%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM519+3 : TPTP v9.3.1. Released v4.0.0.
% 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 : n017.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 : ContradictoryAxioms 36.85s 9.87s
% Output : Refutation 37.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 66 ( 18 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 146 ( 19 ~; 20 |; 23 &; 84 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 14 ( 0 ^; 2 !; 10 ?; 14 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% 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(xn_decl,type,
xn: $i ).
thf(xm_decl,type,
xm: $i ).
thf(xr_decl,type,
xr: $i ).
thf(sk19_decl,type,
sk19: $o ).
thf(sk20_decl,type,
sk20: $i ).
thf(sk21_decl,type,
sk21: $i ).
thf(sk20_def,definition,
( sk20
= ( @+[A: $i] :
( ( xn
= ( A @ ( xr @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i] :
( ( xm
= ( A @ ( xr @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ) ).
thf(54,axiom,
( ( ( xm @ ( xr @ doDivides0 ) )
& ? [A: $i] :
( ( xm
= ( A @ ( xr @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) )
| ( ( xn @ ( xr @ doDivides0 ) )
& ? [A: $i] :
( ( xn
= ( A @ ( xr @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2449) ).
thf(385,plain,
( ( ( xm @ ( xr @ doDivides0 ) )
& ? [A: $i] :
( ( xm
= ( A @ ( xr @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) )
| ( ( xn @ ( xr @ doDivides0 ) )
& ? [A: $i] :
( ( xn
= ( A @ ( xr @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(386,plain,
( ( ( xm @ ( xr @ doDivides0 ) )
| ~ sk19 )
& ( ( xm
= ( sk21 @ ( xr @ sdtasdt0 ) ) )
| ~ sk19 )
& ( ( sk21 @ aNaturalNumber0 )
| ~ sk19 )
& ( sk19
| ( xn @ ( xr @ doDivides0 ) ) )
& ( sk19
| ( xn
= ( sk20 @ ( xr @ sdtasdt0 ) ) ) )
& ( sk19
| ( sk20 @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[385]) ).
thf(391,plain,
( ( xm @ ( xr @ doDivides0 ) )
| ~ sk19 ),
inference(cnfConj,[status(thm)],[386]) ).
thf(29,axiom,
~ ( ( xm @ ( xr @ doDivides0 ) )
| ? [A: $i] :
( ( xm
= ( A @ ( xr @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2698) ).
thf(207,plain,
~ ( ( xm @ ( xr @ doDivides0 ) )
| ? [A: $i] :
( ( xm
= ( A @ ( xr @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(208,plain,
~ ( ( xm @ ( xr @ doDivides0 ) )
| ? [A: $i] :
( ( xm
= ( A @ ( xr @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
inference(polarity_switch,[status(thm)],[207]) ).
thf(209,plain,
! [A: $i] :
( ~ ( xm @ ( xr @ doDivides0 ) )
& ( ( xm
!= ( A @ ( xr @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[208]) ).
thf(211,plain,
~ ( xm @ ( xr @ doDivides0 ) ),
inference(cnfConj,[status(thm)],[209]) ).
thf(389,plain,
( sk19
| ( xn @ ( xr @ doDivides0 ) ) ),
inference(cnfConj,[status(thm)],[386]) ).
thf(20,axiom,
~ ( ( xn @ ( xr @ doDivides0 ) )
| ? [A: $i] :
( ( xn
= ( A @ ( xr @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
thf(150,plain,
~ ( ( xn @ ( xr @ doDivides0 ) )
| ? [A: $i] :
( ( xn
= ( A @ ( xr @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(151,plain,
~ ( ( xn @ ( xr @ doDivides0 ) )
| ? [A: $i] :
( ( xn
= ( A @ ( xr @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
inference(polarity_switch,[status(thm)],[150]) ).
thf(152,plain,
! [A: $i] :
( ~ ( xn @ ( xr @ doDivides0 ) )
& ( ( xn
!= ( A @ ( xr @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[151]) ).
thf(154,plain,
~ ( xn @ ( xr @ doDivides0 ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(805,plain,
( sk19
| $false ),
inference(rewrite,[status(thm)],[389,154]) ).
thf(806,plain,
sk19,
inference(simp,[status(thm)],[805]) ).
thf(13487,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[391,211,806]) ).
thf(13488,plain,
$false,
inference(simp,[status(thm)],[13487]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM519+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.15/0.41 % Computer : n017.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 03:00:17 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 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
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.45/1.25 % [INFO] Parsing done (241ms).
% 1.45/1.26 % [INFO] Running in sequential loop mode.
% 2.31/1.66 % [INFO] eprover registered as external prover.
% 2.31/1.67 % [INFO] Scanning for conjecture ...
% 2.55/1.75 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.55/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.76/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 53 axioms. Running axiom selection ...
% 2.98/1.91 % [INFO] Axiom selection finished. Selected 53 axioms (removed 0 axioms).
% 2.98/1.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.98/1.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.98/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.98/1.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.98/1.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.98/2.00 % [INFO] Problem is first-order (TPTP FOF).
% 2.98/2.02 % [INFO] Type checking passed.
% 2.98/2.02 % [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 ...
% 36.85/9.86 % [INFO] Killing All external provers ...
% 36.85/9.86 % Time passed: 9304ms (effective reasoning time: 8592ms)
% 36.85/9.87 % Axioms used in derivation (3): m__2449, m__2698, m__2487
% 36.85/9.87 % No. of inferences in proof: 19
% 36.85/9.87 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9304 ms resp. 8592 ms w/o parsing
% 37.30/9.90 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 37.30/9.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------