%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV163+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 : n007.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 09:01:33 AM UTC 2026
% Result : Theorem 20.44s 3.97s
% Output : CNFRefutation 20.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 49 ( 4 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 40 ( 13 ~; 10 |; 9 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(gt_0_tptp_minus_1,axiom,
gt(n0,'tptp$uminus$u1') ).
fof(irreflexivity_gt,axiom,
! [X0] : ~ gt(X0,X0) ).
fof(transitivity_leq,axiom,
! [X0,X1,X2] :
( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ) ).
fof(leq_gt_pred,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ) ).
fof(cl5_nebula_norm_0013,conjecture,
( ( ! [X0] :
( ( leq(X0,pred(pv10))
& leq(n0,X0) )
=> sum(n0,n4,'a$uselect3'(q,X0,'tptp$usum$uindex')) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [X1] :
( ( leq(X1,'tptp$uminus$u1')
& leq(n0,X1) )
=> 'a$uselect3'(q,pv10,X1) = divide(sqrt(times(minus('a$uselect3'(center,X1,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,X1,n0),'a$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,
~ ( ( ! [X0] :
( ( leq(X0,pred(pv10))
& leq(n0,X0) )
=> sum(n0,n4,'a$uselect3'(q,X0,'tptp$usum$uindex')) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [X1] :
( ( leq(X1,'tptp$uminus$u1')
& leq(n0,X1) )
=> 'a$uselect3'(q,pv10,X1) = divide(sqrt(times(minus('a$uselect3'(center,X1,n0),'a$uselect2'(x,pv10)),minus('a$uselect3'(center,X1,n0),'a$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_0013]) ).
cnf(c6,plain,
gt(n0,'tptp$uminus$u1'),
inference(clausification,[status(esa)],[gt_0_tptp_minus_1]) ).
cnf(c41,plain,
~ gt(X0,X0),
inference(clausification,[status(esa)],[irreflexivity_gt]) ).
cnf(c43,plain,
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_leq]) ).
cnf(c50,plain,
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(clausification,[status(esa)],[leq_gt_pred]) ).
cnf(c51,plain,
( ~ gt(X1,X0)
| leq(X0,pred(X1)) ),
inference(clausification,[status(esa)],[leq_gt_pred]) ).
cnf(c166,plain,
leq(n0,sK182),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c167,plain,
leq(sK182,'tptp$uminus$u1'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( leq(n0,X0)
| ~ leq(sK182,X0) ),
inference(resolution,[status(thm)],[c43,c166]) ).
cnf(d1,plain,
( leq(n0,pred(X0))
| ~ gt(X0,sK182) ),
inference(resolution,[status(thm)],[c51,d0]) ).
cnf(d2,plain,
( gt(X0,n0)
| ~ gt(X0,sK182) ),
inference(resolution,[status(thm)],[d1,c50]) ).
cnf(d3,plain,
( leq(sK182,X0)
| ~ leq('tptp$uminus$u1',X0) ),
inference(resolution,[status(thm)],[c43,c167]) ).
cnf(d4,plain,
( ~ gt(X0,'tptp$uminus$u1')
| leq(sK182,pred(X0)) ),
inference(resolution,[status(thm)],[d3,c51]) ).
cnf(d5,plain,
( gt(X0,sK182)
| ~ gt(X0,'tptp$uminus$u1') ),
inference(resolution,[status(thm)],[d4,c50]) ).
cnf(d6,plain,
gt(n0,sK182),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
gt(n0,n0),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c41,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV163+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 13:15:23 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.44/3.97 % SZS status Theorem for theBenchmark.p
% 20.44/3.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------