%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA071^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:43 AM UTC 2026
% Result : Theorem 9.25s 3.54s
% Output : Refutation 9.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 322 ( 47 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 636 ( 81 ~; 73 |; 27 &; 444 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 62 ( 0 ^; 48 !; 11 ?; 62 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf('const/sets/sup_decl',type,
'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf('const/sets/IN_decl',type,
'const/sets/IN':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('const/sets/FINITE_decl',type,
'const/sets/FINITE':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('const/sets/EMPTY_decl',type,
'const/sets/EMPTY':
!>[TA: $tType] : ( TA > $o ) ).
thf('const/realax/real_lt_decl',type,
'const/realax/real_lt': 'type/realax/real' > 'type/realax/real' > $o ).
thf('const/realax/real_le_decl',type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(sk1_decl,type,
sk1: 'type/realax/real' > $o ).
thf(sk2_decl,type,
sk2: 'type/realax/real' ).
thf(sk4_decl,type,
sk4: 'type/realax/real' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/realax/real' > $o] :
~ ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ! [B: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ B @ ( 'const/sets/sup' @ A ) )
= ( ? [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
& ( 'const/realax/real_lt' @ B @ C ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ A @ ( 'const/sets/sup' @ sk1 ) )
!= ( ? [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk1 )
& ( 'const/realax/real_lt' @ A @ B ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
& ( 'const/realax/real_lt' @ sk2 @ A ) ) ) ) ).
thf(1,conjecture,
! [A: 'type/realax/real' > $o,B: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ( ( 'const/realax/real_lt' @ B @ ( 'const/sets/sup' @ A ) )
= ( ? [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
& ( 'const/realax/real_lt' @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_LT_SUP_FINITE_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/realax/real' > $o,B: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ( ( 'const/realax/real_lt' @ B @ ( 'const/sets/sup' @ A ) )
= ( ? [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
& ( 'const/realax/real_lt' @ B @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: 'type/realax/real' > $o,B: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ( ( 'const/realax/real_lt' @ B @ ( 'const/sets/sup' @ A ) )
= ( ? [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
& ( 'const/realax/real_lt' @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ! [A: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ! [B: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ B @ ( 'const/sets/sup' @ A ) )
= ( ? [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
& ( 'const/realax/real_lt' @ B @ C ) ) ) ) ),
inference(miniscope,[status(thm)],[5]) ).
thf(7,plain,
( ( 'const/sets/FINITE' @ 'type/realax/real' @ sk1 )
& ( sk1
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ( ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
!= ( ? [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
& ( 'const/realax/real_lt' @ sk2 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(10,plain,
( ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
!= ( ? [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
& ( 'const/realax/real_lt' @ sk2 @ A ) ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(12,plain,
( ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
!= ( ? [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
& ( 'const/realax/real_lt' @ sk2 @ A ) ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(25,plain,
( ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
| ? [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
& ( 'const/realax/real_lt' @ sk2 @ A ) ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(27,plain,
( ( ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 ) )
& ( ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
| ( 'const/realax/real_lt' @ sk2 @ sk4 ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(28,plain,
( ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 ) ),
inference(cnfConj,[status(thm)],[27]) ).
thf(24,plain,
( ~ ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
| ~ ? [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
& ( 'const/realax/real_lt' @ sk2 @ A ) ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(26,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ~ ( 'const/realax/real_lt' @ sk2 @ A ) ),
inference(cnf,[status(esa)],[24]) ).
thf(30,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( ( 'const/realax/real_lt' @ sk2 @ A )
!= ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[26]) ).
thf(31,plain,
( ~ ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( 'const/sets/sup' @ sk1 ))]]) ).
thf(98,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
| ~ $true
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 )
| ( ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
!= ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,31]) ).
thf(99,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 )
| ( ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
!= ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[99:[]]) ).
thf(4,axiom,
! [A: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ A ) @ A )
& ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_FINITE_') ).
thf(15,plain,
! [A: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ A ) @ A )
& ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ A ) @ A ) )
& ( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [A: 'type/realax/real' > $o] :
( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ A ) @ A ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(19,plain,
! [A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ A ) @ A ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(9,plain,
( sk1
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(11,plain,
( sk1
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(190,plain,
! [A: 'type/realax/real' > $o] :
( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ A ) @ A )
| ( ( 'const/sets/EMPTY' @ 'type/realax/real' )
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[19,11]) ).
thf(191,plain,
! [A: 'type/realax/real' > $o] :
( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ A ) @ A )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[190]) ).
thf(192,plain,
( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( sk1 ))]]) ).
thf(8,plain,
'const/sets/FINITE' @ 'type/realax/real' @ sk1,
inference(cnfConj,[status(thm)],[7]) ).
thf(234,plain,
( ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[192,8]) ).
thf(235,plain,
'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1,
inference(simp,[status(thm)],[234]) ).
thf(242,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
| ~ $true ),
inference(rewrite,[status(thm)],[100,235]) ).
thf(243,plain,
'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1,
inference(simp,[status(thm)],[242]) ).
thf(18,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(20,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(298,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ~ $true
| ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[243,20]) ).
thf(299,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ A ) ) ),
inference(simp,[status(thm)],[298]) ).
thf(300,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ sk1 )
| ( 'const/realax/real_le' @ sk4 @ ( 'const/sets/sup' @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[299:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(403,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ $true
| ( 'const/realax/real_le' @ sk4 @ ( 'const/sets/sup' @ sk1 ) ) ),
inference(rewrite,[status(thm)],[300,8]) ).
thf(404,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/realax/real_le' @ sk4 @ ( 'const/sets/sup' @ sk1 ) ) ),
inference(simp,[status(thm)],[403]) ).
thf(405,plain,
'const/realax/real_le' @ sk4 @ ( 'const/sets/sup' @ sk1 ),
inference(simplifyReflect,[status(thm)],[404,11]) ).
thf(29,plain,
( ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
| ( 'const/realax/real_lt' @ sk2 @ sk4 ) ),
inference(cnfConj,[status(thm)],[27]) ).
thf(95,plain,
( ( 'const/realax/real_lt' @ sk2 @ sk4 )
| ~ $true
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 )
| ( ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
!= ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,31]) ).
thf(96,plain,
( ( 'const/realax/real_lt' @ sk2 @ sk4 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 )
| ( ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
!= ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(97,plain,
( ( 'const/realax/real_lt' @ sk2 @ sk4 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[96:[]]) ).
thf(238,plain,
( ( 'const/realax/real_lt' @ sk2 @ sk4 )
| ~ $true ),
inference(rewrite,[status(thm)],[97,235]) ).
thf(239,plain,
'const/realax/real_lt' @ sk2 @ sk4,
inference(simp,[status(thm)],[238]) ).
thf(3,axiom,
! [A: 'type/realax/real',B: 'type/realax/real',C: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ A @ B )
& ( 'const/realax/real_le' @ B @ C ) )
=> ( 'const/realax/real_lt' @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realarith/REAL_LTE_TRANS_') ).
thf(13,plain,
! [A: 'type/realax/real',B: 'type/realax/real',C: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ A @ B )
& ( 'const/realax/real_le' @ B @ C ) )
=> ( 'const/realax/real_lt' @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/realax/real_lt' @ A @ B )
| ~ ( 'const/realax/real_le' @ B @ C )
| ( 'const/realax/real_lt' @ A @ C ) ),
inference(cnf,[status(esa)],[13]) ).
thf(258,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ~ $true
| ~ ( 'const/realax/real_le' @ B @ C )
| ( 'const/realax/real_lt' @ A @ C )
| ( ( 'const/realax/real_lt' @ sk2 @ sk4 )
!= ( 'const/realax/real_lt' @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[239,14]) ).
thf(259,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ B @ C )
| ( 'const/realax/real_lt' @ A @ C )
| ( ( 'const/realax/real_lt' @ sk2 @ sk4 )
!= ( 'const/realax/real_lt' @ A @ B ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(260,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ sk4 @ A )
| ( 'const/realax/real_lt' @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(269,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ sk4 @ A )
| ( 'const/realax/real_lt' @ sk2 @ A ) ),
inference(simp,[status(thm)],[260]) ).
thf(406,plain,
! [A: 'type/realax/real'] :
( ~ $true
| ( 'const/realax/real_lt' @ sk2 @ A )
| ( ( 'const/realax/real_le' @ sk4 @ ( 'const/sets/sup' @ sk1 ) )
!= ( 'const/realax/real_le' @ sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[405,269]) ).
thf(407,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ sk2 @ A )
| ( ( 'const/realax/real_le' @ sk4 @ ( 'const/sets/sup' @ sk1 ) )
!= ( 'const/realax/real_le' @ sk4 @ A ) ) ),
inference(simp,[status(thm)],[406]) ).
thf(408,plain,
'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ),
inference(pattern_uni,[status(thm)],[407:[bind(A,$thf( 'const/sets/sup' @ sk1 ))]]) ).
thf(240,plain,
( ~ ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[31,235]) ).
thf(241,plain,
~ ( 'const/realax/real_lt' @ sk2 @ ( 'const/sets/sup' @ sk1 ) ),
inference(simp,[status(thm)],[240]) ).
thf(421,plain,
$false,
inference(rewrite,[status(thm)],[408,241]) ).
thf(422,plain,
$false,
inference(simp,[status(thm)],[421]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA071^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.20 % Computer : n009.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 17:40:41 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.91/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.99 % [INFO] Parsing done (207ms).
% 1.25/1.00 % [INFO] Running in sequential loop mode.
% 2.10/1.41 % [INFO] eprover registered as external prover.
% 2.10/1.42 % [INFO] Scanning for conjecture ...
% 2.28/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.28/1.56 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.28/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.28/1.58 % [INFO] Type checking passed.
% 2.28/1.58 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 9.25/3.53 % [INFO] Killing All external provers ...
% 9.25/3.54 % Time passed: 3188ms (effective reasoning time: 2527ms)
% 9.25/3.54 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 9.25/3.54 % Axioms used in derivation (2): thm/sets/SUP_FINITE_, thm/realarith/REAL_LTE_TRANS_
% 9.25/3.54 % No. of inferences in proof: 60
% 9.25/3.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3188 ms resp. 2527 ms w/o parsing
% 9.75/3.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.75/3.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------