% 1.50/1.29 inference(avatar_contradiction_clause,[status(thm)],[f115])).
% 1.50/1.29 thf(f115,plain,(
% 1.50/1.29 $false | (~spl4_7 | ~spl4_11)),
% 1.50/1.29 inference(subsumption_resolution,[status(thm)],[f114,f19])).
% 1.50/1.29 thf(f19,plain,(
% 1.50/1.29 (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) != $true)),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f14])).
% 1.50/1.29 thf(f114,plain,(
% 1.50/1.29 (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) = $true) | (~spl4_7 | ~spl4_11)),
% 1.50/1.30 inference(trivial_inequality_removal,[status(thm)],[f113])).
% 1.50/1.30 thf(f113,plain,(
% 1.50/1.30 ($true != $true) | (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) = $true) | (~spl4_7 | ~spl4_11)),
% 1.50/1.30 inference(duplicate_literal_removal,[status(thm)],[f112])).
% 1.50/1.30 thf(f112,plain,(
% 1.50/1.30 ($true != $true) | (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) = $true) | (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) = $true) | (~spl4_7 | ~spl4_11)),
% 1.50/1.30 inference(superposition,[status(thm)],[f68,f105])).
% 1.50/1.30 thf(f105,plain,(
% 1.50/1.30 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ sK1 @ (sK2 @ X0 @ sK0)) = $true) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)) = $true)) ) | ~spl4_11),
% 1.50/1.30 inference(avatar_component_clause,[status(thm)],[f104])).
% 1.50/1.30 thf(f68,plain,(
% 1.50/1.30 ( ! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ (sK2 @ X1 @ sK0)) != $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0)))) ) | ~spl4_7),
% 1.50/1.30 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.50/1.30 thf(f67,definition,(
% 1.50/1.30 spl4_7 <=> ! [X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0))) | (('const/realax/real_le' @ X1 @ (sK2 @ X1 @ sK0)) != $true))),
% 1.50/1.30 introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition])).
% 1.50/1.30 thf(f111,plain,(
% 1.50/1.30 ~spl4_6 | ~spl4_10),
% 1.50/1.30 inference(avatar_contradiction_clause,[status(thm)],[f110])).
% 1.50/1.30 thf(f110,plain,(
% 1.50/1.30 $false | (~spl4_6 | ~spl4_10)),
% 1.50/1.30 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.50/1.30 thf(f107,plain,(
% 1.50/1.30 ($true != $true) | (~spl4_6 | ~spl4_10)),
% 1.50/1.30 inference(superposition,[status(thm)],[f100,f57])).
% 1.50/1.30 thf(f57,plain,(
% 1.50/1.30 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ sK1 @ (sK3 @ X0 @ sK0)) = $true)) ) | ~spl4_6),
% 1.50/1.30 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.50/1.30 thf(f100,plain,(
% 1.50/1.30 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ (sK3 @ X0 @ sK0)) != $true)) ) | ~spl4_10),
% 1.50/1.30 inference(avatar_component_clause,[status(thm)],[f99])).
% 1.50/1.30 thf(f99,definition,(
% 1.50/1.30 spl4_10 <=> ! [X0 : 'type/realax/real'] : (('const/realax/real_le' @ X0 @ (sK3 @ X0 @ sK0)) != $true)),
% 1.50/1.30 introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition])).
% 1.50/1.30 thf(f106,plain,(
% 1.50/1.30 spl4_10 | spl4_11),
% 1.50/1.30 inference(avatar_split_clause,[status(thm)],[f102,f104,f99])).
% 1.50/1.30 thf(f102,plain,(
% 1.50/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)) = $true) | (('const/realax/real_le' @ sK1 @ (sK2 @ X0 @ sK0)) = $true) | ($true != ('const/realax/real_le' @ X1 @ (sK3 @ X1 @ sK0)))) )),
% 1.50/1.30 inference(subsumption_resolution,[status(thm)],[f95,f20])).
% 1.50/1.30 thf(f95,plain,(
% 1.50/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ sK1 @ (sK2 @ X0 @ sK0)) = $true) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)) = $true) | ($true != ('const/realax/real_le' @ X1 @ (sK3 @ X1 @ sK0)))) )),
% 1.50/1.30 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.50/1.30 thf(f94,plain,(
% 1.50/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ sK1 @ (sK2 @ X0 @ sK0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)) = $true) | ($true != ('const/realax/real_le' @ X1 @ (sK3 @ X1 @ sK0))) | ($true != $true)) )),
% 1.50/1.30 inference(superposition,[status(thm)],[f21,f25])).
% 1.50/1.30 thf(f25,plain,(
% 1.50/1.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK2 @ X2 @ X0) @ X0) = $true) | (('const/realax/real_le' @ X4 @ (sK3 @ X4 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)) = $true)) )),
% 1.50/1.30 inference(cnf_transformation,[status(thm)],[f18])).
% 1.50/1.30 thf(f75,plain,(
% 1.50/1.30 spl4_7 | ~spl4_6),
% 1.50/1.30 inference(avatar_split_clause,[status(thm)],[f74,f56,f67])).
% 1.50/1.30 thf(f74,plain,(
% 1.50/1.30 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)) = $true) | (('const/realax/real_le' @ X0 @ (sK2 @ X0 @ sK0)) != $true)) ) | ~spl4_6),
% 1.50/1.30 inference(subsumption_resolution,[status(thm)],[f73,f20])).
% 1.50/1.30 thf(f73,plain,(
% 1.50/1.30 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ X0 @ (sK2 @ X0 @ sK0)) != $true)) ) | ~spl4_6),
% 1.50/1.30 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.50/1.30 thf(f70,plain,(
% 1.50/1.30 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)) = $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ X0 @ (sK2 @ X0 @ sK0)) != $true)) ) | ~spl4_6),
% 1.50/1.30 inference(superposition,[status(thm)],[f23,f57])).
% 1.50/1.30 thf(f23,plain,(
% 1.50/1.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ (sK3 @ X4 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)) = $true) | (('const/realax/real_le' @ X2 @ (sK2 @ X2 @ X0)) != $true)) )),
% 1.50/1.30 inference(cnf_transformation,[status(thm)],[f18])).
% 1.50/1.30 thf(f69,plain,(
% 1.50/1.30 spl4_7 | spl4_6),
% 1.50/1.30 inference(avatar_split_clause,[status(thm)],[f65,f56,f67])).
% 1.50/1.30 thf(f65,plain,(
% 1.50/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0))) | (('const/realax/real_le' @ sK1 @ (sK3 @ X0 @ sK0)) = $true) | (('const/realax/real_le' @ X1 @ (sK2 @ X1 @ sK0)) != $true)) )),
% 1.50/1.30 inference(subsumption_resolution,[status(thm)],[f64,f20])).
% 1.50/1.30 thf(f64,plain,(
% 1.50/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ X1 @ (sK2 @ X1 @ sK0)) != $true) | ($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0))) | (('const/realax/real_le' @ sK1 @ (sK3 @ X0 @ sK0)) = $true)) )),
% 1.50/1.30 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.50/1.30 thf(f63,plain,(
% 1.50/1.30 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK0))) | ($true != $true) | (('const/realax/real_le' @ X1 @ (sK2 @ X1 @ sK0)) != $true) | (('const/realax/real_le' @ sK1 @ (sK3 @ X0 @ sK0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) )),
% 1.50/1.30 inference(superposition,[status(thm)],[f21,f22])).
% 1.50/1.30 thf(f22,plain,(
% 1.50/1.30 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : (($true = ('const/sets/IN' @ 'type/realax/real' @ (sK3 @ X4 @ X0) @ X0)) | (('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0)) = $true) | (('const/realax/real_le' @ X2 @ (sK2 @ X2 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.50/1.30 inference(cnf_transformation,[status(thm)],[f18])).
% 1.50/1.30 % SZS output end Proof for DTF2THF_14920
% 1.50/1.30 % (15123)------------------------------
% 1.50/1.30 % (15123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.30 % (15123)Termination reason: Refutation
% 1.50/1.30
% 1.50/1.30 % (15123)Memory used [KB]: 5628
% 1.50/1.30 % (15123)Time elapsed: 0.011 s
% 1.50/1.30 % (15123)Instructions burned: 17 (million)
% 1.50/1.30 % (15123)------------------------------
% 1.50/1.30 % (15123)------------------------------
% 1.50/1.30 % (15121)Success in time 0.019 s
%------------------------------------------------------------------------------