%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV494^1 : 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 08:37:22 AM UTC 2026
% Result : Theorem 4.76s 2.57s
% Output : Refutation 5.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 89 ( 24 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 245 ( 12 ~; 5 |; 1 &; 220 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 25 ( 0 ^; 23 !; 0 ?; 25 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
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/nums/SUC_decl',type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
thf('const/nums/NUMERAL_decl',type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf('const/nums/BIT1_decl',type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf('const/nums/_0_decl',type,
'const/nums/_0': 'type/nums/num' ).
thf('const/iterate/.._decl',type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf('const/arith/-_decl',type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf('const/arith/<=_decl',type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(sk1_decl,type,
sk1: 'type/nums/num' ).
thf(sk2_decl,type,
sk2: 'type/nums/num' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/nums/num'] :
~ ! [B: 'type/nums/num'] :
( ( 'const/arith/<=' @ A @ ( 'const/nums/SUC' @ B ) )
=> ( ( 'const/iterate/..' @ A @ ( 'const/nums/SUC' @ B ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ B ) @ ( 'const/iterate/..' @ A @ B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/nums/num'] :
~ ( ( 'const/arith/<=' @ sk1 @ ( 'const/nums/SUC' @ A ) )
=> ( ( 'const/iterate/..' @ sk1 @ ( 'const/nums/SUC' @ A ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ A ) @ ( 'const/iterate/..' @ sk1 @ A ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( 'const/arith/<=' @ A @ ( 'const/nums/SUC' @ B ) )
=> ( ( 'const/iterate/..' @ A @ ( 'const/nums/SUC' @ B ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ B ) @ ( 'const/iterate/..' @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NUMSEG_REC_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( 'const/arith/<=' @ A @ ( 'const/nums/SUC' @ B ) )
=> ( ( 'const/iterate/..' @ A @ ( 'const/nums/SUC' @ B ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ B ) @ ( 'const/iterate/..' @ A @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( 'const/arith/<=' @ A @ ( 'const/nums/SUC' @ B ) )
=> ( ( 'const/iterate/..' @ A @ ( 'const/nums/SUC' @ B ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ B ) @ ( 'const/iterate/..' @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( 'const/arith/<=' @ sk1 @ ( 'const/nums/SUC' @ sk2 ) )
& ( ( 'const/iterate/..' @ sk1 @ ( 'const/nums/SUC' @ sk2 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sk2 ) @ ( 'const/iterate/..' @ sk1 @ sk2 ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
'const/arith/<=' @ sk1 @ ( 'const/nums/SUC' @ sk2 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(4,axiom,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( 'const/arith/<=' @ A @ B )
=> ( ( 'const/sets/INSERT' @ 'type/nums/num' @ B @ ( 'const/iterate/..' @ A @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NUMSEG_RREC_') ).
thf(13,plain,
! [A: 'type/nums/num',B: 'type/nums/num'] :
( ( 'const/arith/<=' @ A @ B )
=> ( ( 'const/sets/INSERT' @ 'type/nums/num' @ B @ ( 'const/iterate/..' @ A @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ~ ( 'const/arith/<=' @ A @ B )
| ( ( 'const/sets/INSERT' @ 'type/nums/num' @ B @ ( 'const/iterate/..' @ A @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ A @ B ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( ( 'const/sets/INSERT' @ 'type/nums/num' @ B @ ( 'const/iterate/..' @ A @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ A @ B ) )
| ~ ( 'const/arith/<=' @ A @ B ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(26,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( ( 'const/sets/INSERT' @ 'type/nums/num' @ B @ ( 'const/iterate/..' @ A @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ A @ B ) )
| ~ $true
| ( ( 'const/arith/<=' @ sk1 @ ( 'const/nums/SUC' @ sk2 ) )
!= ( 'const/arith/<=' @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7,15]) ).
thf(27,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( ( 'const/sets/INSERT' @ 'type/nums/num' @ B @ ( 'const/iterate/..' @ A @ ( 'const/arith/-' @ B @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ A @ B ) )
| ( ( 'const/arith/<=' @ sk1 @ ( 'const/nums/SUC' @ sk2 ) )
!= ( 'const/arith/<=' @ A @ B ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(28,plain,
( ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sk2 ) @ ( 'const/iterate/..' @ sk1 @ ( 'const/arith/-' @ ( 'const/nums/SUC' @ sk2 ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ) )
= ( 'const/iterate/..' @ sk1 @ ( 'const/nums/SUC' @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( sk1 )),bind(B,$thf( 'const/nums/SUC' @ sk2 ))]]) ).
thf(3,axiom,
! [A: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/nums/SUC' @ A ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/arith/SUC_SUB1_') ).
thf(10,plain,
! [A: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/nums/SUC' @ A ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [A: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/nums/SUC' @ A ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= A ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [A: 'type/nums/num'] :
( ( 'const/arith/-' @ ( 'const/nums/SUC' @ A ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) )
= A ),
inference(lifteq,[status(thm)],[11]) ).
thf(38,plain,
( ( 'const/iterate/..' @ sk1 @ ( 'const/nums/SUC' @ sk2 ) )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sk2 ) @ ( 'const/iterate/..' @ sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[28,12]) ).
thf(8,plain,
( ( 'const/iterate/..' @ sk1 @ ( 'const/nums/SUC' @ sk2 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sk2 ) @ ( 'const/iterate/..' @ sk1 @ sk2 ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(9,plain,
( ( 'const/iterate/..' @ sk1 @ ( 'const/nums/SUC' @ sk2 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ ( 'const/nums/SUC' @ sk2 ) @ ( 'const/iterate/..' @ sk1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(39,plain,
$false,
inference(simplifyReflect,[status(thm)],[38,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV494^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % 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
% 0.10/0.20 % Computer : n015.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 15:56:32 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.91/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.99 % [INFO] Parsing done (205ms).
% 1.24/1.01 % [INFO] Running in sequential loop mode.
% 2.10/1.42 % [INFO] eprover registered as external prover.
% 2.10/1.43 % [INFO] Scanning for conjecture ...
% 2.28/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.28/1.57 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.28/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.28/1.58 % [INFO] Type checking passed.
% 2.28/1.59 % [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 ...
% 4.76/2.57 % [INFO] Killing All external provers ...
% 4.76/2.57 % Time passed: 2217ms (effective reasoning time: 1553ms)
% 4.76/2.57 % 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)>
% 4.76/2.57 % Axioms used in derivation (2): thm/iterate/NUMSEG_RREC_, thm/arith/SUC_SUB1_
% 4.76/2.57 % No. of inferences in proof: 20
% 4.76/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2217 ms resp. 1553 ms w/o parsing
% 5.13/2.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.13/2.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------