%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 08:16:02 AM UTC 2026
% Result : Unsatisfiable 0.06s 0.36s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 31 ( 15 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 20 ( 1 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a_is_prime,axiom,
prime(a),
file('theBenchmark.p',a_is_prime) ).
cnf(c_1,plain,
prime(a),
inference(clausify,[status(thm)],[a_is_prime]) ).
fof(remainder,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( divides(VAR_0,VAR_2)
| divides(VAR_0,VAR_1)
| ~ divides(VAR_0,VAR_3)
| ~ product(VAR_1,VAR_2,VAR_3)
| ~ prime(VAR_0) ),
file('theBenchmark.p',remainder) ).
cnf(c_2,plain,
( divides(A,C)
| divides(A,B)
| ~ divides(A,D)
| ~ product(B,C,D)
| ~ prime(A) ),
inference(clausify,[status(thm)],[remainder]) ).
cnf(c_3,plain,
( divides(a,B)
| divides(a,A)
| ~ divides(a,C)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_a_divides_b,axiom,
~ divides(a,b),
file('theBenchmark.p',prove_a_divides_b) ).
cnf(c_4,plain,
~ divides(a,b),
inference(clausify,[status(thm)],[prove_a_divides_b]) ).
fof(a_equals_b_squared_by_c_squared,axiom,
product(a,square(c),square(b)),
file('theBenchmark.p',a_equals_b_squared_by_c_squared) ).
cnf(c_5,plain,
product(a,square(c),square(b)),
inference(clausify,[status(thm)],[a_equals_b_squared_by_c_squared]) ).
fof(divides,axiom,
! [VAR_0,VAR_1,VAR_2] :
( divides(VAR_0,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',divides) ).
cnf(c_6,plain,
( divides(A,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[divides]) ).
fof(square,axiom,
! [VAR_0] : product(VAR_0,VAR_0,square(VAR_0)),
file('theBenchmark.p',square) ).
cnf(c_8,plain,
product(A,A,square(A)),
inference(clausify,[status(thm)],[square]) ).
cnf(c_11,plain,
divides(a,square(b)),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_18,plain,
( divides(a,A)
| divides(a,A)
| ~ divides(a,square(A)) ),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_19,plain,
( divides(a,b)
| ~ divides(a,square(b)) ),
inference(resolve,[status(thm)],[c_18,c_4]) ).
cnf(c_20,plain,
~ divides(a,square(b)),
inference(resolve,[status(thm)],[c_19,c_4]) ).
cnf(c_17,plain,
$false,
inference(resolve,[status(thm)],[c_11,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.34 % Computer : n017.cluster.edu
% 0.06/0.34 % Model : x86_64 x86_64
% 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.34 % Memory : 8046.5625MB
% 0.06/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.34 % WCLimit : 300
% 0.06/0.34 % DateTime : Sat Sep 26 01:48:32 UTC 2026
% 0.06/0.35 % CPUTime :
% 0.06/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.35 % Process 3695756 was started by sandbox on n017,
% 0.06/0.35 % Sat Sep 26 01:48:32 2026
% 0.06/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.06/0.35
% 0.06/0.35 % From the command line: assign(max_seconds, 300).
% 0.06/0.36
% 0.06/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.06/0.36
% 0.06/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.06/0.36 % Length of proof is 9.
% 0.06/0.36 % Level of proof is 2.
% 0.06/0.36 % Maximum clause weight is 13.000.
% 0.06/0.36 % Given clauses 6.
% 0.06/0.36
% 0.06/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------