%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM016-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 9.05s 1.95s
% Output : CNFRefutation 9.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 8 unt; 7 nHn; 17 RR)
% Number of literals : 47 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(nothing_is_less_than_itself,axiom,
~ less(X0,X0) ).
cnf(numbers_are_different,axiom,
( ~ less(X1,X0)
| ~ less(X0,X1) ) ).
cnf(a_prime_is_less_than_the_next_one,axiom,
less(X0,'factorial$uplus$uone'(X0)) ).
cnf(divisor_is_smaller,axiom,
( less(X1,X0)
| ~ divides(X0,'factorial$uplus$uone'(X1)) ) ).
cnf(division_by_prime_divisor,axiom,
( divides('prime$udivisor'(X0),X0)
| prime(X0) ) ).
cnf(prime_divsiors,axiom,
( prime('prime$udivisor'(X0))
| prime(X0) ) ).
cnf(smaller_prime_divisors,axiom,
( less('prime$udivisor'(X0),X0)
| prime(X0) ) ).
cnf(prove_there_is_another_prime,negated_conjecture,
( less('factorial$uplus$uone'(a),X0)
| ~ less(a,X0)
| ~ prime(X0) ) ).
cnf(c0,plain,
~ less(X0,X0),
inference(clausification,[status(esa)],[nothing_is_less_than_itself]) ).
cnf(c1,plain,
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[numbers_are_different]) ).
cnf(c2,plain,
less(X0,'factorial$uplus$uone'(X0)),
inference(clausification,[status(esa)],[a_prime_is_less_than_the_next_one]) ).
cnf(c3,plain,
( less(X1,X0)
| ~ divides(X0,'factorial$uplus$uone'(X1)) ),
inference(clausification,[status(esa)],[divisor_is_smaller]) ).
cnf(c4,plain,
( divides('prime$udivisor'(X0),X0)
| prime(X0) ),
inference(clausification,[status(esa)],[division_by_prime_divisor]) ).
cnf(c5,plain,
( prime('prime$udivisor'(X0))
| prime(X0) ),
inference(clausification,[status(esa)],[prime_divsiors]) ).
cnf(c6,plain,
( less('prime$udivisor'(X0),X0)
| prime(X0) ),
inference(clausification,[status(esa)],[smaller_prime_divisors]) ).
cnf(c7,plain,
( less('factorial$uplus$uone'(a),X0)
| ~ less(a,X0)
| ~ prime(X0) ),
inference(clausification,[status(esa)],[prove_there_is_another_prime]) ).
cnf(d0,plain,
( less(X0,'prime$udivisor'('factorial$uplus$uone'(X0)))
| prime('factorial$uplus$uone'(X0)) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(d1,plain,
( ~ less(X0,'prime$udivisor'(X0))
| prime(X0) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d2,plain,
( prime('factorial$uplus$uone'(a))
| ~ prime('prime$udivisor'('factorial$uplus$uone'(a)))
| ~ less(a,'prime$udivisor'('factorial$uplus$uone'(a))) ),
inference(resolution,[status(thm)],[c7,d1]) ).
cnf(d3,plain,
( ~ prime('factorial$uplus$uone'(a))
| ~ less(a,'factorial$uplus$uone'(a)) ),
inference(resolution,[status(thm)],[c7,c0]) ).
cnf(d4,plain,
~ prime('factorial$uplus$uone'(a)),
inference(resolution,[status(thm)],[c2,d3]) ).
cnf(d5,plain,
( ~ prime('prime$udivisor'('factorial$uplus$uone'(a)))
| ~ less(a,'prime$udivisor'('factorial$uplus$uone'(a))) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( prime('factorial$uplus$uone'(a))
| ~ prime('prime$udivisor'('factorial$uplus$uone'(a))) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
~ prime('prime$udivisor'('factorial$uplus$uone'(a))),
inference(resolution,[status(thm)],[d4,d6]) ).
cnf(d8,plain,
prime('factorial$uplus$uone'(a)),
inference(resolution,[status(thm)],[d7,c5]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d4,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM016-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.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 26 01:58:56 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.05/1.95 % SZS status Unsatisfiable for theBenchmark.p
% 9.05/1.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------