%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM291+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 : n017.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 08:11:00 AM UTC 2026
% Result : Theorem 31.58s 7.39s
% Output : CNFRefutation 31.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 30 ( 1 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 7 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 15 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn2,axiom,
'rdn$utranslate'(n2,'rdn$upos'(rdnn(n2))) ).
fof(rdn3,axiom,
'rdn$utranslate'(n3,'rdn$upos'(rdnn(n3))) ).
fof(rdn_positive_less23,axiom,
'rdn$upositive$uless'(rdnn(n2),rdnn(n3)) ).
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(n3_not_less_n2,conjecture,
~ less(n3,n2) ).
fof(negated_conjecture,negated_conjecture,
~ ~ less(n3,n2),
inference(negate_conjecture,[status(cth)],[n3_not_less_n2]) ).
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(c12,plain,
'rdn$upositive$uless'(rdnn(n2),rdnn(n3)),
inference(clausification,[status(esa)],[rdn_positive_less23]) ).
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(c24,plain,
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[less_property]) ).
cnf(c127,plain,
less(n3,n2),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( less(X0,n3)
| ~ 'rdn$upositive$uless'(X1,rdnn(n3))
| ~ 'rdn$utranslate'(X0,'rdn$upos'(X1)) ),
inference(resolution,[status(thm)],[c21,c3]) ).
cnf(d1,plain,
( less(X0,n3)
| ~ 'rdn$utranslate'(X0,'rdn$upos'(rdnn(n2))) ),
inference(resolution,[status(thm)],[d0,c12]) ).
cnf(d2,plain,
less(n2,n3),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
~ less(n2,n3),
inference(resolution,[status(thm)],[c24,c127]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[d3,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM291+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.97 % Computer : n017.cluster.edu
% 0.10/0.97 % Model : x86_64 x86_64
% 0.10/0.97 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.97 % Memory : 8046.5625MB
% 0.10/0.97 % OS : Linux 6.8.0-71-generic
% 0.10/0.97 % CPULimit : 300
% 0.10/0.97 % WCLimit : 300
% 0.10/0.97 % DateTime : Sat Sep 26 02:19:51 UTC 2026
% 0.10/0.98 % CPUTime :
% 0.10/0.98 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.58/7.39 % SZS status Theorem for theBenchmark.p
% 31.58/7.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------