%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA081^1 : 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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:38:49 AM UTC 2026
% Result : Theorem 1.67s 1.31s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 84 ( 4 unt; 0 typ; 8 def)
% Number of atoms : 577 ( 136 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 705 ( 108 ~; 109 |; 25 &; 416 @)
% ( 8 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 19 usr; 14 con; 0-3 aty)
% ( 9 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 66 ( 11 ^; 49 !; 6 ?; 66 :)
% 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/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_5,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_7,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_14,type,
sK0: 'type/realax/real' > $o ).
thf(func_def_15,type,
sK1: 'type/realax/real' ).
thf(func_def_17,type,
sK3: 'type/realax/real' ).
thf(func_def_18,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
sK5: 'type/realax/real' ).
thf(f167,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f42,f51,f56,f98,f102,f106,f127,f139,f149,f166]) ).
thf(f166,plain,
( ~ spl2_1
| ~ spl2_4
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f165]) ).
thf(f165,plain,
( $false
| ~ spl2_1
| ~ spl2_4
| ~ spl2_5 ),
inference(trivial_inequality_removal,[status(thm)],[f164]) ).
thf(f164,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_4
| ~ spl2_5 ),
inference(forward_demodulation,[status(thm)],[f155,f50]) ).
thf(f50,plain,
( ( $false
= ( 'const/realax/real_le' @ sK1 @ sK3 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl2_4
<=> ( $false
= ( 'const/realax/real_le' @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f155,plain,
( ( $true
= ( 'const/realax/real_le' @ sK1 @ sK3 ) )
| ~ spl2_1
| ~ spl2_5 ),
inference(trivial_inequality_removal,[status(thm)],[f151]) ).
thf(f151,plain,
( ( $false = $true )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ sK3 ) )
| ~ spl2_1
| ~ spl2_5 ),
inference(superposition,[status(thm)],[f37,f55]) ).
thf(f55,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 )
= $true )
| ~ spl2_5 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f53,definition,
( spl2_5
<=> ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition]) ).
thf(f37,plain,
( ! [X1: 'type/realax/real'] :
( ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ X1 ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl2_1
<=> ! [X1: 'type/realax/real'] :
( ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f149,plain,
( ~ spl2_2
| ~ spl2_4
| ~ spl2_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f148]) ).
thf(f148,plain,
( $false
| ~ spl2_2
| ~ spl2_4
| ~ spl2_13 ),
inference(trivial_inequality_removal,[status(thm)],[f147]) ).
thf(f147,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_13 ),
inference(forward_demodulation,[status(thm)],[f146,f50]) ).
thf(f146,plain,
( ( $true
= ( 'const/realax/real_le' @ sK1 @ sK3 ) )
| ~ spl2_2
| ~ spl2_13 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ( $true
= ( 'const/realax/real_le' @ sK1 @ sK3 ) )
| ( $true != $true )
| ~ spl2_2
| ~ spl2_13 ),
inference(superposition,[status(thm)],[f142,f41]) ).
thf(f41,plain,
( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl2_2
<=> ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f142,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ sK3 )
= $true ) )
| ~ spl2_13 ),
inference(trivial_inequality_removal,[status(thm)],[f141]) ).
thf(f141,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ sK3 )
= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK0 ) )
!= $true ) )
| ~ spl2_13 ),
inference(superposition,[status(thm)],[f20,f138]) ).
thf(f138,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK3 )
= $true )
| ~ spl2_13 ),
inference(avatar_component_clause,[status(thm)],[f136]) ).
thf(f136,definition,
( spl2_13
<=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_13])],[avatar_definition]) ).
thf(f20,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true ) )
=> ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X0 @ X1 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X0 @ X1 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.7KaT4DNJoh/DTF2THF_10391.p','thm/realax/REAL_LE_TRANS_') ).
thf(f139,plain,
( spl2_10
| spl2_13
| ~ spl2_5 ),
inference(avatar_split_clause,[status(thm)],[f134,f53,f136,f83]) ).
thf(f83,definition,
( spl2_10
<=> ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_10])],[avatar_definition]) ).
thf(f134,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK3 )
= $true )
| ~ spl2_5 ),
inference(trivial_inequality_removal,[status(thm)],[f133]) ).
thf(f133,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK3 )
= $true )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ~ spl2_5 ),
inference(forward_demodulation,[status(thm)],[f132,f22]) ).
thf(f22,plain,
( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true )
& ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
!= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
=> ( 'const/realax/real_le' @ sK1 @ Y0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f18]) ).
thf(f18,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ Y0 ) ) ) ) )
=> ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true )
& ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
!= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
=> ( 'const/realax/real_le' @ sK1 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ Y0 ) ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ Y0 ) ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ 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 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= ( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= ( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= ( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7KaT4DNJoh/DTF2THF_10391.p','thm/sets/REAL_LE_INF_FINITE_') ).
thf(f132,plain,
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK3 )
= $true )
| ~ spl2_5 ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ( $true != $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK3 )
= $true )
| ~ spl2_5 ),
inference(superposition,[status(thm)],[f25,f55]) ).
thf(f25,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true )
& ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
& ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
& ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7KaT4DNJoh/DTF2THF_10391.p','thm/sets/INF_FINITE_') ).
thf(f127,plain,
( ~ spl2_1
| ~ spl2_3
| ~ spl2_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f126]) ).
thf(f126,plain,
( $false
| ~ spl2_1
| ~ spl2_3
| ~ spl2_11 ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_3
| ~ spl2_11 ),
inference(forward_demodulation,[status(thm)],[f120,f46]) ).
thf(f46,plain,
( ( $false
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl2_3
<=> ( $false
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f120,plain,
( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ~ spl2_1
| ~ spl2_11 ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ( $false = $true )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ~ spl2_1
| ~ spl2_11 ),
inference(superposition,[status(thm)],[f37,f89]) ).
thf(f89,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK0 ) @ sK0 )
= $true )
| ~ spl2_11 ),
inference(avatar_component_clause,[status(thm)],[f87]) ).
thf(f87,definition,
( spl2_11
<=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK0 ) @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_11])],[avatar_definition]) ).
thf(f106,plain,
( spl2_11
| spl2_10 ),
inference(avatar_split_clause,[status(thm)],[f105,f83,f87]) ).
thf(f105,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK0 ) @ sK0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f104]) ).
thf(f104,plain,
( ( $true != $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK0 ) @ sK0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(superposition,[status(thm)],[f24,f22]) ).
thf(f24,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f102,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f101]) ).
thf(f101,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(backward_demodulation,[status(thm)],[f41,f46]) ).
thf(f98,plain,
~ spl2_10,
inference(avatar_contradiction_clause,[status(thm)],[f97]) ).
thf(f97,plain,
( $false
| ~ spl2_10 ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ( sK0 != sK0 )
| ~ spl2_10 ),
inference(superposition,[status(thm)],[f23,f85]) ).
thf(f85,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ~ spl2_10 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f23,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f56,plain,
( spl2_5
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f31,f44,f53]) ).
thf(f31,plain,
( ( $false
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $false
= ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 )
=> ( 'const/realax/real_le' @ sK1 @ sK3 ) ) )
| ( $false
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $false
= ( ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
=> ( 'const/realax/real_le' @ sK1 @ Y0 ) )
@ sK3 ) )
| ( $false
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $false
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ( $false
= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
=> ( 'const/realax/real_le' @ sK1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
!= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
=> ( 'const/realax/real_le' @ sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f51,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f30,f48,f44]) ).
thf(f30,plain,
( ( $false
= ( 'const/realax/real_le' @ sK1 @ sK3 ) )
| ( $false
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f42,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f34,f39,f36]) ).
thf(f34,plain,
! [X1: 'type/realax/real'] :
( ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ X1 ) )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: 'type/realax/real'] :
( ( $true
= ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
=> ( 'const/realax/real_le' @ sK1 @ X1 ) ) )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
= $true )
| ( $true
= ( ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
=> ( 'const/realax/real_le' @ sK1 @ Y0 ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $true
= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
=> ( 'const/realax/real_le' @ sK1 @ Y0 ) ) ) )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/inf' @ sK0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA081^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n008.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 03:50:09 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : ANA081^1 : TPTP v9.2.1. Released v7.0.0.
% 0.26/0.46 % Domain : Analysis
% 0.26/0.46 % Problem : REAL_LE_INF_FINITE
% 0.26/0.46 % Version : Especial.
% 0.26/0.46 % English :
% 0.26/0.46
% 0.26/0.46 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.26/0.46 % Source : [Kal16]
% 0.26/0.46 % Names : REAL_LE_INF_FINITE_.p [Kal16]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : 0.00 v7.1.0
% 0.26/0.46 % Syntax : Number of formulae : 9 ( 0 unt; 6 typ; 0 def)
% 0.26/0.46 % Number of atoms : 16 ( 3 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 5 ( 5 avg)
% 0.26/0.46 % Number of connectives : 41 ( 2 ~; 0 |; 4 &; 30 @)
% 0.26/0.46 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 9 ( 8 avg)
% 0.26/0.46 % Number of types : 2 ( 1 usr)
% 0.26/0.46 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 6 ( 5 usr; 0 con; 1-3 aty)
% 0.26/0.47 % Number of variables : 11 ( 0 ^; 8 !; 0 ?; 11 :)
% 0.26/0.47 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.26/0.47 % SPC : TH1_THM_EQU_NAR
% 0.26/0.47
% 0.26/0.47 % Comments : Exported from core HOL Light.
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 thf('thf_type_type/realax/real',type,
% 0.26/0.47 'type/realax/real': $tType ).
% 0.26/0.47
% 0.26/0.47 thf('thf_const_const/sets/inf',type,
% 0.26/0.47 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.26/0.47
% 0.26/0.47 thf('thf_const_const/sets/IN',type,
% 0.26/0.47 'const/sets/IN':
% 0.26/0.47 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.26/0.47
% 0.26/0.47 thf('thf_const_const/sets/FINITE',type,
% 0.26/0.47 'const/sets/FINITE':
% 0.26/0.47 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.26/0.47
% 0.26/0.47 thf('thf_const_const/sets/EMPTY',type,
% 0.26/0.47 'const/sets/EMPTY':
% 0.26/0.47 !>[A: $tType] : ( A > $o ) ).
% 0.26/0.47
% 0.26/0.47 thf('thf_const_const/realax/real_le',type,
% 0.26/0.47 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.26/0.47
% 0.26/0.47 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 0.26/0.47 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.26/0.47 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 0.26/0.47 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.26/0.47 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 0.26/0.47
% 0.26/0.47 thf('thm/sets/INF_FINITE_',axiom,
% 0.26/0.47 ! [A: 'type/realax/real' > $o] :
% 0.26/0.47 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.26/0.47 & ( A
% 0.26/0.47 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.26/0.47 => ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ A ) @ A )
% 0.26/0.47 & ! [A0: 'type/realax/real'] :
% 0.26/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.26/0.47 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf('thm/sets/REAL_LE_INF_FINITE_',conjecture,
% 0.26/0.47 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.26/0.47 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.26/0.47 & ( A
% 0.26/0.47 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.26/0.47 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) )
% 0.26/0.47 = ( ! [A1: 'type/realax/real'] :
% 0.26/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.26/0.47 => ( 'const/realax/real_le' @ A0 @ A1 ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 ------------------------
% 1.49/1.28 ---- Embedded in THF ---
% 1.49/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.28 %%% Generated on Tue Feb 24 03:50:10 EST 2026
% 1.49/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.28 %%% Logic specification used:
% 1.49/1.28 %%% thf(spec, logic, $$dhol).
% 1.49/1.28
% 1.49/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.7KaT4DNJoh/DTF2DTF10391.p
% See solution above
% 1.49/1.28 ------------------------
% 1.49/1.29 ---- Cleaned THF ---
% 1.49/1.29 thf('thf_type_type/realax/real',type,
% 1.49/1.29 'type/realax/real': $tType ).
% 1.49/1.29
% 1.49/1.29 thf('thf_const_const/sets/inf',type,
% 1.49/1.29 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 1.49/1.29
% 1.49/1.29 thf('thf_const_const/sets/IN',type,
% 1.49/1.29 'const/sets/IN':
% 1.49/1.29 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.49/1.29
% 1.49/1.29 thf('thf_const_const/sets/FINITE',type,
% 1.49/1.29 'const/sets/FINITE':
% 1.49/1.29 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.49/1.29
% 1.49/1.29 thf('thf_const_const/sets/EMPTY',type,
% 1.49/1.29 'const/sets/EMPTY':
% 1.49/1.29 !>[A: $tType] : ( A > $o ) ).
% 1.49/1.29
% 1.49/1.29 thf('thf_const_const/realax/real_le',type,
% 1.49/1.29 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.49/1.29
% 1.49/1.29 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 1.49/1.29 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 1.49/1.29 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 1.49/1.29 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 1.49/1.29 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 1.49/1.29
% 1.49/1.29 thf('thm/sets/INF_FINITE_',axiom,
% 1.49/1.29 ! [A: 'type/realax/real' > $o] :
% 1.49/1.29 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 1.49/1.29 & ( A
% 1.49/1.29 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 1.49/1.29 => ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ A ) @ A )
% 1.49/1.29 & ! [A0: 'type/realax/real'] :
% 1.49/1.29 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 1.49/1.29 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) ) ) ) ).
% 1.49/1.29
% 1.49/1.29 thf('thm/sets/REAL_LE_INF_FINITE_',conjecture,
% 1.49/1.29 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 1.49/1.29 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 1.49/1.29 & ( A
% 1.49/1.29 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 1.49/1.29 => ( ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) )
% 1.49/1.29 = ( ! [A1: 'type/realax/real'] :
% 1.49/1.29 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.49/1.29 => ( 'const/realax/real_le' @ A0 @ A1 ) ) ) ) ) ).
% 1.49/1.29 ------------------------
% 1.67/1.31 % (10673)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_10391 for (2999ds/27Mi)
% 1.67/1.31 % (10674)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10391 for (2999ds/2Mi)
% 1.67/1.31 % (10674)Instruction limit reached!
% 1.67/1.31 % (10674)------------------------------
% 1.67/1.31 % (10674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (10674)Termination reason: Unknown
% 1.67/1.31 % (10674)Termination phase: Saturation
% 1.67/1.31
% 1.67/1.31 % (10674)Memory used [KB]: 5500
% 1.67/1.31 % (10674)Time elapsed: 0.002 s
% 1.67/1.31 % (10674)Instructions burned: 2 (million)
% 1.67/1.31 % (10674)------------------------------
% 1.67/1.31 % (10674)------------------------------
% 1.67/1.31 % (10673)First to succeed.
% 1.67/1.31 % (10673)Refutation found. Thanks to Tanya!
% 1.67/1.31 % SZS status Theorem for DTF2THF_10391
% 1.67/1.31 % SZS output start Proof for DTF2THF_10391
% 1.67/1.31 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.67/1.31 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.67/1.31 thf(func_def_1, type, 'const/sets/inf': ('type/realax/real' > $o) > 'type/realax/real').
% 1.67/1.31 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.67/1.31 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.67/1.31 thf(func_def_4, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.67/1.31 thf(func_def_5, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.67/1.31 thf(func_def_7, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.67/1.31 thf(func_def_14, type, sK0: 'type/realax/real' > $o).
% 1.67/1.31 thf(func_def_15, type, sK1: 'type/realax/real').
% 1.67/1.31 thf(func_def_17, type, sK3: 'type/realax/real').
% 1.67/1.31 thf(func_def_18, type, ph4: !>[X0: $tType]:(X0)).
% 1.67/1.31 thf(func_def_19, type, sK5: 'type/realax/real').
% 1.67/1.31 thf(f167,plain,(
% 1.67/1.31 $false),
% 1.67/1.31 inference(avatar_sat_refutation,[status(thm)],[f42,f51,f56,f98,f102,f106,f127,f139,f149,f166])).
% 1.67/1.31 thf(f166,plain,(
% 1.67/1.31 ~spl2_1 | ~spl2_4 | ~spl2_5),
% 1.67/1.31 inference(avatar_contradiction_clause,[status(thm)],[f165])).
% 1.67/1.31 thf(f165,plain,(
% 1.67/1.31 $false | (~spl2_1 | ~spl2_4 | ~spl2_5)),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f164])).
% 1.67/1.31 thf(f164,plain,(
% 1.67/1.31 ($false = $true) | (~spl2_1 | ~spl2_4 | ~spl2_5)),
% 1.67/1.31 inference(forward_demodulation,[status(thm)],[f155,f50])).
% 1.67/1.31 thf(f50,plain,(
% 1.67/1.31 ($false = ('const/realax/real_le' @ sK1 @ sK3)) | ~spl2_4),
% 1.67/1.31 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.67/1.31 thf(f48,definition,(
% 1.67/1.31 spl2_4 <=> ($false = ('const/realax/real_le' @ sK1 @ sK3))),
% 1.67/1.31 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.67/1.31 thf(f155,plain,(
% 1.67/1.31 ($true = ('const/realax/real_le' @ sK1 @ sK3)) | (~spl2_1 | ~spl2_5)),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f151])).
% 1.67/1.31 thf(f151,plain,(
% 1.67/1.31 ($false = $true) | ($true = ('const/realax/real_le' @ sK1 @ sK3)) | (~spl2_1 | ~spl2_5)),
% 1.67/1.31 inference(superposition,[status(thm)],[f37,f55])).
% 1.67/1.31 thf(f55,plain,(
% 1.67/1.31 (('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0) = $true) | ~spl2_5),
% 1.67/1.31 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.67/1.31 thf(f53,definition,(
% 1.67/1.31 spl2_5 <=> (('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0) = $true)),
% 1.67/1.31 introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition])).
% 1.67/1.31 thf(f37,plain,(
% 1.67/1.31 ( ! [X1 : 'type/realax/real'] : (($false = ('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0)) | ($true = ('const/realax/real_le' @ sK1 @ X1))) ) | ~spl2_1),
% 1.67/1.31 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.67/1.31 thf(f36,definition,(
% 1.67/1.31 spl2_1 <=> ! [X1 : 'type/realax/real'] : (($false = ('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0)) | ($true = ('const/realax/real_le' @ sK1 @ X1)))),
% 1.67/1.31 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.67/1.31 thf(f149,plain,(
% 1.67/1.31 ~spl2_2 | ~spl2_4 | ~spl2_13),
% 1.67/1.31 inference(avatar_contradiction_clause,[status(thm)],[f148])).
% 1.67/1.31 thf(f148,plain,(
% 1.67/1.31 $false | (~spl2_2 | ~spl2_4 | ~spl2_13)),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f147])).
% 1.67/1.31 thf(f147,plain,(
% 1.67/1.31 ($false = $true) | (~spl2_2 | ~spl2_4 | ~spl2_13)),
% 1.67/1.31 inference(forward_demodulation,[status(thm)],[f146,f50])).
% 1.67/1.31 thf(f146,plain,(
% 1.67/1.31 ($true = ('const/realax/real_le' @ sK1 @ sK3)) | (~spl2_2 | ~spl2_13)),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.67/1.31 thf(f144,plain,(
% 1.67/1.31 ($true = ('const/realax/real_le' @ sK1 @ sK3)) | ($true != $true) | (~spl2_2 | ~spl2_13)),
% 1.67/1.31 inference(superposition,[status(thm)],[f142,f41])).
% 1.67/1.31 thf(f41,plain,(
% 1.67/1.31 (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) = $true) | ~spl2_2),
% 1.67/1.31 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.67/1.31 thf(f39,definition,(
% 1.67/1.31 spl2_2 <=> (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) = $true)),
% 1.67/1.31 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.67/1.31 thf(f142,plain,(
% 1.67/1.31 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)) != $true) | (('const/realax/real_le' @ X0 @ sK3) = $true)) ) | ~spl2_13),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f141])).
% 1.67/1.31 thf(f141,plain,(
% 1.67/1.31 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ sK3) = $true) | ($true != $true) | (('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK0)) != $true)) ) | ~spl2_13),
% 1.67/1.31 inference(superposition,[status(thm)],[f20,f138])).
% 1.67/1.31 thf(f138,plain,(
% 1.67/1.31 (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK3) = $true) | ~spl2_13),
% 1.67/1.31 inference(avatar_component_clause,[status(thm)],[f136])).
% 1.67/1.31 thf(f136,definition,(
% 1.67/1.31 spl2_13 <=> (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK3) = $true)),
% 1.67/1.31 introduced(definition,[new_symbols(naming,[spl2_13])],[avatar_definition])).
% 1.67/1.31 thf(f20,plain,(
% 1.67/1.31 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) != $true) | (('const/realax/real_le' @ X0 @ X2) = $true) | (('const/realax/real_le' @ X0 @ X1) != $true)) )),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 1.67/1.31 thf(f15,plain,(
% 1.67/1.31 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X1) != $true) | (('const/realax/real_le' @ X0 @ X2) = $true) | (('const/realax/real_le' @ X1 @ X2) != $true))),
% 1.67/1.31 inference(flattening,[status(thm)],[f14])).
% 1.67/1.31 thf(f14,plain,(
% 1.67/1.31 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X2) = $true) | ((('const/realax/real_le' @ X1 @ X2) != $true) | (('const/realax/real_le' @ X0 @ X1) != $true)))),
% 1.67/1.31 inference(ennf_transformation,[status(thm)],[f11])).
% 1.67/1.31 thf(f11,plain,(
% 1.67/1.31 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2) = $true) & (('const/realax/real_le' @ X0 @ X1) = $true)) => (('const/realax/real_le' @ X0 @ X2) = $true))),
% 1.67/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.67/1.31 thf(f10,plain,(
% 1.67/1.31 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 1.67/1.31 inference(rectify,[status(thm)],[f1])).
% 1.67/1.31 thf(f1,axiom,(
% 1.67/1.31 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 1.67/1.31 file('/export/starexec/sandbox/tmp/tmp.7KaT4DNJoh/DTF2THF_10391.p','thm/realax/REAL_LE_TRANS_')).
% 1.67/1.31 thf(f139,plain,(
% 1.67/1.31 spl2_10 | spl2_13 | ~spl2_5),
% 1.67/1.31 inference(avatar_split_clause,[status(thm)],[f134,f53,f136,f83])).
% 1.67/1.31 thf(f83,definition,(
% 1.67/1.31 spl2_10 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK0)),
% 1.67/1.31 introduced(definition,[new_symbols(naming,[spl2_10])],[avatar_definition])).
% 1.67/1.31 thf(f134,plain,(
% 1.67/1.31 ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK3) = $true) | ~spl2_5),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f133])).
% 1.67/1.31 thf(f133,plain,(
% 1.67/1.31 (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK3) = $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ~spl2_5),
% 1.67/1.31 inference(forward_demodulation,[status(thm)],[f132,f22])).
% 1.67/1.31 thf(f22,plain,(
% 1.67/1.31 (('const/sets/FINITE' @ 'type/realax/real' @ sK0) = $true)),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.31 thf(f19,plain,(
% 1.67/1.31 ('const/sets/EMPTY' @ 'type/realax/real' != sK0) & (('const/sets/FINITE' @ 'type/realax/real' @ sK0) = $true) & (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) != (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) => ('const/realax/real_le' @ sK1 @ Y0)))))),
% 1.67/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f18])).
% 1.67/1.31 thf(f18,plain,(
% 1.67/1.31 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) != (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ X1 @ Y0)))))) => (('const/sets/EMPTY' @ 'type/realax/real' != sK0) & (('const/sets/FINITE' @ 'type/realax/real' @ sK0) = $true) & (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) != (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) => ('const/realax/real_le' @ sK1 @ Y0))))))),
% 1.67/1.31 introduced(definition,[],[choice_axiom])).
% 1.67/1.31 thf(f13,plain,(
% 1.67/1.31 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) != (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ X1 @ Y0))))))),
% 1.67/1.31 inference(flattening,[status(thm)],[f12])).
% 1.67/1.31 thf(f12,plain,(
% 1.67/1.31 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) != (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ X1 @ Y0))))) & (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true)))),
% 1.67/1.31 inference(ennf_transformation,[status(thm)],[f9])).
% 1.67/1.31 thf(f9,plain,(
% 1.67/1.31 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true)) => (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X0) => ('const/realax/real_le' @ X1 @ Y0))))))),
% 1.67/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.67/1.31 thf(f8,plain,(
% 1.67/1.31 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))))),
% 1.67/1.31 inference(rectify,[status(thm)],[f4])).
% 1.67/1.31 thf(f4,negated_conjecture,(
% 1.67/1.31 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))))),
% 1.67/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.67/1.31 thf(f3,conjecture,(
% 1.67/1.31 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)) = ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))))),
% 1.67/1.31 file('/export/starexec/sandbox/tmp/tmp.7KaT4DNJoh/DTF2THF_10391.p','thm/sets/REAL_LE_INF_FINITE_')).
% 1.67/1.31 thf(f132,plain,(
% 1.67/1.31 (('const/sets/FINITE' @ 'type/realax/real' @ sK0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK3) = $true) | ~spl2_5),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.67/1.31 thf(f131,plain,(
% 1.67/1.31 ($true != $true) | (('const/sets/FINITE' @ 'type/realax/real' @ sK0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/realax/real_le' @ ('const/sets/inf' @ sK0) @ sK3) = $true) | ~spl2_5),
% 1.67/1.31 inference(superposition,[status(thm)],[f25,f55])).
% 1.67/1.31 thf(f25,plain,(
% 1.67/1.31 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1) = $true) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f17])).
% 1.67/1.31 thf(f17,plain,(
% 1.67/1.31 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | (! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1) = $true)) & (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 1.67/1.31 inference(flattening,[status(thm)],[f16])).
% 1.67/1.31 thf(f16,plain,(
% 1.67/1.31 ! [X0 : 'type/realax/real' > $o] : ((! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1) = $true)) & (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0) = $true)) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 1.67/1.31 inference(ennf_transformation,[status(thm)],[f7])).
% 1.67/1.31 thf(f7,plain,(
% 1.67/1.31 ! [X0 : 'type/realax/real' > $o] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0) = $true) & ! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) = $true) => (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1) = $true))))),
% 1.67/1.31 inference(fool_elimination,[status(thm)],[f6])).
% 1.67/1.31 thf(f6,plain,(
% 1.67/1.31 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1))))),
% 1.67/1.31 inference(rectify,[status(thm)],[f2])).
% 1.67/1.31 thf(f2,axiom,(
% 1.67/1.31 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1))))),
% 1.67/1.31 file('/export/starexec/sandbox/tmp/tmp.7KaT4DNJoh/DTF2THF_10391.p','thm/sets/INF_FINITE_')).
% 1.67/1.31 thf(f127,plain,(
% 1.67/1.31 ~spl2_1 | ~spl2_3 | ~spl2_11),
% 1.67/1.31 inference(avatar_contradiction_clause,[status(thm)],[f126])).
% 1.67/1.31 thf(f126,plain,(
% 1.67/1.31 $false | (~spl2_1 | ~spl2_3 | ~spl2_11)),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.67/1.31 thf(f125,plain,(
% 1.67/1.31 ($false = $true) | (~spl2_1 | ~spl2_3 | ~spl2_11)),
% 1.67/1.31 inference(forward_demodulation,[status(thm)],[f120,f46])).
% 1.67/1.31 thf(f46,plain,(
% 1.67/1.31 ($false = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | ~spl2_3),
% 1.67/1.31 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.67/1.31 thf(f44,definition,(
% 1.67/1.31 spl2_3 <=> ($false = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)))),
% 1.67/1.31 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.67/1.31 thf(f120,plain,(
% 1.67/1.31 (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) = $true) | (~spl2_1 | ~spl2_11)),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.67/1.31 thf(f117,plain,(
% 1.67/1.31 ($false = $true) | (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) = $true) | (~spl2_1 | ~spl2_11)),
% 1.67/1.31 inference(superposition,[status(thm)],[f37,f89])).
% 1.67/1.31 thf(f89,plain,(
% 1.67/1.31 (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0) = $true) | ~spl2_11),
% 1.67/1.31 inference(avatar_component_clause,[status(thm)],[f87])).
% 1.67/1.31 thf(f87,definition,(
% 1.67/1.31 spl2_11 <=> (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0) = $true)),
% 1.67/1.31 introduced(definition,[new_symbols(naming,[spl2_11])],[avatar_definition])).
% 1.67/1.31 thf(f106,plain,(
% 1.67/1.31 spl2_11 | spl2_10),
% 1.67/1.31 inference(avatar_split_clause,[status(thm)],[f105,f83,f87])).
% 1.67/1.31 thf(f105,plain,(
% 1.67/1.31 (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f104])).
% 1.67/1.31 thf(f104,plain,(
% 1.67/1.31 ($true != $true) | (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK0) @ sK0) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)),
% 1.67/1.31 inference(superposition,[status(thm)],[f24,f22])).
% 1.67/1.31 thf(f24,plain,(
% 1.67/1.31 ( ! [X0 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0) = $true)) )),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f17])).
% 1.67/1.31 thf(f102,plain,(
% 1.67/1.31 ~spl2_2 | ~spl2_3),
% 1.67/1.31 inference(avatar_contradiction_clause,[status(thm)],[f101])).
% 1.67/1.31 thf(f101,plain,(
% 1.67/1.31 $false | (~spl2_2 | ~spl2_3)),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.67/1.31 thf(f99,plain,(
% 1.67/1.31 ($false = $true) | (~spl2_2 | ~spl2_3)),
% 1.67/1.31 inference(backward_demodulation,[status(thm)],[f41,f46])).
% 1.67/1.31 thf(f98,plain,(
% 1.67/1.31 ~spl2_10),
% 1.67/1.31 inference(avatar_contradiction_clause,[status(thm)],[f97])).
% 1.67/1.31 thf(f97,plain,(
% 1.67/1.31 $false | ~spl2_10),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.67/1.31 thf(f94,plain,(
% 1.67/1.31 (sK0 != sK0) | ~spl2_10),
% 1.67/1.31 inference(superposition,[status(thm)],[f23,f85])).
% 1.67/1.31 thf(f85,plain,(
% 1.67/1.31 ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ~spl2_10),
% 1.67/1.31 inference(avatar_component_clause,[status(thm)],[f83])).
% 1.67/1.31 thf(f23,plain,(
% 1.67/1.31 ('const/sets/EMPTY' @ 'type/realax/real' != sK0)),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.31 thf(f56,plain,(
% 1.67/1.31 spl2_5 | spl2_3),
% 1.67/1.31 inference(avatar_split_clause,[status(thm)],[f31,f44,f53])).
% 1.67/1.31 thf(f31,plain,(
% 1.67/1.31 ($false = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | (('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0) = $true)),
% 1.67/1.31 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.67/1.31 thf(f29,plain,(
% 1.67/1.31 ($false = (('const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0) => ('const/realax/real_le' @ sK1 @ sK3))) | ($false = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)))),
% 1.67/1.31 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.67/1.31 thf(f28,plain,(
% 1.67/1.31 ($false = ((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) => ('const/realax/real_le' @ sK1 @ Y0))) @ sK3)) | ($false = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)))),
% 1.67/1.31 inference(sigma_clausification,[status(thm)],[f27])).
% 1.67/1.31 thf(f27,plain,(
% 1.67/1.31 ($false = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0))) | ($false = (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) => ('const/realax/real_le' @ sK1 @ Y0)))))),
% 1.67/1.31 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.67/1.31 thf(f21,plain,(
% 1.67/1.31 (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) != (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) => ('const/realax/real_le' @ sK1 @ Y0)))))),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.31 thf(f51,plain,(
% 1.67/1.31 spl2_3 | spl2_4),
% 1.67/1.31 inference(avatar_split_clause,[status(thm)],[f30,f48,f44])).
% 1.67/1.31 thf(f30,plain,(
% 1.67/1.31 ($false = ('const/realax/real_le' @ sK1 @ sK3)) | ($false = ('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)))),
% 1.67/1.31 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.67/1.31 thf(f42,plain,(
% 1.67/1.31 spl2_1 | spl2_2),
% 1.67/1.31 inference(avatar_split_clause,[status(thm)],[f34,f39,f36])).
% 1.67/1.31 thf(f34,plain,(
% 1.67/1.31 ( ! [X1 : 'type/realax/real'] : (($false = ('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0)) | ($true = ('const/realax/real_le' @ sK1 @ X1)) | (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) = $true)) )),
% 1.67/1.31 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.67/1.31 thf(f33,plain,(
% 1.67/1.31 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK0) => ('const/realax/real_le' @ sK1 @ X1))) | (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) = $true)) )),
% 1.67/1.31 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.67/1.31 thf(f32,plain,(
% 1.67/1.31 ( ! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) = $true) | ($true = ((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) => ('const/realax/real_le' @ sK1 @ Y0))) @ X1))) )),
% 1.67/1.31 inference(pi_clausification,[status(thm)],[f26])).
% 1.67/1.31 thf(f26,plain,(
% 1.67/1.31 ($true = (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0) => ('const/realax/real_le' @ sK1 @ Y0))))) | (('const/realax/real_le' @ sK1 @ ('const/sets/inf' @ sK0)) = $true)),
% 1.67/1.31 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.67/1.31 % SZS output end Proof for DTF2THF_10391
% 1.67/1.31 % (10673)------------------------------
% 1.67/1.31 % (10673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (10673)Termination reason: Refutation
% 1.67/1.31
% 1.67/1.31 % (10673)Memory used [KB]: 5628
% 1.67/1.31 % (10673)Time elapsed: 0.008 s
% 1.67/1.31 % (10673)Instructions burned: 13 (million)
% 1.67/1.31 % (10673)------------------------------
% 1.67/1.31 % (10673)------------------------------
% 1.67/1.31 % (10670)Success in time 0.017 s
%------------------------------------------------------------------------------