%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM017-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 08:10:38 AM UTC 2026
% Result : Unsatisfiable 43.62s 14.28s
% Output : CNFRefutation 43.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 45 ( 9 unt; 0 nHn; 33 RR)
% Number of literals : 96 ( 0 equ; 56 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 109 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(symmetry,axiom,
( equalish(X1,X0)
| ~ equalish(X0,X1) ) ).
cnf(divides_substitution1,axiom,
( divides(X2,X1)
| ~ divides(X2,X0)
| ~ equalish(X0,X1) ) ).
cnf(closure_of_product,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(product_associativity1,axiom,
( product(X5,X4,X2)
| ~ product(X0,X3,X5)
| ~ product(X3,X4,X1)
| ~ product(X0,X1,X2) ) ).
cnf(product_commutativity,axiom,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ) ).
cnf(product_left_cancellation,axiom,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ) ).
cnf(divides_implies_product,axiom,
( product(X0,'second$udivided$uby$u1st'(X0,X1),X1)
| ~ divides(X0,X1) ) ).
cnf(product_divisible_by_operand,axiom,
( divides(X0,X2)
| ~ product(X0,X1,X2) ) ).
cnf(primes_lemma1,axiom,
( divides(X0,X2)
| ~ prime(X0)
| ~ product(X2,X2,X1)
| ~ divides(X0,X1) ) ).
cnf(a_is_prime,hypothesis,
prime(a) ).
cnf(prove_there_is_no_common_divisor,negated_conjecture,
( ~ divides(X0,b)
| ~ divides(X0,c) ) ).
cnf(c1,plain,
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[symmetry]) ).
cnf(c6,plain,
( divides(X2,X1)
| ~ divides(X2,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[divides_substitution1]) ).
cnf(c9,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_product]) ).
cnf(c10,plain,
( product(X5,X4,X2)
| ~ product(X0,X3,X5)
| ~ product(X3,X4,X1)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_associativity1]) ).
cnf(c12,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_commutativity]) ).
cnf(c13,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_left_cancellation]) ).
cnf(c16,plain,
( product(X0,'second$udivided$uby$u1st'(X0,X1),X1)
| ~ divides(X0,X1) ),
inference(clausification,[status(esa)],[divides_implies_product]) ).
cnf(c17,plain,
( divides(X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[product_divisible_by_operand]) ).
cnf(c18,plain,
( divides(X0,X2)
| ~ prime(X0)
| ~ product(X2,X2,X1)
| ~ divides(X0,X1) ),
inference(clausification,[status(esa)],[primes_lemma1]) ).
cnf(c19,plain,
prime(a),
inference(clausification,[status(esa)],[a_is_prime]) ).
cnf(c23,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)],[c12,c9]) ).
cnf(d1,plain,
divides(X0,multiply(X1,X0)),
inference(resolution,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
( ~ prime(X0)
| ~ divides(X0,multiply(X1,X1))
| divides(X0,X1) ),
inference(resolution,[status(thm)],[c18,d0]) ).
cnf(d3,plain,
( ~ prime(X0)
| divides(X0,X0) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( divides(X1,X2)
| ~ equalish(multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[c6,d1]) ).
cnf(d5,plain,
( ~ product(X2,X0,multiply(X1,X2))
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c13,d0]) ).
cnf(d6,plain,
( ~ product(X3,X4,X0)
| ~ product(X4,X1,X2)
| product(X0,X1,multiply(X2,X3)) ),
inference(resolution,[status(thm)],[c10,d0]) ).
cnf(d7,plain,
( equalish(X1,X2)
| ~ product(X3,X0,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( ~ product(X2,X1,X2)
| equalish(X0,multiply(X1,X0)) ),
inference(resolution,[status(thm)],[d7,c9]) ).
cnf(d9,plain,
( equalish(multiply(X1,X2),X2)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
( divides(X2,X2)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
( ~ divides(X1,X1)
| divides(X0,X0) ),
inference(resolution,[status(thm)],[d10,c16]) ).
cnf(d12,plain,
( ~ prime(X1)
| divides(X0,X0) ),
inference(resolution,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
( product('second$udivided$uby$u1st'(X0,X1),X0,X1)
| ~ divides(X0,X1) ),
inference(resolution,[status(thm)],[c16,c12]) ).
cnf(d14,plain,
( divides('second$udivided$uby$u1st'(X0,X1),X1)
| ~ divides(X0,X1) ),
inference(resolution,[status(thm)],[d13,c17]) ).
cnf(d15,plain,
( ~ divides('second$udivided$uby$u1st'(X0,c),b)
| ~ divides(X0,c) ),
inference(resolution,[status(thm)],[d14,c23]) ).
cnf(d16,plain,
divides(X0,multiply(X0,X1)),
inference(resolution,[status(thm)],[c17,c9]) ).
cnf(d17,plain,
( divides(X0,X2)
| ~ equalish(multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[c6,d16]) ).
cnf(d18,plain,
( divides(X1,X2)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[d9,d17]) ).
cnf(d19,plain,
( ~ divides(X0,X0)
| divides('second$udivided$uby$u1st'(X0,X0),X1) ),
inference(resolution,[status(thm)],[d18,c16]) ).
cnf(d20,plain,
( ~ divides(c,c)
| ~ divides(c,c) ),
inference(resolution,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
~ prime(X0),
inference(resolution,[status(thm)],[d20,d12]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[d21,c19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM017-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 01:53:44 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.62/14.28 % SZS status Unsatisfiable for theBenchmark.p
% 43.62/14.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------