%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM301+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 08:11:02 AM UTC 2026
% Result : Theorem 39.87s 15.74s
% Output : CNFRefutation 39.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 10 ~; 6 |; 2 &)
% ( 0 <=>; 1 =>; 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 : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 16 ( 3 sgn 4 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdnn2,axiom,
'rdn$utranslate'(nn2,'rdn$uneg'(rdnn(n2))) ).
fof(rdnn3,axiom,
'rdn$utranslate'(nn3,'rdn$uneg'(rdnn(n3))) ).
fof(rdn_positive_less23,axiom,
'rdn$upositive$uless'(rdnn(n2),rdnn(n3)) ).
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(something_less_nn2,conjecture,
? [X0] : less(X0,nn2) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] : less(X0,nn2),
inference(negate_conjecture,[status(cth)],[something_less_nn2]) ).
cnf(c129,plain,
'rdn$utranslate'(nn2,'rdn$uneg'(rdnn(n2))),
inference(clausification,[status(esa)],[rdnn2]) ).
cnf(c130,plain,
'rdn$utranslate'(nn3,'rdn$uneg'(rdnn(n3))),
inference(clausification,[status(esa)],[rdnn3]) ).
cnf(c267,plain,
'rdn$upositive$uless'(rdnn(n2),rdnn(n3)),
inference(clausification,[status(esa)],[rdn_positive_less23]) ).
cnf(c282,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(c406,plain,
~ less(X0,nn2),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( less(X0,nn2)
| ~ 'rdn$upositive$uless'(rdnn(n2),X1)
| ~ 'rdn$utranslate'(X0,'rdn$uneg'(X1)) ),
inference(resolution,[status(thm)],[c282,c129]) ).
cnf(d1,plain,
( ~ 'rdn$upositive$uless'(rdnn(n2),X1)
| ~ 'rdn$utranslate'(X0,'rdn$uneg'(X1)) ),
inference(resolution,[status(thm)],[c406,d0]) ).
cnf(d2,plain,
~ 'rdn$utranslate'(X0,'rdn$uneg'(rdnn(n3))),
inference(resolution,[status(thm)],[d1,c267]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[d2,c130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM301+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/10.46 % Computer : n002.cluster.edu
% 0.19/10.46 % Model : x86_64 x86_64
% 0.19/10.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/10.46 % Memory : 8046.5625MB
% 0.19/10.46 % OS : Linux 6.8.0-71-generic
% 0.19/10.46 % CPULimit : 300
% 0.19/10.46 % WCLimit : 300
% 0.19/10.46 % DateTime : Sat Sep 26 02:28:01 UTC 2026
% 0.19/10.46 % CPUTime :
% 0.19/10.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.87/15.74 % SZS status Theorem for theBenchmark.p
% 39.87/15.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------