%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM342+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 : n012.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 08:11:06 AM UTC 2026
% Result : Theorem 25.79s 3.70s
% Output : CNFRefutation 25.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 19 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 56 ( 25 ~; 22 |; 6 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 50 ( 0 sgn 14 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn0,axiom,
'rdn$utranslate'(n0,'rdn$upos'(rdnn(n0))) ).
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$upos'(X3)) )
=> sum(X0,X1,X2) ) ).
fof(minus_entry_point,axiom,
! [X0,X1,X2] :
( sum(X1,X2,X0)
<=> difference(X0,X1,X2) ) ).
fof(add_digit_digit_digit,axiom,
! [X0,X1,X2,X3,X4] :
( ( 'rdn$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_n0_n4_n0,axiom,
'rdn$udigit$uadd'(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)) ).
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_and_difference,conjecture,
? [X0,X1] :
( difference(X0,X1,n0)
& sum(X0,X1,n8) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1] :
( difference(X0,X1,n0)
& sum(X0,X1,n8) ),
inference(negate_conjecture,[status(cth)],[sum_and_difference]) ).
cnf(c0,plain,
'rdn$utranslate'(n0,'rdn$upos'(rdnn(n0))),
inference(clausification,[status(esa)],[rdn0]) ).
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$upos'(X1)) ),
inference(clausification,[status(esa)],[sum_entry_point_pos_pos]) ).
cnf(c30,plain,
( difference(X2,X0,X1)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[minus_entry_point]) ).
cnf(c32,plain,
( 'rdn$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(c77,plain,
'rdn$udigit$uadd'(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
inference(clausification,[status(esa)],[rdn_digit_add_n4_n0_n4_n0]) ).
cnf(c81,plain,
'rdn$udigit$uadd'(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(clausification,[status(esa)],[rdn_digit_add_n4_n4_n8_n0]) ).
cnf(c117,plain,
'rdn$udigit$uadd'(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(clausification,[status(esa)],[rdn_digit_add_n8_n0_n8_n0]) ).
cnf(c137,plain,
( ~ difference(X0,X1,n0)
| ~ sum(X0,X1,n8) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'rdn$udigit$uadd'(rdnn(n8),rdnn(X0),rdnn(X1),rdnn(n0))
| 'rdn$uadd$uwith$ucarry'(rdnn(X0),rdnn(n4),rdnn(n4),rdnn(X1)) ),
inference(resolution,[status(thm)],[c32,c81]) ).
cnf(d1,plain,
'rdn$uadd$uwith$ucarry'(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)),
inference(resolution,[status(thm)],[d0,c117]) ).
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,
( ~ 'rdn$udigit$uadd'(rdnn(n4),rdnn(X0),rdnn(X1),rdnn(n0))
| 'rdn$uadd$uwith$ucarry'(rdnn(X0),rdnn(n4),rdnn(n0),rdnn(X1)) ),
inference(resolution,[status(thm)],[c32,c77]) ).
cnf(d7,plain,
'rdn$uadd$uwith$ucarry'(rdnn(n0),rdnn(n4),rdnn(n0),rdnn(n4)),
inference(resolution,[status(thm)],[d6,c77]) ).
cnf(d8,plain,
( sum(X2,X0,X1)
| ~ 'rdn$utranslate'(X2,'rdn$upos'(rdnn(n4)))
| ~ 'rdn$utranslate'(X1,'rdn$upos'(rdnn(n4)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n0))) ),
inference(resolution,[status(thm)],[d7,c21]) ).
cnf(d9,plain,
( sum(X0,n0,X1)
| ~ 'rdn$utranslate'(X1,'rdn$upos'(rdnn(n4)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n4))) ),
inference(resolution,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
( sum(n4,n0,X0)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n4))) ),
inference(resolution,[status(thm)],[d9,c4]) ).
cnf(d11,plain,
sum(n4,n0,n4),
inference(resolution,[status(thm)],[d10,c4]) ).
cnf(d12,plain,
difference(n4,n4,n0),
inference(resolution,[status(thm)],[d11,c30]) ).
cnf(d13,plain,
~ sum(n4,n4,n8),
inference(resolution,[status(thm)],[d12,c137]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM342+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sat Sep 26 02:28:20 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.79/3.70 % SZS status Theorem for theBenchmark.p
% 25.79/3.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------