%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM329+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 40.94s 11.42s
% Output : CNFRefutation 40.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 34 ( 15 ~; 13 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 33 ( 0 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn0,axiom,
'rdn$utranslate'(n0,'rdn$upos'(rdnn(n0))) ).
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_n0_n0_n0_n0,axiom,
'rdn$udigit$uadd'(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)) ).
fof(idempotent_element,conjecture,
? [X0] : sum(X0,X0,X0) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] : sum(X0,X0,X0),
inference(negate_conjecture,[status(cth)],[idempotent_element]) ).
cnf(c0,plain,
'rdn$utranslate'(n0,'rdn$upos'(rdnn(n0))),
inference(clausification,[status(esa)],[rdn0]) ).
cnf(c13,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$upos'(X1)) ),
inference(clausification,[status(esa)],[sum_entry_point_pos_pos]) ).
cnf(c22,plain,
( 'rdn$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(c27,plain,
'rdn$udigit$uadd'(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(clausification,[status(esa)],[rdn_digit_add_n0_n0_n0_n0]) ).
cnf(c33,plain,
~ sum(X0,X0,X0),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'rdn$udigit$uadd'(rdnn(X0),rdnn(X1),rdnn(n0),rdnn(n0))
| 'rdn$uadd$uwith$ucarry'(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n0)) ),
inference(resolution,[status(thm)],[c22,c27]) ).
cnf(d1,plain,
'rdn$uadd$uwith$ucarry'(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(resolution,[status(thm)],[d0,c27]) ).
cnf(d2,plain,
( sum(X2,X0,X1)
| ~ 'rdn$utranslate'(X2,'rdn$upos'(rdnn(n0)))
| ~ 'rdn$utranslate'(X1,'rdn$upos'(rdnn(n0)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n0))) ),
inference(resolution,[status(thm)],[d1,c13]) ).
cnf(d3,plain,
( sum(X0,n0,X1)
| ~ 'rdn$utranslate'(X1,'rdn$upos'(rdnn(n0)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n0))) ),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
( sum(n0,n0,X0)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n0))) ),
inference(resolution,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
sum(n0,n0,n0),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c33,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM329+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n003.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 02:29:31 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.94/11.42 % SZS status Theorem for theBenchmark.p
% 40.94/11.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------