%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET063+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 : n007.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 08:35:34 AM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 50 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 50 ( 21 ~; 15 |; 9 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 1 sgn 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('theBenchmark.p',subclass_defn) ).
fof(extensionality,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(Y,X)
& subclass(X,Y) ) ),
file('theBenchmark.p',extensionality) ).
fof(null_class_defn,axiom,
! [X] : ~ member(X,null_class),
file('theBenchmark.p',null_class_defn) ).
fof(corollary_of_null_class_is_subclass,conjecture,
! [X] :
( subclass(X,null_class)
=> X = null_class ),
file('theBenchmark.p',corollary_of_null_class_is_subclass) ).
fof(corollary_of_null_class_is_subclass_neg,negated_conjecture,
~ ! [X] :
( subclass(X,null_class)
=> X = null_class ),
inference(assume_negation,[status(cth)],[corollary_of_null_class_is_subclass]) ).
fof(nnf_42,plain,
? [X] :
( null_class != X
& subclass(X,null_class) ),
inference(fof_nnf,[status(thm)],[corollary_of_null_class_is_subclass_neg]) ).
fof(sk_corollary_of_null_class_is_subclass_neg,plain,
( null_class != sK0
& subclass(sK0,null_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
null_class != sK0,
inference(split_conjunct,[status(thm)],[sk_corollary_of_null_class_is_subclass_neg]) ).
cnf(c_65,negated_conjecture,
sK0 != null_class,
inference(copy,[status(thm)],[c_64]) ).
cnf(c_66,negated_conjecture,
subclass(sK0,null_class),
inference(split_conjunct,[status(thm)],[sk_corollary_of_null_class_is_subclass_neg]) ).
cnf(c_110,plain,
~ member(A,null_class),
inference(clausify,[status(thm)],[null_class_defn]) ).
cnf(c_135,plain,
( ~ subclass(A,B)
| ~ subclass(B,A)
| A = B ),
inference(clausify,[status(thm)],[extensionality]) ).
fof(nnf_1,plain,
! [X,Y] :
( ( ? [U] :
( ~ member(U,Y)
& member(U,X) )
| subclass(X,Y) )
& ( ! [X0] :
( member(X0,Y)
| ~ member(X0,X) )
| ~ subclass(X,Y) ) ),
inference(fof_nnf,[status(thm)],[subclass_defn]) ).
fof(sk_subclass_defn_sk,plain,
! [X,Y] :
( ( ( ~ member(sK1(X,Y),Y)
& member(sK1(X,Y),X) )
| subclass(X,Y) )
& ( ! [X0] :
( member(X0,Y)
| ~ member(X0,X) )
| ~ subclass(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U,sK1(X,Y))],[nnf_1]) ).
fof(sk_subclass_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK1(VAR_0,VAR_1),VAR_1)
| subclass(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK1(VAR_0,VAR_1),VAR_0)
| subclass(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_subclass_defn_sk]) ).
cnf(c_140,plain,
( member(sK1(A,B),A)
| subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_441,negated_conjecture,
( ~ subclass(null_class,sK0)
| null_class = sK0 ),
inference(resolve,[status(thm)],[c_135,c_66]) ).
cnf(c_442,negated_conjecture,
( ~ subclass(null_class,sK0)
| sK0 = null_class ),
inference(copy,[status(thm)],[c_441]) ).
cnf(c_314,negated_conjecture,
~ subclass(null_class,sK0),
inference(resolve,[status(thm)],[c_65,c_442]) ).
cnf(c_443,plain,
member(sK1(null_class,sK0),null_class),
inference(resolve,[status(thm)],[c_314,c_140]) ).
cnf(c_440,plain,
$false,
inference(resolve,[status(thm)],[c_110,c_443]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET063+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n007.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 06:58:54 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3066260 was started by sandbox on n007,
% 0.08/0.35 % Sat Sep 26 06:58:54 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.39
% 0.12/0.39 % SZS status Theorem for theBenchmark
% 0.12/0.39
% 0.12/0.39 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.12/0.39 % Length of proof is 12.
% 0.12/0.39 % Level of proof is 4.
% 0.12/0.39 % Maximum clause weight is 18.000.
% 0.12/0.39 % Given clauses 100.
% 0.12/0.39
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------