%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET065+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 08:35:35 AM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 26 ( 9 ~; 6 |; 7 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 ( 1 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('theBenchmark.p',subclass_defn) ).
fof(class_elements_are_sets,axiom,
! [X] : subclass(X,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
fof(inductive_defn,axiom,
! [X] :
( inductive(X)
<=> ( subclass(image(successor_relation,X),X)
& member(null_class,X) ) ),
file('theBenchmark.p',inductive_defn) ).
fof(infinity,axiom,
? [X] :
( ! [Y] :
( inductive(Y)
=> subclass(X,Y) )
& inductive(X)
& member(X,universal_class) ),
file('theBenchmark.p',infinity) ).
fof(null_class_is_a_set,conjecture,
member(null_class,universal_class),
file('theBenchmark.p',null_class_is_a_set) ).
fof(null_class_is_a_set_neg,negated_conjecture,
~ member(null_class,universal_class),
inference(assume_negation,[status(cth)],[null_class_is_a_set]) ).
cnf(c_45,plain,
( member(null_class,A)
| ~ inductive(A) ),
inference(clausify,[status(thm)],[inductive_defn]) ).
fof(nnf_28,plain,
? [X] :
( ! [Y] :
( subclass(X,Y)
| ~ inductive(Y) )
& inductive(X)
& member(X,universal_class) ),
inference(fof_nnf,[status(thm)],[infinity]) ).
fof(sk_infinity,plain,
( ! [Y] :
( subclass(sK0,Y)
| ~ inductive(Y) )
& inductive(sK0)
& member(sK0,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_28]) ).
cnf(c_46,plain,
inductive(sK0),
inference(split_conjunct,[status(thm)],[sk_infinity]) ).
cnf(c_62,plain,
member(null_class,sK0),
inference(resolve,[status(thm)],[c_46,c_45]) ).
cnf(c_64,negated_conjecture,
~ member(null_class,universal_class),
inference(clausify,[status(thm)],[null_class_is_a_set_neg]) ).
cnf(c_136,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
cnf(c_139,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_defn]) ).
cnf(c_426,plain,
( member(null_class,A)
| ~ subclass(sK0,A) ),
inference(resolve,[status(thm)],[c_139,c_62]) ).
cnf(c_427,negated_conjecture,
~ subclass(sK0,universal_class),
inference(resolve,[status(thm)],[c_426,c_64]) ).
cnf(c_425,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_136,c_427]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET065+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 07:03:52 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 4002242 was started by sandbox on n018,
% 0.09/0.36 % Sat Sep 26 07:03:52 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.40 % Length of proof is 12.
% 0.09/0.40 % Level of proof is 3.
% 0.09/0.40 % Maximum clause weight is 14.000.
% 0.09/0.40 % Given clauses 83.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------