%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA083^1 : 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 : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:38:50 AM UTC 2026
% Result : Theorem 0.22s 1.34s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 2 unt; 0 typ; 4 def)
% Number of atoms : 565 ( 162 equ; 0 cnn)
% Maximal formula atoms : 18 ( 9 avg)
% Number of connectives : 688 ( 104 ~; 96 |; 45 &; 417 @)
% ( 5 <=>; 19 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 76 ( 0 ^; 58 !; 18 ?; 76 :)
% 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_lt': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_6,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_10,type,
sK0: 'type/realax/real' > $o ).
thf(func_def_11,type,
sK1: 'type/realax/real' ).
thf(func_def_12,type,
sK2: 'type/realax/real' ).
thf(func_def_14,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK5: 'type/realax/real' ).
thf(f97,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f39,f44,f49,f80,f96]) ).
thf(f96,plain,
( ~ spl3_1
| spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f95]) ).
thf(f95,plain,
( $false
| ~ spl3_1
| spl3_3
| ~ spl3_4 ),
inference(subsumption_resolution,[status(thm)],[f94,f27]) ).
thf(f27,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( ( $true
!= ( 'const/realax/real_lt' @ sK1 @ sK2 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) ) )
| ( $true
!= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) )
& ( ! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ X3 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f22,f21]) ).
thf(f21,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true ) )
& ( ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X3 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) ) )
| ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( ? [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_lt' @ sK1 @ X2 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 ) ) )
| ( $true
!= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) )
& ( ! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ X3 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_lt' @ sK1 @ X2 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 ) ) )
=> ( ( $true
!= ( 'const/realax/real_lt' @ sK1 @ sK2 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true ) )
& ( ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X3 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) ) )
| ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true ) )
& ( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) )
| ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true ) )
& ( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) )
| ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
<~> ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
<~> ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $true ) )
<=> ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_lt' @ X1 @ X2 ) )
= ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ) ),
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 ) )
=> ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_lt' @ X1 @ X2 ) )
= ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ) ),
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 ) )
=> ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_lt' @ X1 @ X2 ) )
= ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bbF2jburJa/DTF2THF_28221.p','thm/sets/REAL_LT_INF_FINITE_') ).
thf(f94,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ~ spl3_1
| spl3_3
| ~ spl3_4 ),
inference(subsumption_resolution,[status(thm)],[f93,f28]) ).
thf(f28,plain,
( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f93,plain,
( ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ~ spl3_1
| spl3_3
| ~ spl3_4 ),
inference(subsumption_resolution,[status(thm)],[f91,f48]) ).
thf(f48,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl3_4
<=> ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f91,plain,
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ~ spl3_1
| spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
( ( $true != $true )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ~ spl3_1
| spl3_3 ),
inference(superposition,[status(thm)],[f88,f35]) ).
thf(f35,plain,
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl3_1
<=> ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f88,plain,
( ! [X0: 'type/realax/real' > $o] :
( ( $true
!= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ X0 ) ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) )
| spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ! [X0: 'type/realax/real' > $o] :
( ( $true != $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
!= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ X0 ) ) ) )
| spl3_3 ),
inference(superposition,[status(thm)],[f82,f25]) ).
thf(f25,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( '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 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,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(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( ( '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 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( '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 ) ) ),
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.bbF2jburJa/DTF2THF_28221.p','thm/sets/INF_FINITE_') ).
thf(f82,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ sK2 )
!= $true )
| ( ( 'const/realax/real_lt' @ sK1 @ X0 )
!= $true ) )
| spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_lt' @ sK1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ sK2 )
!= $true ) )
| spl3_3 ),
inference(superposition,[status(thm)],[f43,f24]) ).
thf(f24,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_lt' @ 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' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_lt' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_lt' @ X0 @ 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_lt' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_lt' @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
& ( ( 'const/realax/real_lt' @ X0 @ X1 )
= $true ) )
=> ( ( 'const/realax/real_lt' @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/realax/real_lt' @ X0 @ X1 ) )
=> ( 'const/realax/real_lt' @ 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_lt' @ X0 @ X1 ) )
=> ( 'const/realax/real_lt' @ X0 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.bbF2jburJa/DTF2THF_28221.p','thm/realarith/REAL_LTE_TRANS_') ).
thf(f43,plain,
( ( $true
!= ( 'const/realax/real_lt' @ sK1 @ sK2 ) )
| spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl3_3
<=> ( $true
= ( 'const/realax/real_lt' @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f80,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f79,f37,f33]) ).
thf(f37,definition,
( spl3_2
<=> ! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ X3 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f79,plain,
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ~ spl3_2 ),
inference(subsumption_resolution,[status(thm)],[f75,f28]) ).
thf(f75,plain,
( ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ~ spl3_2 ),
inference(subsumption_resolution,[status(thm)],[f74,f27]) ).
thf(f74,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f38,f26]) ).
thf(f26,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( '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(cnf_transformation,[status(thm)],[f17]) ).
thf(f38,plain,
( ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 ) )
| ( $true
= ( 'const/realax/real_lt' @ sK1 @ X3 ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f49,plain,
( ~ spl3_1
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f30,f46,f33]) ).
thf(f30,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) )
| ( $true
!= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f44,plain,
( ~ spl3_3
| ~ spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f31,f33,f41]) ).
thf(f31,plain,
( ( $true
!= ( 'const/realax/real_lt' @ sK1 @ sK2 ) )
| ( $true
!= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f39,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f29,f37,f33]) ).
thf(f29,plain,
! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ X3 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 ) )
| ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/inf' @ sK0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ANA083^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n029.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 03:50:14 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : ANA083^1 : TPTP v9.2.1. Released v7.0.0.
% 0.18/0.38 % Domain : Analysis
% 0.18/0.38 % Problem : REAL_LT_INF_FINITE
% 0.18/0.38 % Version : Especial.
% 0.18/0.38 % English :
% 0.18/0.38
% 0.18/0.38 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.18/0.38 % Source : [Kal16]
% 0.18/0.38 % Names : REAL_LT_INF_FINITE_.p [Kal16]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % Rating : 0.00 v7.1.0
% 0.18/0.38 % Syntax : Number of formulae : 10 ( 0 unt; 7 typ; 0 def)
% 0.18/0.38 % Number of atoms : 16 ( 3 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 5 ( 5 avg)
% 0.18/0.38 % Number of connectives : 41 ( 2 ~; 0 |; 4 &; 30 @)
% 0.18/0.38 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 9 ( 8 avg)
% 0.18/0.38 % Number of types : 2 ( 1 usr)
% 0.18/0.38 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 7 ( 6 usr; 0 con; 1-3 aty)
% 0.18/0.38 % Number of variables : 11 ( 0 ^; 8 !; 0 ?; 11 :)
% 0.18/0.38 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.38 % SPC : TH1_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : Exported from core HOL Light.
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf('thf_type_type/realax/real',type,
% 0.18/0.38 'type/realax/real': $tType ).
% 0.18/0.38
% 0.18/0.38 thf('thf_const_const/sets/inf',type,
% 0.18/0.38 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.18/0.38
% 0.18/0.38 thf('thf_const_const/sets/IN',type,
% 0.18/0.38 'const/sets/IN':
% 0.18/0.38 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf('thf_const_const/sets/FINITE',type,
% 0.18/0.38 'const/sets/FINITE':
% 0.18/0.38 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf('thf_const_const/sets/EMPTY',type,
% 0.18/0.38 'const/sets/EMPTY':
% 0.18/0.38 !>[A: $tType] : ( A > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf('thf_const_const/realax/real_lt',type,
% 0.18/0.38 'const/realax/real_lt': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.18/0.38
% 0.18/0.38 thf('thf_const_const/realax/real_le',type,
% 0.18/0.38 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.18/0.38
% 0.18/0.38 thf('thm/realarith/REAL_LTE_TRANS_',axiom,
% 0.18/0.38 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.18/0.38 ( ( ( 'const/realax/real_lt' @ A @ A0 )
% 0.18/0.38 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.18/0.38 => ( 'const/realax/real_lt' @ A @ A1 ) ) ).
% 0.18/0.38
% 0.18/0.38 thf('thm/sets/INF_FINITE_',axiom,
% 0.18/0.38 ! [A: 'type/realax/real' > $o] :
% 0.18/0.38 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.18/0.38 & ( A
% 0.18/0.38 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.18/0.38 => ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ A ) @ A )
% 0.18/0.38 & ! [A0: 'type/realax/real'] :
% 0.18/0.38 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.18/0.38 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf('thm/sets/REAL_LT_INF_FINITE_',conjecture,
% 0.18/0.38 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.18/0.38 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.18/0.38 & ( A
% 0.18/0.38 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.18/0.38 => ( ( 'const/realax/real_lt' @ A0 @ ( 'const/sets/inf' @ A ) )
% 0.18/0.38 = ( ! [A1: 'type/realax/real'] :
% 0.18/0.38 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.18/0.38 => ( 'const/realax/real_lt' @ A0 @ A1 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 0.22/1.30 ---- Embedded in THF ---
% 0.22/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.22/1.30 %%% Generated on Tue Feb 24 03:50:15 EST 2026
% 0.22/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.22/1.30 %%% Logic specification used:
% 0.22/1.30 %%% thf(spec, logic, $$dhol).
% 0.22/1.30
% 0.22/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.bbF2jburJa/DTF2DTF28221.p
% See solution above
% 0.22/1.30 ------------------------
% 0.22/1.31 ---- Cleaned THF ---
% 0.22/1.31 thf('thf_type_type/realax/real',type,
% 0.22/1.31 'type/realax/real': $tType ).
% 0.22/1.31
% 0.22/1.31 thf('thf_const_const/sets/inf',type,
% 0.22/1.31 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.22/1.31
% 0.22/1.31 thf('thf_const_const/sets/IN',type,
% 0.22/1.31 'const/sets/IN':
% 0.22/1.31 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.22/1.31
% 0.22/1.31 thf('thf_const_const/sets/FINITE',type,
% 0.22/1.31 'const/sets/FINITE':
% 0.22/1.31 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.22/1.31
% 0.22/1.31 thf('thf_const_const/sets/EMPTY',type,
% 0.22/1.31 'const/sets/EMPTY':
% 0.22/1.31 !>[A: $tType] : ( A > $o ) ).
% 0.22/1.31
% 0.22/1.31 thf('thf_const_const/realax/real_lt',type,
% 0.22/1.31 'const/realax/real_lt': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.22/1.31
% 0.22/1.31 thf('thf_const_const/realax/real_le',type,
% 0.22/1.31 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.22/1.31
% 0.22/1.31 thf('thm/realarith/REAL_LTE_TRANS_',axiom,
% 0.22/1.31 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.22/1.31 ( ( ( 'const/realax/real_lt' @ A @ A0 )
% 0.22/1.31 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.22/1.31 => ( 'const/realax/real_lt' @ A @ A1 ) ) ).
% 0.22/1.31
% 0.22/1.31 thf('thm/sets/INF_FINITE_',axiom,
% 0.22/1.31 ! [A: 'type/realax/real' > $o] :
% 0.22/1.31 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.22/1.31 & ( A
% 0.22/1.31 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.22/1.31 => ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ A ) @ A )
% 0.22/1.31 & ! [A0: 'type/realax/real'] :
% 0.22/1.31 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.22/1.31 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) ) ) ) ).
% 0.22/1.31
% 0.22/1.31 thf('thm/sets/REAL_LT_INF_FINITE_',conjecture,
% 0.22/1.31 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.22/1.31 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.22/1.31 & ( A
% 0.22/1.31 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.22/1.31 => ( ( 'const/realax/real_lt' @ A0 @ ( 'const/sets/inf' @ A ) )
% 0.22/1.31 = ( ! [A1: 'type/realax/real'] :
% 0.22/1.31 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.22/1.31 => ( 'const/realax/real_lt' @ A0 @ A1 ) ) ) ) ) ).
% 0.22/1.31 ------------------------
% 0.22/1.33 % (28318)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28221 for (2999ds/183Mi)
% 0.22/1.33 % (28319)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_28221 for (2999ds/4Mi)
% 0.22/1.33 % (28321)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28221 for (2999ds/2Mi)
% 0.22/1.33 % (28322)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_28221 for (2999ds/2Mi)
% 0.22/1.33 % (28320)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_28221 for (2999ds/27Mi)
% 0.22/1.33 % (28324)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28221 for (2999ds/18Mi)
% 0.22/1.33 % (28323)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_28221 for (2999ds/275Mi)
% 0.22/1.33 % (28321)Instruction limit reached!
% 0.22/1.33 % (28321)------------------------------
% 0.22/1.33 % (28321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (28321)Termination reason: Unknown
% 0.22/1.33 % (28321)Termination phase: Saturation
% 0.22/1.33
% 0.22/1.33 % (28321)Memory used [KB]: 5500
% 0.22/1.33 % (28321)Time elapsed: 0.003 s
% 0.22/1.33 % (28321)Instructions burned: 2 (million)
% 0.22/1.33 % (28321)------------------------------
% 0.22/1.33 % (28321)------------------------------
% 0.22/1.33 % (28322)Instruction limit reached!
% 0.22/1.33 % (28322)------------------------------
% 0.22/1.33 % (28322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (28322)Termination reason: Unknown
% 0.22/1.33 % (28322)Termination phase: Saturation
% 0.22/1.33
% 0.22/1.33 % (28322)Memory used [KB]: 5500
% 0.22/1.33 % (28322)Time elapsed: 0.003 s
% 0.22/1.33 % (28322)Instructions burned: 3 (million)
% 0.22/1.33 % (28322)------------------------------
% 0.22/1.33 % (28322)------------------------------
% 0.22/1.33 % (28319)Instruction limit reached!
% 0.22/1.33 % (28319)------------------------------
% 0.22/1.33 % (28319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (28319)Termination reason: Unknown
% 0.22/1.33 % (28319)Termination phase: Saturation
% 0.22/1.33
% 0.22/1.33 % (28319)Memory used [KB]: 5500
% 0.22/1.33 % (28319)Time elapsed: 0.004 s
% 0.22/1.33 % (28319)Instructions burned: 4 (million)
% 0.22/1.33 % (28319)------------------------------
% 0.22/1.33 % (28319)------------------------------
% 0.22/1.33 % (28323)First to succeed.
% 0.22/1.33 % (28324)Also succeeded, but the first one will report.
% 0.22/1.33 % (28318)Also succeeded, but the first one will report.
% 0.22/1.34 % (28323)Refutation found. Thanks to Tanya!
% 0.22/1.34 % SZS status Theorem for DTF2THF_28221
% 0.22/1.34 % SZS output start Proof for DTF2THF_28221
% 0.22/1.34 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.22/1.34 thf(func_def_0, type, 'type/realax/real': $tType).
% 0.22/1.34 thf(func_def_1, type, 'const/sets/inf': ('type/realax/real' > $o) > 'type/realax/real').
% 0.22/1.34 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 0.22/1.34 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 0.22/1.34 thf(func_def_4, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 0.22/1.34 thf(func_def_5, type, 'const/realax/real_lt': 'type/realax/real' > 'type/realax/real' > $o).
% 0.22/1.34 thf(func_def_6, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 0.22/1.34 thf(func_def_10, type, sK0: 'type/realax/real' > $o).
% 0.22/1.34 thf(func_def_11, type, sK1: 'type/realax/real').
% 0.22/1.34 thf(func_def_12, type, sK2: 'type/realax/real').
% 0.22/1.34 thf(func_def_14, type, ph4: !>[X0: $tType]:(X0)).
% 0.22/1.34 thf(func_def_15, type, sK5: 'type/realax/real').
% 0.22/1.34 thf(f97,plain,(
% 0.22/1.34 $false),
% 0.22/1.34 inference(avatar_sat_refutation,[status(thm)],[f39,f44,f49,f80,f96])).
% 0.22/1.34 thf(f96,plain,(
% 0.22/1.34 ~spl3_1 | spl3_3 | ~spl3_4),
% 0.22/1.34 inference(avatar_contradiction_clause,[status(thm)],[f95])).
% 0.22/1.34 thf(f95,plain,(
% 0.22/1.34 $false | (~spl3_1 | spl3_3 | ~spl3_4)),
% 0.22/1.34 inference(subsumption_resolution,[status(thm)],[f94,f27])).
% 0.22/1.34 thf(f27,plain,(
% 0.22/1.34 ('const/sets/EMPTY' @ 'type/realax/real' != sK0)),
% 0.22/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 0.22/1.34 thf(f23,plain,(
% 0.22/1.34 ((($true != ('const/realax/real_lt' @ sK1 @ sK2)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0))) | ($true != ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0)))) & (! [X3 : 'type/realax/real'] : (($true = ('const/realax/real_lt' @ sK1 @ X3)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0))) | ($true = ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0)))) & ($true = ('const/sets/FINITE' @ 'type/realax/real' @ sK0)) & ('const/sets/EMPTY' @ 'type/realax/real' != sK0)),
% 0.22/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f22,f21])).
% 0.22/1.34 thf(f21,plain,(
% 0.22/1.34 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((? [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) | (('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)) != $true)) & (! [X3 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X3) = $true) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) | (('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)) = $true)) & (('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ((? [X2 : 'type/realax/real'] : (($true != ('const/realax/real_lt' @ sK1 @ X2)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0))) | ($true != ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0)))) & (! [X3 : 'type/realax/real'] : (($true = ('const/realax/real_lt' @ sK1 @ X3)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0))) | ($true = ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0)))) & ($true = ('const/sets/FINITE' @ 'type/realax/real' @ sK0)) & ('const/sets/EMPTY' @ 'type/realax/real' != sK0))),
% 0.22/1.34 introduced(definition,[],[choice_axiom])).
% 0.22/1.34 thf(f22,plain,(
% 0.22/1.34 ? [X2 : 'type/realax/real'] : (($true != ('const/realax/real_lt' @ sK1 @ X2)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0))) => (($true != ('const/realax/real_lt' @ sK1 @ sK2)) & ($true = ('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)))),
% 0.22/1.34 introduced(definition,[],[choice_axiom])).
% 0.22/1.34 thf(f20,plain,(
% 0.22/1.34 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((? [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) | (('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)) != $true)) & (! [X3 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X3) = $true) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ X0))) | (('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)) = $true)) & (('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.22/1.34 inference(rectify,[status(thm)],[f19])).
% 0.22/1.34 thf(f19,plain,(
% 0.22/1.34 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((? [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) | (('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)) != $true)) & (! [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true)) | (('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)) = $true)) & (('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.22/1.34 inference(flattening,[status(thm)],[f18])).
% 0.22/1.34 thf(f18,plain,(
% 0.22/1.34 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (((? [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) != $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) | (('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)) != $true)) & (! [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true)) | (('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)) = $true))) & (('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.22/1.34 inference(nnf_transformation,[status(thm)],[f13])).
% 0.22/1.34 thf(f13,plain,(
% 0.22/1.34 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)) = $true) <~> ! [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true))) & (('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0))),
% 0.22/1.34 inference(flattening,[status(thm)],[f12])).
% 0.22/1.34 thf(f12,plain,(
% 0.22/1.34 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)) = $true) <~> ! [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) != $true))) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)))),
% 0.22/1.34 inference(ennf_transformation,[status(thm)],[f11])).
% 0.22/1.34 thf(f11,plain,(
% 0.22/1.34 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) => (('const/realax/real_lt' @ X1 @ X2) = $true)) <=> (('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0)) = $true)))),
% 0.22/1.34 inference(fool_elimination,[status(thm)],[f10])).
% 0.22/1.34 thf(f10,plain,(
% 0.22/1.34 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_lt' @ X1 @ X2)) = ('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0))))),
% 0.22/1.34 inference(rectify,[status(thm)],[f4])).
% 0.22/1.34 thf(f4,negated_conjecture,(
% 0.22/1.34 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_lt' @ X1 @ X2)) = ('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0))))),
% 0.22/1.34 inference(negated_conjecture,[status(cth)],[f3])).
% 0.22/1.34 thf(f3,conjecture,(
% 0.22/1.34 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_lt' @ X1 @ X2)) = ('const/realax/real_lt' @ X1 @ ('const/sets/inf' @ X0))))),
% 0.22/1.34 file('/export/starexec/sandbox/tmp/tmp.bbF2jburJa/DTF2THF_28221.p','thm/sets/REAL_LT_INF_FINITE_')).
% 0.22/1.34 thf(f94,plain,(
% 0.22/1.34 ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (~spl3_1 | spl3_3 | ~spl3_4)),
% 0.22/1.34 inference(subsumption_resolution,[status(thm)],[f93,f28])).
% 0.22/1.34 thf(f28,plain,(
% 0.22/1.34 ($true = ('const/sets/FINITE' @ 'type/realax/real' @ sK0))),
% 0.22/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 0.22/1.34 thf(f93,plain,(
% 0.22/1.34 ($true != ('const/sets/FINITE' @ 'type/realax/real' @ sK0)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (~spl3_1 | spl3_3 | ~spl3_4)),
% 0.22/1.34 inference(subsumption_resolution,[status(thm)],[f91,f48])).
% 0.22/1.34 thf(f48,plain,(
% 0.22/1.34 ($true = ('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)) | ~spl3_4),
% 0.22/1.34 inference(avatar_component_clause,[status(thm)],[f46])).
% 0.22/1.34 thf(f46,definition,(
% 0.22/1.34 spl3_4 <=> ($true = ('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0))),
% 0.22/1.34 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 0.22/1.34 thf(f91,plain,(
% 0.22/1.34 ($true != ('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != ('const/sets/FINITE' @ 'type/realax/real' @ sK0)) | (~spl3_1 | spl3_3)),
% 0.22/1.34 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 0.22/1.34 thf(f89,plain,(
% 0.22/1.34 ($true != $true) | ($true != ('const/sets/FINITE' @ 'type/realax/real' @ sK0)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (~spl3_1 | spl3_3)),
% 0.22/1.34 inference(superposition,[status(thm)],[f88,f35])).
% 0.22/1.34 thf(f35,plain,(
% 0.22/1.34 ($true = ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) | ~spl3_1),
% 0.22/1.34 inference(avatar_component_clause,[status(thm)],[f33])).
% 0.22/1.34 thf(f33,definition,(
% 0.22/1.34 spl3_1 <=> ($true = ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0)))),
% 0.22/1.34 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 0.22/1.34 thf(f88,plain,(
% 0.22/1.34 ( ! [X0 : 'type/realax/real' > $o] : (($true != ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ X0))) | (('const/sets/IN' @ 'type/realax/real' @ sK2 @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true)) ) | spl3_3),
% 0.22/1.34 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 0.22/1.34 thf(f87,plain,(
% 0.22/1.34 ( ! [X0 : 'type/realax/real' > $o] : (($true != $true) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | (('const/sets/IN' @ 'type/realax/real' @ sK2 @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ X0)))) ) | spl3_3),
% 0.22/1.34 inference(superposition,[status(thm)],[f82,f25])).
% 0.22/1.34 thf(f25,plain,(
% 0.22/1.34 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('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) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true)) )),
% 0.22/1.34 inference(cnf_transformation,[status(thm)],[f17])).
% 0.22/1.34 thf(f17,plain,(
% 0.22/1.34 ! [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))))),
% 0.22/1.34 inference(flattening,[status(thm)],[f16])).
% 0.22/1.34 thf(f16,plain,(
% 0.22/1.34 ! [X0 : 'type/realax/real' > $o] : (((('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))) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true)))),
% 0.22/1.34 inference(ennf_transformation,[status(thm)],[f7])).
% 0.22/1.34 thf(f7,plain,(
% 0.22/1.34 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('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)))),
% 0.22/1.34 inference(fool_elimination,[status(thm)],[f6])).
% 0.22/1.34 thf(f6,plain,(
% 0.22/1.34 ! [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))))),
% 0.22/1.34 inference(rectify,[status(thm)],[f2])).
% 0.22/1.34 thf(f2,axiom,(
% 0.22/1.34 ! [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))))),
% 0.22/1.34 file('/export/starexec/sandbox/tmp/tmp.bbF2jburJa/DTF2THF_28221.p','thm/sets/INF_FINITE_')).
% 0.22/1.34 thf(f82,plain,(
% 0.22/1.34 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ sK2) != $true) | (('const/realax/real_lt' @ sK1 @ X0) != $true)) ) | spl3_3),
% 0.22/1.34 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 0.22/1.34 thf(f81,plain,(
% 0.22/1.34 ( ! [X0 : 'type/realax/real'] : (($true != $true) | (('const/realax/real_lt' @ sK1 @ X0) != $true) | (('const/realax/real_le' @ X0 @ sK2) != $true)) ) | spl3_3),
% 0.22/1.34 inference(superposition,[status(thm)],[f43,f24])).
% 0.22/1.34 thf(f24,plain,(
% 0.22/1.34 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_lt' @ X0 @ X2) = $true) | (('const/realax/real_le' @ X1 @ X2) != $true) | (('const/realax/real_lt' @ X0 @ X1) != $true)) )),
% 0.22/1.34 inference(cnf_transformation,[status(thm)],[f15])).
% 0.22/1.34 thf(f15,plain,(
% 0.22/1.34 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) != $true) | (('const/realax/real_lt' @ X0 @ X1) != $true) | (('const/realax/real_lt' @ X0 @ X2) = $true))),
% 0.22/1.34 inference(flattening,[status(thm)],[f14])).
% 0.22/1.34 thf(f14,plain,(
% 0.22/1.34 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X0 @ X2) = $true) | ((('const/realax/real_le' @ X1 @ X2) != $true) | (('const/realax/real_lt' @ X0 @ X1) != $true)))),
% 0.22/1.34 inference(ennf_transformation,[status(thm)],[f9])).
% 0.22/1.34 thf(f9,plain,(
% 0.22/1.34 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2) = $true) & (('const/realax/real_lt' @ X0 @ X1) = $true)) => (('const/realax/real_lt' @ X0 @ X2) = $true))),
% 0.22/1.34 inference(fool_elimination,[status(thm)],[f8])).
% 0.22/1.34 thf(f8,plain,(
% 0.22/1.34 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_lt' @ X0 @ X1)) => ('const/realax/real_lt' @ X0 @ X2))),
% 0.22/1.34 inference(rectify,[status(thm)],[f1])).
% 0.22/1.34 thf(f1,axiom,(
% 0.22/1.34 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_lt' @ X0 @ X1)) => ('const/realax/real_lt' @ X0 @ X2))),
% 0.22/1.34 file('/export/starexec/sandbox/tmp/tmp.bbF2jburJa/DTF2THF_28221.p','thm/realarith/REAL_LTE_TRANS_')).
% 0.22/1.34 thf(f43,plain,(
% 0.22/1.34 ($true != ('const/realax/real_lt' @ sK1 @ sK2)) | spl3_3),
% 0.22/1.34 inference(avatar_component_clause,[status(thm)],[f41])).
% 0.22/1.34 thf(f41,definition,(
% 0.22/1.34 spl3_3 <=> ($true = ('const/realax/real_lt' @ sK1 @ sK2))),
% 0.22/1.34 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 0.22/1.34 thf(f80,plain,(
% 0.22/1.34 spl3_1 | ~spl3_2),
% 0.22/1.34 inference(avatar_split_clause,[status(thm)],[f79,f37,f33])).
% 0.22/1.34 thf(f37,definition,(
% 0.22/1.34 spl3_2 <=> ! [X3 : 'type/realax/real'] : (($true = ('const/realax/real_lt' @ sK1 @ X3)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0)))),
% 0.22/1.34 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 0.22/1.34 thf(f79,plain,(
% 0.22/1.34 ($true = ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) | ~spl3_2),
% 0.22/1.34 inference(subsumption_resolution,[status(thm)],[f75,f28])).
% 0.22/1.34 thf(f75,plain,(
% 0.22/1.34 ($true != ('const/sets/FINITE' @ 'type/realax/real' @ sK0)) | ($true = ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) | ~spl3_2),
% 0.22/1.34 inference(subsumption_resolution,[status(thm)],[f74,f27])).
% 0.22/1.34 thf(f74,plain,(
% 0.22/1.34 ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != ('const/sets/FINITE' @ 'type/realax/real' @ sK0)) | ($true = ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) | ~spl3_2),
% 0.22/1.34 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 0.22/1.34 thf(f73,plain,(
% 0.22/1.34 ($true != ('const/sets/FINITE' @ 'type/realax/real' @ sK0)) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true = ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0))) | ~spl3_2),
% 0.22/1.34 inference(superposition,[status(thm)],[f38,f26])).
% 0.22/1.34 thf(f26,plain,(
% 0.22/1.34 ( ! [X0 : 'type/realax/real' > $o] : ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0) = $true) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.22/1.34 inference(cnf_transformation,[status(thm)],[f17])).
% 0.22/1.34 thf(f38,plain,(
% 0.22/1.34 ( ! [X3 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0)) | ($true = ('const/realax/real_lt' @ sK1 @ X3))) ) | ~spl3_2),
% 0.22/1.34 inference(avatar_component_clause,[status(thm)],[f37])).
% 0.22/1.34 thf(f49,plain,(
% 0.22/1.34 ~spl3_1 | spl3_4),
% 0.22/1.34 inference(avatar_split_clause,[status(thm)],[f30,f46,f33])).
% 0.22/1.34 thf(f30,plain,(
% 0.22/1.34 ($true = ('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0)) | ($true != ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0)))),
% 0.22/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 0.22/1.34 thf(f44,plain,(
% 0.22/1.34 ~spl3_3 | ~spl3_1),
% 0.22/1.34 inference(avatar_split_clause,[status(thm)],[f31,f33,f41])).
% 0.22/1.34 thf(f31,plain,(
% 0.22/1.34 ($true != ('const/realax/real_lt' @ sK1 @ sK2)) | ($true != ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0)))),
% 0.22/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 0.22/1.34 thf(f39,plain,(
% 0.22/1.34 spl3_1 | spl3_2),
% 0.22/1.34 inference(avatar_split_clause,[status(thm)],[f29,f37,f33])).
% 0.22/1.34 thf(f29,plain,(
% 0.22/1.34 ( ! [X3 : 'type/realax/real'] : (($true = ('const/realax/real_lt' @ sK1 @ X3)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0)) | ($true = ('const/realax/real_lt' @ sK1 @ ('const/sets/inf' @ sK0)))) )),
% 0.22/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 0.22/1.34 % SZS output end Proof for DTF2THF_28221
% 0.22/1.34 % (28323)------------------------------
% 0.22/1.34 % (28323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.34 % (28323)Termination reason: Refutation
% 0.22/1.34
% 0.22/1.34 % (28323)Memory used [KB]: 5628
% 0.22/1.34 % (28323)Time elapsed: 0.007 s
% 0.22/1.34 % (28323)Instructions burned: 7 (million)
% 0.22/1.34 % (28323)------------------------------
% 0.22/1.34 % (28323)------------------------------
% 0.22/1.34 % (28317)Success in time 0.011 s
%------------------------------------------------------------------------------