%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM484+1 : 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 : 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 08:08:57 AM UTC 2026
% Result : ContradictoryAxioms 8.73s 8.21s
% Output : Refutation 8.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 7 ( 0 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 0 |; 0 &; 5 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 2 usr; 2 con; 0-1 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(isPrime0_decl,type,
isPrime0: $i > $o ).
thf(xk_decl,type,
xk: $i ).
thf(38,axiom,
~ ~ ( xk @ isPrime0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1737) ).
thf(214,plain,
xk @ isPrime0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(4,axiom,
~ ( xk @ isPrime0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1725) ).
thf(53,plain,
~ ( xk @ isPrime0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(54,plain,
~ ( xk @ isPrime0 ),
inference(polarity_switch,[status(thm)],[53]) ).
thf(273,plain,
$false,
inference(rewrite,[status(thm)],[214,54]) ).
thf(274,plain,
$false,
inference(simp,[status(thm)],[273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM484+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.22/5.49 % Computer : n017.cluster.edu
% 0.22/5.49 % Model : x86_64 x86_64
% 0.22/5.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/5.49 % Memory : 8046.5625MB
% 0.22/5.49 % OS : Linux 6.8.0-71-generic
% 0.22/5.49 % CPULimit : 300
% 0.22/5.49 % WCLimit : 300
% 0.22/5.49 % DateTime : Sat Sep 26 02:51:53 UTC 2026
% 0.22/5.50 % CPUTime :
% 0.22/5.50 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
% 0.26/5.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.54/6.16 % [INFO] Parsing done (183ms).
% 1.54/6.17 % [INFO] Running in sequential loop mode.
% 2.31/6.50 % [INFO] eprover registered as external prover.
% 2.47/6.50 % [INFO] Scanning for conjecture ...
% 2.47/6.57 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/6.58 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/6.58 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/6.59 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/6.60 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/6.62 % [INFO] Found a conjecture (or negated_conjecture) and 42 axioms. Running axiom selection ...
% 2.75/6.69 % [INFO] Axiom selection finished. Selected 42 axioms (removed 0 axioms).
% 3.02/6.71 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.02/6.72 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.02/6.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.02/6.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.02/6.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.02/6.76 % [INFO] Problem is first-order (TPTP FOF).
% 3.02/6.77 % [INFO] Type checking passed.
% 3.02/6.77 % [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 ...
% 8.73/8.20 % [INFO] Killing All external provers ...
% 8.73/8.21 % Time passed: 2572ms (effective reasoning time: 2031ms)
% 8.73/8.21 % Axioms used in derivation (2): m__1737, m__1725
% 8.73/8.21 % No. of inferences in proof: 7
% 8.73/8.21 % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 2572 ms resp. 2031 ms w/o parsing
% 8.73/8.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.73/8.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------