%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM016-1 : 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 : n015.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 2.43s 1.48s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 128 ( 20 ~; 20 |; 0 &; 88 @)
% ( 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 : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(prime_decl,type,
prime: $i > $o ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(factorial_plus_one_decl,type,
factorial_plus_one: $i > $i ).
thf(divides_decl,type,
divides: $i > $i > $o ).
thf(prime_divisor_decl,type,
prime_divisor: $i > $i ).
thf(12,axiom,
a @ prime,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_prime) ).
thf(33,plain,
a @ prime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( A @ ( a @ factorial_plus_one @ less ) )
| ~ ( A @ ( a @ less ) )
| ~ ( A @ prime ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_another_prime) ).
thf(13,plain,
! [A: $i] :
( ( A @ ( a @ factorial_plus_one @ less ) )
| ~ ( A @ ( a @ less ) )
| ~ ( A @ prime ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less ) )
| ~ ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',numbers_are_different) ).
thf(17,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less ) )
| ~ ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ( A @ prime_divisor @ less ) )
| ( A @ prime ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',smaller_prime_divisors) ).
thf(31,plain,
! [A: $i] :
( ( A @ ( A @ prime_divisor @ less ) )
| ( A @ prime ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i] : ( A @ ( A @ divides ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',everything_divides_itself) ).
thf(19,plain,
! [A: $i] : ( A @ ( A @ divides ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [A: $i] :
~ ( A @ ( A @ less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).
thf(15,plain,
! [A: $i] :
~ ( A @ ( A @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i] : ( A @ factorial_plus_one @ ( A @ less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).
thf(24,plain,
! [A: $i] : ( A @ factorial_plus_one @ ( A @ less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ less ) )
| ~ ( B @ factorial_plus_one @ ( A @ divides ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor_is_smaller) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ less ) )
| ~ ( B @ factorial_plus_one @ ( A @ divides ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ divides ) )
| ~ ( C @ ( B @ divides ) )
| ~ ( B @ ( A @ divides ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_divides) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ divides ) )
| ~ ( C @ ( B @ divides ) )
| ~ ( B @ ( A @ divides ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ prime_divisor @ prime )
| ( A @ prime ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_divsiors) ).
thf(29,plain,
! [A: $i] :
( ( A @ prime_divisor @ prime )
| ( A @ prime ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less ) )
| ~ ( B @ ( A @ divides ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',small_divides_large) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less ) )
| ~ ( B @ ( A @ divides ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( A @ prime_divisor @ divides ) )
| ( A @ prime ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',division_by_prime_divisor) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( A @ prime_divisor @ divides ) )
| ( A @ prime ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,plain,
$false,
inference(e,[status(thm)],[33,13,17,31,19,15,24,25,20,29,22,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM016-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.14/0.40 % Computer : n015.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 01:56:43 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.71/0.70 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.79 % [INFO] Parsing done (91ms).
% 0.94/0.80 % [INFO] Running in sequential loop mode.
% 1.15/0.99 % [INFO] eprover registered as external prover.
% 1.15/0.99 % [INFO] Scanning for conjecture ...
% 1.43/1.04 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 1.43/1.06 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.43/1.06 % [INFO] Problem is propositional (TPTP CNF).
% 1.43/1.07 % [INFO] Type checking passed.
% 1.43/1.07 % [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 ...
% 2.43/1.48 % External prover 'e' found a proof!
% 2.43/1.48 % [INFO] Killing All external provers ...
% 2.43/1.48 % Time passed: 984ms (effective reasoning time: 674ms)
% 2.43/1.48 % Axioms used in derivation (11): prime_divsiors, transitivity_of_divides, divisor_is_smaller, smaller_prime_divisors, numbers_are_different, a_is_prime, nothing_is_less_than_itself, everything_divides_itself, small_divides_large, a_prime_is_less_than_the_next_one, division_by_prime_divisor
% 2.43/1.48 % No. of inferences in proof: 25
% 2.43/1.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 984 ms resp. 674 ms w/o parsing
% 2.67/1.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.67/1.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------