%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM292+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 : 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 08:11:01 AM UTC 2026
% Result : Theorem 37.20s 10.71s
% Output : CNFRefutation 37.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 12 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 12 ~; 10 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 4 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn2,axiom,
'rdn$utranslate'(n2,'rdn$upos'(rdnn(n2))) ).
fof(rdn13,axiom,
'rdn$utranslate'(n13,'rdn$upos'(rdn(rdnn(n3),rdnn(n1)))) ).
fof(rdn_digit1,axiom,
'rdn$unon$uzero$udigit'(rdnn(n1)) ).
fof(rdn_extra_digits_positive_less,axiom,
! [X0,X1,X2] :
( 'rdn$unon$uzero'(X2)
=> 'rdn$upositive$uless'(rdnn(X0),rdn(rdnn(X1),X2)) ) ).
fof(rdn_non_zero_by_digit,axiom,
! [X0] :
( 'rdn$unon$uzero$udigit'(rdnn(X0))
=> 'rdn$unon$uzero'(rdnn(X0)) ) ).
fof(less_entry_point_pos_pos,axiom,
! [X0,X1,X2,X3] :
( ( 'rdn$upositive$uless'(X2,X3)
& 'rdn$utranslate'(X1,'rdn$upos'(X3))
& 'rdn$utranslate'(X0,'rdn$upos'(X2)) )
=> less(X0,X1) ) ).
fof(n2_less_n13,conjecture,
less(n2,n13) ).
fof(negated_conjecture,negated_conjecture,
~ less(n2,n13),
inference(negate_conjecture,[status(cth)],[n2_less_n13]) ).
cnf(c2,plain,
'rdn$utranslate'(n2,'rdn$upos'(rdnn(n2))),
inference(clausification,[status(esa)],[rdn2]) ).
cnf(c10,plain,
'rdn$utranslate'(n13,'rdn$upos'(rdn(rdnn(n3),rdnn(n1)))),
inference(clausification,[status(esa)],[rdn13]) ).
cnf(c11,plain,
'rdn$unon$uzero$udigit'(rdnn(n1)),
inference(clausification,[status(esa)],[rdn_digit1]) ).
cnf(c32,plain,
( 'rdn$upositive$uless'(rdnn(X1),rdn(rdnn(X2),X0))
| ~ 'rdn$unon$uzero'(X0) ),
inference(clausification,[status(esa)],[rdn_extra_digits_positive_less]) ).
cnf(c33,plain,
( 'rdn$unon$uzero'(rdnn(X0))
| ~ 'rdn$unon$uzero$udigit'(rdnn(X0)) ),
inference(clausification,[status(esa)],[rdn_non_zero_by_digit]) ).
cnf(c35,plain,
( less(X3,X0)
| ~ 'rdn$utranslate'(X3,'rdn$upos'(X2))
| ~ 'rdn$upositive$uless'(X2,X1)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1)) ),
inference(clausification,[status(esa)],[less_entry_point_pos_pos]) ).
cnf(c159,plain,
~ less(n2,n13),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( less(X0,n13)
| ~ 'rdn$upositive$uless'(X1,rdn(rdnn(n3),rdnn(n1)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1)) ),
inference(resolution,[status(thm)],[c35,c10]) ).
cnf(d1,plain,
( ~ 'rdn$unon$uzero'(rdnn(n1))
| less(X0,n13)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(X1))) ),
inference(resolution,[status(thm)],[d0,c32]) ).
cnf(d2,plain,
'rdn$unon$uzero'(rdnn(n1)),
inference(resolution,[status(thm)],[c33,c11]) ).
cnf(d3,plain,
( less(X0,n13)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(X1))) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
less(n2,n13),
inference(resolution,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c159,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM292+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n002.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 02:27:05 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.20/10.71 % SZS status Theorem for theBenchmark.p
% 37.20/10.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------