%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM491+3 : TPTP v9.3.1. Released v4.0.0.
% 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 : n006.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 : Sun Sep 27 08:08:58 AM UTC 2026
% Result : Theorem 7.49s 3.35s
% Output : Refutation 7.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 6 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 83 ( 10 ~; 6 |; 10 &; 57 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 3 !; 3 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(aNaturalNumber0_decl,type,
aNaturalNumber0: $i > $o ).
thf(doDivides0_decl,type,
doDivides0: $i > $i > $o ).
thf(sdtasdt0_decl,type,
sdtasdt0: $i > $i > $i ).
thf(xp_decl,type,
xp: $i ).
thf(xm_decl,type,
xm: $i ).
thf(xn_decl,type,
xn: $i ).
thf(44,axiom,
( ( xp @ aNaturalNumber0 )
& ( xm @ aNaturalNumber0 )
& ( xn @ aNaturalNumber0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
thf(291,plain,
( ( xp @ aNaturalNumber0 )
& ( xm @ aNaturalNumber0 )
& ( xn @ aNaturalNumber0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(292,plain,
( ( xp @ aNaturalNumber0 )
& ( xm @ aNaturalNumber0 )
& ( xn @ aNaturalNumber0 ) ),
inference(cnf,[status(esa)],[291]) ).
thf(294,plain,
xm @ aNaturalNumber0,
inference(cnfConj,[status(thm)],[292]) ).
thf(1,conjecture,
( ( xm @ ( xp @ sdtasdt0 ) @ ( xp @ doDivides0 ) )
| ? [A: $i] :
( ( ( xm @ ( xp @ sdtasdt0 ) )
= ( A @ ( xp @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xm @ ( xp @ sdtasdt0 ) @ ( xp @ doDivides0 ) )
| ? [A: $i] :
( ( ( xm @ ( xp @ sdtasdt0 ) )
= ( A @ ( xp @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(50,plain,
~ ( ( xm @ ( xp @ sdtasdt0 ) @ ( xp @ doDivides0 ) )
| ? [A: $i] :
( ( ( xm @ ( xp @ sdtasdt0 ) )
= ( A @ ( xp @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(51,plain,
! [A: $i] :
( ~ ( xm @ ( xp @ sdtasdt0 ) @ ( xp @ doDivides0 ) )
& ( ( ( xm @ ( xp @ sdtasdt0 ) )
!= ( A @ ( xp @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
! [A: $i] :
( ( ( xm @ ( xp @ sdtasdt0 ) )
!= ( A @ ( xp @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(54,plain,
! [A: $i] :
( ~ ( A @ aNaturalNumber0 )
| ( ( xm @ ( xp @ sdtasdt0 ) )
!= ( A @ ( xp @ sdtasdt0 ) ) ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(326,plain,
~ ( xm @ aNaturalNumber0 ),
inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( xm ))]]) ).
thf(436,plain,
$false,
inference(rewrite,[status(thm)],[294,326]) ).
thf(437,plain,
$false,
inference(simp,[status(thm)],[436]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM491+3 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.14/0.40 % Computer : n006.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 02:57:56 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.83/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.48/1.21 % [INFO] Parsing done (228ms).
% 1.48/1.22 % [INFO] Running in sequential loop mode.
% 2.17/1.61 % [INFO] eprover registered as external prover.
% 2.17/1.62 % [INFO] Scanning for conjecture ...
% 2.35/1.70 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.35/1.71 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.35/1.72 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.35/1.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.35/1.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.35/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 47 axioms. Running axiom selection ...
% 2.52/1.85 % [INFO] Axiom selection finished. Selected 47 axioms (removed 0 axioms).
% 2.52/1.87 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.52/1.88 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.52/1.89 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/1.91 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/1.91 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/1.95 % [INFO] Problem is first-order (TPTP FOF).
% 2.75/1.96 % [INFO] Type checking passed.
% 2.75/1.97 % [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 ...
% 7.49/3.35 % [INFO] Killing All external provers ...
% 7.49/3.35 % Time passed: 2807ms (effective reasoning time: 2125ms)
% 7.49/3.35 % 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)>
% 7.49/3.35 % Axioms used in derivation (1): m__1837
% 7.49/3.35 % No. of inferences in proof: 13
% 7.49/3.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2807 ms resp. 2125 ms w/o parsing
% 7.49/3.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.49/3.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------