%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM345+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 : 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 08:11:07 AM UTC 2026
% Result : Theorem 33.99s 5.41s
% Output : CNFRefutation 33.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 22 unt; 0 def)
% Number of atoms : 74 ( 4 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 60 ( 25 ~; 22 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 52 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn2,axiom,
'rdn$utranslate'(n2,'rdn$upos'(rdnn(n2))) ).
fof(rdn3,axiom,
'rdn$utranslate'(n3,'rdn$upos'(rdnn(n3))) ).
fof(rdn5,axiom,
'rdn$utranslate'(n5,'rdn$upos'(rdnn(n5))) ).
fof(rdn6,axiom,
'rdn$utranslate'(n6,'rdn$upos'(rdnn(n6))) ).
fof(rdn_positive_less56,axiom,
'rdn$upositive$uless'(rdnn(n5),rdnn(n6)) ).
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(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$upos'(X3)) )
=> sum(X0,X1,X2) ) ).
fof(unique_sum,axiom,
! [X0,X1,X2,X3] :
( ( sum(X0,X1,X3)
& sum(X0,X1,X2) )
=> X2 = X3 ) ).
fof(add_digit_digit_digit,axiom,
! [X0,X1,X2,X3,X4] :
( ( 'rdn$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_n2_n3_less_n6,conjecture,
! [X0] :
( sum(n2,n3,X0)
=> less(X0,n6) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( sum(n2,n3,X0)
=> less(X0,n6) ),
inference(negate_conjecture,[status(cth)],[sum_n2_n3_less_n6]) ).
cnf(c2,plain,
'rdn$utranslate'(n2,'rdn$upos'(rdnn(n2))),
inference(clausification,[status(esa)],[rdn2]) ).
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(c6,plain,
'rdn$utranslate'(n6,'rdn$upos'(rdnn(n6))),
inference(clausification,[status(esa)],[rdn6]) ).
cnf(c15,plain,
'rdn$upositive$uless'(rdnn(n5),rdnn(n6)),
inference(clausification,[status(esa)],[rdn_positive_less56]) ).
cnf(c21,plain,
( less(X0,X2)
| ~ 'rdn$upositive$uless'(X1,X3)
| ~ 'rdn$utranslate'(X2,'rdn$upos'(X3))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1)) ),
inference(clausification,[status(esa)],[less_entry_point_pos_pos]) ).
cnf(c27,plain,
( ~ 'rdn$uadd$uwith$ucarry'(rdnn(n0),X3,X5,X1)
| ~ 'rdn$utranslate'(X4,'rdn$upos'(X5))
| sum(X2,X4,X0)
| ~ 'rdn$utranslate'(X2,'rdn$upos'(X3))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1)) ),
inference(clausification,[status(esa)],[sum_entry_point_pos_pos]) ).
cnf(c33,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[unique_sum]) ).
cnf(c36,plain,
( 'rdn$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(c64,plain,
'rdn$udigit$uadd'(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(clausification,[status(esa)],[rdn_digit_add_n2_n3_n5_n0]) ).
cnf(c91,plain,
'rdn$udigit$uadd'(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(clausification,[status(esa)],[rdn_digit_add_n5_n0_n5_n0]) ).
cnf(c141,plain,
sum(n2,n3,sK104),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c142,plain,
~ less(sK104,n6),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ sum(n2,n3,X0)
| X0 = sK104 ),
inference(resolution,[status(thm)],[c33,c141]) ).
cnf(d1,plain,
( ~ 'rdn$udigit$uadd'(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))
| 'rdn$uadd$uwith$ucarry'(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n5)) ),
inference(resolution,[status(thm)],[c36,c91]) ).
cnf(d2,plain,
'rdn$uadd$uwith$ucarry'(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(resolution,[status(thm)],[d1,c64]) ).
cnf(d3,plain,
( sum(X1,X0,X2)
| ~ 'rdn$utranslate'(X2,'rdn$upos'(rdnn(n5)))
| ~ 'rdn$utranslate'(X1,'rdn$upos'(rdnn(n2)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n3))) ),
inference(resolution,[status(thm)],[d2,c27]) ).
cnf(d4,plain,
( sum(X1,n3,X0)
| ~ 'rdn$utranslate'(X1,'rdn$upos'(rdnn(n2)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n5))) ),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
( sum(X0,n3,n5)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n2))) ),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
sum(n2,n3,n5),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
n5 = sK104,
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
~ less(n5,n6),
inference(demodulation,[status(thm)],[c142,d7]) ).
cnf(d9,plain,
( less(X0,n6)
| ~ 'rdn$upositive$uless'(X1,rdnn(n6))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1)) ),
inference(resolution,[status(thm)],[c21,c6]) ).
cnf(d10,plain,
( less(X0,n6)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n5))) ),
inference(resolution,[status(thm)],[d9,c15]) ).
cnf(d11,plain,
less(n5,n6),
inference(resolution,[status(thm)],[d10,c5]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM345+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
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 02:31:50 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.99/5.41 % SZS status Theorem for theBenchmark.p
% 33.99/5.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------