%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV159+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 09:01:32 AM UTC 2026
% Result : Theorem 5.53s 9.55s
% Output : CNFRefutation 5.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 5 unt; 0 def)
% Number of atoms : 40 ( 14 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 38 ( 7 ~; 3 |; 18 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 17 con; 0-3 aty)
% Number of variables : 7 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_norm_0009,conjecture,
( ( ! [X1] :
( ( leq(X1,pred(pv10))
& leq(n0,X1) )
=> sum(n0,n4,'a$uselect3'(q,X1,'tptp$usum$uindex')) = n1 )
& ! [X0] :
( ( leq(X0,pred(pv47))
& leq(n0,X0) )
=> 'a$uselect3'(q,pv10,X0) = divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,X0)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,X0))),'tptp$uminus$u2'),times('a$uselect2'(sigma,X0),'a$uselect2'(sigma,X0)))),'a$uselect2'(rho,X0)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,X0))),sum(n0,n4,divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,'tptp$usum$uindex')),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,'tptp$usum$uindex'))),'tptp$uminus$u2'),times('a$uselect2'(sigma,'tptp$usum$uindex'),'a$uselect2'(sigma,'tptp$usum$uindex')))),'a$uselect2'(rho,'tptp$usum$uindex')),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,'tptp$usum$uindex'))))) )
& leq(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& leq(n0,pv10)
& pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,'tptp$usum$uindex')),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,'tptp$usum$uindex'))),'tptp$uminus$u2'),times('a$uselect2'(sigma,'tptp$usum$uindex'),'a$uselect2'(sigma,'tptp$usum$uindex')))),'a$uselect2'(rho,'tptp$usum$uindex')),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,'tptp$usum$uindex')))) )
=> ! [X2] :
( ( leq(X2,pred(pv10))
& leq(n0,X2) )
=> ( pv10 != X2
=> sum(n0,n4,'a$uselect3'(q,X2,'tptp$usum$uindex')) = n1 ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( ! [X1] :
( ( leq(X1,pred(pv10))
& leq(n0,X1) )
=> sum(n0,n4,'a$uselect3'(q,X1,'tptp$usum$uindex')) = n1 )
& ! [X0] :
( ( leq(X0,pred(pv47))
& leq(n0,X0) )
=> 'a$uselect3'(q,pv10,X0) = divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,X0)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,X0))),'tptp$uminus$u2'),times('a$uselect2'(sigma,X0),'a$uselect2'(sigma,X0)))),'a$uselect2'(rho,X0)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,X0))),sum(n0,n4,divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,'tptp$usum$uindex')),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,'tptp$usum$uindex'))),'tptp$uminus$u2'),times('a$uselect2'(sigma,'tptp$usum$uindex'),'a$uselect2'(sigma,'tptp$usum$uindex')))),'a$uselect2'(rho,'tptp$usum$uindex')),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,'tptp$usum$uindex'))))) )
& leq(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& leq(n0,pv10)
& pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,'tptp$usum$uindex')),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,'tptp$usum$uindex'))),'tptp$uminus$u2'),times('a$uselect2'(sigma,'tptp$usum$uindex'),'a$uselect2'(sigma,'tptp$usum$uindex')))),'a$uselect2'(rho,'tptp$usum$uindex')),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,'tptp$usum$uindex')))) )
=> ! [X2] :
( ( leq(X2,pred(pv10))
& leq(n0,X2) )
=> ( pv10 != X2
=> sum(n0,n4,'a$uselect3'(q,X2,'tptp$usum$uindex')) = n1 ) ) ),
inference(negate_conjecture,[status(cth)],[cl5_nebula_norm_0009]) ).
cnf(c177,plain,
( sum(n0,n4,'a$uselect3'(q,X0,'tptp$usum$uindex')) = n1
| ~ leq(X0,pred(pv10))
| ~ leq(n0,X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c178,plain,
leq(n0,sK183),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c179,plain,
leq(sK183,pred(pv10)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c181,plain,
sum(n0,n4,'a$uselect3'(q,sK183,'tptp$usum$uindex')) != n1,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ leq(n0,sK183)
| sum(n0,n4,'a$uselect3'(q,sK183,'tptp$usum$uindex')) = n1 ),
inference(resolution,[status(thm)],[c177,c179]) ).
cnf(d1,plain,
sum(n0,n4,'a$uselect3'(q,sK183,'tptp$usum$uindex')) = n1,
inference(resolution,[status(thm)],[c178,d0]) ).
cnf(d2,plain,
$false,
inference(resolution,[status(thm)],[c181,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV159+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.40 % Computer : n003.cluster.edu
% 0.11/5.40 % Model : x86_64 x86_64
% 0.11/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.40 % Memory : 8046.5625MB
% 0.11/5.40 % OS : Linux 6.8.0-71-generic
% 0.11/5.40 % CPULimit : 300
% 0.11/5.40 % WCLimit : 300
% 0.11/5.40 % DateTime : Sat Sep 26 13:18:45 UTC 2026
% 0.18/5.40 % CPUTime :
% 0.18/5.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.53/9.55 % SZS status Theorem for theBenchmark.p
% 5.53/9.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------