%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM299+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 : n006.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 21.33s 5.84s
% Output : CNFRefutation 21.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 15 unt; 0 def)
% Number of atoms : 41 ( 1 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 17 ~; 10 |; 4 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 22 ( 0 sgn 9 !; 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(less_property,axiom,
! [X0,X1] :
( less(X0,X1)
<=> ( X1 != X0
& ~ less(X1,X0) ) ) ).
fof(nn2_not_less_nn4,conjecture,
~ less(nn2,nn4) ).
fof(negated_conjecture,negated_conjecture,
~ ~ less(nn2,nn4),
inference(negate_conjecture,[status(cth)],[nn2_not_less_nn4]) ).
cnf(c4,plain,
'rdn$utranslate'(nn2,'rdn$uneg'(rdnn(n2))),
inference(clausification,[status(esa)],[rdnn2]) ).
cnf(c5,plain,
'rdn$utranslate'(nn4,'rdn$uneg'(rdnn(n4))),
inference(clausification,[status(esa)],[rdnn4]) ).
cnf(c8,plain,
'rdn$upositive$uless'(rdnn(n2),rdnn(n3)),
inference(clausification,[status(esa)],[rdn_positive_less23]) ).
cnf(c9,plain,
'rdn$upositive$uless'(rdnn(n3),rdnn(n4)),
inference(clausification,[status(esa)],[rdn_positive_less34]) ).
cnf(c15,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(c19,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(c20,plain,
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[less_property]) ).
cnf(c72,plain,
less(nn2,nn4),
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)],[c15,c9]) ).
cnf(d1,plain,
'rdn$upositive$uless'(rdnn(n2),rdnn(n4)),
inference(resolution,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
( less(X0,nn2)
| ~ 'rdn$upositive$uless'(rdnn(n2),X1)
| ~ 'rdn$utranslate'(X0,'rdn$uneg'(X1)) ),
inference(resolution,[status(thm)],[c19,c4]) ).
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,c5]) ).
cnf(d5,plain,
~ less(nn4,nn2),
inference(resolution,[status(thm)],[c20,c72]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM299+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
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 02:25:10 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.33/5.84 % SZS status Theorem for theBenchmark.p
% 21.33/5.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------