%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM015-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n020.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 08:08:05 AM UTC 2026
% Result : Unsatisfiable 4.19s 2.16s
% Output : Refutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 112 ( 16 ~; 20 |; 0 &; 76 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(prime_decl,type,
prime: $i > $o ).
thf(divides_decl,type,
divides: $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(divisor_decl,type,
divisor: $i > $i ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(n1_decl,type,
n1: $i ).
thf(factor_of_decl,type,
factor_of: $i > $i ).
thf(1,negated_conjecture,
! [A: $i] :
( ~ ( a @ ( A @ divides ) )
| ~ ( A @ prime ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_has_prime_divisor) ).
thf(10,plain,
! [A: $i] :
( ~ ( a @ ( A @ divides ) )
| ~ ( A @ prime ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
a @ ( n1 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_greater_than_1) ).
thf(25,plain,
a @ ( n1 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ factor_of @ prime )
| ~ ( a @ ( A @ less ) )
| ~ ( A @ ( n1 @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',factor1) ).
thf(21,plain,
! [A: $i] :
( ( A @ factor_of @ prime )
| ~ ( a @ ( A @ less ) )
| ~ ( A @ ( n1 @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ divides ) )
| ~ ( C @ ( B @ divides ) )
| ~ ( B @ ( A @ divides ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_divide) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ divides ) )
| ~ ( C @ ( B @ divides ) )
| ~ ( B @ ( A @ divides ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ divisor @ ( n1 @ less ) )
| ( A @ prime ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor1) ).
thf(17,plain,
! [A: $i] :
( ( A @ divisor @ ( n1 @ less ) )
| ( A @ prime ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ divides ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divide_self) ).
thf(12,plain,
! [A: $i] : ( A @ ( A @ divides ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( A @ factor_of @ divides ) )
| ~ ( a @ ( A @ less ) )
| ~ ( A @ ( n1 @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',factor2) ).
thf(23,plain,
! [A: $i] :
( ( A @ ( A @ factor_of @ divides ) )
| ~ ( a @ ( A @ less ) )
| ~ ( A @ ( n1 @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ( A @ divisor @ less ) )
| ( A @ prime ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor2) ).
thf(19,plain,
! [A: $i] :
( ( A @ ( A @ divisor @ less ) )
| ( A @ prime ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( A @ divisor @ divides ) )
| ( A @ prime ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime) ).
thf(15,plain,
! [A: $i] :
( ( A @ ( A @ divisor @ divides ) )
| ( A @ prime ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,plain,
$false,
inference(e,[status(thm)],[10,25,21,13,17,12,23,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM015-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.25/0.50 % Computer : n020.cluster.edu
% 0.25/0.50 % Model : x86_64 x86_64
% 0.25/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.50 % Memory : 8046.5625MB
% 0.25/0.50 % OS : Linux 6.8.0-71-generic
% 0.25/0.50 % CPULimit : 300
% 0.25/0.50 % WCLimit : 300
% 0.25/0.50 % DateTime : Sat Sep 26 01:54:03 UTC 2026
% 0.25/0.50 % CPUTime :
% 0.25/0.50 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
% 0.96/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.15 % [INFO] Parsing done (151ms).
% 1.48/1.16 % [INFO] Running in sequential loop mode.
% 2.15/1.50 % [INFO] eprover registered as external prover.
% 2.15/1.51 % [INFO] Scanning for conjecture ...
% 2.15/1.58 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.37/1.61 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.37/1.62 % [INFO] Problem is propositional (TPTP CNF).
% 2.37/1.62 % [INFO] Type checking passed.
% 2.37/1.63 % [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 ...
% 4.19/2.15 % External prover 'e' found a proof!
% 4.19/2.15 % [INFO] Killing All external provers ...
% 4.19/2.15 % Time passed: 1520ms (effective reasoning time: 989ms)
% 4.19/2.16 % Axioms used in derivation (8): factor2, divisor1, factor1, divide_self, a_is_greater_than_1, transitive_divide, divisor2, prime
% 4.19/2.16 % No. of inferences in proof: 19
% 4.19/2.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1520 ms resp. 989 ms w/o parsing
% 4.19/2.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.19/2.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------