%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM310+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 : n026.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 08:11:03 AM UTC 2026
% Result : Theorem 48.10s 11.13s
% Output : CNFRefutation 48.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 24 unt; 0 def)
% Number of atoms : 77 ( 6 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 66 ( 30 ~; 23 |; 8 &)
% ( 1 <=>; 4 =>; 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 : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 55 ( 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(rdn4,axiom,
'rdn$utranslate'(n4,'rdn$upos'(rdnn(n4))) ).
fof(rdn6,axiom,
'rdn$utranslate'(n6,'rdn$upos'(rdnn(n6))) ).
fof(rdn_positive_less34,axiom,
'rdn$upositive$uless'(rdnn(n3),rdnn(n4)) ).
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(less_property,axiom,
! [X0,X1] :
( less(X0,X1)
<=> ( X1 != X0
& ~ less(X1,X0) ) ) ).
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$upos'(X3)) )
=> sum(X0,X1,X2) ) ).
fof(unique_RHS,axiom,
! [X0,X1,X2,X3] :
( ( sum(X0,X2,X3)
& sum(X0,X1,X3) )
=> X1 = X2 ) ).
fof(add_digit_digit_digit,axiom,
! [X0,X1,X2,X3,X4] :
( ( 'rdn$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_n4_n6_n0,axiom,
'rdn$udigit$uadd'(rdnn(n2),rdnn(n4),rdnn(n6),rdnn(n0)) ).
fof(rdn_digit_add_n6_n0_n6_n0,axiom,
'rdn$udigit$uadd'(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)) ).
fof(sum_n2_n3_not_n6,conjecture,
~ sum(n2,n3,n6) ).
fof(negated_conjecture,negated_conjecture,
~ ~ sum(n2,n3,n6),
inference(negate_conjecture,[status(cth)],[sum_n2_n3_not_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(c4,plain,
'rdn$utranslate'(n4,'rdn$upos'(rdnn(n4))),
inference(clausification,[status(esa)],[rdn4]) ).
cnf(c6,plain,
'rdn$utranslate'(n6,'rdn$upos'(rdnn(n6))),
inference(clausification,[status(esa)],[rdn6]) ).
cnf(c22,plain,
'rdn$upositive$uless'(rdnn(n3),rdnn(n4)),
inference(clausification,[status(esa)],[rdn_positive_less34]) ).
cnf(c34,plain,
( less(X3,X0)
| ~ 'rdn$utranslate'(X3,'rdn$upos'(X2))
| ~ 'rdn$upositive$uless'(X2,X1)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1)) ),
inference(clausification,[status(esa)],[less_entry_point_pos_pos]) ).
cnf(c38,plain,
( X0 != X1
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[less_property]) ).
cnf(c44,plain,
( ~ 'rdn$utranslate'(X5,'rdn$upos'(X3))
| sum(X0,X4,X5)
| ~ 'rdn$utranslate'(X4,'rdn$upos'(X2))
| ~ 'rdn$uadd$uwith$ucarry'(rdnn(n0),X1,X2,X3)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1)) ),
inference(clausification,[status(esa)],[sum_entry_point_pos_pos]) ).
cnf(c52,plain,
( X1 = X3
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[unique_RHS]) ).
cnf(c53,plain,
( 'rdn$uadd$uwith$ucarry'(rdnn(X1),rdnn(X3),rdnn(X4),rdnn(X2))
| ~ 'rdn$udigit$uadd'(rdnn(X3),rdnn(X4),rdnn(X0),rdnn(n0))
| ~ 'rdn$udigit$uadd'(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(clausification,[status(esa)],[add_digit_digit_digit]) ).
cnf(c82,plain,
'rdn$udigit$uadd'(rdnn(n2),rdnn(n4),rdnn(n6),rdnn(n0)),
inference(clausification,[status(esa)],[rdn_digit_add_n2_n4_n6_n0]) ).
cnf(c118,plain,
'rdn$udigit$uadd'(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)),
inference(clausification,[status(esa)],[rdn_digit_add_n6_n0_n6_n0]) ).
cnf(c158,plain,
sum(n2,n3,n6),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ sum(n2,X0,n6)
| X0 = n3 ),
inference(resolution,[status(thm)],[c52,c158]) ).
cnf(d1,plain,
( ~ 'rdn$udigit$uadd'(rdnn(n6),rdnn(X0),rdnn(X1),rdnn(n0))
| 'rdn$uadd$uwith$ucarry'(rdnn(X0),rdnn(n2),rdnn(n4),rdnn(X1)) ),
inference(resolution,[status(thm)],[c53,c82]) ).
cnf(d2,plain,
'rdn$uadd$uwith$ucarry'(rdnn(n0),rdnn(n2),rdnn(n4),rdnn(n6)),
inference(resolution,[status(thm)],[d1,c118]) ).
cnf(d3,plain,
( sum(X1,X0,X2)
| ~ 'rdn$utranslate'(X2,'rdn$upos'(rdnn(n6)))
| ~ 'rdn$utranslate'(X1,'rdn$upos'(rdnn(n2)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n4))) ),
inference(resolution,[status(thm)],[d2,c44]) ).
cnf(d4,plain,
( sum(X1,n4,X0)
| ~ 'rdn$utranslate'(X1,'rdn$upos'(rdnn(n2)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n6))) ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
( sum(X0,n4,n6)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n2))) ),
inference(resolution,[status(thm)],[d4,c6]) ).
cnf(d6,plain,
sum(n2,n4,n6),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
n4 = n3,
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
( less(X0,n4)
| ~ 'rdn$upositive$uless'(X1,rdnn(n4))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1)) ),
inference(resolution,[status(thm)],[c34,c4]) ).
cnf(d9,plain,
( less(X0,n4)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n3))) ),
inference(resolution,[status(thm)],[d8,c22]) ).
cnf(d10,plain,
less(n3,n4),
inference(resolution,[status(thm)],[d9,c3]) ).
cnf(d11,plain,
less(n3,n3),
inference(demodulation,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
~ less(X0,X0),
inference(equality_resolution,[status(thm)],[c38]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM310+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n026.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 02:28:25 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.10/11.13 % SZS status Theorem for theBenchmark.p
% 48.10/11.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------