%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM303+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 : n015.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 08:11:02 AM UTC 2026
% Result : Theorem 30.55s 14.19s
% Output : CNFRefutation 30.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 38 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 17 ~; 10 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 26 ( 3 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn21,axiom,
'rdn$utranslate'(n21,'rdn$upos'(rdn(rdnn(n1),rdnn(n2)))) ).
fof(rdn31,axiom,
'rdn$utranslate'(n31,'rdn$upos'(rdn(rdnn(n1),rdnn(n3)))) ).
fof(rdn_positive_less23,axiom,
'rdn$upositive$uless'(rdnn(n2),rdnn(n3)) ).
fof(rdn_positive_less_multi_digit_high,axiom,
! [X0,X1,X2,X3] :
( 'rdn$upositive$uless'(X1,X3)
=> 'rdn$upositive$uless'(rdn(rdnn(X0),X1),rdn(rdnn(X2),X3)) ) ).
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(n31_not_n12,conjecture,
n31 != n21 ).
fof(negated_conjecture,negated_conjecture,
~ ( n31 != n21 ),
inference(negate_conjecture,[status(cth)],[n31_not_n12]) ).
cnf(c21,plain,
'rdn$utranslate'(n21,'rdn$upos'(rdn(rdnn(n1),rdnn(n2)))),
inference(clausification,[status(esa)],[rdn21]) ).
cnf(c31,plain,
'rdn$utranslate'(n31,'rdn$upos'(rdn(rdnn(n1),rdnn(n3)))),
inference(clausification,[status(esa)],[rdn31]) ).
cnf(c267,plain,
'rdn$upositive$uless'(rdnn(n2),rdnn(n3)),
inference(clausification,[status(esa)],[rdn_positive_less23]) ).
cnf(c275,plain,
( 'rdn$upositive$uless'(rdn(rdnn(X2),X0),rdn(rdnn(X3),X1))
| ~ 'rdn$upositive$uless'(X0,X1) ),
inference(clausification,[status(esa)],[rdn_positive_less_multi_digit_high]) ).
cnf(c280,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(c284,plain,
( X1 != X0
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[less_property]) ).
cnf(c406,plain,
n31 = n21,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'rdn$utranslate'(n21,'rdn$upos'(rdn(rdnn(n1),rdnn(n3)))),
inference(demodulation,[status(thm)],[c31,c406]) ).
cnf(d1,plain,
( less(X0,n21)
| ~ 'rdn$upositive$uless'(X1,rdn(rdnn(n1),rdnn(n3)))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1)) ),
inference(resolution,[status(thm)],[c280,d0]) ).
cnf(d2,plain,
( ~ 'rdn$upositive$uless'(X2,rdnn(n3))
| less(X0,n21)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdn(rdnn(X1),X2))) ),
inference(resolution,[status(thm)],[d1,c275]) ).
cnf(d3,plain,
( less(n21,n21)
| ~ 'rdn$upositive$uless'(rdnn(n2),rdnn(n3)) ),
inference(resolution,[status(thm)],[d2,c21]) ).
cnf(d4,plain,
less(n21,n21),
inference(resolution,[status(thm)],[c267,d3]) ).
cnf(d5,plain,
~ less(X0,X0),
inference(equality_resolution,[status(thm)],[c284]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM303+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
% 0.11/10.39 % Computer : n015.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Sat Sep 26 02:28:38 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.55/14.19 % SZS status Theorem for theBenchmark.p
% 30.55/14.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------