%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM016^5 : 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 : n019.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 : Wed Sep 30 08:17:49 AM UTC 2026
% Result : Theorem 4.71s 2.65s
% Output : Refutation 4.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 0 equ; 0 cnn)
% Maximal formula atoms : 22 ( 16 avg)
% Number of connectives : 230 ( 35 ~; 30 |; 33 &; 132 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 15 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 : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_decl,type,
a: $i ).
thf(factorial_plus_one_decl,type,
factorial_plus_one: $i > $i ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(prime_decl,type,
prime: $i > $o ).
thf(prime_divisor_decl,type,
prime_divisor: $i > $i ).
thf(divides_decl,type,
divides: $i > $i > $o ).
thf(1,conjecture,
~ ( ! [A: $i] :
~ ( less @ A @ A )
& ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( divides @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ~ ( divides @ A @ B )
| ~ ( divides @ B @ C )
| ( divides @ A @ C ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( less @ A @ ( factorial_plus_one @ A ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ ( factorial_plus_one @ B ) )
| ( less @ B @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( divides @ ( prime_divisor @ A ) @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( prime @ ( prime_divisor @ A ) ) )
& ! [A: $i] :
( ( prime @ A )
| ( less @ ( prime_divisor @ A ) @ A ) )
& ( prime @ a )
& ! [A: $i] :
( ~ ( prime @ A )
| ~ ( less @ a @ A )
| ( less @ ( factorial_plus_one @ a ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cNUM016_1) ).
thf(2,negated_conjecture,
~ ~ ( ! [A: $i] :
~ ( less @ A @ A )
& ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( divides @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ~ ( divides @ A @ B )
| ~ ( divides @ B @ C )
| ( divides @ A @ C ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( less @ A @ ( factorial_plus_one @ A ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ ( factorial_plus_one @ B ) )
| ( less @ B @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( divides @ ( prime_divisor @ A ) @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( prime @ ( prime_divisor @ A ) ) )
& ! [A: $i] :
( ( prime @ A )
| ( less @ ( prime_divisor @ A ) @ A ) )
& ( prime @ a )
& ! [A: $i] :
( ~ ( prime @ A )
| ~ ( less @ a @ A )
| ( less @ ( factorial_plus_one @ a ) @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ( ! [A: $i] :
~ ( less @ A @ A )
& ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( divides @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ~ ( divides @ A @ B )
| ~ ( divides @ B @ C )
| ( divides @ A @ C ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ B )
| ~ ( less @ B @ A ) )
& ! [A: $i] : ( less @ A @ ( factorial_plus_one @ A ) )
& ! [A: $i,B: $i] :
( ~ ( divides @ A @ ( factorial_plus_one @ B ) )
| ( less @ B @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( divides @ ( prime_divisor @ A ) @ A ) )
& ! [A: $i] :
( ( prime @ A )
| ( prime @ ( prime_divisor @ A ) ) )
& ! [A: $i] :
( ( prime @ A )
| ( less @ ( prime_divisor @ A ) @ A ) )
& ( prime @ a )
& ! [A: $i] :
( ~ ( prime @ A )
| ~ ( less @ a @ A )
| ( less @ ( factorial_plus_one @ a ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM016^5 : 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
% 0.28/0.33 % Computer : n019.cluster.edu
% 0.28/0.33 % Model : x86_64 x86_64
% 0.28/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.28/0.33 % Memory : 8046.5625MB
% 0.28/0.33 % OS : Linux 6.8.0-71-generic
% 0.28/0.33 % CPULimit : 300
% 0.28/0.33 % WCLimit : 300
% 0.28/0.33 % DateTime : Tue Sep 29 11:52:02 UTC 2026
% 0.28/0.33 % CPUTime :
% 0.28/0.33 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
% 1.43/1.18 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.83/1.46 % [INFO] Parsing done (273ms).
% 1.83/1.48 % [INFO] Running in sequential loop mode.
% 2.62/1.95 % [INFO] eprover registered as external prover.
% 2.62/1.95 % [INFO] Scanning for conjecture ...
% 2.62/2.05 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.97/2.08 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.97/2.08 % [INFO] Problem is higher-order (TPTP THF).
% 2.97/2.09 % [INFO] Type checking passed.
% 2.97/2.09 % [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 ...
% 4.71/2.65 % External prover 'e' found a proof!
% 4.71/2.65 % [INFO] Killing All external provers ...
% 4.71/2.65 % Time passed: 2103ms (effective reasoning time: 1162ms)
% 4.71/2.65 % 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)>
% 4.71/2.65 % Axioms used in derivation (0):
% 4.71/2.65 % No. of inferences in proof: 4
% 4.71/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2103 ms resp. 1162 ms w/o parsing
% 4.95/2.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.95/2.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------