%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA091^1 : 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 : n013.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 16.35s 5.14s
% Output : Refutation 16.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 10
% Syntax : Number of formulae : 64 ( 14 unt; 0 typ; 6 def)
% Number of atoms : 324 ( 54 equ; 0 cnn)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 670 ( 73 ~; 71 |; 29 &; 468 @)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 134 ( 4 ^; 113 !; 11 ?; 134 :)
% ( 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' ).
thf(sk5_decl,type,
sk5: ( 'type/realax/real' > $o ) > $o ).
thf(sk6_decl,type,
sk6: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(sk7_decl,type,
sk7: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/realax/real' > $o] :
~ ! [B: 'type/realax/real',C: 'type/realax/real'] :
( ? [D: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ D @ A )
& ( 'const/realax/real_le' @ D @ C )
& ! [E: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ E @ A )
=> ( 'const/realax/real_le' @ B @ E ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ C ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/realax/real'] :
~ ! [B: 'type/realax/real'] :
( ? [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ sk1 )
& ( 'const/realax/real_le' @ C @ B )
& ! [D: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ D @ sk1 )
=> ( 'const/realax/real_le' @ A @ D ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ B ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: 'type/realax/real'] :
~ ( ? [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk1 )
& ( 'const/realax/real_le' @ B @ A )
& ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ sk1 )
=> ( 'const/realax/real_le' @ sk2 @ C ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ A ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
& ( 'const/realax/real_le' @ A @ sk3 )
& ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk1 )
=> ( 'const/realax/real_le' @ sk2 @ B ) ) ) ) ) ).
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(sk7_def,definition,
( sk7
= ( ^ [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(1,conjecture,
! [A: 'type/realax/real' > $o,B: 'type/realax/real',C: 'type/realax/real',D: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ D @ A )
& ( 'const/realax/real_le' @ D @ C )
& ! [E: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ E @ A )
=> ( 'const/realax/real_le' @ B @ E ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_INF_LE_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/realax/real' > $o,B: 'type/realax/real',C: 'type/realax/real',D: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ D @ A )
& ( 'const/realax/real_le' @ D @ C )
& ! [E: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ E @ A )
=> ( 'const/realax/real_le' @ B @ E ) ) )
=> ( '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',D: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ D @ A )
& ( 'const/realax/real_le' @ D @ C )
& ! [E: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ E @ A )
=> ( 'const/realax/real_le' @ B @ E ) ) )
=> ( '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' > $o,B: 'type/realax/real',C: 'type/realax/real'] :
( ? [D: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ D @ A )
& ( 'const/realax/real_le' @ D @ C )
& ! [E: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ E @ A )
=> ( 'const/realax/real_le' @ B @ E ) ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ C ) ),
inference(miniscope,[status(thm)],[6]) ).
thf(8,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
& ( 'const/realax/real_le' @ sk4 @ sk3 )
& ( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( 'const/realax/real_le' @ sk2 @ A ) )
& ~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk3 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1,
inference(cnfConj,[status(thm)],[8]) ).
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' @ ( sk6 @ B @ A ) @ A )
| ( sk5 @ A ) )
& ( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/realax/real_le' @ B @ ( sk6 @ B @ A ) )
| ( sk5 @ A ) )
& ( ~ ( sk5 @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ C ) )
& ( ~ ( sk5 @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk7 @ D @ A ) @ A )
| ( 'const/realax/real_le' @ D @ ( 'const/sets/inf' @ A ) ) )
& ( ~ ( sk5 @ A )
| ~ ( 'const/realax/real_le' @ D @ ( sk7 @ D @ A ) )
| ( 'const/realax/real_le' @ D @ ( 'const/sets/inf' @ A ) ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(24,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ B @ A ) @ A )
| ( sk5 @ A ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(25,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ B @ A ) @ A )
| ( sk5 @ A ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(20,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk5 @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(26,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk5 @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) ),
inference(simp,[status(thm)],[20]) ).
thf(34,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk5 @ A )
| ~ $true
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,26]) ).
thf(35,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( sk5 @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ A ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(36,plain,
( ~ ( sk5 @ sk1 )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk4 ) ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(10,plain,
'const/realax/real_le' @ sk4 @ sk3,
inference(cnfConj,[status(thm)],[8]) ).
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(12,plain,
~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk3 ),
inference(cnfConj,[status(thm)],[8]) ).
thf(89,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 )
| ~ $true
| ( ( 'const/realax/real_le' @ A @ C )
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,12]) ).
thf(90,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ B )
| ~ ( 'const/realax/real_le' @ B @ C )
| ( ( 'const/realax/real_le' @ A @ C )
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk3 ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(91,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ A )
| ~ ( 'const/realax/real_le' @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( 'const/sets/inf' @ sk1 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(119,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ A )
| ~ ( 'const/realax/real_le' @ A @ sk3 ) ),
inference(simp,[status(thm)],[91]) ).
thf(123,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ A )
| ~ $true
| ( ( 'const/realax/real_le' @ sk4 @ sk3 )
!= ( 'const/realax/real_le' @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[10,119]) ).
thf(124,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ A )
| ( ( 'const/realax/real_le' @ sk4 @ sk3 )
!= ( 'const/realax/real_le' @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(125,plain,
~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk4 ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( sk4 ))]]) ).
thf(227,plain,
( ~ ( sk5 @ sk1 )
| $false ),
inference(rewrite,[status(thm)],[36,125]) ).
thf(228,plain,
~ ( sk5 @ sk1 ),
inference(simp,[status(thm)],[227]) ).
thf(296,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ B @ A ) @ A )
| ~ $true
| ( ( sk5 @ A )
!= ( sk5 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[25,228]) ).
thf(297,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ B @ A ) @ A )
| ( ( sk5 @ A )
!= ( sk5 @ sk1 ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(298,plain,
! [A: 'type/realax/real'] :
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(320,plain,
! [A: 'type/realax/real'] :
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A @ sk1 ) @ sk1 ) ),
inference(simp,[status(thm)],[298]) ).
thf(11,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( 'const/realax/real_le' @ sk2 @ A ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(2107,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ $true
| ( 'const/realax/real_le' @ sk2 @ B )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[320,11]) ).
thf(2108,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/realax/real_le' @ sk2 @ B )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A @ sk1 ) @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk1 ) ) ),
inference(simp,[status(thm)],[2107]) ).
thf(2109,plain,
! [A: 'type/realax/real'] :
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/realax/real_le' @ sk2 @ ( sk6 @ A @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[2108:[bind(A,$thf( C )),bind(B,$thf( sk6 @ C @ sk1 ))]]) ).
thf(2182,plain,
! [A: 'type/realax/real'] :
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/realax/real_le' @ sk2 @ ( sk6 @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[2109]) ).
thf(23,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/realax/real_le' @ B @ ( sk6 @ B @ A ) )
| ( sk5 @ 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 @ ( sk6 @ B @ A ) )
| ( sk5 @ A ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(2612,plain,
! [C: 'type/realax/real',B: 'type/realax/real' > $o,A: 'type/realax/real'] :
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( B
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ $true
| ( sk5 @ B )
| ( ( 'const/realax/real_le' @ sk2 @ ( sk6 @ A @ sk1 ) )
!= ( 'const/realax/real_le' @ C @ ( sk6 @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[2182,29]) ).
thf(2613,plain,
! [C: 'type/realax/real',B: 'type/realax/real' > $o,A: 'type/realax/real'] :
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( B
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( sk5 @ B )
| ( ( 'const/realax/real_le' @ sk2 @ ( sk6 @ A @ sk1 ) )
!= ( 'const/realax/real_le' @ C @ ( sk6 @ C @ B ) ) ) ),
inference(simp,[status(thm)],[2612]) ).
thf(2614,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( sk5 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2613:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(2678,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( sk5 @ sk1 ) ),
inference(simp,[status(thm)],[2614]) ).
thf(2696,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| $false ),
inference(rewrite,[status(thm)],[2678,228]) ).
thf(2697,plain,
( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ),
inference(simp,[status(thm)],[2696]) ).
thf(2699,plain,
'const/sets/IN' @ 'type/realax/real' @ sk4 @ ( 'const/sets/EMPTY' @ 'type/realax/real' ),
inference(rewrite,[status(thm)],[9,2697]) ).
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(44,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(46,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( 'const/sets/IN' @ TA @ B @ A )
| ( A
!= ( 'const/sets/EMPTY' @ TA ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(47,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A
!= ( 'const/sets/EMPTY' @ TA ) )
| ~ ( 'const/sets/IN' @ TA @ B @ A ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(48,plain,
! [TA: $tType,A: TA] :
~ ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/EMPTY' @ TA ) ),
inference(simp,[status(thm)],[47]) ).
thf(2891,plain,
$false,
inference(rewrite,[status(thm)],[2699,48]) ).
thf(2892,plain,
$false,
inference(simp,[status(thm)],[2891]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA091^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % 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
% 0.10/0.21 % Computer : n013.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 17:40:21 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.85/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/0.98 % [INFO] Parsing done (197ms).
% 1.16/0.99 % [INFO] Running in sequential loop mode.
% 1.80/1.39 % [INFO] eprover registered as external prover.
% 2.00/1.40 % [INFO] Scanning for conjecture ...
% 2.15/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.15/1.54 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.15/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.15/1.56 % [INFO] Type checking passed.
% 2.15/1.56 % [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 ...
% 16.35/5.14 % [INFO] Killing All external provers ...
% 16.35/5.14 % Time passed: 4784ms (effective reasoning time: 4138ms)
% 16.35/5.14 % 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)>
% 16.35/5.14 % Axioms used in derivation (3): thm/sets/INF_, thm/realax/REAL_LE_TRANS_, thm/sets/MEMBER_NOT_EMPTY_
% 16.35/5.14 % No. of inferences in proof: 58
% 16.35/5.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4784 ms resp. 4138 ms w/o parsing
% 16.58/5.22 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.58/5.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------