%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM321+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 : n001.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 08:11:04 AM UTC 2026
% Result : Theorem 33.25s 6.22s
% Output : CNFRefutation 33.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 37 ( 24 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 56 ( 25 ~; 22 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 45 ( 2 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn3,axiom,
'rdn$utranslate'(n3,'rdn$upos'(rdnn(n3))) ).
fof(rdn5,axiom,
'rdn$utranslate'(n5,'rdn$upos'(rdnn(n5))) ).
fof(rdnn2,axiom,
'rdn$utranslate'(nn2,'rdn$uneg'(rdnn(n2))) ).
fof(rdn_positive_less23,axiom,
'rdn$upositive$uless'(rdnn(n2),rdnn(n3)) ).
fof(rdn_positive_less34,axiom,
'rdn$upositive$uless'(rdnn(n3),rdnn(n4)) ).
fof(rdn_positive_less45,axiom,
'rdn$upositive$uless'(rdnn(n4),rdnn(n5)) ).
fof(rdn_positive_less_transitivity,axiom,
! [X0,X1,X2] :
( ( 'rdn$upositive$uless'(rdnn(X1),rdnn(X2))
& 'rdn$upositive$uless'(rdnn(X0),rdnn(X1)) )
=> 'rdn$upositive$uless'(rdnn(X0),rdnn(X2)) ) ).
fof(sum_entry_point_pos_neg_2,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( 'rdn$utranslate'(X2,'rdn$upos'(X5))
& 'rdn$uadd$uwith$ucarry'(rdnn(n0),X4,X5,X3)
& 'rdn$upositive$uless'(X4,X3)
& 'rdn$utranslate'(X1,'rdn$uneg'(X4))
& 'rdn$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_n2_n3_n5_n0,axiom,
'rdn$udigit$uadd'(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) ).
fof(rdn_digit_add_n5_n0_n5_n0,axiom,
'rdn$udigit$uadd'(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) ).
fof(sum_n5_nn2_what,conjecture,
? [X0] : sum(n5,nn2,X0) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] : sum(n5,nn2,X0),
inference(negate_conjecture,[status(cth)],[sum_n5_nn2_what]) ).
cnf(c3,plain,
'rdn$utranslate'(n3,'rdn$upos'(rdnn(n3))),
inference(clausification,[status(esa)],[rdn3]) ).
cnf(c5,plain,
'rdn$utranslate'(n5,'rdn$upos'(rdnn(n5))),
inference(clausification,[status(esa)],[rdn5]) ).
cnf(c10,plain,
'rdn$utranslate'(nn2,'rdn$uneg'(rdnn(n2))),
inference(clausification,[status(esa)],[rdnn2]) ).
cnf(c13,plain,
'rdn$upositive$uless'(rdnn(n2),rdnn(n3)),
inference(clausification,[status(esa)],[rdn_positive_less23]) ).
cnf(c14,plain,
'rdn$upositive$uless'(rdnn(n3),rdnn(n4)),
inference(clausification,[status(esa)],[rdn_positive_less34]) ).
cnf(c15,plain,
'rdn$upositive$uless'(rdnn(n4),rdnn(n5)),
inference(clausification,[status(esa)],[rdn_positive_less45]) ).
cnf(c20,plain,
( 'rdn$upositive$uless'(rdnn(X0),rdnn(X2))
| ~ 'rdn$upositive$uless'(rdnn(X1),rdnn(X2))
| ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(X1)) ),
inference(clausification,[status(esa)],[rdn_positive_less_transitivity]) ).
cnf(c25,plain,
( sum(X0,X5,X4)
| ~ 'rdn$utranslate'(X5,'rdn$uneg'(X2))
| ~ 'rdn$upositive$uless'(X2,X1)
| ~ 'rdn$utranslate'(X4,'rdn$upos'(X3))
| ~ 'rdn$uadd$uwith$ucarry'(rdnn(n0),X2,X3,X1)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1)) ),
inference(clausification,[status(esa)],[sum_entry_point_pos_neg_2]) ).
cnf(c31,plain,
( 'rdn$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(c59,plain,
'rdn$udigit$uadd'(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(clausification,[status(esa)],[rdn_digit_add_n2_n3_n5_n0]) ).
cnf(c86,plain,
'rdn$udigit$uadd'(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(clausification,[status(esa)],[rdn_digit_add_n5_n0_n5_n0]) ).
cnf(c136,plain,
~ sum(n5,nn2,X0),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'rdn$udigit$uadd'(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))
| 'rdn$uadd$uwith$ucarry'(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n5)) ),
inference(resolution,[status(thm)],[c31,c86]) ).
cnf(d1,plain,
'rdn$uadd$uwith$ucarry'(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(resolution,[status(thm)],[d0,c59]) ).
cnf(d2,plain,
( sum(X0,X2,X1)
| ~ 'rdn$upositive$uless'(rdnn(n2),rdnn(n5))
| ~ 'rdn$utranslate'(X2,'rdn$uneg'(rdnn(n2)))
| ~ 'rdn$utranslate'(X1,'rdn$upos'(rdnn(n3)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n5))) ),
inference(resolution,[status(thm)],[d1,c25]) ).
cnf(d3,plain,
( ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(n4))
| 'rdn$upositive$uless'(rdnn(X0),rdnn(n5)) ),
inference(resolution,[status(thm)],[c20,c15]) ).
cnf(d4,plain,
( ~ 'rdn$upositive$uless'(rdnn(X0),rdnn(n3))
| 'rdn$upositive$uless'(rdnn(X0),rdnn(n4)) ),
inference(resolution,[status(thm)],[c20,c14]) ).
cnf(d5,plain,
'rdn$upositive$uless'(rdnn(n2),rdnn(n4)),
inference(resolution,[status(thm)],[d4,c13]) ).
cnf(d6,plain,
'rdn$upositive$uless'(rdnn(n2),rdnn(n5)),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( sum(X2,X0,X1)
| ~ 'rdn$utranslate'(X2,'rdn$upos'(rdnn(n5)))
| ~ 'rdn$utranslate'(X1,'rdn$upos'(rdnn(n3)))
| ~ 'rdn$utranslate'(X0,'rdn$uneg'(rdnn(n2))) ),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( sum(X0,nn2,X1)
| ~ 'rdn$utranslate'(X1,'rdn$upos'(rdnn(n3)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n5))) ),
inference(resolution,[status(thm)],[d7,c10]) ).
cnf(d9,plain,
( sum(n5,nn2,X0)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n3))) ),
inference(resolution,[status(thm)],[d8,c5]) ).
cnf(d10,plain,
~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n3))),
inference(resolution,[status(thm)],[c136,d9]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,c3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM321+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 02:32:27 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.25/6.22 % SZS status Theorem for theBenchmark.p
% 33.25/6.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------