%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA081^1 : 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 : n003.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 10.32s 3.89s
% Output : Refutation 10.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 9 unt; 0 typ; 3 def)
% Number of atoms : 333 ( 47 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 683 ( 101 ~; 82 |; 15 &; 462 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 66 ( 0 ^; 63 !; 0 ?; 66 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% 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/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_le_decl',type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(sk1_decl,type,
sk1: 'type/realax/real' > $o ).
thf(sk2_decl,type,
sk2: 'type/realax/real' ).
thf(sk4_decl,type,
sk4: 'type/realax/real' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/realax/real' > $o] :
~ ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ! [B: 'type/realax/real'] :
( ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
= ( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/realax/real'] :
( ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk1 ) )
!= ( ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk1 )
=> ( 'const/realax/real_le' @ A @ B ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: 'type/realax/real'] :
~ ( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_le' @ sk2 @ A ) ) ) ) ).
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/inf' @ A ) @ A )
& ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_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/inf' @ A ) @ A )
& ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B ) ) ) ),
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/inf' @ 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' @ ( 'const/sets/inf' @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[15]) ).
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' @ ( 'const/sets/inf' @ A ) @ B ) ),
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' @ ( 'const/sets/inf' @ A ) @ B ) ),
inference(lifteq,[status(thm)],[18]) ).
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_le' @ B @ ( 'const/sets/inf' @ A ) )
= ( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_LE_INF_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_le' @ B @ ( 'const/sets/inf' @ A ) )
= ( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: 'type/realax/real' > $o,B: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ( ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
= ( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ! [A: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ! [B: 'type/realax/real'] :
( ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
= ( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ A )
=> ( 'const/realax/real_le' @ B @ C ) ) ) ) ),
inference(miniscope,[status(thm)],[5]) ).
thf(7,plain,
( ( 'const/sets/FINITE' @ 'type/realax/real' @ sk1 )
& ( sk1
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
!= ( ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_le' @ sk2 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(10,plain,
( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
!= ( ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_le' @ sk2 @ A ) ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(12,plain,
( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
!= ( ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_le' @ sk2 @ A ) ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(25,plain,
( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_le' @ sk2 @ A ) ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(29,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( 'const/realax/real_le' @ sk2 @ A ) ),
inference(cnf,[status(esa)],[25]) ).
thf(157,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( ( 'const/realax/real_le' @ sk2 @ A )
!= ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29]) ).
thf(161,plain,
( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( 'const/sets/inf' @ sk1 ))]]) ).
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/inf' @ 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/inf' @ 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(406,plain,
! [A: 'type/realax/real' > $o] :
( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ A ) @ A )
| ( ( 'const/sets/EMPTY' @ 'type/realax/real' )
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[19,11]) ).
thf(407,plain,
! [A: 'type/realax/real' > $o] :
( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ A ) @ A )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[406]) ).
thf(408,plain,
( ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[407:[bind(A,$thf( sk1 ))]]) ).
thf(8,plain,
'const/sets/FINITE' @ 'type/realax/real' @ sk1,
inference(cnfConj,[status(thm)],[7]) ).
thf(436,plain,
( ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[408,8]) ).
thf(437,plain,
'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1,
inference(simp,[status(thm)],[436]) ).
thf(438,plain,
( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[161,437]) ).
thf(439,plain,
'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ),
inference(simp,[status(thm)],[438]) ).
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(24,plain,
( ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ~ ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
=> ( 'const/realax/real_le' @ sk2 @ A ) ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(26,plain,
( ( ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 ) )
& ( ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ~ ( 'const/realax/real_le' @ sk2 @ sk4 ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(28,plain,
( ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ~ ( 'const/realax/real_le' @ sk2 @ sk4 ) ),
inference(cnfConj,[status(thm)],[26]) ).
thf(50,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' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ~ $true
| ( ( 'const/realax/real_le' @ A @ C )
!= ( 'const/realax/real_le' @ sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[14,28]) ).
thf(51,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ B )
| ~ ( 'const/realax/real_le' @ B @ C )
| ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ( ( 'const/realax/real_le' @ A @ C )
!= ( 'const/realax/real_le' @ sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(52,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ sk2 @ A )
| ~ ( 'const/realax/real_le' @ A @ sk4 )
| ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(62,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ sk2 @ A )
| ~ ( 'const/realax/real_le' @ A @ sk4 )
| ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(721,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ sk2 @ A )
| ~ ( 'const/realax/real_le' @ A @ sk4 )
| ~ $true ),
inference(rewrite,[status(thm)],[62,439]) ).
thf(722,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ sk2 @ A )
| ~ ( 'const/realax/real_le' @ A @ sk4 ) ),
inference(simp,[status(thm)],[721]) ).
thf(734,plain,
! [A: 'type/realax/real'] :
( ~ $true
| ~ ( 'const/realax/real_le' @ A @ sk4 )
| ( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
!= ( 'const/realax/real_le' @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[439,722]) ).
thf(735,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ sk4 )
| ( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
!= ( 'const/realax/real_le' @ sk2 @ A ) ) ),
inference(simp,[status(thm)],[734]) ).
thf(736,plain,
~ ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk4 ),
inference(pattern_uni,[status(thm)],[735:[bind(A,$thf( 'const/sets/inf' @ sk1 ))]]) ).
thf(761,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 )
| ~ $true
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B )
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[20,736]) ).
thf(762,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( A
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B )
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk1 ) @ sk4 ) ) ),
inference(simp,[status(thm)],[761]) ).
thf(763,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ ( 'const/sets/FINITE' @ 'type/realax/real' @ sk1 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[762:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(27,plain,
( ~ ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 ) ),
inference(cnfConj,[status(thm)],[26]) ).
thf(154,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
| ( ( 'const/realax/real_le' @ sk2 @ A )
!= ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,27]) ).
thf(155,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
| ( ( 'const/realax/real_le' @ sk2 @ A )
!= ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(156,plain,
( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( 'const/sets/inf' @ sk1 ))]]) ).
thf(280,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
| ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
| ( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
!= ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,27]) ).
thf(281,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 )
| ( ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) )
!= ( 'const/realax/real_le' @ sk2 @ ( 'const/sets/inf' @ sk1 ) ) ) ),
inference(simp,[status(thm)],[280]) ).
thf(282,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sk1 ) @ sk1 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[281:[]]) ).
thf(440,plain,
( ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1 ) ),
inference(rewrite,[status(thm)],[282,437]) ).
thf(441,plain,
'const/sets/IN' @ 'type/realax/real' @ sk4 @ sk1,
inference(simp,[status(thm)],[440]) ).
thf(798,plain,
( ( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[763,8,441]) ).
thf(799,plain,
( sk1
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ),
inference(simp,[status(thm)],[798]) ).
thf(800,plain,
$false,
inference(simplifyReflect,[status(thm)],[799,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA081^1 : 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
% 0.10/0.22 % Computer : n003.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 17:42:29 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.01/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/1.00 % [INFO] Parsing done (202ms).
% 1.21/1.02 % [INFO] Running in sequential loop mode.
% 2.04/1.43 % [INFO] eprover registered as external prover.
% 2.04/1.44 % [INFO] Scanning for conjecture ...
% 2.23/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.23/1.58 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.23/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.40/1.60 % [INFO] Type checking passed.
% 2.40/1.60 % [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 ...
% 10.32/3.88 % [INFO] Killing All external provers ...
% 10.32/3.89 % Time passed: 3526ms (effective reasoning time: 2862ms)
% 10.32/3.89 % 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)>
% 10.32/3.89 % Axioms used in derivation (2): thm/sets/INF_FINITE_, thm/realax/REAL_LE_TRANS_
% 10.32/3.89 % No. of inferences in proof: 58
% 10.32/3.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3526 ms resp. 2862 ms w/o parsing
% 10.85/3.96 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.85/3.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------