%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA109^1 : 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 : n016.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 3.54s 2.29s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 2 def)
% Number of atoms : 48 ( 18 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 113 ( 7 ~; 0 |; 0 &; 106 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-4 aty)
% Number of variables : 25 ( 0 ^; 23 !; 0 ?; 25 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf('type/nums/num_type',type,
'type/nums/num': $tType ).
thf('const/sets/INSERT_decl',type,
'const/sets/INSERT':
!>[TA: $tType] : ( TA > ( TA > $o ) > TA > $o ) ).
thf('const/sets/EMPTY_decl',type,
'const/sets/EMPTY':
!>[TA: $tType] : ( TA > $o ) ).
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' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/nums/num' > 'type/realax/real'] :
~ ! [B: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ B ) @ A )
= ( A @ B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ A ) @ sk1 )
!= ( sk1 @ A ) ) ) ) ).
thf(1,conjecture,
! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ B ) @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_SING_NUMSEG_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ B ) @ A )
= ( A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ B ) @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk2 @ sk2 ) @ sk1 )
!= ( sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk2 @ sk2 ) @ sk1 )
!= ( sk1 @ sk2 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(4,axiom,
! [A: 'type/nums/num'] :
( ( 'const/iterate/..' @ A @ A )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ A @ ( 'const/sets/EMPTY' @ 'type/nums/num' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NUMSEG_SING_') ).
thf(11,plain,
! [A: 'type/nums/num'] :
( ( 'const/iterate/..' @ A @ A )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ A @ ( 'const/sets/EMPTY' @ 'type/nums/num' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
! [A: 'type/nums/num'] :
( ( 'const/iterate/..' @ A @ A )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ A @ ( 'const/sets/EMPTY' @ 'type/nums/num' ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [A: 'type/nums/num'] :
( ( 'const/iterate/..' @ A @ A )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ A @ ( 'const/sets/EMPTY' @ 'type/nums/num' ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(14,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/sets/INSERT' @ 'type/nums/num' @ sk2 @ ( 'const/sets/EMPTY' @ 'type/nums/num' ) ) @ sk1 )
!= ( sk1 @ sk2 ) ),
inference(rewrite,[status(thm)],[7,13]) ).
thf(3,axiom,
! [TA: $tType,A: TA > 'type/realax/real',B: TA] :
( ( 'const/iterate/sum' @ TA @ ( 'const/sets/INSERT' @ TA @ B @ ( 'const/sets/EMPTY' @ TA ) ) @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_SING_') ).
thf(8,plain,
! [TA: $tType,A: TA > 'type/realax/real',B: TA] :
( ( 'const/iterate/sum' @ TA @ ( 'const/sets/INSERT' @ TA @ B @ ( 'const/sets/EMPTY' @ TA ) ) @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
! [TA: $tType,B: TA,A: TA > 'type/realax/real'] :
( ( 'const/iterate/sum' @ TA @ ( 'const/sets/INSERT' @ TA @ B @ ( 'const/sets/EMPTY' @ TA ) ) @ A )
= ( A @ B ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
! [TA: $tType,B: TA,A: TA > 'type/realax/real'] :
( ( 'const/iterate/sum' @ TA @ ( 'const/sets/INSERT' @ TA @ B @ ( 'const/sets/EMPTY' @ TA ) ) @ A )
= ( A @ B ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(16,plain,
$false,
inference(simplifyReflect,[status(thm)],[14,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA109^1 : 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
% 0.14/0.26 % Computer : n016.cluster.edu
% 0.14/0.26 % Model : x86_64 x86_64
% 0.14/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.26 % Memory : 8046.5625MB
% 0.14/0.26 % OS : Linux 6.8.0-71-generic
% 0.14/0.27 % CPULimit : 300
% 0.14/0.27 % WCLimit : 300
% 0.14/0.27 % DateTime : Tue Sep 29 17:49:41 UTC 2026
% 0.14/0.27 % CPUTime :
% 0.14/0.27 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
% 0.93/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.34/1.03 % [INFO] Parsing done (199ms).
% 1.34/1.05 % [INFO] Running in sequential loop mode.
% 1.87/1.46 % [INFO] eprover registered as external prover.
% 1.87/1.46 % [INFO] Scanning for conjecture ...
% 2.08/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.08/1.59 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.25/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.25/1.61 % [INFO] Type checking passed.
% 2.25/1.61 % [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 ...
% 3.54/2.28 % [INFO] Killing All external provers ...
% 3.54/2.28 % Time passed: 1877ms (effective reasoning time: 1227ms)
% 3.54/2.28 % 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)>
% 3.54/2.29 % Axioms used in derivation (2): thm/iterate/NUMSEG_SING_, thm/iterate/SUM_SING_
% 3.54/2.29 % No. of inferences in proof: 15
% 3.54/2.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1877 ms resp. 1227 ms w/o parsing
% 3.83/2.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.83/2.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------