%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n007.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 3.12s 2.21s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 90 ( 12 ~; 12 |; 0 &; 66 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(divides_decl,type,
divides: $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(square_decl,type,
square: $i > $i ).
thf(prime_decl,type,
prime: $i > $o ).
thf(c_decl,type,
c: $i ).
thf(2,axiom,
! [A: $i] : ( A @ square @ ( A @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square) ).
thf(10,plain,
! [A: $i] : ( A @ square @ ( A @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ divides ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ divides ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
a @ prime,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_prime) ).
thf(17,plain,
a @ prime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
b @ square @ ( c @ square @ ( a @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b_squared_by_c_squared) ).
thf(18,plain,
b @ square @ ( c @ square @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
~ ( b @ ( a @ divides ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divides_b) ).
thf(8,plain,
~ ( b @ ( a @ divides ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ divides ) )
| ( B @ ( A @ divides ) )
| ~ ( D @ ( A @ divides ) )
| ~ ( D @ ( C @ ( B @ product ) ) )
| ~ ( A @ prime ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',remainder) ).
thf(15,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ divides ) )
| ( B @ ( A @ divides ) )
| ~ ( D @ ( A @ divides ) )
| ~ ( D @ ( C @ ( B @ product ) ) )
| ~ ( A @ prime ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
$false,
inference(e,[status(thm)],[10,13,17,18,11,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.14/0.39 % Computer : n007.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 01:51:08 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.17 % [INFO] Parsing done (187ms).
% 1.22/1.18 % [INFO] Running in sequential loop mode.
% 1.74/1.59 % [INFO] eprover registered as external prover.
% 1.91/1.60 % [INFO] Scanning for conjecture ...
% 1.91/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.08/1.71 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.08/1.72 % [INFO] Problem is propositional (TPTP CNF).
% 2.08/1.73 % [INFO] Type checking passed.
% 2.08/1.73 % [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 ...
% 3.12/2.20 % External prover 'e' found a proof!
% 3.12/2.20 % [INFO] Killing All external provers ...
% 3.12/2.21 % Time passed: 1671ms (effective reasoning time: 1015ms)
% 3.12/2.21 % Axioms used in derivation (6): remainder, a_equals_b_squared_by_c_squared, divides, square, a_is_prime, commutativity
% 3.12/2.21 % No. of inferences in proof: 15
% 3.12/2.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1671 ms resp. 1015 ms w/o parsing
% 3.12/2.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.12/2.25 % [INFO] Killing All external provers ...
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