%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM297+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:11:01 AM UTC 2026
% Result : Theorem 34.60s 6.22s
% Output : CNFRefutation 34.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 9 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 18 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdnn2,axiom,
'rdn$utranslate'(nn2,'rdn$uneg'(rdnn(n2))) ).
fof(rdnn4,axiom,
'rdn$utranslate'(nn4,'rdn$uneg'(rdnn(n4))) ).
fof(rdn_positive_less23,axiom,
'rdn$upositive$uless'(rdnn(n2),rdnn(n3)) ).
fof(rdn_positive_less34,axiom,
'rdn$upositive$uless'(rdnn(n3),rdnn(n4)) ).
fof(rdn_positive_less_transitivity,axiom,
! [X0,X1,X2] :
( ( 'rdn$upositive$uless'(rdnn(X1),rdnn(X2))
& 'rdn$upositive$uless'(rdnn(X0),rdnn(X1)) )
=> 'rdn$upositive$uless'(rdnn(X0),rdnn(X2)) ) ).
fof(less_entry_point_neg_neg,axiom,
! [X0,X1,X2,X3] :
( ( 'rdn$upositive$uless'(X3,X2)
& 'rdn$utranslate'(X1,'rdn$uneg'(X3))
& 'rdn$utranslate'(X0,'rdn$uneg'(X2)) )
=> less(X0,X1) ) ).
fof(nn4_less_nn2,conjecture,
less(nn4,nn2) ).
fof(negated_conjecture,negated_conjecture,
~ less(nn4,nn2),
inference(negate_conjecture,[status(cth)],[nn4_less_nn2]) ).
cnf(c10,plain,
'rdn$utranslate'(nn2,'rdn$uneg'(rdnn(n2))),
inference(clausification,[status(esa)],[rdnn2]) ).
cnf(c11,plain,
'rdn$utranslate'(nn4,'rdn$uneg'(rdnn(n4))),
inference(clausification,[status(esa)],[rdnn4]) ).
cnf(c14,plain,
'rdn$upositive$uless'(rdnn(n2),rdnn(n3)),
inference(clausification,[status(esa)],[rdn_positive_less23]) ).
cnf(c15,plain,
'rdn$upositive$uless'(rdnn(n3),rdnn(n4)),
inference(clausification,[status(esa)],[rdn_positive_less34]) ).
cnf(c21,plain,
( 'rdn$upositive$uless'(rdnn(X0),rdnn(X2))
| ~ 'rdn$upositive$uless'(rdnn(X1),rdnn(X2))
| ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(X1)) ),
inference(clausification,[status(esa)],[rdn_positive_less_transitivity]) ).
cnf(c29,plain,
( less(X0,X2)
| ~ 'rdn$upositive$uless'(X3,X1)
| ~ 'rdn$utranslate'(X2,'rdn$uneg'(X3))
| ~ 'rdn$utranslate'(X0,'rdn$uneg'(X1)) ),
inference(clausification,[status(esa)],[less_entry_point_neg_neg]) ).
cnf(c147,plain,
~ less(nn4,nn2),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(n3))
| 'rdn$upositive$uless'(rdnn(X0),rdnn(n4)) ),
inference(resolution,[status(thm)],[c21,c15]) ).
cnf(d1,plain,
'rdn$upositive$uless'(rdnn(n2),rdnn(n4)),
inference(resolution,[status(thm)],[d0,c14]) ).
cnf(d2,plain,
( less(X0,nn2)
| ~ 'rdn$upositive$uless'(rdnn(n2),X1)
| ~ 'rdn$utranslate'(X0,'rdn$uneg'(X1)) ),
inference(resolution,[status(thm)],[c29,c10]) ).
cnf(d3,plain,
( less(X0,nn2)
| ~ 'rdn$utranslate'(X0,'rdn$uneg'(rdnn(n4))) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
less(nn4,nn2),
inference(resolution,[status(thm)],[d3,c11]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c147,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM297+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 02:24:59 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.60/6.22 % SZS status Theorem for theBenchmark.p
% 34.60/6.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------