%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM330+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 : n003.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 08:11:05 AM UTC 2026
% Result : Theorem 54.36s 7.64s
% Output : CNFRefutation 54.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 12 unt; 0 def)
% Number of atoms : 50 ( 7 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 46 ( 20 ~; 16 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 37 ( 0 sgn 11 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn4,axiom,
'rdn$utranslate'(n4,'rdn$upos'(rdnn(n4))) ).
fof(rdn8,axiom,
'rdn$utranslate'(n8,'rdn$upos'(rdnn(n8))) ).
fof(sum_entry_point_pos_pos,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( 'rdn$utranslate'(X2,'rdn$upos'(X5))
& 'rdn$uadd$uwith$ucarry'(rdnn(n0),X3,X4,X5)
& 'rdn$utranslate'(X1,'rdn$upos'(X4))
& 'rdn$utranslate'(X0,'rdn$upos'(X3)) )
=> sum(X0,X1,X2) ) ).
fof(add_digit_digit_digit,axiom,
! [X0,X1,X2,X3,X4] :
( ( 'rdn$udigit$uadd'(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
& 'rdn$udigit$uadd'(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) )
=> 'rdn$uadd$uwith$ucarry'(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ) ).
fof(rdn_digit_add_n4_n4_n8_n0,axiom,
'rdn$udigit$uadd'(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)) ).
fof(rdn_digit_add_n8_n0_n8_n0,axiom,
'rdn$udigit$uadd'(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)) ).
fof(sum_n4_n4_n8,conjecture,
? [X0,X1] :
( X1 = n4
& X0 = n4
& sum(X0,X1,n8) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1] :
( X1 = n4
& X0 = n4
& sum(X0,X1,n8) ),
inference(negate_conjecture,[status(cth)],[sum_n4_n4_n8]) ).
cnf(c4,plain,
'rdn$utranslate'(n4,'rdn$upos'(rdnn(n4))),
inference(clausification,[status(esa)],[rdn4]) ).
cnf(c8,plain,
'rdn$utranslate'(n8,'rdn$upos'(rdnn(n8))),
inference(clausification,[status(esa)],[rdn8]) ).
cnf(c21,plain,
( ~ 'rdn$utranslate'(X2,'rdn$upos'(X4))
| ~ 'rdn$utranslate'(X3,'rdn$upos'(X5))
| ~ 'rdn$uadd$uwith$ucarry'(rdnn(n0),X4,X1,X5)
| sum(X2,X0,X3)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1)) ),
inference(clausification,[status(esa)],[sum_entry_point_pos_pos]) ).
cnf(c30,plain,
( 'rdn$uadd$uwith$ucarry'(rdnn(X3),rdnn(X0),rdnn(X1),rdnn(X4))
| ~ 'rdn$udigit$uadd'(rdnn(X2),rdnn(X3),rdnn(X4),rdnn(n0))
| ~ 'rdn$udigit$uadd'(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(clausification,[status(esa)],[add_digit_digit_digit]) ).
cnf(c79,plain,
'rdn$udigit$uadd'(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(clausification,[status(esa)],[rdn_digit_add_n4_n4_n8_n0]) ).
cnf(c115,plain,
'rdn$udigit$uadd'(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(clausification,[status(esa)],[rdn_digit_add_n8_n0_n8_n0]) ).
cnf(c135,plain,
( X1 != n4
| X0 != n4
| ~ sum(X0,X1,n8) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'rdn$udigit$uadd'(rdnn(X0),rdnn(X1),rdnn(n8),rdnn(n0))
| 'rdn$uadd$uwith$ucarry'(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n8)) ),
inference(resolution,[status(thm)],[c30,c115]) ).
cnf(d1,plain,
'rdn$uadd$uwith$ucarry'(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)),
inference(resolution,[status(thm)],[d0,c79]) ).
cnf(d2,plain,
( sum(X2,X0,X1)
| ~ 'rdn$utranslate'(X2,'rdn$upos'(rdnn(n4)))
| ~ 'rdn$utranslate'(X1,'rdn$upos'(rdnn(n8)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n4))) ),
inference(resolution,[status(thm)],[d1,c21]) ).
cnf(d3,plain,
( sum(X0,n4,X1)
| ~ 'rdn$utranslate'(X1,'rdn$upos'(rdnn(n8)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n4))) ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( sum(n4,n4,X0)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n8))) ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
sum(n4,n4,n8),
inference(resolution,[status(thm)],[d4,c8]) ).
cnf(d6,plain,
( ~ sum(n4,X0,n8)
| X0 != n4 ),
inference(equality_resolution,[status(thm)],[c135]) ).
cnf(d7,plain,
~ sum(n4,n4,n8),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM330+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
% 0.17/0.58 % Computer : n003.cluster.edu
% 0.17/0.58 % Model : x86_64 x86_64
% 0.17/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.58 % Memory : 8046.5625MB
% 0.17/0.58 % OS : Linux 6.8.0-71-generic
% 0.17/0.58 % CPULimit : 300
% 0.17/0.58 % WCLimit : 300
% 0.17/0.58 % DateTime : Sat Sep 26 02:29:53 UTC 2026
% 0.17/0.58 % CPUTime :
% 0.17/0.59 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 54.36/7.64 % SZS status Theorem for theBenchmark.p
% 54.36/7.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------