%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV164+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 : n019.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 16.04s 2.73s
% Output : CNFRefutation 16.04s
% 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 : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 16 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_0014,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(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,X1)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,X1))),'tptp$uminus$u2'),times('a$uselect2'(sigma,X1),'a$uselect2'(sigma,X1)))),'a$uselect2'(rho,X1)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus('a$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,
~ ( ( ! [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(divide(times(exp(divide(divide(times(minus('a$uselect2'(x,pv10),'a$uselect2'(mu,X1)),minus('a$uselect2'(x,pv10),'a$uselect2'(mu,X1))),'tptp$uminus$u2'),times('a$uselect2'(sigma,X1),'a$uselect2'(sigma,X1)))),'a$uselect2'(rho,X1)),times(sqrt(times(n2,'tptp$upi')),'a$uselect2'(sigma,X1))),sum(n0,n4,divide(times(exp(divide(divide(times(minus('a$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_0014]) ).
cnf(c6,plain,
gt(n0,'tptp$uminus$u1'),
inference(clausification,[status(esa)],[gt_0_tptp_minus_1]) ).
cnf(c49,plain,
~ gt(X0,X0),
inference(clausification,[status(esa)],[irreflexivity_gt]) ).
cnf(c51,plain,
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_leq]) ).
cnf(c58,plain,
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(clausification,[status(esa)],[leq_gt_pred]) ).
cnf(c59,plain,
( ~ gt(X1,X0)
| leq(X0,pred(X1)) ),
inference(clausification,[status(esa)],[leq_gt_pred]) ).
cnf(c174,plain,
leq(n0,sK182),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c175,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)],[c51,c174]) ).
cnf(d1,plain,
( leq(n0,pred(X0))
| ~ gt(X0,sK182) ),
inference(resolution,[status(thm)],[c59,d0]) ).
cnf(d2,plain,
( gt(X0,n0)
| ~ gt(X0,sK182) ),
inference(resolution,[status(thm)],[d1,c58]) ).
cnf(d3,plain,
( leq(sK182,X0)
| ~ leq('tptp$uminus$u1',X0) ),
inference(resolution,[status(thm)],[c51,c175]) ).
cnf(d4,plain,
( ~ gt(X0,'tptp$uminus$u1')
| leq(sK182,pred(X0)) ),
inference(resolution,[status(thm)],[d3,c59]) ).
cnf(d5,plain,
( gt(X0,sK182)
| ~ gt(X0,'tptp$uminus$u1') ),
inference(resolution,[status(thm)],[d4,c58]) ).
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)],[c49,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV164+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 13:17:33 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.04/2.73 % SZS status Theorem for theBenchmark.p
% 16.04/2.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------