%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 08:51:38 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 14 unt; 2 nHn; 17 RR)
% Number of literals : 28 ( 0 equ; 10 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 8 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(square,axiom,
product(X,X,square(X)),
file('theBenchmark.p',square) ).
cnf(divides,axiom,
( divides(X,Z)
| ~ product(X,Y,Z) ),
file('theBenchmark.p',divides) ).
cnf(remainder,axiom,
( divides(X,Z)
| divides(X,Y)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ),
file('theBenchmark.p',remainder) ).
cnf(a_is_prime,hypothesis,
prime(a),
file('theBenchmark.p',a_is_prime) ).
cnf(a_equals_b_squared_by_c_squared,hypothesis,
product(a,square(c),square(b)),
file('theBenchmark.p',a_equals_b_squared_by_c_squared) ).
cnf(prove_a_divides_b,negated_conjecture,
~ divides(a,b),
file('theBenchmark.p',prove_a_divides_b) ).
cnf(t1,plain,
~ divides(a,b),
inference(start,[status(thm),parent(0:0)],[prove_a_divides_b]) ).
cnf(t2,plain,
( ~ product(b,b,square(b))
| ~ divides(a,square(b))
| divides(a,b)
| ~ prime(a)
| divides(a,b) ),
inference(extension,[status(thm),parent(t1:1)],[remainder]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
prime(a),
inference(extension,[status(thm),parent(t2:2)],[a_is_prime]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
$false,
inference(reduction,[status(thm),parent(t2:3)],[t2:3,t1:1]) ).
cnf(t7,plain,
( ~ product(a,square(c),square(b))
| divides(a,square(b)) ),
inference(extension,[status(thm),parent(t2:4)],[divides]) ).
cnf(t8,plain,
$false,
inference(connection,[status(thm),parent(t7:1)],[t7:1,t2:4]) ).
cnf(t9,plain,
product(a,square(c),square(b)),
inference(extension,[status(thm),parent(t7:2)],[a_equals_b_squared_by_c_squared]) ).
cnf(t10,plain,
$false,
inference(connection,[status(thm),parent(t9:1)],[t9:1,t7:2]) ).
cnf(t11,plain,
product(b,b,square(b)),
inference(extension,[status(thm),parent(t2:5)],[square]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t2:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 17:35:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------