%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM514+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 : n018.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 08:09:02 AM UTC 2026
% Result : Theorem 45.86s 19.09s
% Output : Refutation 45.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 24 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 253 ( 16 ~; 9 |; 21 &; 204 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 5 !; 3 ?; 8 :)
% 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(sdtsldt0_decl,type,
sdtsldt0: $i > $i > $i ).
thf(xn_decl,type,
xn: $i ).
thf(xr_decl,type,
xr: $i ).
thf(xm_decl,type,
xm: $i ).
thf(xp_decl,type,
xp: $i ).
thf(xk_decl,type,
xk: $i ).
thf(41,axiom,
( ( ( xr @ ( xk @ sdtsldt0 ) @ ( xp @ sdtasdt0 ) )
= ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) ) )
& ( xn
= ( xr @ ( xn @ sdtsldt0 ) @ ( xr @ sdtasdt0 ) ) )
& ( xr @ ( xn @ sdtsldt0 ) @ aNaturalNumber0 )
& ( xk
= ( xr @ ( xk @ sdtsldt0 ) @ ( xr @ sdtasdt0 ) ) )
& ( xr @ ( xk @ sdtsldt0 ) @ aNaturalNumber0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2613) ).
thf(315,plain,
( ( ( xr @ ( xk @ sdtsldt0 ) @ ( xp @ sdtasdt0 ) )
= ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) ) )
& ( xn
= ( xr @ ( xn @ sdtsldt0 ) @ ( xr @ sdtasdt0 ) ) )
& ( xr @ ( xn @ sdtsldt0 ) @ aNaturalNumber0 )
& ( xk
= ( xr @ ( xk @ sdtsldt0 ) @ ( xr @ sdtasdt0 ) ) )
& ( xr @ ( xk @ sdtsldt0 ) @ aNaturalNumber0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(316,plain,
( ( ( xr @ ( xk @ sdtsldt0 ) @ ( xp @ sdtasdt0 ) )
= ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) ) )
& ( xn
= ( xr @ ( xn @ sdtsldt0 ) @ ( xr @ sdtasdt0 ) ) )
& ( xr @ ( xn @ sdtsldt0 ) @ aNaturalNumber0 )
& ( xk
= ( xr @ ( xk @ sdtsldt0 ) @ ( xr @ sdtasdt0 ) ) )
& ( xr @ ( xk @ sdtsldt0 ) @ aNaturalNumber0 ) ),
inference(cnf,[status(esa)],[315]) ).
thf(318,plain,
( ( xr @ ( xk @ sdtsldt0 ) @ ( xp @ sdtasdt0 ) )
= ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) ) ),
inference(cnfConj,[status(thm)],[316]) ).
thf(324,plain,
( ( xr @ ( xk @ sdtsldt0 ) @ ( xp @ sdtasdt0 ) )
= ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) ) ),
inference(lifteq,[status(thm)],[318]) ).
thf(1,conjecture,
( ( ( xn
= ( xr @ ( xn @ sdtsldt0 ) @ ( xr @ sdtasdt0 ) ) )
& ( xr @ ( xn @ sdtsldt0 ) @ aNaturalNumber0 ) )
=> ( ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) @ ( xp @ doDivides0 ) )
| ? [A: $i] :
( ( ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) )
= ( A @ ( xp @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( xn
= ( xr @ ( xn @ sdtsldt0 ) @ ( xr @ sdtasdt0 ) ) )
& ( xr @ ( xn @ sdtsldt0 ) @ aNaturalNumber0 ) )
=> ( ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) @ ( xp @ doDivides0 ) )
| ? [A: $i] :
( ( ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) )
= ( A @ ( xp @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(58,plain,
~ ( ( ( xn
= ( xr @ ( xn @ sdtsldt0 ) @ ( xr @ sdtasdt0 ) ) )
& ( xr @ ( xn @ sdtsldt0 ) @ aNaturalNumber0 ) )
=> ( ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) @ ( xp @ doDivides0 ) )
| ? [A: $i] :
( ( ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) )
= ( A @ ( xp @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(59,plain,
! [A: $i] :
( ~ ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) @ ( xp @ doDivides0 ) )
& ( ( ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) )
!= ( A @ ( xp @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) )
& ( xn
= ( xr @ ( xn @ sdtsldt0 ) @ ( xr @ sdtasdt0 ) ) )
& ( xr @ ( xn @ sdtsldt0 ) @ aNaturalNumber0 ) ),
inference(cnf,[status(esa)],[58]) ).
thf(62,plain,
! [A: $i] :
( ( ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) )
!= ( A @ ( xp @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[59]) ).
thf(65,plain,
! [A: $i] :
( ~ ( A @ aNaturalNumber0 )
| ( ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) )
!= ( A @ ( xp @ sdtasdt0 ) ) ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(20349,plain,
! [A: $i] :
( ( ( xr @ ( xk @ sdtsldt0 ) @ ( xp @ sdtasdt0 ) )
!= ( A @ ( xp @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 )
| ( ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) )
!= ( xm @ ( xr @ ( xn @ sdtsldt0 ) @ sdtasdt0 ) ) ) ),
inference(paramod_ordered,[status(thm)],[324,65]) ).
thf(20350,plain,
! [A: $i] :
( ( ( xr @ ( xk @ sdtsldt0 ) @ ( xp @ sdtasdt0 ) )
!= ( A @ ( xp @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[20349]) ).
thf(20351,plain,
~ ( xr @ ( xk @ sdtsldt0 ) @ aNaturalNumber0 ),
inference(pattern_uni,[status(thm)],[20350:[bind(A,$thf( xr @ ( xk @ sdtsldt0 ) ))]]) ).
thf(317,plain,
xr @ ( xk @ sdtsldt0 ) @ aNaturalNumber0,
inference(cnfConj,[status(thm)],[316]) ).
thf(20993,plain,
~ $true,
inference(rewrite,[status(thm)],[20351,317]) ).
thf(20994,plain,
$false,
inference(simp,[status(thm)],[20993]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM514+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
% 0.13/5.41 % Computer : n018.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Sat Sep 26 03:05:42 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 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
% 0.18/5.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.42/6.25 % [INFO] Parsing done (257ms).
% 1.42/6.27 % [INFO] Running in sequential loop mode.
% 2.37/6.67 % [INFO] eprover registered as external prover.
% 2.37/6.68 % [INFO] Scanning for conjecture ...
% 2.59/6.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/6.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/6.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/6.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/6.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.79/6.83 % [INFO] Found a conjecture (or negated_conjecture) and 55 axioms. Running axiom selection ...
% 2.97/6.93 % [INFO] Axiom selection finished. Selected 55 axioms (removed 0 axioms).
% 2.97/6.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.97/6.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.97/6.99 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.97/7.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.97/7.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.32/7.03 % [INFO] Problem is first-order (TPTP FOF).
% 3.32/7.05 % [INFO] Type checking passed.
% 3.32/7.05 % [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 ...
% 45.86/19.08 % [INFO] Killing All external provers ...
% 45.86/19.08 % Time passed: 13529ms (effective reasoning time: 12805ms)
% 45.86/19.08 % 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)>
% 45.86/19.08 % Axioms used in derivation (1): m__2613
% 45.86/19.08 % No. of inferences in proof: 17
% 45.86/19.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 13529 ms resp. 12805 ms w/o parsing
% 45.86/19.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 45.86/19.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------