%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA072^1 : 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 07:45:43 AM UTC 2026
% Result : Theorem 9.47s 3.66s
% Output : Refutation 9.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 11 unt; 0 typ; 3 def)
% Number of atoms : 291 ( 44 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 576 ( 74 ~; 62 |; 15 &; 401 @)
% ( 0 <=>; 24 =>; 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 ^; 59 !; 0 ?; 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(sk7_decl,type,
sk7: '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' @ ( 'const/sets/sup' @ A ) @ B )
= ( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_lt' @ C @ B ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ A )
!= ( ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk1 )
=> ( 'const/realax/real_lt' @ B @ A ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: 'type/realax/real'] :
~ ( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_lt' @ A @ sk2 ) ) ) ) ).
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' @ ( 'const/sets/sup' @ A ) @ B )
= ( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_lt' @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_SUP_LT_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' @ ( 'const/sets/sup' @ A ) @ B )
= ( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_lt' @ C @ B ) ) ) ) ),
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' @ ( 'const/sets/sup' @ A ) @ B )
= ( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_lt' @ C @ B ) ) ) ) ),
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' @ ( 'const/sets/sup' @ A ) @ B )
= ( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_lt' @ C @ B ) ) ) ) ),
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' @ ( 'const/sets/sup' @ sk1 ) @ sk2 )
!= ( ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_lt' @ A @ sk2 ) ) ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(10,plain,
( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ sk2 )
!= ( ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_lt' @ A @ sk2 ) ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(12,plain,
( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ sk2 )
!= ( ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_lt' @ A @ sk2 ) ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(25,plain,
( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ sk2 )
| ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_lt' @ A @ sk2 ) ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(29,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ sk2 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( 'const/realax/real_lt' @ A @ sk2 ) ),
inference(cnf,[status(esa)],[25]) ).
thf(97,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ sk2 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( ( 'const/realax/real_lt' @ A @ sk2 )
!= ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29]) ).
thf(99,plain,
( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ sk2 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( 'const/sets/sup' @ sk1 ))]]) ).
thf(118,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 )
| ~ ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_lt' @ A @ sk2 ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ sk2 )
!= ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[99,12]) ).
thf(119,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 )
| ~ ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_lt' @ A @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[118:[]]) ).
thf(140,plain,
( ( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk7 @ sk1 ) )
& ( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 )
| ~ ( 'const/realax/real_lt' @ sk7 @ sk2 ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(141,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk7 @ sk1 ) ),
inference(cnfConj,[status(thm)],[140]) ).
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/sandbox/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(216,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(217,plain,
! [A: 'type/realax/real' > $o] :
( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ A ) @ A )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[216]) ).
thf(218,plain,
( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[217:[bind(A,$thf( sk1 ))]]) ).
thf(8,plain,
'const/sets/FINITE' @ 'type/realax/real' @ sk1,
inference(cnfConj,[status(thm)],[7]) ).
thf(242,plain,
( ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[218,8]) ).
thf(243,plain,
'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1,
inference(simp,[status(thm)],[242]) ).
thf(246,plain,
( ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ sk7 @ sk1 ) ),
inference(rewrite,[status(thm)],[141,243]) ).
thf(247,plain,
'const/sets/IN' @ 'type/realax/real' @ sk7 @ sk1,
inference(simp,[status(thm)],[246]) ).
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(316,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' @ sk7 @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[247,20]) ).
thf(317,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/sup' @ A ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sk7 @ sk1 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ A ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(318,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ sk1 )
| ( 'const/realax/real_le' @ sk7 @ ( 'const/sets/sup' @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( sk1 )),bind(B,$thf( sk7 ))]]) ).
thf(469,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ $true
| ( 'const/realax/real_le' @ sk7 @ ( 'const/sets/sup' @ sk1 ) ) ),
inference(rewrite,[status(thm)],[318,8]) ).
thf(470,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( 'const/realax/real_le' @ sk7 @ ( 'const/sets/sup' @ sk1 ) ) ),
inference(simp,[status(thm)],[469]) ).
thf(471,plain,
'const/realax/real_le' @ sk7 @ ( 'const/sets/sup' @ sk1 ),
inference(simplifyReflect,[status(thm)],[470,11]) ).
thf(252,plain,
( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ sk2 )
| ~ $true ),
inference(rewrite,[status(thm)],[99,243]) ).
thf(253,plain,
'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ sk2,
inference(simp,[status(thm)],[252]) ).
thf(3,axiom,
! [A: 'type/realax/real',B: 'type/realax/real',C: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ A @ B )
& ( 'const/realax/real_lt' @ B @ C ) )
=> ( 'const/realax/real_lt' @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realarith/REAL_LET_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_lt' @ 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_le' @ A @ B )
| ~ ( 'const/realax/real_lt' @ B @ C )
| ( 'const/realax/real_lt' @ A @ C ) ),
inference(cnf,[status(esa)],[13]) ).
thf(297,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ B )
| ~ $true
| ( 'const/realax/real_lt' @ A @ C )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ sk2 )
!= ( 'const/realax/real_lt' @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[253,14]) ).
thf(298,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ B )
| ( 'const/realax/real_lt' @ A @ C )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sk1 ) @ sk2 )
!= ( 'const/realax/real_lt' @ B @ C ) ) ),
inference(simp,[status(thm)],[297]) ).
thf(299,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ ( 'const/sets/sup' @ sk1 ) )
| ( 'const/realax/real_lt' @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[298:[bind(A,$thf( A )),bind(B,$thf( 'const/sets/sup' @ sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(485,plain,
! [A: 'type/realax/real'] :
( ~ $true
| ( 'const/realax/real_lt' @ A @ sk2 )
| ( ( 'const/realax/real_le' @ sk7 @ ( 'const/sets/sup' @ sk1 ) )
!= ( 'const/realax/real_le' @ A @ ( 'const/sets/sup' @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[471,299]) ).
thf(486,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ A @ sk2 )
| ( ( 'const/realax/real_le' @ sk7 @ ( 'const/sets/sup' @ sk1 ) )
!= ( 'const/realax/real_le' @ A @ ( 'const/sets/sup' @ sk1 ) ) ) ),
inference(simp,[status(thm)],[485]) ).
thf(487,plain,
'const/realax/real_lt' @ sk7 @ sk2,
inference(pattern_uni,[status(thm)],[486:[bind(A,$thf( sk7 ))]]) ).
thf(142,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sk1 ) @ sk1 )
| ~ ( 'const/realax/real_lt' @ sk7 @ sk2 ) ),
inference(cnfConj,[status(thm)],[140]) ).
thf(244,plain,
( ~ $true
| ~ ( 'const/realax/real_lt' @ sk7 @ sk2 ) ),
inference(rewrite,[status(thm)],[142,243]) ).
thf(245,plain,
~ ( 'const/realax/real_lt' @ sk7 @ sk2 ),
inference(simp,[status(thm)],[244]) ).
thf(492,plain,
$false,
inference(rewrite,[status(thm)],[487,245]) ).
thf(493,plain,
$false,
inference(simp,[status(thm)],[492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA072^1 : 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
% 0.11/0.21 % Computer : n013.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 17:40:02 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 1.03/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.01 % [INFO] Parsing done (193ms).
% 1.22/1.02 % [INFO] Running in sequential loop mode.
% 2.05/1.42 % [INFO] eprover registered as external prover.
% 2.05/1.43 % [INFO] Scanning for conjecture ...
% 2.27/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.27/1.58 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.27/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.27/1.59 % [INFO] Type checking passed.
% 2.27/1.60 % [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 ...
% 9.47/3.65 % [INFO] Killing All external provers ...
% 9.47/3.65 % Time passed: 3291ms (effective reasoning time: 2624ms)
% 9.47/3.65 % 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)>
% 9.47/3.66 % Axioms used in derivation (2): thm/sets/SUP_FINITE_, thm/realarith/REAL_LET_TRANS_
% 9.47/3.66 % No. of inferences in proof: 54
% 9.47/3.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3291 ms resp. 2624 ms w/o parsing
% 9.98/3.73 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.98/3.73 % [INFO] Killing All external provers ...
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