%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV158+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 18.08s 4.06s
% Output : CNFRefutation 18.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 11 unt; 0 def)
% Number of atoms : 41 ( 20 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 37 ( 9 ~; 0 |; 18 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 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 : 6 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_norm_0008,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$uindex')))) )
=> ! [X2] :
( ( leq(X2,pv47)
& leq(n0,X2) )
=> ( pv47 = X2
=> divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,pv47)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,pv47))),pv84) = divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,X2)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,X2))),'tptp$uminus$u2'),times('a$uselect2'(sigma,X2),'a$uselect2'(sigma,X2)))),'a$uselect2'(rho,X2)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,X2))),sum(n0,n4,divide(times(exp(divide(divide(times(minus('a$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'))))) ) ) ) ).
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$uindex')))) )
=> ! [X2] :
( ( leq(X2,pv47)
& leq(n0,X2) )
=> ( pv47 = X2
=> divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,pv47)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,pv47))),pv84) = divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,X2)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,X2))),'tptp$uminus$u2'),times('a$uselect2'(sigma,X2),'a$uselect2'(sigma,X2)))),'a$uselect2'(rho,X2)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,X2))),sum(n0,n4,divide(times(exp(divide(divide(times(minus('a$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'))))) ) ) ),
inference(negate_conjecture,[status(cth)],[cl5_nebula_norm_0008]) ).
cnf(c171,plain,
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$uindex')))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c180,plain,
pv47 = sK183,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c181,plain,
divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,pv47)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,pv47))),pv84) != divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,sK183)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,sK183))),'tptp$uminus$u2'),times('a$uselect2'(sigma,sK183),'a$uselect2'(sigma,sK183)))),'a$uselect2'(rho,sK183)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,sK183))),sum(n0,n4,divide(times(exp(divide(divide(times(minus('a$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'))))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,pv47)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,pv47))),pv84) != divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,sK183))),'tptp$uminus$u2'),times('a$uselect2'(sigma,sK183),'a$uselect2'(sigma,sK183)))),'a$uselect2'(rho,sK183)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,sK183))),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$uindex'))))),
inference(demodulation,[status(thm)],[c181,c180]) ).
cnf(d1,plain,
divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,pv47)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,pv47))),pv84) != divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,sK183),'a$uselect2'(sigma,sK183)))),'a$uselect2'(rho,sK183)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,sK183))),sum(n0,n4,divide(times(exp(divide(divide(times(minus('a$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'))))),
inference(demodulation,[status(thm)],[d0,c180]) ).
cnf(d2,plain,
divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,pv47)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,pv47))),pv84) != divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,sK183)))),'a$uselect2'(rho,sK183)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,sK183))),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$uindex'))))),
inference(demodulation,[status(thm)],[d1,c180]) ).
cnf(d3,plain,
divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,pv47)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,pv47))),pv84) != divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,sK183)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,sK183))),sum(n0,n4,divide(times(exp(divide(divide(times(minus('a$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'))))),
inference(demodulation,[status(thm)],[d2,c180]) ).
cnf(d4,plain,
divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,pv47)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,pv47))),pv84) != divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,pv47)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,sK183))),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$uindex'))))),
inference(demodulation,[status(thm)],[d3,c180]) ).
cnf(d5,plain,
divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,pv47)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,pv47))),pv84) != divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,pv47)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,pv47))),sum(n0,n4,divide(times(exp(divide(divide(times(minus('a$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'))))),
inference(demodulation,[status(thm)],[d4,c180]) ).
cnf(d6,plain,
divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,pv47)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,pv47))),pv84) != divide(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,pv47))),'tptp$uminus$u2'),times('a$uselect2'(sigma,pv47),'a$uselect2'(sigma,pv47)))),'a$uselect2'(rho,pv47)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,pv47))),pv84),
inference(demodulation,[status(thm)],[d5,c171]) ).
cnf(d7,plain,
$false,
inference(equality_resolution,[status(thm)],[d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV158+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.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 13:17:00 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.08/4.06 % SZS status Theorem for theBenchmark.p
% 18.08/4.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------