%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:10:39 AM UTC 2026
% Result : Unsatisfiable 8.56s 5.56s
% Output : CNFRefutation 8.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 38 ( 13 unt; 0 nHn; 29 RR)
% Number of literals : 77 ( 11 equ; 42 neg)
% Maximal clause size : 4 ( 2 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 : 88 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_product,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(product_associativity2,axiom,
( product(X5,X4,X2)
| ~ product(X5,X3,X0)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ) ).
cnf(product_commutativity,axiom,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ) ).
cnf(product_left_cancellation,axiom,
( X1 = X3
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(well_defined_product,axiom,
( X3 = X2
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(divides_implies_product,axiom,
( product(X0,'second$udivided$uby$u1st'(X0,X1),X1)
| ~ divides(X0,X1) ) ).
cnf(product_divisible_by_operand,axiom,
( divides(X0,X2)
| ~ product(X0,X1,X2) ) ).
cnf(primes_lemma1,axiom,
( divides(X0,X2)
| ~ prime(X0)
| ~ product(X2,X2,X1)
| ~ divides(X0,X1) ) ).
cnf(a_is_prime,hypothesis,
prime(a) ).
cnf(prove_there_is_no_common_divisor,negated_conjecture,
( ~ divides(X0,b)
| ~ divides(X0,c) ) ).
cnf(c0,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_product]) ).
cnf(c2,plain,
( product(X5,X4,X2)
| ~ product(X5,X3,X0)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_associativity2]) ).
cnf(c3,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_commutativity]) ).
cnf(c4,plain,
( X1 = X3
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_left_cancellation]) ).
cnf(c6,plain,
( X3 = X2
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[well_defined_product]) ).
cnf(c7,plain,
( product(X0,'second$udivided$uby$u1st'(X0,X1),X1)
| ~ divides(X0,X1) ),
inference(clausification,[status(esa)],[divides_implies_product]) ).
cnf(c8,plain,
( divides(X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_divisible_by_operand]) ).
cnf(c9,plain,
( divides(X0,X2)
| ~ prime(X0)
| ~ product(X2,X2,X1)
| ~ divides(X0,X1) ),
inference(clausification,[status(esa)],[primes_lemma1]) ).
cnf(c10,plain,
prime(a),
inference(clausification,[status(esa)],[a_is_prime]) ).
cnf(c14,plain,
( ~ divides(X0,b)
| ~ divides(X0,c) ),
inference(clausification,[status(esa)],[prove_there_is_no_common_divisor]) ).
cnf(d0,plain,
product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d1,plain,
divides(X0,multiply(X1,X0)),
inference(resolution,[status(thm)],[c8,d0]) ).
cnf(d2,plain,
( ~ product(X2,X1,multiply(X2,X0))
| X0 = X1 ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d3,plain,
( ~ product(X3,X0,X4)
| product(X3,X2,multiply(X4,X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d4,plain,
( ~ product(X0,X2,X3)
| product(X0,multiply(X1,X2),multiply(X3,X1)) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( X2 = multiply(X2,X1)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
divides(X0,multiply(X0,X1)),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(d7,plain,
( ~ prime(X0)
| divides(X0,X1)
| ~ divides(X0,multiply(X1,X1)) ),
inference(resolution,[status(thm)],[c9,d0]) ).
cnf(d8,plain,
( ~ prime(X0)
| divides(X0,X0) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(d10,plain,
( ~ divides(X0,X1)
| multiply(X0,'second$udivided$uby$u1st'(X0,X1)) = X1 ),
inference(resolution,[status(thm)],[d9,c7]) ).
cnf(d11,plain,
( ~ prime(X0)
| multiply(X0,'second$udivided$uby$u1st'(X0,X0)) = X0 ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
multiply(a,'second$udivided$uby$u1st'(a,a)) = a,
inference(resolution,[status(thm)],[d11,c10]) ).
cnf(d13,plain,
product(a,'second$udivided$uby$u1st'(a,a),a),
inference(superposition,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
X0 = multiply(X0,'second$udivided$uby$u1st'(a,a)),
inference(resolution,[status(thm)],[d13,d5]) ).
cnf(d15,plain,
divides('second$udivided$uby$u1st'(a,a),X0),
inference(superposition,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
~ divides('second$udivided$uby$u1st'(a,a),b),
inference(resolution,[status(thm)],[d15,c14]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[d15,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.41 % Computer : n014.cluster.edu
% 0.09/0.41 % Model : x86_64 x86_64
% 0.09/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.41 % Memory : 8046.5625MB
% 0.09/0.41 % OS : Linux 6.8.0-71-generic
% 0.09/0.41 % CPULimit : 300
% 0.09/0.41 % WCLimit : 300
% 0.09/0.41 % DateTime : Sat Sep 26 01:53:31 UTC 2026
% 0.09/0.42 % CPUTime :
% 0.09/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.56/5.56 % SZS status Unsatisfiable for theBenchmark.p
% 8.56/5.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------