%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV510^1 : 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 : n014.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 08:37:23 AM UTC 2026
% Result : Theorem 44.98s 14.13s
% Output : Refutation 45.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 7 unt; 0 typ; 4 def)
% Number of atoms : 310 ( 49 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 1008 ( 72 ~; 65 |; 11 &; 841 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 67 ( 67 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 176 ( 53 ^; 119 !; 0 ?; 176 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf('type/nums/num_type',type,
'type/nums/num': $tType ).
thf(skt1_type,type,
skt1: $tType ).
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/CARD_decl',type,
'const/sets/CARD':
!>[TA: $tType] : ( ( TA > $o ) > 'type/nums/num' ) ).
thf('const/realax/real_of_num_decl',type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf('const/realax/real_mul_decl',type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('const/realax/real_le_decl',type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf('const/iterate/sum_decl',type,
'const/iterate/sum':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(sk1_decl,type,
sk1: skt1 > $o ).
thf(sk2_decl,type,
sk2: skt1 > 'type/realax/real' ).
thf(sk3_decl,type,
sk3: 'type/realax/real' ).
thf(sk4_decl,type,
sk4:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > 'type/realax/real' ) > ( TA > 'type/realax/real' ) > TA ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > $o] :
~ ! [B: skt1 > 'type/realax/real',C: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ skt1 @ A )
& ! [D: skt1] :
( ( 'const/sets/IN' @ skt1 @ D @ A )
=> ( 'const/realax/real_le' @ ( B @ D ) @ C ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ A @ B ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ A ) ) @ C ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > 'type/realax/real'] :
~ ! [B: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ skt1 @ sk1 )
& ! [C: skt1] :
( ( 'const/sets/IN' @ skt1 @ C @ sk1 )
=> ( 'const/realax/real_le' @ ( A @ C ) @ B ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ A ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ B ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: 'type/realax/real'] :
~ ( ( ( 'const/sets/FINITE' @ skt1 @ sk1 )
& ! [B: skt1] :
( ( 'const/sets/IN' @ skt1 @ B @ sk1 )
=> ( 'const/realax/real_le' @ ( sk2 @ B ) @ A ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ sk2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ A ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [TA: $tType,A: TA > $o,B: TA > 'type/realax/real',C: TA > 'type/realax/real'] :
@+[D: TA] :
~ ( ( 'const/sets/IN' @ TA @ D @ A )
=> ( 'const/realax/real_le' @ ( C @ D ) @ ( B @ D ) ) ) ) ) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o,B: TA > 'type/realax/real',C: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ TA @ A )
& ! [D: TA] :
( ( 'const/sets/IN' @ TA @ D @ A )
=> ( 'const/realax/real_le' @ ( B @ D ) @ C ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ TA @ A @ B ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ TA @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_BOUND_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o,B: TA > 'type/realax/real',C: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ TA @ A )
& ! [D: TA] :
( ( 'const/sets/IN' @ TA @ D @ A )
=> ( 'const/realax/real_le' @ ( B @ D ) @ C ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ TA @ A @ B ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ TA @ A ) ) @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA > $o,B: TA > 'type/realax/real',C: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ TA @ A )
& ! [D: TA] :
( ( 'const/sets/IN' @ TA @ D @ A )
=> ( 'const/realax/real_le' @ ( B @ D ) @ C ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ TA @ A @ B ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ TA @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
! [A: skt1] :
( ( 'const/sets/FINITE' @ skt1 @ sk1 )
& ( ~ ( 'const/sets/IN' @ skt1 @ A @ sk1 )
| ( 'const/realax/real_le' @ ( sk2 @ A ) @ sk3 ) )
& ~ ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ sk2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ sk3 ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
'const/sets/FINITE' @ skt1 @ sk1,
inference(cnfConj,[status(thm)],[6]) ).
thf(4,axiom,
! [TA: $tType,A: 'type/realax/real',B: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ B )
=> ( ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : A )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ TA @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_CONST_') ).
thf(14,plain,
! [TA: $tType,A: 'type/realax/real',B: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ B )
=> ( ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : A )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ TA @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
! [TA: $tType,B: TA > $o,A: 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ TA @ B )
| ( ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : A )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ TA @ B ) ) @ A ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [TA: $tType,B: TA > $o,A: 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : A )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ TA @ B ) ) @ A ) )
| ~ ( 'const/sets/FINITE' @ TA @ B ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(20,plain,
! [TA: $tType,B: TA > $o,A: 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : A )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ TA @ B ) ) @ A ) )
| ~ $true
| ( ( 'const/sets/FINITE' @ skt1 @ sk1 )
!= ( 'const/sets/FINITE' @ TA @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7,16]) ).
thf(21,plain,
! [TA: $tType,B: TA > $o,A: 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : A )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ TA @ B ) ) @ A ) )
| ( ( 'const/sets/FINITE' @ skt1 @ sk1 )
!= ( 'const/sets/FINITE' @ TA @ B ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(22,plain,
! [A: 'type/realax/real'] :
( ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [B: skt1] : A )
= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[21:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(3,axiom,
! [TA: $tType,A: TA > 'type/realax/real',B: TA > 'type/realax/real',C: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ C )
& ! [D: TA] :
( ( 'const/sets/IN' @ TA @ D @ C )
=> ( 'const/realax/real_le' @ ( A @ D ) @ ( B @ D ) ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_LE_') ).
thf(10,plain,
! [TA: $tType,A: TA > 'type/realax/real',B: TA > 'type/realax/real',C: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ C )
& ! [D: TA] :
( ( 'const/sets/IN' @ TA @ D @ C )
=> ( 'const/realax/real_le' @ ( A @ D ) @ ( B @ D ) ) ) )
=> ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [TA: $tType,C: TA > $o,B: TA > 'type/realax/real',A: TA > 'type/realax/real'] :
( ( ~ ( 'const/sets/FINITE' @ TA @ C )
| ( 'const/sets/IN' @ TA @ ( sk4 @ TA @ C @ B @ A ) @ C )
| ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) )
& ( ~ ( 'const/sets/FINITE' @ TA @ C )
| ~ ( 'const/realax/real_le' @ ( A @ ( sk4 @ TA @ C @ B @ A ) ) @ ( B @ ( sk4 @ TA @ C @ B @ A ) ) )
| ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [TA: $tType,C: TA > $o,B: TA > 'type/realax/real',A: TA > 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ TA @ C )
| ( 'const/sets/IN' @ TA @ ( sk4 @ TA @ C @ B @ A ) @ C )
| ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(78,plain,
! [TA: $tType,C: TA > $o,B: TA > 'type/realax/real',A: TA > 'type/realax/real'] :
( ~ $true
| ( 'const/sets/IN' @ TA @ ( sk4 @ TA @ C @ B @ A ) @ C )
| ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) )
| ( ( 'const/sets/FINITE' @ skt1 @ sk1 )
!= ( 'const/sets/FINITE' @ TA @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7,12]) ).
thf(79,plain,
! [TA: $tType,C: TA > $o,B: TA > 'type/realax/real',A: TA > 'type/realax/real'] :
( ( 'const/sets/IN' @ TA @ ( sk4 @ TA @ C @ B @ A ) @ C )
| ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) )
| ( ( 'const/sets/FINITE' @ skt1 @ sk1 )
!= ( 'const/sets/FINITE' @ TA @ C ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(80,plain,
! [B: skt1 > 'type/realax/real',A: skt1 > 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ sk1 @ B @ A ) @ sk1 )
| ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ A ) @ ( 'const/iterate/sum' @ skt1 @ sk1 @ B ) ) ),
inference(pattern_uni,[status(thm)],[79:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(9,plain,
~ ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ sk2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ sk3 ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(131,plain,
! [B: skt1 > 'type/realax/real',A: skt1 > 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ sk1 @ B @ A ) @ sk1 )
| ~ $true
| ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ A ) @ ( 'const/iterate/sum' @ skt1 @ sk1 @ B ) )
!= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ sk2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[80,9]) ).
thf(132,plain,
! [B: skt1 > 'type/realax/real',A: skt1 > 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ sk1 @ B @ A ) @ sk1 )
| ( ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ A ) @ ( 'const/iterate/sum' @ skt1 @ sk1 @ B ) )
!= ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ sk2 ) @ ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ sk3 ) ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(150,plain,
! [B: skt1 > 'type/realax/real',A: skt1 > 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ sk1 @ B @ A ) @ sk1 )
| ( ( 'const/iterate/sum' @ skt1 @ sk1 @ A )
!= ( 'const/iterate/sum' @ skt1 @ sk1 @ sk2 ) )
| ( ( 'const/iterate/sum' @ skt1 @ sk1 @ B )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ sk3 ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(3215,plain,
! [B: skt1 > 'type/realax/real',A: skt1 > 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ sk1 @ B @ A ) @ sk1 )
| ( sk1 != sk1 )
| ( A != sk2 )
| ( ( 'const/iterate/sum' @ skt1 @ sk1 @ B )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ sk3 ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(3293,plain,
! [A: skt1 > 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ sk1 @ A @ sk2 ) @ sk1 )
| ( ( 'const/iterate/sum' @ skt1 @ sk1 @ A )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ sk3 ) ) ),
inference(simp,[status(thm)],[3215]) ).
thf(3337,plain,
! [B: skt1 > 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ sk1 @ B @ sk2 ) @ sk1 )
| ( ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [C: skt1] : A )
!= ( 'const/iterate/sum' @ skt1 @ sk1 @ B ) )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ A )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[22,3293]) ).
thf(3338,plain,
! [A: skt1 > 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ sk1 @ A @ sk2 ) @ sk1 )
| ( ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [B: skt1] : sk3 )
!= ( 'const/iterate/sum' @ skt1 @ sk1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[3337:[bind(A,$thf( sk3 ))]]) ).
thf(3386,plain,
! [A: skt1 > 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ sk1 @ A @ sk2 ) @ sk1 )
| ( ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [B: skt1] : sk3 )
!= ( 'const/iterate/sum' @ skt1 @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[3338]) ).
thf(3444,plain,
! [B: skt1 > 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1 @ ( sk4 @ skt1 @ sk1 @ B @ sk2 ) @ sk1 )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ A )
!= ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [C: skt1] : sk3 ) )
| ( ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [C: skt1] : A )
!= ( 'const/iterate/sum' @ skt1 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22,3386]) ).
thf(3445,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1
@ ( sk4 @ skt1 @ sk1
@ ^ [B: skt1] : A
@ sk2 )
@ sk1 )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ A )
!= ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [B: skt1] : sk3 ) ) ),
inference(pattern_uni,[status(thm)],[3444:[bind(A,$thf( A )),bind(B,$thf( ^ [C: skt1] : A ))]]) ).
thf(3910,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1
@ ( sk4 @ skt1 @ sk1
@ ^ [C: skt1] : B
@ sk2 )
@ sk1 )
| ( ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [C: skt1] : A )
!= ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [C: skt1] : sk3 ) )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ A )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22,3445]) ).
thf(3911,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1
@ ( sk4 @ skt1 @ sk1
@ ^ [B: skt1] : A
@ sk2 )
@ sk1 )
| ( ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [B: skt1] : A )
!= ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [B: skt1] : sk3 ) ) ),
inference(pattern_uni,[status(thm)],[3910:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(4082,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1
@ ( sk4 @ skt1 @ sk1
@ ^ [B: skt1] : A
@ sk2 )
@ sk1 )
| ( sk1 != sk1 )
| ( ( ^ [B: skt1] : A )
!= ( ^ [B: skt1] : sk3 ) ) ),
inference(simp,[status(thm)],[3911]) ).
thf(4148,plain,
! [A: 'type/realax/real'] :
( ( 'const/sets/IN' @ skt1
@ ( sk4 @ skt1 @ sk1
@ ^ [B: skt1] : A
@ sk2 )
@ sk1 )
| ( ( ^ [B: skt1] : A )
!= ( ^ [B: skt1] : sk3 ) ) ),
inference(simp,[status(thm)],[4082]) ).
thf(8,plain,
! [A: skt1] :
( ~ ( 'const/sets/IN' @ skt1 @ A @ sk1 )
| ( 'const/realax/real_le' @ ( sk2 @ A ) @ sk3 ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(4188,plain,
! [B: skt1,A: 'type/realax/real'] :
( ( ( ^ [C: skt1] : A )
!= ( ^ [C: skt1] : sk3 ) )
| ~ $true
| ( 'const/realax/real_le' @ ( sk2 @ B ) @ sk3 )
| ( ( 'const/sets/IN' @ skt1
@ ( sk4 @ skt1 @ sk1
@ ^ [C: skt1] : A
@ sk2 )
@ sk1 )
!= ( 'const/sets/IN' @ skt1 @ B @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[4148,8]) ).
thf(4189,plain,
! [B: skt1,A: 'type/realax/real'] :
( ( ( ^ [C: skt1] : A )
!= ( ^ [C: skt1] : sk3 ) )
| ( 'const/realax/real_le' @ ( sk2 @ B ) @ sk3 )
| ( ( 'const/sets/IN' @ skt1
@ ( sk4 @ skt1 @ sk1
@ ^ [C: skt1] : A
@ sk2 )
@ sk1 )
!= ( 'const/sets/IN' @ skt1 @ B @ sk1 ) ) ),
inference(simp,[status(thm)],[4188]) ).
thf(4190,plain,
! [A: 'type/realax/real'] :
( ( ( ^ [B: skt1] : A )
!= ( ^ [B: skt1] : sk3 ) )
| ( 'const/realax/real_le'
@ ( sk2
@ ( sk4 @ skt1 @ sk1
@ ^ [B: skt1] : A
@ sk2 ) )
@ sk3 ) ),
inference(pattern_uni,[status(thm)],[4189:[bind(A,$thf( A )),bind(B,$thf( sk4 @ skt1 @ sk1 @ ^ [C: skt1] : A @ sk2 ))]]) ).
thf(13,plain,
! [TA: $tType,C: TA > $o,B: TA > 'type/realax/real',A: TA > 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ TA @ C )
| ~ ( 'const/realax/real_le' @ ( A @ ( sk4 @ TA @ C @ B @ A ) ) @ ( B @ ( sk4 @ TA @ C @ B @ A ) ) )
| ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(181,plain,
! [TA: $tType,C: TA > $o,B: TA > 'type/realax/real',A: TA > 'type/realax/real'] :
( ~ $true
| ~ ( 'const/realax/real_le' @ ( A @ ( sk4 @ TA @ C @ B @ A ) ) @ ( B @ ( sk4 @ TA @ C @ B @ A ) ) )
| ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) )
| ( ( 'const/sets/FINITE' @ skt1 @ sk1 )
!= ( 'const/sets/FINITE' @ TA @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7,13]) ).
thf(182,plain,
! [TA: $tType,C: TA > $o,B: TA > 'type/realax/real',A: TA > 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ ( A @ ( sk4 @ TA @ C @ B @ A ) ) @ ( B @ ( sk4 @ TA @ C @ B @ A ) ) )
| ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) )
| ( ( 'const/sets/FINITE' @ skt1 @ sk1 )
!= ( 'const/sets/FINITE' @ TA @ C ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(183,plain,
! [B: skt1 > 'type/realax/real',A: skt1 > 'type/realax/real'] :
( ~ ( 'const/realax/real_le' @ ( A @ ( sk4 @ skt1 @ sk1 @ B @ A ) ) @ ( B @ ( sk4 @ skt1 @ sk1 @ B @ A ) ) )
| ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ A ) @ ( 'const/iterate/sum' @ skt1 @ sk1 @ B ) ) ),
inference(pattern_uni,[status(thm)],[182:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(4688,plain,
! [C: skt1 > 'type/realax/real',B: skt1 > 'type/realax/real',A: 'type/realax/real'] :
( ( ( ^ [D: skt1] : A )
!= ( ^ [D: skt1] : sk3 ) )
| ~ $true
| ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ B ) @ ( 'const/iterate/sum' @ skt1 @ sk1 @ C ) )
| ( ( 'const/realax/real_le'
@ ( sk2
@ ( sk4 @ skt1 @ sk1
@ ^ [D: skt1] : A
@ sk2 ) )
@ sk3 )
!= ( 'const/realax/real_le' @ ( B @ ( sk4 @ skt1 @ sk1 @ C @ B ) ) @ ( C @ ( sk4 @ skt1 @ sk1 @ C @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4190,183]) ).
thf(4689,plain,
! [C: skt1 > 'type/realax/real',B: skt1 > 'type/realax/real',A: 'type/realax/real'] :
( ( ( ^ [D: skt1] : A )
!= ( ^ [D: skt1] : sk3 ) )
| ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ B ) @ ( 'const/iterate/sum' @ skt1 @ sk1 @ C ) )
| ( ( 'const/realax/real_le'
@ ( sk2
@ ( sk4 @ skt1 @ sk1
@ ^ [D: skt1] : A
@ sk2 ) )
@ sk3 )
!= ( 'const/realax/real_le' @ ( B @ ( sk4 @ skt1 @ sk1 @ C @ B ) ) @ ( C @ ( sk4 @ skt1 @ sk1 @ C @ B ) ) ) ) ),
inference(simp,[status(thm)],[4688]) ).
thf(4717,plain,
( ( ( ^ [A: skt1] : sk3 )
!= ( ^ [A: skt1] : sk3 ) )
| ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ sk2 )
@ ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [A: skt1] : sk3 ) ) ),
inference(pre_uni,[status(thm)],[4689:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 )),bind(C,$thf( ^ [D: skt1] : sk3 ))]]) ).
thf(4719,plain,
( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ sk2 )
@ ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [A: skt1] : sk3 ) ),
inference(pattern_uni,[status(thm)],[4717:[]]) ).
thf(24,plain,
! [TA: $tType,B: TA > $o,A: 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ TA @ B )
| ~ ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ sk2 )
@ ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : A ) )
| ( ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ TA @ B ) ) @ A )
!= ( 'const/realax/real_mul' @ ( 'const/realax/real_of_num' @ ( 'const/sets/CARD' @ skt1 @ sk1 ) ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[16,9]) ).
thf(25,plain,
( ~ ( 'const/sets/FINITE' @ skt1 @ sk1 )
| ~ ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ sk2 )
@ ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [A: skt1] : sk3 ) ) ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(26,plain,
( ~ $true
| ~ ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ sk2 )
@ ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [A: skt1] : sk3 ) ) ),
inference(rewrite,[status(thm)],[25,7]) ).
thf(27,plain,
~ ( 'const/realax/real_le' @ ( 'const/iterate/sum' @ skt1 @ sk1 @ sk2 )
@ ( 'const/iterate/sum' @ skt1 @ sk1
@ ^ [A: skt1] : sk3 ) ),
inference(simp,[status(thm)],[26]) ).
thf(4823,plain,
$false,
inference(rewrite,[status(thm)],[4719,27]) ).
thf(4824,plain,
$false,
inference(simp,[status(thm)],[4823]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV510^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % 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
% 0.10/0.19 % Computer : n014.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 15:54:45 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.87/0.76 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.95 % [INFO] Parsing done (189ms).
% 1.21/0.96 % [INFO] Running in sequential loop mode.
% 1.83/1.35 % [INFO] eprover registered as external prover.
% 1.83/1.36 % [INFO] Scanning for conjecture ...
% 2.00/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.00/1.50 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.16/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.16/1.51 % [INFO] Type checking passed.
% 2.16/1.52 % [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 ...
% 44.98/14.12 % [INFO] Killing All external provers ...
% 44.98/14.12 % Time passed: 13785ms (effective reasoning time: 13150ms)
% 44.98/14.12 % 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)>
% 44.98/14.12 % Axioms used in derivation (2): thm/iterate/SUM_CONST_, thm/iterate/SUM_LE_
% 44.98/14.13 % No. of inferences in proof: 52
% 44.98/14.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 13785 ms resp. 13150 ms w/o parsing
% 45.37/14.21 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 45.37/14.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------