%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV046+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 : n004.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 09:01:18 AM UTC 2026
% Result : Theorem 38.44s 9.99s
% Output : CNFRefutation 38.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 21 unt; 0 def)
% Number of atoms : 90 ( 59 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 99 ( 45 ~; 34 |; 14 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 15 con; 0-3 aty)
% Number of variables : 12 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_plus_base,axiom,
! [X0] : sum(n0,'tptp$uminus$u1',X0) = n0 ).
fof(succ_tptp_minus_1,axiom,
succ('tptp$uminus$u1') = n0 ).
fof(pred_minus_1,axiom,
! [X0] : minus(X0,n1) = pred(X0) ).
fof(pred_succ,axiom,
! [X0] : pred(succ(X0)) = X0 ).
fof(sel2_update_1,axiom,
! [X0,X1,X2] : 'a$uselect2'('tptp$uupdate2'(X0,X1,X2),X1) = X2 ).
fof(ttrue,axiom,
true ).
fof(cl5_nebula_norm_0010,conjecture,
( ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv80 = sum(n0,minus(n135300,n1),times('a$uselect3'(q,pv81,pv35),'a$uselect2'(x,pv81)))
& pv78 = sum(n0,minus(n135300,n1),'a$uselect3'(q,pv79,pv35)) )
=> ( ( n0 = pv44
=> true )
& ( n0 != pv44
=> ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv78 = sum(n0,minus(n135300,n1),'a$uselect3'(q,pv79,pv35))
& n0 = sum(n0,minus(n0,n1),times(minus('a$uselect2'(x,pv83),'a$uselect2'('tptp$uupdate2'(mu,pv35,divide(pv80,pv44)),pv35)),times(minus('a$uselect2'(x,pv83),'a$uselect2'('tptp$uupdate2'(mu,pv35,divide(pv80,pv44)),pv35)),'a$uselect3'(q,pv83,pv35)))) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv80 = sum(n0,minus(n135300,n1),times('a$uselect3'(q,pv81,pv35),'a$uselect2'(x,pv81)))
& pv78 = sum(n0,minus(n135300,n1),'a$uselect3'(q,pv79,pv35)) )
=> ( ( n0 = pv44
=> true )
& ( n0 != pv44
=> ( leq(pv35,minus(n5,n1))
& leq(n0,pv35)
& pv78 = sum(n0,minus(n135300,n1),'a$uselect3'(q,pv79,pv35))
& n0 = sum(n0,minus(n0,n1),times(minus('a$uselect2'(x,pv83),'a$uselect2'('tptp$uupdate2'(mu,pv35,divide(pv80,pv44)),pv35)),times(minus('a$uselect2'(x,pv83),'a$uselect2'('tptp$uupdate2'(mu,pv35,divide(pv80,pv44)),pv35)),'a$uselect3'(q,pv83,pv35)))) ) ) ) ),
inference(negate_conjecture,[status(cth)],[cl5_nebula_norm_0010]) ).
cnf(c128,plain,
sum(n0,'tptp$uminus$u1',X0) = n0,
inference(clausification,[status(esa)],[sum_plus_base]) ).
cnf(c130,plain,
succ('tptp$uminus$u1') = n0,
inference(clausification,[status(esa)],[succ_tptp_minus_1]) ).
cnf(c141,plain,
pred(X0) = minus(X0,n1),
inference(clausification,[status(esa)],[pred_minus_1]) ).
cnf(c142,plain,
pred(succ(X0)) = X0,
inference(clausification,[status(esa)],[pred_succ]) ).
cnf(c156,plain,
'a$uselect2'('tptp$uupdate2'(X0,X1,X2),X1) = X2,
inference(clausification,[status(esa)],[sel2_update_1]) ).
cnf(c161,plain,
true,
inference(clausification,[status(esa)],[ttrue]) ).
cnf(c164,plain,
leq(pv35,minus(n5,n1)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c165,plain,
leq(n0,pv35),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c166,plain,
sum(n0,minus(n135300,n1),'a$uselect3'(q,pv79,pv35)) = pv78,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c168,plain,
( ~ true
| pv44 != n0 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c169,plain,
( ~ leq(pv35,minus(n5,n1))
| sum(n0,minus(n135300,n1),'a$uselect3'(q,pv79,pv35)) != pv78
| sum(n0,minus(n0,n1),times(minus('a$uselect2'(x,pv83),'a$uselect2'('tptp$uupdate2'(mu,pv35,divide(pv80,pv44)),pv35)),times(minus('a$uselect2'(x,pv83),'a$uselect2'('tptp$uupdate2'(mu,pv35,divide(pv80,pv44)),pv35)),'a$uselect3'(q,pv83,pv35)))) != n0
| pv44 = n0
| ~ leq(n0,pv35) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
sum(n0,pred(n135300),'a$uselect3'(q,pv79,pv35)) = pv78,
inference(demodulation,[status(thm)],[c166,c141]) ).
cnf(d1,plain,
pred(n0) = 'tptp$uminus$u1',
inference(superposition,[status(thm)],[c130,c142]) ).
cnf(d2,plain,
( ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| pv44 = n0
| sum(n0,minus(n0,n1),times(minus('a$uselect2'(x,pv83),'a$uselect2'('tptp$uupdate2'(mu,pv35,divide(pv80,pv44)),pv35)),times(minus('a$uselect2'(x,pv83),'a$uselect2'('tptp$uupdate2'(mu,pv35,divide(pv80,pv44)),pv35)),'a$uselect3'(q,pv83,pv35)))) != n0
| sum(n0,pred(n135300),'a$uselect3'(q,pv79,pv35)) != pv78 ),
inference(demodulation,[status(thm)],[c169,c141]) ).
cnf(d3,plain,
( ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| pv44 = n0
| sum(n0,pred(n0),times(minus('a$uselect2'(x,pv83),'a$uselect2'('tptp$uupdate2'(mu,pv35,divide(pv80,pv44)),pv35)),times(minus('a$uselect2'(x,pv83),'a$uselect2'('tptp$uupdate2'(mu,pv35,divide(pv80,pv44)),pv35)),'a$uselect3'(q,pv83,pv35)))) != n0
| sum(n0,pred(n135300),'a$uselect3'(q,pv79,pv35)) != pv78 ),
inference(demodulation,[status(thm)],[d2,c141]) ).
cnf(d4,plain,
( ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| pv44 = n0
| sum(n0,pred(n0),times(minus('a$uselect2'(x,pv83),divide(pv80,pv44)),times(minus('a$uselect2'(x,pv83),'a$uselect2'('tptp$uupdate2'(mu,pv35,divide(pv80,pv44)),pv35)),'a$uselect3'(q,pv83,pv35)))) != n0
| sum(n0,pred(n135300),'a$uselect3'(q,pv79,pv35)) != pv78 ),
inference(demodulation,[status(thm)],[d3,c156]) ).
cnf(d5,plain,
( ~ leq(pv35,minus(n5,n1))
| ~ leq(n0,pv35)
| pv44 = n0
| sum(n0,pred(n0),times(minus('a$uselect2'(x,pv83),divide(pv80,pv44)),times(minus('a$uselect2'(x,pv83),divide(pv80,pv44)),'a$uselect3'(q,pv83,pv35)))) != n0
| sum(n0,pred(n135300),'a$uselect3'(q,pv79,pv35)) != pv78 ),
inference(demodulation,[status(thm)],[d4,c156]) ).
cnf(d6,plain,
( ~ leq(pv35,pred(n5))
| ~ leq(n0,pv35)
| pv44 = n0
| sum(n0,pred(n0),times(minus('a$uselect2'(x,pv83),divide(pv80,pv44)),times(minus('a$uselect2'(x,pv83),divide(pv80,pv44)),'a$uselect3'(q,pv83,pv35)))) != n0
| sum(n0,pred(n135300),'a$uselect3'(q,pv79,pv35)) != pv78 ),
inference(demodulation,[status(thm)],[d5,c141]) ).
cnf(d7,plain,
( ~ leq(pv35,pred(n5))
| pv44 = n0
| sum(n0,pred(n0),times(minus('a$uselect2'(x,pv83),divide(pv80,pv44)),times(minus('a$uselect2'(x,pv83),divide(pv80,pv44)),'a$uselect3'(q,pv83,pv35)))) != n0
| sum(n0,pred(n135300),'a$uselect3'(q,pv79,pv35)) != pv78 ),
inference(resolution,[status(thm)],[c165,d6]) ).
cnf(d8,plain,
pv44 != n0,
inference(resolution,[status(thm)],[c161,c168]) ).
cnf(d9,plain,
( ~ leq(pv35,pred(n5))
| sum(n0,pred(n0),times(minus('a$uselect2'(x,pv83),divide(pv80,pv44)),times(minus('a$uselect2'(x,pv83),divide(pv80,pv44)),'a$uselect3'(q,pv83,pv35)))) != n0
| sum(n0,pred(n135300),'a$uselect3'(q,pv79,pv35)) != pv78 ),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
leq(pv35,pred(n5)),
inference(demodulation,[status(thm)],[c164,c141]) ).
cnf(d11,plain,
( sum(n0,pred(n0),times(minus('a$uselect2'(x,pv83),divide(pv80,pv44)),times(minus('a$uselect2'(x,pv83),divide(pv80,pv44)),'a$uselect3'(q,pv83,pv35)))) != n0
| sum(n0,pred(n135300),'a$uselect3'(q,pv79,pv35)) != pv78 ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( sum(n0,'tptp$uminus$u1',times(minus('a$uselect2'(x,pv83),divide(pv80,pv44)),times(minus('a$uselect2'(x,pv83),divide(pv80,pv44)),'a$uselect3'(q,pv83,pv35)))) != n0
| sum(n0,pred(n135300),'a$uselect3'(q,pv79,pv35)) != pv78 ),
inference(demodulation,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
( sum(n0,pred(n135300),'a$uselect3'(q,pv79,pv35)) != pv78
| n0 != n0 ),
inference(demodulation,[status(thm)],[d12,c128]) ).
cnf(d14,plain,
( pv78 != pv78
| n0 != n0 ),
inference(demodulation,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
pv78 != pv78,
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
$false,
inference(equality_resolution,[status(thm)],[d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV046+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n004.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
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 13:09:22 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.44/9.99 % SZS status Theorem for theBenchmark.p
% 38.44/9.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------