%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV154+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 : 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 09:01:31 AM UTC 2026
% Result : Theorem 27.20s 3.97s
% Output : CNFRefutation 27.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 7 unt; 0 def)
% Number of atoms : 37 ( 16 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 33 ( 5 ~; 0 |; 18 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-3 aty)
% Number of variables : 6 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_norm_0004,conjecture,
( ( ! [X1] :
( ( leq(X1,pred(pv10))
& leq(n0,X1) )
=> sum(n0,n4,'a$uselect3'(q,X1,'tptp$usum$uindex')) = n1 )
& ! [X0] :
( ( leq(X0,pred(pv12))
& leq(n0,X0) )
=> 'a$uselect3'(q,pv10,X0) = divide(sqrt(times(minus('a$uselect3'(center,X0,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,X0,n0),'a$uselect2'(x,pv10)))),sum(n0,n4,sqrt(times(minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)))))) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10))))) )
=> ! [X2] :
( ( leq(X2,pv12)
& leq(n0,X2) )
=> ( pv12 = X2
=> divide(sqrt(times(minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)))),pv70) = divide(sqrt(times(minus('a$uselect3'(center,X2,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,X2,n0),'a$uselect2'(x,pv10)))),sum(n0,n4,sqrt(times(minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)))))) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( ! [X1] :
( ( leq(X1,pred(pv10))
& leq(n0,X1) )
=> sum(n0,n4,'a$uselect3'(q,X1,'tptp$usum$uindex')) = n1 )
& ! [X0] :
( ( leq(X0,pred(pv12))
& leq(n0,X0) )
=> 'a$uselect3'(q,pv10,X0) = divide(sqrt(times(minus('a$uselect3'(center,X0,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,X0,n0),'a$uselect2'(x,pv10)))),sum(n0,n4,sqrt(times(minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)))))) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10))))) )
=> ! [X2] :
( ( leq(X2,pv12)
& leq(n0,X2) )
=> ( pv12 = X2
=> divide(sqrt(times(minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)))),pv70) = divide(sqrt(times(minus('a$uselect3'(center,X2,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,X2,n0),'a$uselect2'(x,pv10)))),sum(n0,n4,sqrt(times(minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)))))) ) ) ),
inference(negate_conjecture,[status(cth)],[cl5_nebula_norm_0004]) ).
cnf(c163,plain,
pv70 = sum(n0,n4,sqrt(times(minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10))))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c172,plain,
pv12 = sK183,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c173,plain,
divide(sqrt(times(minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)))),pv70) != divide(sqrt(times(minus('a$uselect3'(center,sK183,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,sK183,n0),'a$uselect2'(x,pv10)))),sum(n0,n4,sqrt(times(minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)))))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
divide(sqrt(times(minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)))),pv70) != divide(sqrt(times(minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,sK183,n0),'a$uselect2'(x,pv10)))),sum(n0,n4,sqrt(times(minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)))))),
inference(demodulation,[status(thm)],[c173,c172]) ).
cnf(d1,plain,
divide(sqrt(times(minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)))),pv70) != divide(sqrt(times(minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)))),sum(n0,n4,sqrt(times(minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,'tptp$usum$uindex',n0),'a$uselect2'(x,pv10)))))),
inference(demodulation,[status(thm)],[d0,c172]) ).
cnf(d2,plain,
divide(sqrt(times(minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)))),pv70) != divide(sqrt(times(minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,pv12,n0),'a$uselect2'(x,pv10)))),pv70),
inference(demodulation,[status(thm)],[d1,c163]) ).
cnf(d3,plain,
$false,
inference(equality_resolution,[status(thm)],[d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV154+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n003.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 13:17:54 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.20/3.97 % SZS status Theorem for theBenchmark.p
% 27.20/3.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------