%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA106^1 : 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 : n015.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 07:45:47 AM UTC 2026
% Result : Theorem 4.58s 2.52s
% Output : Refutation 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 11 unt; 0 typ; 4 def)
% Number of atoms : 69 ( 20 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 357 ( 17 ~; 5 |; 0 &; 333 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 65 ( 17 ^; 44 !; 0 ?; 65 :)
% ( 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('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/iterate/sum_decl',type,
'const/iterate/sum':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > 'type/realax/real' ) > 'type/realax/real' ) ).
thf('const/iterate/.._decl',type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(sk1_decl,type,
sk1: 'type/nums/num' > 'type/realax/real' ).
thf(sk2_decl,type,
sk2: 'type/nums/num' > 'type/realax/real' ).
thf(sk3_decl,type,
sk3: 'type/nums/num' ).
thf(sk4_decl,type,
sk4: 'type/nums/num' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/nums/num' > 'type/realax/real'] :
~ ! [B: 'type/nums/num' > 'type/realax/real',C: 'type/nums/num',D: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( A @ E ) @ ( B @ E ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D ) @ A ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D ) @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/nums/num' > 'type/realax/real'] :
~ ! [B: 'type/nums/num',C: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ C )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sk1 @ D ) @ ( A @ D ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ C ) @ sk1 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ C ) @ A ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: 'type/nums/num'] :
~ ! [B: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ B )
@ ^ [C: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ B ) @ sk1 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ B ) @ sk2 ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ A )
@ ^ [B: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sk1 @ B ) @ ( sk2 @ B ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ A ) @ sk1 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ A ) @ sk2 ) ) ) ) ) ).
thf(3,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_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(8,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)],[3]) ).
thf(9,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_sub' @ ( A @ D ) @ ( B @ D ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,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_sub' @ ( A @ D ) @ ( B @ D ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) ) )
| ~ ( 'const/sets/FINITE' @ TA @ C ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(1,conjecture,
! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num' > 'type/realax/real',C: 'type/nums/num',D: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( A @ E ) @ ( B @ E ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D ) @ A ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_SUB_NUMSEG_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num' > 'type/realax/real',C: 'type/nums/num',D: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( A @ E ) @ ( B @ E ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D ) @ A ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D ) @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num' > 'type/realax/real',C: 'type/nums/num',D: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D )
@ ^ [E: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( A @ E ) @ ( B @ E ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D ) @ A ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [A: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 ) @ sk1 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 ) @ sk2 ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [A: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 ) @ sk1 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 ) @ sk2 ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(17,plain,
! [TA: $tType,C: TA > $o,B: TA > 'type/realax/real',A: TA > 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ TA @ C )
| ( ( 'const/iterate/sum' @ TA @ C
@ ^ [D: TA] : ( 'const/realax/real_sub' @ ( A @ D ) @ ( B @ D ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sk1 @ D ) @ ( sk2 @ D ) ) ) )
| ( ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ TA @ C @ A ) @ ( 'const/iterate/sum' @ TA @ C @ B ) )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 ) @ sk1 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 ) @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,7]) ).
thf(18,plain,
( ~ ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 ) )
| ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [A: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 )
@ ^ [A: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( 'const/iterate/..' @ sk3 @ sk4 )),bind_type(TA,$thf( 'type/nums/num' ))]]) ).
thf(26,plain,
~ ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[18]) ).
thf(4,axiom,
! [A: 'type/nums/num',B: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/FINITE_NUMSEG_') ).
thf(11,plain,
! [A: 'type/nums/num',B: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ B ) ),
inference(cnf,[status(esa)],[11]) ).
thf(30,plain,
~ $true,
inference(rewrite,[status(thm)],[26,12]) ).
thf(31,plain,
$false,
inference(simp,[status(thm)],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA106^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.07/0.20 % Computer : n015.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 17:45:03 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 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
% 1.01/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/1.00 % [INFO] Parsing done (187ms).
% 1.19/1.01 % [INFO] Running in sequential loop mode.
% 1.93/1.41 % [INFO] eprover registered as external prover.
% 1.93/1.42 % [INFO] Scanning for conjecture ...
% 2.08/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.08/1.56 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.08/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.58 % [INFO] Type checking passed.
% 2.08/1.58 % [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 ...
% 4.58/2.52 % [INFO] Killing All external provers ...
% 4.58/2.52 % Time passed: 2166ms (effective reasoning time: 1500ms)
% 4.58/2.52 % 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)>
% 4.58/2.52 % Axioms used in derivation (2): thm/iterate/SUM_SUB_, thm/iterate/FINITE_NUMSEG_
% 4.58/2.52 % No. of inferences in proof: 17
% 4.58/2.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2166 ms resp. 1500 ms w/o parsing
% 4.91/2.61 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.91/2.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------