%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA089^1 : 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 : n024.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 0.85s 0.87s
% Output : Refutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 83 ( 5 unt; 0 typ; 5 def)
% Number of atoms : 685 ( 187 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 887 ( 89 ~; 112 |; 37 &; 628 @)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 121 ( 0 ^; 112 !; 9 ?; 121 :)
% 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_neg': 'type/realax/real' > 'type/realax/real' ).
thf(func_def_5,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_6,type,
'const/realax/real_abs': 'type/realax/real' > 'type/realax/real' ).
thf(func_def_11,type,
sK0: 'type/realax/real' > 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_12,type,
sK1: 'type/realax/real' > $o ).
thf(func_def_13,type,
sK2: 'type/realax/real' ).
thf(func_def_15,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK5: 'type/realax/real' ).
thf(f188,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f74,f119,f130,f145,f167,f187]) ).
thf(f187,plain,
( spl3_7
| ~ spl3_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f186]) ).
thf(f186,plain,
( $false
| spl3_7
| ~ spl3_8 ),
inference(subsumption_resolution,[status(thm)],[f184,f114]) ).
thf(f114,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
!= $true )
| spl3_7 ),
inference(avatar_component_clause,[status(thm)],[f113]) ).
thf(f113,definition,
( spl3_7
<=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition]) ).
thf(f184,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
= $true )
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f176]) ).
thf(f176,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
= $true )
| ( $true != $true )
| ~ spl3_8 ),
inference(superposition,[status(thm)],[f118,f90]) ).
thf(f90,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK2 ) @ ( sK0 @ X0 @ X1 @ sK1 ) )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 )
= $true )
| ( $true = $false )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK2 ) @ ( sK0 @ X0 @ X1 @ sK1 ) )
= $true ) ),
inference(superposition,[status(thm)],[f77,f30]) ).
thf(f30,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= $false )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= $false )
| ( ( ( 'const/realax/real_le' @ X0 @ X1 )
& ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= ( ( 'const/realax/real_le' @ X0 @ X1 )
& ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= ( ( 'const/realax/real_le' @ X0 @ X1 )
& ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 ) )
& ( 'const/realax/real_le' @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 ) )
& ( 'const/realax/real_le' @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.7kKN1kG8JG/DTF2THF_28218.p','thm/real/REAL_ABS_BOUNDS_') ).
thf(f77,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( sK0 @ X0 @ X1 @ sK1 ) ) @ sK2 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f76,f24]) ).
thf(f24,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X2 ) @ sK2 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK1 ) ) )
& ( $true
!= ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/inf' @ sK1 ) ) @ sK2 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f13,f18]) ).
thf(f18,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X2 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) )
& ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/inf' @ X0 ) ) @ X1 )
!= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X2 ) @ sK2 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK1 ) ) )
& ( $true
!= ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/inf' @ sK1 ) ) @ sK2 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X2 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) )
& ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/inf' @ X0 ) ) @ X1 )
!= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/inf' @ X0 ) ) @ X1 )
!= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X2 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,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' @ ( 'const/realax/real_abs' @ X2 ) @ X1 )
= $true ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/inf' @ X0 ) ) @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X2 ) @ X1 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/inf' @ X0 ) ) @ X1 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [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' @ ( 'const/realax/real_abs' @ X2 ) @ X1 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/inf' @ X0 ) ) @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [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' @ ( 'const/realax/real_abs' @ X2 ) @ X1 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/inf' @ X0 ) ) @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.7kKN1kG8JG/DTF2THF_28218.p','thm/sets/REAL_ABS_INF_LE_') ).
thf(f76,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( sK0 @ X0 @ X1 @ sK1 ) ) @ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( sK0 @ X0 @ X1 @ sK1 ) ) @ sK2 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) ),
inference(superposition,[status(thm)],[f26,f22]) ).
thf(f22,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( ( 'const/realax/real_le' @ ( sK0 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X2 @ X1 @ X0 ) )
!= $true ) ) )
| ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ? [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( ( 'const/realax/real_le' @ X3 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X3 )
!= $true ) ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( ( 'const/realax/real_le' @ ( sK0 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X2 @ X1 @ X0 ) )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ? [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( ( 'const/realax/real_le' @ X3 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X3 )
!= $true ) ) )
| ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
= $true ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
= $true ) )
| ? [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( ( 'const/realax/real_le' @ X3 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X3 )
!= $true ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
=> ( ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( ( 'const/realax/real_le' @ X3 @ X2 )
& ( 'const/realax/real_le' @ X1 @ X3 ) ) ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
& ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( ( 'const/realax/real_le' @ X3 @ X2 )
& ( 'const/realax/real_le' @ X1 @ X3 ) ) ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
& ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7kKN1kG8JG/DTF2THF_28218.p','thm/sets/REAL_INF_BOUNDS_') ).
thf(f26,plain,
! [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X2 ) @ sK2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f118,plain,
( ! [X0: 'type/realax/real'] :
( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK0 @ sK2 @ X0 @ sK1 ) ) )
| ~ spl3_8 ),
inference(avatar_component_clause,[status(thm)],[f117]) ).
thf(f117,definition,
( spl3_8
<=> ! [X0: 'type/realax/real'] :
( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK0 @ sK2 @ X0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition]) ).
thf(f167,plain,
( ~ spl3_6
| ~ spl3_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f166]) ).
thf(f166,plain,
( $false
| ~ spl3_6
| ~ spl3_9 ),
inference(trivial_inequality_removal,[status(thm)],[f160]) ).
thf(f160,plain,
( ( $true = $false )
| ~ spl3_6
| ~ spl3_9 ),
inference(superposition,[status(thm)],[f73,f155]) ).
thf(f155,plain,
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK2 ) @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ~ spl3_9 ),
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK2 ) @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( $true != $true )
| ~ spl3_9 ),
inference(duplicate_literal_removal,[status(thm)],[f146]) ).
thf(f146,plain,
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK2 ) @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK2 ) @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ~ spl3_9 ),
inference(superposition,[status(thm)],[f123,f104]) ).
thf(f104,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK2 ) @ ( sK0 @ X0 @ X1 @ sK1 ) )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK2 ) @ ( sK0 @ X0 @ X1 @ sK1 ) )
= $true )
| ( $true = $false )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) )
= $true ) ),
inference(superposition,[status(thm)],[f97,f30]) ).
thf(f97,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( sK0 @ X0 @ X1 @ sK1 ) ) @ sK2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f96,f24]) ).
thf(f96,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( sK0 @ X0 @ X1 @ sK1 ) ) @ sK2 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( sK0 @ X0 @ X1 @ sK1 ) ) @ sK2 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) )
= $true ) ),
inference(superposition,[status(thm)],[f26,f23]) ).
thf(f23,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f123,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK0 @ sK2 @ X0 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true ) )
| ~ spl3_9 ),
inference(avatar_component_clause,[status(thm)],[f122]) ).
thf(f122,definition,
( spl3_9
<=> ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK0 @ sK2 @ X0 @ sK1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_9])],[avatar_definition]) ).
thf(f73,plain,
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK2 ) @ ( 'const/sets/inf' @ sK1 ) )
= $false )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f71]) ).
thf(f71,definition,
( spl3_6
<=> ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK2 ) @ ( 'const/sets/inf' @ sK1 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f145,plain,
spl3_9,
inference(avatar_split_clause,[status(thm)],[f144,f122]) ).
thf(f144,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK0 @ sK2 @ X0 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f143,f24]) ).
thf(f143,plain,
! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK0 @ sK2 @ X0 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f142]) ).
thf(f142,plain,
! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK0 @ sK2 @ X0 @ sK1 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f139]) ).
thf(f139,plain,
! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK0 @ sK2 @ X0 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) ),
inference(superposition,[status(thm)],[f21,f105]) ).
thf(f105,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK0 @ X0 @ X1 @ sK1 ) @ sK2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( ( 'const/realax/real_le' @ ( sK0 @ X0 @ X1 @ sK1 ) @ sK2 )
= $true )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f97,f31]) ).
thf(f31,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= $false )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f21,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK0 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X2 @ X1 @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f130,plain,
( ~ spl3_5
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f129]) ).
thf(f129,plain,
( $false
| ~ spl3_5
| ~ spl3_7 ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $true = $false )
| ~ spl3_5
| ~ spl3_7 ),
inference(superposition,[status(thm)],[f115,f69]) ).
thf(f69,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
= $false )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f67,definition,
( spl3_5
<=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f115,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
= $true )
| ~ spl3_7 ),
inference(avatar_component_clause,[status(thm)],[f113]) ).
thf(f119,plain,
( spl3_7
| spl3_8 ),
inference(avatar_split_clause,[status(thm)],[f111,f117,f113]) ).
thf(f111,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK0 @ sK2 @ X0 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f110,f24]) ).
thf(f110,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK0 @ sK2 @ X0 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f109]) ).
thf(f109,plain,
! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK0 @ sK2 @ X0 @ sK1 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f107]) ).
thf(f107,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK0 @ sK2 @ X0 @ sK1 ) ) )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
= $true ) ),
inference(superposition,[status(thm)],[f20,f89]) ).
thf(f89,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK0 @ X0 @ X1 @ sK1 ) @ sK2 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK0 @ X0 @ X1 @ sK1 ) @ sK2 )
= $true )
| ( $true = $false )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f77,f31]) ).
thf(f20,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK0 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X2 @ X1 @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f74,plain,
( spl3_5
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f65,f71,f67]) ).
thf(f65,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
= $false )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK2 ) @ ( 'const/sets/inf' @ sK1 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ sK2 ) @ ( 'const/sets/inf' @ sK1 ) )
= $false )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 )
= $false ) ),
inference(superposition,[status(thm)],[f25,f32]) ).
thf(f32,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 )
= $false )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ X0 ) @ X1 )
= $true )
| ( ( ( 'const/realax/real_le' @ X0 @ X1 )
& ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ X1 ) @ X0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f25,plain,
( $true
!= ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/inf' @ sK1 ) ) @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ANA089^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon Feb 23 22:49:55 EST 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.24 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : ANA089^1 : TPTP v9.2.1. Released v7.0.0.
% 0.07/0.31 % Domain : Analysis
% 0.07/0.31 % Problem : REAL_ABS_INF_LE
% 0.07/0.31 % Version : Especial.
% 0.07/0.31 % English :
% 0.07/0.31
% 0.07/0.31 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.07/0.31 % Source : [Kal16]
% 0.07/0.31 % Names : REAL_ABS_INF_LE_.p [Kal16]
% 0.07/0.31
% 0.07/0.31 % Status : Theorem
% 0.07/0.31 % Rating : 0.00 v7.1.0
% 0.07/0.31 % Syntax : Number of formulae : 10 ( 1 unt; 7 typ; 0 def)
% 0.07/0.31 % Number of atoms : 16 ( 3 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 6 ( 5 avg)
% 0.07/0.31 % Number of connectives : 44 ( 2 ~; 0 |; 5 &; 33 @)
% 0.07/0.31 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 11 ( 8 avg)
% 0.07/0.31 % Number of types : 2 ( 1 usr)
% 0.07/0.31 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 7 ( 6 usr; 0 con; 1-3 aty)
% 0.07/0.31 % Number of variables : 11 ( 0 ^; 9 !; 0 ?; 11 :)
% 0.07/0.31 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.07/0.31 % SPC : TH1_THM_EQU_NAR
% 0.07/0.31
% 0.07/0.31 % Comments : Exported from core HOL Light.
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 thf('thf_type_type/realax/real',type,
% 0.07/0.31 'type/realax/real': $tType ).
% 0.07/0.31
% 0.07/0.31 thf('thf_const_const/sets/inf',type,
% 0.07/0.31 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.07/0.31
% 0.07/0.31 thf('thf_const_const/sets/IN',type,
% 0.07/0.31 'const/sets/IN':
% 0.07/0.31 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.07/0.31
% 0.07/0.31 thf('thf_const_const/sets/EMPTY',type,
% 0.07/0.31 'const/sets/EMPTY':
% 0.07/0.31 !>[A: $tType] : ( A > $o ) ).
% 0.07/0.31
% 0.07/0.31 thf('thf_const_const/realax/real_neg',type,
% 0.07/0.31 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
% 0.07/0.31
% 0.07/0.31 thf('thf_const_const/realax/real_le',type,
% 0.07/0.31 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.07/0.31
% 0.07/0.31 thf('thf_const_const/realax/real_abs',type,
% 0.07/0.31 'const/realax/real_abs': 'type/realax/real' > 'type/realax/real' ).
% 0.07/0.31
% 0.07/0.31 thf('thm/sets/REAL_INF_BOUNDS_',axiom,
% 0.07/0.31 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.07/0.31 ( ( ( A
% 0.07/0.31 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.07/0.31 & ! [A2: 'type/realax/real'] :
% 0.07/0.31 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 0.07/0.31 => ( ( 'const/realax/real_le' @ A0 @ A2 )
% 0.07/0.31 & ( 'const/realax/real_le' @ A2 @ A1 ) ) ) )
% 0.07/0.31 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) )
% 0.07/0.31 & ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A1 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 thf('thm/real/REAL_ABS_BOUNDS_',axiom,
% 0.07/0.31 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.07/0.31 ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ A ) @ A0 )
% 0.07/0.31 = ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ A0 ) @ A )
% 0.07/0.31 & ( 'const/realax/real_le' @ A @ A0 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 thf('thm/sets/REAL_ABS_INF_LE_',conjecture,
% 0.07/0.31 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.07/0.31 ( ( ( A
% 0.07/0.31 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.07/0.31 & ! [A1: 'type/realax/real'] :
% 0.07/0.31 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.07/0.31 => ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ A1 ) @ A0 ) ) )
% 0.07/0.31 => ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/inf' @ A ) ) @ A0 ) ) ).
% 0.07/0.31
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 ------------------------
% 0.85/0.84 ---- Embedded in THF ---
% 0.85/0.84 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.85/0.84 %%% Generated on Mon Feb 23 22:49:56 EST 2026
% 0.85/0.84 %%% using '$$dhol' embedding, version 1.3.0.
% 0.85/0.84 %%% Logic specification used:
% 0.85/0.84 %%% thf(spec, logic, $$dhol).
% 0.85/0.84
% 0.85/0.84 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.7kKN1kG8JG/DTF2DTF28218.p
% See solution above
% 0.85/0.84 ------------------------
% 0.85/0.84 ---- Cleaned THF ---
% 0.85/0.85 thf('thf_type_type/realax/real',type,
% 0.85/0.85 'type/realax/real': $tType ).
% 0.85/0.85
% 0.85/0.85 thf('thf_const_const/sets/inf',type,
% 0.85/0.85 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.85/0.85
% 0.85/0.85 thf('thf_const_const/sets/IN',type,
% 0.85/0.85 'const/sets/IN':
% 0.85/0.85 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.85/0.85
% 0.85/0.85 thf('thf_const_const/sets/EMPTY',type,
% 0.85/0.85 'const/sets/EMPTY':
% 0.85/0.85 !>[A: $tType] : ( A > $o ) ).
% 0.85/0.85
% 0.85/0.85 thf('thf_const_const/realax/real_neg',type,
% 0.85/0.85 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
% 0.85/0.85
% 0.85/0.85 thf('thf_const_const/realax/real_le',type,
% 0.85/0.85 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.85/0.85
% 0.85/0.85 thf('thf_const_const/realax/real_abs',type,
% 0.85/0.85 'const/realax/real_abs': 'type/realax/real' > 'type/realax/real' ).
% 0.85/0.85
% 0.85/0.85 thf('thm/sets/REAL_INF_BOUNDS_',axiom,
% 0.85/0.85 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.85/0.85 ( ( ( A
% 0.85/0.85 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.85/0.85 & ! [A2: 'type/realax/real'] :
% 0.85/0.85 ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 0.85/0.85 => ( ( 'const/realax/real_le' @ A0 @ A2 )
% 0.85/0.85 & ( 'const/realax/real_le' @ A2 @ A1 ) ) ) )
% 0.85/0.85 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) )
% 0.85/0.85 & ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A1 ) ) ) ).
% 0.85/0.85
% 0.85/0.85 thf('thm/real/REAL_ABS_BOUNDS_',axiom,
% 0.85/0.85 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.85/0.85 ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ A ) @ A0 )
% 0.85/0.85 = ( ( 'const/realax/real_le' @ ( 'const/realax/real_neg' @ A0 ) @ A )
% 0.85/0.85 & ( 'const/realax/real_le' @ A @ A0 ) ) ) ).
% 0.85/0.85
% 0.85/0.85 thf('thm/sets/REAL_ABS_INF_LE_',conjecture,
% 0.85/0.85 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.85/0.85 ( ( ( A
% 0.85/0.85 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.85/0.85 & ! [A1: 'type/realax/real'] :
% 0.85/0.85 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.85/0.85 => ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ A1 ) @ A0 ) ) )
% 0.85/0.85 => ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/sets/inf' @ A ) ) @ A0 ) ) ).
% 0.85/0.85 ------------------------
% 0.85/0.86 % (28418)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_28218 for (3000ds/4Mi)
% 0.85/0.86 % (28419)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_28218 for (3000ds/27Mi)
% 0.85/0.86 % (28417)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28218 for (3000ds/183Mi)
% 0.85/0.86 % (28420)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28218 for (3000ds/2Mi)
% 0.85/0.86 % (28421)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_28218 for (3000ds/2Mi)
% 0.85/0.86 % (28422)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_28218 for (3000ds/275Mi)
% 0.85/0.86 % (28424)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28218 for (3000ds/18Mi)
% 0.85/0.86 % (28420)Instruction limit reached!
% 0.85/0.86 % (28420)------------------------------
% 0.85/0.86 % (28420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.85/0.86 % (28420)Termination reason: Unknown
% 0.85/0.86 % (28420)Termination phase: Saturation
% 0.85/0.86
% 0.85/0.86 % (28420)Memory used [KB]: 5500
% 0.85/0.86 % (28420)Time elapsed: 0.002 s
% 0.85/0.86 % (28420)Instructions burned: 2 (million)
% 0.85/0.86 % (28420)------------------------------
% 0.85/0.86 % (28420)------------------------------
% 0.85/0.86 % (28421)Instruction limit reached!
% 0.85/0.86 % (28421)------------------------------
% 0.85/0.86 % (28421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.85/0.86 % (28421)Termination reason: Unknown
% 0.85/0.86 % (28421)Termination phase: Saturation
% 0.85/0.86
% 0.85/0.86 % (28421)Memory used [KB]: 5500
% 0.85/0.86 % (28421)Time elapsed: 0.002 s
% 0.85/0.86 % (28421)Instructions burned: 3 (million)
% 0.85/0.86 % (28421)------------------------------
% 0.85/0.86 % (28421)------------------------------
% 0.85/0.86 % (28418)Instruction limit reached!
% 0.85/0.86 % (28418)------------------------------
% 0.85/0.86 % (28418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.85/0.86 % (28418)Termination reason: Unknown
% 0.85/0.86 % (28418)Termination phase: Saturation
% 0.85/0.86
% 0.85/0.86 % (28418)Memory used [KB]: 5500
% 0.85/0.86 % (28418)Time elapsed: 0.003 s
% 0.85/0.86 % (28418)Instructions burned: 5 (million)
% 0.85/0.86 % (28418)------------------------------
% 0.85/0.86 % (28418)------------------------------
% 0.85/0.86 % (28422)Refutation not found, incomplete strategy
% 0.85/0.86 % (28422)------------------------------
% 0.85/0.86 % (28422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.85/0.86 % (28422)Termination reason: Refutation not found, incomplete strategy
% 0.85/0.86
% 0.85/0.86
% 0.85/0.86 % (28422)Memory used [KB]: 5500
% 0.85/0.86 % (28422)Time elapsed: 0.003 s
% 0.85/0.86 % (28422)Instructions burned: 5 (million)
% 0.85/0.86 % (28422)------------------------------
% 0.85/0.86 % (28422)------------------------------
% 0.85/0.86 % (28424)Instruction limit reached!
% 0.85/0.86 % (28424)------------------------------
% 0.85/0.86 % (28424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.85/0.86 % (28424)Termination reason: Unknown
% 0.85/0.86 % (28424)Termination phase: Saturation
% 0.85/0.86
% 0.85/0.86 % (28424)Memory used [KB]: 5500
% 0.85/0.86 % (28424)Time elapsed: 0.007 s
% 0.85/0.86 % (28424)Instructions burned: 18 (million)
% 0.85/0.86 % (28424)------------------------------
% 0.85/0.86 % (28424)------------------------------
% 0.85/0.87 % (28417)First to succeed.
% 0.85/0.87 % (28419)Instruction limit reached!
% 0.85/0.87 % (28419)------------------------------
% 0.85/0.87 % (28419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.85/0.87 % (28419)Termination reason: Unknown
% 0.85/0.87 % (28419)Termination phase: Saturation
% 0.85/0.87
% 0.85/0.87 % (28419)Memory used [KB]: 5628
% 0.85/0.87 % (28419)Time elapsed: 0.011 s
% 0.85/0.87 % (28419)Instructions burned: 29 (million)
% 0.85/0.87 % (28419)------------------------------
% 0.85/0.87 % (28419)------------------------------
% 0.85/0.87 % (28425)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28218 for (2999ds/3Mi)
% 0.85/0.87 % (28426)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_28218 for (2999ds/37Mi)
% 0.85/0.87 % (28427)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_28218 for (2999ds/15Mi)
% 0.85/0.87 % (28417)Refutation found. Thanks to Tanya!
% 0.85/0.87 % SZS status Theorem for DTF2THF_28218
% 0.85/0.87 % SZS output start Proof for DTF2THF_28218
% 0.85/0.87 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.85/0.87 thf(func_def_0, type, 'type/realax/real': $tType).
% 0.85/0.87 thf(func_def_1, type, 'const/sets/inf': ('type/realax/real' > $o) > 'type/realax/real').
% 0.85/0.87 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 0.85/0.87 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 0.85/0.87 thf(func_def_4, type, 'const/realax/real_neg': 'type/realax/real' > 'type/realax/real').
% 0.85/0.87 thf(func_def_5, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 0.85/0.87 thf(func_def_6, type, 'const/realax/real_abs': 'type/realax/real' > 'type/realax/real').
% 0.85/0.87 thf(func_def_11, type, sK0: 'type/realax/real' > 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 0.85/0.87 thf(func_def_12, type, sK1: 'type/realax/real' > $o).
% 0.85/0.87 thf(func_def_13, type, sK2: 'type/realax/real').
% 0.85/0.87 thf(func_def_15, type, ph4: !>[X0: $tType]:(X0)).
% 0.85/0.87 thf(func_def_16, type, sK5: 'type/realax/real').
% 0.85/0.87 thf(f188,plain,(
% 0.85/0.87 $false),
% 0.85/0.87 inference(avatar_sat_refutation,[status(thm)],[f74,f119,f130,f145,f167,f187])).
% 0.85/0.87 thf(f187,plain,(
% 0.85/0.87 spl3_7 | ~spl3_8),
% 0.85/0.87 inference(avatar_contradiction_clause,[status(thm)],[f186])).
% 0.85/0.87 thf(f186,plain,(
% 0.85/0.87 $false | (spl3_7 | ~spl3_8)),
% 0.85/0.87 inference(subsumption_resolution,[status(thm)],[f184,f114])).
% 0.85/0.87 thf(f114,plain,(
% 0.85/0.87 (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) != $true) | spl3_7),
% 0.85/0.87 inference(avatar_component_clause,[status(thm)],[f113])).
% 0.85/0.87 thf(f113,definition,(
% 0.85/0.87 spl3_7 <=> (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) = $true)),
% 0.85/0.87 introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition])).
% 0.85/0.87 thf(f184,plain,(
% 0.85/0.87 (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) = $true) | ~spl3_8),
% 0.85/0.87 inference(trivial_inequality_removal,[status(thm)],[f176])).
% 0.85/0.87 thf(f176,plain,(
% 0.85/0.87 (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) = $true) | ($true != $true) | ~spl3_8),
% 0.85/0.87 inference(superposition,[status(thm)],[f118,f90])).
% 0.85/0.87 thf(f90,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ (sK0 @ X0 @ X1 @ sK1)) = $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0) = $true)) )),
% 0.85/0.87 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 0.85/0.87 thf(f83,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0) = $true) | ($true = $false) | (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ (sK0 @ X0 @ X1 @ sK1)) = $true)) )),
% 0.85/0.87 inference(superposition,[status(thm)],[f77,f30])).
% 0.85/0.87 thf(f30,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = $false) | (('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) = $true)) )),
% 0.85/0.87 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 0.85/0.87 thf(f29,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = $false) | ((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) = $true)) )),
% 0.85/0.87 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 0.85/0.87 thf(f27,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = (('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)))) )),
% 0.85/0.87 inference(cnf_transformation,[status(thm)],[f11])).
% 0.85/0.87 thf(f11,plain,(
% 0.85/0.87 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = (('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)))),
% 0.85/0.87 inference(fool_elimination,[status(thm)],[f10])).
% 0.85/0.87 thf(f10,plain,(
% 0.85/0.87 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = ('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) & ('const/realax/real_le' @ X0 @ X1))),
% 0.85/0.87 inference(rectify,[status(thm)],[f2])).
% 0.85/0.87 thf(f2,axiom,(
% 0.85/0.87 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = ('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) & ('const/realax/real_le' @ X0 @ X1))),
% 0.85/0.87 file('/export/starexec/sandbox2/tmp/tmp.7kKN1kG8JG/DTF2THF_28218.p','thm/real/REAL_ABS_BOUNDS_')).
% 0.85/0.87 thf(f77,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2) = $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0) = $true)) )),
% 0.85/0.87 inference(subsumption_resolution,[status(thm)],[f76,f24])).
% 0.85/0.87 thf(f24,plain,(
% 0.85/0.87 ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.85/0.87 inference(cnf_transformation,[status(thm)],[f19])).
% 0.85/0.87 thf(f19,plain,(
% 0.85/0.87 ! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ sK2) = $true) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1))) & ($true != ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ sK1)) @ sK2)) & ('const/sets/EMPTY' @ 'type/realax/real' != sK1)),
% 0.85/0.87 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f13,f18])).
% 0.85/0.87 thf(f18,plain,(
% 0.85/0.87 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true)) & (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ X0)) @ X1) != $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ sK2) = $true) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1))) & ($true != ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ sK1)) @ sK2)) & ('const/sets/EMPTY' @ 'type/realax/real' != sK1))),
% 0.85/0.87 introduced(definition,[],[choice_axiom])).
% 0.85/0.87 thf(f13,plain,(
% 0.85/0.87 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true)) & (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ X0)) @ X1) != $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.85/0.87 inference(flattening,[status(thm)],[f12])).
% 0.85/0.87 thf(f12,plain,(
% 0.85/0.87 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ X0)) @ X1) != $true) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X2 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true))))),
% 0.85/0.87 inference(ennf_transformation,[status(thm)],[f9])).
% 0.85/0.87 thf(f9,plain,(
% 0.85/0.87 ~! [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' @ ('const/realax/real_abs' @ X2) @ X1) = $true))) => (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ X0)) @ X1) = $true))),
% 0.85/0.87 inference(fool_elimination,[status(thm)],[f8])).
% 0.85/0.87 thf(f8,plain,(
% 0.85/0.87 ~! [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' @ ('const/realax/real_abs' @ X2) @ X1)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ X0)) @ X1))),
% 0.85/0.87 inference(rectify,[status(thm)],[f4])).
% 0.85/0.87 thf(f4,negated_conjecture,(
% 0.85/0.87 ~! [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' @ ('const/realax/real_abs' @ X2) @ X1)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ X0)) @ X1))),
% 0.85/0.87 inference(negated_conjecture,[status(cth)],[f3])).
% 0.85/0.87 thf(f3,conjecture,(
% 0.85/0.87 ! [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' @ ('const/realax/real_abs' @ X2) @ X1)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ X0)) @ X1))),
% 0.85/0.87 file('/export/starexec/sandbox2/tmp/tmp.7kKN1kG8JG/DTF2THF_28218.p','thm/sets/REAL_ABS_INF_LE_')).
% 0.85/0.87 thf(f76,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0) = $true) | (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2) = $true)) )),
% 0.85/0.87 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 0.85/0.87 thf(f75,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2) = $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.85/0.87 inference(superposition,[status(thm)],[f26,f22])).
% 0.85/0.87 thf(f22,plain,(
% 0.85/0.87 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1 @ X0) @ X0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) = $true)) )),
% 0.85/0.87 inference(cnf_transformation,[status(thm)],[f17])).
% 0.85/0.87 thf(f17,plain,(
% 0.85/0.87 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1 @ X0) @ X0) = $true) & ((('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2) != $true) | (('const/realax/real_le' @ X1 @ (sK0 @ X2 @ X1 @ X0)) != $true))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = $true) & (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) = $true)))),
% 0.85/0.87 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f16])).
% 0.85/0.87 thf(f16,plain,(
% 0.85/0.87 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : (? [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) & ((('const/realax/real_le' @ X3 @ X2) != $true) | (('const/realax/real_le' @ X1 @ X3) != $true))) => ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1 @ X0) @ X0) = $true) & ((('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2) != $true) | (('const/realax/real_le' @ X1 @ (sK0 @ X2 @ X1 @ X0)) != $true))))),
% 0.85/0.87 introduced(definition,[],[choice_axiom])).
% 0.85/0.87 thf(f15,plain,(
% 0.85/0.87 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ? [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) & ((('const/realax/real_le' @ X3 @ X2) != $true) | (('const/realax/real_le' @ X1 @ X3) != $true))) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = $true) & (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) = $true)))),
% 0.85/0.87 inference(flattening,[status(thm)],[f14])).
% 0.85/0.87 thf(f14,plain,(
% 0.85/0.87 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = $true) & (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) = $true)) | (? [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) & ((('const/realax/real_le' @ X3 @ X2) != $true) | (('const/realax/real_le' @ X1 @ X3) != $true))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 0.85/0.87 inference(ennf_transformation,[status(thm)],[f7])).
% 0.85/0.87 thf(f7,plain,(
% 0.85/0.87 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) => ((('const/realax/real_le' @ X1 @ X3) = $true) & (('const/realax/real_le' @ X3 @ X2) = $true))) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = $true) & (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) = $true)))),
% 0.85/0.87 inference(fool_elimination,[status(thm)],[f6])).
% 0.85/0.87 thf(f6,plain,(
% 0.85/0.87 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3)))) => (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) & ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)))),
% 0.85/0.87 inference(rectify,[status(thm)],[f1])).
% 0.85/0.87 thf(f1,axiom,(
% 0.85/0.87 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => (('const/realax/real_le' @ X3 @ X2) & ('const/realax/real_le' @ X1 @ X3)))) => (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) & ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2)))),
% 0.85/0.87 file('/export/starexec/sandbox2/tmp/tmp.7kKN1kG8JG/DTF2THF_28218.p','thm/sets/REAL_INF_BOUNDS_')).
% 0.85/0.87 thf(f26,plain,(
% 0.85/0.87 ( ! [X2 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X2 @ sK1)) | (('const/realax/real_le' @ ('const/realax/real_abs' @ X2) @ sK2) = $true)) )),
% 0.85/0.87 inference(cnf_transformation,[status(thm)],[f19])).
% 0.85/0.87 thf(f118,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) ) | ~spl3_8),
% 0.85/0.87 inference(avatar_component_clause,[status(thm)],[f117])).
% 0.85/0.87 thf(f117,definition,(
% 0.85/0.87 spl3_8 <=> ! [X0 : 'type/realax/real'] : ($true != ('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))),
% 0.85/0.87 introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition])).
% 0.85/0.87 thf(f167,plain,(
% 0.85/0.87 ~spl3_6 | ~spl3_9),
% 0.85/0.87 inference(avatar_contradiction_clause,[status(thm)],[f166])).
% 0.85/0.87 thf(f166,plain,(
% 0.85/0.87 $false | (~spl3_6 | ~spl3_9)),
% 0.85/0.87 inference(trivial_inequality_removal,[status(thm)],[f160])).
% 0.85/0.87 thf(f160,plain,(
% 0.85/0.87 ($true = $false) | (~spl3_6 | ~spl3_9)),
% 0.85/0.87 inference(superposition,[status(thm)],[f73,f155])).
% 0.85/0.87 thf(f155,plain,(
% 0.85/0.87 (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1)) = $true) | ~spl3_9),
% 0.85/0.87 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 0.85/0.87 thf(f154,plain,(
% 0.85/0.87 (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1)) = $true) | ($true != $true) | ~spl3_9),
% 0.85/0.87 inference(duplicate_literal_removal,[status(thm)],[f146])).
% 0.85/0.87 thf(f146,plain,(
% 0.85/0.87 (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1)) = $true) | ($true != $true) | (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1)) = $true) | ~spl3_9),
% 0.85/0.87 inference(superposition,[status(thm)],[f123,f104])).
% 0.85/0.87 thf(f104,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ (sK0 @ X0 @ X1 @ sK1)) = $true) | (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)) = $true)) )),
% 0.85/0.87 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 0.85/0.87 thf(f98,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ (sK0 @ X0 @ X1 @ sK1)) = $true) | ($true = $false) | (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)) = $true)) )),
% 0.85/0.87 inference(superposition,[status(thm)],[f97,f30])).
% 0.85/0.87 thf(f97,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2) = $true) | (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)) = $true)) )),
% 0.85/0.87 inference(subsumption_resolution,[status(thm)],[f96,f24])).
% 0.85/0.87 thf(f96,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)) = $true) | (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.85/0.87 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 0.85/0.87 thf(f95,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true != $true) | (('const/realax/real_le' @ ('const/realax/real_abs' @ (sK0 @ X0 @ X1 @ sK1)) @ sK2) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)) = $true)) )),
% 0.85/0.87 inference(superposition,[status(thm)],[f26,f23])).
% 0.85/0.87 thf(f23,plain,(
% 0.85/0.87 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X2 @ X1 @ X0) @ X0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = $true)) )),
% 0.85/0.87 inference(cnf_transformation,[status(thm)],[f17])).
% 0.85/0.87 thf(f123,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true)) ) | ~spl3_9),
% 0.85/0.87 inference(avatar_component_clause,[status(thm)],[f122])).
% 0.85/0.87 thf(f122,definition,(
% 0.85/0.87 spl3_9 <=> ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true) | ($true != ('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))))),
% 0.85/0.87 introduced(definition,[new_symbols(naming,[spl3_9])],[avatar_definition])).
% 0.85/0.87 thf(f73,plain,(
% 0.85/0.87 (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1)) = $false) | ~spl3_6),
% 0.85/0.87 inference(avatar_component_clause,[status(thm)],[f71])).
% 0.85/0.87 thf(f71,definition,(
% 0.85/0.87 spl3_6 <=> (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1)) = $false)),
% 0.85/0.87 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 0.85/0.87 thf(f145,plain,(
% 0.85/0.87 spl3_9),
% 0.85/0.87 inference(avatar_split_clause,[status(thm)],[f144,f122])).
% 0.85/0.87 thf(f144,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true)) )),
% 0.85/0.87 inference(subsumption_resolution,[status(thm)],[f143,f24])).
% 0.85/0.87 thf(f143,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true != ('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true)) )),
% 0.85/0.87 inference(trivial_inequality_removal,[status(thm)],[f142])).
% 0.85/0.87 thf(f142,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true) | ($true != ('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1)))) )),
% 0.85/0.87 inference(duplicate_literal_removal,[status(thm)],[f139])).
% 0.85/0.87 thf(f139,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true) | ($true != $true) | ($true != ('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK1)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.85/0.87 inference(superposition,[status(thm)],[f21,f105])).
% 0.85/0.87 thf(f105,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2) = $true) | (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)) = $true)) )),
% 0.85/0.87 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 0.85/0.87 thf(f99,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK1)) = $true) | (('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2) = $true) | ($true = $false)) )),
% 0.85/0.87 inference(superposition,[status(thm)],[f97,f31])).
% 0.85/0.87 thf(f31,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = $false) | (('const/realax/real_le' @ X0 @ X1) = $true)) )),
% 0.85/0.87 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 0.85/0.87 thf(f21,plain,(
% 0.85/0.87 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2) != $true) | (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ X1 @ (sK0 @ X2 @ X1 @ X0)) != $true)) )),
% 0.85/0.87 inference(cnf_transformation,[status(thm)],[f17])).
% 0.85/0.87 thf(f130,plain,(
% 0.85/0.87 ~spl3_5 | ~spl3_7),
% 0.85/0.87 inference(avatar_contradiction_clause,[status(thm)],[f129])).
% 0.85/0.87 thf(f129,plain,(
% 0.85/0.87 $false | (~spl3_5 | ~spl3_7)),
% 0.85/0.87 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 0.85/0.87 thf(f125,plain,(
% 0.85/0.87 ($true = $false) | (~spl3_5 | ~spl3_7)),
% 0.85/0.87 inference(superposition,[status(thm)],[f115,f69])).
% 0.85/0.87 thf(f69,plain,(
% 0.85/0.87 (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) = $false) | ~spl3_5),
% 0.85/0.87 inference(avatar_component_clause,[status(thm)],[f67])).
% 0.85/0.87 thf(f67,definition,(
% 0.85/0.87 spl3_5 <=> (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) = $false)),
% 0.85/0.87 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 0.85/0.87 thf(f115,plain,(
% 0.85/0.87 (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) = $true) | ~spl3_7),
% 0.85/0.87 inference(avatar_component_clause,[status(thm)],[f113])).
% 0.85/0.87 thf(f119,plain,(
% 0.85/0.87 spl3_7 | spl3_8),
% 0.85/0.87 inference(avatar_split_clause,[status(thm)],[f111,f117,f113])).
% 0.85/0.87 thf(f111,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) = $true)) )),
% 0.85/0.87 inference(subsumption_resolution,[status(thm)],[f110,f24])).
% 0.85/0.87 thf(f110,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.85/0.87 inference(trivial_inequality_removal,[status(thm)],[f109])).
% 0.85/0.87 thf(f109,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real'] : (($true != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) = $true) | ($true != ('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.85/0.87 inference(duplicate_literal_removal,[status(thm)],[f107])).
% 0.85/0.87 thf(f107,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_le' @ X0 @ (sK0 @ sK2 @ X0 @ sK1))) | ($true != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) = $true)) )),
% 0.85/0.87 inference(superposition,[status(thm)],[f20,f89])).
% 0.85/0.87 thf(f89,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2) = $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0) = $true)) )),
% 0.85/0.87 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 0.85/0.87 thf(f84,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK0 @ X0 @ X1 @ sK1) @ sK2) = $true) | ($true = $false) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0) = $true)) )),
% 0.85/0.87 inference(superposition,[status(thm)],[f77,f31])).
% 0.85/0.87 thf(f20,plain,(
% 0.85/0.87 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ (sK0 @ X2 @ X1 @ X0) @ X2) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) = $true) | (('const/realax/real_le' @ X1 @ (sK0 @ X2 @ X1 @ X0)) != $true)) )),
% 0.85/0.87 inference(cnf_transformation,[status(thm)],[f17])).
% 0.85/0.87 thf(f74,plain,(
% 0.85/0.87 spl3_5 | spl3_6),
% 0.85/0.87 inference(avatar_split_clause,[status(thm)],[f65,f71,f67])).
% 0.85/0.87 thf(f65,plain,(
% 0.85/0.87 (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) = $false) | (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1)) = $false)),
% 0.85/0.87 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 0.85/0.87 thf(f58,plain,(
% 0.85/0.87 ($true != $true) | (('const/realax/real_le' @ ('const/realax/real_neg' @ sK2) @ ('const/sets/inf' @ sK1)) = $false) | (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ sK2) = $false)),
% 0.85/0.87 inference(superposition,[status(thm)],[f25,f32])).
% 0.85/0.87 thf(f32,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = $true) | (('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0) = $false) | (('const/realax/real_le' @ X0 @ X1) = $false)) )),
% 0.85/0.87 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 0.85/0.87 thf(f28,plain,(
% 0.85/0.87 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ X0) @ X1) = $true) | ((('const/realax/real_le' @ X0 @ X1) & ('const/realax/real_le' @ ('const/realax/real_neg' @ X1) @ X0)) = $false)) )),
% 0.85/0.87 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 0.85/0.87 thf(f25,plain,(
% 0.85/0.87 ($true != ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/sets/inf' @ sK1)) @ sK2))),
% 0.85/0.87 inference(cnf_transformation,[status(thm)],[f19])).
% 0.85/0.87 % SZS output end Proof for DTF2THF_28218
% 0.85/0.87 % (28417)------------------------------
% 0.85/0.87 % (28417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.85/0.87 % (28417)Termination reason: Refutation
% 0.85/0.87
% 0.85/0.87 % (28417)Memory used [KB]: 5628
% 0.85/0.87 % (28417)Time elapsed: 0.011 s
% 0.85/0.87 % (28417)Instructions burned: 26 (million)
% 0.85/0.87 % (28417)------------------------------
% 0.85/0.87 % (28417)------------------------------
% 0.85/0.87 % (28416)Success in time 0.017 s
%------------------------------------------------------------------------------