%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA076^1 : 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 : n019.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 07:45:44 AM UTC 2026
% Result : Theorem 19.11s 5.95s
% Output : Refutation 19.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 10
% Syntax : Number of formulae : 84 ( 13 unt; 0 typ; 6 def)
% Number of atoms : 448 ( 62 equ; 0 cnn)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 959 ( 118 ~; 113 |; 31 &; 671 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 143 ( 6 ^; 124 !; 7 ?; 143 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% 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/EMPTY_decl',type,
'const/sets/EMPTY':
!>[TA: $tType] : ( TA > $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(sk3_decl,type,
sk3: 'type/realax/real' ).
thf(sk4_decl,type,
sk4: ( 'type/realax/real' > $o ) > $o ).
thf(sk5_decl,type,
sk5: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(sk6_decl,type,
sk6: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(sk8_decl,type,
sk8:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/realax/real' > $o] :
~ ! [B: 'type/realax/real',C: 'type/realax/real'] :
( ( ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ! [D: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ D @ A )
=> ( ( 'const/realax/real_le' @ B @ D )
& ( 'const/realax/real_le' @ D @ C ) ) ) )
=> ( ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) )
& ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ C ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/realax/real'] :
~ ! [B: 'type/realax/real'] :
( ( ( sk1
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ sk1 )
=> ( ( 'const/realax/real_le' @ A @ C )
& ( 'const/realax/real_le' @ C @ B ) ) ) )
=> ( ( 'const/realax/real_le' @ A @ ( 'const/sets/sup' @ sk1 ) )
& ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ B ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: 'type/realax/real'] :
~ ( ( ( sk1
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk1 )
=> ( ( 'const/realax/real_le' @ sk2 @ B )
& ( 'const/realax/real_le' @ B @ A ) ) ) )
=> ( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
& ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ A ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: 'type/realax/real',B: 'type/realax/real' > $o] :
@+[C: 'type/realax/real'] :
~ ( ( 'const/sets/IN' @ 'type/realax/real' @ C @ B )
=> ( 'const/realax/real_le' @ C @ A ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: 'type/realax/real',B: 'type/realax/real' > $o] :
@+[C: 'type/realax/real'] :
~ ( ( 'const/sets/IN' @ 'type/realax/real' @ C @ B )
=> ( 'const/realax/real_le' @ C @ A ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [TA: $tType,A: TA > $o] :
@+[B: TA] : ( 'const/sets/IN' @ TA @ B @ A ) ) ) ).
thf(5,axiom,
! [A: 'type/realax/real' > $o] :
( ( ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ? [B: 'type/realax/real'] :
! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ C @ B ) ) )
=> ( ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) ) )
& ! [B: 'type/realax/real'] :
( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ C @ B ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_') ).
thf(18,plain,
! [A: 'type/realax/real' > $o] :
( ( ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ? [B: 'type/realax/real'] :
! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ C @ B ) ) )
=> ( ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) ) )
& ! [B: 'type/realax/real'] :
( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ C @ B ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
! [D: 'type/realax/real',C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ B @ A ) @ A )
| ( sk4 @ A ) )
& ( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/realax/real_le' @ ( sk5 @ B @ A ) @ B )
| ( sk4 @ A ) )
& ( ~ ( sk4 @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
| ( 'const/realax/real_le' @ C @ ( 'const/sets/sup' @ A ) ) )
& ( ~ ( sk4 @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ D @ A ) @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ D ) )
& ( ~ ( sk4 @ A )
| ~ ( 'const/realax/real_le' @ ( sk6 @ D @ A ) @ D )
| ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ D ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(24,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ B @ A ) @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ B ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(25,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ B @ A ) @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ B ) ),
inference(simp,[status(thm)],[24]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o] :
( ( ? [B: TA] : ( 'const/sets/IN' @ TA @ B @ A ) )
= ( A
!= ( 'const/sets/EMPTY' @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_') ).
thf(15,plain,
! [TA: $tType,A: TA > $o] :
( ( ? [B: TA] : ( 'const/sets/IN' @ TA @ B @ A ) )
= ( A
!= ( 'const/sets/EMPTY' @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
! [TA: $tType,A: TA > $o] :
( ( ? [B: TA] : ( 'const/sets/IN' @ TA @ B @ A ) )
= ( A
!= ( 'const/sets/EMPTY' @ TA ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [TA: $tType,A: TA > $o] :
( ( ? [B: TA] : ( 'const/sets/IN' @ TA @ B @ A ) )
= ( A
!= ( 'const/sets/EMPTY' @ TA ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(34,plain,
! [TA: $tType,A: TA > $o] :
( ? [B: TA] : ( 'const/sets/IN' @ TA @ B @ A )
| ~ ( ( A
!= ( 'const/sets/EMPTY' @ TA ) ) ) ),
inference(bool_ext,[status(thm)],[17]) ).
thf(38,plain,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ ( sk8 @ TA @ A ) @ A )
| ( A
= ( 'const/sets/EMPTY' @ TA ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(39,plain,
! [TA: $tType,A: TA > $o] :
( ( A
= ( 'const/sets/EMPTY' @ TA ) )
| ( 'const/sets/IN' @ TA @ ( sk8 @ TA @ A ) @ A ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(1,conjecture,
! [A: 'type/realax/real' > $o,B: 'type/realax/real',C: 'type/realax/real'] :
( ( ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ! [D: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ D @ A )
=> ( ( 'const/realax/real_le' @ B @ D )
& ( 'const/realax/real_le' @ D @ C ) ) ) )
=> ( ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) )
& ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_SUP_BOUNDS_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/realax/real' > $o,B: 'type/realax/real',C: 'type/realax/real'] :
( ( ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ! [D: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ D @ A )
=> ( ( 'const/realax/real_le' @ B @ D )
& ( 'const/realax/real_le' @ D @ C ) ) ) )
=> ( ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) )
& ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: 'type/realax/real' > $o,B: 'type/realax/real',C: 'type/realax/real'] :
( ( ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ! [D: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ D @ A )
=> ( ( 'const/realax/real_le' @ B @ D )
& ( 'const/realax/real_le' @ D @ C ) ) ) )
=> ( ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) )
& ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
! [A: 'type/realax/real'] :
( ( sk1
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( 'const/realax/real_le' @ sk2 @ A ) )
& ( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( 'const/realax/real_le' @ A @ sk3 ) )
& ( ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
| ~ ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
( sk1
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(12,plain,
( sk1
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(159,plain,
! [A: 'type/realax/real' > $o] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk8 @ 'type/realax/real' @ A ) @ A )
| ( ( 'const/sets/EMPTY' @ 'type/realax/real' )
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[39,12]) ).
thf(160,plain,
! [A: 'type/realax/real' > $o] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk8 @ 'type/realax/real' @ A ) @ A )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[159]) ).
thf(161,plain,
'const/sets/IN' @ 'type/realax/real' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ sk1,
inference(pattern_uni,[status(thm)],[160:[bind(A,$thf( sk1 ))]]) ).
thf(20,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(26,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(341,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ~ $true
| ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[161,26]) ).
thf(342,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ A ) ) ),
inference(simp,[status(thm)],[341]) ).
thf(343,plain,
( ~ ( sk4 @ sk1 )
| ( 'const/realax/real_le' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ ( 'const/sets/sup' @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[342:[bind(A,$thf( sk1 )),bind(B,$thf( sk8 @ 'type/realax/real' @ sk1 ))]]) ).
thf(23,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ B @ A ) @ A )
| ( sk4 @ A ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(29,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ B @ A ) @ A )
| ( sk4 @ A ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(999,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ B @ A ) @ A )
| ( sk4 @ A )
| ( ( 'const/sets/EMPTY' @ 'type/realax/real' )
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[29,12]) ).
thf(1000,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ B @ A ) @ A )
| ( sk4 @ A )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[999]) ).
thf(1001,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk1 ) @ sk1 )
| ( sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1000:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(1130,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk1 ) @ sk1 )
| ( sk4 @ sk1 ) ),
inference(simp,[status(thm)],[1001]) ).
thf(10,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( 'const/realax/real_le' @ A @ sk3 ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(1288,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( sk4 @ sk1 )
| ~ $true
| ( 'const/realax/real_le' @ B @ sk3 )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1130,10]) ).
thf(1289,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( sk4 @ sk1 )
| ( 'const/realax/real_le' @ B @ sk3 )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk1 ) ) ),
inference(simp,[status(thm)],[1288]) ).
thf(1290,plain,
! [A: 'type/realax/real'] :
( ( sk4 @ sk1 )
| ( 'const/realax/real_le' @ ( sk5 @ A @ sk1 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1289:[bind(A,$thf( C )),bind(B,$thf( sk5 @ C @ sk1 ))]]) ).
thf(1338,plain,
! [A: 'type/realax/real'] :
( ( sk4 @ sk1 )
| ( 'const/realax/real_le' @ ( sk5 @ A @ sk1 ) @ sk3 ) ),
inference(simp,[status(thm)],[1290]) ).
thf(22,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/realax/real_le' @ ( sk5 @ B @ A ) @ B )
| ( sk4 @ A ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(28,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/realax/real_le' @ ( sk5 @ B @ A ) @ B )
| ( sk4 @ A ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(1399,plain,
! [C: 'type/realax/real',B: 'type/realax/real' > $o,A: 'type/realax/real'] :
( ( sk4 @ sk1 )
| ( B
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ $true
| ( sk4 @ B )
| ( ( 'const/realax/real_le' @ ( sk5 @ A @ sk1 ) @ sk3 )
!= ( 'const/realax/real_le' @ ( sk5 @ C @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1338,28]) ).
thf(1400,plain,
! [C: 'type/realax/real',B: 'type/realax/real' > $o,A: 'type/realax/real'] :
( ( sk4 @ sk1 )
| ( B
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( sk4 @ B )
| ( ( 'const/realax/real_le' @ ( sk5 @ A @ sk1 ) @ sk3 )
!= ( 'const/realax/real_le' @ ( sk5 @ C @ B ) @ C ) ) ),
inference(simp,[status(thm)],[1399]) ).
thf(1401,plain,
( ( sk4 @ sk1 )
| ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1400:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 )),bind(C,$thf( sk3 ))]]) ).
thf(1457,plain,
( ( sk4 @ sk1 )
| ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) ),
inference(simp,[status(thm)],[1401]) ).
thf(1463,plain,
sk4 @ sk1,
inference(simplifyReflect,[status(thm)],[1457,12]) ).
thf(1466,plain,
( ~ $true
| ( 'const/realax/real_le' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ ( 'const/sets/sup' @ sk1 ) ) ),
inference(rewrite,[status(thm)],[343,1463]) ).
thf(1467,plain,
'const/realax/real_le' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ ( 'const/sets/sup' @ sk1 ),
inference(simp,[status(thm)],[1466]) ).
thf(3,axiom,
! [A: 'type/realax/real',B: 'type/realax/real',C: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ A @ B )
& ( 'const/realax/real_le' @ B @ C ) )
=> ( 'const/realax/real_le' @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_') ).
thf(13,plain,
! [A: 'type/realax/real',B: 'type/realax/real',C: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ A @ B )
& ( 'const/realax/real_le' @ B @ C ) )
=> ( 'const/realax/real_le' @ 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_le' @ A @ B )
| ~ ( 'const/realax/real_le' @ B @ C )
| ( 'const/realax/real_le' @ A @ C ) ),
inference(cnf,[status(esa)],[13]) ).
thf(11,plain,
( ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/sup' @ sk1 ) )
| ~ ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(80,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ B )
| ~ ( 'const/realax/real_le' @ B @ C )
| ~ $true
| ~ ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 )
| ( ( 'const/realax/real_le' @ A @ C )
!= ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/sup' @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,11]) ).
thf(81,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ B )
| ~ ( 'const/realax/real_le' @ B @ C )
| ~ ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 )
| ( ( 'const/realax/real_le' @ A @ C )
!= ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/sup' @ sk1 ) ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(82,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ sk2 @ A )
| ~ ( 'const/realax/real_le' @ A @ ( 'const/sets/sup' @ sk1 ) )
| ~ ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( 'const/sets/sup' @ sk1 ))]]) ).
thf(89,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ sk2 @ A )
| ~ ( 'const/realax/real_le' @ A @ ( 'const/sets/sup' @ sk1 ) )
| ~ ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 ) ),
inference(simp,[status(thm)],[82]) ).
thf(3381,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ sk2 @ A )
| ~ $true
| ~ ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 )
| ( ( 'const/realax/real_le' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ ( 'const/sets/sup' @ sk1 ) )
!= ( 'const/realax/real_le' @ A @ ( 'const/sets/sup' @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1467,89]) ).
thf(3382,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ sk2 @ A )
| ~ ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 )
| ( ( 'const/realax/real_le' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ ( 'const/sets/sup' @ sk1 ) )
!= ( 'const/realax/real_le' @ A @ ( 'const/sets/sup' @ sk1 ) ) ) ),
inference(simp,[status(thm)],[3381]) ).
thf(3383,plain,
( ~ ( 'const/realax/real_le' @ sk2 @ ( sk8 @ 'type/realax/real' @ sk1 ) )
| ~ ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[3382:[bind(A,$thf( sk8 @ 'type/realax/real' @ sk1 ))]]) ).
thf(9,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( 'const/realax/real_le' @ sk2 @ A ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(198,plain,
! [A: 'type/realax/real'] :
( ~ $true
| ( 'const/realax/real_le' @ sk2 @ A )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[161,9]) ).
thf(199,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sk2 @ A )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(200,plain,
'const/realax/real_le' @ sk2 @ ( sk8 @ 'type/realax/real' @ sk1 ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( sk8 @ 'type/realax/real' @ sk1 ))]]) ).
thf(3719,plain,
( ~ $true
| ~ ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 ) ),
inference(rewrite,[status(thm)],[3383,200]) ).
thf(3720,plain,
~ ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 ),
inference(simp,[status(thm)],[3719]) ).
thf(3740,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ B @ A ) @ A )
| ~ $true
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ B )
!= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[25,3720]) ).
thf(3741,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ B @ A ) @ A )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ B )
!= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 ) ) ),
inference(simp,[status(thm)],[3740]) ).
thf(3742,plain,
( ~ ( sk4 @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk3 @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[3741:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(4849,plain,
( ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk3 @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[3742,1463]) ).
thf(4850,plain,
'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk3 @ sk1 ) @ sk1,
inference(simp,[status(thm)],[4849]) ).
thf(4864,plain,
! [A: 'type/realax/real'] :
( ~ $true
| ( 'const/realax/real_le' @ A @ sk3 )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk3 @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[4850,10]) ).
thf(4865,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_le' @ A @ sk3 )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk3 @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[4864]) ).
thf(4866,plain,
'const/realax/real_le' @ ( sk6 @ sk3 @ sk1 ) @ sk3,
inference(pattern_uni,[status(thm)],[4865:[bind(A,$thf( sk6 @ sk3 @ sk1 ))]]) ).
thf(21,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ~ ( 'const/realax/real_le' @ ( sk6 @ B @ A ) @ B )
| ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ B ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(27,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ~ ( 'const/realax/real_le' @ ( sk6 @ B @ A ) @ B )
| ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ B ) ),
inference(simp,[status(thm)],[21]) ).
thf(5010,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ~ $true
| ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ B )
| ( ( 'const/realax/real_le' @ ( sk6 @ sk3 @ sk1 ) @ sk3 )
!= ( 'const/realax/real_le' @ ( sk6 @ B @ A ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4866,27]) ).
thf(5011,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/sup' @ A ) @ B )
| ( ( 'const/realax/real_le' @ ( sk6 @ sk3 @ sk1 ) @ sk3 )
!= ( 'const/realax/real_le' @ ( sk6 @ B @ A ) @ B ) ) ),
inference(simp,[status(thm)],[5010]) ).
thf(5012,plain,
( ~ ( sk4 @ sk1 )
| ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sk1 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[5011:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(5093,plain,
( ~ $true
| $false ),
inference(rewrite,[status(thm)],[5012,1463,3720]) ).
thf(5094,plain,
$false,
inference(simp,[status(thm)],[5093]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA076^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % 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
% 0.11/0.22 % Computer : n019.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 17:40:43 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.99 % [INFO] Parsing done (205ms).
% 1.16/1.01 % [INFO] Running in sequential loop mode.
% 1.93/1.40 % [INFO] eprover registered as external prover.
% 1.93/1.41 % [INFO] Scanning for conjecture ...
% 2.11/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.11/1.55 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.11/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.11/1.57 % [INFO] Type checking passed.
% 2.11/1.58 % [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 ...
% 19.11/5.95 % [INFO] Killing All external provers ...
% 19.11/5.95 % Time passed: 5585ms (effective reasoning time: 4935ms)
% 19.11/5.95 % 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)>
% 19.11/5.95 % Axioms used in derivation (3): thm/sets/SUP_, thm/sets/MEMBER_NOT_EMPTY_, thm/realax/REAL_LE_TRANS_
% 19.11/5.95 % No. of inferences in proof: 78
% 19.11/5.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5585 ms resp. 4935 ms w/o parsing
% 19.11/6.00 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.11/6.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------