%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 9.07s 1.62s
% Output : CNFRefutation 9.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 65 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 34 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 5 sgn 24 !; 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(primes_lemma1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( divides(VAR_0,VAR_2)
| ~ prime(VAR_0)
| ~ product(VAR_2,VAR_2,VAR_1)
| ~ divides(VAR_0,VAR_1) ),
file('theBenchmark.p',primes_lemma1) ).
cnf(c_2,plain,
( divides(A,C)
| ~ prime(A)
| ~ product(C,C,B)
| ~ divides(A,B) ),
inference(clausify,[status(thm)],[primes_lemma1]) ).
cnf(c_3,plain,
( divides(a,B)
| ~ product(B,B,A)
| ~ divides(a,A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_there_is_no_common_divisor,axiom,
! [VAR_0] :
( ~ divides(VAR_0,b)
| ~ divides(VAR_0,c) ),
file('theBenchmark.p',prove_there_is_no_common_divisor) ).
cnf(c_4,plain,
( ~ divides(A,b)
| ~ divides(A,c) ),
inference(clausify,[status(thm)],[prove_there_is_no_common_divisor]) ).
fof(product_divisible_by_operand,axiom,
! [VAR_0,VAR_1,VAR_2] :
( divides(VAR_0,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_divisible_by_operand) ).
cnf(c_8,plain,
( divides(A,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_divisible_by_operand]) ).
fof(divides_implies_product,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,second_divided_by_1st(VAR_0,VAR_1),VAR_1)
| ~ divides(VAR_0,VAR_1) ),
file('theBenchmark.p',divides_implies_product) ).
cnf(c_9,plain,
( product(A,second_divided_by_1st(A,B),B)
| ~ divides(A,B) ),
inference(clausify,[status(thm)],[divides_implies_product]) ).
fof(product_left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = VAR_3
| ~ product(VAR_0,VAR_3,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_left_cancellation) ).
cnf(c_12,plain,
( B = D
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
fof(product_commutativity,axiom,
! [VAR_0,VAR_1,VAR_2] :
( product(VAR_1,VAR_0,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_commutativity) ).
cnf(c_13,plain,
( product(B,A,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_commutativity]) ).
fof(product_associativity2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( product(VAR_5,VAR_4,VAR_2)
| ~ product(VAR_5,VAR_3,VAR_0)
| ~ product(VAR_3,VAR_1,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_associativity2) ).
cnf(c_14,plain,
( product(F,E,C)
| ~ product(F,D,A)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_associativity2]) ).
fof(closure_of_product,axiom,
! [VAR_0,VAR_1] : product(VAR_0,VAR_1,multiply(VAR_0,VAR_1)),
file('theBenchmark.p',closure_of_product) ).
cnf(c_16,plain,
product(A,B,multiply(A,B)),
inference(clausify,[status(thm)],[closure_of_product]) ).
cnf(c_38,plain,
product(A,B,multiply(B,A)),
inference(resolve,[status(thm)],[c_13,c_16]) ).
cnf(c_41,plain,
divides(A,multiply(A,B)),
inference(resolve,[status(thm)],[c_8,c_16]) ).
cnf(c_2474,plain,
( divides(a,A)
| ~ product(A,A,multiply(a,B)) ),
inference(resolve,[status(thm)],[c_3,c_41]) ).
cnf(c_52,plain,
divides(a,a),
inference(resolve,[status(thm)],[c_2474,c_16]) ).
cnf(c_53,plain,
product(a,second_divided_by_1st(a,a),a),
inference(resolve,[status(thm)],[c_9,c_52]) ).
cnf(c_131,plain,
divides(A,multiply(B,A)),
inference(resolve,[status(thm)],[c_8,c_38]) ).
cnf(c_2475,plain,
( product(D,C,multiply(B,E))
| ~ product(D,A,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_14,c_38]) ).
cnf(c_2476,plain,
( product(A,multiply(D,B),multiply(D,C))
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_2475,c_38]) ).
cnf(c_223,plain,
product(a,multiply(A,second_divided_by_1st(a,a)),multiply(A,a)),
inference(resolve,[status(thm)],[c_2476,c_53]) ).
cnf(c_2477,plain,
( C = B
| ~ product(A,B,multiply(C,A)) ),
inference(resolve,[status(thm)],[c_12,c_38]) ).
cnf(c_2478,plain,
A = multiply(A,second_divided_by_1st(a,a)),
inference(resolve,[status(thm)],[c_2477,c_223]) ).
cnf(c_2342,plain,
multiply(A,second_divided_by_1st(a,a)) = A,
inference(copy,[status(thm)],[c_2478]) ).
cnf(c_2357,plain,
divides(second_divided_by_1st(a,a),A),
inference(paramod,[status(thm)],[c_2342,c_131]) ).
cnf(c_2479,plain,
~ divides(second_divided_by_1st(a,a),b),
inference(resolve,[status(thm)],[c_4,c_2357]) ).
cnf(c_2473,plain,
$false,
inference(resolve,[status(thm)],[c_2479,c_2357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 01:54:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2544204 was started by sandbox on n008,
% 0.09/0.37 % Sat Sep 26 01:54:24 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 9.07/1.62
% 9.07/1.62 % SZS status Unsatisfiable for theBenchmark
% 9.07/1.62
% 9.07/1.62 % Proof 1 at 0.93 (+ 0.29) seconds.
% 9.07/1.62 % Length of proof is 19.
% 9.07/1.62 % Level of proof is 7.
% 9.07/1.62 % Maximum clause weight is 25.000.
% 9.07/1.62 % Given clauses 160.
% 9.07/1.62
% 9.07/1.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------