%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET065+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:31:51 AM UTC 2026
% Result : Theorem 13.76s 3.49s
% Output : CNFRefutation 13.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 8 ~; 5 |; 3 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 4 sgn 6 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(class_elements_are_sets,axiom,
! [X0] : subclass(X0,'universal$uclass') ).
fof(inductive_defn,axiom,
! [X0] :
( inductive(X0)
<=> ( subclass(image('successor$urelation',X0),X0)
& member('null$uclass',X0) ) ) ).
fof(infinity,axiom,
? [X0] :
( ! [X1] :
( inductive(X1)
=> subclass(X0,X1) )
& inductive(X0)
& member(X0,'universal$uclass') ) ).
fof(null_class_is_a_set,conjecture,
member('null$uclass','universal$uclass') ).
fof(negated_conjecture,negated_conjecture,
~ member('null$uclass','universal$uclass'),
inference(negate_conjecture,[status(cth)],[null_class_is_a_set]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_defn]) ).
cnf(c3,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c55,plain,
( member('null$uclass',X0)
| ~ inductive(X0) ),
inference(clausification,[status(esa)],[inductive_defn]) ).
cnf(c59,plain,
inductive(sK58),
inference(clausification,[status(esa)],[infinity]) ).
cnf(c89,plain,
~ member('null$uclass','universal$uclass'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d1,plain,
( ~ inductive(X0)
| member('null$uclass','universal$uclass') ),
inference(resolution,[status(thm)],[d0,c55]) ).
cnf(d2,plain,
~ inductive(X0),
inference(resolution,[status(thm)],[c89,d1]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[d2,c59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET065+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 07:03:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.76/3.49 % SZS status Theorem for theBenchmark.p
% 13.76/3.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------