%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA092^1 : 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 : n007.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 82.76s 25.80s
% Output : Refutation 83.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 9
% Syntax : Number of formulae : 96 ( 11 unt; 0 typ; 6 def)
% Number of atoms : 576 ( 63 equ; 0 cnn)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 1199 ( 136 ~; 156 |; 18 &; 853 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 150 ( 4 ^; 133 !; 7 ?; 150 :)
% ( 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' ).
thf(sk2_decl,type,
sk2: 'type/realax/real' > $o ).
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: 'type/realax/real' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/realax/real'] :
~ ! [B: 'type/realax/real' > $o] :
( ( ( B
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ? [C: 'type/realax/real'] :
! [D: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ D @ B )
=> ( 'const/realax/real_le' @ C @ D ) ) )
=> ( ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ B ) )
= ( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ B )
=> ( 'const/realax/real_le' @ A @ C ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[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 ) ) )
=> ( ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ A ) )
= ( ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
=> ( 'const/realax/real_le' @ sk1 @ B ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: 'type/realax/real'] :
! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk2 )
=> ( 'const/realax/real_le' @ A @ B ) ) ) ) ).
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
= ( @+[A: 'type/realax/real'] :
~ ( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
=> ( 'const/realax/real_le' @ sk1 @ A ) ) ) ) ).
thf(1,conjecture,
! [TA: $tType,A: 'type/realax/real',B: 'type/realax/real' > $o,C: TA] :
( ( ( B
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ? [D: 'type/realax/real'] :
! [E: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ E @ B )
=> ( 'const/realax/real_le' @ D @ E ) ) )
=> ( ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ B ) )
= ( ! [D: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ D @ B )
=> ( 'const/realax/real_le' @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_LE_INF_EQ_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: 'type/realax/real',B: 'type/realax/real' > $o,C: TA] :
( ( ( B
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ? [D: 'type/realax/real'] :
! [E: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ E @ B )
=> ( 'const/realax/real_le' @ D @ E ) ) )
=> ( ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ B ) )
= ( ! [D: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ D @ B )
=> ( 'const/realax/real_le' @ A @ D ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: 'type/realax/real',B: 'type/realax/real' > $o] :
( ( ( B
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ? [C: 'type/realax/real'] :
! [D: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ D @ B )
=> ( 'const/realax/real_le' @ C @ D ) ) )
=> ( ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ B ) )
= ( ! [C: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ C @ B )
=> ( 'const/realax/real_le' @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
! [A: 'type/realax/real'] :
( ( sk2
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
| ( 'const/realax/real_le' @ sk3 @ A ) )
& ( ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
!= ( ! [B: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk2 )
=> ( 'const/realax/real_le' @ sk1 @ B ) ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(9,plain,
( ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
!= ( ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
=> ( 'const/realax/real_le' @ sk1 @ A ) ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(11,plain,
( ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
!= ( ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
=> ( 'const/realax/real_le' @ sk1 @ A ) ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(30,plain,
( ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
=> ( 'const/realax/real_le' @ sk1 @ A ) ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(34,plain,
! [A: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
| ( 'const/realax/real_le' @ sk1 @ A ) ),
inference(cnf,[status(esa)],[30]) ).
thf(4,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(14,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)],[4]) ).
thf(15,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)],[14]) ).
thf(18,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)],[15]) ).
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(lifteq,[status(thm)],[18]) ).
thf(7,plain,
( sk2
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(10,plain,
( sk2
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(146,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 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[23,10]) ).
thf(147,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ B @ A ) @ A )
| ( sk4 @ A )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[146]) ).
thf(148,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk2 ) @ sk2 )
| ( sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( sk2 )),bind(B,$thf( B ))]]) ).
thf(209,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk2 ) @ sk2 )
| ( sk4 @ sk2 ) ),
inference(simp,[status(thm)],[148]) ).
thf(8,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
| ( 'const/realax/real_le' @ sk3 @ A ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(230,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( sk4 @ sk2 )
| ~ $true
| ( 'const/realax/real_le' @ sk3 @ B )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk2 ) @ sk2 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[209,8]) ).
thf(231,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( sk4 @ sk2 )
| ( 'const/realax/real_le' @ sk3 @ B )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk5 @ A @ sk2 ) @ sk2 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ B @ sk2 ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(232,plain,
! [A: 'type/realax/real'] :
( ( sk4 @ sk2 )
| ( 'const/realax/real_le' @ sk3 @ ( sk5 @ A @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( C )),bind(B,$thf( sk5 @ C @ sk2 ))]]) ).
thf(242,plain,
! [A: 'type/realax/real'] :
( ( sk4 @ sk2 )
| ( 'const/realax/real_le' @ sk3 @ ( sk5 @ A @ sk2 ) ) ),
inference(simp,[status(thm)],[232]) ).
thf(19,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)],[15]) ).
thf(25,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)],[19]) ).
thf(1309,plain,
! [C: 'type/realax/real',B: 'type/realax/real' > $o,A: 'type/realax/real'] :
( ( sk4 @ sk2 )
| ( B
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ~ $true
| ( sk4 @ B )
| ( ( 'const/realax/real_le' @ sk3 @ ( sk5 @ A @ sk2 ) )
!= ( 'const/realax/real_le' @ C @ ( sk5 @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[242,25]) ).
thf(1310,plain,
! [C: 'type/realax/real',B: 'type/realax/real' > $o,A: 'type/realax/real'] :
( ( sk4 @ sk2 )
| ( B
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( sk4 @ B )
| ( ( 'const/realax/real_le' @ sk3 @ ( sk5 @ A @ sk2 ) )
!= ( 'const/realax/real_le' @ C @ ( sk5 @ C @ B ) ) ) ),
inference(simp,[status(thm)],[1309]) ).
thf(1311,plain,
( ( sk4 @ sk2 )
| ( sk2
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
| ( sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1310:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(1414,plain,
( ( sk4 @ sk2 )
| ( sk2
= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) ),
inference(simp,[status(thm)],[1311]) ).
thf(1457,plain,
sk4 @ sk2,
inference(simplifyReflect,[status(thm)],[1414,10]) ).
thf(17,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)],[15]) ).
thf(22,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)],[17]) ).
thf(1466,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ $true
| ~ ( 'const/realax/real_le' @ B @ ( sk6 @ B @ A ) )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
| ( ( sk4 @ sk2 )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1457,22]) ).
thf(1467,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( 'const/realax/real_le' @ B @ ( sk6 @ B @ A ) )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
| ( ( sk4 @ sk2 )
!= ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[1466]) ).
thf(1468,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ ( sk6 @ A @ sk2 ) )
| ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1467:[bind(A,$thf( sk2 )),bind(B,$thf( B ))]]) ).
thf(1474,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ ( sk6 @ A @ sk2 ) )
| ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk2 ) ) ),
inference(simp,[status(thm)],[1468]) ).
thf(40733,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
| ~ $true
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ sk2 ) )
| ( ( 'const/realax/real_le' @ sk1 @ A )
!= ( 'const/realax/real_le' @ B @ ( sk6 @ B @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,1474]) ).
thf(40734,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ sk2 ) )
| ( ( 'const/realax/real_le' @ sk1 @ A )
!= ( 'const/realax/real_le' @ B @ ( sk6 @ B @ sk2 ) ) ) ),
inference(simp,[status(thm)],[40733]) ).
thf(40735,plain,
( ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
| ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[40734:[bind(A,$thf( sk6 @ sk1 @ sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(40871,plain,
( ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 @ sk2 ) @ sk2 ) ),
inference(simp,[status(thm)],[40735]) ).
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' @ ( 'const/sets/inf' @ A ) @ B ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(21,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)],[20]) ).
thf(1463,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ $true
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B )
| ( ( sk4 @ sk2 )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1457,21]) ).
thf(1464,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ B @ A )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ B )
| ( ( sk4 @ sk2 )
!= ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[1463]) ).
thf(1465,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk2 ) @ A ) ),
inference(pattern_uni,[status(thm)],[1464:[bind(A,$thf( sk2 )),bind(B,$thf( B ))]]) ).
thf(1473,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
| ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk2 ) @ A ) ),
inference(simp,[status(thm)],[1465]) ).
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(12,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(13,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)],[12]) ).
thf(29,plain,
( ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ~ ! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
=> ( 'const/realax/real_le' @ sk1 @ A ) ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(31,plain,
( ( ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 ) )
& ( ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ~ ( 'const/realax/real_le' @ sk1 @ sk8 ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(33,plain,
( ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ~ ( 'const/realax/real_le' @ sk1 @ sk8 ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(87,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' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ~ $true
| ( ( 'const/realax/real_le' @ A @ C )
!= ( 'const/realax/real_le' @ sk1 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[13,33]) ).
thf(88,plain,
! [C: 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ A @ B )
| ~ ( 'const/realax/real_le' @ B @ C )
| ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ( ( 'const/realax/real_le' @ A @ C )
!= ( 'const/realax/real_le' @ sk1 @ sk8 ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(89,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ sk1 @ A )
| ~ ( 'const/realax/real_le' @ A @ sk8 )
| ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk8 ))]]) ).
thf(98,plain,
! [A: 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ sk1 @ A )
| ~ ( 'const/realax/real_le' @ A @ sk8 )
| ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(6238,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
| ~ ( 'const/realax/real_le' @ sk1 @ B )
| ~ $true
| ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk2 ) @ A )
!= ( 'const/realax/real_le' @ B @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[1473,98]) ).
thf(6239,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 )
| ~ ( 'const/realax/real_le' @ sk1 @ B )
| ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sk2 ) @ A )
!= ( 'const/realax/real_le' @ B @ sk8 ) ) ),
inference(simp,[status(thm)],[6238]) ).
thf(6240,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[6239:[bind(A,$thf( sk8 )),bind(B,$thf( 'const/sets/inf' @ sk2 ))]]) ).
thf(6349,plain,
( ~ ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ),
inference(simp,[status(thm)],[6240]) ).
thf(16,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)],[15]) ).
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' @ B @ ( 'const/sets/inf' @ A ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(1458,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ B @ A ) @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
| ( ( sk4 @ sk2 )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1457,24]) ).
thf(1459,plain,
! [B: 'type/realax/real',A: 'type/realax/real' > $o] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ B @ A ) @ A )
| ( 'const/realax/real_le' @ B @ ( 'const/sets/inf' @ A ) )
| ( ( sk4 @ sk2 )
!= ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[1458]) ).
thf(1460,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A @ sk2 ) @ sk2 )
| ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1459:[bind(A,$thf( sk2 )),bind(B,$thf( B ))]]) ).
thf(1471,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A @ sk2 ) @ sk2 )
| ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk2 ) ) ),
inference(simp,[status(thm)],[1460]) ).
thf(32,plain,
( ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(1830,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A @ sk2 ) @ sk2 )
| ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ( ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk2 ) )
!= ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1471,32]) ).
thf(1831,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A @ sk2 ) @ sk2 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ( ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk2 ) )
!= ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ) ),
inference(simp,[status(thm)],[1830]) ).
thf(1832,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
| ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1831:[bind(A,$thf( sk1 ))]]) ).
thf(2075,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ~ $true
| ( 'const/realax/real_le' @ sk1 @ A )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[1832,34]) ).
thf(2076,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ( 'const/realax/real_le' @ sk1 @ A )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
!= ( 'const/sets/IN' @ 'type/realax/real' @ A @ sk2 ) ) ),
inference(simp,[status(thm)],[2075]) ).
thf(2077,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ( 'const/realax/real_le' @ sk1 @ ( sk6 @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[2076:[bind(A,$thf( sk6 @ sk1 @ sk2 ))]]) ).
thf(40682,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ~ $true
| ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk2 ) )
| ( ( 'const/realax/real_le' @ sk1 @ ( sk6 @ sk1 @ sk2 ) )
!= ( 'const/realax/real_le' @ A @ ( sk6 @ A @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2077,1474]) ).
thf(40683,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk2 ) )
| ( ( 'const/realax/real_le' @ sk1 @ ( sk6 @ sk1 @ sk2 ) )
!= ( 'const/realax/real_le' @ A @ ( sk6 @ A @ sk2 ) ) ) ),
inference(simp,[status(thm)],[40682]) ).
thf(40684,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
| ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[40683:[bind(A,$thf( sk1 ))]]) ).
thf(40885,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ),
inference(simp,[status(thm)],[40684]) ).
thf(49065,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ~ $true
| ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ( ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
!= ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[40885,32]) ).
thf(49066,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ( ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) )
!= ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ) ),
inference(simp,[status(thm)],[49065]) ).
thf(49067,plain,
'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2,
inference(pattern_uni,[status(thm)],[49066:[]]) ).
thf(49487,plain,
( ~ $true
| ~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ),
inference(rewrite,[status(thm)],[6349,49067]) ).
thf(49488,plain,
~ ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ),
inference(simp,[status(thm)],[49487]) ).
thf(6415,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A @ sk2 ) @ sk2 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ~ $true
| ( ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk2 ) )
!= ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1471,6349]) ).
thf(6416,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ A @ sk2 ) @ sk2 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 )
| ( ( 'const/realax/real_le' @ A @ ( 'const/sets/inf' @ sk2 ) )
!= ( 'const/realax/real_le' @ sk1 @ ( 'const/sets/inf' @ sk2 ) ) ) ),
inference(simp,[status(thm)],[6415]) ).
thf(6417,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
| ~ ( 'const/sets/IN' @ 'type/realax/real' @ sk8 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6416:[bind(A,$thf( sk1 ))]]) ).
thf(49494,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 @ sk2 ) @ sk2 )
| ~ $true ),
inference(rewrite,[status(thm)],[6417,49067]) ).
thf(49495,plain,
'const/sets/IN' @ 'type/realax/real' @ ( sk6 @ sk1 @ sk2 ) @ sk2,
inference(simp,[status(thm)],[49494]) ).
thf(57082,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[40871,49488,49495]) ).
thf(57083,plain,
$false,
inference(simp,[status(thm)],[57082]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA092^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % 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 : n007.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 17:38:55 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.00 % [INFO] Parsing done (212ms).
% 1.22/1.02 % [INFO] Running in sequential loop mode.
% 2.06/1.42 % [INFO] eprover registered as external prover.
% 2.06/1.43 % [INFO] Scanning for conjecture ...
% 2.22/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.22/1.57 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.22/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.59 % [INFO] Type checking passed.
% 2.22/1.60 % [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 ...
% 82.76/25.79 % [INFO] Killing All external provers ...
% 82.76/25.79 % Time passed: 25441ms (effective reasoning time: 24769ms)
% 82.76/25.79 % 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)>
% 82.76/25.80 % Axioms used in derivation (2): thm/sets/INF_, thm/realax/REAL_LE_TRANS_
% 82.76/25.80 % No. of inferences in proof: 90
% 82.76/25.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 25441 ms resp. 24769 ms w/o parsing
% 83.28/25.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 83.28/25.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------