%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA107^1 : 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 : n005.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 4.87s 2.89s
% Output : Refutation 5.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 5 unt; 0 typ; 3 def)
% Number of atoms : 53 ( 5 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 236 ( 14 ~; 4 |; 0 &; 216 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 50 ( 14 ^; 33 !; 0 ?; 50 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% 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_le_decl',type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf('const/realax/real_abs_decl',type,
'const/realax/real_abs': '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' ).
thf(sk3_decl,type,
sk3: 'type/nums/num' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/nums/num' > 'type/realax/real'] :
~ ! [B: 'type/nums/num',C: 'type/nums/num'] :
( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ C ) @ A ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ C )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_abs' @ ( A @ D ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/nums/num'] :
~ ! [B: 'type/nums/num'] :
( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ B ) @ sk1 ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ B )
@ ^ [C: 'type/nums/num'] : ( 'const/realax/real_abs' @ ( sk1 @ C ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: 'type/nums/num'] :
~ ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk2 @ A ) @ sk1 ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk2 @ A )
@ ^ [B: 'type/nums/num'] : ( 'const/realax/real_abs' @ ( sk1 @ B ) ) ) ) ) ) ).
thf(3,axiom,
! [TA: $tType,A: TA > 'type/realax/real',B: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ B )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ TA @ B @ A ) )
@ ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : ( 'const/realax/real_abs' @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_ABS_') ).
thf(7,plain,
! [TA: $tType,A: TA > 'type/realax/real',B: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ B )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ TA @ B @ A ) )
@ ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : ( 'const/realax/real_abs' @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [TA: $tType,B: TA > $o,A: TA > 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ TA @ B )
| ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ TA @ B @ A ) )
@ ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : ( 'const/realax/real_abs' @ ( A @ C ) ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(1,conjecture,
! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num',C: 'type/nums/num'] :
( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ C ) @ A ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ C )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_abs' @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_ABS_NUMSEG_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num',C: 'type/nums/num'] :
( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ C ) @ A ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ C )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_abs' @ ( A @ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: 'type/nums/num' > 'type/realax/real',B: 'type/nums/num',C: 'type/nums/num'] :
( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ C ) @ A ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ B @ C )
@ ^ [D: 'type/nums/num'] : ( 'const/realax/real_abs' @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk2 @ sk3 ) @ sk1 ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk2 @ sk3 )
@ ^ [A: 'type/nums/num'] : ( 'const/realax/real_abs' @ ( sk1 @ A ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(11,plain,
! [TA: $tType,B: TA > $o,A: TA > 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ TA @ B )
| ~ $true
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ TA @ B @ A ) )
@ ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : ( 'const/realax/real_abs' @ ( A @ C ) ) ) )
!= ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk2 @ sk3 ) @ sk1 ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk2 @ sk3 )
@ ^ [C: 'type/nums/num'] : ( 'const/realax/real_abs' @ ( sk1 @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,6]) ).
thf(12,plain,
! [TA: $tType,B: TA > $o,A: TA > 'type/realax/real'] :
( ~ ( 'const/sets/FINITE' @ TA @ B )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ TA @ B @ A ) )
@ ( 'const/iterate/sum' @ TA @ B
@ ^ [C: TA] : ( 'const/realax/real_abs' @ ( A @ C ) ) ) )
!= ( 'const/realax/real_le' @ ( 'const/realax/real_abs' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk2 @ sk3 ) @ sk1 ) )
@ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk2 @ sk3 )
@ ^ [C: 'type/nums/num'] : ( 'const/realax/real_abs' @ ( sk1 @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(13,plain,
~ ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[12:[bind(A,$thf( sk1 )),bind(B,$thf( 'const/iterate/..' @ sk2 @ sk3 )),bind_type(TA,$thf( 'type/nums/num' ))]]) ).
thf(4,axiom,
! [A: 'type/nums/num',B: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/FINITE_NUMSEG_') ).
thf(9,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(10,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ B ) ),
inference(cnf,[status(esa)],[9]) ).
thf(17,plain,
~ $true,
inference(rewrite,[status(thm)],[13,10]) ).
thf(18,plain,
$false,
inference(simp,[status(thm)],[17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA107^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.09 % 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
% 0.12/0.26 % Computer : n005.cluster.edu
% 0.12/0.26 % Model : x86_64 x86_64
% 0.12/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.26 % Memory : 8046.5625MB
% 0.12/0.26 % OS : Linux 6.8.0-71-generic
% 0.12/0.26 % CPULimit : 300
% 0.12/0.26 % WCLimit : 300
% 0.12/0.26 % DateTime : Tue Sep 29 17:41:46 UTC 2026
% 0.12/0.27 % CPUTime :
% 0.12/0.27 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
% 1.15/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.59/1.19 % [INFO] Parsing done (216ms).
% 1.71/1.21 % [INFO] Running in sequential loop mode.
% 2.33/1.66 % [INFO] eprover registered as external prover.
% 2.33/1.67 % [INFO] Scanning for conjecture ...
% 2.69/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.69/1.87 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.69/1.88 % [INFO] Problem is higher-order (TPTP THF).
% 2.69/1.89 % [INFO] Type checking passed.
% 2.69/1.90 % [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 ...
% 4.87/2.89 % [INFO] Killing All external provers ...
% 4.87/2.89 % Time passed: 2404ms (effective reasoning time: 1670ms)
% 4.87/2.89 % 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)>
% 4.87/2.89 % Axioms used in derivation (2): thm/iterate/SUM_ABS_, thm/iterate/FINITE_NUMSEG_
% 4.87/2.89 % No. of inferences in proof: 15
% 4.87/2.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2404 ms resp. 1670 ms w/o parsing
% 5.11/2.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.11/2.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------