TSTP Solution File: NUM016-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM016-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:39:45 EDT 2023
% Result : Unsatisfiable 2.69s 1.55s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 23 ( 5 unt; 6 typ; 0 def)
% Number of atoms : 31 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 88 ( 12 ~; 14 |; 0 &; 62 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(prime_type,type,
prime: $i > $o ).
thf(less_type,type,
less: $i > $i > $o ).
thf(a_type,type,
a: $i ).
thf(factorial_plus_one_type,type,
factorial_plus_one: $i > $i ).
thf(divides_type,type,
divides: $i > $i > $o ).
thf(prime_divisor_type,type,
prime_divisor: $i > $i ).
thf(7,axiom,
! [A: $i] :
( ( prime @ A )
| ( prime @ ( prime_divisor @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_divsiors) ).
thf(20,plain,
! [A: $i] :
( ( prime @ A )
| ( prime @ ( prime_divisor @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ~ ( prime @ A )
| ~ ( less @ a @ A )
| ( less @ ( factorial_plus_one @ a ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_another_prime) ).
thf(9,plain,
! [A: $i] :
( ~ ( prime @ A )
| ~ ( less @ a @ A )
| ( less @ ( factorial_plus_one @ a ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',numbers_are_different) ).
thf(13,plain,
! [B: $i,A: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i] :
( ( prime @ A )
| ( less @ ( prime_divisor @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_prime_divisors) ).
thf(22,plain,
! [A: $i] :
( ( prime @ A )
| ( less @ ( prime_divisor @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i] :
( ( prime @ A )
| ( divides @ ( prime_divisor @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',division_by_prime_divisor) ).
thf(18,plain,
! [A: $i] :
( ( prime @ A )
| ( divides @ ( prime_divisor @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( divides @ A @ ( factorial_plus_one @ B ) )
| ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_is_smaller) ).
thf(16,plain,
! [B: $i,A: $i] :
( ~ ( divides @ A @ ( factorial_plus_one @ B ) )
| ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [A: $i] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).
thf(11,plain,
! [A: $i] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i] : ( less @ A @ ( factorial_plus_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).
thf(15,plain,
! [A: $i] : ( less @ A @ ( factorial_plus_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,plain,
$false,
inference(e,[status(thm)],[20,9,13,22,18,16,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM016-2 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 17:32:30 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.93/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.94 % [INFO] Parsing done (105ms).
% 1.23/0.94 % [INFO] Running in sequential loop mode.
% 1.62/1.15 % [INFO] eprover registered as external prover.
% 1.62/1.15 % [INFO] cvc4 registered as external prover.
% 1.62/1.15 % [INFO] Scanning for conjecture ...
% 1.70/1.20 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 1.70/1.22 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.70/1.23 % [INFO] Problem is propositional (TPTP CNF).
% 1.70/1.23 % [INFO] Type checking passed.
% 1.89/1.23 % [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 ...
% 2.69/1.54 % External prover 'e' found a proof!
% 2.69/1.54 % [INFO] Killing All external provers ...
% 2.69/1.54 % Time passed: 1036ms (effective reasoning time: 596ms)
% 2.69/1.54 % 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)>
% 2.69/1.54 % Axioms used in derivation (7): prime_divsiors, divisor_is_smaller, smaller_prime_divisors, numbers_are_different, nothing_is_less_than_itself, a_prime_is_less_than_the_next_one, division_by_prime_divisor
% 2.69/1.54 % No. of inferences in proof: 17
% 2.69/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1036 ms resp. 596 ms w/o parsing
% 2.78/1.61 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.78/1.61 % [INFO] Killing All external provers ...
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