%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA088^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 07:45:45 AM UTC 2026
% Result : Theorem 16.10s 5.07s
% Output : Refutation 16.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 10
% Syntax : Number of formulae : 88 ( 14 unt; 0 typ; 6 def)
% Number of atoms : 494 ( 69 equ; 0 cnn)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 1019 ( 132 ~; 122 |; 31 &; 708 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 144 ( 6 ^; 125 !; 7 ?; 144 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf('const/sets/inf_decl',type,
'const/sets/inf': ( '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/inf' @ A ) )
& ( 'const/realax/real_le' @ ( 'const/sets/inf' @ 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/inf' @ sk1 ) )
& ( 'const/realax/real_le' @ ( 'const/sets/inf' @ 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/inf' @ sk1 ) )
& ( 'const/realax/real_le' @ ( 'const/sets/inf' @ 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' @ A @ C ) ) ) ) ).
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' @ A @ C ) ) ) ) ).
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' @ B @ C ) ) )
=> ( ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) )
& ! [B: 'type/realax/real'] :
( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) )
=> ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_') ).
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' @ B @ C ) ) )
=> ( ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) )
& ! [B: 'type/realax/real'] :
( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) )
=> ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) ) ) ) ),
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' @ B @ ( sk5 @ B @ A ) )
| ( sk4 @ A ) )
& ( ~ ( sk4 @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ C ) )
& ( ~ ( sk4 @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ D @ A ) @ A )
| ( 'const/realax/real_le' @ D @ ( 'const/sets/inf' @ A ) ) )
& ( ~ ( sk4 @ A )
| ~ ( 'const/realax/real_le' @ D @ ( sk6 @ D @ A ) )
| ( 'const/realax/real_le' @ D @ ( 'const/sets/inf' @ A ) ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(22,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(28,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)],[22]) ).
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/inf' @ A ) )
& ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_INF_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/inf' @ A ) )
& ( 'const/realax/real_le' @ ( 'const/sets/inf' @ 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/inf' @ A ) )
& ( 'const/realax/real_le' @ ( 'const/sets/inf' @ 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/inf' @ sk1 ) )
| ~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ 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(635,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)],[28,12]) ).
thf(636,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ B @ A ) @ A )
| ( sk4 @ A )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[635]) ).
thf(637,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk1 ) @ sk1 )
| ( sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[636:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(763,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk1 ) @ sk1 )
| ( sk4 @ sk1 ) ),
inference(simp,[status(thm)],[637]) ).
thf(20,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' @ B @ ( 'const/sets/inf' @ 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' @ ( sk6 @ B @ A ) @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o] :
( ( ? [B: TA] : ( 'const/sets/IN' @ TA @ B @ A ) )
= ( A
!= ( 'const/sets/EMPTY' @ TA ) ) ),
file('/export/starexec/sandbox/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(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(24,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ 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' @ B @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) ),
inference(simp,[status(thm)],[24]) ).
thf(258,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ~ $true
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B )
| ( ( '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)],[161,25]) ).
thf(259,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ A ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(260,plain,
( ~ ( sk4 @ sk1 )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ ( sk8 @ 'type/realax/real' @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( sk1 )),bind(B,$thf( sk8 @ 'type/realax/real' @ sk1 ))]]) ).
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(193,plain,
! [A: 'type/realax/real'] :
( ~ $true
| ( 'const/realax/real_le' @ A @ sk3 )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[161,10]) ).
thf(194,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_le' @ A @ sk3 )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(195,plain,
'const/realax/real_le' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ sk3,
inference(pattern_uni,[status(thm)],[194:[bind(A,$thf( sk8 @ 'type/realax/real' @ sk1 ))]]) ).
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/sandbox/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(216,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ B )
| ~ $true
| ( 'const/realax/real_le' @ A @ C )
| ( ( 'const/realax/real_le' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ sk3 )
!= ( 'const/realax/real_le' @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[195,14]) ).
thf(217,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ B )
| ( 'const/realax/real_le' @ A @ C )
| ( ( 'const/realax/real_le' @ ( sk8 @ 'type/realax/real' @ sk1 ) @ sk3 )
!= ( 'const/realax/real_le' @ B @ C ) ) ),
inference(simp,[status(thm)],[216]) ).
thf(218,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ ( sk8 @ 'type/realax/real' @ sk1 ) )
| ( 'const/realax/real_le' @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[217:[bind(A,$thf( A )),bind(B,$thf( sk8 @ 'type/realax/real' @ sk1 )),bind(C,$thf( sk3 ))]]) ).
thf(400,plain,
! [A: 'type/realax/real'] :
( ~ ( sk4 @ sk1 )
| ~ $true
| ( 'const/realax/real_le' @ A @ sk3 )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ ( sk8 @ 'type/realax/real' @ sk1 ) )
!= ( 'const/realax/real_le' @ A @ ( sk8 @ 'type/realax/real' @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[260,218]) ).
thf(401,plain,
! [A: 'type/realax/real'] :
( ~ ( sk4 @ sk1 )
| ( 'const/realax/real_le' @ A @ sk3 )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ ( sk8 @ 'type/realax/real' @ sk1 ) )
!= ( 'const/realax/real_le' @ A @ ( sk8 @ 'type/realax/real' @ sk1 ) ) ) ),
inference(simp,[status(thm)],[400]) ).
thf(402,plain,
( ~ ( sk4 @ sk1 )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[401:[bind(A,$thf( 'const/sets/inf' @ sk1 ))]]) ).
thf(11,plain,
( ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk3 ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(40,plain,
( ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk3 )
!= ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11]) ).
thf(41,plain,
( ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk3 )
!= ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(500,plain,
( ~ ( sk4 @ sk1 )
| ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk3 )
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[402,41]) ).
thf(501,plain,
( ~ ( sk4 @ sk1 )
| ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk3 )
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk3 ) ) ),
inference(simp,[status(thm)],[500]) ).
thf(502,plain,
( ~ ( sk4 @ sk1 )
| ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[501:[]]) ).
thf(545,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ B @ A ) @ A )
| ~ ( sk4 @ sk1 )
| ~ $true
| ( ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
!= ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,502]) ).
thf(546,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ B @ A ) @ A )
| ~ ( sk4 @ sk1 )
| ( ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
!= ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ) ),
inference(simp,[status(thm)],[545]) ).
thf(547,plain,
( ~ ( sk4 @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk2 @ sk1 ) @ sk1 )
| ~ ( sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[546:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(565,plain,
( ~ ( sk4 @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk2 @ sk1 ) @ sk1 ) ),
inference(simp,[status(thm)],[547]) ).
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(925,plain,
! [A: 'type/realax/real'] :
( ~ ( sk4 @ sk1 )
| ~ $true
| ( 'const/realax/real_le' @ sk2 @ A )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk2 @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[565,9]) ).
thf(926,plain,
! [A: 'type/realax/real'] :
( ~ ( sk4 @ sk1 )
| ( 'const/realax/real_le' @ sk2 @ A )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk2 @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[925]) ).
thf(927,plain,
( ~ ( sk4 @ sk1 )
| ( 'const/realax/real_le' @ sk2 @ ( sk6 @ sk2 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[926:[bind(A,$thf( sk6 @ sk2 @ sk1 ))]]) ).
thf(21,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ~ ( 'const/realax/real_le' @ B @ ( sk6 @ B @ A ) )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(27,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ A )
| ~ ( 'const/realax/real_le' @ B @ ( sk6 @ B @ A ) )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(1353,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ sk1 )
| ~ ( sk4 @ A )
| ~ $true
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
| ( ( 'const/realax/real_le' @ sk2 @ ( sk6 @ sk2 @ sk1 ) )
!= ( 'const/realax/real_le' @ B @ ( sk6 @ B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[927,27]) ).
thf(1354,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk4 @ sk1 )
| ~ ( sk4 @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
| ( ( 'const/realax/real_le' @ sk2 @ ( sk6 @ sk2 @ sk1 ) )
!= ( 'const/realax/real_le' @ B @ ( sk6 @ B @ A ) ) ) ),
inference(simp,[status(thm)],[1353]) ).
thf(1355,plain,
( ~ ( sk4 @ sk1 )
| ~ ( sk4 @ sk1 )
| ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1354:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(1376,plain,
( ~ ( sk4 @ sk1 )
| ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ),
inference(simp,[status(thm)],[1355]) ).
thf(1430,plain,
( ~ ( sk4 @ sk1 )
| ~ ( sk4 @ sk1 )
| ~ $true
| ( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
!= ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1376,502]) ).
thf(1431,plain,
( ~ ( sk4 @ sk1 )
| ( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
!= ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ) ),
inference(simp,[status(thm)],[1430]) ).
thf(1432,plain,
~ ( sk4 @ sk1 ),
inference(pattern_uni,[status(thm)],[1431:[]]) ).
thf(1450,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk1 ) @ sk1 )
| $false ),
inference(rewrite,[status(thm)],[763,1432]) ).
thf(1451,plain,
! [A: 'type/realax/real'] : ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk1 ) @ sk1 ),
inference(simp,[status(thm)],[1450]) ).
thf(1475,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ~ $true
| ( 'const/realax/real_le' @ sk2 @ B )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1451,9]) ).
thf(1476,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sk2 @ B )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk1 ) ) ),
inference(simp,[status(thm)],[1475]) ).
thf(1477,plain,
! [A: 'type/realax/real'] : ( 'const/realax/real_le' @ sk2 @ ( sk5 @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1476:[bind(A,$thf( C )),bind(B,$thf( sk5 @ C @ sk1 ))]]) ).
thf(1499,plain,
! [A: 'type/realax/real'] : ( 'const/realax/real_le' @ sk2 @ ( sk5 @ A @ sk1 ) ),
inference(simp,[status(thm)],[1477]) ).
thf(23,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/realax/real_le' @ B @ ( sk5 @ B @ 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/realax/real_le' @ B @ ( sk5 @ B @ A ) )
| ( sk4 @ A ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(1577,plain,
! [C: 'type/realax/real',B: 'type/realax/real' > $o,A: 'type/realax/real'] :
( ( B
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ $true
| ( sk4 @ B )
| ( ( 'const/realax/real_le' @ sk2 @ ( sk5 @ A @ sk1 ) )
!= ( 'const/realax/real_le' @ C @ ( sk5 @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[1499,29]) ).
thf(1578,plain,
! [C: 'type/realax/real',B: 'type/realax/real' > $o,A: 'type/realax/real'] :
( ( B
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( sk4 @ B )
| ( ( 'const/realax/real_le' @ sk2 @ ( sk5 @ A @ sk1 ) )
!= ( 'const/realax/real_le' @ C @ ( sk5 @ C @ B ) ) ) ),
inference(simp,[status(thm)],[1577]) ).
thf(1579,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1578:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(1611,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| $false ),
inference(rewrite,[status(thm)],[1579,1432]) ).
thf(1612,plain,
( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ),
inference(simp,[status(thm)],[1611]) ).
thf(1613,plain,
$false,
inference(simplifyReflect,[status(thm)],[1612,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA088^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.24 % Computer : n015.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 17:44:03 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.10/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.03 % [INFO] Parsing done (205ms).
% 1.61/1.04 % [INFO] Running in sequential loop mode.
% 2.19/1.44 % [INFO] eprover registered as external prover.
% 2.19/1.45 % [INFO] Scanning for conjecture ...
% 2.40/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.40/1.59 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.58/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 2.58/1.62 % [INFO] Type checking passed.
% 2.58/1.62 % [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 ...
% 16.10/5.07 % [INFO] Killing All external provers ...
% 16.10/5.07 % Time passed: 4690ms (effective reasoning time: 4024ms)
% 16.10/5.07 % 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)>
% 16.10/5.07 % Axioms used in derivation (3): thm/sets/INF_, thm/sets/MEMBER_NOT_EMPTY_, thm/realax/REAL_LE_TRANS_
% 16.10/5.07 % No. of inferences in proof: 82
% 16.10/5.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4690 ms resp. 4024 ms w/o parsing
% 16.10/5.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.10/5.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------