%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA101^1 : 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 : n019.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 07:45:46 AM UTC 2026
% Result : Theorem 23.05s 6.83s
% Output : Refutation 23.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 16 unt; 0 typ; 3 def)
% Number of atoms : 126 ( 59 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 653 ( 49 ~; 28 |; 1 &; 567 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 139 ( 50 ^; 86 !; 0 ?; 139 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/FINITE_decl',type,
'const/sets/FINITE':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('const/realax/real_sub_decl',type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf('const/realax/real_neg_decl',type,
'const/realax/real_neg': 'type/realax/real' > 'type/realax/real' ).
thf('const/realax/real_add_decl',type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
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 > 'type/realax/real' ).
thf(sk2_decl,type,
sk2: skt1 > 'type/realax/real' ).
thf(sk3_decl,type,
sk3: skt1 > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > 'type/realax/real'] :
~ ! [B: skt1 > 'type/realax/real',C: skt1 > $o] :
( ( 'const/sets/FINITE' @ skt1 @ C )
=> ( ( 'const/iterate/sum' @ skt1 @ C
@ ^ [D: skt1] : ( 'const/realax/real_sub' @ ( A @ D ) @ ( B @ D ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ skt1 @ C @ A ) @ ( 'const/iterate/sum' @ skt1 @ C @ B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > 'type/realax/real'] :
~ ! [B: skt1 > $o] :
( ( 'const/sets/FINITE' @ skt1 @ B )
=> ( ( 'const/iterate/sum' @ skt1 @ B
@ ^ [C: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ C ) @ ( A @ C ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ skt1 @ B @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ B @ A ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: skt1 > $o] :
~ ( ( 'const/sets/FINITE' @ skt1 @ A )
=> ( ( 'const/iterate/sum' @ skt1 @ A
@ ^ [B: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ B ) @ ( sk2 @ B ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ skt1 @ A @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ A @ sk2 ) ) ) ) ) ) ).
thf(3,axiom,
! [TA: $tType,A: TA > 'type/realax/real',B: TA > $o] :
( ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : ( 'const/realax/real_neg' @ ( A @ C ) ) )
= ( 'const/realax/real_neg' @ ( 'const/iterate/sum' @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_NEG_') ).
thf(11,plain,
! [TA: $tType,A: TA > 'type/realax/real',B: TA > $o] :
( ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : ( 'const/realax/real_neg' @ ( A @ C ) ) )
= ( 'const/realax/real_neg' @ ( 'const/iterate/sum' @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [TA: $tType,B: TA > $o,A: TA > 'type/realax/real'] :
( ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : ( 'const/realax/real_neg' @ ( A @ C ) ) )
= ( 'const/realax/real_neg' @ ( 'const/iterate/sum' @ TA @ B @ A ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [TA: $tType,B: TA > $o,A: TA > 'type/realax/real'] :
( ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : ( 'const/realax/real_neg' @ ( A @ C ) ) )
= ( 'const/realax/real_neg' @ ( 'const/iterate/sum' @ TA @ B @ A ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(5,axiom,
! [A: 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/realax/real_sub' @ A @ B )
= ( 'const/realax/real_add' @ A @ ( 'const/realax/real_neg' @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/real_sub_') ).
thf(17,plain,
! [A: 'type/realax/real',B: 'type/realax/real'] :
( ( 'const/realax/real_sub' @ A @ B )
= ( 'const/realax/real_add' @ A @ ( 'const/realax/real_neg' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_sub' @ A @ B )
= ( 'const/realax/real_add' @ A @ ( 'const/realax/real_neg' @ B ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [B: 'type/realax/real',A: 'type/realax/real'] :
( ( 'const/realax/real_add' @ A @ ( 'const/realax/real_neg' @ B ) )
= ( 'const/realax/real_sub' @ A @ B ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(4,axiom,
! [TA: $tType,A: TA > 'type/realax/real',B: TA > 'type/realax/real',C: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ C )
=> ( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_add' @ ( A @ D ) @ ( B @ D ) ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_ADD_') ).
thf(14,plain,
! [TA: $tType,A: TA > 'type/realax/real',B: TA > 'type/realax/real',C: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ C )
=> ( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_add' @ ( A @ D ) @ ( B @ D ) ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
! [TA: $tType,C: TA > $o,B: TA > 'type/realax/real',A: TA > 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ TA @ C )
| ( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_add' @ ( A @ D ) @ ( B @ D ) ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [TA: $tType,C: TA > $o,B: TA > 'type/realax/real',A: TA > 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_add' @ ( A @ D ) @ ( B @ D ) ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) )
| ~ ( 'const/sets/FINITE' @ TA @ C ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(48,plain,
! [TA: $tType,E: TA > $o,D: TA > 'type/realax/real',C: TA > 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ A @ B )
= ( 'const/iterate/sum' @ TA @ E
@ ^ [F: TA] : ( 'const/realax/real_add' @ ( C @ F ) @ ( D @ F ) ) ) )
| ~ ( 'const/sets/FINITE' @ TA @ E )
| ( ( 'const/realax/real_add' @ A @ ( 'const/realax/real_neg' @ B ) )
!= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ TA @ E @ C ) @ ( 'const/iterate/sum' @ TA @ E @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,16]) ).
thf(49,plain,
! [TA: $tType,E: TA > $o,D: TA > 'type/realax/real',C: TA > 'type/realax/real',B: 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ A @ B )
= ( 'const/iterate/sum' @ TA @ E
@ ^ [F: TA] : ( 'const/realax/real_add' @ ( C @ F ) @ ( D @ F ) ) ) )
| ~ ( 'const/sets/FINITE' @ TA @ E )
| ( A
!= ( 'const/iterate/sum' @ TA @ E @ C ) )
| ( ( 'const/realax/real_neg' @ B )
!= ( 'const/iterate/sum' @ TA @ E @ D ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(51,plain,
! [TA: $tType,D: TA > $o,C: TA > 'type/realax/real',B: TA > 'type/realax/real',A: 'type/realax/real'] :
( ( ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ TA @ D @ B ) @ A )
= ( 'const/iterate/sum' @ TA @ D
@ ^ [E: TA] : ( 'const/realax/real_add' @ ( B @ E ) @ ( C @ E ) ) ) )
| ~ ( 'const/sets/FINITE' @ TA @ D )
| ( ( 'const/realax/real_neg' @ A )
!= ( 'const/iterate/sum' @ TA @ D @ C ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > 'type/realax/real',B: TA > 'type/realax/real',C: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ C )
=> ( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_sub' @ ( A @ D ) @ ( B @ D ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_SUB_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > 'type/realax/real',B: TA > 'type/realax/real',C: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ C )
=> ( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_sub' @ ( A @ D ) @ ( B @ D ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [TA: $tType,A: TA > 'type/realax/real',B: TA > 'type/realax/real',C: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ C )
=> ( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_sub' @ ( A @ D ) @ ( B @ D ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( ( 'const/sets/FINITE' @ skt1 @ sk3 )
& ( ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [A: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk2 ) ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(9,plain,
( ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [A: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk2 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(10,plain,
( ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [A: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(58,plain,
! [TA: $tType,D: TA > $o,C: TA > 'type/realax/real',B: TA > 'type/realax/real',A: 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ TA @ D )
| ( ( 'const/realax/real_neg' @ A )
!= ( 'const/iterate/sum' @ TA @ D @ C ) )
| ( ( 'const/iterate/sum' @ TA @ D
@ ^ [E: TA] : ( 'const/realax/real_add' @ ( B @ E ) @ ( C @ E ) ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [E: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ E ) @ ( sk2 @ E ) ) ) )
| ( ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ TA @ D @ B ) @ A )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk1 ) @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,10]) ).
thf(59,plain,
! [A: skt1 > 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ skt1 @ sk3 )
| ( ( 'const/realax/real_neg' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk2 ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3 @ A ) )
| ( ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [B: skt1] : ( 'const/realax/real_add' @ ( sk1 @ B ) @ ( A @ B ) ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [B: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( 'const/iterate/sum' @ skt1 @ sk3 @ sk2 )),bind(B,$thf( sk1 )),bind(C,$thf( C )),bind(D,$thf( sk3 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(104,plain,
! [A: skt1 > 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ skt1 @ sk3 )
| ( ( 'const/realax/real_neg' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk2 ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3 @ A ) )
| ( ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [B: skt1] : ( 'const/realax/real_add' @ ( sk1 @ B ) @ ( A @ B ) ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [B: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(8,plain,
'const/sets/FINITE' @ skt1 @ sk3,
inference(cnfConj,[status(thm)],[7]) ).
thf(697,plain,
! [A: skt1 > 'type/realax/real'] :
( ~ $true
| ( ( 'const/realax/real_neg' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk2 ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3 @ A ) )
| ( ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [B: skt1] : ( 'const/realax/real_add' @ ( sk1 @ B ) @ ( A @ B ) ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [B: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(rewrite,[status(thm)],[104,8]) ).
thf(698,plain,
! [A: skt1 > 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk2 ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3 @ A ) )
| ( ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [B: skt1] : ( 'const/realax/real_add' @ ( sk1 @ B ) @ ( A @ B ) ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [B: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[697]) ).
thf(699,plain,
! [A: skt1 > 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk2 ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3 @ A ) )
| ( sk3 != sk3 )
| ( ( ^ [B: skt1] : ( 'const/realax/real_add' @ ( sk1 @ B ) @ ( A @ B ) ) )
!= ( ^ [B: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[698]) ).
thf(785,plain,
! [A: skt1 > 'type/realax/real'] :
( ( ( 'const/realax/real_neg' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk2 ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3 @ A ) )
| ( ( ^ [B: skt1] : ( 'const/realax/real_add' @ ( sk1 @ B ) @ ( A @ B ) ) )
!= ( ^ [B: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[699]) ).
thf(833,plain,
! [TA: $tType,C: skt1 > 'type/realax/real',B: TA > $o,A: TA > 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ TA @ B
@ ^ [D: TA] : ( 'const/realax/real_neg' @ ( A @ D ) ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3 @ C ) )
| ( ( ^ [D: skt1] : ( 'const/realax/real_add' @ ( sk1 @ D ) @ ( C @ D ) ) )
!= ( ^ [D: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ D ) @ ( sk2 @ D ) ) ) )
| ( ( 'const/realax/real_neg' @ ( 'const/iterate/sum' @ TA @ B @ A ) )
!= ( 'const/realax/real_neg' @ ( 'const/iterate/sum' @ skt1 @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,785]) ).
thf(834,plain,
! [A: skt1 > 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [B: skt1] : ( 'const/realax/real_neg' @ ( sk2 @ B ) ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3 @ A ) )
| ( ( ^ [B: skt1] : ( 'const/realax/real_add' @ ( sk1 @ B ) @ ( A @ B ) ) )
!= ( ^ [B: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[833:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( C )),bind_type(TA,$thf( skt1 ))]]) ).
thf(864,plain,
! [A: skt1 > 'type/realax/real'] :
( ( ( 'const/iterate/sum' @ skt1 @ sk3
@ ^ [B: skt1] : ( 'const/realax/real_neg' @ ( sk2 @ B ) ) )
!= ( 'const/iterate/sum' @ skt1 @ sk3 @ A ) )
| ( ( ^ [B: skt1] : ( 'const/realax/real_add' @ ( sk1 @ B ) @ ( A @ B ) ) )
!= ( ^ [B: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[834]) ).
thf(876,plain,
! [A: skt1 > 'type/realax/real'] :
( ( sk3 != sk3 )
| ( ( ^ [B: skt1] : ( 'const/realax/real_neg' @ ( sk2 @ B ) ) )
!= A )
| ( ( ^ [B: skt1] : ( 'const/realax/real_add' @ ( sk1 @ B ) @ ( A @ B ) ) )
!= ( ^ [B: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ B ) @ ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[864]) ).
thf(910,plain,
( ( ^ [A: skt1] : ( 'const/realax/real_add' @ ( sk1 @ A ) @ ( 'const/realax/real_neg' @ ( sk2 @ A ) ) ) )
!= ( ^ [A: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ),
inference(simp,[status(thm)],[876]) ).
thf(917,plain,
( ( ^ [A: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( ^ [A: skt1] : ( 'const/realax/real_sub' @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ),
inference(rewrite,[status(thm)],[910,19]) ).
thf(918,plain,
$false,
inference(simp,[status(thm)],[917]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA101^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.11 % 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
% 0.24/0.29 % Computer : n019.cluster.edu
% 0.24/0.29 % Model : x86_64 x86_64
% 0.24/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.29 % Memory : 8046.5625MB
% 0.24/0.29 % OS : Linux 6.8.0-71-generic
% 0.24/0.30 % CPULimit : 300
% 0.24/0.30 % WCLimit : 300
% 0.24/0.30 % DateTime : Tue Sep 29 17:41:32 UTC 2026
% 0.24/0.30 % CPUTime :
% 0.24/0.30 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
% 1.31/1.10 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.78/1.33 % [INFO] Parsing done (226ms).
% 1.78/1.34 % [INFO] Running in sequential loop mode.
% 2.44/1.77 % [INFO] eprover registered as external prover.
% 2.44/1.78 % [INFO] Scanning for conjecture ...
% 2.64/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.84/1.93 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.84/1.94 % [INFO] Problem is higher-order (TPTP THF).
% 2.84/1.95 % [INFO] Type checking passed.
% 2.84/1.95 % [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 ...
% 23.05/6.82 % [INFO] Killing All external provers ...
% 23.05/6.83 % Time passed: 6323ms (effective reasoning time: 5476ms)
% 23.05/6.83 % 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)>
% 23.05/6.83 % Axioms used in derivation (3): thm/iterate/SUM_NEG_, thm/realax/real_sub_, thm/iterate/SUM_ADD_
% 23.05/6.83 % No. of inferences in proof: 36
% 23.05/6.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6323 ms resp. 5476 ms w/o parsing
% 23.55/6.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.55/6.93 % [INFO] Killing All external provers ...
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