%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA071^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 08:38:47 AM UTC 2026
% Result : Theorem 0.84s 0.89s
% Output : Refutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 2 unt; 0 typ; 4 def)
% Number of atoms : 571 ( 161 equ; 0 cnn)
% Maximal formula atoms : 18 ( 9 avg)
% Number of connectives : 692 ( 109 ~; 94 |; 51 &; 416 @)
% ( 5 <=>; 15 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 78 ( 0 ^; 54 !; 24 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_5,type,
'const/realax/real_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(f92,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f40,f44,f49,f80,f84,f91]) ).
thf(f91,plain,
( spl3_3
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f90,f37,f42]) ).
thf(f42,definition,
( spl3_3
<=> ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ sK1 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f37,definition,
( spl3_2
<=> ( ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f90,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_lt' @ sK1 @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) ) )
| spl3_2 ),
inference(subsumption_resolution,[status(thm)],[f89,f31]) ).
thf(f31,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true )
& ( ( ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ sK1 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
!= $true ) ) )
& ( ( ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ( ( ( 'const/realax/real_lt' @ sK1 @ sK2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true ) ) ) ),
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'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/sup' @ 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/sup' @ X0 ) )
= $true )
| ? [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X3 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true ) ) ) )
=> ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true )
& ( ( ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ sK1 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
!= $true ) ) )
& ( ( ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ? [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ X3 ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ X3 ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 )
= $true ) )
=> ( ( ( 'const/realax/real_lt' @ sK1 @ sK2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,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_lt' @ X1 @ ( 'const/sets/sup' @ 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/sup' @ X0 ) )
= $true )
| ? [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X3 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,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_lt' @ X1 @ ( 'const/sets/sup' @ 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/sup' @ X0 ) )
= $true )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[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_lt' @ X1 @ ( 'const/sets/sup' @ 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/sup' @ X0 ) )
= $true )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
<~> ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
<~> ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
<=> ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) ) ) ),
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_lt' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
& ( 'const/realax/real_lt' @ 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_lt' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
& ( 'const/realax/real_lt' @ 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_lt' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
& ( 'const/realax/real_lt' @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.sTi19EDxeV/DTF2THF_27020.p','thm/sets/REAL_LT_SUP_FINITE_') ).
thf(f89,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
!= ( 'const/realax/real_lt' @ sK1 @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) )
| spl3_2 ),
inference(subsumption_resolution,[status(thm)],[f88,f30]) ).
thf(f30,plain,
( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f88,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( $true
!= ( 'const/realax/real_lt' @ sK1 @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) )
| spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( $true
!= ( 'const/realax/real_lt' @ sK1 @ X0 ) ) )
| spl3_2 ),
inference(superposition,[status(thm)],[f86,f24]) ).
thf(f24,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true )
& ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true )
& ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(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/sup' @ X0 ) @ X0 )
= $true )
& ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ 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 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 ) ) ),
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 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.sTi19EDxeV/DTF2THF_27020.p','thm/sets/SUP_FINITE_') ).
thf(f86,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| ( $true
!= ( 'const/realax/real_lt' @ sK1 @ X0 ) ) )
| spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| ( $true
!= ( 'const/realax/real_lt' @ sK1 @ X0 ) ) )
| spl3_2 ),
inference(superposition,[status(thm)],[f38,f26]) ).
thf(f26,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)],[f17]) ).
thf(f17,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 @ X2 )
= $true )
| ( ( 'const/realax/real_lt' @ X0 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,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)],[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_lt' @ X0 @ X1 )
= $true ) )
=> ( ( 'const/realax/real_lt' @ 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_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/sandbox2/tmp/tmp.sTi19EDxeV/DTF2THF_27020.p','thm/realarith/REAL_LTE_TRANS_') ).
thf(f38,plain,
( ( ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f84,plain,
( ~ spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f83]) ).
thf(f83,plain,
( $false
| ~ spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(subsumption_resolution,[status(thm)],[f82,f48]) ).
thf(f48,plain,
( ( ( 'const/realax/real_lt' @ sK1 @ sK2 )
= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl3_4
<=> ( ( 'const/realax/real_lt' @ sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f82,plain,
( ( ( 'const/realax/real_lt' @ sK1 @ sK2 )
!= $true )
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( ( 'const/realax/real_lt' @ sK1 @ sK2 )
!= $true )
| ( $true != $true )
| ~ spl3_1
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f43,f35]) ).
thf(f35,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl3_1
<=> ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f43,plain,
( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
!= $true )
| ( ( 'const/realax/real_lt' @ sK1 @ X2 )
!= $true ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f80,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f79]) ).
thf(f79,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f78,f30]) ).
thf(f78,plain,
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ~ spl3_2
| ~ spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f77,f31]) ).
thf(f77,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ~ spl3_2
| ~ spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f76,f39]) ).
thf(f39,plain,
( ( ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f76,plain,
( ( ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true != $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f43,f25]) ).
thf(f25,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f49,plain,
( spl3_4
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f28,f37,f46]) ).
thf(f28,plain,
( ( ( 'const/realax/real_lt' @ sK1 @ sK2 )
= $true )
| ( ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f44,plain,
( spl3_3
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f29,f37,f42]) ).
thf(f29,plain,
! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ sK1 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
!= $true )
| ( ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f40,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f27,f37,f33]) ).
thf(f27,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true )
| ( ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ANA071^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.24 % Computer : n012.cluster.edu
% 0.08/0.24 % Model : x86_64 x86_64
% 0.08/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.24 % Memory : 8042.1875MB
% 0.08/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.24 % CPULimit : 300
% 0.08/0.24 % WCLimit : 300
% 0.08/0.24 % DateTime : Tue Feb 24 03:50:00 EST 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.31 ---- Original DTF file ---
% 0.08/0.31 thf(spec,logic,$$dhol).
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 % File : ANA071^1 : TPTP v9.2.1. Released v7.0.0.
% 0.08/0.31 % Domain : Analysis
% 0.08/0.31 % Problem : REAL_LT_SUP_FINITE
% 0.08/0.31 % Version : Especial.
% 0.08/0.31 % English :
% 0.08/0.31
% 0.08/0.31 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.08/0.31 % Source : [Kal16]
% 0.08/0.31 % Names : REAL_LT_SUP_FINITE_.p [Kal16]
% 0.08/0.31
% 0.08/0.31 % Status : Theorem
% 0.08/0.31 % Rating : 0.00 v7.1.0
% 0.08/0.31 % Syntax : Number of formulae : 10 ( 0 unt; 7 typ; 0 def)
% 0.08/0.31 % Number of atoms : 16 ( 3 equ; 0 cnn)
% 0.08/0.31 % Maximal formula atoms : 5 ( 5 avg)
% 0.08/0.31 % Number of connectives : 41 ( 2 ~; 0 |; 5 &; 30 @)
% 0.08/0.31 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.08/0.31 % Maximal formula depth : 9 ( 8 avg)
% 0.08/0.31 % Number of types : 2 ( 1 usr)
% 0.08/0.31 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.08/0.31 % Number of symbols : 7 ( 6 usr; 0 con; 1-3 aty)
% 0.08/0.31 % Number of variables : 11 ( 0 ^; 7 !; 1 ?; 11 :)
% 0.08/0.31 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.08/0.31 % SPC : TH1_THM_EQU_NAR
% 0.08/0.31
% 0.08/0.31 % Comments : Exported from core HOL Light.
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 thf('thf_type_type/realax/real',type,
% 0.08/0.31 'type/realax/real': $tType ).
% 0.08/0.31
% 0.08/0.31 thf('thf_const_const/sets/sup',type,
% 0.08/0.31 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.08/0.31
% 0.08/0.31 thf('thf_const_const/sets/IN',type,
% 0.08/0.31 'const/sets/IN':
% 0.08/0.31 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.08/0.31
% 0.08/0.31 thf('thf_const_const/sets/FINITE',type,
% 0.08/0.31 'const/sets/FINITE':
% 0.08/0.31 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.08/0.31
% 0.08/0.31 thf('thf_const_const/sets/EMPTY',type,
% 0.08/0.31 'const/sets/EMPTY':
% 0.08/0.31 !>[A: $tType] : ( A > $o ) ).
% 0.08/0.31
% 0.08/0.31 thf('thf_const_const/realax/real_lt',type,
% 0.08/0.31 'const/realax/real_lt': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.08/0.31
% 0.08/0.31 thf('thf_const_const/realax/real_le',type,
% 0.08/0.31 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.08/0.31
% 0.08/0.31 thf('thm/realarith/REAL_LTE_TRANS_',axiom,
% 0.08/0.31 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.08/0.31 ( ( ( 'const/realax/real_lt' @ A @ A0 )
% 0.08/0.31 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.08/0.31 => ( 'const/realax/real_lt' @ A @ A1 ) ) ).
% 0.08/0.31
% 0.08/0.31 thf('thm/sets/SUP_FINITE_',axiom,
% 0.08/0.31 ! [A: 'type/realax/real' > $o] :
% 0.08/0.31 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.08/0.31 & ( A
% 0.08/0.31 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.08/0.31 => ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ A ) @ A )
% 0.08/0.31 & ! [A0: 'type/realax/real'] :
% 0.08/0.31 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.08/0.31 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf('thm/sets/REAL_LT_SUP_FINITE_',conjecture,
% 0.08/0.31 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.08/0.31 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.08/0.31 & ( A
% 0.08/0.31 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.08/0.31 => ( ( 'const/realax/real_lt' @ A0 @ ( 'const/sets/sup' @ A ) )
% 0.08/0.31 = ( ? [A1: 'type/realax/real'] :
% 0.08/0.31 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.08/0.31 & ( 'const/realax/real_lt' @ A0 @ A1 ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 ------------------------
% 0.84/0.86 ---- Embedded in THF ---
% 0.84/0.87 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.84/0.87 %%% Generated on Tue Feb 24 03:50:01 EST 2026
% 0.84/0.87 %%% using '$$dhol' embedding, version 1.3.0.
% 0.84/0.87 %%% Logic specification used:
% 0.84/0.87 %%% thf(spec, logic, $$dhol).
% 0.84/0.87
% 0.84/0.87 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.sTi19EDxeV/DTF2DTF27020.p
% See solution above
% 0.84/0.87 ------------------------
% 0.84/0.87 ---- Cleaned THF ---
% 0.84/0.87 thf('thf_type_type/realax/real',type,
% 0.84/0.87 'type/realax/real': $tType ).
% 0.84/0.87
% 0.84/0.87 thf('thf_const_const/sets/sup',type,
% 0.84/0.87 'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.84/0.87
% 0.84/0.87 thf('thf_const_const/sets/IN',type,
% 0.84/0.87 'const/sets/IN':
% 0.84/0.87 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.84/0.87
% 0.84/0.87 thf('thf_const_const/sets/FINITE',type,
% 0.84/0.87 'const/sets/FINITE':
% 0.84/0.87 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.84/0.87
% 0.84/0.87 thf('thf_const_const/sets/EMPTY',type,
% 0.84/0.87 'const/sets/EMPTY':
% 0.84/0.87 !>[A: $tType] : ( A > $o ) ).
% 0.84/0.87
% 0.84/0.87 thf('thf_const_const/realax/real_lt',type,
% 0.84/0.87 'const/realax/real_lt': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.84/0.87
% 0.84/0.87 thf('thf_const_const/realax/real_le',type,
% 0.84/0.87 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.84/0.87
% 0.84/0.87 thf('thm/realarith/REAL_LTE_TRANS_',axiom,
% 0.84/0.87 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.84/0.87 ( ( ( 'const/realax/real_lt' @ A @ A0 )
% 0.84/0.87 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.84/0.87 => ( 'const/realax/real_lt' @ A @ A1 ) ) ).
% 0.84/0.87
% 0.84/0.87 thf('thm/sets/SUP_FINITE_',axiom,
% 0.84/0.87 ! [A: 'type/realax/real' > $o] :
% 0.84/0.87 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.84/0.87 & ( A
% 0.84/0.87 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.84/0.87 => ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ A ) @ A )
% 0.84/0.87 & ! [A0: 'type/realax/real'] :
% 0.84/0.87 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.84/0.87 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/sup' @ A ) ) ) ) ) ).
% 0.84/0.87
% 0.84/0.87 thf('thm/sets/REAL_LT_SUP_FINITE_',conjecture,
% 0.84/0.87 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real'] :
% 0.84/0.87 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.84/0.87 & ( A
% 0.84/0.87 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.84/0.87 => ( ( 'const/realax/real_lt' @ A0 @ ( 'const/sets/sup' @ A ) )
% 0.84/0.87 = ( ? [A1: 'type/realax/real'] :
% 0.84/0.87 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.84/0.87 & ( 'const/realax/real_lt' @ A0 @ A1 ) ) ) ) ) ).
% 0.84/0.87 ------------------------
% 0.84/0.88 % (27221)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_27020 for (3000ds/27Mi)
% 0.84/0.88 % (27222)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27020 for (3000ds/2Mi)
% 0.84/0.88 % (27219)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27020 for (3000ds/183Mi)
% 0.84/0.88 % (27220)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_27020 for (3000ds/4Mi)
% 0.84/0.88 % (27223)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_27020 for (3000ds/2Mi)
% 0.84/0.88 % (27225)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27020 for (3000ds/18Mi)
% 0.84/0.88 % (27224)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_27020 for (3000ds/275Mi)
% 0.84/0.88 % (27222)Instruction limit reached!
% 0.84/0.88 % (27222)------------------------------
% 0.84/0.88 % (27222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.84/0.88 % (27222)Termination reason: Unknown
% 0.84/0.88 % (27222)Termination phase: Saturation
% 0.84/0.88
% 0.84/0.88 % (27222)Memory used [KB]: 895
% 0.84/0.88 % (27222)Time elapsed: 0.002 s
% 0.84/0.88 % (27222)Instructions burned: 2 (million)
% 0.84/0.88 % (27222)------------------------------
% 0.84/0.88 % (27222)------------------------------
% 0.84/0.88 % (27223)Instruction limit reached!
% 0.84/0.88 % (27223)------------------------------
% 0.84/0.88 % (27223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.84/0.88 % (27223)Termination reason: Unknown
% 0.84/0.88 % (27223)Termination phase: Saturation
% 0.84/0.88
% 0.84/0.88 % (27223)Memory used [KB]: 895
% 0.84/0.88 % (27223)Time elapsed: 0.002 s
% 0.84/0.88 % (27223)Instructions burned: 2 (million)
% 0.84/0.88 % (27223)------------------------------
% 0.84/0.88 % (27223)------------------------------
% 0.84/0.89 % (27220)Instruction limit reached!
% 0.84/0.89 % (27220)------------------------------
% 0.84/0.89 % (27220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.84/0.89 % (27220)Termination reason: Unknown
% 0.84/0.89 % (27220)Termination phase: Saturation
% 0.84/0.89
% 0.84/0.89 % (27220)Memory used [KB]: 5500
% 0.84/0.89 % (27220)Time elapsed: 0.003 s
% 0.84/0.89 % (27220)Instructions burned: 4 (million)
% 0.84/0.89 % (27220)------------------------------
% 0.84/0.89 % (27220)------------------------------
% 0.84/0.89 % (27224)First to succeed.
% 0.84/0.89 % (27225)Also succeeded, but the first one will report.
% 0.84/0.89 % (27219)Also succeeded, but the first one will report.
% 0.84/0.89 % (27224)Refutation found. Thanks to Tanya!
% 0.84/0.89 % SZS status Theorem for DTF2THF_27020
% 0.84/0.89 % SZS output start Proof for DTF2THF_27020
% 0.84/0.89 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.84/0.89 thf(func_def_0, type, 'type/realax/real': $tType).
% 0.84/0.89 thf(func_def_1, type, 'const/sets/sup': ('type/realax/real' > $o) > 'type/realax/real').
% 0.84/0.89 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 0.84/0.89 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 0.84/0.89 thf(func_def_4, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 0.84/0.89 thf(func_def_5, type, 'const/realax/real_lt': 'type/realax/real' > 'type/realax/real' > $o).
% 0.84/0.89 thf(func_def_6, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 0.84/0.89 thf(func_def_10, type, sK0: 'type/realax/real' > $o).
% 0.84/0.89 thf(func_def_11, type, sK1: 'type/realax/real').
% 0.84/0.89 thf(func_def_12, type, sK2: 'type/realax/real').
% 0.84/0.89 thf(func_def_14, type, ph4: !>[X0: $tType]:(X0)).
% 0.84/0.89 thf(func_def_15, type, sK5: 'type/realax/real').
% 0.84/0.89 thf(f92,plain,(
% 0.84/0.89 $false),
% 0.84/0.89 inference(avatar_sat_refutation,[status(thm)],[f40,f44,f49,f80,f84,f91])).
% 0.84/0.89 thf(f91,plain,(
% 0.84/0.89 spl3_3 | spl3_2),
% 0.84/0.89 inference(avatar_split_clause,[status(thm)],[f90,f37,f42])).
% 0.84/0.89 thf(f42,definition,(
% 0.84/0.89 spl3_3 <=> ! [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ sK1 @ X2) != $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0) != $true))),
% 0.84/0.89 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 0.84/0.89 thf(f37,definition,(
% 0.84/0.89 spl3_2 <=> (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)) = $true)),
% 0.84/0.89 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 0.84/0.89 thf(f90,plain,(
% 0.84/0.89 ( ! [X0 : 'type/realax/real'] : (($true != ('const/realax/real_lt' @ sK1 @ X0)) | ($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0))) ) | spl3_2),
% 0.84/0.89 inference(subsumption_resolution,[status(thm)],[f89,f31])).
% 0.84/0.89 thf(f31,plain,(
% 0.84/0.89 ('const/sets/EMPTY' @ 'type/realax/real' != sK0)),
% 0.84/0.89 inference(cnf_transformation,[status(thm)],[f23])).
% 0.84/0.89 thf(f23,plain,(
% 0.84/0.89 ('const/sets/EMPTY' @ 'type/realax/real' != sK0) & (('const/sets/FINITE' @ 'type/realax/real' @ sK0) = $true) & ((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)) != $true) | ! [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ sK1 @ X2) != $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0) != $true))) & ((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)) = $true) | ((('const/realax/real_lt' @ sK1 @ sK2) = $true) & (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) = $true)))),
% 0.84/0.89 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f22,f21])).
% 0.84/0.89 thf(f21,plain,(
% 0.84/0.89 ? [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_lt' @ X1 @ ('const/sets/sup' @ 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/sup' @ X0)) = $true) | ? [X3 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X3) = $true) & (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true)))) => (('const/sets/EMPTY' @ 'type/realax/real' != sK0) & (('const/sets/FINITE' @ 'type/realax/real' @ sK0) = $true) & ((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)) != $true) | ! [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ sK1 @ X2) != $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0) != $true))) & ((('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)) = $true) | ? [X3 : 'type/realax/real'] : (($true = ('const/realax/real_lt' @ sK1 @ X3)) & (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0) = $true))))),
% 0.84/0.89 introduced(definition,[],[choice_axiom])).
% 0.84/0.89 thf(f22,plain,(
% 0.84/0.89 ? [X3 : 'type/realax/real'] : (($true = ('const/realax/real_lt' @ sK1 @ X3)) & (('const/sets/IN' @ 'type/realax/real' @ X3 @ sK0) = $true)) => ((('const/realax/real_lt' @ sK1 @ sK2) = $true) & (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) = $true))),
% 0.84/0.89 introduced(definition,[],[choice_axiom])).
% 0.84/0.89 thf(f20,plain,(
% 0.84/0.89 ? [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_lt' @ X1 @ ('const/sets/sup' @ 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/sup' @ X0)) = $true) | ? [X3 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X3) = $true) & (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true))))),
% 0.84/0.89 inference(rectify,[status(thm)],[f19])).
% 0.84/0.89 thf(f19,plain,(
% 0.84/0.89 ? [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_lt' @ X1 @ ('const/sets/sup' @ 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/sup' @ X0)) = $true) | ? [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) = $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true))))),
% 0.84/0.89 inference(flattening,[status(thm)],[f18])).
% 0.84/0.89 thf(f18,plain,(
% 0.84/0.89 ? [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_lt' @ X1 @ ('const/sets/sup' @ 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/sup' @ X0)) = $true) | ? [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) = $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)))))),
% 0.84/0.89 inference(nnf_transformation,[status(thm)],[f15])).
% 0.84/0.89 thf(f15,plain,(
% 0.84/0.89 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' != X0) & (('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & (? [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) = $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true)) <~> (('const/realax/real_lt' @ X1 @ ('const/sets/sup' @ X0)) = $true)))),
% 0.84/0.89 inference(flattening,[status(thm)],[f14])).
% 0.84/0.89 thf(f14,plain,(
% 0.84/0.89 ? [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/sup' @ X0)) = $true)) & ((('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)))),
% 0.84/0.89 inference(ennf_transformation,[status(thm)],[f9])).
% 0.84/0.89 thf(f9,plain,(
% 0.84/0.89 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (((('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ((('const/realax/real_lt' @ X1 @ ('const/sets/sup' @ X0)) = $true) <=> ? [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ X1 @ X2) = $true) & (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true))))),
% 0.84/0.89 inference(fool_elimination,[status(thm)],[f8])).
% 0.84/0.89 thf(f8,plain,(
% 0.84/0.89 ~! [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_lt' @ X1 @ ('const/sets/sup' @ X0)) = ? [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) & ('const/realax/real_lt' @ X1 @ X2))))),
% 0.84/0.89 inference(rectify,[status(thm)],[f4])).
% 0.84/0.89 thf(f4,negated_conjecture,(
% 0.84/0.89 ~! [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_lt' @ X1 @ ('const/sets/sup' @ X0)) = ? [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) & ('const/realax/real_lt' @ X1 @ X2))))),
% 0.84/0.89 inference(negated_conjecture,[status(cth)],[f3])).
% 0.84/0.89 thf(f3,conjecture,(
% 0.84/0.89 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (('const/realax/real_lt' @ X1 @ ('const/sets/sup' @ X0)) = ? [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) & ('const/realax/real_lt' @ X1 @ X2))))),
% 0.84/0.89 file('/export/starexec/sandbox2/tmp/tmp.sTi19EDxeV/DTF2THF_27020.p','thm/sets/REAL_LT_SUP_FINITE_')).
% 0.84/0.89 thf(f89,plain,(
% 0.84/0.89 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0)) | ($true != ('const/realax/real_lt' @ sK1 @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) ) | spl3_2),
% 0.84/0.89 inference(subsumption_resolution,[status(thm)],[f88,f30])).
% 0.84/0.89 thf(f30,plain,(
% 0.84/0.89 (('const/sets/FINITE' @ 'type/realax/real' @ sK0) = $true)),
% 0.84/0.89 inference(cnf_transformation,[status(thm)],[f23])).
% 0.84/0.89 thf(f88,plain,(
% 0.84/0.89 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0)) | (('const/sets/FINITE' @ 'type/realax/real' @ sK0) != $true) | ($true != ('const/realax/real_lt' @ sK1 @ X0)) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0)) ) | spl3_2),
% 0.84/0.89 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 0.84/0.89 thf(f87,plain,(
% 0.84/0.89 ( ! [X0 : 'type/realax/real'] : (($true != ('const/sets/IN' @ 'type/realax/real' @ X0 @ sK0)) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/sets/FINITE' @ 'type/realax/real' @ sK0) != $true) | ($true != ('const/realax/real_lt' @ sK1 @ X0))) ) | spl3_2),
% 0.84/0.89 inference(superposition,[status(thm)],[f86,f24])).
% 0.84/0.89 thf(f24,plain,(
% 0.84/0.89 ( ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true)) )),
% 0.84/0.89 inference(cnf_transformation,[status(thm)],[f13])).
% 0.84/0.89 thf(f13,plain,(
% 0.84/0.89 ! [X0 : 'type/realax/real' > $o] : (((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ X0) @ X0) = $true) & ! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true))) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.84/0.89 inference(flattening,[status(thm)],[f12])).
% 0.84/0.89 thf(f12,plain,(
% 0.84/0.89 ! [X0 : 'type/realax/real' > $o] : (((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ X0) @ X0) = $true) & ! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) != $true) | (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true))) | ((('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 0.84/0.89 inference(ennf_transformation,[status(thm)],[f7])).
% 0.84/0.89 thf(f7,plain,(
% 0.84/0.89 ! [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/sup' @ X0) @ X0) = $true) & ! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) = $true) => (('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0)) = $true))))),
% 0.84/0.89 inference(fool_elimination,[status(thm)],[f6])).
% 0.84/0.89 thf(f6,plain,(
% 0.84/0.89 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) & ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ X0) @ X0)))),
% 0.84/0.89 inference(rectify,[status(thm)],[f2])).
% 0.84/0.89 thf(f2,axiom,(
% 0.84/0.89 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ X1 @ ('const/sets/sup' @ X0))) & ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ X0) @ X0)))),
% 0.84/0.89 file('/export/starexec/sandbox2/tmp/tmp.sTi19EDxeV/DTF2THF_27020.p','thm/sets/SUP_FINITE_')).
% 0.84/0.89 thf(f86,plain,(
% 0.84/0.89 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK0)) != $true) | ($true != ('const/realax/real_lt' @ sK1 @ X0))) ) | spl3_2),
% 0.84/0.89 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 0.84/0.89 thf(f85,plain,(
% 0.84/0.89 ( ! [X0 : 'type/realax/real'] : (($true != $true) | (('const/realax/real_le' @ X0 @ ('const/sets/sup' @ sK0)) != $true) | ($true != ('const/realax/real_lt' @ sK1 @ X0))) ) | spl3_2),
% 0.84/0.89 inference(superposition,[status(thm)],[f38,f26])).
% 0.84/0.89 thf(f26,plain,(
% 0.84/0.89 ( ! [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)) )),
% 0.84/0.89 inference(cnf_transformation,[status(thm)],[f17])).
% 0.84/0.89 thf(f17,plain,(
% 0.84/0.89 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) != $true) | (('const/realax/real_lt' @ X0 @ X2) = $true) | (('const/realax/real_lt' @ X0 @ X1) != $true))),
% 0.84/0.89 inference(flattening,[status(thm)],[f16])).
% 0.84/0.89 thf(f16,plain,(
% 0.84/0.89 ! [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)))),
% 0.84/0.89 inference(ennf_transformation,[status(thm)],[f11])).
% 0.84/0.89 thf(f11,plain,(
% 0.84/0.89 ! [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))),
% 0.84/0.89 inference(fool_elimination,[status(thm)],[f10])).
% 0.84/0.89 thf(f10,plain,(
% 0.84/0.89 ! [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))),
% 0.84/0.89 inference(rectify,[status(thm)],[f1])).
% 0.84/0.89 thf(f1,axiom,(
% 0.84/0.89 ! [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))),
% 0.84/0.89 file('/export/starexec/sandbox2/tmp/tmp.sTi19EDxeV/DTF2THF_27020.p','thm/realarith/REAL_LTE_TRANS_')).
% 0.84/0.89 thf(f38,plain,(
% 0.84/0.89 (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)) != $true) | spl3_2),
% 0.84/0.89 inference(avatar_component_clause,[status(thm)],[f37])).
% 0.84/0.89 thf(f84,plain,(
% 0.84/0.89 ~spl3_1 | ~spl3_3 | ~spl3_4),
% 0.84/0.89 inference(avatar_contradiction_clause,[status(thm)],[f83])).
% 0.84/0.89 thf(f83,plain,(
% 0.84/0.89 $false | (~spl3_1 | ~spl3_3 | ~spl3_4)),
% 0.84/0.89 inference(subsumption_resolution,[status(thm)],[f82,f48])).
% 0.84/0.89 thf(f48,plain,(
% 0.84/0.89 (('const/realax/real_lt' @ sK1 @ sK2) = $true) | ~spl3_4),
% 0.84/0.89 inference(avatar_component_clause,[status(thm)],[f46])).
% 0.84/0.89 thf(f46,definition,(
% 0.84/0.89 spl3_4 <=> (('const/realax/real_lt' @ sK1 @ sK2) = $true)),
% 0.84/0.89 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 0.84/0.89 thf(f82,plain,(
% 0.84/0.89 (('const/realax/real_lt' @ sK1 @ sK2) != $true) | (~spl3_1 | ~spl3_3)),
% 0.84/0.89 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 0.84/0.89 thf(f81,plain,(
% 0.84/0.89 (('const/realax/real_lt' @ sK1 @ sK2) != $true) | ($true != $true) | (~spl3_1 | ~spl3_3)),
% 0.84/0.89 inference(superposition,[status(thm)],[f43,f35])).
% 0.84/0.89 thf(f35,plain,(
% 0.84/0.89 (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) = $true) | ~spl3_1),
% 0.84/0.89 inference(avatar_component_clause,[status(thm)],[f33])).
% 0.84/0.89 thf(f33,definition,(
% 0.84/0.89 spl3_1 <=> (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) = $true)),
% 0.84/0.89 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 0.84/0.89 thf(f43,plain,(
% 0.84/0.89 ( ! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0) != $true) | (('const/realax/real_lt' @ sK1 @ X2) != $true)) ) | ~spl3_3),
% 0.84/0.89 inference(avatar_component_clause,[status(thm)],[f42])).
% 0.84/0.89 thf(f80,plain,(
% 0.84/0.89 ~spl3_2 | ~spl3_3),
% 0.84/0.89 inference(avatar_contradiction_clause,[status(thm)],[f79])).
% 0.84/0.89 thf(f79,plain,(
% 0.84/0.89 $false | (~spl3_2 | ~spl3_3)),
% 0.84/0.89 inference(subsumption_resolution,[status(thm)],[f78,f30])).
% 0.84/0.89 thf(f78,plain,(
% 0.84/0.89 (('const/sets/FINITE' @ 'type/realax/real' @ sK0) != $true) | (~spl3_2 | ~spl3_3)),
% 0.84/0.89 inference(subsumption_resolution,[status(thm)],[f77,f31])).
% 0.84/0.89 thf(f77,plain,(
% 0.84/0.89 ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/sets/FINITE' @ 'type/realax/real' @ sK0) != $true) | (~spl3_2 | ~spl3_3)),
% 0.84/0.89 inference(subsumption_resolution,[status(thm)],[f76,f39])).
% 0.84/0.89 thf(f39,plain,(
% 0.84/0.89 (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)) = $true) | ~spl3_2),
% 0.84/0.89 inference(avatar_component_clause,[status(thm)],[f37])).
% 0.84/0.89 thf(f76,plain,(
% 0.84/0.89 (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | (('const/sets/FINITE' @ 'type/realax/real' @ sK0) != $true) | ~spl3_3),
% 0.84/0.89 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 0.84/0.89 thf(f75,plain,(
% 0.84/0.89 (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK0) | ($true != $true) | (('const/sets/FINITE' @ 'type/realax/real' @ sK0) != $true) | ~spl3_3),
% 0.84/0.89 inference(superposition,[status(thm)],[f43,f25])).
% 0.84/0.89 thf(f25,plain,(
% 0.84/0.89 ( ! [X0 : 'type/realax/real' > $o] : ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/sup' @ X0) @ X0) = $true) | (('const/sets/FINITE' @ 'type/realax/real' @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.84/0.89 inference(cnf_transformation,[status(thm)],[f13])).
% 0.84/0.89 thf(f49,plain,(
% 0.84/0.89 spl3_4 | spl3_2),
% 0.84/0.89 inference(avatar_split_clause,[status(thm)],[f28,f37,f46])).
% 0.84/0.89 thf(f28,plain,(
% 0.84/0.89 (('const/realax/real_lt' @ sK1 @ sK2) = $true) | (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)) = $true)),
% 0.84/0.89 inference(cnf_transformation,[status(thm)],[f23])).
% 0.84/0.89 thf(f44,plain,(
% 0.84/0.89 spl3_3 | ~spl3_2),
% 0.84/0.89 inference(avatar_split_clause,[status(thm)],[f29,f37,f42])).
% 0.84/0.89 thf(f29,plain,(
% 0.84/0.89 ( ! [X2 : 'type/realax/real'] : ((('const/realax/real_lt' @ sK1 @ X2) != $true) | (('const/sets/IN' @ 'type/realax/real' @ X2 @ sK0) != $true) | (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)) != $true)) )),
% 0.84/0.89 inference(cnf_transformation,[status(thm)],[f23])).
% 0.84/0.89 thf(f40,plain,(
% 0.84/0.89 spl3_1 | spl3_2),
% 0.84/0.89 inference(avatar_split_clause,[status(thm)],[f27,f37,f33])).
% 0.84/0.89 thf(f27,plain,(
% 0.84/0.89 (('const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0) = $true) | (('const/realax/real_lt' @ sK1 @ ('const/sets/sup' @ sK0)) = $true)),
% 0.84/0.89 inference(cnf_transformation,[status(thm)],[f23])).
% 0.84/0.89 % SZS output end Proof for DTF2THF_27020
% 0.84/0.89 % (27224)------------------------------
% 0.84/0.89 % (27224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.84/0.89 % (27224)Termination reason: Refutation
% 0.84/0.89
% 0.84/0.89 % (27224)Memory used [KB]: 5628
% 0.84/0.89 % (27224)Time elapsed: 0.005 s
% 0.84/0.89 % (27224)Instructions burned: 6 (million)
% 0.84/0.89 % (27224)------------------------------
% 0.84/0.89 % (27224)------------------------------
% 0.84/0.89 % (27218)Success in time 0.013 s
%------------------------------------------------------------------------------