%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 08:10:37 AM UTC 2026
% Result : Unsatisfiable 21.57s 3.22s
% Output : CNFRefutation 21.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 7 unt; 3 nHn; 14 RR)
% Number of literals : 24 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 8 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_zero_is_a_natural,negated_conjecture,
~ member('empty$uset','natural$unumbers') ).
cnf(a2,axiom,
( 'little$uset'(X0)
| ~ member(X0,X1) ) ).
cnf(infinity2,axiom,
member('empty$uset',infinity) ).
cnf(natural_numbers4,axiom,
( member('empty$uset',f44(X0))
| ~ 'little$uset'(X0)
| member(X0,'natural$unumbers') ) ).
cnf(natural_numbers6,axiom,
( ~ member(X0,f44(X0))
| member(X0,'natural$unumbers') ) ).
cnf(c0,plain,
~ member('empty$uset','natural$unumbers'),
inference(clausification,[status(esa)],[prove_zero_is_a_natural]) ).
cnf(c1,plain,
( 'little$uset'(X0)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[a2]) ).
cnf(c61,plain,
member('empty$uset',infinity),
inference(clausification,[status(esa)],[infinity2]) ).
cnf(c169,plain,
( member('empty$uset',f44(X0))
| ~ 'little$uset'(X0)
| member(X0,'natural$unumbers') ),
inference(clausification,[status(esa)],[natural_numbers4]) ).
cnf(c171,plain,
( ~ member(X0,f44(X0))
| member(X0,'natural$unumbers') ),
inference(clausification,[status(esa)],[natural_numbers6]) ).
cnf(d0,plain,
( ~ 'little$uset'('empty$uset')
| member('empty$uset','natural$unumbers')
| member('empty$uset','natural$unumbers') ),
inference(resolution,[status(thm)],[c171,c169]) ).
cnf(d1,plain,
~ 'little$uset'('empty$uset'),
inference(resolution,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
'little$uset'('empty$uset'),
inference(resolution,[status(thm)],[c61,c1]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[d2,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 01:55:20 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.57/3.22 % SZS status Unsatisfiable for theBenchmark.p
% 21.57/3.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------