%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n005.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 08:08:06 AM UTC 2026
% Result : Unsatisfiable 6.06s 2.92s
% Output : Refutation 6.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 254 ( 42 ~; 38 |; 0 &; 174 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(divides_decl,type,
divides: $i > $i > $o ).
thf(c_decl,type,
c: $i ).
thf(b_decl,type,
b: $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(second_divided_by_1st_decl,type,
second_divided_by_1st: $i > $i > $i ).
thf(prime_decl,type,
prime: $i > $o ).
thf(a_decl,type,
a: $i ).
thf(d_decl,type,
d: $i ).
thf(e_decl,type,
e: $i ).
thf(14,axiom,
e @ ( c @ ( c @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_squared) ).
thf(41,plain,
e @ ( c @ ( c @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
a @ prime,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_prime) ).
thf(39,plain,
a @ prime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ divides ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_divisible_by_operand) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ divides ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,axiom,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product) ).
thf(18,plain,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ~ ( b @ ( A @ divides ) )
| ~ ( c @ ( A @ divides ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_no_common_divisor) ).
thf(16,plain,
! [A: $i] :
( ~ ( b @ ( A @ divides ) )
| ~ ( c @ ( A @ divides ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(15,axiom,
~ ( d @ ( e @ ( a @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_squared_is_not_b_squared) ).
thf(42,plain,
~ ( d @ ( e @ ( a @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ divides ) )
| ~ ( A @ prime )
| ~ ( B @ ( C @ ( C @ product ) ) )
| ~ ( B @ ( A @ divides ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',primes_lemma1) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ divides ) )
| ~ ( A @ prime )
| ~ ( B @ ( C @ ( C @ product ) ) )
| ~ ( B @ ( A @ divides ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ~ ( C @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ~ ( C @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ divides ) )
| ~ ( A @ ( C @ divides ) )
| ~ ( B @ ( A @ divides ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_divides) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ divides ) )
| ~ ( A @ ( C @ divides ) )
| ~ ( B @ ( A @ divides ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( F @ product ) ) )
| ~ ( A @ ( D @ ( F @ product ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_associativity2) ).
thf(21,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( F @ product ) ) )
| ~ ( A @ ( D @ ( F @ product ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ second_divided_by_1st ) @ ( A @ product ) ) )
| ~ ( B @ ( A @ divides ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_implies_product) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ second_divided_by_1st ) @ ( A @ product ) ) )
| ~ ( B @ ( A @ divides ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
d @ ( b @ ( b @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_squared) ).
thf(40,plain,
d @ ( b @ ( b @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_commutativity) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = C )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined_product) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = C )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( F @ product ) ) )
| ~ ( F @ ( D @ ( A @ product ) ) )
| ~ ( B @ ( E @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_associativity1) ).
thf(19,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( F @ product ) ) )
| ~ ( F @ ( D @ ( A @ product ) ) )
| ~ ( B @ ( E @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(120,plain,
$false,
inference(e,[status(thm)],[41,39,35,18,16,42,37,25,28,21,33,40,23,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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
% 0.22/0.49 % Computer : n005.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Sat Sep 26 01:53:31 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 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
% 0.97/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/1.12 % [INFO] Parsing done (143ms).
% 1.31/1.13 % [INFO] Running in sequential loop mode.
% 2.07/1.43 % [INFO] eprover registered as external prover.
% 2.07/1.44 % [INFO] Scanning for conjecture ...
% 2.31/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.48/1.60 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.48/1.64 % [INFO] Problem is propositional (TPTP CNF).
% 2.48/1.65 % [INFO] Type checking passed.
% 2.48/1.66 % [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 ...
% 6.06/2.92 % External prover 'e' found a proof!
% 6.06/2.92 % [INFO] Killing All external provers ...
% 6.06/2.92 % Time passed: 2288ms (effective reasoning time: 1780ms)
% 6.06/2.92 % Axioms used in derivation (14): c_squared, well_defined_product, product_associativity1, divides_implies_product, a_is_prime, product_commutativity, product_associativity2, product_divisible_by_operand, primes_lemma1, a_times_c_squared_is_not_b_squared, transitivity_of_divides, b_squared, product_left_cancellation, closure_of_product
% 6.06/2.92 % No. of inferences in proof: 31
% 6.06/2.92 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2288 ms resp. 1780 ms w/o parsing
% 6.06/2.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.06/2.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------